Figure 2.4 Different designs of mechanical stirrers [Harnby et al. 1997].

고강도 전단 용탕 처리: 주조 마그네슘 및 알루미늄 복합재의 기계적 특성을 극대화하는 방법

이 기술 요약은 Spyridon Tzamtzis가 2011년 Brunel University에서 발표한 박사 학위 논문 “Solidification Behaviour and Mechanical Properties of Cast Mg-alloys and Al-based Particulate Metal Matrix Composites Under Intensive Shearing”을 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 고강도 전단 용탕 처리 (High-Intensity Shear Melt Conditioning)
  • Secondary Keywords: 마그네슘 합금, 알루미늄 복합재, 고압 다이캐스팅(HPDC), 미세구조 미세화, 기계적 특성, 주조 결함, 용탕 컨디셔닝

Executive Summary

  • 도전 과제: 기존의 주조 공정으로 생산된 마그네슘 합금 및 알루미늄 기반 복합재는 불균일한 미세구조와 입자 응집, 주조 결함으로 인해 연성과 같은 기계적 특성이 저하되는 한계가 있습니다.
  • 해결 방법: 주조 직전에 용융 금속에 고강도 전단을 가하는 새로운 “용탕 컨디셔닝 고압 다이캐스팅(MC-HPDC)” 공정을 적용했습니다.
  • 핵심 돌파구: 고강도 전단은 강화재 및 산화물 입자 클러스터를 효과적으로 파괴하고 균일하게 분산시켜, 결정립 미세화, 기공률 감소, 결함 밴드 제거라는 획기적인 결과를 가져왔습니다.
  • 핵심 결론: MC-HPDC 공정은 주조 부품의 강도와 연성을 동시에 향상시키며, 고급 마그네슘 스크랩의 물리적 재활용에도 탁월한 잠재력을 보여줍니다.

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

자동차, 항공우주, 전자 산업에서 경량 소재의 중요성은 날로 커지고 있습니다. 특히 마그네슘(Mg) 합금과 알루미늄 기반 입자 강화 금속 매트릭스 복합재(PMMC)는 뛰어난 비강도로 주목받고 있습니다. 그러나 기존의 주조 기술, 특히 고압 다이캐스팅(HPDC) 공정은 몇 가지 근본적인 문제점을 안고 있습니다.

  1. PMMC의 강화재 응집: PMMC의 기계적 특성을 향상시키기 위해 첨가되는 SiC나 흑연 같은 강화 입자들이 용탕 내에서 균일하게 분포되지 않고 덩어리(응집체)를 형성하는 경향이 있습니다. 이 입자 클러스터는 응력 집중 부위로 작용하여 부품의 연성을 크게 저하시키고, 예측보다 낮은 응력에서 파괴를 유발하는 주원인이 됩니다.
  2. Mg 합금의 불균일한 미세구조: Mg 합금은 주조 시 조대하고 불균일한 수지상 조직을 형성하기 쉽습니다. 특히 HPDC 공정에서는 샷 슬리브에서 형성된 외부 응고 결정(ESC)이 주조 중심부에 집중되고, 그 주위로 용질과 기공이 풍부한 ‘결함 밴드(defect band)’가 형성되는 고질적인 문제가 있습니다. 이러한 미세구조적 불균일성과 기공은 부품의 신뢰성과 기계적 성능을 저하시킵니다.
Figure 2.1 Classification of composites depending on size and shape of
reinforcement [Rohatgi 2001].
Figure 2.1 Classification of composites depending on size and shape of reinforcement [Rohatgi 2001].

이러한 문제들은 고성능 경량 부품의 양산을 가로막는 기술적 장벽이었습니다. 따라서 주조 공정 자체를 혁신하여 용탕 단계에서부터 미세구조를 제어하고 결함을 억제할 수 있는 새로운 기술이 절실히 요구되었습니다.

접근 방식: 연구 방법론 분석

본 연구는 기존 주조 공정의 한계를 극복하기 위해 ‘용탕 컨디셔닝 고압 다이캐스팅(MC-HPDC)’이라는 혁신적인 접근법을 채택했습니다. 이 방법론의 핵심은 특수 설계된 MCAST(Melt Conditioning by Advanced Shear Technology) 장치를 기존 HPDC 기계에 결합한 것입니다.

  • 핵심 장비 (MCAST): MCAST 장치는 서로 맞물려 같은 방향으로 회전하는 한 쌍의 트윈 스크류(twin-screw)로 구성됩니다. 용융 금속은 이 트윈 스크류 장치를 통과하면서 매우 높은 전단율(high shear rate)과 강한 난류(high intensity of turbulence)를 겪게 됩니다. 이 과정이 바로 ‘고강도 전단 용탕 처리’입니다.
  • 연구 설계: 연구는 두 가지 주요 흐름으로 진행되었습니다.
    1. 기존 공정과의 비교: LM24, LM25 알루미늄 합금에 SiC 및 흑연 입자를 강화한 PMMC와 AZ91D, AM60B, AJ62 마그네슘 합금을 기존의 HPDC 공정과 MC-HPDC 공정으로 각각 주조하여 그 미세구조와 기계적 특성을 비교 분석했습니다.
    2. 공정 변수 최적화: 특히 AM 계열 Mg 합금 스크랩의 재활용 가능성을 탐구하기 위해, MC-HPDC 공정의 주요 변수(전단 온도, 전단 시간, 다이 온도, 증압 시점 등)가 최종 주조물의 품질에 미치는 영향을 체계적으로 분석하여 최적의 공정 조건을 도출했습니다.
  • 데이터 분석: 주조된 시편의 미세구조는 광학 현미경(OM)과 주사 전자 현미경(SEM)을 통해 정성적, 정량적으로 분석되었습니다. 강화 입자의 분포는 Quadrat 분석과 같은 통계적 방법을 사용하여 균일성을 평가했으며, 기계적 특성은 인장 시험 및 경도 측정을 통해 평가되었습니다.
Figure 2.2 Schematic diagram of a liquid drop on a solid surface showing interfacial forces and wetting angle [Oh et al. 1989].
Figure 2.2 Schematic diagram of a liquid drop on a solid surface showing interfacial forces and wetting angle [Oh et al. 1989].

이러한 체계적인 접근을 통해 고강도 전단 처리가 용탕의 응고 거동과 최종 부품의 품질에 미치는 영향을 명확히 규명할 수 있었습니다.

돌파구: 주요 발견 및 데이터

고강도 전단 용탕 처리는 PMMC와 Mg 합금 모두에서 기존의 통념을 뛰어넘는 획기적인 미세구조 개선 효과를 보여주었습니다.

발견 1: PMMC 강화 입자의 완벽한 균일 분산 달성

기존 HPDC 공정으로 제작된 PMMC는 강화 입자들이 불균일하게 응집된 미세구조를 보였습니다. 그러나 MC-HPDC 공정을 적용하자 이러한 입자 클러스터가 거의 완벽하게 해체되고 개별 입자들이 매트릭스 전체에 균일하게 분산되었습니다.

  • Quadrat 통계 분석 결과(Figure 4.18), 기존 HPDC 시편의 입자 분포는 클러스터링을 의미하는 ‘음이항 분포(negative binomial distribution)’를 따랐지만, MC-HPDC 시편은 균일한 무작위 분포를 의미하는 ‘푸아송(Poisson)’ 또는 ‘이항 분포(binomial)’에 가깝게 변화했습니다.
  • 이러한 미세구조 개선은 기계적 특성 향상으로 직결되었습니다. LM24-10 vol.% SiC 복합재의 경우(Figure 4.24), MC-HPDC 공정을 통해 인장강도(UTS)와 연신율이 동시에 약 25% 증가하는 놀라운 결과를 보였습니다. 이는 강도와 연성이 상충 관계에 있다는 일반적인 재료 공학의 상식을 뛰어넘는 결과입니다.
Figure 2.4 Different designs of mechanical stirrers [Harnby et al. 1997].
Figure 2.4 Different designs of mechanical stirrers [Harnby et al. 1997].

발견 2: 마그네슘 합금의 획기적인 결정립 미세화 및 균일화

고강도 전단 처리는 Mg 합금의 응고 거동을 근본적으로 변화시켰습니다.

  • AZ91D 합금을 650°C에서 주조했을 때(Figure 5.1), 기존 공정에서는 평균 690µm의 조대한 결정립이 형성된 반면, MC-HPDC 공정에서는 평균 175µm의 미세하고 균일한 결정립이 형성되었습니다. 이는 용탕 내에 존재하는 미세한 산화물(주로 MgO) 입자들이 고강도 전단에 의해 효과적으로 분산되어 이종 핵생성 사이트(potent nucleation sites)로 활성화되었기 때문입니다.
  • 또한, 기존 HPDC에서 관찰되던 조대한 수지상 조직이 완벽하게 사라지고, 미세한 구형의 초정 Mg 입자가 균일하게 분포하는 미세구조(Figure 5.7)를 얻었습니다.

발견 3: 고질적인 주조 결함(결함 밴드, 기공)의 효과적 억제

MC-HPDC 공정은 HPDC의 대표적인 결함인 결함 밴드와 기공을 크게 감소시켰습니다.

  • AZ91D 주조품의 단면 분석 결과(Figure 5.8), 기존 HPDC에서 뚜렷하게 나타났던 결함 밴드가 MC-HPDC 시편에서는 거의 관찰되지 않았습니다. 이는 미세하고 균일한 초정 입자들이 응고 과정에서 용탕의 유동성을 개선하여 결함 밴드 형성 메커니즘을 억제한 결과입니다.
  • 기공률 또한 획기적으로 감소했습니다. 이미지 분석 결과(Figure 5.11), 기존 HPDC 시편의 기공률이 1.25-1.44%였던 것에 비해, MC-HPDC 시편의 기공률은 0.35-0.41%로 약 70% 이상 감소했습니다.

R&D 및 운영을 위한 실질적 시사점

본 연구 결과는 경량 합금 부품을 다루는 다양한 분야의 엔지니어들에게 중요한 실용적 가이드를 제공합니다.

  • 공정 엔지니어: 이 연구는 고강도 전단 용탕 처리가 고품질 주조품 생산을 위한 강력한 도구임을 시사합니다. 특히 Mg 합금 스크랩 재활용 시 문제가 되는 핫 크랙(hot cracking)과 같은 결함은 액상선 온도 바로 위(예: TL + 5°C)에서 용탕을 처리하고, 증압 시점을 앞당겨(intensifier position 감소) 캐비티 충전 시간을 단축함으로써 효과적으로 제어할 수 있습니다.
  • 품질 관리팀: 논문의 Figure 5.32는 최적화된 MC-HPDC 공정으로 생산된 부품의 기계적 특성(UTS, 연신율)이 매우 일관성 있게 나타남을 보여줍니다. 이는 미세구조의 균일성이 곧 제품 성능의 신뢰성으로 이어진다는 것을 의미하며, 새로운 품질 검사 기준으로 미세구조 균일성 평가를 도입할 수 있음을 시사합니다.
  • 설계 엔지니어: 고강도 전단 처리를 통해 확보된 향상된 용탕 유동성과 결함 억제 능력은 더 복잡하고 얇은 벽(thin-walled)을 가진 부품 설계의 자유도를 높여줍니다. 기존 공법으로는 성형이 어려웠던 디자인도 구조적 무결성을 유지하며 구현할 수 있는 가능성을 열어줍니다.

논문 정보


Solidification Behaviour and Mechanical Properties of Cast Mg-alloys and Al-based Particulate Metal Matrix Composites Under Intensive Shearing

1. 개요:

  • 제목: Solidification Behaviour and Mechanical Properties of Cast Mg-alloys and Al-based Particulate Metal Matrix Composites Under Intensive Shearing
  • 저자: Spyridon Tzamtzis
  • 발행 연도: 2011
  • 발행 학술지/학회: Brunel University (PhD thesis)
  • 키워드: Magnesium alloys, Metal Matrix Composites, Intensive Shearing, Solidification, High Pressure Die Casting, Mechanical Properties, Microstructure

2. 초록:

마그네슘 합금은 가장 가벼운 구조용 금속 재료이며, 알루미늄 기반 입자 강화 금속 매트릭스 복합재(PMMC)는 금속과 세라믹의 특성을 통합하여 자동차, 항공우주, 전자 및 레크리에이션 산업에서 관심이 증가하고 있습니다. PMMC의 현재 공정 기술은 미세 강화재의 균일한 분포를 달성하지 못하고 연성 매트릭스에 응집된 입자를 생성하여 연성에 해롭습니다. 동시에, 용융 마그네슘 합금은 불순물과 산화물을 포함하며, 기존 방식으로 주조될 때 최종 부품은 일반적으로 다양한 주조 결함과 함께 조대하고 불균일한 미세구조를 나타냅니다. 본 논문의 핵심 아이디어는 용융물에 존재하는 고체 입자를 분산시키고 독특한 응고 거동, 향상된 유동성 및 주조 중 다이 충전성을 제공할 수 있는 충분한 전단 응력을 적용하는 새로운 고강도 용탕 컨디셔닝 공정을 채택하는 것이었습니다.

용탕 컨디셔닝 고압 다이캐스팅(MC-HPDC) 공정은 합금 용탕에 직접 고강도 전단을 가한 후 기존 HPDC 공정으로 주조하는 방식으로, PMMC 및 마그네슘 합금 주조품 생산에 사용되었습니다. PMMC에 대한 MC-HPDC 공정은 매트릭스 내 강화재의 균일한 분산을 유도하며, 이는 정량적 통계 분석으로 확인되었고, 복합재의 경도 및 인장 특성 증가로 나타나는 기계적 성능 향상으로 이어졌습니다. 우리는 알루미늄을 포함하는 마그네슘 합금에 대한 응고 경로를 설명하며, 주조 전 고강도 전단이 고체 산화물 입자의 효과적인 분산을 유도하여 마그네슘 결정립의 핵생성 사이트로 효과적으로 작용함으로써 상당한 결정립 미세화를 초래합니다. MC-HPDC로 처리된 마그네슘 주조품은 기공 수준 및 주조 결함이 감소된 매우 미세한 미세구조를 가집니다. 주조품의 기계적 특성 평가는 고강도 전단의 유익한 효과를 보여줍니다. 신중한 최적화 후, MC-HPDC 공정은 고순도 마그네슘 다이캐스팅 스크랩의 직접 재활용에 유망한 잠재력을 보여주며, 1차 마그네슘 합금과 비슷한 기계적 특성을 가진 주조품을 생산합니다.

3. 서론:

전 세계 운송 및 레크리에이션 산업은 최종 제품의 성능, 효율성 및 비용 절감을 지속적으로 추구하고 있습니다. 동시에, 전반적인 연료 효율성 및 CO2 배출 감소를 위한 까다로운 안전 규정 및 환경 법규가 존재하며, 이는 경량 재료에 대한 관심을 증대시켰습니다. 모든 구조용 금속 재료 중 가장 가벼운 마그네슘 합금과 금속 및 세라믹 특성의 통합된 조합을 제공하는 알루미늄 기반 입자 강화 금속 매트릭스 복합재(PMMC)는 광범위한 응용 분야에 이상적인 후보로 부상했습니다.

4. 연구 요약:

연구 주제의 배경:

경량화 요구에 따라 마그네슘 합금과 알루미늄 복합재(PMMC)의 수요가 증가하고 있으나, 기존 주조 공정은 재료의 잠재력을 최대한 발휘하지 못하게 하는 미세구조적 한계를 가지고 있습니다. PMMC에서는 강화 입자의 응집이, Mg 합금에서는 조대하고 불균일한 조직 및 결함 발생이 주된 문제입니다.

이전 연구 현황:

PMMC의 입자 분산을 위해 다양한 교반 방법이 시도되었으나, 미세 입자의 클러스터를 효과적으로 파괴하기에는 전단력이 부족했습니다. Mg 합금의 결정립 미세화를 위해 탄소나 지르코늄을 첨가하는 화학적 방법이나, 과열처리, 초음파 진동과 같은 물리적 방법이 연구되었으나, 산업적 적용에는 한계가 있었습니다.

연구 목적:

본 연구의 목적은 ‘고강도 전단 용탕 처리’라는 새로운 물리적 접근법을 통해 PMMC와 Mg 합금의 근본적인 주조 문제를 해결하는 것입니다. 구체적으로, 고강도 전단이 용탕 내 고체 입자(강화재, 산화물) 분산, 응고 거동, 최종 미세구조 및 기계적 특성에 미치는 영향을 규명하고, 이를 통해 고품질 부품 생산 및 스크랩 재활용을 위한 새로운 공정 기술의 가능성을 제시하고자 합니다.

핵심 연구:

  1. PMMC: 기존 교반 공정과 MC-HPDC 공정으로 Al-SiC, Al-Graphite 복합재를 제조하고, 강화 입자 분포의 균일성과 기계적 특성(경도, 인장강도, 연신율) 변화를 정량적으로 비교 분석.
  2. Mg 합금: AZ91D, AM60B, AJ62 합금에 고강도 전단을 적용하여 결정립 미세화 효과를 평가. 특히 AZ91D 합금을 대상으로 MC-HPDC 공정을 적용하여 결함 밴드, 기공률 등 주조 결함 감소 효과와 그에 따른 기계적 특성 향상을 분석.
  3. Mg 합금 스크랩 재활용: AM 계열 스크랩을 MC-HPDC 공정으로 재활용할 때 발생하는 문제점(숄더 크랙)을 규명하고, 공정 변수 최적화를 통해 이를 해결하여 신재(virgin alloy)와 동등한 수준의 기계적 특성을 확보하는 가능성을 탐구.

5. 연구 방법론

연구 설계:

비교 실험 설계를 기반으로, 기존 공정(교반 캐스팅, HPDC)과 제안된 신규 공정(MCAST, MC-HPDC)의 결과를 직접 비교했습니다. 재료 시스템은 PMMC(LM24/LM25 + SiC/Graphite)와 Mg 합금(AZ91D, AM60B, AJ62, AM 스크랩)으로 다양화하여 공정의 범용성을 평가했습니다.

데이터 수집 및 분석 방법:

  • 미세구조 분석: 광학 현미경(OM)과 편광을 이용해 결정립 크기를 측정하고, 주사 전자 현미경(SEM) 및 에너지 분산형 X선 분광법(EDX)으로 개재물과 입자의 형태 및 성분을 분석했습니다.
  • 입자 분포 정량화: Lacey Index와 Quadrat 방법을 사용하여 강화 입자 분포의 균일성을 통계적으로 평가하고, 특히 분포의 비대칭성을 나타내는 왜도(skewness) 값을 핵심 지표로 사용했습니다.
  • 기계적 특성 평가: 만능 인장 시험기를 사용하여 인장강도(UTS), 항복강도, 연신율을 측정하고, 비커스 경도 시험을 수행했습니다.
  • 결함 분석: Prefil® 가압 여과 기술을 사용하여 용탕 내 미세한 산화물 및 개재물을 포집하고 분석했습니다.

연구 주제 및 범위:

본 연구는 고강도 전단이 (1) Al 기반 PMMC의 강화 입자 분산 및 기계적 특성, (2) Mg 합금의 결정립 미세화, (3) HPDC 공정에서의 주조 결함 형성, (4) Mg 합금 스크랩의 물리적 재활용 가능성에 미치는 영향을 중심으로 다룹니다.

6. 주요 결과:

주요 결과:

  • MC-HPDC 공정은 PMMC의 강화 입자(SiC, 흑연)를 매우 균일하게 분산시켜, 인장강도와 연신율을 동시에 15~25% 향상시켰습니다.
  • 고강도 전단 처리는 AZ91D, AM60B, AJ62 등 다양한 Mg 합금에서 일관되게 상당한 결정립 미세화 효과를 보였습니다.
  • MC-HPDC 공정은 AZ91D 합금의 HPDC 주조 시 발생하는 고질적인 결함 밴드를 억제하고, 기공률을 70% 이상 감소시켰습니다.
  • 고강도 전단은 Mg 합금 스크랩에 포함된 산화물 필름(MgO)을 수백 나노미터 크기의 미세 입자로 파쇄 및 분산시켜, 이들이 효과적인 이종 핵생성 사이트로 작용하게 함을 확인했습니다.
  • MC-HPDC 공정 변수(증압 시점, 다이 온도, 용탕 온도)를 최적화함으로써, Mg 합금 스크랩 재활용 시 발생하던 숄더 크랙 결함을 완전히 제거하고 신재와 동등한 수준의 안정적인 기계적 특성을 확보했습니다.
Figure 5.6 The effect of intensive shearing on the average grain size of AJ62
magnesium alloy, as a function of temperature. The MCAST process refines the
grain size and reduces its temperature dependence.
Figure 5.6 The effect of intensive shearing on the average grain size of AJ62 magnesium alloy, as a function of temperature. The MCAST process refines the grain size and reduces its temperature dependence.

Figure List:

  • Figure 2.1 Classification of composites depending on size and shape of reinforcement [Rohatgi 2001].
  • Figure 2.2 Schematic diagram of a liquid drop on a solid surface showing interfacial forces and wetting angle [Oh et al. 1989].
  • Figure 2.3 Schematic illustration of MMC mixing set-up during the stir casting process [Aniban et al. 2002].
  • Figure 2.4 Different designs of mechanical stirrers [Harnby et al. 1997].
  • Figure 2.5 Twin screw design; (a) co-rotating, (b) fully intermeshing and (c) self wiping screws [Fan et al. 1999].
  • Figure 2.6 Schematic illustrations of flow pattern in a closely intermeshing, self-wiping and co-rotating twin screw mechanism; (a) ‘figure 8’ flow pattern in screw channels and (b) Movement of the melt from one screw to the other [Fan et al. 2001].
  • Figure 2.7 Back-scattered Field Emission Gun (FEG) SEM image showing small (X) and large (Y) clusters of TiB2 particles in a commercial purity Al-matrix [Watson et al. 2005].
  • Figure 2.8 A schematic illustration of the forces acting on a particle in the vicinity of the solid–liquid interface [Youssef et al. 2005].
  • Figure 2.9 Magnesium unit cell crystal. (a) Principal [1 2 1 0] planes , basal plane, face plane (b) Principal [1 1 0 0] planes. (c) Principal directions [Polmear 1995].
  • Figure 3.1 SiC particle size distribution used in this study.
  • Figure 3.2 Schematic diagram of the distributive mixing equipment.
  • Figure 3.3 Schematic illustration of the geometry of (a) the clay graphite crucible and (b) the stainless steel impeller used for distributive mixing.
  • Figure 3.4 Schematic illustration of the twin-screw mechanism used in the MCAST process.
  • Figure 3.5 Schematic diagram of TP-1 grain refining test mould ladle [The Aluminium Association 1990].
  • Figure 3.6 Schematic illustration of the Prefil® equipment used for the pressurised filtration of the Mg-alloys in this study.
  • Figure 3.7 A schematic illustration of the cold chamber high pressure die-casting (HPDC) set-up.
  • Figure 3.8 Schematic illustration of the die-cast component produced by the HPDC machine, showing the two tensile test specimen (labelled A and C) and the two fatigue test specimen (labelled B and D).
  • Figure 3.9 Schematic illustration of the MC-HPDC process.
  • Figure 3.10 Identification of the locations where the cast tensile specimen where cut for the preparation of metallographic specimen for microstructural characterisation.
  • Figure 3.11 Schematic representation of the quadrat method, using four quadrats.
  • Figure 3.12 Application of the Quadrat method performed on the microstructure of a LM25 – 5 vol. % SiCp composite.
  • Figure 3.13 Schematic representation of the mean line intercept method performed on the microstructure of an AJ62 casting.
  • Figure 4.1 Typical microstructures of distributive mixed LM25 – 5 vol. % SiCp composites cast at 630 ºC.
  • Figure 4.2 Higher magnification of a typical microstructure of LM25 – 5 vol. % SiC PMMC produced with the HPDC process at 630 ºC, revealing the presence of SiC particle clusters.
  • Figure 4.3 Representative optical micrographs of PMMC castings produced with the HPDC process at 610 ºC.
  • Figure 4.4 Typical optical microstructure of LM24 – 5 vol. % graphite composite produced with the conventional HPDC process at 610 ºC.
  • Figure 4.5 Fluid flow characteristics during distributive mixing.
  • Figure 4.6 Typical microstructures of dispersive mixed LM25 – 5 vol. % SiCp composites with the implementation of intensive shearing at 630 ºC.
  • Figure 4.7 Higher magnification of a typical microstructure of LM25 – 5 vol. % SiCp produced with (a) the MC-HPDC process and (b) the HPDC process.
  • Figure 4.8 Microstructure of a MC-HPDC at 630 ºC LM25 – 5 vol. % SiCp composite.
  • Figure 4.9 SEM microstructure of LM25 – 5 vol. % SiC PMMC produced with the MC-HPDC at 630 ºC.
  • Figure 4.10 Representative optical micrographs of PMMC castings produced with the MC-HPDC process at 610 ºC.
  • Figure 4.11 Typical optical microstructure of LM24 – 5 vol. % graphite composite samples produced by MC-HPDC at 610 ºC.
  • Figure 4.12 SEM micrograph of LM24 – 5 vol. % graphite composite produced by MC-HPDC at 610 ºC.
  • Figure 4.13 A schematic illustration of the high shear zones at the intermeshing regions of the screws and the fluid flow during intensive mixing.
  • Figure 4.14 Fluid flow patterns inside the twin screw machine.
  • Figure 4.15 The Lacey Index M of LM25 – 5 vol. % SiC PMMCs processed with or without the implementation of intensive shearing.
  • Figure 4.16 Experimental results from the Quadrat analysis for HPDC and MC-HPDC processed LM25 – 5 vol. % SiC PMMCs.
  • Figure 4.17 The effect of shearing time on the skewness β of the particle distribution in HPDC and MC-HPDC processed LM25 – 5 vol. % SiC PMMCs.
  • Figure 4.18 Experimental results from the Quadrat analysis for HPDC and MC-HPDC processed LM24 – 10 vol. % SiCp PMMCS.
  • Figure 4.19 The effect of intensive shearing speed on the skewness of the reinforcement distribution of LM24 – SiCp composites.
  • Figure 4.20 The effect of shearing time at various processing temperatures of LM24 – 5 vol. % SiCp composites.
  • Figure 4.21 Experimental results from the Quadrat analysis for HPDC and MC-HPDC processes for LM24 – 5 vol. % C composites.
  • Figure 4.22 Comparison of the tensile properties of LM25 – 5 vol. % SiC PMMCs produced with the HPDC and MC-HPDC processes.
  • Figure 4.23 Hashin-Shtrikman bounds and measured average values of the Young’s modulus for LM25 – 5 vol. % SiC PMMCs.
  • Figure 4.24 Comparison of the tensile properties of LM24 – 10 vol. % SiCp composites.
  • Figure 4.25 Hashin-Shtrikman bounds and measured values of the Young’s modulus for LM24 – SiC PMMCs.
  • Figure 4.26 Fractograph of LM24- 5 % volume fraction SiC PMMC produced with the MC-HPDC process.
  • Figure 4.27 Comparison of mechanical properties of LM24 – 5 vol. % graphite composites.
  • Figure 5.1 Microstructure of AZ91D alloy cast in a TP1 mould at 650 °C.
  • Figure 5.2 The effect of intensive shearing on the average grain size of AZ91D magnesium alloy.
  • Figure 5.3 Microstructure of AM60B magnesium alloy cast in a TP1 mould at 650 °C.
  • Figure 5.4 The effect of intensive shearing on the average grain size of AM60B magnesium alloy.
  • Figure 5.5 Microstructure of AJ62 magnesium alloy cast in a TP1 mould at 650 °C.
  • Figure 5.6 The effect of intensive shearing on the average grain size of AJ62 magnesium alloy.
  • Figure 5.7 Polarised optical micrographs showing the detailed solidification microstructure of AZ91D alloy.
  • Figure 5.8 Cross-sectional micrographs of an AZ91D alloy cast component.
  • Figure 5.9 Variation of the primary Mg grains volume fraction as a function of the distance from the centre of the sample for AZ91D Mg-alloy.
  • Figure 5.10 Porosity in AZ91D alloy castings produced at different temperatures by HPDC and MC-HPDC processes.
  • Figure 5.11 The levels of porosity in AZ91D alloy produced by HPDC and MC-HPDC processes.
  • Figure 5.12 Relative area fraction of primary Mg grains depending on their grain size, for both HPDC and MC-HPDC processes.
  • Figure 5.13 Comparison of the mechanical properties of AZ91D alloy produced by HPDC and MC-HPDC processes.
  • Figure 5.14 Al8Mn5 intermetallic particles in the non-sheared AM series alloy scrap.
  • Figure 5.15 High magnification backscattered electron SEM micrograph showing the two different types of oxide inclusions in the non-sheared AM series alloy scrap.
  • Figure 5.16 High magnification backscattered electron SEM micrograph showing the MgAl2O4 (spinel) particles.
  • Figure 5.17 High magnification backscattered electron SEM micrograph showing the large MgO particle clusters and the ingot skins.
  • Figure 5.18 Al8Mn5 intermetallic particles in the sheared AM series alloy scrap.
  • Figure 5.19 The Al8Mn5 intermetallic particle size distributions of the non-sheared and sheared AM series alloy scrap.
  • Figure 5.20 High magnification backscattered electron SEM micrograph showing the two different types of oxide inclusions in the sheared AM series alloy scrap.
  • Figure 5.21 High magnification backscattered electron SEM micrograph showing the MgAl2O4 (spinel) particles.
  • Figure 5.22 Backscattered electron SEM micrograph, showing the MgO particles, present in the sheared AM series alloy scrap.
  • Figure 5.23 High magnification backscattered electron SEM micrograph of the MgO particles in the sheared AM series alloy scrap.
  • Figure 5.24 The variation of mechanical properties of MC-HPDC recycled AM series scrap.
  • Figure 5.25 Visual examination revealed the presence of dark line on the sample surface.
  • Figure 5.26 (a) Shoulder crack; (b) The detailed structure of a shoulder crack.
  • Figure 5.27 Relationships between Mg die-casting defects and casting parameters.
  • Figure 5.28 The casting defective rate determined by visual examination, as a function of the intensifier position.
  • Figure 5.29 The casting defective rate determined by visual and microstructural examination, as a function of the die temperature.
  • Figure 5.30 The casting defective rate determined by visual and microstructural examination, as a function of the processing temperature.
  • Figure 5.31 Polarised optical micrographs showing the detailed solidification microstructures of AM-series recycled alloy scrap.
  • Figure 5.32 Consistency of the mechanical properties after the process optimization.

7. 결론:

본 연구는 고강도 전단 용탕 처리 기술이 Al 기반 PMMC와 Mg 합금의 주조 품질을 획기적으로 개선할 수 있는 강력한 대안임을 입증했다. 주요 결론은 다음과 같다.

  • PMMC: 기존 교반 공정은 강화 입자의 심각한 응집을 유발하지만, MC-HPDC 공정의 고강도 전단은 입자 클러스터를 효과적으로 파괴하여 균일한 분산을 달성한다. 이는 기계적 특성의 현저한 향상으로 이어진다.
  • Mg 합금: 고강도 전단은 용탕 내 고유의 산화물 입자를 미세하게 분산시켜 이종 핵생성 사이트로 활성화함으로써, 별도의 첨가제 없이도 상당한 결정립 미세화 효과를 달성한다.
  • 주조 품질: MC-HPDC 공정은 미세하고 균일한 미세구조를 형성하여 HPDC 공정의 고질적인 문제인 결함 밴드 형성을 억제하고 기공률을 크게 감소시킨다. 이는 강도와 연성을 동시에 향상시키는 결과로 나타난다.
  • 재활용: MC-HPDC 공정은 공정 변수 최적화를 통해 고품질 Mg 합금 스크랩의 물리적 재활용에 탁월한 잠재력을 보여주며, 신재와 동등한 수준의 기계적 특성을 가진 부품을 안정적으로 생산할 수 있다.

8. 참고문헌:

  • [Abramov 1994] Abramov OV (1994). Ultrasound in Liquid and Solid Metals, Boca Raton, FL: CRC Press.
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전문가 Q&A: 주요 질문과 답변

Q1: 고강도 전단을 구현하기 위해 왜 특별히 트윈 스크류(twin-screw) 메커니즘을 선택했습니까?

A1: 트윈 스크류 메커니즘은 용탕 전체에 걸쳐 균일하고 강한 전단을 가하는 데 매우 효과적이기 때문입니다. 논문의 3.2.3절에서 설명하듯이, 서로 맞물려 회전하는 스크류는 용탕에 높은 전단율, 강한 난류, 그리고 ‘정량 이송(positive displacement)’ 효과를 동시에 부여합니다. 이는 용탕이 정체 구간 없이 강제적으로 혼합되도록 하여, 기존의 임펠러 교반 방식으로는 불가능했던 미세 입자 클러스터의 완벽한 파괴와 분산을 가능하게 합니다.

Q2: 논문에서 MgAl2O4와 MgO라는 두 종류의 산화물 개재물이 언급되었습니다. 고강도 전단은 이 둘에 각각 어떻게 다른 영향을 미쳤습니까?

A2: 매우 중요한 질문입니다. 5.4.1절과 5.5.1절에 따르면, 고강도 전단은 두 산화물에 다른 영향을 미쳤습니다. 상대적으로 크고 각진 형태의 MgAl2O4(스피넬) 입자는 전단 후에도 크기나 형태에 큰 변화가 없었습니다. 하지만 잉곳 스킨이나 클러스터 형태로 존재하던 MgO는 고강도 전단에 의해 100-200nm 크기의 매우 미세한 개별 입자로 효과적으로 파쇄되고 분산되었습니다. 바로 이 미세하게 분산된 MgO 입자들이 이후 응고 과정에서 Mg 결정립의 핵생성 사이트로 작용하여 획기적인 결정립 미세화를 이끌어낸 핵심 요인입니다.

Q3: MC-HPDC 공정은 기존 HPDC에서 나타나는 ‘결함 밴드’를 구체적으로 어떻게 방지합니까?

A3: 결함 밴드는 주조품 내 고상 분율(solid fraction)의 불균일한 구배 때문에 발생합니다. 5.5.3절의 논의에 따르면, 기존 HPDC에서는 샷 슬리브에서 형성된 크고 불균일한 외부 응고 결정(ESC)이 중심부에 몰리면서 급격한 고상 분율 구배를 만듭니다. MC-HPDC 공정은 고강도 전단을 통해 훨씬 더 작고 균일하며 구형에 가까운 ESC를 소량 생성합니다. 이 균일한 입자들은 용탕 내에 고르게 분포하여 전체적으로 완만한 고상 분율 구배를 형성하고, 결함 밴드가 형성되는 전단 평면 자체의 생성을 억제하는 것입니다.

Q4: Mg 합금 스크랩을 핫 크랙 없이 성공적으로 재활용하는 데 있어 핵심적인 공정 조건은 무엇이었습니까?

A4: 5.4.2.3절과 5.5.4절에서 설명하듯이, 공정 최적화가 핵심이었습니다. 가장 중요한 세 가지 요소는 (1) 증압 시점, (2) 다이 온도, (3) 용탕 처리 온도였습니다. 특히, 증압 시점을 기존보다 앞당겨(intensifier position 180mm) 캐비티 충전 시간을 단축하고, 다이 온도를 180°C로 낮춰 냉각 속도를 높였습니다. 또한, 용탕 처리 온도를 액상선 바로 위(TL + 5°C)로 설정하여 미세하고 균일한 결정립 구조를 유도한 것이 핫 크랙 발생을 억제하고 안정적인 기계적 특성을 확보하는 데 결정적인 역할을 했습니다.

Q5: 이 연구에서는 강도와 연신율이 동시에 증가하는 결과가 나타났습니다. 이는 일반적인 재료의 거동과 다른데, 어떻게 이것이 가능합니까?

A5: 맞습니다. 일반적으로 강도와 연성은 상충 관계에 있습니다. 그러나 본 연구의 결과(5.5.5절 참조)는 두 가지 메커니즘의 시너지 효과로 설명할 수 있습니다. 첫째, 홀-페치(Hall-Petch) 관계에 따라, 고강도 전단으로 인한 결정립 미세화는 재료의 강도를 직접적으로 향상시킵니다. 둘째, 동시에 MC-HPDC 공정은 기공, 조대한 수지상 조직, 입자 클러스터와 같은 결함들을 제거합니다. 이러한 결함들은 균열의 시작점으로 작용하여 연성을 저하시키는 주된 요인이므로, 이를 제거함으로써 재료의 연성이 크게 향상된 것입니다. 즉, 결함 제거를 통한 연성 향상 효과가 매우 커서 강도 증가와 동시에 나타날 수 있었습니다.


결론: 더 높은 품질과 생산성을 향한 길

본 연구는 기존 주조 공정의 한계를 명확히 보여주고, 고강도 전단 용탕 처리라는 혁신적인 기술이 마그네슘 합금 및 알루미늄 복합재의 품질을 한 차원 높일 수 있음을 증명했습니다. 용탕 단계에서 미세구조를 근본적으로 제어함으로써, 강화 입자의 완벽한 분산, 획기적인 결정립 미세화, 고질적인 주조 결함 억제가 가능해졌습니다. 그 결과, 강도와 연성이 동시에 향상되는 이상적인 기계적 특성을 구현했으며, 고부가가치 스크랩 재활용의 길을 열었습니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 돕는 데 전념하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보시기 바랍니다.

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저작권 정보

  • 이 콘텐츠는 Spyridon Tzamtzis의 논문 “Solidification Behaviour and Mechanical Properties of Cast Mg-alloys and Al-based Particulate Metal Matrix Composites Under Intensive Shearing”을 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://bura.brunel.ac.uk/handle/2438/5488

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

Figure 5. Ultimate tensile strength (UTS) and hardness of 2017 A Al alloy manufactured in various conditions.

스퀴즈 캐스팅 최적화: Taguchi 방법을 활용한 2017A 알루미늄 합금의 기계적 물성 극대화 방안

이 기술 요약은 Najib Souissi 외 저자들이 2014년 Metals 학술지에 게재한 논문 “Optimization of Squeeze Casting Parameters for 2017 A Wrought Al Alloy Using Taguchi Method”를 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

Keywords

  • Primary Keyword: 스퀴즈 캐스팅 최적화
  • Secondary Keywords: 2017A 알루미늄 합금, Taguchi 방법, 기계적 물성, 공정 변수, 고압 주조

Executive Summary

  • The Challenge: 스퀴즈 캐스팅은 우수한 알루미늄 합금 부품을 생산하지만, 최적의 기계적 특성을 달성하기 위해서는 가압 압력, 용탕 온도, 금형 온도와 같은 공정 변수에 대한 정밀한 제어가 필요합니다.
  • The Method: 본 연구는 Taguchi L9 직교 배열법을 사용하여 스퀴즈 압력, 용탕 온도, 금형 온도가 2017A 알루미늄 합금의 극한 인장 강도(UTS) 및 경도에 미치는 영향을 체계적으로 조사했습니다.
  • The Key Breakthrough: 스퀴즈 압력은 UTS와 경도 변화에 각각 83% 이상 기여하는 가장 지배적인 요인입니다. 압력을 15 MPa에서 90 MPa로 높이면 UTS는 46%, 경도는 58% 향상되었습니다.
  • The Bottom Line: 고성능 2017A 알루미늄 부품의 경우, 스퀴즈 압력을 극대화하는 것이 미세조직을 미세화하고 기계적 특성을 획기적으로 향상시키는 가장 효과적인 전략입니다.

The Challenge: Why This Research Matters for CFD Professionals

알루미늄 합금은 낮은 밀도, 우수한 성형성, 높은 열전도율 등 다양한 장점 덕분에 자동차, 항공우주 산업에서 핵심 소재로 사용되고 있습니다. 그러나 기존의 주조 방식은 수축 및 가스 기공과 같은 결함으로 인해 부품의 무결성과 기계적 특성을 저하시킬 수 있습니다.

스퀴즈 캐스팅(액상 단조)은 용융된 금속을 유압 프레스의 폐쇄된 금형 내에서 고압으로 응고시키는 공정으로, 이러한 한계를 극복할 수 있는 대안으로 주목받고 있습니다. 이 기술은 수축 및 기공을 효과적으로 제거하여 기계적 특성이 향상된 고품질 부품을 생산할 수 있습니다. 하지만 스퀴즈 캐스팅의 성공은 가압 압력, 용탕 온도, 금형 온도 등 여러 공정 변수들의 복잡한 상호작용에 따라 달라집니다. 이러한 변수들을 최적화하여 일관된 고품질을 달성하는 것은 제조 현장의 중요한 과제이며, 본 연구는 이 문제를 해결하기 위해 시작되었습니다.

The Approach: Unpacking the Methodology

본 연구는 최소한의 실험으로 공정 변수들의 영향을 효율적으로 평가하기 위해 통계적 설계 기법인 Taguchi 방법을 채택했습니다. 연구진은 2017A 단조 알루미늄 합금을 사용하여 스퀴즈 캐스팅 공정을 분석했습니다.

주요 공정 변수로는 스퀴즈 압력(A), 용탕 온도(B), 금형 온도(C)를 선정하고, 각 변수마다 3개의 수준(Level)을 설정했습니다. 실험은 L9 직교 배열표에 따라 총 9가지 조건 조합으로 수행되었으며, 각 조건마다 3개의 시편을 제작하여 결과의 정확성을 확보했습니다. 제작된 시편에 대해서는 극한 인장 강도(UTS)와 비커스 경도(HV)를 측정하여 기계적 특성을 평가했습니다. 수집된 데이터는 주 효과 분석, 분산 분석(ANOVA), 신호 대 잡음비(S/N ratio) 분석을 통해 각 변수가 기계적 특성에 미치는 영향의 정도와 최적의 공정 조건을 도출하는 데 사용되었습니다.

The Breakthrough: Key Findings & Data

Finding 1: 스퀴즈 압력이 기계적 물성을 지배하는 핵심 인자임이 입증되다

분산 분석(ANOVA) 결과, 스퀴즈 압력은 2017A 알루미늄 합금의 기계적 특성에 가장 결정적인 영향을 미치는 요인으로 밝혀졌습니다. Table 4와 Table 5에 따르면, 스퀴즈 압력(A)은 극한 인장 강도(UTS) 변화에 85.93%, 경도 변화에 83.06% 기여하는 것으로 나타났습니다. 이는 용탕 온도(B)와 금형 온도(C)의 기여도를 압도하는 수치로, 스퀴즈 캐스팅 공정에서 압력 제어의 중요성을 명확히 보여줍니다. Figure 3의 기여도 그래프는 이러한 결과를 시각적으로 뒷받침합니다.

Figure 3. Percentage contribution of significant control factors.
Figure 3. Percentage contribution of significant control factors.

Finding 2: 압력 증가는 미세조직 미세화와 기계적 강도 향상으로 직결되다

실험 결과, 스퀴즈 압력을 높일수록 기계적 특성이 획기적으로 향상되었습니다. Figure 5에서 볼 수 있듯이, 스퀴즈 압력을 15 MPa에서 90 MPa로 높였을 때 UTS는 150 MPa에서 219.66 MPa로 46% 증가했으며, 경도는 58%나 향상되었습니다. 이러한 개선은 압력 증가로 인한 미세조직의 변화와 직접적인 관련이 있습니다. Figure 4의 광학 현미경 사진은 압력이 높을수록 초정 α-상 덴드라이트가 더 미세하고 작아지는 것을 보여줍니다. 이는 높은 압력이 응고점 상승을 유발하여 과냉각도를 높이고, 합금과 금형 사이의 열전달을 촉진하여 냉각 속도를 증가시킨 결과입니다. 결과적으로 미세하고 치밀한 조직이 형성되어 기계적 강도가 크게 향상됩니다.

Practical Implications for R&D and Operations

  • For Process Engineers: 본 연구는 UTS와 경도를 극대화하기 위한 최적의 공정 조건으로 스퀴즈 압력 90 MPa, 용탕 온도 700°C, 금형 온도 200°C (A3 B1 C1)를 제시합니다. 이는 고강도 부품 생산을 위한 구체적인 가이드라인으로 활용될 수 있습니다.
  • For Quality Control Teams: Figure 5에서 확인된 스퀴즈 압력과 기계적 특성 간의 강력한 상관관계는 압력 모니터링 및 제어가 일관된 제품 품질을 보증하는 데 매우 중요함을 시사합니다. 또한, Figure 4의 미세조직 사진은 품질 평가를 위한 시각적 기준으로 활용될 수 있습니다.
  • For Design Engineers: 연구 결과는 스퀴즈 캐스팅이 기존 주조법에 비해 월등한 기계적 특성을 가진 부품을 생산할 수 있음을 확인시켜 줍니다. 이는 특히 고압 적용이 가능한 경우, 더 가볍고 강한 부품 설계를 가능하게 하여 제품 혁신의 기회를 제공합니다.

Paper Details


Optimization of Squeeze Casting Parameters for 2017 A Wrought Al Alloy Using Taguchi Method

1. Overview:

  • Title: Optimization of Squeeze Casting Parameters for 2017 A Wrought Al Alloy Using Taguchi Method
  • Author: Najib Souissi, Slim Souissi, Christophe Le Niniven, Mohamed Ben Amar, Chedly Bradai and Foued Elhalouani
  • Year of publication: 2014
  • Journal/academic society of publication: Metals
  • Keywords: 2017A Al alloy; squeeze casting parameters; Taguchi method; optimization; mechanical properties

2. Abstract:

이 연구는 Taguchi 방법을 적용하여 스퀴즈 캐스팅 2017A 단조 알루미늄 합금의 극한 인장 강도, 경도와 공정 변수 간의 관계를 조사합니다. 스퀴즈 압력, 용탕 온도, 금형 온도를 포함한 다양한 주조 변수들의 효과가 연구되었습니다. 따라서 스퀴즈 캐스팅 공정에 대한 Taguchi 방법의 목표는 공정 변수들의 최적 조합을 확립하고, 단 몇 번의 실험만으로 품질 변동을 줄이는 것입니다. 실험 결과는 스퀴즈 압력이 2017A 알루미늄 합금의 미세조직과 기계적 특성에 상당한 영향을 미친다는 것을 보여줍니다.

3. Introduction:

최근 알루미늄 및 그 합금은 낮은 밀도, 우수한 성형성, 높은 열전도율, 높은 비강성, 우수한 내식성, 높은 주조성 및 매력적인 인장 강도와 같은 다양한 장점 덕분에 높은 기술적 가치와 광범위한 산업 응용 분야로 인해 큰 주목을 받고 있습니다. 이러한 이유로 알루미늄 합금은 특히 주조 산업의 가장 중요한 산업 재료로 널리 사용됩니다. 한편, 이들은 기계, 자동차 및 항공우주 산업과 같은 다양한 분야에서 중요한 응용 기회를 제공합니다.

4. Summary of the study:

Background of the research topic:

알루미늄 합금은 자동차 및 항공우주 산업에서 경량화와 고성능을 동시에 만족시키기 위한 핵심 소재입니다. 스퀴즈 캐스팅은 기존 주조법의 한계인 기공 및 수축 결함을 극복하고, 기계적 특성을 향상시킬 수 있는 첨단 주조 기술입니다.

Status of previous research:

많은 연구에서 스퀴즈 캐스팅 공정 변수(가압 압력, 용탕 온도, 금형 온도)가 알루미늄 및 마그네슘 합금의 품질에 중요한 영향을 미친다고 보고했습니다. 압력 증가는 결정립 크기를 감소시키고 경도를 향상시키는 것으로 알려졌으나, 여러 변수들의 복합적인 영향을 효율적으로 최적화하는 연구는 여전히 필요합니다.

Purpose of the study:

본 연구의 목적은 Taguchi 방법을 사용하여 2017A 단조 알루미늄 합금의 스퀴즈 캐스팅 공정에서 최적의 변수 조합(가압 압력, 용탕 온도, 금형 온도)을 찾아내고, 최소한의 실험으로 기계적 특성(UTS, 경도)을 극대화하는 것입니다.

Core study:

Taguchi L9 직교 배열을 사용하여 9가지 실험 조건에서 2017A 알루미늄 합금을 스퀴즈 캐스팅하고, 각 조건에서 UTS와 경도를 측정했습니다. 분산 분석(ANOVA)과 신호 대 잡음비(S/N ratio) 분석을 통해 각 공정 변수가 기계적 특성에 미치는 영향의 크기를 정량화하고, 최적의 공정 조건을 도출했습니다. 또한, 스퀴즈 압력이 미세조직과 기계적 특성에 미치는 영향을 심층적으로 분석했습니다.

5. Research Methodology

Research Design:

본 연구는 3개의 공정 변수(스퀴즈 압력, 용탕 온도, 금형 온도)를 각각 3개의 수준으로 설정하고, Taguchi L9 (3³) 직교 배열 실험 설계를 사용했습니다. 이를 통해 전체 27가지 조합 대신 9가지 실험만으로 변수의 영향을 평가할 수 있었습니다.

Data Collection and Analysis Methods:

  • 시편 제작: 유압 프레스를 사용하여 각 실험 조건에 따라 스퀴즈 캐스팅 시편을 제작했습니다.
  • 기계적 특성 평가: 만능 시험기(INSTRON)를 사용하여 극한 인장 강도(UTS)를 측정하고, 비커스 경도 시험기(MEKTON)를 사용하여 경도(HV)를 측정했습니다.
  • 통계 분석: 측정된 데이터에 대해 주 효과 분석, 분산 분석(ANOVA), 신호 대 잡음비(S/N ratio) 분석을 수행하여 각 변수의 영향도와 최적 수준을 결정했습니다.

Research Topics and Scope:

  • 연구 대상: 2017A 단조 알루미늄 합금
  • 주요 변수:
    • A: 스퀴즈 압력 (30, 60, 90 MPa)
    • B: 용탕 온도 (700, 750, 800 °C)
    • C: 금형 온도 (200, 250, 300 °C)
  • 평가 항목: 극한 인장 강도(UTS), 경도(HV), 미세조직

6. Key Results:

Key Results:

  • 스퀴즈 압력은 UTS와 경도에 가장 큰 영향을 미치는 변수로, 각각 85.93%와 83.06%의 기여도를 보였습니다.
  • 기계적 특성을 극대화하는 최적의 공정 조건 조합은 스퀴즈 압력 90 MPa, 용탕 온도 700°C, 금형 온도 200°C (A3 B1 C1)로 나타났습니다.
  • 신호 대 잡음비(S/N ratio) 분석 결과, 목표값으로부터의 편차를 최소화하는 최적의 조합은 A3 B1 C3 (90 MPa, 700°C, 300°C)로 확인되었습니다.
  • 스퀴즈 압력을 15 MPa에서 90 MPa로 증가시켰을 때, UTS는 46%, 경도는 58% 향상되었습니다.
  • 압력 증가는 결정립 미세화를 유발하며, 이것이 기계적 특성 향상의 주된 원인임이 확인되었습니다.
Figure 5. Ultimate tensile strength (UTS) and hardness of 2017 A Al alloy manufactured in various conditions.
Figure 5. Ultimate tensile strength (UTS) and hardness of 2017 A Al alloy manufactured in various conditions.

Figure List:

  • Figure 1. Main effects graph for ultimate tensile strength (UTS).
  • Figure 2. Main effects graph for hardness.
  • Figure 3. Percentage contribution of significant control factors.
  • Figure 4. Optical micrographs of the squeeze cast sample (a) 15 MPa; (b) 30 MPa; (c) 60 MPa; and (d) 90 MPa applied pressure.
  • Figure 5. Ultimate tensile strength (UTS) and hardness of 2017 A Al alloy manufactured in various conditions.
  • Figure 6. Experimental setup of squeeze casting process.
  • Figure 7. Schematic representation of squeeze casting process.

7. Conclusion:

  1. 스퀴즈 압력 90 MPa, 용탕 온도 700°C, 금형 온도 200°C의 조합(A3 B1 C1)이 2017A 알루미늄 합금의 스퀴즈 캐스팅에서 더 높은 기계적 특성을 얻기 위해 권장됩니다.
  2. 분산 분석(ANOVA) 결과, 스퀴즈 압력, 용탕 온도, 금형 온도는 모두 유의미한 공정 변수로 확인되었으며, 특히 스퀴즈 압력의 기여도가 UTS와 경도에서 가장 컸습니다.
  3. 신호 대 잡음비(S/N ratio) 분석 결과, A3 B1 C3 조합이 목표값에 대한 편차를 최소화하면서 최적의 기계적 특성을 산출하는 것으로 나타났습니다.
  4. 미세조직의 미세화가 스퀴즈 캐스트 시편의 기계적 특성을 향상시키는 주된 이유였습니다.

8. References:

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Expert Q&A: Your Top Questions Answered

Q1: 전체 요인 설계(Full Factorial Design) 대신 Taguchi 방법을 선택한 이유는 무엇인가요?

A1: 3개 변수와 3개 수준을 모두 조합하는 전체 요인 설계는 총 27번의 실험이 필요합니다. 논문에 따르면, Taguchi 방법의 L9 직교 배열을 사용하면 실험 횟수를 9번으로 크게 줄일 수 있습니다. 이는 시간과 비용을 절약하면서도 각 공정 변수가 기계적 특성에 미치는 영향을 효과적으로 분석하고 최적의 조건을 찾을 수 있게 해주는 효율적인 접근법입니다.

Q2: 주 효과 분석에서는 최적 조건이 A3 B1 C1로, S/N비 분석에서는 A3 B1 C3로 나타났습니다. 이 차이는 왜 발생하며, 어떤 것을 더 중요하게 고려해야 하나요?

A2: 주 효과 분석은 UTS나 경도 같은 반응치의 ‘평균’을 최대화하는 데 초점을 맞춥니다. 반면, S/N비 분석은 제어 불가능한 요인(노이즈)에 덜 민감하고, 목표값으로부터의 ‘편차(분산)’를 최소화하는 강건한(robust) 공정 조건을 찾는 데 중점을 둡니다. 논문에서는 A3 B1 C3 조합이 “목표값에 대한 최소한의 편차로 최적의 기계적 특성을 산출한다”고 언급했는데, 이는 일관된 품질의 제품을 생산하는 것이 중요한 목표임을 시사합니다. 따라서 생산 안정성을 중시한다면 S/N비 분석 결과를 우선적으로 고려할 수 있습니다.

Q3: 스퀴즈 압력이 기계적 특성을 그토록 극적으로 향상시키는 물리적 메커니즘은 무엇인가요?

A3: 논문의 2.5절과 참고문헌[6]에 따르면 두 가지 주요 메커니즘이 있습니다. 첫째, 높은 압력은 Clausius-Clapeyron 방정식에 따라 합금의 응고점을 상승시킵니다. 이는 더 큰 과냉각을 유발하여 미세한 결정핵 생성을 촉진합니다. 둘째, 압력은 용융 합금과 금형 벽 사이의 공기 간극(air gap)을 제거하여 접촉 면적을 넓히고 열전달 계수를 높입니다. 이로 인해 냉각 속도가 빨라져 결정립이 더욱 미세해지고, 결과적으로 기계적 강도가 향상됩니다.

Q4: 기계적 특성의 개선 정도는 구체적으로 어느 정도였나요?

A4: 논문의 2.5절에 명시된 바와 같이, 스퀴즈 압력을 15 MPa에서 90 MPa로 증가시켰을 때 극한 인장 강도(UTS)는 46% (150 MPa에서 219.66 MPa로), 경도(HV)는 58% 증가했습니다. 이는 스퀴즈 압력이 기계적 물성 향상에 매우 효과적인 변수임을 정량적으로 보여주는 결과입니다.

Q5: 예측된 최적 조건의 결과가 실험적으로 검증되었나요?

A5: 네, 검증되었습니다. 논문의 2.4절에 따르면, 도출된 최적 조건에서 3번의 확인 실험을 수행했습니다. 그 결과, 실험적으로 얻은 평균값(UTS 219.333 MPa, 경도 86.666 HV)이 모델을 통해 예측된 값(UTS 216.986 MPa, 경도 85.406 HV)과 거의 차이가 없어 모델의 신뢰성이 입증되었습니다.


Conclusion: Paving the Way for Higher Quality and Productivity

본 연구 분석을 통해 2017A 알루미늄 합금의 스퀴즈 캐스팅 최적화에서 스퀴즈 압력이 가장 지배적인 변수임이 명확해졌습니다. 압력을 정밀하게 제어하고 최적화하는 것은 미세조직을 개선하고, 궁극적으로는 부품의 강도와 경도를 극대화하여 더 높은 품질과 생산성을 달성하는 핵심 열쇠입니다. 이러한 공정 최적화는 자동차 및 항공우주 분야에서 요구되는 고성능 경량 부품 생산에 직접적으로 기여할 수 있습니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 이 백서에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 알아보십시오.

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Copyright Information

  • This content is a summary and analysis based on the paper “Optimization of Squeeze Casting Parameters for 2017 A Wrought Al Alloy Using Taguchi Method” by “Najib Souissi et al.”.
  • Source: https://doi.org/10.3390/met4020141

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Figure 5 Thermal stress analysis; a) 100 °C; b) 150 °C; c) 200 °C

AA 7075 중력 다이캐스팅 해석: 금형 예열 온도가 기계적 특성에 미치는 영향 분석

이 기술 요약은 Hakan GÖKMEŞE, Şaban BÜLBÜL, Onur GÖK이 저술하여 Technical Gazette (2021)에 게재한 논문 “Casting of AA 7075 Aluminium Alloy into Gravity Die and Effect of the Die Preheating Temperature on Microstructure and Mechanical Properties”를 바탕으로 STI C&D의 기술 전문가들이 분석하고 정리한 내용입니다.

키워드

  • Primary Keyword: 중력 다이캐스팅 해석
  • Secondary Keywords: AA 7075 알루미늄 합금, 기계적 특성, 미세구조, 금형 예열, 열응력, 유한요소해석

Executive Summary

  • The Challenge: 고강도 AA 7075 알루미늄 합금의 중력 다이캐스팅 공정에서 금형 예열 온도와 같은 핵심 변수를 제어하는 것은 결함 없는 고품질 제품 생산에 필수적이지만, 시행착오에 의존하는 방식은 시간과 비용 소모가 큽니다.
  • The Method: 유한요소해석(FEA)을 사용하여 100°C, 150°C, 200°C의 각기 다른 금형 예열 온도에서 발생하는 열응력과 변형을 모델링하고, 실제 주조 실험을 통해 미세구조 및 기계적 특성에 미치는 영향을 검증했습니다.
  • The Key Breakthrough: 금형 예열 온도를 높이면 금형의 열응력은 증가하지만, 주조품의 인장 연신율은 200°C에서 최대 4.85%까지 향상되었습니다. 반면, 예열 온도가 높을수록 결정립이 조대해지고 경도는 감소하는 상충 관계가 확인되었습니다.
  • The Bottom Line: 금형 예열 온도는 금형 수명과 최종 제품 품질 사이의 중요한 상충 관계를 결정하는 변수이며, 중력 다이캐스팅 해석을 통해 물리적 테스트 없이 이 영향을 예측하고 공정을 최적화할 수 있습니다.

The Challenge: Why This Research Matters for CFD Professionals

항공우주 및 자동차 산업에서 ‘전략적 금속’으로 불리는 AA 7075 알루미늄 합금은 높은 강도와 경도로 인해 널리 사용됩니다. 이러한 고성능 부품을 생산하는 중력 다이캐스팅 공정은 효율적이지만, 용탕의 충전 시간, 주조 온도, 금형 예열과 같은 여러 변수를 정밀하게 제어해야 합니다. 특히 금형 예열은 용탕이 금형 내부를 효과적으로 채우도록 하는 데 결정적인 역할을 합니다.

기존의 시행착오 방식은 불필요하고 부정확한 생산을 초래하여 비용을 증가시킵니다. 따라서 주조 공정을 컴퓨터 환경에서 설계, 모델링 및 분석하는 것은 오류율을 최소화하고 결함 없는 제품을 생산하는 데 매우 중요합니다. 이 연구는 금형 예열 온도가 금형 자체의 열적 스트레스와 최종 주조품의 기계적 특성에 미치는 복합적인 영향을 규명하여, 시뮬레이션 기반의 공정 최적화 가능성을 제시하고자 했습니다.

The Approach: Unpacking the Methodology

본 연구는 AA 7075 알루미늄 합금의 중력 다이캐스팅 공정을 시뮬레이션 및 실험을 통해 체계적으로 분석했습니다.

  • 재료 및 금형 설계: 주조 재료로는 AA 7075 알루미늄 합금이 사용되었으며, 단일 인장 시험편을 생산하기 위해 특별히 설계된 H13 공구강 재질의 금형이 제작되었습니다.
  • 시뮬레이션 (FEA): 주조 공정에 앞서, 유한요소해석(FEA)을 통해 800°C의 용탕 주입 시 각기 다른 금형 예열 온도(100°C, 150°C, 200°C)가 금형 표면에 가하는 열응력 분포와 변형을 예측했습니다.
  • 실험 조건: 800°C로 용해된 AA 7075 합금을 100°C, 150°C, 200°C로 각각 예열된 금형에 주입하여 인장 시험편을 제작했습니다.
  • 특성 분석: 주조된 시험편은 인장 강도, 미세/거시 경도(시효 처리 전후), 미세구조(SEM), 파단면 형태(EDS) 등 다양한 기계적 및 야금학적 특성을 평가받았습니다. 시효 열처리는 480°C에서 120분 용체화 처리 후 120°C에서 1440분간 진행되었습니다.
Figure 1 Metallic die design and tensile test samples
Figure 1 Metallic die design and tensile test samples

The Breakthrough: Key Findings & Data

Finding 1: 금형 예열 온도 증가 시 금형의 열응력 및 변형 심화

유한요소해석 결과, 금형 예열 온도를 높이는 것이 금형 수명에 부정적인 영향을 미칠 수 있음을 확인했습니다. Figure 5에서 볼 수 있듯이, 예열 온도가 100°C에서 200°C로 증가함에 따라 인장 시험편으로 전환되는 반경 연결부(a, b, c 영역)와 탕구(feeder) 연결부(d, e, f 영역)에서 열응력과 변형이 집중적으로 심화되었습니다. 이는 높은 예열 온도가 열 피로를 가중시켜 금형의 사용 수명을 단축시킬 수 있음을 시사합니다.

Finding 2: 예열 온도에 따른 기계적 특성의 상충 관계 (연신율 vs. 경도)

실제 주조 실험 결과, 금형 예열 온도는 최종 제품의 기계적 특성에 직접적인 영향을 미쳤습니다.

  • 연신율: Figure 13에 따르면, 금형 예열 온도가 증가할수록 인장 연신율이 향상되었습니다. 200°C에서 주조된 시편은 4.85%로 가장 높은 연신율을 보였으며, 이는 100°C(2.40%)와 150°C(3.35%)에 비해 현저히 높은 수치입니다. 이는 높은 예열 온도가 냉각 속도를 늦춰 더 연성적인 파괴 거동을 유도했기 때문입니다.
  • 경도: 반면, 경도는 예열 온도가 낮을수록 높게 나타났습니다. Figure 14에 따르면, 시효 열처리 후 100°C에서 주조된 시편의 미세경도는 152.16 HV로 가장 높았으며, 200°C 시편의 경도(데이터 미제공, 그래프상 약 120 HV)보다 월등히 높았습니다. 이는 낮은 예열 온도가 더 빠른 냉각을 유도하여 미세한 결정립 구조를 형성했기 때문입니다(Figure 6 참조).

Practical Implications for R&D and Operations

  • For Process Engineers: 이 연구는 금형 예열 온도가 제품의 연성과 경도 사이의 상충 관계를 제어하는 핵심 변수임을 보여줍니다. 높은 경도가 요구되는 부품에는 100°C와 같은 낮은 예열 온도를, 파괴 인성이 중요한 부품에는 200°C와 같은 높은 예열 온도를 적용하는 등 목표 성능에 맞춰 공정 조건을 최적화할 수 있습니다.
  • For Quality Control Teams: Figure 14의 데이터는 예열 온도와 시효 처리 후 경도 간의 명확한 반비례 관계를 보여줍니다. 이는 공정 윈도우를 설정하고 품질 검사 기준을 수립하는 데 활용될 수 있습니다. 또한 Figures 7, 8, 9의 파단면 이미지는 파괴 분석 시 유용한 시각적 참조 자료를 제공합니다.
  • For Design Engineers: Figure 5의 해석 결과는 금형의 반경 연결부와 같은 특정 부위에 열응력이 집중됨을 보여줍니다. 이는 특히 높은 예열 온도가 요구될 때, 열 피로를 완화하기 위한 금형 설계(예: 필렛 반경 최적화)가 중요함을 시사합니다.
Figure 3 Aging process diagram of AA 7075 alloy
Figure 3 Aging process diagram of AA 7075 alloy

Paper Details


Casting of AA 7075 Aluminium Alloy into Gravity Die and Effect of the Die Preheating Temperature on Microstructure and Mechanical Properties

1. Overview:

  • Title: Casting of AA 7075 Aluminium Alloy into Gravity Die and Effect of the Die Preheating Temperature on Microstructure and Mechanical Properties
  • Author: Hakan GÖKMEŞE, Şaban BÜLBÜL, Onur GÖK
  • Year of publication: 2021
  • Journal/academic society of publication: Technical Gazette
  • Keywords: aluminium, analysis; casting; gravity die casting; mechanical properties

2. Abstract:

본 연구에서는 중력 다이캐스팅 응용 분야에서 중요한 부분을 차지하는 경합금 주조 기술을 조사했습니다. 이를 위해 유한요소해석법을 사용하여 100°C, 150°C, 200°C의 예열 온도에서 금속 인장 시험편 금형의 모델링 및 분석 연구를 수행한 후 주조 시험을 진행했습니다. AA 7075 알루미늄 합금의 중력 다이캐스팅 시험은 800°C에서 다양한 금형 예열 온도 조건 하에 수행되었습니다. 주조 공정 후, 인장 시험편을 준비하여 시험 샘플의 인장 시험 측정 및 경도 측정을 수행했습니다. 경도 측정은 시효 열처리(120°C – 1440분) 전후에 거시경도와 미세경도 모두 측정되었습니다. 시험 샘플의 미세구조 및 파단면 검사를 위해 SEM 및 EDS 분석이 수행되었습니다. 모델링 및 분석 연구를 통해 금형 예열 온도를 높이면 열응력과 변형이 증가하고, 인장 특성 측면에서 가장 높은 연신율은 4.85%인 것으로 확인되었습니다. 시효 열처리 전후의 경도 값은 금형 예열 온도가 증가함에 따라 감소하는 경향을 보였습니다.

3. Introduction:

오늘날 알루미늄 및 알루미늄 합금은 기술의 급속한 발전과 함께 우리 생활에서 가장 널리 사용되는 금속 재료 중 하나가 되었으며, 그 사용이 더욱 확산되고 있습니다. 7xxx계 합금은 높은 기계적 특성, 강도 및 경도, 우수한 내식성 및 다른 알루미늄 합금들 사이에서 뛰어난 용접성으로 인해 항공우주, 자동차, 스포츠 용품 및 기타 분야에서 널리 사용됩니다. 일반적으로 AA 7075 알루미늄 합금을 생산하는 주조 방법은 부품의 크기와 모양에 제한 없이 기존 주조 장비를 사용할 수 있어 간단하고 경제적입니다. 주조 기술을 이용한 제조에서, 용탕의 품질을 평가하기 위해 인장 시험봉은 주조 공정(사형 또는 중력 다이)과 별도로 생산될 수 있습니다. 주조 모델링 및 분석과 같은 프로그램은 시행착오 방식의 불필요하고 부정확한 주조 생산 없이 컴퓨터 환경에서 설계하여 결함 없는 주조 응용 분야에서 매우 중요합니다.

4. Summary of the study:

Background of the research topic:

AA 7075 알루미늄 합금은 항공우주 및 자동차 산업에서 요구되는 고강도, 고경도 특성을 만족시키는 핵심 소재입니다. 중력 다이캐스팅은 이러한 부품을 경제적으로 생산하는 주요 공법 중 하나입니다.

Status of previous research:

기존 연구들은 중력 다이캐스팅의 품질 향상과 금형 수명 연장을 위해 다양한 재료와 공정 변수에 초점을 맞춰왔습니다. 그러나 금형 예열 온도가 금형 자체의 열적 거동과 최종 주조품의 미세구조 및 기계적 특성에 미치는 복합적인 영향을 체계적으로 분석한 연구는 부족했습니다.

Purpose of the study:

본 연구의 목적은 AA 7075 알루미늄 합금의 중력 다이캐스팅 공정에서 금형 예열 온도가 (1) 금형의 열응력 및 변형, (2) 주조품의 미세구조 및 기계적 특성(인장 강도, 경도)에 미치는 영향을 규명하는 것입니다. 이를 통해 시뮬레이션 기반의 공정 최적화 가능성을 탐색하고자 했습니다.

Core study:

연구의 핵심은 유한요소해석(FEA)을 통한 금형의 열응력 예측과 실제 주조 실험을 통한 기계적 특성 검증을 결합한 것입니다. 100°C, 150°C, 200°C의 세 가지 금형 예열 온도 조건을 변수로 설정하고, 각 조건이 금형 수명과 제품 품질에 미치는 상반된 영향을 정량적으로 분석했습니다.

5. Research Methodology

Research Design:

본 연구는 시뮬레이션과 실험적 접근법을 결합하여 설계되었습니다. 먼저 CAD 모델링 및 유한요소해석을 통해 금형 예열 온도에 따른 열응력 분포를 예측하고, 이를 바탕으로 실제 주조 실험을 수행하여 시뮬레이션 결과와 실제 현상 간의 관계를 분석했습니다.

Data Collection and Analysis Methods:

  • 시뮬레이션: 유한요소해석 소프트웨어를 사용하여 금형의 열응력 및 변형을 계산했습니다.
  • 주조 실험: 설계된 금형을 사용하여 800°C의 AA 7075 용탕을 100°C, 150°C, 200°C로 예열된 금형에 주입했습니다.
  • 기계적 특성 평가: 만능시험기(Universal Tester)를 사용하여 인장 강도 및 연신율을 측정했으며, 로크웰 및 비커스 경도계를 사용하여 시효 처리 전후의 경도를 측정했습니다.
  • 미세구조 분석: 주사전자현미경(SEM)과 에너지 분산형 분광기(EDS)를 사용하여 미세구조 및 파단면의 형태와 성분 분포를 분석했습니다.

Research Topics and Scope:

연구 범위는 AA 7075 알루미늄 합금의 중력 다이캐스팅 공정에 국한되며, 주요 연구 주제는 금형 예열 온도(100°C, 150°C, 200°C)가 금형의 열적 거동과 주조품의 미세구조 및 기계적 특성에 미치는 영향입니다.

6. Key Results:

Key Results:

  • 유한요소해석 결과, 금형 예열 온도가 100°C에서 200°C로 증가함에 따라 금형의 열응력과 변형이 심화되어 금형 수명에 부정적인 영향을 미칠 것으로 예측되었습니다.
  • 금형 예열 온도가 높을수록 주조품의 결정립이 조대해지는 경향을 보였습니다. 100°C에서 예열된 금형에서 얻은 시편의 결정립 크기가 상대적으로 가장 작았습니다.
  • 인장 시험 결과, 금형 예열 온도가 증가함에 따라 연신율이 증가하여 200°C에서 4.85%로 최대치를 기록했습니다. 반면 인장 강도는 200°C에서 164 MPa로 가장 높게 나타났습니다.
  • 파단면 분석 결과, 예열 온도가 증가함에 따라 취성 파괴 형태에서 연성 파괴 형태로 변화하는 경향이 관찰되었습니다.
  • 경도 측정 결과, 시효 열처리 전후 모두 금형 예열 온도가 증가할수록 경도 값이 감소했습니다. 시효 처리 후 가장 높은 경도 값은 100°C 예열 조건에서 얻은 시편(152.16 HV, 110.77 HRB)에서 측정되었습니다.
Figure 5 Thermal stress analysis; a) 100 °C; b) 150 °C; c) 200 °C
Figure 5 Thermal stress analysis; a) 100 °C; b) 150 °C; c) 200 °C

Figure List:

  • Figure 1 Metallic die design and tensile test samples
  • Figure 2 Tensile test bar
  • Figure 3 Aging process diagram of AA 7075 alloy
  • Figure 4. Metallic die design
  • Figure 5 Thermal stress analysis; a) 100 °C; b) 150 °C; c) 200 °C
  • Figure 6 AA 7075 alloy microstructure images cast at different preheating temperatures: a) 100 °C; b) 150 °C; c) 200 °C
  • Figure 7 SEM images of the fractured surface after the tensile test and casting with 100 °C preheating
  • Figure 8 SEM images of the fracture surfaces after the casting and tensile test with 150 °C preheating
  • Figure 9 SEM images of the fracture surface after casting and tensile test with 200 °C preheating
  • Figure 10 Fracture surface EDS analysis after the casting and tensile test with 100 °C preheating
  • Figure 11 Fracture surface EDS analysis after the casting and tensile test with 150 °C preheating
  • Figure 12 Fracture surface EDS analysis after the casting and tensile test with 200 °C preheating
  • Figure 13 Tensile test results of samples cast at different preheating temperatures
  • Figure 14 The hardness results of the samples cast at different preheating temperatures: a) Microhardness; b) Macrohardness

7. Conclusion:

본 연구의 실험 결과는 다음과 같이 요약됩니다. 중력 다이캐스팅 CAD 모델링 연구를 통해 금형 예열 온도가 증가하면 열응력, 변형 및 금형 수명 측면에서 부정적인 영향을 미치는 것으로 확인되었습니다. 증가하는 금형 예열 온도에서 주조 미세구조는 결정립 크기 측면에서 조대해졌습니다. 인장 시험 후, 파단면 형태의 취성 파괴 거동은 증가하는 금형 예열 온도에 따라 결정립계에서 연성 거동으로 대체되었으나, 결정립 내부의 편석에 따라 취성 결정립에서 분리가 발생했습니다. 또한, 시편의 인장 연신율 값이 증가하여 200°C 금형 예열 온도에서 4.85%로 확인되었습니다. 적용된 시효 열처리 공정 후 미세경도 및 거시경도 값은 100°C 금형 예열 공정에서 주조된 시험 시편에서 152.16 HV 및 110.77 HRB로 얻어졌습니다. 명시된 결과를 검토할 때, 금형 예열 온도는 특히 경합금(Al, Zn, Mg 등) 주조에서 효과적일 수 있습니다. 따라서 금형 성형, 금형 변형 및 수명, 미세구조 및 기계적 특성은 중력 다이캐스팅 응용 분야에서 직접적인 영향을 받을 수 있습니다.

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Expert Q&A: Your Top Questions Answered

Q1: 이 연구에서 표준 ASTM B108 금형 대신 맞춤형 금형을 설계한 이유는 무엇입니까?

A1: 논문에 따르면, “이 금형은 ASTM B108로 알려진 금형과 달리 단일 인장 시험편을 생산하도록 설계되었습니다.” 이는 연구의 목적이 특정하고 단순화된 형상에 대한 예열 효과를 명확히 분리하여 관찰하는 데 있었음을 시사합니다. 복잡한 형상의 영향을 배제하고 예열 온도라는 단일 변수가 기본적인 주조품의 특성에 미치는 영향을 집중적으로 분석하기 위한 설계로 보입니다.

Q2: Figure 5는 200°C에서 열응력이 증가함을 보여주는데, 이것이 실제 금형 수명에 어떤 영향을 미칩니까?

A2: 논문은 이것이 “금형 사용 수명에 부정적인 영향을 미칠 것”이라고 언급합니다. 이는 중력 다이캐스팅 금형의 일반적인 파손 원인인 열 피로 균열 때문입니다. 시뮬레이션을 통해 엔지니어는 그림에 나타난 반경 연결부와 같은 고응력 영역을 미리 예측하고, 해당 부위를 보강하거나 공정 조건을 최적화하여 임계 응력 임계값 이하로 유지함으로써 금형 수명을 연장할 수 있습니다.

Q3: 논문에서는 연신율과 경도 사이의 상충 관계를 언급했습니다. 어떤 예열 온도가 ‘최적’이라고 할 수 있습니까?

A3: 단 하나의 ‘최적’ 온도는 없습니다. 이는 부품의 최종 적용 분야 요구사항에 따라 달라집니다. 높은 경도와 강도가 필요한 부품(예: 구조 부재)의 경우, 100°C로 예열 후 시효 처리를 하는 것이 최적의 선택(152.16 HV)입니다. 반면, 더 높은 연성과 파괴 저항이 필요한 부품(예: 충격 흡수 부품)의 경우, 200°C 예열이 더 나은 선택(4.85% 연신율)이 될 것입니다.

Q4: 예열 온도가 증가함에 따라 파단면이 취성에서 연성으로 변하는 원인은 무엇입니까?

A4: 논문은 높은 예열 온도가 냉각 속도를 늦춘다고 설명합니다. 이는 “결정립 성장”과 합금 원소의 “편석 경향이 있는 영역 형성”을 유발합니다(Figure 6). 느린 응고 속도와 조대해진 결정립은 결과적으로 100°C에서 관찰된 취성 입계 파괴(Figure 7)에서 200°C에서 보이는 더 큰 딤플을 가진 연성 파괴(Figure 9)로의 전환을 이끌어냈습니다.

Q5: 시효 열처리를 통한 경도 향상 효과는 얼마나 중요했습니까?

A5: 매우 중요했습니다. 100°C 예열 시편의 경우, 미세경도는 평균 129.53 HV에서 152.16 HV로 17.8% 증가했습니다. 거시경도는 86.36 HRB에서 110.77 HRB로 27.9%나 증가했습니다(Figure 14). 이는 AA 7075 합금의 최종 기계적 특성을 확보하는 데 있어 주조 후 열처리가 필수적인 공정임을 명확히 보여줍니다.


Conclusion: Paving the Way for Higher Quality and Productivity

이 연구는 AA 7075 알루미늄 합금의 중력 다이캐스팅 공정에서 금형 예열 온도가 금형 수명과 제품 품질에 미치는 복합적인 영향을 명확히 보여주었습니다. 시뮬레이션은 높은 예열 온도가 금형에 가하는 열적 부담을 예측했으며, 실험은 이것이 제품의 연성을 향상시키는 대신 경도를 저하시키는 상충 관계를 가짐을 입증했습니다.

이러한 결과는 중력 다이캐스팅 해석이 단순히 용탕의 유동을 예측하는 것을 넘어, 공정 변수가 최종 제품의 기계적 특성과 생산 설비의 수명에 미치는 영향까지 종합적으로 최적화할 수 있는 강력한 도구임을 증명합니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 이 백서에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 알아보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
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Copyright Information

  • This content is a summary and analysis based on the paper “Casting of AA 7075 Aluminium Alloy into Gravity Die and Effect of the Die Preheating Temperature on Microstructure and Mechanical Properties” by “Hakan GÖKMEŞE, Şaban BÜLBÜL, Onur GÖK”.
  • Source: https://doi.org/10.17559/TV-20200819135453

This material is for informational purposes only. Unauthorized commercial use is prohibited. Copyright © 2025 STI C&D. All rights reserved.

Figure 1. Materials used in casting (a) Mg, (b) TiB, (c) Al356.

다이캐스팅 공정 최적화: TiB 및 Mg 첨가제를 통한 Al356 합금 미세구조 제어 기술

이 기술 요약은 E.I. Bhiftime이 작성하여 2022년 Biomedical and Mechanical Engineering Journal (BIOMEJ)에 발표한 논문 “Microstructure on the TiB and Mg Reinforced of Al356 Alloy with Die Casting Process”를 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 다이캐스팅 (Die Casting)
  • Secondary Keywords: 알루미늄 합금 (Aluminum Alloy), Al356, 금속 매트릭스 복합재료 (Metal Matrix Composites), 미세구조 (Microstructure), 입자 크기 (Grain Size), TiB, Mg

Executive Summary

  • 도전 과제: 고성능 알루미늄 매트릭스 복합재료는 높은 비용과 교반 주조 시 발생하는 산화 문제 등 제조상의 어려움으로 인해 널리 사용되지 못하고 있습니다.
  • 연구 방법: Al356 합금에 고정된 양의 TiB(2 wt%)와 다양한 비율의 Mg(3-5 wt%)를 강화재로 첨가하여 다이캐스팅 공정을 통해 복합재료를 제조했습니다.
  • 핵심 돌파구: Mg 함량을 0%에서 5%로 증가시킴에 따라 평균 결정 입자 크기가 109.46 µm에서 35.09 µm로 체계적으로 감소하여 훨씬 미세하고 균일한 미세구조를 형성했습니다.
  • 핵심 결론: 다이캐스팅 공정에서 TiB와 Mg를 첨가하는 것은 Al356 합금의 결정립을 미세화하는 효과적인 방법이며, 이는 기계적 특성 향상에 결정적인 역할을 합니다.
Figure 1. Materials used in casting (a) Mg, (b) TiB, (c) Al356.
Figure 1. Materials used in casting (a) Mg, (b) TiB, (c) Al356.

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

알루미늄 매트릭스 복합재료(AMC)는 높은 비강성과 비강도로 인해 경량화가 필수적인 분야에서 큰 관심을 받고 있습니다. 하지만 강화재, 제조 공정, 2차 변형 등 세 가지 측면에서 발생하는 높은 비용 때문에 사용이 제한적입니다. 경제적인 생산 방법 중 하나인 교반 주조(stir casting)는 균일한 입자 분포를 얻기 위해 긴 교반 시간이 필요하며, 이 과정에서 과도한 가스 유입이나 Mg 매트릭스의 산화 같은 문제가 발생할 수 있습니다. 따라서 고품질의 복합재료를 제조하기 위해 교반 시간을 줄이면서도 재료의 강도와 인성을 높일 수 있는 효율적인 생산 방법의 개발이 시급합니다. 이 연구는 이러한 산업적 요구에 부응하여 다이캐스팅 공정을 통해 Al356 합금의 미세구조를 제어하는 방안을 제시합니다.

연구 접근법: 방법론 분석

본 연구는 Al356 알루미늄 합금을 기지(matrix)로, 마그네슘(Mg)과 티타늄 보론(TiB) 입자를 강화재(reinforcement)로 사용하여 다이캐스팅 공정으로 금속 매트릭스 복합재료를 제조했습니다. 실험의 핵심 변수는 Mg의 첨가량으로, 각각 3, 4, 5 wt%로 변화시켰으며, TiB는 2 wt%로 고정했습니다.

제조 공정은 다음과 같습니다. 1. Al356 잉곳을 800°C로 가열하여 완전히 용해시킵니다. 2. 온도를 640°C로 낮춘 후, 정해진 양의 Mg와 TiB를 용탕에 투입합니다. 3. 기계식 교반기를 사용하여 200 rpm의 속도로 120초간 철저히 교반합니다. 4. 다시 760°C의 주입 온도로 재가열한 후, 250°C로 예열된 다이캐스팅 금형에 주입합니다. 5. 360초간 유지 후 금형에서 주물을 분리하고 상온에서 냉각시킵니다.

제조된 시편은 광학 현미경(Olympus, 200X)과 주사전자현미경(SEM)을 사용하여 미세구조를 분석했으며, 결정 입자 크기는 ASTM E112-96 표준에 따른 선형 절편법(linear intercept method)을 사용하여 정량적으로 계산되었습니다.

핵심 돌파구: 주요 발견 및 데이터

결과 1: Mg 첨가량 증가에 따른 결정 입자 미세화

연구의 가장 중요한 발견은 Mg 첨가량이 증가할수록 Al356 합금의 결정 입자 크기가 현저하게 감소한다는 것입니다. Table 3의 데이터에 따르면, Mg를 첨가하지 않은(0 wt%) 시편의 평균 입자 크기는 109.46 µm였습니다. 반면, 2 wt%의 TiB와 함께 Mg를 3 wt% 첨가했을 때 입자 크기는 71.84 µm로 감소했으며, 4 wt%에서는 52.12 µm, 5 wt%에서는 35.09 µm까지 미세화되었습니다. Figure 8은 이러한 경향을 명확하게 보여주며, Mg가 효과적인 결정립 미세화제 역할을 함을 입증합니다.

Figure 7. Diameter grain size calculation AlTiBMg
Figure 7. Diameter grain size calculation AlTiBMg

결과 2: 강화 입자의 균일한 분산 및 결합 형태 확인

주사전자현미경(SEM)으로 촬영한 Figure 9와 Figure 10의 형태학적 분석 결과, 강화 입자들이 알루미늄 기지 내에 균일하게 융합되어 있음을 확인했습니다. Mg 입자들은 Al 합금 기지를 둘러싸며 서로 결합하는 형태를 보였고, TiB의 첨가는 입자 형상을 더 매끄럽고 고르게 분산시키는 데 기여했습니다. 이는 강화 입자와 기지 간의 우수한 결합이 이루어졌음을 의미하며, 복합재료의 기계적 성능 향상에 필수적인 요소입니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 다이캐스팅 공정에서 Mg 첨가량을 조절하는 것이 Al356 합금의 결정립 미세화를 위한 직접적인 수단임을 시사합니다. 이는 최종 제품의 강도와 인성을 예측하고 제어하는 데 활용될 수 있습니다.
  • 품질 관리팀: 논문의 Table 3과 Figure 8에 제시된 데이터는 Mg 함량과 결정 입자 크기 간의 명확한 상관관계를 제공합니다. 이를 바탕으로 원재료 조성을 제어하여 목표 입자 크기 범위를 설정하는 새로운 품질 검사 기준을 수립할 수 있습니다.
  • 설계 엔지니어: 연구 결과는 TiB와 Mg 강화재가 결정립을 미세화할 뿐만 아니라 균일한 입자 분산을 보장한다는 것을 보여줍니다. 이는 해당 소재로 설계된 부품이 전체적으로 더 일관되고 예측 가능한 기계적 특성을 가질 것임을 의미하며, 초기 설계 단계에서 중요한 고려 사항이 될 수 있습니다.

논문 상세 정보


Microstructure on the TiB and Mg Reinforced of Al356 Alloy with Die Casting Process

1. 개요:

  • 제목: Microstructure on the TiB and Mg Reinforced of Al356 Alloy with Die Casting Process
  • 저자: E.I. Bhiftime
  • 발행 연도: 2022
  • 학술지/학회: Biomedical and Mechanical Engineering Journal (BIOMEJ)
  • 키워드: Alumunium alloy, Mg, TiB, Die Casting

2. 초록:

티타늄 보론(TiB)과 마그네슘(Mg)으로 강화된 금속 매트릭스 복합재료(MMC)는 높은 기계적 및 물리적 특성을 제공합니다. 다이캐스팅 공정으로 TiB와 Mg 입자로 강화된 Al356 합금을 제조하는 것은 가장 간단한 방법이었습니다. 본 연구의 목적은 TiB와 Mg 입자로 강화된 Al356 합금의 미세구조 차이와 TiB 및 Mg의 추가적인 수준이 미치는 변화 효과를 조사하는 것이었습니다. 기지 재료로는 Al356 합금을, 강화재로는 TiB와 Mg(3, 4, 5 wt%)를 사용했습니다. 연구에 사용된 주조 공정은 다이캐스팅이었습니다. 다양한 매개변수로 제작된 복합재료의 미세구조는 반용융(semi-solid) 방법이 균일한 입자 분포를 개선했음을 나타냈습니다. 3-5 wt%의 TiB와 Mg 복합재료는 새로운 공정으로 제작되었습니다. 이 복합재료들에서 입자 분포는 균일했습니다. TiB를 첨가함으로써 복합재료의 결정립 크기는 훨씬 더 미세해질 것입니다. 입자 함량이 증가함에 따라 결정립 크기가 향상되었습니다. 강화 입자와 Al356 합금 기지 사이의 복합재료 형태는 균일하게 결합되고 분산되었습니다. 이 논문은 미세구조와 SEM 분석만을 다룹니다.

3. 서론:

알루미늄 매트릭스 복합재료는 높은 비강성과 비강도로 인해 경량화 분야에서 큰 관심을 끌고 있습니다. 그러나 높은 비용으로 인해 제한적으로 사용됩니다. 높은 비용은 주로 강화재, 제조 공정, 2차 변형의 세 가지 측면에서 발생합니다. 따라서 경제적인 입자와 고효율 생산 방법이 개발되어야 합니다. 마이크로 입자는 저렴한 가격과 제조 중 용이한 분산으로 인해 매우 경제적입니다. 마이크로 입자 강화 알루미늄 매트릭스 복합재료는 상대적으로 저렴한 비용과 우수한 기계적 특성으로 상업적 사용 잠재력이 있습니다. 교반 주조는 모든 방법 중에서 가장 생산적이고 경제적인 것으로 간주됩니다. 그러나 균일한 입자 분포를 얻기 위해서는 긴 교반 시간이 필요하며, 이는 종종 Mg 매트릭스에 너무 많은 가스와 산화를 유발합니다. 따라서 고품질 복합재료를 제작하기 위해 교반 시간을 줄일 필요가 있습니다. A356을 기지로 하고 마그네슘(Mg)과 티타늄 보론(TiB) 입자를 강화재로 사용하는 알루미늄 합금 제조는 금속의 강도와 인성을 증가시킬 수 있기 때문입니다. A356 합금은 경량(밀도 2.7 g/cm3), 172 MPa의 인장 강도, 내식성 등의 장점이 있지만 60 HB의 낮은 경도를 가집니다.

4. 연구 요약:

연구 주제의 배경:

경량 고강도 소재에 대한 산업적 수요가 증가함에 따라 알루미늄 매트릭스 복합재료(AMC)가 주목받고 있으나, 높은 생산 비용이 상용화의 걸림돌이 되고 있습니다. 교반 주조와 같은 경제적인 공정은 산화 및 가스 유입 등의 품질 저하 문제를 안고 있습니다.

이전 연구 현황:

이전 연구들은 AlTiC, AlTiB 등을 첨가하여 결정립 크기를 미세화하는 효과를 확인했습니다. 예를 들어, 1% TiB 첨가로 결정립 크기가 작아졌으며, 다른 연구에서는 TiB 함량을 1-4 wt%로 변화시켰을 때 결정립이 크게 감소함을 보였습니다. 하지만 이러한 연구들은 종종 복잡한 공정을 사용하거나, 교반 주조의 근본적인 문제점을 해결하지 못했습니다.

연구 목적:

본 연구의 목적은 다이캐스팅 공정을 이용하여 TiB와 Mg 입자로 강화된 Al356 합금의 미세구조 변화를 조사하는 것입니다. 특히 Mg의 함량 변화(0, 3, 4, 5 wt%)가 미세구조 및 결정립 크기에 미치는 영향을 정량적으로 분석하고자 합니다.

핵심 연구:

Al356 합금에 2 wt%의 TiB와 0, 3, 4, 5 wt%의 Mg를 첨가하여 다이캐스팅으로 시편을 제작하고, 광학 현미경 및 SEM을 통해 미세구조, 결정립 크기, 강화 입자의 분포 및 형태를 분석하여 첨가 원소의 영향을 규명합니다.

5. 연구 방법론

연구 설계:

Al356 합금을 기지로 하고, Mg 함량을 0, 3, 4, 5 wt%로 변화시키는 실험군을 설정했습니다. 모든 실험군에는 2 wt%의 TiB를 공통적으로 첨가하여 Mg 함량 변화에 따른 효과를 집중적으로 관찰했습니다.

데이터 수집 및 분석 방법:

  • 미세구조 분석: 제작된 시편을 절단, 연마, 에칭한 후 광학 현미경(Olympus, 200X)을 사용하여 미세구조 사진을 촬영했습니다.
  • 결정립 크기 계산: ASTM E112-96 표준에 따라 선형 절편법을 사용하여 각 시편의 상단(Top), 중앙(Center), 하단(Bottom)에서 결정립 크기를 측정하고 평균값을 계산했습니다.
  • 형태학적 분석: 주사전자현미경(SEM)을 사용하여 300X 및 500X 배율로 파단면 또는 표면의 형태를 관찰하여 강화 입자와 기지 간의 결합 상태를 분석했습니다.

연구 주제 및 범위:

본 연구는 Al356 합금에 TiB와 Mg를 첨가하여 다이캐스팅으로 제조했을 때 나타나는 미세구조적 변화에 초점을 맞춥니다. 기계적 특성에 대한 심층 분석 대신, 미세구조, 결정립 크기, 입자 분포 및 형태 분석에 국한됩니다.

6. 주요 결과:

주요 결과:

  • Mg 첨가량이 0 wt%에서 5 wt%로 증가함에 따라, Al356 합금의 평균 결정 입자 크기는 109.46 µm에서 35.09 µm로 크게 감소했습니다.
  • 5 wt% Mg를 첨가한 시편이 가장 미세한 결정립 구조를 보였습니다.
  • TiB와 Mg 원소는 주조 결과물에서 더 미세한 결정립 크기를 형성하는 데 기여했습니다.
  • 각 시편의 상단, 중앙, 하단에서 측정한 결정립 크기는 비교적 균일하여, 주조물 전체에 걸쳐 균질한 미세구조가 형성되었음을 나타냅니다.
  • SEM 분석 결과, 강화 입자(Mg, TiB)와 Al 기지는 균일하게 융합되었으며, 입자들은 매끄럽고 고르게 분산되었습니다.
Figure 8. Diameter Average grain size calculation AlTiBMg
Figure 8. Diameter Average grain size calculation AlTiBMg

Figure 목록:

  • Figure 1. Materials used in casting (a) Mg, (b) TiB, (c) Al356.
  • Figure 2. Casting results, and dividing the test area boundaris.
  • Figure 3. Micro Al-TiB-Mg 0% wt (a) Top, (b) Center, (c) Battom
  • Figure 4. Micro Al-2TiB-Mg 3% wt (a) Top, (b) Center, (c) Battom
  • Figure 5. Micro Al-2TiB-Mg 4% wt (a) Top, (b) Center, (c) Battom
  • Figure 6. Micro Al-2TiB-Mg 5% wt (a) Top, (b) Center, (c) Battom
  • Figure 7. Diameter grain size calculation AlTiBMg
  • Figure 8. Diameter Average grain size calculation AlTiBMg
  • Figure 9. Morphology Magnification 300X
  • Figure 10. Morphology Magnification 500X

7. 결론:

본 연구의 결과는 다음과 같습니다: Micro Al-TiB-Mg 5% wt는 Al-TiB-Mg 3% wt 및 Al-2TiB-Mg 4% wt와 비교했을 때 더 미세한 결정립 크기를 보였는데, 이는 Mg 비율의 첨가가 접착력과 크기 변화에 영향을 미치기 때문입니다. 상단, 중앙, 하단 사이의 Al-TiB-Mg 5% wt는 비교적 동일한 결정립 크기를 보였습니다. Al-2TiB-Mg 3 wt%와 Al-2TiB-Mg 4 wt% 변형 간의 결정립 크기 값 차이는 52.12 µm입니다. 반면 Al-2TiB-Mg 4 wt%와 Al-2TiB-Mg 5 wt% 변형 간의 차이는 17.03 µm입니다. 따라서 Al-2TiB-Mg 5 wt% 변형은 다른 변형과 비교했을 때 가장 작은 결정립 크기 값을 가집니다. 각 변형에서 결정립 크기의 평균 변화는 35.59 µm입니다. Al-2TiB-Mg 변형에서는 Al 합금 매트릭스를 둘러싸고 서로 결합하는 Mg 입자가 있습니다. 한편, Al-2TiB-Mg는 TiB-Mg와 잘 섞일 수 있는 Al 합금 매트릭스 사이에서 볼 수 있습니다. 그런 다음 TiB의 첨가는 입자의 모양을 더 매끄럽고 균일하게 분산되도록 변화시킬 수 있습니다. 형태학적으로 Al-2TiB-Mg는 강화 입자와 매트릭스 사이에서 균일하게 융합될 수 있습니다.

8. 참고 문헌:

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  2. Habibi MK, Joshi SP, Gupta M. Hierarchical magnesium nano-composites for enhanced mechanical response. Acta Mater 2010;58:6104–14.
  3. Wang XJ, Hu XS, Wu K, Zheng MY, Zhen L, Zhai QJ. The interfacial characterization of SiCp/AZ91 magnesium matrix composites fabricated by stir casting. J Mater Sci 2009;44:2759–64.
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전문가 Q&A: 주요 질문에 대한 답변

Q1: 서론에서 언급된 교반 주조 대신 다이캐스팅 공정을 선택한 이유는 무엇입니까?

A1: 논문은 다이캐스팅 공정이 “가장 간단한 방법”이라고 언급하며, 연구의 목적 중 하나가 효율적이고 간단한 제조법을 찾는 것이었음을 시사합니다. 교반 주조는 긴 교반 시간으로 인해 산화 및 가스 유입 문제가 발생할 수 있지만, 다이캐스팅은 상대적으로 빠른 공정으로 이러한 문제를 최소화하면서 복합재료를 제조할 수 있는 장점이 있습니다.

Q2: 모든 실험에서 TiB를 2 wt%로 고정했는데, TiB의 구체적인 역할은 무엇이며 이 비율을 선택한 이유는 무엇입니까?

A2: 논문에 따르면 TiB는 결정립 크기를 “훨씬 더 미세하게” 만들고 입자 분포를 “더 매끄럽고 균일하게” 만드는 역할을 합니다. 즉, 효과적인 결정립 미세화제(grain refiner) 및 분산제(dispersant)로 작용합니다. 2 wt%로 고정한 이유는 Mg 함량 변화라는 핵심 변수의 효과를 명확히 분리하여 관찰하기 위함으로 보입니다.

Q3: Table 3에서 시편의 상단, 중앙, 하단에서 측정한 결정립 크기가 거의 일정한 것이 왜 중요한가요?

A3: 이는 주조된 부품 전체에 걸쳐 균일하고 균질한 미세구조가 형성되었음을 의미합니다. 재료의 기계적 특성이 특정 부위에 치우치지 않고 전체적으로 일관성을 가지게 되므로, 제품의 신뢰성을 높이고 약한 지점(weak spot)이 발생할 가능성을 줄이는 데 매우 중요합니다.

Q4: Figure 9와 10의 SEM 이미지가 강화재와 기지 사이의 결합에 대해 알려주는 바는 무엇입니까?

A4: SEM 이미지는 강화 입자들이 알루미늄 기지와 “균일하게 융합(uniformly fused)”되었음을 보여줍니다. 특히 Mg 입자들이 Al 기지를 둘러싸며 결합하고, TiB-Mg 입자들이 잘 섞이는 모습은 강화재와 기지 간의 우수한 습윤성(wettability)과 접착력을 나타냅니다. 이러한 강한 계면 결합은 외부 하중이 기지에서 강화재로 효과적으로 전달되게 하여 복합재료의 전체적인 기계적 성능을 향상시키는 핵심 요소입니다.

Q5: 결론에서 “각 변형에서 결정립 크기의 평균 변화는 35.59 µm”라고 언급했는데, 이 값의 실질적인 의미는 무엇입니까?

A5: 이 값은 Mg 함량을 0%에서 3%, 3%에서 4%, 4%에서 5%로 단계적으로 증가시킬 때 나타나는 결정립 크기 감소량의 평균을 나타냅니다. 이는 Mg 첨가량 증가에 따라 결정립 크기가 얼마나 민감하게 반응하는지를 정량적으로 보여주는 지표로, Mg가 매우 효과적이고 일관된 미세화 효과를 가지고 있음을 의미합니다.


결론: 더 높은 품질과 생산성을 향한 길

본 연구는 다이캐스팅 공정에서 Al356 합금에 Mg와 TiB를 첨가하는 것이 미세구조를 효과적으로 제어하고 결정립을 미세화하는 강력한 방법임을 명확히 보여주었습니다. 특히 Mg 함량이 증가할수록 결정립 크기가 체계적으로 감소하여, 최종 제품의 기계적 특성을 향상시킬 수 있는 잠재력을 입증했습니다. 이는 고비용 및 공정상의 어려움이라는 기존의 장벽을 넘어, 고성능 경량 부품 생산을 위한 실용적인 길을 제시합니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 “E.I. Bhiftime”의 논문 “Microstructure on the TiB and Mg Reinforced of Al356 Alloy with Die Casting Process”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: Biomedical and Mechanical Engineering Journal (BIOMEJ), Vol. 2, No.2, October 2022, pp 1-12

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

Fig 4.5: 3D graphs to show effects of (a) P and S on weld resistance length, SL for F = 400μm, and (b) P and S on shearing force, Fs for F = 300μm.

스테인리스강 레이저 용접 공정 최적화: 실험 데이터를 통한 수학적 모델링 및 품질 향상 전략

이 기술 요약은 Mohammad Muhshin Aziz Khan이 2012년 피사 대학교(UNIVERSITÀ DI PISA)에 제출한 박사 학위 논문 “LASER BEAM WELDING OF STAINLESS STEELS”을 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 레이저 용접 공정 최적화
  • Secondary Keywords: 스테인리스강 용접, 레이저 빔 용접, 용접 시뮬레이션, 용접 품질, 열전달 해석, CFD

Executive Summary

  • 도전 과제: 수많은 공정 변수 간의 복잡한 상호작용으로 인해 스테인리스강 레이저 용접 시 용접 품질을 정확하게 예측하고 제어하는 것은 매우 어렵습니다.
  • 연구 방법: 본 연구는 실험계획법(DOE)과 반응표면분석법(RSM)을 활용하여 레이저 출력, 용접 속도와 같은 공정 변수와 용접부 형상, 전단 강도 등 용접 특성 간의 관계를 설명하는 수학적 모델을 개발했습니다.
  • 핵심 성과: 용접 저항 길이와 전단 강도는 ‘에너지 제한적’ 특성을 보인다는 사실을 규명했습니다. 즉, 특정 에너지 밀도를 초과하면 에너지를 더 투입해도 이러한 핵심 물성이 향상되지 않아 비효율적일 수 있습니다.
  • 핵심 결론: 예측 수학 모델을 활용하면, 비용이 많이 드는 시행착오 없이 원하는 용접 품질을 달성하고 결함을 최소화하며 공정 효율성을 높이는 최적의 레이저 용접 변수를 결정할 수 있습니다.

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

레이저 빔 용접은 높은 에너지 밀도, 정밀성, 자동화 가능성 덕분에 자동차, 전자, 항공우주 등 첨단 산업에서 필수적인 접합 기술로 자리 잡았습니다. 특히, 연료 인젝터와 같은 복잡하고 열에 민감한 부품을 제작할 때 스테인리스강의 레이저 용접은 높은 생산성과 품질을 보장하는 핵심 공정입니다.

하지만 문제는 레이저 출력, 용접 속도, 초점 거리, 입사각 등 수많은 공정 변수들이 용접부의 형상, 기계적 강도, 미세조직에 복합적으로 영향을 미친다는 점입니다. 특히 서로 다른 종류의 스테인리스강(예: 페라이트계와 오스테나이트계)을 용접할 경우, 재료의 물리적, 기계적, 야금학적 특성 차이로 인해 공정 제어는 더욱 복잡해집니다. 기존의 경험이나 시행착오에 의존하는 방식은 시간과 비용이 많이 들 뿐만 아니라, 최적의 공정 조건을 찾는 데 한계가 있습니다. 따라서 용접 품질을 과학적으로 예측하고 레이저 용접 공정 최적화를 달성하기 위한 체계적인 접근법이 절실히 요구됩니다.

Fig. 1.2: Variation in heat input with the power density of heat source [2]
Fig. 1.2: Variation in heat input with the power density of heat source [2]

연구 접근법: 방법론 분석

본 연구는 마르텐사이트계 스테인리스강(AISI 416, 440FSe)의 유사 재료 겹치기 용접과 페라이트/오스테나이트계 스테인리스강(AISI 430, 304L)의 이종 재료 필릿 용접에 대한 포괄적인 실험을 수행했습니다. 연구의 핵심은 통계적 기법을 활용하여 공정 변수와 결과 간의 관계를 모델링하는 것이었습니다.

  • 사용 장비: 1.1kW 연속파(CW) Nd:YAG 레이저 시스템
  • 핵심 공정 변수:
    • 레이저 출력 (P): 600W ~ 1100W
    • 용접 속도 (S): 2.0 m/min ~ 7.5 m/min
    • 광섬유 직경 (F): 300 µm, 400 µm
    • 초점 이탈 거리 (D): -1.5 mm ~ +1.5 mm
    • 빔 입사각 (A): 10° ~ 30°
  • 분석 방법론: 실험계획법(DOE)의 일환으로 완전요인설계(FFD)와 반응표면분석법(RSM)을 적용하여 각 공정 변수가 용접 특성에 미치는 영향을 분석했습니다.
  • 측정된 용접 특성 (응답 변수):
    • 용접부 형상: 용접 폭(W), 용입 깊이(Dp), 저항 길이(SL), 반경 방향 용입(Pr)
    • 기계적 특성: 전단 강도(Fs)
    • 미세조직 및 경도: SEM, EDS 분석 및 비커스 경도 측정

이러한 체계적인 접근을 통해 연구진은 각 응답 변수에 대한 예측 수학 모델을 개발하고, 이를 통해 공정 최적화를 수행할 수 있었습니다.

핵심 성과: 주요 발견 및 데이터

성과 1: 용접 강도의 “에너지 제한적(Energy-Limited)” 특성 규명

본 연구의 가장 중요한 발견 중 하나는 용접 강도가 특정 에너지 밀도 범위 내에서만 효과적으로 증가한다는 점입니다. 마르텐사이트계 스테인리스강의 겹치기 용접 실험에서, 용접 저항 길이(SL)와 전단 강도(Fs)는 에너지 밀도(ED)가 증가함에 따라 특정 지점까지는 급격히 향상되지만, 그 이후에는 거의 증가하지 않는 현상을 보였습니다.

논문의 그림 2.14에 따르면, 약 27.7 J/mm²의 에너지 밀도에서 전단 강도는 최대치에 가까운 6230N에 도달합니다. 이 값을 초과하여 에너지를 더 투입해도 전단 강도는 거의 향상되지 않았습니다. 반면, 최소 요구 강도인 4000N을 확보하기 위해서는 최소 20.8 J/mm²의 에너지 밀도가 필요했습니다. 이는 최적의 에너지 밀도 범위가 20.8 ~ 27.7 J/mm²임을 시사합니다. 이 범위를 벗어난 과도한 에너지 투입은 용입 깊이만 증가시킬 뿐, 실제 접합 강도 향상에는 기여하지 못하고 오히려 에너지 낭비와 과도한 열 영향으로 인한 변형을 유발할 수 있습니다.

성과 2: 공정 최적화를 위한 예측 모델의 높은 신뢰성 확보

본 연구는 반응표면분석법(RSM)을 통해 레이저 공정 변수와 주요 용접 특성 간의 관계를 설명하는 다중 회귀 모델을 성공적으로 개발했습니다. 개발된 모델들은 통계적으로 매우 유의미했으며(p-value < 0.0001), 실제 용접 결과와 예측값 사이에 높은 정확도를 보였습니다.

Fig 2.5 (a) Perturbation plot showing the effects of all factors, and contour graphs
illustrating the interaction effects of (b) P and S for F = 300μm; (c) S and F for P =
950W; and (d) P and F for S= 6 m/min on weld width
Fig 2.5 (a) Perturbation plot showing the effects of all factors, and contour graphs illustrating the interaction effects of (b) P and S for F = 300μm; (c) S and F for P = 950W; and (d) P and F for S= 6 m/min on weld width

예를 들어, 표 4.16의 검증 실험 결과에 따르면, 예측값과 실제 측정값 사이의 오차율은 대부분 5% 미만으로 매우 낮았습니다. 이는 개발된 수학 모델이 실제 생산 환경에서도 용접 품질을 신뢰성 있게 예측하는 데 사용될 수 있음을 의미합니다. 이러한 모델을 활용하면, 엔지니어는 목표로 하는 용접 품질(예: 최대의 전단 강도, 최소의 용접 폭)을 설정하고, 이를 달성하기 위한 최적의 공정 변수 조합(레이저 출력, 용접 속도 등)을 신속하게 도출할 수 있습니다. 논문에서는 마르텐사이트계 강 용접 시, 800-840W의 레이저 출력과 4.75-5.37 m/min의 용접 속도가 강하고 우수한 용접부를 얻기 위한 최적의 조건 중 하나로 제시되었습니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 특정 에너지 밀도 범위 내에서 공정을 운영하는 것이 효율적임을 보여줍니다. 예를 들어, 마르텐사이트강 용접 시 20.8-27.7 J/mm² 범위 내에서 레이저 출력과 용접 속도를 조절하면, 에너지 낭비를 막으면서도 최대의 용접 강도를 확보할 수 있습니다.
  • 품질 관리팀: 논문의 그림 3.8 및 3.9에서 볼 수 있듯이, 에너지 입력, 미세조직(덴드라이트 크기), 그리고 국부적 미세 경도 사이에는 명확한 상관관계가 있습니다. 이는 공정 변수로부터 기계적 특성을 예측하는 근거가 되어, 파괴 검사의 빈도를 줄이고 공정 중 품질 관리를 강화하는 데 기여할 수 있습니다.
  • 설계 엔지니어: 필릿 용접에서 빔 입사각이 용접 특성에 큰 영향을 미친다는 결과(5장)는 복잡한 형상의 부품 설계 시 레이저 헤드의 접근성과 위치 선정이 매우 중요함을 시사합니다. 초기 설계 단계에서부터 용접 공정을 고려하면 결함 발생 가능성을 줄일 수 있습니다.

논문 상세 정보


LASER BEAM WELDING OF STAINLESS STEELS

1. 개요:

  • 제목: LASER BEAM WELDING OF STAINLESS STEELS
  • 저자: Ing. Mohammad Muhshin Aziz Khan
  • 발행 연도: 2012
  • 발행 학술지/학회: Tesi di Dottorato di Ricerca (PhD Thesis), UNIVERSITÀ DI PISA
  • 키워드: laser beam welding, stainless steels, process optimization, weld bead geometry, mechanical properties, microstructure, mathematical modeling, response surface methodology (RSM)

2. 초록:

본 연구의 주요 목적은 스테인리스강의 레이저 빔 용접을 연구하는 것입니다. 실험에서는 1.1kW 연속파 Nd:YAG 레이저를 사용하여 각각 겹치기 및 필릿 이음 구성에서 유사 마르텐사이트계 및 이종 오스테나이트/페라이트계 스테인리스강을 용접했습니다. 레이저 출력, 용접 속도, 광섬유 직경, 입사각, 초점 이탈 거리와 같은 다양한 작동 변수와 이들의 상호작용이 용접 비드 형상 및 기계적 특성에 미치는 영향을 조사했습니다. 에너지 관점에서의 두 가지 핵심 공정 변수인 에너지 밀도와 선 에너지가 용접 비드 특성에 미치는 영향도 조사하여, 에너지 의존적인 특정 용접 현상을 이해하고 앞서 언급한 요인들에 대한 결과적인 영향을 보였습니다. 또한, 응고 미세조직의 형성 및 용접부 내 편석된 합금 원소의 분포 패턴을 다양한 에너지 입력에 따라 연구하고, 국부 미세 경도의 해당 변화와 연관시켰습니다.

자동차 산업에서 경제적으로 중요하고 기술적으로 중요한 이 스테인리스강의 레이저 용접을 예측하고 최적화하기 위해, 완전요인설계(FFD)와 반응표면분석법(RSM)이 각각 실험계획법(DOE) 접근 방식으로 사용되어 실험을 설계하고, 수학적 모델을 개발하며, 용접 작업을 최적화했습니다. 이 연구들에서, 각 용접된 재료에 대해 요구되는 응답을 예측하기 위한 수학적 모델이 개발되었습니다. 나아가, 개발된 모델들은 우수한 용접 품질을 생산하기 위한 입력 공정 변수들의 최상의 조합을 결정함으로써 최적화되었습니다.

마지막으로, 실험 기반 증거, 즉 용접 저항 길이는 에너지 제한적이며 용접 침투 깊이는 저항 길이를 결정하는 특성 요인이라는 점을 고려하여, 겹치기 이음 구성에서 페라이트계 스테인리스강의 레이저 용접을 위한 단순화된 에너지 기반 모델이 개발되었습니다. 개발된 모델은 용접이 전도 제한적인 경우, 용접 입력 변수로부터 직접 용접 침투 깊이를 예측하는 데 있어 상당히 정확합니다.

3. 서론:

용접은 두 작업물(주로 금속)의 표면을 국부적인 융합을 통해 접합하는 공정입니다. 이는 재료를 접합하는 정밀하고 신뢰할 수 있으며 비용 효율적인 첨단 기술 방법입니다. 현대 사회의 건물, 교량, 차량, 컴퓨터, 의료 기기 등 대부분의 친숙한 물체들은 용접 없이는 생산될 수 없었습니다. 오늘날 용접은 레이저 및 플라즈마 아크와 같은 첨단 기술을 사용하여 다양한 재료와 제품에 적용됩니다. 이종 및 비금속 재료를 접합하고 혁신적인 모양과 디자인의 제품을 만들기 위한 방법이 고안됨에 따라 용접의 미래는 더욱 큰 가능성을 가지고 있습니다. 이 장에서는 스테인리스강의 레이저 빔 용접에 관한 다양한 배경 문제를 명확히 하고자 합니다.

4. 연구 요약:

연구 주제의 배경:

레이저 용접은 높은 에너지 밀도를 가진 공정으로, 자동차 산업과 같이 정밀성과 높은 생산성이 요구되는 분야에서 널리 사용됩니다. 특히 스테인리스강은 내식성과 기계적 특성이 우수하여 다양한 산업 부품에 사용되며, 용접은 이러한 부품을 제조하는 주요 접합 방법입니다.

이전 연구 현황:

많은 연구자들이 레이저 용접 공정 변수가 용접부 형상, 기계적 특성, 미세조직에 미치는 영향에 대해 보고해왔습니다. 그러나 여러 공정 변수를 동시에 고려하여 특정 재료 조합과 접합 구성에 대한 공정을 체계적으로 최적화하고, 이를 예측 모델로 개발하는 연구는 제한적이었습니다.

연구 목적:

본 연구의 주된 목적은 유사 및 이종 스테인리스강의 레이저 용접에 대한 과학적이고 체계적인 연구를 수행하는 것입니다. 이를 통해 레이저-재료 상호작용의 다양한 결과에 대한 지식을 습득하고, 이를 생산 라인의 레이저 용접 관련 문제에 대한 해결책으로 직접 적용하고자 합니다. 구체적인 목표는 다음과 같습니다. 1. 용접 공정 변수가 용접 비드 형상 및 기계적 특성에 미치는 영향 분석 2. 에너지 밀도 및 선 에너지가 용접 미세조직 변화와 국부 경도에 미치는 영향 규명 3. 실험계획법을 적용하여 레이저 용접 공정 최적화 수행 4. 페라이트계 스테인리스강의 용입 깊이 예측을 위한 단순화된 에너지 기반 모델 개발

핵심 연구:

본 연구는 크게 세 가지 범주로 나뉩니다. 1. 마르텐사이트계 스테인리스강의 겹치기 용접 연구: 공정 변수 및 에너지 밀도가 용접부 형상, 기계적 특성, 미세조직에 미치는 영향을 분석하고, 실험계획법을 통해 공정을 최적화합니다. 2. 이종 페라이트/오스테나이트계 스테인리스강의 필릿 용접 연구: 공정 변수 및 선 에너지가 용접 특성에 미치는 영향을 분석하고, 반응표면분석법을 통해 공정을 최적화합니다. 3. 단순화된 에너지 기반 모델 개발: 페라이트계 스테인리스강의 겹치기 용접 시 용입 깊이를 예측하기 위한 이론적 모델을 개발합니다.

5. 연구 방법론

연구 설계:

본 연구는 통계적 실험계획법(DOE)에 기반한 완전요인설계(FFD)와 중심합성계획(CCD)을 포함하는 반응표면분석법(RSM)을 채택했습니다. 이를 통해 최소한의 실험으로 공정 변수와 결과(응답) 간의 수학적 관계를 모델링하고 최적의 조건을 도출하고자 했습니다.

데이터 수집 및 분석 방법:

  • 용접 실험: 1.1kW 연속파 Nd:YAG 레이저를 사용하여 원형 겹치기 및 필릿 이음 용접을 수행했습니다. 아르곤 가스를 보호 가스로 사용했습니다.
  • 용접부 특성 분석: 용접된 시편을 축 방향으로 절단한 후, 광학 현미경(Leica MZ125)과 이미지 분석 소프트웨어(Leica IM500)를 사용하여 용접 폭, 용입 깊이, 저항 길이 등을 측정했습니다.
  • 기계적 특성 평가: 인스트론 만능시험기(모델 3367)를 이용한 푸시 아웃(push-out) 시험을 통해 용접부의 전단 강도를 측정했습니다.
  • 미세조직 및 성분 분석: 주사전자현미경(SEM)과 에너지 분산형 분광분석기(EDS)를 사용하여 용접부의 미세조직과 합금 원소 분포를 분석했으며, 비커스 경도계를 사용하여 국부 경도를 측정했습니다.

연구 주제 및 범위:

  • 재료: 마르텐사이트계 스테인리스강(AISI 416, 440FSe) 및 이종 페라이트/오스테나이트계 스테인리스강(AISI 430, 304L)
  • 접합 구성: 겹치기 이음(Overlap joint) 및 필릿 이음(Fillet joint)
  • 주요 공정 변수: 레이저 출력(P), 용접 속도(S), 광섬유 직경(F), 빔 입사각(A), 초점 이탈 거리(D)
  • 주요 응답 변수: 용접부 형상(폭, 용입 깊이, 저항 길이, 반경 방향 용입), 전단 강도

6. 주요 결과:

주요 결과:

  • 레이저 출력과 용접 속도는 용접부 형상과 전단 강도에 가장 큰 영향을 미치는 변수입니다.
  • 용접 저항 길이와 전단 강도는 에너지 밀도에 비례하여 특정 값까지 증가한 후 더 이상 증가하지 않는 ‘에너지 제한적’ 특성을 보입니다.
  • 완전요인설계(FFD) 및 반응표면분석법(RSM)을 통해 개발된 수학적 모델은 용접 특성을 높은 정확도로 예측할 수 있으며, 공정 최적화에 효과적으로 사용될 수 있습니다.
  • 이종 재료 필릿 용접 시, 빔 입사각은 용접부 내 모재의 용융 비율을 결정하는 핵심 요소로, 용접부 특성에 큰 영향을 미칩니다.
  • 에너지 입력량에 따라 용접부의 미세조직(셀룰러, 덴드라이트 등)과 국부 미세 경도가 체계적으로 변화하며, 이는 합금 원소의 편석과 관련이 있습니다.
  • 전도 지배 용접에 한해, 용입 깊이를 예측할 수 있는 단순화된 에너지 기반 모델을 개발하고 검증했습니다.
Fig 4.5: 3D graphs to show effects of (a) P and S on weld resistance length, SL for
F = 400μm, and (b) P and S on shearing force, Fs for F = 300μm.
Fig 4.5: 3D graphs to show effects of (a) P and S on weld resistance length, SL for F = 400μm, and (b) P and S on shearing force, Fs for F = 300μm.

Figure List:

  • Fig. 1.1: Relative power densities of different heat sources
  • Fig. 1.2: Variation in heat input with the power density of heat source
  • Fig. 1.3: Modes of welding with laser: (a) conduction and (b) keyhole welding
  • Fig. 1.4: Energy coupling into the material through (a) isotropic and (b) preferential z conduction depending on energy density input.
  • Fig. 1.5: (a) Energy coupling into the material, and (b) keyhole shape and energy absorption during keyhole welding
  • Fig. 1.6: External and internal weld defects that can occur in laser welding of (a) a butt joint and (b) a lap joint.
  • Fig. 1.7: Ishikawa diagram showing the factors affecting the laser weld quality
  • Fig. 1.8: Action plan showing the activities performed during the three years of PhD research.
  • Fig 2.1: Characterization of welding cross-section (W: Weld width, DP: Weld penetration depth, SL: Weld resistance length)
  • Fig 2.2: Photographic views of the experimental set-up for (a) laser welding and (b) shearing test
  • Fig 2.3: Composite photograph of keyhole profile at different welding speed and power
  • Fig 2.4: Relationship between curve of the keyhole and welding speed for P=800W
  • Fig 2.5 (a) Perturbation plot showing the effects of all factors, and contour graphs illustrating the interaction effects of (b) P and S for F = 300µm; (c) S and F for P = 950W; and (d) P and F for S= 6 m/min on weld width
  • Fig 2.6: (a) perturbation plot showing the effect of all factors on weld penetration depth, and (b) variation in weld penetration depth with energy density input
  • Fig 2.7: Contour graphs to show effects of (a) P and S for F= 300µm, and (b) S and F depth for P = 950W on weld penetration depth.
  • Fig 2.8: Perturbation plot showing the effect of all factors on weld resistance length.
  • Fig 2.9: Contour graphs illustrating the interaction effects of (b) P and S for F = 300µm, (c) S and F for P = 950W, and (d) P and F for S= 6 m/min on weld resistance length.
  • Fig 2.10: Variation in weld resistance length with energy density input, (b) relationship between weld resistance length and penetration depth.
  • Fig 2.11: Perturbation plot showing the effect of all factors on weld shearing force.
  • Fig 2.12: Contour graphs illustrating the interaction effects of (b) P and S for F = 300µm, (c) S and F for P = 950W, and (d) P and F for S= 6 m/min on weld shearing force.
  • Fig 2.13: Variation in weld shearing force with (a) energy density, and (b) weld resistance length
  • Fig 2.14: Relationship between weld shearing force and energy density input
  • Fig. 3.1: SEM micrograph of the weld cross-section showing hardness profile and the selected points for microstructure evaluation
  • Fig. 3.2: Schematic view illustrating the effects of temperature gradient G and growth rate R on the morphology of solidification microstructure
  • Fig. 3.3: SEM views illustrating the change in morphology of the solidification microstructure with energy density input in the fusion zone for S = 6.0 m/min
  • Fig. 3.4: SEM micrographs showing the variation in solidification mode across the fusion zone from fusion boundary at (a) inner shell and (b) outer shell to (c) near maximum pool temperature zone for energy density input of 26.7 J/mm2.
  • Fig. 3.5: Variation in solidification mode across the fusion zone from near fusion boundary at (a) inner shell and (b) outer shell to (c) near the maximum pool temperature zone for energy density input of 36.7 J/mm2.
  • Fig. 3.6: Variation in mean dendrite width with energy density input near fusion zone boundary.
  • Fig. 3.7: Variation in mean dendrite width with (a) laser power for S= 6.0 m/min & F= 300 µm and (b) welding speed for P= 800 W & F= 300 µm
  • Fig. 3.8: Vicker’s microhardness profile at the inner shell of the overlap joint for different energy density input.
  • Fig. 3.9: Vicker’s microhardness profile at the outer shell of the overlap joint at various energy density inputs.
  • Fig. 3.10: Fusion boundary microstructure (a) at bottom and (b) at upper side of the inner part of the weld, (c) near the weld resistance section, and (d) at the outer portion of the weld for energy density input of 35.6 J/mm2.
  • Fig. 3.11: Microstructure at (a) base metal in as-received condition, and HAZ of the inner shell for (b) ED = 26.7 J/mm2 and (c) ED = 35.6 J/mm2. [X: Primary Carbide, Y: Secondary Carbide]
  • Fig. 3.12: EDS spectrum taken from spherodized particles of carbides indicated as (a) X and (b) Y in the Fig. 3.11.
  • Fig. 3.13: Microstructure at (a) base metal in as-received condition, and HAZ of the outer shell for (b) ED = 23.8 J/mm2 and (c) ED = 26.7 J/mm2. [Z: Manganese Sulfide, W: δ-Ferrite]
  • Fig. 3.14: EDS spectrum taken from manganese sulfide indicated as W in the Fig. 3.15.
  • Fig 4.1: Characterization of welding cross-section (W: Weld width, P: Penetration depth, S: Resistance length) and their prerequisite values.
  • Fig 4.2: Photographic views of the experimental set-up for (a) laser welding and (b) shearing test
  • Fig. 4.3: Flow chart of optimization step
  • Fig 4.4: 3D graphs to show effects of (a) F and P on weld width, W for S = 6.0m/min, and (b) P and S on penetration depth, DP for F = 300µm.
  • Fig 4.5: 3D graphs to show effects of (a) P and S on weld resistance length, SL for F = 400µm, and (b) P and S on shearing force, Fs for F = 300µm.
  • Fig. 6.8: Normal probability plot for weld (a) width, and (b) penetration depth.
  • Fig. 4.7: Studentized residual vs predicted plot for weld (a) width, and (b) penetration depth.
  • Fig. 4.8: Scatter diagrams of weld (a) width, (b) penetration depth, (c) resistance length, and (d) shearing force.
  • Fig 4.9: Overlay plot shows the region of optimal welding condition based on (a) first criterion and (b) second criterion at F=300µm
  • Fig. 5.1: Diagrams showing (a) bead characteristics of a welded fillet joint (W: Weld Width; SL: Weld Resistance Length; Dp: Weld Penetration Depth; and Pr: Weld Radial Penetration), and (b) adopted laser-welding procedure
  • Fig. 5.2: Photographic view of Nd:YAG laser-welding system
  • Fig. 5.3: Perturbation plot showing effect of all factors on weld (a) width, (b) penetration depth, (c) radial penetration, and (d) resistance length.
  • Fig. 5.4: Contour graphs to show the interaction effects of P and S on weld (a) width, (b) penetration depth, (c) radial penetration, and (d) resistance length at A = 20° and D = 0.0 mm.
  • Fig. 5.5: (a) perturbation plot showing effect of all factors on weld shearing force and (b) relationship between weld shearing force and resistance length.
  • Fig. 5.6: Contour graphs to show the interaction effects of (a) P and S, (b) D and P, and (c) A and P on weld shearing force.
  • Fig. 5.7: Effect of line energy on weld (a) penetration depth, (b) radial penetration, (c) resistance length for different incident angles (A) at D = 0.0 mm.
  • Fig. 5.8: Effect of line energy on weld (a) penetration depth, (b) radial penetration, (c) resistance length for different defocus distance (D) at A = 20°.
  • Fig. 5.9: Effect of line energy on weld width for different (a) defocus distance (D) at A = 20°, (b) angle of incidence (A) at D = 0.0 mm, and (c) effect of line energy on penetration size factor for different defocus distance at A = 20°.
  • Fig. 5.10: Pictural and schematic views showing the change in shape factor with LE (i) conduction limited (12-<15kJ/m), (ii) keyhole formation (15-17kJ/m), and (iii) keyhole with upper plasma plume (>17kJ/m)
  • Fig. 5.11: Effect of line energy on weld shearing force for different (a) angle of incidence (A) at D = 0.0 mm, and (b) defocus distance (D) at A = 20°.
  • Fig. 5.12: Photographic view of the angular distortion test setup
  • Fig. 5.13: Typical micrograph of laser welding of ferritic AISI 430 and austenitic AISI 304L stainless steels.
  • Fig. 5.14: Formation of microstructure in the fusion zone area indicated as (a) A and (b) B in the Fig. 5.13
  • Fig. 5.15: Microstructures of as-supplied base metal, HAZ and fusion zone indicated as C in the Fig. 5.13.
  • Fig. 5.16: Microstructure of (a) as-supplied base metal and HAZ indicated as D and (b) fusion zone indicated as E in the Fig. 5.13.
  • Fig. 5.17: Variation in local microhardness profile for different laser beam incident angles for LE = 15.4 kJ/m and D = 0 mm.
  • Fig. 6.1: Diagrams showing (a) bead characteristics of a welded fillet joint, and (b) adopted laser-welding procedure.
  • Fig. 6.2: Photographic view of Nd:YAG laser-welding system
  • Fig. 6.3: Photographic view of the experimental setup for push out test
  • Fig. 6.4: Flow chart of optimization step
  • Fig. 6.5: 3D graphs show effects of (a) P and D, and (b) P and S on weld radial penetration depth.
  • Fig. 6.6: 3D graphs show effects of (a) P and A, and (b) P and S on weld resistance length.
  • Fig. 6.7: 3D graphs show effects of (a) P and D, and (b) P and S weld penetration depth.
  • Fig. 6.8: Normal probability plot for weld (a) penetration depth, (b) radial penetration, (c) resistance length, and (d) shearing force
  • Fig. 6.9: Studentized residual vs predicted plot for weld (a) penetration depth, (b) radial penetration, (c) resistance length, and (d) shearing force.
  • Fig. 6.10: Scatter diagrams of weld (a) penetration depth, (b) radial penetration, (c) resistance length, and (d) shearing force.
  • Fig. 6.11: Overlay plots show the region of optimal welding condition based on (a) the first criterion at A = 10° & D = 0 and (b) the second criterion at A = 12° & D = 0.
  • Fig. 7.1 (a) draft of the weld cross section (b) assumed melt volume and related geometrical parameters.
  • Fig. 7.2: (a) weld characteristics W weld width, DP penetration depth, S resistance length and (b) tip of the fuel injector.
  • Fig. 7.3: Temperature measurement technique
  • Fig. 7.4: Variation in weld resistance length to weld width ratio with energy density input (R2 = 0.97)
  • Fig. 7.5: Variation in weld penetration depth and resistance length with energy density input
  • Fig. 7.6: Variation in penetration size factor (W/DP) with energy density input (R2 = 0.97)
  • Fig. 7.7: Variation in predicted and experimental weld penetration depth with energy density input

7. 결론:

본 논문은 유사 및 이종 스테인리스강의 레이저 용접에 대한 포괄적인 분석을 수행했다. 주요 결론은 다음과 같다. – 용접 비드 특성: 레이저 출력과 용접 속도가 가장 중요한 변수이며, 서로 반대의 효과를 가진다. 용입 깊이와 전단 강도는 에너지 입력 및 용접 저항 길이와 선형적인 관계를 보인다. 특히, 겹치기 용접에서는 용입 깊이가 저항 길이를 결정하며, 저항 길이와 전단 강도는 ‘에너지 제한적’이다. 필릿 용접에서는 빔 입사각이 용융 비율을 제어하는 핵심 요소이며, 특정 에너지 범위에서 키홀(keyhole) 형성은 용접부 형상과 기계적 특성의 급격한 변화를 유발한다. – 용접 미세조직 및 미세 경도: 모재의 화학 조성과 냉각 속도가 응고 거동과 고상 변태를 제어한다. 마르텐사이트계 강 용접부에서는 마르텐사이트와 델타 페라이트가 혼합된 조직이 나타나며, 덴드라이트 크기와 합금 원소 분포는 에너지 입력과 밀접한 관련이 있다. 이종 재료 용접부에서는 복잡한 페라이트-오스테나이트 미세조직이 형성되며, 국부 미세 경도의 변화는 각 모재의 혼합 비율 및 합금 원소의 편석과 연관된다. – 공정 최적화 및 모델링: 실험계획법(FFD, RSM)은 최적의 공정 변수 범위를 찾는 데 매우 효과적인 기법이다. 개발된 수학적 모델은 설계 공간 내에서 용접 특성을 정확하게 예측할 수 있으며, 그래픽 최적화 기법은 산업 현장에서 최적의 용접 조건을 신속하게 선택하는 데 실용적이다. 또한, 전도 지배 용접에 대한 단순화된 에너지 기반 모델은 추가적인 비용 소모 없이 용입 깊이를 예측하는 데 사용될 수 있다.

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전문가 Q&A: 주요 질문과 답변

Q1: 왜 개별 공정 변수 대신 ‘에너지 밀도’를 핵심 상관 변수로 선택했나요?

A1: 본 논문에서는 에너지 밀도(ED)를 핵심 변수로 사용했는데, 이는 레이저 출력, 용접 속도, 초점 직경이라는 세 가지 개별 변수의 복합적인 효과를 단일 인자로 표현할 수 있기 때문입니다. 2장에서 설명된 바와 같이, 이를 통해 용접 저항 길이의 ‘에너지 제한적’ 특성과 같은 에너지 의존적 현상을 더 명확하게 이해할 수 있습니다. 개별 변수만으로는 이러한 복합적인 현상을 직관적으로 파악하기 어렵습니다.

Q2: 특정 에너지 밀도를 초과하면 용접 저항과 전단 강도가 더 이상 증가하지 않는다고 하셨는데, 초과된 에너지는 어디로 가며 어떤 부정적인 영향을 미치나요?

A2: 그림 2.6(b)와 2.10에서 볼 수 있듯이, 한계 에너지 밀도에 도달한 후 추가로 투입된 에너지는 주로 용입 깊이를 증가시키는 데 사용됩니다. 이는 용접 저항 길이나 전단 강도 향상에는 거의 기여하지 않습니다. 이러한 과도한 에너지 투입은 비효율적일 뿐만 아니라, 불필요한 열 영향부(HAZ)를 넓히고 부품의 열 변형 위험을 증가시키는 등 잠재적인 결함의 원인이 될 수 있습니다.

Q3: 개발된 수학적 모델(FFD, RSM)은 실제 생산 환경에서 용접 품질을 예측하는 데 얼마나 신뢰할 수 있나요?

A3: 4장에서는 개발된 모델의 높은 신뢰성을 입증합니다. 분산분석(ANOVA) 표(4.12-4.15)는 모델의 높은 통계적 유의성(p-value < 0.0001)을 보여줍니다. 또한, 표 4.16의 검증 실험 결과, 예측값과 실제 측정값 사이의 오차율이 대부분 5% 이내로 매우 낮게 나타나 실제 생산 공정에 적용할 수 있을 만큼 정확하다는 것을 검증했습니다.

Q4: 이종 재료 용접(5장)에서 빔 입사각은 최종 용접 품질에 구체적으로 어떤 영향을 미칩니까?

A4: 빔 입사각은 핵심적인 제어 요소입니다. 서로 다른 열적 특성을 가진 두 금속(오스테나이트계 및 페라이트계)의 용융 비율을 제어하기 때문입니다. 그림 5.3에서 볼 수 있듯이, 입사각을 증가시키면 용입 깊이와 저항 길이는 감소하는 반면, 반경 방향 용입은 증가할 수 있습니다. 이를 통해 재료 특성 차이를 보상하고 건전한 접합부를 얻기 위해 용접 비드를 정밀하게 조정할 수 있습니다.

Q5: 7장에서 제안된 단순화된 에너지 기반 모델은 복잡한 RSM 모델과 어떻게 다르며, 그 한계는 무엇인가요?

A5: 7장의 단순화된 모델은 에너지 균형 방정식에 기반한 물리적 이론 모델로, 용접이 ‘열전도’에 의해 지배된다는 가정 하에 용입 깊이를 예측합니다. 이는 실험 데이터의 통계적 적합을 통해 도출된 경험적 RSM 모델과는 다릅니다. 이 모델의 주된 한계는 키홀 형성이나 플라즈마 효과가 중요해지는 영역(즉, 전도 지배 용접 범위를 벗어나는 경우)에서는 예측 오차가 5%에서 10%로 증가한다는 점입니다.

Q6: 연구에서 가장 중요한 미세조직 관련 발견은 무엇이며, 이는 용접부의 기계적 특성과 어떻게 연관되나요?

A6: 3장의 핵심 발견 중 하나는 마르텐사이트강 용접 시, 용융부와 열영향부 사이에 잔류 초석 페라이트를 포함하는 뚜렷한 경계 영역이 형성된다는 점입니다. 그림 3.8에서 볼 수 있듯이, 이 영역은 국부적인 연화(미세 경도 감소) 현상을 보이며, 이는 기계적 취약점이 될 수 있습니다. 이처럼 에너지 입력, 미세조직, 그리고 국부 경도 간의 연관성을 이해하는 것은 용접부의 성능을 예측하는 데 매우 중요합니다.


결론: 더 높은 품질과 생산성을 향한 길

본 연구는 시행착오에 의존하는 기존 방식에서 벗어나, 데이터 기반의 통계적 모델링이 레이저 용접 공정 최적화에 얼마나 효과적인지를 명확히 보여줍니다. 실험계획법과 반응표면분석법을 통해 개발된 예측 모델은 시간과 비용을 절감하고, 용접 품질을 획기적으로 향상시킬 수 있는 강력한 도구입니다. 특히 ‘에너지 제한적’ 특성을 이해하고 최적의 에너지 밀도 내에서 공정을 운영하는 것은 생산 효율성을 극대화하는 핵심 전략입니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
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저작권 정보

  • 이 콘텐츠는 Mohammad Muhshin Aziz Khan의 논문 “LASER BEAM WELDING OF STAINLESS STEELS”을 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://etd.adm.unipi.it/theses/available/etd-11222012-180124/

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

Fig. 6. Chemical fluctuations analysis around an APB region on a (111) plane in alloy 0Ti. (a) HAADF-STEM image of the ' precipitate with APBs taken along [011] beam direction. (b) Magnified image of white rectangular marked in (a). (c) Composite chemical map of elements Co, Ni, Al, Mo and W. (d)-(h) Net intensity elemental maps of elements Co, Ni, Al, Mo and W. (i) and (j) EDS line scan integrated along the APB in the region marked in (c).

코발트-니켈 초합금의 티타늄(Ti) 함량 최적화: 크리프 저항성과 미세조직 변형의 비밀

이 기술 요약은 Zhida Liang 외 저자가 발표한 “High-Ti inducing local η-phase transformation and creep-twinning in CoNi-based superalloys” 논문을 기반으로 하며, STI C&D가 기술 전문가를 위해 분석 및 요약했습니다.

키워드

  • Primary Keyword: 코발트-니켈 초합금(CoNi-based superalloys)
  • Secondary Keywords: 크리프 저항성(creep resistance), 상변태(phase transformation), 티타늄 함량(Ti content), 미세 트위닝(microtwinning), 평면 결함(planar defects)

Executive Summary

  • The Challenge: 고온 초합금의 강도와 연성을 동시에 확보하기 위해 합금 원소가 석출물 전단 메커니즘에 미치는 영향을 정밀하게 제어하는 것이 핵심 과제입니다.
  • The Method: 티타늄(Ti)과 알루미늄(Al)의 비율을 다르게 설정한 코발트-니켈(CoNi) 기반 초합금을 제작하여, 950°C 고온 크리프 시험, 주사투과전자현미경(STEM) 분석 및 제일원리계산(DFT)을 통해 변형 메커니즘을 분석했습니다.
  • The Key Breakthrough: Ti 함량이 증가함에 따라 주된 석출물 전단 메커니즘이 역위상 경계(APB)에서 초격자 외부 적층결함(SESF)으로 전환되며, 이 SESF 영역에서 국부적으로 강화상인 η상이 형성됨을 최초로 규명했습니다.
  • The Bottom Line: 높은 Ti 함량은 크리프 저항성을 향상시키지만, 동시에 재료에 해로운 미세 트윈(microtwin) 형성을 촉진하므로, 초합금 설계 시 최적의 Ti/Al 비율(본 연구에서는 0 < Ti/Al < 1을 제안)을 찾는 것이 매우 중요합니다.

The Challenge: Why This Research Matters for CFD Professionals

항공우주 및 발전 터빈과 같은 고온 환경에서 사용되는 초합금의 성능은 크리프 저항성에 의해 결정됩니다. 크리프 저항성은 주로 합금 내에 존재하는 γ'(감마 프라임) 석출물이 고온에서 전위의 이동을 얼마나 효과적으로 막아주는지에 달려있습니다. 하지만 고온 및 응력 환경에서는 전위가 석출물을 잘라내며(shearing) 소성 변형을 일으키는데, 이 전단 메커니즘은 합금의 조성에 따라 복잡하게 변화합니다. 특히 티타늄(Ti)과 같은 합금 원소는 γ’ 석출물의 안정성과 변형 거동에 큰 영향을 미치지만, Ti 함량 변화가 CoNi 기반 초합금의 평면 결함 유형(APB, SESF 등)과 국부적인 상변태에 미치는 영향에 대한 연구는 제한적이었습니다. 이러한 미세조직 변화를 예측하고 제어하지 못하면 부품의 수명과 신뢰성을 보장할 수 없으므로, 이는 재료 개발자와 엔지니어에게 중요한 기술적 과제입니다.

Fig. 1. Supercell models of first-principles calculations. (a) supercell models of bulk optimization for binary, ternary and quaternary L12-Co-based phases; (b) top view of stacking fault supercells with atomic distributions of A, B and C layers; (c) generation of APB and CSF through planar shearing; (d) generation of SISF and SESF through planar shearing along [1̅1̅2] direction.
Fig. 1. Supercell models of first-principles calculations. (a) supercell models of bulk optimization for binary, ternary and quaternary L12-Co-based phases; (b) top view of stacking fault supercells with atomic distributions of A, B and C layers; (c) generation of APB and CSF through planar shearing; (d) generation of SISF and SESF through planar shearing along [1̅1̅2] direction.

The Approach: Unpacking the Methodology

본 연구는 CoNi 기반 초합금에서 Ti/Al 비율 변화가 크리프 변형 메커니즘에 미치는 영향을 규명하기 위해 체계적인 실험과 계산을 병행했습니다.

  • 소재: 연구진은 Co-30Ni-(12.5-x)Al-xTi-2.5Mo-2.5W (x=0, 4, 8 at.%) 조성을 갖는 다결정 CoNi 기반 초합금(0Ti, 4Ti, 8Ti)을 진공 아크 용해로 제작했습니다. 이후 1250°C에서 24시간 균질화 처리 및 900°C에서 220시간 시효 처리를 통해 안정적인 γ/γ’ 미세조직을 형성했습니다.
  • 크리프 시험: 각 합금 시편에 대해 950°C의 고온 및 241 MPa의 압축 응력 조건에서 크리프 시험을 수행하여 변형 저항성을 평가했습니다.
  • 미세조직 분석: 크리프 변형 후 시편의 미세조직 변화를 관찰하기 위해 주사전자현미경(SEM-BSE), 전자후방산란회절(EBSD) 분석을 수행했습니다. 또한, 원자 수준의 결함 구조와 국부적인 화학 조성을 분석하기 위해 고각 환형 암시야상(HAADF-STEM) 및 에너지 분산형 X선 분광법(EDS)을 활용했습니다.
  • 이론 계산: 관찰된 평면 결함의 형성 경향성을 이론적으로 뒷받침하기 위해, 제일원리계산(DFT)을 이용하여 다양한 조성의 L1₂ 구조에서 역위상 경계(APB), 복합 적층결함(CSF), 초격자 고유/외부 적층결함(SISF/SESF)의 형성 에너지를 계산했습니다.
Fig. 2. Compression creep test of alloys 0Ti, 4Ti and 8Ti at 950 C with applied stress of 241 MPa.
Fig. 2. Compression creep test of alloys 0Ti, 4Ti and 8Ti at 950 C with applied stress of 241 MPa.

The Breakthrough: Key Findings & Data

본 연구를 통해 Ti 함량이 CoNi 초합금의 크리프 변형 메커니즘과 미세조직 안정성에 미치는 영향에 대한 두 가지 핵심적인 발견을 이루었습니다.

Finding 1: Ti 함량이 평면 결함 유형을 결정 (APB → SESF 전환)

Ti 함량은 γ’ 석출물의 주된 전단 메커니즘을 근본적으로 변화시켰습니다. 그림 3(b)의 STEM 이미지에서 볼 수 있듯이, Ti가 없거나(0Ti) 낮은(4Ti) 합금에서는 역위상 경계(APB)가 주된 평면 결함으로 관찰되었습니다. 반면, Ti 함량이 높은(8Ti) 합금에서는 초격자 외부 적층결함(SESF)이 지배적으로 형성되었습니다. 이는 그림 11의 DFT 계산 결과로 뒷받침되는데, 저-Ti 합금에서는 APB 형성 에너지가 CSF 에너지보다 낮아 APB 형성이 유리하지만, 고-Ti 합금에서는 이 경향이 역전되어 CSF 형성, 즉 적층결함(SF) 형성이 더 유리해지기 때문입니다.

Finding 2: 화학적 편석이 국부적 상변태를 유도

평면 결함 주변의 원소 편석 현상은 국부적인 상변태를 유발하여 재료의 기계적 특성을 변화시켰습니다.

  • 저-Ti 합금 (APB): 그림 6의 EDS 분석 결과, APB 영역에는 Co가 농축되고 Ni, Al, Mo, W가 결핍되었습니다. 이는 국부적으로 γ’ 상(L1₂)이 무질서한 γ 상(A1)으로 변태하여 연화(softening)되는 현상을 의미합니다.
  • 고-Ti 합금 (SESF): 그림 8의 분석 결과, SESF 영역에는 Co, Mo, W 및 Ti가 농축되고 Ni, Al이 결핍되었습니다. 이러한 조성 변화는 국부적으로 정렬된 η 상(D0₂₄)을 형성하여 강화(strengthening) 효과를 나타냅니다. 하지만 이 강화된 SESF는 크리프 변형을 가중시키는 미세 트윈의 ‘배아’ 역할을 하여 장기적인 크리프 수명에는 오히려 해로울 수 있습니다.

Practical Implications for R&D and Operations

  • 공정 엔지니어 (재료/합금 설계자): 본 연구는 Ti/Al 비율이 크리프 거동을 제어하는 핵심 변수임을 시사합니다. 0과 1 사이의 Ti/Al 비율을 적용하면 SESF 형성을 통한 강화 효과를 활용하면서도 과도한 미세 트위닝 위험을 완화하여 강도와 수명을 최적화할 수 있습니다.
  • 품질 관리팀: 고-Ti 합금에서 크리프 변형 후 관찰되는 미세 트윈(그림 4의 EBSD 분석)은 잠재적인 취성 파괴의 주요 지표가 될 수 있습니다. 이는 고온 환경에서 사용되는 부품의 새로운 품질 검사 기준으로 활용될 수 있습니다.
  • 설계 엔지니어: 고-Ti 함량이 η 상과 트위닝을 촉진한다는 결과는, 특히 고온 저응력 크리프 환경에 노출되는 부품 설계 시 과도하지 않게 정밀 제어된 Ti 함량을 갖는 초합금을 지정하는 것이 장기적인 구조적 안정성 확보에 매우 중요함을 의미합니다.

Paper Details


High-Ti inducing local η-phase transformation and creep-twinning in CoNi-based superalloys

1. Overview:

  • Title: High-Ti inducing local η-phase transformation and creep-twinning in CoNi-based superalloys
  • Author: Zhida Liang, Jing Zhang, Li Wang, Florian Pyczak
  • Year of publication:
  • Journal/academic society of publication:
  • Keywords: Superalloys, Transmission electron microscopy, First-principles calculations, Twinning, Phase transformation

2. Abstract:

본 연구에서는 Ti/Al 비율이 다른 L1₂ 함유 CoNi 기반 합금의 압축 크리프 중 석출물 전단 메커니즘을 조사했다. 950°C, 241 MPa의 일정 하중 응력 하에서 중단 크리프 시험을 수행했다. CoNi 기반 합금에서 Ti/Al 비율이 증가함에 따라 크리프 저항성이 증가하는 것을 발견했다. 또한, Ti 함량이 증가함에 따라 석출물 전단 중 (111) 평면의 평면 결함 유형이 역위상 경계(APB)에서 초격자 외부 적층결함(SESF)으로 변하는 것을 처음으로 발견했다. 즉, γ’ 상의 전단은 Ti가 없거나 낮은 합금에서는 주로 APB에 의해 지배되지만, 고-Ti 합금에서는 SESF에 의해 지배된다. 밀도범함수이론(DFT)을 사용하여 Ti가 없거나 낮은 합금에서는 APB 에너지가 복합 적층결함(CSF) 에너지보다 낮지만, 고-Ti 함유 합금에서는 이 상황이 반대가 됨을 발견했다. 추가적으로, L1₂-(Co,Ni)₃Ti 구조에서 SESF 에너지는 SISF 에너지보다 낮아 고-Ti 합금에서 SESF 형성을 강력하게 지지한다. 주사투과전자현미경 모드에서의 에너지 분산형 X선 분광법 분석을 통해, 관찰된 화학적 편석이 Ti가 없거나 낮은 합금에서는 APB가 무질서한 γ상 구조로 변하게 하고, 고-Ti 합금에서는 SESF가 국부적으로 정렬된 η상 구조로 변하게 함을 확인했다. 그러나 미세 트윈 또한 고-Ti 합금에서 발견되었는데, 이는 일반적으로 SESF나 APB와 같은 다른 평면 결함보다 더 높은 크리프 변형을 유발한다. 이 발견은 초합금 설계에서 Ti 함량을 합리적으로 사용하는 방법에 대한 새로운 통찰력을 제공한다.

3. Introduction:

초합금의 고온 크리프 저항성은 전위의 활주와 전단을 막는 정합적인 정렬된 석출물의 높은 함량에서 비롯된다. 크리프 중 석출물에 축적된 응력은 결국 전단을 일으킬 만큼 높아진다. 합금 조성, 적용 응력, 시험 온도의 차이에 따라 다양한 γ’ 석출물 전단 모드가 활성화된다. 일반적으로 낮은 응력과 높은 온도에서는 Ni 기반 및 CoNi 기반 초합금의 γ’ 석출물 전단은 역위상 경계(APB)를 남기는 쌍을 이룬 a/2<110> 전위의 이동에 의해 지배된다. 그러나 Co 기반 초합금에서의 γ’ 석출물 전단은 단일 a/3<112> 초-쇼클리 부분 전위의 활주에 의해 발생하며, 초격자 고유 적층결함(SISF)을 남긴다. 중간 온도 범위(600~850°C)에서는 초격자 적층결함(SSF) 및 변형 트위닝을 포함한 재배열 매개 γ’ 석출물 전단 모드가 우세해진다. 본 연구는 CoNi 기반 초합금에서 Ti 함량 변화가 이러한 변형 메커니즘, 특히 평면 결함의 유형 변화와 국부적 상변태에 미치는 영향을 규명하고자 한다.

4. Summary of the study:

Background of the research topic:

초합금은 항공기 엔진, 발전 터빈 등 고온 고응력 환경에서 사용되는 핵심 소재로, 크리프 저항성이 성능을 좌우한다. 이 저항성은 기지상(γ)에 분포된 강화상(γ’) 석출물에 의해 발현된다.

Status of previous research:

기존 연구들은 Ni 기반 또는 Co 기반 초합금에서 다양한 변형 메커니즘(APB, SISF, SESF, 트위닝)을 규명해왔다. 특히 Nb, Ta과 같은 원소가 SESF를 따라 η상을 형성시켜 강화 효과를 나타낸다는 보고가 있었으나, CoNi 기반 초합금에서 Ti 원소가 크리프 변형 및 상변태에 미치는 영향에 대한 연구는 매우 제한적이었다.

Purpose of the study:

본 연구의 목적은 CoNi 기반 초합금에서 Ti/Al 비율을 체계적으로 변화시키면서 고온 저응력 크리프 조건 하에서 발생하는 석출물 전단 메커니즘의 변화를 규명하는 것이다. 특히 Ti 함량이 평면 결함의 종류(APB vs. SESF)를 결정하고, 결함 주변의 원소 편석을 통해 국부적인 상변태(γ’→γ 또는 γ’→η)를 유도하며, 최종적으로 미세 트위닝에 미치는 영향을 밝히고자 한다.

Core study:

Ti 함량이 다른 CoNi 기반 합금(0Ti, 4Ti, 8Ti)을 대상으로 950°C에서 크리프 시험을 수행하고, STEM-EDS와 같은 첨단 분석 기법을 이용하여 변형 후 미세조직을 원자 수준에서 분석했다. 또한, DFT 계산을 통해 실험적으로 관찰된 평면 결함의 안정성을 이론적으로 검증했다. 이를 통해 Ti 함량이 증가함에 따라 ①크리프 저항성 증가, ②주요 평면 결함이 APB에서 SESF로 전환, ③SESF에서 국부적 η상 형성, ④미세 트윈 형성 촉진이라는 일련의 과정을 종합적으로 규명했다.

5. Research Methodology

Research Design:

본 연구는 실험적 접근과 이론적 계산을 결합한 설계 방식을 채택했다. 실험적으로는 CoNi 기반 초합금의 Ti/Al 비율을 주요 변수로 설정하여 세 종류의 합금(0Ti, 4Ti, 8Ti)을 설계 및 제작했다. 이 합금들을 동일한 고온 크리프 조건에 노출시킨 후, 미세조직의 변화, 특히 평면 결함의 유형과 분포를 비교 분석했다.

Data Collection and Analysis Methods:

  • 데이터 수집: 크리프 시험기(Satec Systems)를 사용하여 시간-변형률 곡선을 수집했다. FE-SEM, EBSD, TEM(Thermo Fisher Scientific Themis Z, Talos 200i)을 이용하여 변형 후 미세조직 이미지, 결정 방위 정보, 원자 분해능 구조 이미지, 그리고 결함 주변의 국부 화학 조성(EDS 맵핑 및 라인 스캔) 데이터를 수집했다.
  • 데이터 분석: 수집된 크리프 곡선을 비교하여 Ti 함량에 따른 크리프 저항성을 정량적으로 평가했다. TEM 이미지를 통해 평면 결함의 유형(APB, SESF)을 식별하고, EBSD 데이터를 분석하여 미세 트윈의 존재와 결정학적 관계를 확인했다. EDS 데이터를 정량 분석하여 결함 영역에서의 원소 편석 경향을 파악했다. VASP 코드를 이용한 DFT 계산을 통해 각 결함의 형성 에너지를 계산하고 실험 결과와 비교하여 메커니즘을 해석했다.

Research Topics and Scope:

본 연구는 L1₂ 강화 CoNi 기반 다결정 초합금을 대상으로 한다. 연구의 핵심 주제는 ‘Ti 함량이 고온 크리프 변형 중 석출물 전단 메커니즘, 국부적 상변태 및 미세 트위닝에 미치는 영향’이다. 연구 범위는 합금 설계 및 제조, 고온 크리프 시험, 다중 스케일 미세조직 분석(SEM, EBSD, STEM), 그리고 제일원리계산을 포함한다.

6. Key Results:

Key Results:

  • Ti/Al 비율이 증가할수록 CoNi 기반 초합금의 크리프 저항성이 현저히 향상되었다.
  • Ti 함량이 증가함에 따라 γ’ 석출물 내 주된 평면 결함의 유형이 역위상 경계(APB)에서 초격자 외부 적층결함(SESF)으로 변화했다.
  • 저-Ti 합금의 APB에서는 Co가 농축되어 국부적으로 무질서한 γ상으로 변태(연화)하는 경향을 보였다.
  • 고-Ti 합금의 SESF에서는 Co, Ti, Mo, W가 농축되어 국부적으로 정렬된 η상으로 변태(강화)하는 경향을 보였다.
  • Ti 함량이 8 at.% 이상인 합금에서는 장시간 시효 처리 시 벌크(bulk) η상이 형성되었으며, 크리프 변형 중에는 미세 트윈이 형성되었다.
  • DFT 계산 결과, 고-Ti 합금에서 APB 에너지보다 CSF 에너지가 낮아져 SF 형성이 유리해지며, SESF가 SISF보다 안정적인 것으로 나타나 실험 결과를 뒷받침했다.
Fig. 6. Chemical fluctuations analysis around an APB region on a (111) plane in alloy 0Ti. (a) HAADF-STEM image of the ' precipitate with APBs taken along [011] beam direction. (b) Magnified image of white rectangular marked in (a). (c) Composite chemical map of elements Co, Ni, Al, Mo and W. (d)-(h) Net intensity elemental maps of elements Co, Ni, Al, Mo and W. (i) and (j) EDS line scan integrated along the APB in the region marked in (c).
Fig. 6. Chemical fluctuations analysis around an APB region on a (111) plane in alloy 0Ti. (a) HAADF-STEM image of the ’ precipitate with APBs taken along [011] beam direction. (b) Magnified image of white rectangular marked in (a). (c) Composite chemical map of elements Co, Ni, Al, Mo and W. (d)-(h) Net intensity elemental maps of elements Co, Ni, Al, Mo and W. (i) and (j) EDS line scan integrated along the APB in the region marked in (c).

Figure List:

  • Fig. 1. Supercell models of first-principles calculations. (a) supercell models of bulk optimization for binary, ternary and quaternary L1₂-Co-based phases; (b) top view of stacking fault supercells with atomic distributions of A, B and C layers; (c) generation of APB and CSF through planar shearing; (d) generation of SISF and SESF through planar shearing along [112] direction.
  • Fig. 2. Compression creep test of alloys 0Ti, 4Ti and 8Ti at 950 °C with applied stress of 241 MPa.
  • Fig. 3. (a) Post-mortem SEM-BSE images for compressive creep specimens of alloys 0Ti, 4Ti and 8Ti. (b) HAADF-STEM (0Ti, 4Ti and 8Ti) images of dislocation networks and planar defects (SESF and APBs) taken near the [110] zone axis. (The white arrows indicate planar defects and red arrows indicate dislocation networks.)
  • Fig. 4. Creep twinning identification by EBSD in the crept specimen of alloys 8Ti. (a) Pattern quality map, (b) Inverse pole figure (IPF) map and (c) Misorientation distribution of IPF in (b).
  • Fig. 5. (a) HAADF-STEM image of ‘isolated’ SESFs taken near the [110] zone axis in alloy 8Ti. (b) HRSTEM micrograph showing an SESF terminating in an ISF. (c) Center of symmetry (COS) visualization of the area highlighting the deviations from crystal symmetry produced by the stacking fault in Fig. 5(b).
  • Fig. 6. Chemical fluctuations analysis around an APB region on a (111) plane in alloy 0Ti. (a) HAADF-STEM image of the γ’ precipitate with APBs taken along [011] beam direction. (b) Magnified image of white rectangular marked in (a). (c) Composite chemical map of elements Co, Ni, Al, Mo and W. (d)-(h) Net intensity elemental maps of elements Co, Ni, Al, Mo and W. (i) and (j) EDS line scan integrated along the APB in the region marked in (c).
  • Fig. 7. Chemical fluctuations analysis around an APB region on a (001) plane in alloy 4Ti. (a) HAADF-STEM image of the γ’ precipitate with an APB taken along [001] beam direction. (b) Magnified image of white rectangular marked in (a). (c) Composite chemical map of elements Co, Ni, Al, Ti, Mo and W. (d) and (e) EDS line scan integrated along the APB in the region marked in (c).
  • Fig. 8. Chemical fluctuations analysis in alloy 8Ti. (a) HAADF-STEM image of SESFs in [011] beam direction. (b) Net intensity elemental maps of two vertical SESFs. (c) The integrated EDS line scanning curves represent the area incorporated into the vertically integrated line scan shown from (b).
  • Fig. 9. (a) SEM-BSE image with the coarse lath-like η phase in alloy 8Ti after 1036 h aging heat treatment at 900 °C. (b) Compositions (at.%) comparison of the γ’ phase, SESF region (local η phase) and lath η phase. (The composition details were shown in Table 2.)
  • Fig. 10. SEM-BSE images (a-g) and EBSD images (h₁ and h₂) of alloys 0Ti, 2Ti, 4Ti, 6Ti, 8Ti, 10Ti and 12.5Ti after homogenization heat treatment at 1250 °C. (In the EBSD images, the red phases are the η phases and the blue phases are the mixed γ and γ’ phases.)
  • Fig. 11. (a) E(111)APB and E(111)CSF energies (mJ/m²) of the L1₂-Co₃Ti, L1₂-Co₃(Al,W) and L1₂-Ni₃Al structures calculated by the DFT method in literatures [33-39]. (b) E(111)APB and E(111)CSF energies (mJ/m²) of the L1₂-(Co₀.₅,Ni₀.₅)₃(Al₀.₅,Mo₀.₅), L1₂-(Co₀.₅,Ni₀.₅)₃(Al₀.₅,Ti₀.₅) and L1₂-(Co₀.₅,Ni₀.₅)₃Ti structures calculated by DFT method. (c) The discrepancy of the calculated E(111)SISF and E(111)SESF energies (mJ/m²) of the L1₂-(Co₀.₅,Ni₀.₅)₃Ti structures by DFT method.
  • Fig. 12. Comparison of dislocation-precipitate shearing mechanisms during creep at high temperatures, i.e. 950 °C, in Ti-free, low-Ti and high-Ti CoNi based superalloys.
  • Fig. 13. (a) HAADF-STEM image of L1₂-γ’ phase, SESF and D0₂₄-η lath in 10Ti alloy taken close to [110] beam direction. (b) Selected area electron diffraction (SAED) pattern obtained from L1₂-γ’ phase and D0₂₄-η phase.
  • Fig. 14. Summary of Ti content dependent fault shearing modes and local phase transformation (LPT) effects.

7. Conclusion:

본 연구는 950°C 저응력 크리프 조건에서 Ti 함량이 다른 CoNi 기반 초합금의 γ’ 석출물 전단 메커니즘을 조사했다. 선호되는 전단 모드는 γ’ 석출물 내에 존재하는 평면 결함의 종류를 결정하는 APB와 CSF 에너지에 의해 영향을 받을 가능성이 높다. Ti가 없거나 낮은 초합금에서는 APB 에너지가 CSF 에너지보다 낮다. 따라서 γ’ 상의 전단은 주로 a/2<110> 초격자 전위에 의해 발생하며, (111) 및 (001) 결정면의 APB에서 원소 편석에 의해 γ상으로의 국부적 상변태를 유발한다. 고-Ti 초합금에서는 APB 에너지가 CSF 에너지보다 높다. APB 형성은 불리해지고, γ’ 전단은 a/6<121> 부분 전위의 이동에 의해 발생하여 높은 에너지의 CSF를 생성한다. 이후 이 CSF들은 고온에서 원소 재배열 및 편석을 동반하여 낮은 에너지의 SESF로 변환된다. SESF에서의 편석은 γ’ 석출물 내부에 정렬된 η상을 형성함으로써 국부적인 상변태 강화를 일으키는 것으로 나타났다. 문헌에 따르면, η형 SESF 형성은 크리프 트위닝 형성을 어느 정도 억제할 수 있지만, 크리프 변형과 시간이 지남에 따라 이 SESF는 더 두꺼워져 미세 트윈으로 변형될 수 있다. 미세 트위닝은 전체 크리프 변형에 상당한 기여를 할 수 있으므로, 크리프 저항성을 향상시키기 위해서는 크리프 유발 미세 트윈의 형성을 완전히 방지하기 위해 낮은 Ti 함량을 사용해야 한다.

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Expert Q&A: Your Top Questions Answered

Q1: Ti 함량이 증가하면서 석출물 전단 메커니즘이 APB에서 SESF로 전환된 근본적인 이유는 무엇입니까?

A1: 이는 평면 결함 형성 에너지의 상대적인 차이 때문입니다. 본 논문의 DFT 계산 결과(그림 11)에 따르면, Ti가 없거나 낮은 합금에서는 APB 형성 에너지가 CSF(적층결함의 전구체) 형성 에너지보다 낮아 전위가 APB를 형성하며 이동하는 것이 에너지적으로 더 유리합니다. 하지만 Ti 함량이 증가하면 L1₂ 구조의 정렬도가 향상되어 APB 에너지가 급격히 증가하고, 상대적으로 CSF 에너지보다 높아집니다. 이로 인해 고-Ti 합금에서는 APB 형성 대신 CSF를 거쳐 SESF를 형성하는 전단 메커니즘이 활성화됩니다.

Q2: 평면 결함에서 관찰된 화학적 편석 현상은 구체적으로 어떤 의미를 가집니까?

A2: 이 편석 현상은 국부적인 상변태를 유도하여 재료의 기계적 특성을 변화시키는 핵심적인 역할을 합니다. 저-Ti 합금의 APB에서는 Co와 같은 γ상 형성 원소가 농축되어, 국부적으로 강화상인 γ’가 연한 γ상으로 변태(연화)됩니다. 반면, 고-Ti 합금의 SESF에서는 Co, Ti, Mo, W와 같은 η상 형성 원소들이 농축되어, 국부적으로 더 단단하고 정렬된 η상을 형성(강화)합니다. 이는 Ti 함량에 따라 동일한 크리프 조건에서도 미세조직이 국부적으로 연화되거나 강화될 수 있음을 의미합니다.

Q3: 논문에서는 고-Ti 합금에서 η상 형성을 통한 강화 효과와 미세 트위닝을 통한 연화 효과를 모두 언급했습니다. 장기적인 크리프 수명 관점에서 어떤 효과가 더 지배적입니까?

A3: 단기적으로는 SESF에서 형성된 국부적 η상이 전위 이동을 방해하여 재료를 강화시킬 수 있습니다. 하지만 논문은 이러한 SESF가 미세 트윈의 ‘배아’ 역할을 한다고 지적합니다. 미세 트위닝은 APB나 SESF와 같은 다른 평면 결함보다 훨씬 더 큰 크리프 변형을 유발하며(전체 소성 변형의 73%-96% 기여), 트윈 경계에서의 응력 집중으로 인해 균열 핵 생성 및 전파를 유발하여 취성 파괴를 일으킬 수 있습니다. 따라서 장기적인 크리프 수명 관점에서는 미세 트위닝으로 인한 해로운 효과가 강화 효과를 압도하며 더 지배적이라고 할 수 있습니다.

Q4: 본 연구에서 제안된 SESF 형성 메커니즘은 무엇입니까?

A4: 논문에서는 콜베(Kolbe) 메커니즘을 가능한 경로 중 하나로 제시합니다. 이 메커니즘은 γ 기지 내에서 두 개의 <110> 전위가 상호작용하여 2층짜리 CSF(복합 적층결함)를 형성하는 것으로 시작됩니다. 이후 이 높은 에너지의 CSF 영역으로 Co, Ti, Mo, W와 같은 원소들이 확산하여 편석되면서 결함의 에너지를 낮추고, 최종적으로 더 안정한 저에너지 SESF로 변환된다는 것입니다. 즉, 전위의 기계적인 이동(displacive)과 원자의 확산(diffusional)이 결합된 과정입니다.

Q5: 이 연구 결과를 바탕으로 실제 초합금 설계에 적용할 수 있는 실용적인 권장 사항은 무엇입니까?

A5: 고온 저응력 환경에서 석출물의 과도한 전단을 피하고 해로운 미세 트윈 형성을 억제하기 위해, 적절한 Ti 농도를 사용하는 것이 핵심입니다. 본 연구는 Ti 함량이 너무 높으면 크리프 저항성은 초기에는 좋을 수 있으나 결국 미세 트위닝으로 인해 파괴에 이를 수 있음을 보여줍니다. 따라서 연구진은 코발트-니켈 초합금 설계 시 Ti/Al 비율을 1 미만(0 < Ti/Al < 1)으로 조절할 것을 제안합니다. 이는 강화와 장기 안정성 사이의 균형을 맞추는 최적의 설계 방안이 될 수 있습니다.


Conclusion: Paving the Way for Higher Quality and Productivity

본 연구는 코발트-니켈 초합금의 성능을 좌우하는 티타늄(Ti)의 역할이 양날의 검과 같다는 것을 명확히 보여주었습니다. Ti 함량을 높이면 초기 크리프 저항성은 향상되지만, 이는 변형 메커니즘을 변화시켜 결국 재료의 파괴를 앞당길 수 있는 미세 트위닝을 촉진합니다. APB에서 SESF로의 전환, 그리고 결함 주변의 국부적 상변태에 대한 심도 있는 이해는 차세대 초합금의 신뢰성과 수명을 극대화하는 데 필수적입니다. 이 연구는 합금 설계 시 단순히 강도뿐만 아니라 장기적인 미세조직 안정성을 함께 고려해야 한다는 중요한 교훈을 줍니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

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  • This content is a summary and analysis based on the paper “High-Ti inducing local η-phase transformation and creep-twinning in CoNi-based superalloys” by “Zhida Liang, Jing Zhang, Li Wang, Florian Pyczak”.
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Figure 2. Microstructure evolution at seven sampling locations (S1-S7) along the plate, (a) advent of segregation band at last one-third of the plate shown by red arrows, (b) comparison of α-Al particles.

HPDC 결함 예측: 상평형장 모델링을 통한 알루미늄 합금의 이중 수지상정 응고 현상 분석

이 기술 요약은 Maryam Torfeh, Zhichao Niu, Hamid Assadi가 Metals (2025)에 발표한 논문 “Phase-Field Modelling of Bimodal Dendritic Solidification During Al Alloy Die Casting”을 기반으로 하며, (주)에스티아이씨앤디의 기술 전문가에 의해 분석 및 요약되었습니다.

Keywords

  • Primary Keyword: 상평형장 모델링 (Phase-Field Modeling)
  • Secondary Keywords: 고압 다이캐스팅(HPDC), 알루미늄 합금, 응고 해석, 미세조직 예측, 이중 수지상정

Executive Summary

  • The Challenge: 고압 다이캐스팅(HPDC) 공정에서 발생하는 급격한 냉각 속도 변화와 난류로 인해 불균일한 이중(bimodal) 미세조직이 형성되어 최종 제품의 기계적 물성을 저하시키는 문제.
  • The Method: 샷 슬리브(shot sleeve)의 상대적으로 느린 냉각에서 다이 캐비티(die cavity)의 급속 냉각으로 전환되는 과정을 모사하기 위해, 고체-액체 계면의 특성(두께, 에너지, 이동도)을 체계적으로 변경하는 2차원 상평형장 모델을 사용.
  • The Key Breakthrough: 상평형장 모델의 계면 두께를 줄임으로써, 난류가 유발하는 국부적 과냉각 및 미세한 2차 수지상정 가지의 핵 생성 및 성장을 성공적으로 재현.
  • The Bottom Line: 상평형장 모델링은 HPDC 공정의 복잡한 응고 현상을 예측하고, 최종 제품의 미세조직 제어를 통해 품질을 향상시키는 데 효과적인 도구임을 입증했습니다.

The Challenge: Why This Research Matters for CFD Professionals

고압 다이캐스팅(HPDC)은 경량 알루미늄 합금 부품을 경제적으로 대량 생산하는 핵심 기술입니다. 하지만 이 공정은 샷 슬리브에서의 느린 냉각(약 100 K/s)과 다이 캐비티 주입 시의 급속 냉각(약 1000 K/s)이라는 극적인 열 조건 변화를 동반합니다. 이러한 급격한 변화와 용탕의 격렬한 난류는 최종 제품의 미세조직에 결정적인 영향을 미칩니다.

특히, 샷 슬리브에서 미리 형성된 조대한 ‘외부 응고 결정(Externally Solidified Crystals, ESCs)’이 다이 캐비티 내에서 급속 냉각된 미세한 결정들과 섞여 ‘이중 미세조직(bimodal microstructure)’을 형성하는 것이 주요 문제입니다. 이러한 불균일한 미세조직은 부품의 기계적 특성(예: 항복 강도, 연신율)을 저하시키고 예측 불가능하게 만들어 품질 관리에 심각한 어려움을 초래합니다. 기존의 수치 해석 방법들은 유동 및 열 전달에 초점을 맞추었지만, 이러한 복잡한 수지상정 구조의 진화 과정을 직접 분석하는 데는 한계가 있었습니다.

Figure 1. Sampling region on the plate manufactured by HPDC.
Figure 1. Sampling region on the plate manufactured by HPDC.

The Approach: Unpacking the Methodology

본 연구팀은 이 문제를 해결하기 위해 2차원 상평형장(Phase-Field) 모델을 사용하여 아공정 Al-7% Si 합금의 응고 거동을 조사했습니다. 이 모델은 HPDC 공정을 두 단계로 나누어 시뮬레이션합니다.

  1. 1단계 (샷 슬리브 조건): 초기 온도 650K, 냉각 속도 100 K/s 조건에서 초기 수지상정의 성장을 모사합니다. 이는 다이 캐비티로 주입되기 전의 상태를 나타냅니다.
  2. 2단계 (다이 캐비티 조건): 1단계에서 성장한 수지상정을 기반으로, 초기 온도를 450K로 낮추고 냉각 속도를 1000 K/s로 높여 급속 응고를 시뮬레이션합니다.

가장 핵심적인 접근법은 샷 슬리브에서 다이 캐비티로 전환될 때 발생하는 물리적 현상(특히 난류로 인한 열 및 용질 전달 향상)을 모델링하기 위해, 고체-액체(S/L) 계면의 주요 파라미터인 두께(thickness), 에너지(energy), 이동도(mobility)를 체계적으로 변경한 것입니다. 이를 통해 모델이 실제 공정에서 관찰되는 미세조직 변화를 정확하게 예측할 수 있는지 검증했습니다.

The Breakthrough: Key Findings & Data

Finding 1: 실험적 미세조직 관찰을 통한 이중 구조 확인

실제 HPDC로 제조된 주조품의 위치별 미세조직을 분석한 결과, 명확한 이중 구조가 확인되었습니다.

  • 입자 크기 변화: 인게이트(in-gate) 부근(S1)에서는 평균 α-Al 입자 크기가 약 21 µm였으나, 주조품 끝단(S7)으로 갈수록 약 3 µm로 급격히 감소했습니다(Figure 3 참조).
  • 이중 미세조직: 인게이트 부근에서는 조대한 ESCs 주위로 미세하게 분산된 α-Al 입자들이 공존하는 이질적인 미세조직이 관찰되었습니다. 특히, 기존에 형성된 수지상정 파편 위에서 새로운 가지들이 핵 생성되는 모습이 뚜렷하게 나타났습니다(Figure 4b의 화살표 참조).

이는 샷 슬리브에서 형성된 결정이 다이 캐비티의 급속 냉각 환경에서 새로운 응고의 핵으로 작용했음을 시사합니다.

Finding 2: 상평형장 모델을 통한 이중 수지상정 성장 메커니즘 규명

상평형장 시뮬레이션은 실험에서 관찰된 이중 수지상정 형성 과정을 성공적으로 재현했습니다.

  • 샷 슬리브 성장 모사: 샷 슬리브 조건(계면 두께 700 nm, 에너지 0.16 J/m², 이동도 0.003 m/sK)에서 2ms 동안 성장시킨 결과, 실험에서 관찰된 것과 유사한 초기 수지상정 형태를 얻었습니다(Figure 5b,c).
  • 다이 캐비티 성장 재현: 다이 캐비티의 급속 냉각 및 난류 효과를 모사하기 위해 S/L 계면 두께를 700 nm에서 500 nm로 줄였을 때, 기존 수지상정 표면에서 더 미세하고 날카로운 3차 수지상정 가지가 형성되는 현상을 포착했습니다(Figure 6, state 01 vs state 03). 이는 계면 두께 감소가 난류로 인한 열/용질 전달 향상 효과를 효과적으로 반영하며, 이중 미세조직 형성의 핵심 메커니즘을 설명할 수 있음을 보여줍니다.
Figure 2. Microstructure evolution at seven sampling locations (S1-S7) along the plate, (a) advent of segregation band at last one-third of the plate shown by red arrows, (b) comparison of α-Al particles.
Figure 2. Microstructure evolution at seven sampling locations (S1-S7) along the plate, (a) advent of segregation band at last one-third of the plate shown by red arrows, (b) comparison of α-Al particles.

Practical Implications for R&D and Operations

  • For Process Engineers: 이 연구는 난류 및 냉각 속도와 같은 공정 조건이 고체-액체 계면 거동에 미치는 영향을 간접적으로 모델링할 수 있음을 보여줍니다. 이는 최종 미세조직 제어를 통해 기계적 물성을 최적화하는 데 중요한 단서를 제공합니다.
  • For Quality Control Teams: 논문의 Figure 3과 Figure 4에서 볼 수 있듯이, 주조품 위치에 따라 α-Al 입자 크기 분포가 크게 달라집니다. 이를 바탕으로 위치별 미세조직 분석을 통해 기계적 물성의 편차를 예측하고 새로운 품질 검사 기준을 수립하는 데 활용할 수 있습니다.
  • For Design Engineers: 게이트 통과 시 발생하는 강한 전단력과 난류가 기존에 형성된 수지상정을 파편화시키고 새로운 핵생성 사이트로 작용한다는 점은, 게이트 시스템 설계가 최종 미세조직에 미치는 영향을 고려해야 함을 시사합니다. 이는 초기 설계 단계에서 결함을 최소화하는 데 중요한 고려사항입니다.

Paper Details


Phase-Field Modelling of Bimodal Dendritic Solidification During Al Alloy Die Casting

1. Overview:

  • Title: Phase-Field Modelling of Bimodal Dendritic Solidification During Al Alloy Die Casting
  • Author: Maryam Torfeh, Zhichao Niu and Hamid Assadi
  • Year of publication: 2025
  • Journal/academic society of publication: Metals
  • Keywords: phase-field modelling; HPDC; interface behaviour

2. Abstract:

Al-Si 합금의 고압 다이캐스팅(HPDC) 중 미세조직 진화를 추적하는 것은 급속한 응고, 변화하는 열 조건, 그리고 심한 난류 때문에 어려운 과제입니다. 이 공정은 샷 슬리브에서의 느린 냉각에서 다이 캐비티에서의 급속 냉각으로 전환되며, 이는 이중 수지상정 미세조직과 기존에 외부에서 응고된 결정 위에 새로운 미세한 수지상정 가지가 핵 생성되는 결과를 낳습니다. 본 연구에서는 2차원 상평형장 모델을 사용하여 아공정 Al-7% Si 합금의 HPDC 중 응고 거동을 조사했습니다. 이 모델은 상변태열, 열 경계 조건, 그리고 액상 및 고상에서의 용질 확산으로 인한 온도 변화를 설명하는 열역학적 공식에 기반합니다. 관찰된 이중 미세조직을 재현하기 위해, 고체-액체 계면의 특성(두께, 에너지, 이동도 등)을 체계적으로 변경하여 샷 슬리브에서 다이 캐비티로의 전환을 반영했습니다. 결과는 모델이 샷 슬리브 조건 하에서의 수지상정 성장과 다이 캐비티의 급속 냉각 조건 하에서의 새로운 수지상정 가지의 핵 생성 및 발달을 포착할 수 있는 능력을 보여주었습니다.

3. Introduction:

고압 다이캐스팅(HPDC)은 거의 최종 형상에 가까운 경량 알루미늄 합금을 제조하는 경제적인 방법입니다. HPDC 공정 중 여러 요인들이 제품의 최종 품질에 근본적인 영향을 미칠 수 있습니다. 가압 압력, 플런저 속도, 다이 온도와 같은 공정 요인들은 많은 연구자들에 의해 연구되었습니다. HPDC에서 샷 슬리브의 냉각 속도는 약 100 K/s인 반면, 다이에서는 약 1000 K/s입니다. 최종 부품의 미세조직은 단지 냉각 속도에만 의존하지 않습니다. 주입 단계에서의 심한 전단 및 난류는 미세조직에 현저한 영향을 미칩니다. 샷 슬리브에서의 응고 조건은 단순 중력 주조와 매우 유사합니다. Al-7% Si 용탕의 온도는 약 620°C로 보고되었으며, 이는 합금의 액상선 온도와 매우 가깝습니다. HPDC에서는 금속 유동 속도가 고체-액체 계면 속도를 초과합니다. 1차 수지상정은 샷 슬리브에서 형성을 시작하며, 급속한 응고와 높은 금속 속도 때문에 얇은 채널 내에서 주상 수지상정이 발달할 수 없어 비수지상정 구조를 형성합니다. 이러한 미세조직적 특징은 주조품의 최종 특성에 상당한 영향을 미칩니다. 알루미늄 합금의 HPDC에서 가장 빈번하게 보고되는 미세조직 문제 중 하나는 최종 제품에 외부 응고 결정(ESCs)이 존재하는 것입니다.

4. Summary of the study:

Background of the research topic:

HPDC 공정은 샷 슬리브와 다이 캐비티 간의 극심한 냉각 속도 차이와 난류로 인해 복잡한 응고 현상을 보입니다. 이로 인해 형성되는 이중 미세조직은 제품의 기계적 물성을 저하시키는 주요 원인이 됩니다.

Status of previous research:

이전 연구들은 주로 유한요소법(FEM)을 사용하여 유체 역학 및 열 전달 모델링에 집중했으며, 일부는 셀룰러 오토마타(CA)와 결합하여 최종 주조품의 결정립 크기를 예측하려 시도했습니다. 그러나 수지상정 구조의 진화와 이중 가지 형성 과정을 미시적으로 분석하기 위해 상평형장 모델을 HPDC에 적용한 사례는 드물었습니다.

Purpose of the study:

본 연구의 목적은 상평형장 모델을 사용하여 HPDC 공정 중 수지상정 구조의 진화를 분석하고, 급속 응고가 어떻게 이중 수지상정 가지의 형성으로 이어지는지에 대한 통찰력을 제공하는 것입니다.

Core study:

연구의 핵심은 2단계 시뮬레이션 접근법입니다. 첫째, 샷 슬리브의 느린 냉각 조건을 모사하여 초기 수지상정을 성장시킵니다. 둘째, 이 결과를 초기 조건으로 사용하여 다이 캐비티의 급속 냉각 조건을 적용합니다. 이 과정에서 고체-액체 계면의 물리적 특성(두께, 에너지, 이동도)을 체계적으로 변경하여, 난류와 급랭이 미세조직에 미치는 영향을 간접적으로 모델링하고 실험 결과와 비교 검증했습니다.

5. Research Methodology

Research Design:

실험적 미세조직 분석과 수치적 상평형장 모델링을 결합한 연구 설계를 채택했습니다. 실제 HPDC 공정으로 제작된 시편의 미세조직을 관찰하여 모델 검증을 위한 기준 데이터를 확보하고, 이를 바탕으로 2단계 상평형장 시뮬레이션을 수행하여 이중 미세조직 형성 메커니즘을 규명했습니다.

Data Collection and Analysis Methods:

  • 미세조직 분석: HPDC로 제작된 Al-Si 합금 평판의 여러 위치(S1-S7)에서 시편을 채취하여 연마 및 아노다이징 처리 후, 광학 현미경(Zeiss Axio-Vision)을 사용하여 α-Al 입자의 크기, 분포, 형태를 관찰하고 정량적으로 분석했습니다.
  • 상평형장 모델링: 2차원 상평형장 모델을 사용하여 500×500 셀 그리드에서 시뮬레이션을 수행했습니다. 샷 슬리브(냉각속도 100 K/s)와 다이 캐비티(냉각속도 1000 K/s)의 열 조건을 각각 적용하고, 고체-액체 계면의 두께, 에너지, 이동도를 변화시키며 수지상정 성장을 계산했습니다.

Research Topics and Scope:

연구는 아공정 Al-7% Si 합금의 HPDC 공정에 초점을 맞춥니다. 주요 연구 주제는 샷 슬리브에서 다이 캐비티로의 전환 과정에서 발생하는 이중 수지상정 응고 현상입니다. 연구 범위는 상평형장 모델을 이용한 미세조직 진화의 수치적 재현과, 고체-액체 계면 특성 변화가 수지상정 형태에 미치는 영향 분석에 한정됩니다.

6. Key Results:

Key Results:

  • 주조품의 인게이트에서 끝단으로 갈수록 평균 α-Al 입자 크기가 21 µm에서 3 µm로 현저히 감소했습니다.
  • 인게이트 부근에서 조대한 ESCs와 미세한 α-Al 입자가 공존하는 이중 미세조직이 관찰되었으며, 파편화된 수지상정 위에서 새로운 가지가 핵 생성되는 현상이 확인되었습니다.
  • 상평형장 모델은 샷 슬리브 조건에서의 초기 수지상정 성장을 성공적으로 모사했습니다.
  • 다이 캐비티 조건을 모사하기 위해 고체-액체 계면 두께를 700 nm에서 500 nm로 줄였을 때, 실험에서 관찰된 것과 유사한 미세한 3차 수지상정 가지의 형성을 재현할 수 있었습니다. 이는 난류 효과를 모델에 효과적으로 반영한 결과입니다.
Figure 3. Size distribution of α-Al particles along the plate.
Figure 3. Size distribution of α-Al particles along the plate.

Figure List:

  • Figure 1. Sampling region on the plate manufactured by HPDC.
  • Figure 2. Microstructure evolution at seven sampling locations (S1-S7) along the plate, (a) advent of segregation band at last one-third of the plate shown by red arrows, (b) comparison of a-Al particles.
  • Figure 3. Size distribution of a-Al particles along the plate.
  • Figure 4. Comparison of a-Al particles along the plate, (a) and (b) near the in-gate, (c) at the end of the plate (the arrows show the new arms nucleated on fragmented dendrites).
  • Figure 5. (a) Externally solidified crystals at the in-gate, (b,c) phase-field and Si concentration of dendrites at shot sleeve after 2 ms, (d,e) after 15 ms.
  • Figure 6. Comparison of secondary nucleation on a dendrite grew in the shot sleeve for 2 ms and transferred to die cavity (states 1-3 show interface thicknesses of 700–500 nm).

7. Conclusion:

난류에 의한 파편화는 Al-Si 합금의 HPDC 공정 중 수지상정 형태를 변형시키는 중요한 요인입니다. 샷 슬리브에서 다이 캐비티로의 고속 용탕 이송은 2차 수지상정 가지의 파편화를 촉진하며, 이 파편들은 이후 새로운 가지 성장의 핵으로 작용합니다. 이러한 현상은 용질 및 열 구배가 높은 영역에서 특히 두드러지며, 난류는 국부적 과냉각과 용질 재분배를 강화합니다.

상평형장 모델링 접근법은 고체-액체 계면 특성을 체계적으로 변경함으로써 새로운 수지상정 가지의 시작과 성장을 성공적으로 포착했습니다. 선택된 파라미터 세트(특히 계면 두께 감소)는 난류와 급속 냉각에 의해 유도된 형태학적 변화를 효과적으로 나타냈습니다. 이는 HPDC 조건 하에서 수지상정 진화에 있어 동역학적 및 열역학적 요인 간의 상호작용을 강조합니다.

이러한 발견은 수지상정 응고에서 난류의 역할에 대한 중요한 통찰력을 제공하며, 복잡한 미세조직 현상을 재현하는 데 있어 상평형장 모델링의 유용성을 보여줍니다. 또한 결과는 공정별 조건에 맞춰 계면 특성을 조정하는 것의 중요성을 강조하며, Al-Si 합금의 HPDC 공정 최적화 및 미세조직 제어를 위한 경로를 제공합니다.

8. References:

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Expert Q&A: Your Top Questions Answered

Q1: 왜 상평형장 모델에서 고체-액체(S/L) 계면 특성(두께, 에너지, 이동도)을 주요 변수로 선택했습니까?

A1: 이들 계면 특성은 수지상정의 형태(morphology), 성장 속도, 가지 안정성을 직접적으로 결정하는 핵심 물리량이기 때문입니다. HPDC 공정은 샷 슬리브에서 다이 캐비티로 넘어가면서 열 및 유동 조건이 극적으로 변합니다. 모델이 유체 역학적 난류를 직접 계산하지 않는 대신, 난류가 야기하는 물리적 효과(예: 더 가파른 열 및 용질 구배)를 이러한 계면 파라미터를 조정함으로써 간접적으로, 그러나 효과적으로 모사할 수 있었습니다.

Q2: 시뮬레이션에서 계면 두께를 700nm에서 500nm로 줄인 것이 물리적으로 어떤 의미를 가집니까?

A2: 계면 두께 감소는 액상에서 고상으로의 상변태가 더 ‘날카로운’ 또는 급격한 구배를 통해 일어남을 의미합니다. 물리적으로 이는 다이 캐비티 내의 격렬한 난류가 열 추출을 가속화하여 계면에서의 온도 및 용질 구배를 더 가파르게 만드는 현상을 반영합니다. 이처럼 더 얇아진 계면은 모델이 실험에서 관찰된 것과 같이 더 미세하고 날카로운 수지상정 구조의 형성을 재현할 수 있게 하는 핵심적인 조정이었습니다.

Q3: 이 연구는 실제 HPDC 공정의 3차원적이고 복잡한 유동을 2차원 모델로 단순화했는데, 그 한계와 타당성은 무엇입니까?

A3: 본 연구의 주된 목적은 거시적인 유동 패턴이 아닌, 기존 결정 위에서 새로운 수지상정 가지가 핵 생성되고 성장하는 미시적 ‘응고 물리’ 현상을 포착하는 것이었습니다. 이러한 메커니즘을 규명하는 데는 2차원 모델로도 충분한 타당성을 가집니다. 물론 3차원 효과를 완전히 반영하지 못하는 한계는 있지만, 열 조건 변화에 따른 수지상정 형태 변화라는 핵심 현상을 성공적으로 재현함으로써 연구 목적을 달성했습니다.

Q4: 논문에서 언급된 ‘분리대(segregation band)’의 형성을 이 시뮬레이션이 재현할 수 있습니까?

A4: 본 연구에서 사용된 상평형장 모델은 수지상정 성장과 같은 미세조직 스케일의 응고 현상에 초점을 맞추고 있습니다. 논의(Discussion) 섹션에서 언급된 분리대는 유동이 난류에서 층류로 바뀌거나 ESCs의 분율이 낮아지는 등 주조품 전체에 걸친 거시적인 현상과 관련이 있습니다. 따라서 이 모델의 범위에서는 분리대 형성을 직접 재현하지는 않았습니다.

Q5: 샷 슬리브와 다이 캐비티의 냉각 속도를 각각 100 K/s와 1000 K/s로 설정한 근거는 무엇입니까?

A5: 이 값들은 실제 HPDC 공정에서 일반적으로 보고되는 대표적인 냉각 속도입니다. 논문의 서론 부분에서 “The cooling rate in HPDC in the shot sleeve is about 100 K/s, while in the die is about 1000 K/s [4,5]”라고 명시하고 있습니다. 이는 시뮬레이션이 산업적으로 유의미한 실제 공정 조건을 기반으로 수행되었음을 보여줍니다.


Conclusion: Paving the Way for Higher Quality and Productivity

이 연구는 상평형장 모델링이 고압 다이캐스팅(HPDC) 공정에서 발생하는 복잡한 이중 미세조직 형성 메커니즘을 얼마나 정밀하게 예측할 수 있는지를 명확히 보여주었습니다. 샷 슬리브에서 다이 캐비티로의 급격한 환경 변화, 특히 난류의 영향을 고체-액체 계면 특성 조정을 통해 성공적으로 모델링함으로써, 최종 제품의 품질을 좌우하는 미세조직 제어에 대한 중요한 통찰력을 제공합니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
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Copyright Information

  • This content is a summary and analysis based on the paper “Phase-Field Modelling of Bimodal Dendritic Solidification During Al Alloy Die Casting” by “Maryam Torfeh, Zhichao Niu and Hamid Assadi”.
  • Source: https://doi.org/10.3390/met15010066

This material is for informational purposes only. Unauthorized commercial use is prohibited. Copyright © 2025 STI C&D. All rights reserved.

Fig. 5. Optical micrographs taken from samples prior to etching to reveal the intermetallic phase particles. (a) Non-sheared produced sample (inset shows needle-shaped β-AlFeSi intermetallics phase) and (b) sheared produced sample. (c) -AlSiMnFe particle size distribution curves for both samples (d) Particle group number, Nq (number of particles per Quadrat) distribution. Solid lines are fits to various statistical distribution curves. To plot these curves in (c), 8 micrographs were taken randomly along the cross-section and analysed where (i) and (ii) stand for -AlSiMnFe and β-AlFeSi, respectively. The processing temperature was 630°C.

HPDC 공정의 고강도 전단(Intensive Shearing): Al-Si 합금 미세구조 및 결함 감소의 혁신

이 기술 요약은 H.R. Kotadia 외 저자가 Brunel University Research Archive에 발표한 “Solidification Behavior of Intensively Sheared Hypoeutectic Al-Si Alloy Liquid” 논문을 기반으로 하며, STI C&D가 기술 전문가를 위해 분석하고 요약했습니다.

Keywords

  • Primary Keyword: 고강도 전단(Intensive Shearing)
  • Secondary Keywords: 고압 다이캐스팅(HPDC), Al-Si 합금, 미세구조 미세화, 결함 밴드, 응고

Executive Summary

  • 도전 과제: 기존의 고압 다이캐스팅(HPDC) 공정으로 생산된 Al-Si 합금은 불균일한 미세구조와 결함으로 인해 기계적 성능이 저하되는 한계가 있었습니다.
  • 해결 방법: 주조 전 용탕에 고강도 전단을 가하는 새로운 공정(MC-HPDC)을 기존 HPDC 공정과 비교 분석했습니다.
  • 핵심 돌파구: 고강도 전단은 주조품의 결정립 크기, 기공, 결함 밴드를 획기적으로 감소시켜 미세하고 균일한 미세구조를 형성했습니다.
  • 핵심 결론: HPDC 공정 전 Al-Si 합금 용탕에 고강도 전단을 적용하면 최종 주조 부품의 기계적 물성을 더욱 우수하고 신뢰성 있게 만들 수 있습니다.

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

자동차 및 항공우주 산업에서 경량화와 고성능 요구가 증가함에 따라 Al-Si 주조 합금의 사용이 확대되고 있습니다. 특히 고압 다이캐스팅(HPDC)은 높은 생산성과 복잡한 형상 구현 능력 덕분에 널리 사용되는 공정입니다. 하지만 기존 HPDC 공정은 몇 가지 고질적인 문제를 안고 있습니다.

용탕이 응고되는 과정에서 불균일한 수지상(dendritic) 조직이 형성되고, 외부 고상 결정(ESC)이 특정 부위에 집중되면서 ‘결함 밴드(defect band)’라는 취약한 영역이 발생합니다. 또한, 응고 수축 및 가스로 인한 기공(porosity)과 유해한 금속간 화합물(intermetallic)의 편석은 부품의 인장 강도와 피로 수명을 저하시키는 주된 원인이 됩니다. 이러한 문제들은 고성능 구조 부품의 신뢰성을 확보하는 데 큰 걸림돌이 되어 왔습니다.

Fig. 5. Optical micrographs taken from samples prior to etching to reveal the intermetallic phase particles. (a) Non-sheared produced sample (inset shows needle-shaped β-AlFeSi intermetallics phase) and (b) sheared produced sample. (c) -AlSiMnFe particle size distribution curves for both samples (d) Particle group number, Nq (number of particles per Quadrat) distribution. Solid lines are fits to various statistical distribution curves. To plot these curves in (c), 8 micrographs were taken randomly along the cross-section and analysed where (i) and (ii) stand for -AlSiMnFe and β-AlFeSi, respectively. The processing temperature was 630°C.
Fig. 5. Optical micrographs taken from samples prior to etching to reveal the intermetallic phase particles. (a) Non-sheared produced sample (inset shows needle-shaped β-AlFeSi intermetallics phase) and (b) sheared produced sample. (c) α-AlSiMnFe particle size distribution curves for both samples (d) Particle group number, Nq (number of particles per Quadrat) distribution. Solid lines are fits to various statistical distribution curves. To plot these curves in (c), 8 micrographs were taken randomly along the cross-section and analysed where (i) and (ii) stand for α-AlSiMnFe and β-AlFeSi, respectively. The processing temperature was 630°C.

해결 방법: 연구 방법론 분석

본 연구는 고강도 전단이 Al-Si 합금의 응고 거동에 미치는 영향을 규명하기 위해 두 가지 공정을 비교하는 방식으로 설계되었습니다.

  • 사용 합금: Al-9.4%Si (A380)
  • 비교 공정:
    1. 기존 HPDC: 일반적인 고압 다이캐스팅 공정.
    2. MC-HPDC: 용탕을 HPDC 기계에 주입하기 전, MCAST(Melt Conditioning by an Advanced Shear Technology) 장치를 이용해 60초간 500rpm의 속도로 고강도 전단을 가하는 공정.
  • 주요 변수: 용탕 처리 온도(585°C ~ 650°C)를 변경하며 각 조건에서 시편을 제작했습니다.
  • 분석 방법: 제작된 시편의 단면을 채취하여 광학 현미경으로 미세구조(결정립 크기, 금속간 화합물, 결함 밴드, 기공률)를 정량적으로 분석했으며, 인장 시험을 통해 기계적 물성(인장 강도, 연신율)을 측정했습니다.

핵심 돌파구: 주요 발견 및 데이터

고강도 전단을 적용한 MC-HPDC 공정은 기존 HPDC 공정 대비 모든 측면에서 뚜렷한 개선 효과를 보였습니다.

발견 1: 획기적인 미세구조 미세화 및 균일성 확보

고강도 전단은 주조품의 미세구조를 근본적으로 변화시켰습니다. 기존 HPDC 시편에서 관찰된 크고 불균일한 수지상 조직(그림 1a)과 달리, MC-HPDC 시편에서는 미세하고 균일한 구상의 α-Al 입자가 전체적으로 분포하는 것을 확인했습니다(그림 1b). 특히 그림 2(c)의 데이터는 MC-HPDC 공정이 시편 단면 전체에 걸쳐 α-Al 입자 분율을 훨씬 더 균일하게 분포시킨다는 것을 보여줍니다. 이는 응고 과정에서 핵생성을 촉진하고 균일한 성장을 유도한 결과입니다.

발견 2: 결함 및 금속간 화합물의 크기 감소

고강도 전단은 주조품의 품질을 저하하는 주요 결함들을 효과적으로 제어했습니다. – 기공 감소: 그림 6에서 볼 수 있듯이, 기존 HPDC 공정에서 약 1%에 달했던 기공 면적 분율이 MC-HPDC 공정에서는 약 0.3%로 크게 감소했습니다. – 결함 밴드 두께 감소: 그림 4(d)는 MC-HPDC 공정이 모든 처리 온도에서 결함 밴드의 두께를 현저히 줄였음을 보여줍니다. – 금속간 화합물 미세화: 그림 5(c)에 따르면, 유해한 α-Al(Fe,Mn)Si 금속간 화합물의 평균 크기가 기존 8µm에서 5µm로 감소했으며, 분포 또한 더욱 균일해졌습니다.

R&D 및 운영을 위한 실질적 시사점

본 연구 결과는 주조 부품의 품질과 생산성을 향상시키기 위한 중요한 통찰을 제공합니다.

  • 공정 엔지니어: 용탕에 고강도 전단을 가하는 물리적 처리만으로 화학적 첨가제 없이 결정립을 미세화하고 결함을 줄일 수 있습니다. 이는 더 안정적이고 반복 가능한 공정 설계를 가능하게 합니다.
  • 품질 관리팀: 그림 7의 데이터는 MC-HPDC 공정이 인장 강도와 연신율을 향상시킬 뿐만 아니라, 공정 온도 변화에 대한 민감도를 낮춘다는 것을 보여줍니다. 이는 더 넓은 공정 창(processing window)을 의미하며, 일관된 품질의 제품을 생산하는 데 유리합니다.
  • 설계 엔지니어: 결함 밴드가 줄어들고 미세구조가 균일해짐에 따라 부품의 기계적 신뢰성이 향상됩니다. 이를 통해 성능 저하 없이 더 얇은 벽이나 복잡한 형상의 부품 설계가 가능해져 제품 경량화와 설계 자유도를 높일 수 있습니다.

논문 상세 정보


Solidification Behavior of Intensively Sheared Hypoeutectic Al-Si Alloy Liquid

1. 개요:

  • 제목: Solidification Behavior of Intensively Sheared Hypoeutectic Al-Si Alloy Liquid
  • 저자: H.R. Kotadia, N. Hari Babu, H. Zhang, S. Arumuganathar, Z. Fan
  • 발표 연도: N/A
  • 발행 학술지/학회: Brunel University Research Archive
  • 키워드: Al-Si alloys; Solidification; HPDC; Intensive shearing.

2. 초록:

고강도 전단 처리된 액상 금속으로부터 응고된 Al-Si(아공정) 합금의 미세구조 및 기계적 특성에 대한 공정 온도의 영향을 체계적으로 조사했습니다. 고강도 전단은 결정립 크기와 금속간 화합물 입자 크기를 상당히 미세화합니다. 또한, 고압 다이캐스팅 부품의 금속간 화합물 형태, 결함 밴드 및 미세 결함이 액상 금속에 대한 고강도 전단에 의해 영향을 받는 것으로 관찰되었습니다. 우리는 이러한 효과에 대한 가능한 메커니즘을 논의하고자 합니다.

3. 서론:

Al-Si 주조 합금은 낮은 밀도, 우수한 주조성, 용접성, 내식성, 그리고 특히 우수한 인장 및 피로 특성으로 인해 자동차 및 항공우주 산업의 중요한 구조용 응용 분야에서 점점 더 많이 사용되고 있습니다. 이 합금의 기계적 특성은 응고 공정을 통해 제어될 수 있는 1차 α-Al 및 공정상의 미세구조를 변경함으로써 크게 달라질 수 있습니다. HPDC 공정으로 생산된 시편의 미세구조는 매우 복잡하며, 미세하고 균일한 미세구조와 최소한의 주조 결함이 더 나은 기계적 특성을 얻는 데 중요합니다. 결함 밴드는 HPDC 알루미늄 및 마그네슘 합금, 특히 얇은 벽 주물에서 관찰되는 일반적인 특징입니다.

4. 연구 요약:

연구 주제의 배경:

Al-Si 합금은 자동차 및 항공우주 분야에서 널리 사용되지만, 고압 다이캐스팅(HPDC) 공정 시 발생하는 미세구조 불균일성(수지상 조직, 결함 밴드, 기공 등)이 기계적 물성을 저해하는 주요 원인이 됩니다.

이전 연구 현황:

기존 연구들은 응고 조건 변경이나 합금 원소 첨가를 통해 기계적 특성을 향상시키려는 노력을 해왔으나, 결함 밴드와 같은 고질적인 문제 해결에는 한계가 있었습니다.

연구 목적:

본 연구는 용탕 단계에서 ‘고강도 전단(intensive shearing)’이라는 물리적 처리 기술을 적용하여, 이것이 아공정 Al-Si 합금의 응고 후 미세구조와 기계적 물성에 미치는 영향을 평가하고, 그 메커니즘을 규명하는 것을 목표로 합니다.

핵심 연구:

기존 HPDC 공정과 고강도 전단을 적용한 MC-HPDC 공정을 비교하여, 미세구조(α-Al 상, 금속간 화합물), 결함(결함 밴드, 기공) 및 기계적 특성(인장 강도, 연신율)의 변화를 체계적으로 분석했습니다.

5. 연구 방법론

연구 설계:

본 연구는 기존의 고압 다이캐스팅(HPDC) 공정과, 용탕을 주입하기 전에 MCAST(Melt Conditioning by an Advanced Shear Technology) 장치를 통해 고강도 전단을 가하는 MC-HPDC 공정을 비교하는 실험적 설계를 채택했습니다.

데이터 수집 및 분석 방법:

  • 재료: Al-9.4%Si (A380) 합금을 사용했습니다.
  • 시편 제작: 두 공정 조건 하에서 표준 인장 시험 시편을 제작했습니다.
  • 미세구조 분석: 시편 단면을 채취하여 광학 현미경(OM)을 사용하여 α-Al 상의 크기, 형상 인자, 금속간 화합물의 크기 및 분포, 기공률을 정량적으로 측정했습니다.
  • 기계적 특성 평가: Instron 5569 시험기를 사용하여 인장 강도(UTS)와 파단 연신율을 측정했습니다.

연구 주제 및 범위:

연구 범위는 고강도 전단이 아공정 Al-Si 합금의 응고 거동에 미치는 영향에 초점을 맞춥니다. 구체적으로 미세구조 미세화, 결함 밴드 및 기공 형성 억제, 금속간 화합물 형태 제어, 그리고 이러한 미세구조 변화가 최종 기계적 특성에 미치는 상관관계를 규명하는 것을 포함합니다.

6. 주요 결과:

주요 결과:

  • 고강도 용탕 전단은 1차 α-Al의 상당한 결정립 미세화를 제공하며 주조 시편 전체에 걸쳐 균일한 결정립 크기를 보입니다.
  • 고강도 전단은 α-Al(Mn,Fe)Si 금속간 화합물 상의 분포를 개선하고 좁은 크기 분포를 가지게 하며, 평균 입자 크기를 8µm에서 5µm로 감소시켰습니다.
  • 결함 밴드는 전단 처리된 HPDC 인장 시편과 처리되지 않은 시편 모두에서 관찰되었습니다. 그러나 고강도 전단은 ESCs를 더 균일하게 분포시키고, 구형의 1차 α-Al 핵생성에 이상적인 조건을 제공하여 결함 밴드 크기와 기공률을 크게 감소시킵니다.
  • MCAST 장치 하에서 기공 형성 감소의 가능한 메커니즘은 (i) 용융된 액체에 이미 존재하는 가스 기포가 고강도 전단 적용으로 붕괴되거나 더 작은 기포로 분산될 수 있다는 것, (ii) 기공의 잠재적 핵생성 사이트인 건조한 산화막이 완전히 젖은 산화물 입자로 분해될 수 있다는 것, (iii) 미세 등축정 구조의 형성이 액체 이동성을 향상시켜 최종 응고 단계에서 액체 공급을 원활하게 한다는 것입니다.

Figure List:

  • Fig. 1. Optical micrographs of Al-9.4Si samples produced by (a) HPDC and (b) MC-HPDC processes. Note that these are taken from etched surfaces. The primary a-Al dendrites can be clearly seen in samples produced by HPDC while samples produced by MC-HPDC are virtually free of primary a-Al dendrites. It can be seen that the MC-HPDC process produces a finer and more uniform microstructure in comparison with HPDC. Primary dendritic fragments (α₁) that are formed in the shot sleeve and fine spherical particles (a2) formed inside the die cavity can be seen.
  • Fig. 2. Cross-sectional images of the microstructures of the tensile samples produced by (a) HPDC process, showing a defect band and large central grains with segregated ESC particles and (b) MC-HPDC process. The bright phase in both images is primary a-Al and the black contrast regions are the eutectic phase regions. (c) Spatial variation of area fraction of primary a-Al particles (sum of a₁ and a2) across the tensile specimen cross section. Each data point represents the measured area fraction of primary a-Al in a total area of one micrograph frame measuring 850 μm x 1250 μm.
  • Fig. 3. Area fraction of the ESC particles as a function of the processing temperature.
  • Fig. 4. Typical optical micrographs of Al-9.4%Si alloy produced by the HPDC process (a) across the cross sectional surface (b) higher magnification images at various locations (i) outside the band (ii) inside the band, and (ii) centre of the tensile specimen; (c) and (d) are band thickness and skin thickness as a function of processing temperature.
  • Fig. 5. Optical micrographs taken from samples prior to etching to reveal the intermetallic phase particles. (a) Non-sheared produced sample (inset shows needle-shaped β-AlFeSi intermetallics phase) and (b) sheared produced sample. (c) a-AlSiMnFe particle size distribution curves for both samples (d) Particle group number, Nq (number of particles per Quadrat) distribution. Solid lines are fits to various statistical distribution curves. To plot these curves in (c), 8 micrographs were taken randomly along the cross-section and analysed where (i) and (ii) stand for a-AlSiMnFe and β-AlFeSi, respectively. The processing temperature was 630°C.
  • Fig. 6. Measured porosity as a function of the processing temperature.
  • Fig. 7. Tensile properties (a) elongation to failure and (b) UTS (ultimate tensile strength) as a function of the processing temperature.

7. 결론:

액상선 온도 이상의 동적 고강도 전단 조건 하에서 아공정 Al-Si 주조 합금의 형태, 결함 및 미세구조 미세화를 조사하고 기존 HPDC 공정과 비교했습니다. 실험 결과로부터 다음과 같은 결론을 얻었습니다:

  1. 고강도 용탕 전단은 1차 α-Al의 상당한 결정립 미세화를 제공하며 주조 시편 전체에 걸쳐 균일한 결정립 크기를 보입니다.
  2. 고강도 전단은 α-Al(Mn,Fe)Si 금속간 화합물 상의 분포를 개선하고 좁은 크기 분포를 가지게 하며, 평균 입자 크기를 8µm에서 5µm로 감소시켰습니다.
  3. 결함 밴드는 전단 처리된 HPDC 인장 시편과 처리되지 않은 시편 모두에서 관찰되었습니다. 그러나 고강도 전단은 ESCs를 더 균일하게 분포시키고, 구형의 1차 α-Al 핵생성에 이상적인 조건을 제공하여 결함 밴드 크기와 기공률을 크게 감소시킵니다.
  4. MCAST 장치 하에서 기공 형성 감소의 가능한 메커니즘은 다음과 같습니다: (i) 용융된 액체에 이미 존재하는 가스 기포가 고강도 전단 적용으로 붕괴되거나 더 작은 기포로 분산될 수 있습니다. (ii) 기공의 잠재적 핵생성 사이트인 건조한 산화막이 완전히 젖은 산화물 입자로 분해되어 더 이상 잠재적 핵생성 사이트가 아니게 될 수 있습니다. (iii) 미세 등축정 구조의 형성이 액체 이동성을 향상시켜 최종 응고 단계에서 액체 공급을 원활하게 합니다.

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Expert Q&A: 전문가 Q&A

Q1: 왜 고상-액상 구간이 아닌 액상선 온도 이상에서 고강도 전단을 적용했나요?

A1: 본 연구의 목적은 반용융 상태에서의 수지상 파쇄 효과가 아닌, 완전한 액상 금속 자체에 가해진 전단의 영향을 규명하는 것이었습니다. 액상선 온도 이상에서 전단을 가함으로써, 미세구조 개선이 단순히 고상의 파편화 때문이 아니라 액체 상태에서의 핵생성 조건 향상에 기인한다는 것을 보여줍니다. 논문의 토론 섹션에서는 이것이 온도와 조성을 균일하게 하고, 잠재적인 핵생성제를 용탕 전체에 고르게 분산시킴으로써 달성된다고 설명합니다.

Q2: 논문에서는 외부 고상 결정(ESC)이 감소했다고 언급합니다. 고강도 전단은 어떻게 이를 달성하며, 이것이 왜 중요한가요?

A2: 그림 3은 MC-HPDC 공정에서 모든 처리 온도에 걸쳐 ESC의 면적 분율이 상당히 감소했음을 보여줍니다. 논문은 고강도 전단이 용탕 내 균일한 온도를 만들어, 상대적으로 차가운 숏 슬리브(shot sleeve)에서 조기에 응고되어 큰 수지상 조직이 형성되는 것을 방지한다고 설명합니다. ESC는 주로 이 숏 슬리브에서 형성됩니다. ESC의 높은 집중도와 수지상 형태는 결함 밴드를 유발하고 다이 충전 시 유동 저항을 높이기 때문에, 이를 줄이는 것은 주조 품질 향상에 매우 중요합니다.

Q3: 그림 5(d)에 나타난 금속간 화합물 입자 분포의 변화는 기계적 물성에 어떤 영향을 미칩니까?

A3: 그림 5(d)는 전단 처리되지 않은 시편의 입자 분포가 군집(clustering)을 나타내는 음이항 분포를 따르는 반면, 전단 처리된 시편은 더 무작위적이거나 균일한 분포를 의미하는 푸아송 또는 이항 분포에 가깝다는 것을 보여줍니다. 논문은 크고 군집된 금속간 화합물이 연성에 해롭다고 명시합니다. 고강도 전단은 이러한 군집을 파괴하고 더 작고 균일한 입자 분포를 만들어 응력 집중 지점을 제거함으로써, 특히 연성과 같은 기계적 물성을 향상시키는 데 기여합니다.

Q4: MCAST 공정이 공기를 유입시킬 가능성이 있음에도 불구하고 기공이 감소한 메커니즘은 무엇인가요?

A4: 논문은 결론에서 세 가지 메커니즘을 제안합니다. 첫째, 고강도 전단이 기존의 가스 기포를 붕괴시키거나 더 작고 덜 해로운 미세 기공으로 분산시킬 수 있습니다. 둘째, 가스 기공의 잠재적 핵생성 사이트인 건조한 산화 피막(bifilm)을 파괴하고, 그 결과 생성된 개별 산화물 입자를 용탕으로 완전히 적셔 비활성화시킵니다. 셋째, 결과적으로 형성된 미세 등축정 구조가 응고 마지막 단계에서 용탕의 유동성을 향상시켜 수축 기공을 줄이는 데 도움을 줍니다.

Q5: 그림 7을 보면 MC-HPDC 시편의 기계적 물성이 공정 온도에 덜 민감합니다. 이것의 실질적인 이점은 무엇인가요?

A5: 이는 더 안정적이고 견고한 제조 공정을 의미합니다. 넓은 공정 창(processing window)은 용탕 온도의 사소한 변동이 최종 부품의 기계적 물성에 미치는 영향을 최소화한다는 뜻입니다. 이는 자동차 산업과 같은 대량 생산 환경에서 수율을 높이고 불량률을 줄이며, 일관된 제품 품질을 보장하는 데 매우 유리합니다.


결론: 더 높은 품질과 생산성을 향한 길

본 연구는 고강도 전단(Intensive Shearing) 기술이 Al-Si 합금의 기존 고압 다이캐스팅(HPDC) 공정이 가진 핵심적인 한계를 극복할 수 있는 강력한 물리적 처리 방법임을 입증했습니다. 이 기술은 미세구조를 미세하고 균일하게 만들고, 결함을 획기적으로 줄여 궁극적으로 더 우수하고 신뢰성 있는 기계적 물성을 제공합니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

Copyright Information

  • 이 콘텐츠는 H.R. Kotadia 등의 논문 “Solidification Behavior of Intensively Sheared Hypoeutectic Al-Si Alloy Liquid”를 기반으로 요약 및 분석되었습니다.
  • 출처: https://core.ac.uk/download/pdf/132717.pdf

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

Fig. 1: Illustration of the atomic configuration of SrTiO3, SrFeO2.5 and SrTi1-xFexO3-0.5x lattices. The SrTi1-xFexO3-0.5x can be regarded as a mix of SrTiO3 and SrFeO2.5 with disorder of Fe and Ti cations.

차세대 연료전지 소재의 비밀: 혼합 이온-전자 전도체(MIEC)의 구조적 무질서와 전자 구조 분석

이 기술 요약은 Bin Ouyang 외 저자의 학술 논문 “Structural Disorder and Electronic Structure of Sr(TixFe1-x)O3-x/2 Solid Solutions: A Computational Framework”를 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 혼합 이온-전자 전도체 (MIEC)
  • Secondary Keywords: Sr(TixFe1-x)O3-x/2 (STF), 클러스터 확장법, 몬테카를로 시뮬레이션, 밀도범함수이론, 고체산화물 연료전지 (SOFC), 전산 재료 과학

Executive Summary

  • The Challenge: 복잡한 혼합 이온-전자 전도체(MIEC) 소재는 원자 배열의 경우의 수가 너무 많아, 원자 수준의 정확한 모델링과 물성 예측이 매우 어려웠습니다.
  • The Method: 클러스터 확장법(Cluster Expansion), 몬테카를로 시뮬레이션(Monte Carlo simulations), 그리고 밀도범함수이론(DFT+U) 계산을 결합한 계산 프레임워크를 사용하여 무질서한 STF 합금의 구조와 에너지를 모델링했습니다.
  • The Key Breakthrough: Ti/Fe 양이온의 무작위 혼합과 산소 공공(vacancy)이 Fe 원자 주위에 모이는 특정 유형의 원자 무질서가 전하 수송에 유리한 비편재화된(delocalized) 전자 상태를 형성한다는 것을 발견했습니다.
  • The Bottom Line: 이 모델링 프레임워크는 ‘유익한 무질서’를 공학적으로 설계하여 연료전지와 같은 응용 분야에서 고성능 MIEC 소재를 이해하고 개발하는 강력한 도구를 제공합니다.

The Challenge: Why This Research Matters for CFD Professionals

고체산화물 연료전지(SOFC), 전해조, 산소 분리막 등 다양한 고체 전해질 장치에서 높은 이온 및 전자 전도도를 동시에 갖는 혼합 이온-전자 전도체(MIEC)는 핵심 소재로 주목받고 있습니다. 특히 Sr(Ti1-xFex)O3-y (STF) 합금은 조성과 환경에 따라 전도도를 폭넓게 조절할 수 있어 기술적으로 매우 중요합니다.

하지만 이러한 비희석(non-dilute), 무질서(disordered) 합금은 원자 배열의 조합이 기하급수적으로 많아 현실적인 원자 구조를 구현하기 어렵습니다. 이는 소재의 구조와 물성 간의 관계를 명확히 규명하고 예측 모델을 개발하는 데 큰 걸림돌이 되어 왔습니다. 본 연구는 이러한 문제를 해결하기 위해 조성, 합금 배열, 전자 구조, 광학 특성 간의 상관관계를 규명하는 계산 프레임워크를 제시하는 것을 목표로 합니다.

Fig. 1: Illustration of the atomic configuration of SrTiO3, SrFeO2.5 and SrTi1-xFexO3-0.5x lattices. The
SrTi1-xFexO3-0.5x can be regarded as a mix of SrTiO3 and SrFeO2.5 with disorder of Fe and Ti cations.
Fig. 1: Illustration of the atomic configuration of SrTiO3, SrFeO2.5 and SrTi1-xFexO3-0.5x lattices. The SrTi1-xFexO3-0.5x can be regarded as a mix of SrTiO3 and SrFeO2.5 with disorder of Fe and Ti cations.

The Approach: Unpacking the Methodology

본 연구는 무질서한 STF 합금의 특성을 원자 수준에서 규명하기 위해 다단계 계산 프레임워크를 도입했습니다.

  1. 클러스터 확장(Cluster Expansion, CE) 모델 개발: 먼저, 밀도범함수이론(DFT+U) 계산을 통해 다양한 원자 배열을 가진 350개의 STF 구조에 대한 총 에너지를 계산했습니다. 이 데이터를 기반으로 특정 원자 배열의 에너지를 빠르고 정확하게 예측할 수 있는 클러스터 확장 모델을 구축했습니다. 이 모델은 Ti/Fe 양이온과 산소/산소 공공의 분포에 따른 에너지 변화를 설명합니다.
  2. 현실적 원자 구조 예측: 개발된 CE 모델을 클러스터 확장 몬테카를로(CEMC) 시뮬레이션에 적용하여, 주어진 조성과 온도(T=0K, T=1000K)에서 가장 안정적인(가장 낮은 에너지를 갖는) 원자 배열을 예측했습니다. 이를 통해 무작위로 원자를 배열하는 것이 아닌, 물리적으로 가장 가능성 높은 현실적인 구조를 얻을 수 있었습니다.
  3. 전자 구조 및 물성 분석: CEMC를 통해 얻은 현실적인 구조와 비교를 위해 가상으로 설정한 두 가지 규칙적 배열(ordered mixture, superlattice) 구조에 대해 DFT+U 계산을 수행했습니다. 이를 통해 각 구조의 전자 구조, 밴드갭, 광학적 특성을 분석하고, 원자 배열의 무질서가 물성에 미치는 영향을 심도 있게 비교 분석했습니다.

The Breakthrough: Key Findings & Data

Finding 1: 원자 무질서가 에너지 안정성을 결정

CEMC 시뮬레이션 결과, STF 합금은 규칙적인 배열을 형성하거나 두 개의 상(SrTiO3, Sr2Fe2O5)으로 분리되는 것보다 무질서한 고용체를 형성하는 것이 에너지적으로 더 안정적이었습니다. 특히, 가장 안정한 구조는 Ti와 Fe 양이온이 B-자리에 무작위로 섞이는 경향을 보이면서도, 산소 공공은 Ti 원자보다 Fe 원자 주위에 모이는(clustering) 특징을 보였습니다. Figure 2(b)에서 볼 수 있듯이, CEMC로 예측된 가장 낮은 에너지 상태(파란색 선)는 가상으로 설정된 규칙적 혼합물(Ordered mixture)이나 초격자(Superlattice) 구조보다 항상 에너지가 낮아, 이러한 특정 형태의 ‘단거리 질서(short-ranged order)’를 갖는 무질서 구조가 더 선호됨을 확인했습니다.

Finding 2: 조성에 따른 예측 가능한 밴드갭 변화

CEMC로 예측된 현실적인 무질서 구조의 밴드갭은 Fe 함량(x)이 증가함에 따라 2.13 eV에서 0.95 eV로 거의 선형적으로 부드럽게 감소했습니다. Figure 3에서 볼 수 있듯이, 이러한 경향은 기존의 실험 결과와 매우 일치합니다. 반면, 가상으로 설정된 두 가지 규칙적 구조는 Fe 함량 변화에 따라 밴드갭이 불규칙하게 변동하며 체계적인 경향을 보이지 않았습니다. 이는 본 연구의 계산 프레임워크가 실제 소재의 전자적 특성을 정확하게 예측할 수 있음을 시사합니다.

Fig. 2: (a) Linear least squares fitting of mixing enthalpy using cluster expansion; ‘u.c.’ denotes the
five atom unit cell of the conventional perovskite lattice. (b) Convex hull showing the lowest energy
configurations predicted from Monte Carlo simulation. The training data and two ordered structures are
shown for comparison. (c) Atomic configurations of CEMC predicted lowest energy state, CEMC
predicted structure at T = 1000 K, and two types of ordered structures. For the convenience of
visualization, A-site strontium atoms are not shown.
Figure 2(b) shows the distribution of mixing
Fig. 2: (a) Linear least squares fitting of mixing enthalpy using cluster expansion; ‘u.c.’ denotes the
five atom unit cell of the conventional perovskite lattice. (b) Convex hull showing the lowest energy
configurations predicted from Monte Carlo simulation. The training data and two ordered structures are
shown for comparison. (c) Atomic configurations of CEMC predicted lowest energy state, CEMC
predicted structure at T = 1000 K, and two types of ordered structures. For the convenience of
visualization, A-site strontium atoms are not shown.

Finding 3: ‘유익한 무질서’가 전자 수송을 촉진

가장 중요한 발견은 원자 배열의 무질서가 전자 수송 특성에 미치는 영향입니다. Figure 5는 x=0.5 조성에서 가전자대 상단(VBM)과 전도대 하단(CBM)의 전하 밀도 분포를 보여줍니다. CEMC로 예측된 현실적인 무질서 구조에서는 VBM과 CBM이 전체 초격자(supercell)에 걸쳐 넓게 비편재화(delocalized)되어 있습니다. 이는 전하 운반체(전자, 정공)가 격자 내에서 자유롭게 이동할 수 있어 높은 전도도에 기여함을 의미합니다. 반면, 규칙적인 구조에서는 VBM과 CBM이 특정 원자(주로 Fe) 주변에 국소화(localized)되어 전하 운반체를 포획하는 ‘트랩(trap)’으로 작용하여 전도도를 저해할 수 있습니다. 즉, Ti/Fe의 무작위 혼합과 산소 공공 클러스터링이라는 특정 유형의 무질서는 전자 수송에 ‘유익하게’ 작용합니다.

Practical Implications for R&D and Operations

  • For Process Engineers: 본 연구는 Ti/Fe의 무작위 혼합을 촉진하면서 산소 공공이 Fe 원자 주위에 위치하도록 유도하는 공정 조건이 STF 계열 소재의 전자 전도도를 향상시킬 수 있음을 시사합니다.
  • For Quality Control Teams: 논문의 Figure 3과 Figure 6에서 보듯이, Fe 함량과 밴드갭(또는 광 흡수 스펙트럼) 사이에는 명확한 상관관계가 있습니다. 이는 소재의 조성을 비파괴적으로 검증하는 품질 관리 기준으로 활용될 수 있습니다.
  • For Design Engineers: 이 프레임워크는 새로운 MIEC 소재를 설계하는 강력한 도구가 될 수 있습니다. 완벽한 결정 구조를 목표로 하기보다, 특정 유형의 ‘유익한 무질서’를 의도적으로 설계하여 연료전지나 센서용 고성능 소재를 개발하는 전략을 제시합니다.

Paper Details


Structural Disorder and Electronic Structure of Sr(TixFe1-x)O3-x/2 Solid Solutions: A Computational Framework

1. Overview:

  • Title: Structural Disorder and Electronic Structure of Sr(TixFe1-x)O3-x/2 Solid Solutions: A Computational Framework
  • Author: Bin Ouyang, Tim Mueller, Nicola H. Perry, N. R. Aluru, Elif Ertekin
  • Year of publication:
  • Journal/academic society of publication:
  • Keywords: Mixed ionic/electronic conductors (MIECs), Sr(Ti,Fe)O3-δ (STF), cluster expansion, Monte Carlo simulation, electronic structure, band gap, solid solution

2. Abstract:

연료전지나 전해조의 전극으로 사용되는 여러 혼합 이온-전자 전도체(MIEC)는 페로브스카이트 산화물과 정렬된 산소 공공 화합물 간의 고용체 혼합물로 간주될 수 있다. 예를 들어, 모델 MIEC인 Sr(Ti1-xFex)O3-x/2+δ (STF)는 페로브스카이트 SrTiO3와 브라운밀러라이트 Sr2Fe2O5의 혼합물로 기술될 수 있다. 이러한 비희석, 무질서 합금의 거대한 배열 공간은 역사적으로 직접적인 원자 규모 모델링을 방해하여 심도 있는 이해와 예측 분석을 불가능하게 했다. 본 연구에서는 전체 고용체 조성 공간 Sr(Ti1-xFex)O3-x/2 (0<x<1, δ=0) 내에서 무질서한 STF 합금의 에너지를 기술하기 위한 클러스터 확장 프레임워크를 제시한다. 클러스터 확장 몬테카를로(CEMC) 시뮬레이션을 수행하여 최저 에너지 원자 배열을 결정하고 격자 무질서의 기원과 정도를 조사한다. 다른 온도에서 CEMC로부터 얻은 현실적인 배열을 사용하여, 다른 화학량론에서의 용액의 전자 구조를 조사하여 그들의 전자 구조, 밴드갭, 광학적 특성을 이해하고 가상적인 정렬 구조와 비교 및 대조한다. 우리의 원자 모델을 사용하여 예측된 밴드갭과 광 흡수의 조성에 따른 변화는 실험과 일치한다. 한편, 밴드 가장자리 분석은 B 양이온 부격자에서의 Fe/Ti 무질서의 동시 존재와 산소 공공이 Fe 원자 주위에 군집하는 경향으로부터 합금 내 전자 수송이 이점을 얻는다는 것을 명확히 한다. SrTiO3/Sr2Fe2O5 합금을 예로 사용하여, 여기서 채택된 모델링 프레임워크는 다른 MIEC 재료로 확장될 수 있다.

3. Introduction:

큰 전자 및 산소 이온 전도성을 나타내는 혼합 이온 전자 전도체(MIEC)는 고체 산화물 연료 및 전해조 전극, 산소 분리막, 산소 센서 및 촉매를 포함한 다양한 고체 상태 전기화학 장치에서 중요하다. SrTi1-xFexO3-y 합금(STF로 지칭)은 복잡한 MIEC 합금의 고전적인 예이다. STF 조성 공간은 0 < x < 1 사이의 연속적인 고용체를 형성하며, Ti/Fe 조성 및 열역학적 환경에 따라 크고 가변적인 이온 및 전자 전도성을 나타낸다. 이는 STF 고용체를 여러 실제 응용 분야에서 기술적으로 중요하게 만들며, 특히 조성, 산소 풍부/결핍 및 배열을 조절하여 특성을 제어할 수 있다면 더욱 그렇다. STF의 배열, 전자 구조 및 수송 특성을 이해하는 것은 여전히 어려운 과제이며, 구조/특성 관계에 대한 통일된 그림은 아직 없다. 이는 비희석, 무질서 용액의 배열에 대한 현실적인 원자 규모 표현을 달성하기 어렵기 때문이며, 기계론적 이해와 예측 모델링을 어렵게 만든다. 이 연구의 목표는 조성, 합금 배열, 전자 구조 및 광학 특성을 연관시키는 계산 프레임워크를 소개하는 것이다. 우리는 클러스터 확장 모델을 기반으로 전체 조성 공간 0 < x < 1에 걸쳐 원자 규모 배열에 대한 자체 일관된 설명을 제시한다. 클러스터 계수는 밀도 함수 이론 계산에 맞춰 배열 에너지를 설명하며, 결과 모델은 세부 사항을 확립하는 데 사용된다.

4. Summary of the study:

Background of the research topic:

혼합 이온-전자 전도체(MIEC)는 고체산화물 연료전지(SOFC)와 같은 차세대 에너지 변환 장치의 핵심 소재이다. 이 중 Sr(Ti,Fe)O3-y (STF)는 조성에 따라 이온 및 전자 전도도를 조절할 수 있어 큰 잠재력을 가지고 있다.

Status of previous research:

기존 연구들은 희석 용액(dilute-solution) 관점에서 STF를 이해하려는 시도가 있었으나, STF는 두 개의 다른 물질(SrTiO3와 Sr2Fe2O5)이 넓은 조성 범위에서 섞인 비희석 고용체이다. 이러한 복잡한 무질서 합금의 거대한 원자 배열 경우의 수 때문에, 현실적인 원자 구조를 모델링하고 물성을 정확히 예측하는 데 한계가 있었다.

Purpose of the study:

본 연구는 클러스터 확장법과 몬테카를로 시뮬레이션을 결합한 계산 프레임워크를 개발하여, 전체 조성 범위(0<x<1)에 걸쳐 STF 합금의 현실적인 원자 구조를 예측하고, 이를 통해 구조적 무질서가 전자 구조, 밴드갭, 광학 특성에 미치는 영향을 규명하는 것을 목표로 한다.

Core study:

본 연구는 STF 고용체를 페로브스카이트 구조의 SrTiO3와 브라운밀러라이트 구조의 Sr2Fe2O5 사이의 혼합물로 정의했다. 밀도범함수이론(DFT+U) 계산을 통해 얻은 350개 구조의 에너지 데이터를 사용하여 클러스터 확장(CE) 모델을 훈련시켰다. 이 CE 모델을 몬테카를로(CEMC) 시뮬레이션에 적용하여 다양한 조성과 온도에서 가장 안정적인 원자 구조를 예측했다. 마지막으로, 예측된 현실적인 구조와 가상으로 설정한 규칙적인 구조들의 전자 구조를 DFT+U로 계산하여, 무질서가 밴드갭과 전하 수송 특성에 미치는 영향을 분석했다.

5. Research Methodology

Research Design:

본 연구는 전산 재료 과학(computational materials science) 접근법을 사용했다. 클러스터 확장법을 통해 무질서한 합금의 에너지 모델을 구축하고, 몬테카를로 시뮬레이션으로 통계역학적 평형 상태의 원자 구조를 찾은 뒤, 양자역학 기반의 제일원리계산(first-principles calculations)으로 해당 구조의 전자 물성을 분석하는 다단계 프레임워크를 설계했다.

Data Collection and Analysis Methods:

  • 제일원리계산 (DFT+U): VASP 코드를 사용하여 다양한 STF 원자 배열의 총 에너지와 전자 구조를 계산했다. 전이 금속(Ti, Fe)의 3d 전자 상태를 정확히 기술하기 위해 Hubbard U 보정을 적용했다(Ti에 U=3 eV, Fe에 U=5 eV).
  • 클러스터 확장 모델링 및 몬테카를로 시뮬레이션: 350개의 DFT+U 계산 결과를 바탕으로 클러스터 상호작용 계수를 피팅하여 CE 모델을 구축했다. 이 모델을 사용하여 CEMC 시뮬레이션을 수행, 최저 에너지 구조와 고온(1000K)에서의 대표 구조를 예측했다.
  • 비교 분석: CEMC로 얻은 현실적인 무질서 구조의 특성을 두 종류의 가상적 규칙 구조(ordered mixture, superlattice)와 비교하여 무질서의 효과를 명확히 분석했다.

Research Topics and Scope:

연구는 Sr(Ti1-xFex)O3-x/2 (δ=0) 조성을 갖는 STF 고용체에 초점을 맞췄다. 이는 Ti+4, Fe+3의 안정적인 산화 상태를 유지하는 기준 조성이다. 연구 범위는 전체 조성 공간(0 < x < 1)에 걸친 에너지 안정성, 원자 배열(단거리 질서), 밴드갭 변화, 전자 상태 밀도(PDOS), 밴드 가장자리 전하 분포 및 광학적 흡수 특성 분석을 포함한다.

6. Key Results:

Key Results:

  • 클러스터 확장 모델은 DFT+U 계산 결과를 4.33 meV/atom의 낮은 RMSE로 정확하게 예측했으며, 무질서한 STF 고용체가 상분리보다 에너지적으로 안정적임을 보였다.
  • 가장 안정한 구조는 Ti/Fe 양이온이 무작위로 혼합되면서 산소 공공이 Fe 원자 주위에 모이는 경향을 보였다.
  • Fe 함량이 증가함에 따라 밴드갭은 실험 결과와 일치하게 거의 선형적으로 감소했다. 이는 가상적인 규칙 구조의 불규칙한 밴드갭 변화와 대조적이다.
  • 현실적인 무질서 구조는 전하 수송에 유리한 비편재화된(delocalized) 밴드 가장자리 상태를 형성하는 반면, 규칙적인 구조는 전하 트랩으로 작용할 수 있는 국소화된(localized) 상태를 보였다.
Fig. 4: Site and orbital projected density of states (PDOS) of the four configurations of
Sr(Ti1-xFex)O3-x/2 at (a) x = 0.5 and (b) x = 0.875.
Fig. 4: Site and orbital projected density of states (PDOS) of the four configurations of Sr(Ti1-xFex)O3-x/2 at (a) x = 0.5 and (b) x = 0.875.

Figure List:

  • Fig. 1: Illustration of the atomic configuration of SrTiO3, SrFeO2.5 and SrTi1-xFexO3-0.5x lattices. The SrTi1-xFexO3-0.5x can be regarded as a mix of SrTiO3 and SrFeO2.5 with disorder of Fe and Ti cations.
  • Fig. 2: (a) Linear least squares fitting of mixing enthalpy using cluster expansion; ‘u.c.’ denotes the five atom unit cell of the conventional perovskite lattice. (b) Convex hull showing the lowest energy configurations predicted from Monte Carlo simulation. The training data and two ordered structures are shown for comparison. (c) Atomic configurations of CEMC predicted lowest energy state, CEMC predicted structure at T = 1000 K, and two types of ordered structures. For the convenience of visualization, A-site strontium atoms are not shown.
  • Fig. 3: The evolution of band gap with Fe content. For the lowest energy state and T = 1000 K structures, the band gap smoothly decreases with increasing Fe content with little degree of bowing evident. The band gap of the ordered structures are shown for comparison.
  • Fig. 4: Site and orbital projected density of states (PDOS) of the four configurations of Sr(Ti1-xFex)O3-x/2 at (a) x = 0.5 and (b) x = 0.875.
  • Fig. 5: Charge density of the SrTi0.5Fe0.5O2.75 valence band maximums (VBM) and conduction band minimums (CBM).
  • Fig. 6: Optical absorption for selected compositions of Sr(Ti1-xFex)O3-x/2 alloy for the lowest energy configurations.

7. Conclusion:

결론적으로, 본 연구는 STF MIEC 고용체의 조성과 질서/무질서 효과를 고려하기 위한 계산 프레임워크를 제시했다. 클러스터 확장 모델링과 몬테카를로 시뮬레이션을 사용하여 SrTiO3에서 Sr2Fe2O5에 이르는 전체 조성 공간에 걸쳐 Sr(Ti1-xFex)O3-x/2의 에너지와 현실적인 배열을 예측할 수 있다. 우리는 이 프레임워크를 사용하여 대표적인 배열을 생성하고 밀도범함수이론을 사용하여 그 특성을 평가한다. 분석 결과, Ti/Fe 양이온 무질서와 산소 공공 분포가 전자 구조에 미치는 연관성이 드러났다. 나아가, Ti/Fe 양이온 무질서와 Fe 원자 주위의 산소 공공 군집이 함께 공간적으로 비편재화된 밴드 가장자리 상태를 유발하며, 이는 격자 내 전자 수송을 촉진할 수 있음이 밝혀졌다. 이 연구는 Sr(Ti1-xFex)O3-x/2의 무질서와 전자 구조에 대한 기계론적 이해를 제공할 뿐만 아니라, 연료 및 전해조 응용을 위한 복잡한 페로브스카이트 용액 분석을 위한 계산 전략을 제안한다.

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Expert Q&A: Your Top Questions Answered

Q1: 왜 표준 DFT-PBE 대신 DFT+U 방법을 선택했나요?

A1: 표준 DFT-PBE 계산은 STF와 같은 전이 금속 산화물의 밴드갭을 실제보다 현저히 낮게 예측하는 경향이 있습니다. 본 연구에서는 양 끝단 물질인 SrTiO3와 Sr2Fe2O5의 실험적 밴드갭과 잘 일치하도록 Ti와 Fe 원자에 대해 보정된 Hubbard U 값을 적용했습니다. 이를 통해 계산 정확도와 효율성 사이의 합리적인 절충점을 찾아, 대규모 구조 계산에 필요한 신뢰도를 확보할 수 있었습니다.

Q2: 논문에서 Sr(Ti1-xFex)O3-x/2라는 특정 화학량론에 집중한 이유는 무엇인가요?

A2: 이 ‘기준 조성’은 전체 조성 범위에 걸쳐 전이 금속이 가장 선호하는 산화 상태(Ti+4, Fe+3)를 평균적으로 유지하게 합니다. 실제 작동 환경에서는 산소 함량이 변할 수 있지만, 이 기준 조성은 서로 다른 결정 구조를 갖는 두 물질 사이의 전체 고용체 공간에 걸쳐 클러스터 확장 모델을 개발하기 위한 현실적이고 계산적으로 다루기 쉬운 기준선을 제공합니다.

Q3: Figure 5에서 무질서가 전자 수송에 유리하다고 하셨는데, 그 메커니즘을 더 자세히 설명해 주실 수 있나요?

A3: 규칙적인 구조에서는 6개의 산소와 배위된 Fe와 4개의 산소와 배위된 Fe처럼 화학적 환경이 뚜렷하게 구분됩니다. 이러한 환경 차이는 특정 위치에 에너지가 국소화된 상태를 만들어 전하 운반체를 포획하는 트랩 역할을 합니다. 반면, CEMC로 예측된 무질서 구조에서는 Ti/Fe가 무작위로 섞여 이러한 환경들이 평균화되고, 그 결과 밴드 가장자리 상태가 물질 전체에 넓게 퍼지게(비편재화) 됩니다. 이는 전하 운반체가 특정 위치에 갇히지 않고 더 자유롭게 이동할 수 있게 해줍니다.

Q4: 모델이 예측한 거의 선형적인 밴드갭 변화(Figure 3)는 이론 및 실험과 어떻게 비교되나요?

A4: 이 결과는 Rothschild 등이 발표한 실험 결과와 매우 일치합니다. 많은 합금에서 조성에 따른 밴드갭 변화는 포물선 형태의 ‘보잉(bowing)’ 효과를 보이지만, STF의 경우 이 보잉 파라미터가 매우 작아 거의 선형적인 추세로 나타납니다. 이는 본 연구에서 사용된 클러스터 확장 접근법이 실제 소재의 전자적 특성을 성공적으로 예측할 수 있음을 검증하는 결과입니다.

Q5: 최저 에너지 구조에서 발견된 Fe-Vo-Fe 삼량체(trimer)는 어떤 의미를 갖나요?

A5: 이 삼량체는 Sr2Fe2O5의 브라운밀러라이트 구조에서 발견되는 국소적인 구조 모티프입니다. 혼합된 합금 내에서도 이러한 구조가 나타난다는 것은 단거리 질서(short-range order)가 존재함을 의미하며, 산소 공공이 왜 Fe 원자 주위에 모이는 것을 에너지적으로 선호하는지를 설명합니다. 이는 결과적으로 앞서 언급한 유익한 전자적 특성을 달성하는 핵심 요인 중 하나입니다.


Conclusion: Paving the Way for Higher Quality and Productivity

복잡한 혼합 이온-전자 전도체(MIEC) 소재의 성능을 예측하고 최적화하는 것은 기존의 방법론으로는 큰 도전이었습니다. 본 연구는 클러스터 확장법과 몬테카를로 시뮬레이션을 결합한 강력한 계산 프레임워크를 통해, 특정 유형의 원자 ‘무질서’가 실제로는 전자 수송 특성을 향상시키는 ‘유익한’ 역할을 할 수 있음을 규명했습니다. 이 발견은 완벽한 결정 구조만이 최선이라는 통념을 넘어, 소재의 성능을 극대화하기 위해 무질서를 공학적으로 제어하는 새로운 설계 패러다임을 제시합니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 최선을 다하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

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  • This content is a summary and analysis based on the paper “Structural Disorder and Electronic Structure of Sr(TixFe1-x)O3-x/2 Solid Solutions: A Computational Framework” by “Bin Ouyang, et al.”.
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Fig. 10. Optical micrograph of an onion ring feature in FSW AA6061/Al2O3/20p crosssection [35].

알루미늄 복합재의 미래: 마찰교반용접(FSW)의 과제와 돌파구

이 기술 요약은 Omar S. Salih, Hengan Ou, W. Sun, D.G. McCartney가 Materials & Design (2015)에 발표한 논문 “A review of friction stir welding of aluminium matrix composites”를 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 마찰교반용접(Friction Stir Welding)
  • Secondary Keywords: 알루미늄 매트릭스 복합재(Aluminium Matrix Composites), AMC 용접, 고체상태접합(Solid State Joining), 용접 결함(Welding Defects), 공구 마모(Tool Wear)

Executive Summary

  • 도전 과제: 기존의 융합 용접 방식으로는 알루미늄 매트릭스 복합재(AMC)를 접합할 때 취성 상 형성, 기공, 균열 등의 문제로 인해 효율적인 접합이 어렵습니다.
  • 해결 방법: 용융점 이하의 온도에서 접합하는 고체상태접합 방식인 마찰교반용접(FSW)을 적용하여 AMC의 접합 가능성을 검토했습니다.
  • 핵심 돌파구: FSW는 강화재의 용해나 유해한 반응 없이 AMC를 성공적으로 접합할 수 있으며, 용접부의 미세구조를 제어하여 모재에 가까운 기계적 특성을 확보할 수 있음을 확인했습니다.
  • 핵심 결론: FSW는 항공우주 및 자동차 산업에서 경량 고강도 소재인 AMC의 활용을 확대할 핵심 기술이지만, 공구 마모와 최적 공정 조건 확보라는 과제를 해결해야 합니다.

도전 과제: 왜 이 연구가 CFD 전문가에게 중요한가?

알루미늄 매트릭스 복합재(AMC)는 가볍고 강도가 높아 항공우주 분야에서 차세대 소재로 주목받고 있습니다. 하지만 기존의 아크 용접이나 레이저 용접과 같은 융합 용접(fusion welding) 방식으로는 이 소재를 효과적으로 접합하기 어렵습니다. 용접 시 높은 열로 인해 알루미늄 매트릭스와 강화재(SiC, Al2O3 등)가 반응하여 취성이 강한 2차 상을 형성하거나, 강화재 자체가 분해되어 버리기 때문입니다. 이는 접합부의 강도를 심각하게 저하시키는 주요 원인이 됩니다. 또한, 기공, 균열, 왜곡과 같은 결함이 발생하기 쉬워 AMC의 광범위한 산업 적용에 큰 걸림돌이 되어 왔습니다. 따라서 소재의 우수한 특성을 유지하면서 안정적인 접합을 구현할 수 있는 새로운 용접 기술이 절실히 요구되는 상황입니다.

접근 방식: 방법론 분석

본 연구는 특정 실험이 아닌, 마찰교반용접(FSW)을 AMC에 적용한 기존의 다양한 연구들을 종합적으로 검토하고 분석하는 리뷰(Review) 형식으로 진행되었습니다. FSW는 비소모성 회전 툴(Tool)을 사용하여 접합할 소재에 마찰열을 발생시키고, 소성 변형을 통해 고체 상태에서 접합하는 혁신적인 기술입니다.

Fig. 1. Schematic drawing of FSW.
Fig. 1. Schematic drawing of FSW.

주요 분석 대상은 다음과 같습니다. – FSW 공정: 툴의 회전 속도, 이동 속도, 축 방향 하중 등 핵심 공정 변수들이 용접 품질에 미치는 영향을 분석했습니다. – 미세구조 분석: 용접 후 너겟존(Nugget Zone, NZ), 열-기계적 영향부(TMAZ), 열영향부(HAZ) 등 각 영역의 미세구조 변화, 특히 강화 입자의 분포와 크기 변화를 중점적으로 관찰했습니다. – 기계적 특성 평가: 용접부의 미세 경도, 인장 강도, 피로 강도 등을 측정하여 모재와 비교하고, 접합 효율을 평가했습니다. – 공구 마모: AMC 내의 단단한 강화 입자로 인해 발생하는 FSW 툴의 마모 현상을 분석하고, 이를 해결하기 위한 방안을 검토했습니다.

Fig. 3. Reinforcement types — (a) fibres, (b) whiskers, and (c) particles [19].
Fig. 3. Reinforcement types — (a) fibres, (b) whiskers, and (c) particles [19].

이러한 종합적인 분석을 통해 FSW가 AMC 접합에 있어 기존 융합 용접의 한계를 어떻게 극복할 수 있는지, 그리고 상용화를 위해 해결해야 할 과제는 무엇인지 명확히 제시합니다.

돌파구: 주요 발견 및 데이터

발견 1: 용접부 미세구조 제어를 통한 결함 최소화

FSW 공정은 용접부의 미세구조를 효과적으로 제어하여 고품질의 접합을 가능하게 합니다. 논문은 여러 연구를 통해 FSW 용접부에서 나타나는 특징적인 미세구조와 결함을 분석했습니다.

  • 강화재의 균일한 분포: FSW의 강력한 교반 작용은 불균일하게 분포되어 있던 강화 입자 클러스터를 파괴하고 용접 너겟존(NZ) 전체에 균일하게 재분배시킵니다. 이는 접합부의 기계적 특성을 향상시키는 핵심 요인입니다(논문 Section 5.2).
  • 결함 제어: 터널 결함(Tunnel Defect)은 부적절한 열 입력이나 소성 유동으로 인해 발생합니다. 논문의 그림 12는 낮은 회전 속도(1200 rpm, 85 mm/min)에서 터널 결함이 발생한 AA6061/AlN/10p 접합부 단면을 보여줍니다. 연구에 따르면, 툴 회전 속도를 높여 열 입력을 최적화하면 이러한 결함을 최소화할 수 있습니다.
  • 양파링 구조(Onion Ring): 그림 10에서 볼 수 있듯이, 용접부 단면에는 특징적인 양파링 구조가 나타납니다. 이는 소성 유동과 재결정 과정에서 발생하는 현상으로, 용접 품질을 시각적으로 평가하는 지표가 될 수 있습니다.
Fig. 10. Optical micrograph of an onion ring feature in FSW AA6061/Al2O3/20p crosssection
[35].
Fig. 10. Optical micrograph of an onion ring feature in FSW AA6061/Al2O3/20p crosssection [35].

발견 2: 용접 변수 최적화를 통한 기계적 특성 극대화

FSW 공정 변수는 최종 접합부의 기계적 특성에 직접적인 영향을 미칩니다.

  • 미세 경도 프로파일: FSW 용접부는 일반적으로 모재(BM)보다 높은 경도 값을 보입니다. 이는 동적 재결정으로 인한 결정립 미세화와 강화 입자의 균일한 분포 때문입니다. 그림 14는 AA6061/SiC/10p 용접부의 경도 프로파일을 보여주며, 열 입력(755 J/mm ~ 1133 J/mm)이 증가할수록 너겟존(NZ)의 경도가 높아지는 경향을 명확히 보여줍니다.
  • 인장 강도: 표 1은 다양한 AMC 소재와 FSW 공정 조건에 따른 인장 강도 및 접합 효율을 요약합니다. 예를 들어, AA2009/SiC/17p 소재의 경우, 1000 rpm 회전 속도와 800 mm/min의 높은 이동 속도에서 모재 대비 97%에 달하는 높은 접합 효율을 달성했습니다. 이는 공정 변수 최적화를 통해 모재에 가까운 강도를 구현할 수 있음을 시사합니다.
  • 공구 마모와 그 영향: AMC의 단단한 강화 입자는 FSW 공구, 특히 핀(pin) 부분에 심각한 마모를 유발합니다. 그림 18은 용접 거리가 증가함에 따라 공구 핀이 마모되는 과정을 보여줍니다. 이러한 마모는 재료 유동에 영향을 미쳐 용접 품질을 저하시킬 수 있으며, 심한 경우 Fe와 같은 공구 재료가 용접부로 유입되어 Cu2FeAl7과 같은 취성 금속간화합물을 형성하여 접합 강도를 떨어뜨리는 원인이 됩니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 툴 회전 속도, 이동 속도, 축 방향 하중이 용접부의 열 입력과 재료 유동을 결정하는 핵심 변수임을 강조합니다. 터널 결함을 방지하고 최적의 기계적 특성을 얻기 위해 각 AMC 소재에 맞는 용접 윈도우(welding window)를 설정하는 것이 중요합니다.
  • 품질 관리팀: 그림 8과 그림 12에서 제시된 용접부 단면의 거시적 구조(너겟 형상, 터널 결함 유무, 양파링 구조 등)는 용접 품질을 비파괴적으로 예측하는 중요한 지표가 될 수 있습니다. 미세 경도 측정(그림 14, 15)을 통해 용접 영역별 기계적 특성 변화를 정량적으로 평가하고 품질 기준을 수립할 수 있습니다.
  • 설계 엔지니어: FSW는 기존 용접법으로는 접합이 어려웠던 고강도 AMC 소재의 활용 가능성을 열어줍니다. 특히 이종 소재 접합에도 적용 가능하므로, 경량화와 고성능이 동시에 요구되는 부품 설계 시 더 넓은 소재 선택의 폭을 제공할 수 있습니다.

논문 상세 정보


A review of friction stir welding of aluminium matrix composites

1. 개요:

  • Title: A review of friction stir welding of aluminium matrix composites
  • Author: Omar S. Salih, Hengan Ou, W. Sun, D.G. McCartney
  • Year of publication: 2015
  • Journal/academic society of publication: Materials & Design
  • Keywords: Friction stir welding, Aluminium matrix composites, Macrostructure and microstructure, Mechanical properties, Tool wear

2. 초록:

고체상태접합 공정인 마찰교반용접(FSW)은 알루미늄 매트릭스 복합재(AMC)를 접합하는 유망한 접근법으로 입증되었습니다. 그러나 최근 몇 년간 상당한 진전이 있었음에도 불구하고, FSW를 사용하여 AMC를 접합하는 데에는 여전히 과제가 남아 있습니다. 이 리뷰 논문은 AMC 소재의 FSW 기술 현황에 대한 개요를 제공합니다. 특히 (a) AMC 접합부의 거시구조 및 미세구조, (b) 접합부의 기계적 특성 평가, (c) 알루미늄 매트릭스 내 강화재 존재로 인한 FSW 공구의 마모에 대해 중점적으로 비판적인 평가를 수행했습니다. 이 리뷰는 향후 연구 방향에 대한 권장 사항으로 마무리됩니다.

3. 서론:

알루미늄 매트릭스 복합재(AMC)와 같은 첨단 소재는 매력적인 기계적 특성과 항공우주 분야에서의 명확한 잠재력으로 인해 상당한 주목을 받아왔습니다. 따라서 경량 고강도 소재의 새로운 세대로서 이상적인 후보로 간주됩니다. 그러나 AMC의 구현은 제한적이며, 부분적으로는 기존의 용접 공정으로 이러한 금속을 접합하는 것과 관련된 어려움 때문에 항공 산업에서 널리 사용되지 않고 있습니다.

강화재와 매트릭스 간의 반응으로 인해 용접 풀에 취성 2차 상이 형성되거나 용융 금속에서 강화재가 분해되는 문제 때문에, 융합 기반 용접 방법으로는 AMC 소재의 강도 측면에서 효율적인 접합을 달성할 수 없습니다. 용접 공정과 관련하여, 여러 연구에서 마찰교반용접(FSW)을 채택할 때 기공, 균열, 왜곡 및 강화재 용해가 훨씬 감소된 더 효율적인 접합을 달성할 수 있음이 입증되었습니다. 그러나 강화 입자의 존재로 인해, FSW로 AMC를 용접하는 주된 어려움은 단일 알루미늄 합금에 비해 좁은 용접 윈도우(성공적인 용접이 가능한 용접 매개변수 범위)입니다.

4. 연구 요약:

연구 주제의 배경:

알루미늄 매트릭스 복합재(AMC)는 경량, 고강도, 고강성의 특성으로 인해 항공우주, 자동차 등 첨단 산업에서 주목받는 소재입니다. 하지만 기존 융합 용접 방식으로는 강화재와 기지 금속 간의 유해한 반응으로 인해 건전한 접합부를 얻기 어려워 실제 적용에 한계가 있었습니다.

이전 연구 현황:

마찰교반용접(FSW)은 알루미늄 합금 접합에 널리 사용되어 왔으며, 그 가능성을 AMC로 확장하려는 여러 연구가 진행되었습니다. 이전 연구들은 FSW가 기공이나 균열과 같은 결함을 줄이고 AMC를 성공적으로 접합할 수 있음을 보여주었지만, 접합부의 미세구조, 기계적 특성, 그리고 심각한 문제인 공구 마모에 대한 체계적인 이해는 부족했습니다.

연구 목적:

본 연구의 목적은 AMC의 마찰교반용접에 관한 기존 연구들을 종합적으로 검토하여 현재 기술 수준(state-of-the-art)을 평가하는 것입니다. 특히, 접합부의 거시/미세구조, 기계적 특성, 공구 마모 현상에 초점을 맞추어 문제점을 분석하고, 이를 통해 향후 연구 개발에 필요한 방향을 제시하고자 합니다.

핵심 연구:

본 논문은 FSW로 접합된 AMC의 세 가지 핵심 이슈를 심층적으로 분석합니다. 1. 거시/미세구조: 용접 너겟존(NZ)의 형상, 양파링 구조, 터널 결함 등 거시적 특징과, 강화 입자의 분포, 결정립 크기 등 미세구조 변화를 분석합니다. 2. 기계적 특성: 미세 경도, 인장 강도, 피로 특성 등 접합부의 기계적 성능에 영향을 미치는 공정 변수(툴 형상, 회전 속도 등)의 효과를 평가합니다. 3. 공구 마모: AMC 내의 단단한 강화재로 인해 발생하는 공구 마모 메커니즘을 분석하고, 공구 수명 향상을 위한 재료 및 설계 방안을 검토합니다.

5. 연구 방법론

연구 설계:

본 연구는 실험적 연구가 아닌, 기존에 발표된 학술 논문들을 체계적으로 수집하고 분석하는 문헌 연구(Literature Review) 방식으로 설계되었습니다.

데이터 수집 및 분석 방법:

다양한 종류의 AMC(예: AA6061/SiC, AA2009/SiC, AA7005/Al2O3 등)에 FSW를 적용한 연구 결과들을 수집했습니다. 수집된 데이터는 접합부의 (a) 거시/미세구조 이미지, (b) 기계적 특성 데이터(경도, 인장 강도 등), (c) 공구 마모 관련 데이터로 분류되었습니다. 이 데이터들을 비교 분석하여 FSW 공정 변수와 용접 품질 간의 상관관계를 도출하고, 일반적인 경향과 문제점을 종합적으로 평가했습니다.

연구 주제 및 범위:

연구 범위는 마찰교반용접(FSW) 기술을 알루미늄 매트릭스 복합재(AMC)에 적용하는 것으로 한정됩니다. 주요 연구 주제는 FSW 공정이 AMC 접합부의 거시구조, 미세구조, 기계적 특성, 그리고 공구 마모에 미치는 영향입니다. 다른 용접 공정과의 비교는 AMC에 대한 FSW의 적합성을 설명하기 위한 배경으로만 다룹니다.

Fig. 14. Microhardness profile across the weld region of AA6061/SiC/10p at different heat
inputs following FSW[42].
Fig. 14. Microhardness profile across the weld region of AA6061/SiC/10p at different heat inputs following FSW[42].

6. 주요 결과:

주요 결과:

  • FSW는 기존 융합 용접과 달리 강화재의 용해나 유해한 2차 상 형성 없이 AMC의 건전한 접합을 가능하게 합니다.
  • FSW의 교반 작용은 불균일한 강화 입자 클러스터를 파괴하고 용접 너겟존에 균일하게 분산시켜 기계적 특성을 향상시킵니다.
  • 용접부의 미세구조는 동적 재결정에 의해 미세한 등축정으로 변화하며, 이는 접합부의 경도와 강도를 높이는 주요 요인입니다.
  • 툴 회전 속도, 이동 속도, 툴 형상과 같은 공정 변수는 접합부의 결함 생성(예: 터널 결함)과 기계적 특성에 결정적인 영향을 미치며, 소재별 최적화가 필수적입니다.
  • AMC 내의 단단한 강화 입자는 심각한 공구 마모를 유발하며, 이는 용접 품질 저하와 비용 상승의 주요 원인입니다. 공구 재질 개선, 코팅, 형상 최적화 등을 통해 이를 완화할 수 있습니다.

Figure List:

  • Fig. 1. Schematic drawing of FSW.
  • Fig. 2. Global demand for MMCs [17].
  • Fig. 3. Reinforcement types – (a) fibres, (b) whiskers, and (c) particles [19].
  • Fig. 4. Trapped porosity in a fusion weld [25].
  • Fig. 5. Centre-line cracks in AA6082 plate/4043 filler metal TIG weld [25].
  • Fig. 6. Optical micrograph of a laser beam fusion weld in AA6061/Al2O3/20p [28].
  • Fig. 7. Optical micrograph of a laser beam fusion weld in AA2124/SiC/20w [28].
  • Fig. 8. Cross-sectional macrostructure of FSW AA2009/SiC/17p joint [29].
  • Fig. 9. Nugget shape – (a) basin, (b) elliptical [10].
  • Fig. 10. Optical micrograph of an onion ring feature in FSW AA6061/Al203/20p cross-section [35].
  • Fig. 11. Partial appearance of an onion ring in a cross-section of an AA6063/B4C/10.5p welded by FSW [38].
  • Fig. 12. Tunnel defect in cross-section morphology of an AA6061/AlN/10p joint welded at 1200 rpm and 85 mm/min [41].
  • Fig. 13. Reorientation of reinforcement in FSW AA2124/SiC/20w [28].
  • Fig. 14. Microhardness profile across the weld region of AA6061/SiC/10p at different heat inputs following FSW [42].
  • Fig. 15. Microhardness profile across the weld region of AA2124/SiC/25p following FSW [36].
  • Fig. 16. Hysteresis loops at different strain amplitudes for the FSW (a) and the base metal (b) AA6061/Al2O03/20p [35].
  • Fig. 17. Fatigue failures in the FSW joint of AA6061/Al2O3/22p (a) within the stirred FSW zone, (b) out of the FSW zone [45].
  • Fig. 18. Wear features of FSW tool pin (a) – (d) at different weld distance (in metres) and constant tool rotation speed of 1000 rpm at different traverse speeds: (a) 1, (b) 3, (c) 6, and (d) 9 mm/s; (e) wear rate versus weld length at different traverse speed and (f) wear rate versus weld speed [63].
  • Fig. 19. Pin tool wear as a percent of initial tool shape projections versus weld traverse distance for different tool rotation and traverse speeds [65].

7. 결론:

본 리뷰는 FSW 공정, MMC의 적용, 알루미늄 및 AMC 소재의 용접성, FSW 접합부의 거시/미세구조, 기계적 특성, 공구 마모 등 특정 이슈들을 논의하며 AMC의 FSW 접합에 대한 현재 기술 수준을 요약하는 것을 목표로 합니다. 고체상태용접 공정인 FSW는 AMC 소재를 접합하는 잠재적으로 실행 가능한 경로로 간주됩니다. 비용 절감, 접합 효율 향상, 높은 생산 정확도에서의 잠재적 이점은 비용접성 시리즈인 AA2xxx, AA6xxx, AA7xxx에 대해 더욱 매력적으로 만듭니다. 그러나 이 접합 공정을 사용하여 AMC를 용접하는 기술의 성숙도는 아직 연구 초기 단계에 있으며 산업에 완전히 구현되지 않았습니다.

FSW로 접합된 AMC의 기계적 특성은 AMC의 조성과 FSW 공정 조건의 복합적인 효과에 크게 의존합니다. FSW 접합부의 기계적 성능은 그에 따라 평가되어야 합니다. 초기 연구들은 FSW가 AMC의 무결함 접합을 달성하는 잠재적인 용접 공정임을 보여주었습니다. 설계 및 생산 요구 사항을 충족시키기 위해 이러한 소재에 대한 FSW의 영향을 적절한 깊이로 이해하기 위한 더 많은 노력이 명백히 필요합니다.

결론적으로, FSW 공구, 특히 핀의 마모는 현재 AMC를 접합할 때 주요 문제이며 산업에서 FSW 공정을 적용하는 데 주요 장애물입니다. 프러스텀 형태(자체 최적화된 형태)를 가진 새로운 공구 설계, 기판과 호환되는 적절한 재료로 핀을 표면 코팅하는 것, 표면 열처리 기술 등이 공구 수명과 접합 효율을 모두 향상시키는 실행 가능한 해결책이 될 수 있습니다.

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전문가 Q&A: 자주 묻는 질문

Q1: AMC 접합에 있어 마찰교반용접(FSW)이 기존 융합 용접보다 나은 근본적인 이유는 무엇인가요?

A1: 가장 큰 차이점은 ‘온도’입니다. 융합 용접은 금속을 녹여서 붙이는 방식이지만, FSW는 소재의 용융점 이하(약 80%) 온도에서 마찰열과 압력으로 접합하는 ‘고체상태접합’입니다. 이 덕분에 융합 용접 시 발생하는 문제, 즉 알루미늄 기지와 강화재 사이의 유해한 화학 반응을 원천적으로 차단할 수 있습니다. 결과적으로 강화재의 특성을 그대로 유지하면서 취성 금속간화합물 생성을 억제하여 훨씬 더 강하고 신뢰성 있는 접합부를 만들 수 있습니다.

Q2: 논문에서 언급된 ‘터널 결함(Tunnel Defect)’은 왜 발생하며, 어떻게 방지할 수 있나요?

A2: 터널 결함은 주로 용접부의 열 입력이 부족하거나 재료의 소성 유동이 원활하지 않을 때 발생합니다. 즉, 툴 회전 속도가 너무 낮거나 이동 속도가 너무 빠르면 재료가 충분히 부드러워지지 않아 툴 뒤쪽 공간을 완전히 채우지 못하고 빈 공간(터널)이 남게 됩니다. 이를 방지하기 위해서는 툴 회전 속도를 높이거나 이동 속도를 낮춰 충분한 열 입력을 확보하고, 재료가 원활하게 유동할 수 있도록 공정 변수를 최적화해야 합니다.

Q3: 일부 AMC 용접부에서 ‘W’자 형태의 미세 경도 프로파일이 나타나는 이유는 무엇인가요 (그림 15)?

A3: ‘W’자 프로파일은 용접 너겟존(NZ)의 중앙부보다 열-기계적 영향부(TMAZ)와 열영향부(HAZ)의 경도가 더 낮게 나타나는 현상입니다. 너겟존은 동적 재결정으로 결정립이 미세해져 경도가 높습니다. 반면, HAZ는 용접열로 인해 기존의 강화 석출물이 과시효(over-aging)되거나 용해되어 연화(softening)가 일어나 경도가 가장 낮아집니다. TMAZ는 소성 변형과 열의 영향을 동시에 받아 HAZ보다는 높지만 NZ보다는 낮은 경도를 보입니다. 이 때문에 전체적으로 ‘W’자 형태의 경도 분포가 나타나게 됩니다.

Q4: FSW 공구의 핀(pin) 형상이 접합 강도에 구체적으로 어떤 영향을 미치나요?

A4: 핀 형상은 재료의 수직 및 수평 유동을 결정하는 핵심적인 역할을 합니다. 예를 들어, 나사산이 있는 원통형 핀이나 다각형(사각형, 육각형 등) 핀은 평평한 원통형 핀보다 재료를 더 효과적으로 아래로 밀어내고 혼합하여 강력한 소성 유동을 만듭니다. 이는 강화 입자를 더 균일하게 분산시키고 내부 결함 발생을 억제하여 최종적으로 접합부의 인장 강도를 높이는 데 기여합니다. 논문에서는 사각형 핀이 다른 형태의 핀보다 높은 접합 효율을 보인 연구 결과를 소개하고 있습니다.

Q5: AMC 용접 시 ‘공구의 자기 최적화(self-optimisation)’ 현상이란 무엇이며, 왜 중요한가요?

A5: ‘자기 최적화’란 용접 초기 단계에서 단단한 강화 입자에 의해 공구 핀이 마모되면서, 특정 시간이 지나면 더 이상 마모가 급격히 진행되지 않는 안정된 형상으로 변하는 현상을 말합니다(그림 19 참조). 이 마모된 형상은 해당 공정 조건에서 가장 효율적인 재료 유동을 만들어내는 형태로 최적화된 것입니다. 이 현상은 초기에는 공구 마모가 단점처럼 보이지만, 안정화된 후에는 오히려 일관된 품질의 용접을 지속적으로 수행할 수 있게 해준다는 점에서 중요합니다.


결론: 더 높은 품질과 생산성을 향한 길

알루미늄 매트릭스 복합재(AMC)의 접합은 기존 융합 용접 방식의 한계로 인해 오랫동안 산업계의 난제로 남아있었습니다. 본 논문은 마찰교반용접(Friction Stir Welding)이 이러한 문제를 해결할 수 있는 혁신적인 대안임을 종합적으로 보여줍니다. FSW는 소재를 녹이지 않고 고체 상태에서 접합함으로써 강화재의 손상 없이 결함이 적고 기계적 특성이 우수한 접합부를 구현할 수 있습니다.

물론, 단단한 강화 입자로 인한 공구 마모와 각 소재에 맞는 최적의 공정 조건을 찾는 것은 여전히 해결해야 할 과제입니다. 하지만 공구 재질의 혁신, 코팅 기술의 발전, 그리고 공정 변수에 대한 깊이 있는 이해를 통해 이러한 과제들은 충분히 극복 가능합니다. 이 연구는 마찰교반용접 기술이 AMC의 활용 범위를 항공우주, 자동차 산업 전반으로 확대하여 제품의 경량화와 고성능화를 이끌 핵심 동력이 될 것임을 명확히 시사합니다.

STI C&D에서는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 지원하는 데 전념하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
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Copyright Information

  • This content is a summary and analysis based on the paper “A review of friction stir welding of aluminium matrix composites” by “Omar S. Salih, Hengan Ou, W. Sun, and D.G. McCartney”.
  • Source: http://dx.doi.org/10.1016/j.matdes.2015.07.071

This material is for informational purposes only. Unauthorized commercial use is prohibited. Copyright © 2025 STI C&D. All rights reserved.

Fig. 11 SEM images show microcracks caused by TiN precipitates (exceeds 1 lm), FSW EH46 W2E SZ at steady state

강재 마찰교반용접 결함 완벽 분석: 두 가지 새로운 결함 유형과 최적 공정 조건

이 기술 요약은 M. Al-Moussawi와 A. J. Smith가 작성하여 2018년 Metallography, Microstructure, and Analysis에 게재한 학술 논문 “Defects in Friction Stir Welding of Steel”을 기반으로 합니다. STI C&D의 기술 전문가가 분석하고 요약했습니다.

키워드

  • Primary Keyword: 마찰교반용접 결함
  • Secondary Keywords: 강재 용접, TiN 석출, 미세균열, DH36, EH46, 공정 파라미터 최적화, SEM 분석

Executive Summary

  • The Challenge: 마찰교반용접(FSW)은 많은 장점에도 불구하고, 공정 파라미터 제어 실패 시 웜홀, 미완전 용융 등 다양한 결함이 발생하여 고품질 접합부 확보에 어려움을 겪습니다.
  • The Method: DH36 및 EH46 강재에 대해 공구 회전 속도와 이송 속도를 달리하여 마찰교반용접을 수행하고, SEM 및 무한초점 현미경(IFM)을 사용하여 용접부 결함을 정밀 분석했습니다.
  • The Key Breakthrough: 기존에 보고되지 않은 두 가지 새로운 유형의 결함을 발견했습니다. 첫째, 플런지-정상 상태 전환 구간에서 부적절한 공구 이송 속도로 인한 미세균열, 둘째, 과도한 공구 회전 속도로 인한 TiN 석출물에 의한 교반 영역(Stirred Zone) 내부 미세균열입니다.
  • The Bottom Line: 강재의 마찰교반용접 결함을 방지하기 위해서는 플런지-정상 상태 전환 시 공구 가속도를 제어해야 하며, 공구 회전 속도를 200-500 RPM 범위로 유지하여 1200°C 이상의 과도한 온도 상승을 막는 것이 중요합니다.

The Challenge: Why This Research Matters for CFD Professionals

마찰교반용접(FSW)은 비소모성 공구를 사용하여 재료를 녹이지 않고 고상 상태에서 접합하는 혁신적인 기술입니다. 이로 인해 용융 용접에서 발생하는 많은 문제점을 피할 수 있지만, FSW 공정 역시 완벽하지는 않습니다. 특히 강재와 같은 고융점 재료의 경우, 부적절한 공정 파라미터는 치명적인 결함으로 이어질 수 있습니다.

기존 연구들은 주로 웜홀(Wormholes), 키싱 본드(Kissing Bonds), 불완전 용융(Incomplete Fusion)과 같은 거시적 결함에 집중해왔습니다. 하지만 용접 품질과 기계적 특성에 큰 영향을 미치는 미세균열의 발생 메커니즘, 특히 공정 단계 전환 시점이나 재료의 미세조직 변화와 관련된 결함에 대한 이해는 부족했습니다. 이러한 결함들은 제품의 피로 수명을 단축시키고 신뢰성을 저하시키는 주요 원인이 되므로, 그 원인을 규명하고 제어 방안을 찾는 것은 산업 현장에서 매우 중요한 과제입니다.

Fig. 2 Microcrack started from the top surface of FSW DH36 W1D between steady state and the plunge regions. (a) low magnification, (b) high
magnification. The sample was cut in the direction of the weld line
Fig. 2 Microcrack started from the top surface of FSW DH36 W1D between steady state and the plunge regions. (a) low magnification, (b) high magnification. The sample was cut in the direction of the weld line

The Approach: Unpacking the Methodology

본 연구에서는 두 종류의 강재, 즉 6-8mm 두께의 열간 압연 DH36 강재와 14mm 두께의 EH46 강재를 대상으로 마찰교반용접을 수행했습니다.

  • 장비 및 공구: TWI/Yorkshire의 PowerStir FSW 장비를 사용했으며, 공구는 PCBN(다결정 입방정 질화붕소) 재질의 Q70 하이브리드 FSW 공구를 사용했습니다.
  • 주요 변수: 결함 발생에 미치는 영향을 파악하기 위해 핵심 독립 변수인 공구 회전 속도(150-550 RPM)와 공구 이송 속도(50-400 mm/min)를 체계적으로 변경하며 실험을 진행했습니다. (Table 3 참조)
  • 분석 기법: 용접부 결함의 유형과 원인을 정밀하게 식별하기 위해 주사전자현미경(SEM)과 에너지 분산형 분광분석법(EDS)을 활용하여 미세조직과 원소 분포를 관찰했습니다. 또한, 무한초점 현미경(IFM)을 통해 결함의 3차원 형상을 분석했습니다. 인장 및 피로 시험을 통해 결함이 기계적 특성에 미치는 영향도 평가했습니다.

The Breakthrough: Key Findings & Data

본 연구는 강재 마찰교반용접에서 발생하는 두 가지 새로운 유형의 미세균열을 명확히 규명하고 그 발생 원인을 밝혔습니다.

Finding 1: 공정 전환 구간에서의 미세균열 발생

연구진은 플런지(plunge) 단계에서 정상 상태(steady state)로 전환되는 구간에서 새로운 유형의 미세균열을 발견했습니다.

DH36 강재 용접 샘플 W1D(200 RPM, 100 mm/min)에서 폭 2-5 µm의 미세균열이 관찰되었습니다(Figure 2). Figure 3의 이송 속도 그래프를 분석한 결과, 이 균열은 공구가 단 2mm를 이동하는 동안 이송 속도가 50mm/min에서 100mm/min으로 급격하게 증가한 구간에서 발생했습니다. 낮은 공구 회전 속도로 인해 열 입력이 충분하지 않은 상태에서 이송 속도가 갑자기 빨라지자 재료 유동이 부족해졌고, 이것이 균열의 시작점이 된 것입니다. 반면, 점진적으로 속도를 높인 샘플 W2D에서는 이러한 유형의 균열이 발견되지 않았습니다.

Fig. 3 Feed rate and the distance travelled by tool in the DH36 plates
just before the steady state
Fig. 3 Feed rate and the distance travelled by tool in the DH36 plates just before the steady state

Finding 2: 과도한 열 입력으로 인한 TiN 석출과 미세균열

두 번째로 발견된 결함은 교반 영역(Stirred Zone, SZ) 내부에서 발생한 미세균열로, 원소 석출이 원인이었습니다.

특히 높은 공구 회전 속도(550 RPM)로 용접된 DH36 샘플 W2D와 EH46 샘플 W2E에서 TiN(질화티타늄) 입자를 중심으로 미세균열이 시작된 것이 SEM-EDS 분석을 통해 확인되었습니다(Figure 10a, Figure 11). 연구에 따르면, 이러한 TiN 석출은 교반 영역 상단의 최고 온도가 1200°C를 초과할 때 발생합니다. 과도한 공구 회전 속도가 국부적인 온도 급상승을 유발했고, 이로 인해 형성된 TiN 석출물이 응력 집중점으로 작용하여 미세균열을 유발한 것입니다. 이 결함은 W2D 샘플의 피로 파괴 사이클을 W1D의 642,935회에서 115,078회로 급격히 감소시키는 주요 원인이었습니다.

Practical Implications for R&D and Operations

  • For Process Engineers: 이 연구는 공정 파라미터의 미세 조정이 결함 제어에 얼마나 중요한지 보여줍니다. 특히 플런지에서 정상 상태로 전환 시, 이송 속도를 급격히 바꾸기보다 최대 이송 속도의 0.1 범위 내에서 가속하며 최소 20mm 이상 이동하는 방식을 적용하여 재료 유동 부족으로 인한 미세균열을 예방할 수 있습니다. 또한, 강재 용접 시 공구 회전 속도를 500 RPM 이하로 유지하여 TiN 석출을 억제하는 것이 중요합니다.
  • For Quality Control Teams: SEM-EDS 분석은 TiN과 같은 미세 석출물이 피로 파괴의 시작점이 될 수 있음을 명확히 보여줍니다(Figure 10, 11). 이는 기존의 비파괴 검사로는 탐지하기 어려운 미세 결함이 제품의 장기 신뢰성에 치명적일 수 있음을 시사합니다. 따라서 고속 회전으로 용접된 부위는 미세조직 분석을 통해 석출물 형성 여부를 확인하는 새로운 품질 검사 기준을 도입할 필요가 있습니다.
  • For Design Engineers: 본 연구 결과는 용접 공정 중 발생하는 열 이력이 재료의 미세조직을 변화시키고 결함을 유발할 수 있음을 보여줍니다. 특히 티타늄(Ti)이 함유된 강재를 사용하는 경우, 설계 단계에서부터 FSW 공정의 열적 특성을 고려하여 과도한 온도 상승을 피할 수 있는 공정 윈도우를 확보하는 것이 중요합니다.

Paper Details


Defects in Friction Stir Welding of Steel

1. Overview:

  • Title: Defects in Friction Stir Welding of Steel
  • Author: M. Al-Moussawi, A. J. Smith
  • Year of publication: 2018
  • Journal/academic society of publication: Metallography, Microstructure, and Analysis
  • Keywords: Friction stir welding, TiN precipitation, Microcracks, DH36 and EH46 steel grades, SEM

2. Abstract:

DH36 및 EH46 두 강종의 마찰교반용접과 관련된 결함을 조사했습니다. 공구 회전 및 이송(선형) 속도를 포함한 다양한 용접 파라미터를 적용하여 미세균열 및 기공 형성을 포함한 용접 심 결함에 미치는 영향을 이해했습니다. 결함 유형을 식별하기 위해 SEM 이미지와 무한초점 현미경을 사용했습니다. 이 연구에서는 마찰교반용접 공정과 관련된 두 가지 새로운 결함을 소개합니다. 첫 번째로 식별된 결함은 플런지 영역과 정상 상태 영역 사이에서 발견된 미세균열로, 플런지-정지에서 정상 상태 단계로 부적절한 속도로 공구가 이송 이동한 것에 기인합니다. 공구 이송 속도는 정상 상태에 도달할 때까지 최대 이송 속도의 0.1 범위의 가속 속도로 20mm 더 이동하는 것이 권장됩니다. 정상 상태에서의 최대 권장 이송 속도는 재료 유동 부족을 피하기 위해 400mm/min 미만으로 제안되었습니다. 이 연구에서 관찰된 두 번째 유형의 결함은 TiN의 원소 석출로 인해 교반 영역 내부에 발생한 미세균열이었습니다. TiN 석출물은 교반 영역 상단에서 최고 온도가 1200°C를 초과하게 만든 높은 공구 회전 속도에 기인하며, 이는 이전 연구를 기반으로 합니다. 공구 회전 속도의 한계는 FSW 샘플에 대한 기계적 실험을 기반으로 200-500 RPM 범위로 유지하는 것이 권장되었습니다.

3. Introduction:

마찰교반용접(FSW) 공정은 많은 장점에도 불구하고 항상 결함 없는 접합부를 생성하지는 않습니다. 고품질 용접 접합부를 생산하기 위해 FSW 공정을 제어하는 것은 공구 회전/이송 속도와 같은 독립 변수, 힘과 토크 같은 종속 변수, 공구 재질, 공구 설계, 공작물 재료 및 두께 등 수많은 파라미터와 관련되어 있어 어려운 과제입니다. 알루미늄 및 강재 접합부의 FSW에서 보고된 결함 유형으로는 불충분한 열 입력 및 재료 유동 부족으로 인한 웜홀, 기공, 터널; 화학적 및 기계적 결합이 부족한 키싱 본드; 과도한 열 및 접촉 시간으로 인한 루트 스티킹; 불완전 용융 랩; 과도한 축 방향 힘으로 인한 플래시 형성 및 재료 얇아짐; 용접 루트 결함; 산화 등이 있습니다.

4. Summary of the study:

Background of the research topic:

강재의 마찰교반용접은 고품질 접합부를 얻을 수 있는 잠재력이 크지만, 부적절한 공정 파라미터는 다양한 결함을 유발하여 기계적 특성을 저하시킬 수 있습니다.

Status of previous research:

이전 연구들은 주로 웜홀, 키싱 본드 등 거시적 결함에 초점을 맞추었으며, 공정 단계 전환 시 발생하는 미세 결함이나 원소 석출에 의한 결함 형성 메커니즘에 대한 연구는 부족했습니다.

Purpose of the study:

본 연구의 목적은 DH36 및 EH46 강재의 마찰교반용접 시 공구 회전 속도와 이송 속도가 결함 형성에 미치는 영향을 규명하는 것입니다. 특히, 기존에 보고되지 않은 새로운 유형의 미세 결함을 식별하고 그 발생 원인을 분석하여 결함 없는 용접부를 얻기 위한 공정 조건을 제시하고자 합니다.

Core study:

다양한 용접 조건(Table 3)에서 FSW를 수행한 후, SEM, EDS, IFM을 사용하여 용접부의 미세 결함을 정밀하게 분석했습니다. 이를 통해 플런지-정상 상태 전환 구간에서의 미세균열과 교반 영역 내 TiN 석출물에 의한 미세균열이라는 두 가지 새로운 결함 유형을 발견하고, 각각의 발생 메커니즘을 공정 파라미터와 연관 지어 설명했습니다.

5. Research Methodology

Research Design:

두 종류의 강재(DH36, EH46)에 대해 공구 회전 속도와 이송 속도를 주요 변수로 설정하여 마찰교반용접을 수행했습니다. 용접된 시편은 종단 방향으로 절단하여 결함을 관찰했습니다.

Data Collection and Analysis Methods:

  • 결함 식별: SEM을 사용하여 미세조직 내 결함을 관찰하고, EDS를 통해 결함 부위의 원소 성분을 분석했습니다. IFM을 사용하여 결함의 3차원 형상과 크기를 측정했습니다.
  • 기계적 특성 평가: 인장 시험과 피로 시험을 통해 결함이 용접부의 강도와 내구성에 미치는 영향을 평가했습니다.

Research Topics and Scope:

연구는 DH36 및 EH46 강재의 마찰교반용접에 국한됩니다. 주요 연구 주제는 공구 회전 속도 및 이송 속도 변화에 따른 미세균열 및 기공 결함의 형성 메커니즘을 규명하는 것입니다. 특히 플런지-정상 상태 전환 구간과 교반 영역 내에서의 결함 발생에 초점을 맞췄습니다.

6. Key Results:

Key Results:

  • 플런지에서 정상 상태로 전환 시, 부적절하게 빠른 공구 이송 속도는 재료 유동 부족을 야기하여 용접부 상단에서 시작되는 미세균열을 유발했습니다 (W1D 샘플).
  • 높은 공구 회전 속도(550 RPM)는 용접부 온도를 1200°C 이상으로 상승시켜 교반 영역 내에 TiN 석출물을 형성시켰습니다. 이 석출물들은 응력 집중점으로 작용하여 미세균열을 발생시키는 원인이 되었습니다 (W2D 샘플).
  • 고속 이송 조건(400 mm/min)에서는 용접 루트 결함, 키싱 본드, 기공 등 다양한 거시적 결함도 관찰되었습니다 (W2D, W2E 샘플).
  • TiN 석출물에 의한 미세균열은 용접부의 피로 저항을 크게 감소시켰습니다 (W2D 샘플의 피로 수명은 W1D 대비 약 82% 감소).
  • 결함 방지를 위한 최적 공정 조건으로 공구 회전 속도 200-500 RPM, 최대 이송 속도 400 mm/min 미만, 그리고 점진적인 이송 속도 증가가 권장되었습니다.
Fig. 11 SEM images show microcracks caused by TiN precipitates
(exceeds 1 lm), FSW EH46 W2E SZ at steady state
Fig. 11 SEM images show microcracks caused by TiN precipitates (exceeds 1 μm), FSW EH46 W2E SZ at steady state

Figure List:

  • Fig. 1 Tensile and fatigue sample dimensions (in mm) according to EN-BS 895:1995 and BS 7270 standards [5]
  • Fig. 2 Microcrack started from the top surface of FSW DH36 W1D between steady state and the plunge regions. (a) low magnification, (b) high magnification. The sample was cut in the direction of the weld line
  • Fig. 3 Feed rate and the distance travelled by tool in the DH36 plates just before the steady state
  • Fig. 4 Microcracks inside the SZ. (a) Between plunge-steady state regions of FSW DH36 W2D (b) between plunge-steady state regions of FSW DH36 W2D. The sample was cut in the direction of the welding line
  • Fig. 5 Weld root and kissing bond in 6-mm FSW DH36 (W2D)
  • Fig. 6 SEM of the first and second defects of DH36 6-mm W2D shown in Fig. 5. (a) Weld root, (b) kissing bond
  • Fig. 7 Nonmetallic layer of (Fe, Mn, Si, Al and O) between the SZ and HAZ found in W2D, (a) 10 µm at plunge period, (b) 1.3 µm at steady state period
  • Fig. 8 A void found in EH46 steel W2E (steady state) in AS
  • Fig. 9 High amount of BN particles found near the void at AS, EH46 steel W2E (steady state)
  • Fig. 10 SEM of the SZ of DH36 W2D (a) microcrack caused by TiN particle, (b) microcrack caused by Al P S elemental precipitates
  • Fig. 11 SEM images show microcracks caused by TiN precipitates (exceeds 1 µm), FSW EH46 W2E SZ at steady state
  • Fig. 12 SEM-EDS shows elemental segregation of Mn, O and Si in the SZ of FSW DH36 at high tool speeds (W2D)

7. Conclusion:

결론적으로, DH36 및 EH46 강종의 FSW 공정과 관련된 결함이 연구되었습니다. DH36 W2D 및 EH46 W2E와 같이 높은 공구 이송 속도는 기공, 용접 루트 결함 및 키싱 본드와 같은 결함 형성을 유발하는 것으로 밝혀졌습니다. 정체 영역 형성으로 인한 재료 유동 부족이 이러한 결함의 주된 원인이었습니다. 플런지와 정상 상태 사이의 미세균열 또한 부적절한 공구 이송 속도 사용으로 인한 재료 유동 부족으로 발생한 결함의 예입니다. 또한 높은 공구 회전 속도가 500 RPM을 초과할 때 용접 온도가 1250°C 이상으로 증가함에 따라 FSW 접합부 미세조직에서도 결함이 발견되었습니다. 주로 TiN과 같은 원소 석출 및 Mn, Si, Al, O의 원소 편석이 그 결과였습니다. 이러한 원소 석출/편석은 미세균열 및 응력 집중 시작 지점을 유발하여 용접 접합부의 기계적 특성을 감소시킬 수 있습니다.

8. References:

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  2. K. Elangovan, V. Balasubramanian, Influences of pin profile and rotational speed of the tool on the formation of friction stir processing zone in AA2219 aluminium alloy. Mater. Sci. Eng. A 459(2007), 7-18 (2007)
  3. A.K. Lakshminarayanan, V. Balasubramanian, Understanding the parameters controlling friction stir welding of AISI 409 M ferritic stainless steel. Met. Mater. Int. 17(6), 969–998 (2011)
  4. R. Ruzek, M. Kadlec, Friction stir welded structures: kissing bond defects. Int. J. Terraspace Sci. Eng. 6(2), 77-83 (2014)
  5. S. Ryan, A. Toumpis, A. Galloway, Defect tolerance of friction stir welds in DH36 steel. Mater. Des. 87(15), 701-711 (2015)
  6. Y.G. Kim, H. Fujii, T. Tsumura, T. Komazaki, K. Nakata, Three defect types in friction stir welding of aluminum die casting alloy. Mater. Sci. Eng. A 415, 250-254 (2006)
  7. J.M. Seaman, B. Thompson, Challenges of friction stir welding of thick-section steel, in Proceedings of the Twenty-First International Offshore and Polar Engineering Conference, Maui, Hawaii, USA, 2011, 19-24 June 2011
  8. S. Cater, Forge welding turns full circle: friction stir welding of steel. Ironmak. Steelmak. 40(7), 490-495 (2013). https://doi.org/10.1179/0301923313Z.000000000224
  9. A. Toumpis, A. Gallawi, H. Polezhayeva, L. Molter, Fatigue assessment of friction stir welded DH36 steel. Frict. Stir Weld. Process. VIII, 11-19 (2015)
  10. D.M. Failla, Friction stir welding and microstructure simulation of HSLA-65 and austenitic stainless steels, Thesis, The Ohio State University, 2009
  11. C. Tingey, A. Galloway, A. Toumpis, S. Cater, Effect of tool centreline deviation on the mechanical properties of friction stir welded DH36 steel. Mater. Des. (1980-2015) 65, 896–906 (2015)
  12. A. Toumpis, A. Gallawi, S. Cater, N. McPherson, Development of a process envelope for friction stir welding of DH36 steel-a step change. Mater. Des. 62, 64-75 (2014)
  13. Y. Morisada, T. Imaizumi, H. Fujii, Clarification of material flow and defect formation during friction stir welding. Sci. Technol. Weld. Join. 20(2), 130–137 (2015)
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Expert Q&A: Your Top Questions Answered

Q1: 500 RPM 이하의 회전 속도를 권장하는 구체적인 이유는 무엇인가요?

A1: 본 연구에서 550 RPM(W2D 샘플)과 같이 높은 회전 속도를 사용했을 때, 교반 영역의 최고 온도가 TiN이 석출되는 임계 온도인 1200°C를 초과하는 것으로 나타났습니다. 이 TiN 석출물은 미세균열의 시작점으로 작용하여 용접부의 피로 저항을 심각하게 저하시켰습니다. 실제로 W2D 샘플의 평균 피로 파괴 사이클은 115,078회로, 낮은 속도로 용접된 W1D 샘플의 642,935회에 비해 현저히 낮았습니다. 따라서 원소 석출 및 편석을 방지하고 우수한 기계적 특성을 확보하기 위해 500 RPM 이하로 회전 속도를 제한할 것을 권장합니다.

Q2: 플런지-정상 상태 전환 구간의 미세균열(Figure 2)을 방지하기 위한 구체적인 공정 제어 방안은 무엇인가요?

A2: 이 미세균열은 불충분한 열 입력 상태에서 이송 속도가 급격히 증가하여 발생한 재료 유동 부족이 원인입니다. 논문에서는 이를 방지하기 위해, 플런지-정지 상태에서 정상 상태로 전환할 때 최대 이송 속도의 0.1 범위 내의 가속도로 최소 20mm 이상을 이동하며 점진적으로 속도를 높일 것을 제안합니다. 이렇게 하면 재료가 충분히 연화되고 유동할 시간을 확보하여 균열 발생을 억제할 수 있습니다.

Q3: W2D 샘플에서 발견된 비금속층(Figure 7)의 정체는 무엇이며, 왜 형성되었나요?

A3: SEM-EDS 분석 결과, 이 비금속층은 철(Fe), 망간(Mn), 규소(Si), 알루미늄(Al), 산소(O)로 구성되어 있었습니다. 이 층은 높은 공구 회전 속도로 인해 용접부 온도가 국부적인 용융점에 가까워지면서 발생한 원소 편석의 결과입니다. 공구의 원심력에 의해 이들 원소가 교반 영역(SZ)의 가장자리로 밀려나 SZ와 열영향부(HAZ) 사이 경계에 퇴적된 것입니다.

Q4: 키싱 본드(Figure 5, 6b)는 왜 문제가 되며, 어떻게 식별할 수 있나요?

A4: 키싱 본드는 접합면이 서로 맞닿아 있지만 화학적, 기계적 결합이 이루어지지 않은 상태의 결함입니다. 이는 용접부의 강도를 심각하게 저하시키는 원인이 됩니다. 가장 큰 문제는 초음파와 같은 일반적인 비파괴 검사로는 탐지가 매우 어렵다는 점입니다. 본 연구에서는 용접부를 절단하고 연마 및 에칭한 후 SEM으로 관찰하여 식별했습니다. 이는 키싱 본드 결함의 존재 가능성을 인지하고 정밀한 미세조직 검사를 수행해야 함을 시사합니다.

Q5: EH46 강재에서 발견된 기공(Figure 8) 근처에서 다량의 BN 입자가 발견된 이유는 무엇인가요?

A5: Figure 9에서 볼 수 있듯이, EH46 강재(W2E 샘플)의 기공 주변에서 다량의 BN(질화붕소) 입자가 발견되었습니다. 이 입자들은 PCBN 재질의 FSW 공구가 마모되면서 분리된 것입니다. 기공 형성의 주된 원인은 높은 이송 속도로 인한 재료 교반 부족이지만, 공구 마모 입자들이 결함 부위에 집중적으로 존재하는 것은 주목할 만한 현상입니다. 이는 공구 마모가 결함 형성에 간접적인 영향을 미칠 수 있음을 시사합니다.


Conclusion: Paving the Way for Higher Quality and Productivity

본 연구는 강재의 마찰교반용접 결함 발생 메커니즘에 대한 깊이 있는 통찰을 제공합니다. 특히 플런지-정상 상태 전환 시의 부적절한 가속도와 과도한 회전 속도로 인한 고온이 각각 새로운 유형의 미세균열을 유발할 수 있음을 실험적으로 증명했습니다. 이러한 발견은 단순히 학술적인 의미를 넘어, 공정 엔지니어가 결함을 사전에 방지하고 용접 품질을 획기적으로 개선할 수 있는 구체적이고 실용적인 가이드라인(회전 속도 500 RPM 이하 유지, 점진적 이송 속도 제어)을 제시합니다.

STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 돕는 데 전념하고 있습니다. 만약 본 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 부품에 어떻게 구현할 수 있는지 논의해 보십시오.

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Copyright Information

  • This content is a summary and analysis based on the paper “Defects in Friction Stir Welding of Steel” by “M. Al-Moussawi, A. J. Smith”.
  • Source: https://doi.org/10.1007/s13632-018-0438-1

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Fig. 93 Microstructure of Alloy 690 base material for sample CIEMAT SMAW.

원자력 발전소의 안전을 좌우하는 이종 금속 용접: 니켈 합금 용접부 미세구조 분석을 통한 파손 예측 및 방지

이 기술 요약은 Roman Mouginot와 Hannu Hänninen이 작성하여 Aalto University에서 2013년에 발표한 “Microstructures of nickel-base alloy dissimilar metal welds” 논문을 기반으로 합니다. STI C&D의 기술 전문가들이 분석하고 요약했습니다.

키워드

  • Primary Keyword: 이종 금속 용접 (Dissimilar Metal Welding)
  • Secondary Keywords: 니켈 합금(Nickel Alloy), Inconel, 저합금강(Low-Alloy Steel), 용접후열처리(PWHT), 응력 부식 균열(Stress Corrosion Cracking), 미세구조 분석(Microstructure Analysis), 용접부 경도(Weld Hardness)

Executive Summary

  • 도전 과제: 원자력 발전소와 같은 고온, 고압 환경의 이종 금속 용접(DMW) 부위는 용접 계면에서 발생하는 복잡한 야금학적 변화로 인해 응력 부식 균열 등 조기 파손에 취약합니다.
  • 연구 방법: 저합금강(LAS)과 니켈 기반 합금(Alloy 690)을 다양한 필러 금속(Inconel 52, 152, 52M)과 협개선 용접(NGW) 기술로 접합한 8개의 시편을 제작하여, 용접 상태(as-welded)와 용접후열처리(PWHT) 후의 미세구조 및 경도 변화를 분석했습니다.
  • 핵심 발견: 용접후열처리(PWHT)는 저합금강(LAS) 측의 탄소고갈영역(CDZ)을 약 10배 확장시키고, 용접 금속 내에 광범위한 크롬 카바이드(chromium carbide) 석출을 유발하여 용융선 근처에서 급격한 경도 피크를 형성하는 것으로 나타났습니다.
  • 핵심 결론: 극한 환경에서 사용되는 이종 금속 용접부의 장기적인 안전성과 신뢰성을 확보하기 위해서는 필러 금속의 종류와 용접후열처리(PWHT)가 미세구조 및 경도 프로파일에 미치는 영향을 정확히 이해하고 제어하는 것이 매우 중요합니다.
Fig. 8 Scheme of a RPV safe-end (a) and the four materials composing the DMW (b):
A- ferritic LAS SA508,
B- buttering alloy Inconel 82,
C- weld alloy Inconel 182,
D- austenitic stainless steel 316L or alloy Inconel 600. (Wang et al. 2011)
Fig. 8 Scheme of a RPV safe-end (a) and the four materials composing the DMW (b): A- ferritic LAS SA508, B- buttering alloy Inconel 82, C- weld alloy Inconel 182, D- austenitic stainless steel 316L or alloy Inconel 600. (Wang et al. 2011)

도전 과제: 왜 이 연구가 CFD 전문가에게 중요한가

원자력 발전소(NPP)의 배관 시스템은 비용 효율성과 고온 내식성을 동시에 만족시키기 위해 저합금강(LAS), 스테인리스강(SS), 니켈 기반 합금 등 다양한 재료를 함께 사용합니다. 이러한 서로 다른 금속을 연결하는 이종 금속 용접(DMW)은 필수적이지만, 구조적 완전성 측면에서 가장 취약한 지점이기도 합니다.

특히 용접 과정에서 발생하는 열 영향으로 인해 용접 열영향부(HAZ)에서는 잔류 응력, 탄소 이동, 예상치 못한 상(phase) 형성 등 복잡한 야금학적 변화가 일어납니다. 이러한 변화는 응력 부식 균열(SCC)과 같은 심각한 손상을 유발하여 부품의 조기 파손으로 이어질 수 있습니다. 최근에는 기존 Inconel 600 계열의 SCC 민감성 문제로 인해 크롬 함량이 높은 Alloy 690과 필러 금속 Inconel 52, 152, 52M이 새로운 대안으로 떠오르고 있습니다. 또한, 경제적인 후판 용접을 위해 협개선 용접(NGW) 기술이 도입되고 있습니다.

하지만 이러한 신소재와 신공법은 실제 운용 경험이 부족하여 장기적인 거동에 대한 데이터가 거의 없습니다. 따라서 이들 재료와 공법으로 제작된 용접부의 물리적, 구조적 특성을 사전에 정밀하게 분석하고 예측하는 것은 원자력 발전소의 안전성과 경제성을 확보하는 데 매우 중요합니다.

Fig. 16 Schematic illustration of four distinct microstructural zones existing in DMWs: fusion
zone (FZ), unmixed zone (UMZ), partially melted zone (PMZ) and heat affected zone (HAZ).
(DuPont et al. 2010)
Fig. 16 Schematic illustration of four distinct microstructural zones existing in DMWs: fusion zone (FZ), unmixed zone (UMZ), partially melted zone (PMZ) and heat affected zone (HAZ). (DuPont et al. 2010)

연구 접근법: 방법론 분석

본 연구는 광범위한 문헌 검토와 함께 실제적인 실험 분석을 병행하여 이종 금속 용접부의 특성을 규명했습니다. 연구진은 총 8개의 시편을 분석했으며, 이 중 2개는 프로젝트에서 직접 제작한 협개선 용접(DM-NGW) 모의 시편이고, 6개는 EPRI(전력 연구소)에서 제공한 모의 용접 시편입니다.

  • 주요 재료:
    • 모재(Base Metal): 원자로 압력용기(RPV) 노즐에 사용되는 저합금강 SA 508, SA 533 Gr.B와 내부식성이 뛰어난 니켈 기반 합금 Alloy 690.
    • 필러 금속(Filler Metal): 크롬 함량이 높은 Inconel 52, 152, 52M.
  • 주요 공정 및 조건:
    • 용접 기술: 최신 원자로 설계에 적용되는 협개선 GTAW(NG-GTAW) 및 기존의 SMAW.
    • 열처리 조건: 용접된 상태 그대로(As-Welded, AW)와 실제 원자로 용접부에 적용되는 용접후열처리(Post-Weld Heat Treatment, PWHT)를 거친 상태를 비교 분석했습니다.
  • 분석 방법:
    • 미세구조 분석: 광학 현미경(Optical Microscopy)을 사용하여 용접 계면, 열영향부(HAZ), 용접 금속의 결정립 크기, 상 분포, 석출물 형태 등을 관찰했습니다.
    • 경도 측정: 마이크로 경도(Microhardness) 및 나노 압입(Nanoindentation) 시험을 통해 용접부 단면의 위치별 기계적 특성 변화를 정밀하게 측정했습니다. 이를 통해 탄소 이동으로 인한 연화 및 경화 영역을 식별했습니다.

핵심 발견: 주요 결과 및 데이터

결과 1: 용접후열처리(PWHT)가 용접 계면의 미세구조와 경도를 극적으로 변화시킴

용접후열처리(PWHT)는 용접부의 잔류 응력을 완화하지만, 계면의 미세구조와 기계적 특성에 심각한 변화를 초래했습니다. 특히 SA 508(LAS)과 Inconel 52 필러 금속으로 제작된 협개선 용접 시편에서 이러한 변화가 뚜렷하게 나타났습니다.

  • 탄소고갈영역(CDZ) 확장: 용접 상태(AW) 시편에서는 LAS 측 용융선에 약 10-20 µm 폭의 좁은 탄소고갈영역(CDZ)이 관찰되었습니다. 하지만 PWHT를 거친 시편에서는 이 영역의 폭이 약 100 µm까지, 즉 5배에서 10배가량 넓어졌습니다. 이는 PWHT 중 고온에서 LAS의 탄소가 크롬 친화력이 높은 Inconel 52 측으로 확산되었기 때문입니다.
  • 경도 피크 형성: 가장 주목할 만한 결과는 경도 변화입니다. AW 시편의 용접 금속 경도는 약 210-220 HV로 비교적 균일했으나, PWHT 시편에서는 용융선으로부터 약 50 µm 떨어진 Inconel 52 용접 금속 내에서 경도가 최대 340 HV까지 급증하는 날카로운 피크가 형성되었습니다(그림 80 참조). 이는 확산된 탄소가 크롬과 결합하여 미세한 크롬 카바이드(chromium carbide)를 광범위하게 석출시켜 조직을 경화시켰기 때문입니다. 이 경화된 영역은 균열 발생의 시작점이 될 수 있습니다.

결과 2: 필러 금속의 종류가 용접부 특성에 결정적인 영향을 미침

다양한 필러 금속을 사용한 시편들을 비교한 결과, 필러 금속의 미세한 조성 차이가 용접부의 최종 경도와 탄소 이동 거동에 큰 차이를 만드는 것으로 확인되었습니다.

  • 경도 차이: Alloy 690 모재를 용접했을 때, Inconel 52M 필러 금속의 평균 경도가 약 250 HV로 가장 높았고, Inconel 152(SMAW)가 약 224 HV, Inconel 52(GTAW)가 약 207 HV 순으로 나타났습니다. Inconel 52M의 높은 경도는 더 미세한 덴드라이트 구조와 합금 원소 함량 차이에 기인합니다.
  • 탄소 이동 거동: MHI 시편(SA508/Inconel 152)에서는 용융선에 넓고 어둡게 식각된 탄소 농화대(carbon-enriched zone)가 다수 관찰되었습니다. 이는 Inconel 152가 Inconel 52보다 탄소 확산에 대한 저항이 커서, 탄소가 용접 금속 깊이 퍼지지 못하고 용융선 근처에 집중적으로 축적되었음을 시사합니다. 이러한 불균일한 탄소 농화대는 예측 불가능한 국부적 취성을 유발할 수 있습니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 PWHT가 잔류 응력 완화라는 긍정적 효과와 함께, 계면에 연성(CDZ) 및 취성(카바이드 석출) 영역을 동시에 생성하는 양면성을 가짐을 보여줍니다. 이는 PWHT의 온도와 유지 시간을 정밀하게 제어하여 두 효과 사이의 최적점을 찾는 것이 용접부 품질 확보에 매우 중요함을 의미합니다.
  • 품질 관리팀: PWHT 후 Inconel 52 용접 금속에서 관찰된 최대 340 HV의 날카로운 경도 피크(그림 80)는 잠재적인 취화 영역을 나타내는 핵심 지표입니다. 따라서 용접부의 품질을 평가할 때, 모재나 용접 금속 중앙부뿐만 아니라 용융선 직교 방향으로 미세 경도 프로파일을 측정하여 이러한 국부적인 경도 이상을 확인하는 절차가 반드시 포함되어야 합니다.
  • 설계 엔지니어: 필러 금속(52, 152, 52M)에 따라 탄소 이동 거동과 최종 경도 분포가 크게 달라진다는 사실은 설계 단계에서부터 재료 선택이 매우 중요함을 시사합니다. 특히 Inconel 152에서 관찰된 불균일한 탄소 농화대는 장기적인 구조 건전성 측면에서 잠재적 위험 요소가 될 수 있으므로, 설계 시 이를 고려해야 합니다.

논문 상세 정보


Microstructures of nickel-base alloy dissimilar metal welds

1. 개요:

  • 제목: Microstructures of nickel-base alloy dissimilar metal welds
  • 저자: Roman Mouginot and Hannu Hänninen
  • 발행 연도: 2013
  • 발행 학술지/기관: Aalto University publication series, SCIENCE + TECHNOLOGY 5/2013
  • 키워드: Dissimilar metal weld, nuclear power plant, Alloy 690, Inconel 52, Inconel 152, Inconel 52M, SA 508, SA 533 Gr.B, narrow gap weld, safe-end, interface, metallurgical changes, hardness.

2. 초록:

저합금강(LAS), 스테인리스강(SS), 니켈 기반 합금 간의 이종 금속 용접(DMW)은 재래식 및 원자력 발전소(NPP) 설계에 매우 중요합니다. 이 용접은 고온 환경에서 더 나은 성능을 달성하는 데 도움을 주지만, 부품의 조기 파손을 유발할 수 있습니다. 파손은 종종 모재의 열영향부(HAZ) 균열과 관련이 있습니다. 본 연구에서는 원자력 분야 적용을 위한 Inconel 니켈 기반 합금 및 LAS의 DMW 내 거동에 대한 문헌 검토를 수행했습니다. 연구는 용접후열처리(PWHT) 시 페라이트/오스테나이트 DMW 계면에서 발생하는 야금학적 변화, Inconel 필러 금속의 용접성, 그리고 NPP 설계에 새롭게 등장하는 협개선 용접(NGW) 기술에 중점을 두었습니다. 목표는 현대 가압수형 원자로(PWR) 설계에 존재하는 NGW를 특성화하는 것이었습니다. 이 설계는 Inconel 필러 금속을 사용하여 원자로 압력용기 노즐과 세이프-엔드를 접합합니다. 또한, Alloy 690의 거동도 연구되었습니다. 총 8개의 시편이 특성화되었습니다. SINI 프로젝트에서 제작된 협개선 Alloy 52 모의 시편은 용접 상태와 PWHT 후 상태로 연구되었습니다. 그 결과 PWHT는 LAS 측의 탄소 고갈을 증가시키고 용접 금속 내에 광범위한 크롬 카바이드 석출을 유발했으며, 이는 용접 금속의 날카로운 경도 피크의 원인이었습니다. EPRI(전력 연구소)로부터 제공받은 시편들은 ENVIS 프로젝트를 위해 특성화되었으며, 다른 용접 구성을 보여주었습니다.

3. 서론:

원자력 공학에서 용접은 시간과 비용이 많이 소요되는 분야이며, 원자력 안전과 전체 공정의 경제적 실행 가능성에 근본적인 영향을 미칩니다. 운전 경험에 따르면 부품의 수명은 용접부의 거동에 의해 좌우되며, 조기 파손은 용접이 구조 건전성에 미치는 해로운 영향을 나타냅니다. 특히 탄소강, 스테인리스강, 니켈 기반 합금 및 오버레이 용접을 포함하는 다양한 접합부 때문에 이종 금속 용접(DMW)이 주요 관심사입니다. DMW를 사용하면 고온, 부식 환경 및 고압이 요구되는 응용 분야에서 더 나은 성능을 충족시키면서 부품의 건설 비용을 절감할 수 있습니다. 그러나 DMW는 제작 및 야금학적 문제가 있으며, 이는 기존의 용접 문제와 서로 다른 특성을 가진 재료 간의 상호 작용을 모두 포함합니다. 이는 운전 중 파손으로 이어질 수 있습니다. 본 연구는 새로운 재료를 위한 이종 금속 접합부의 측정, 평가 및 설계를 위한 신뢰할 수 있는 연구 방법을 개발하는 것을 주된 목표로 하는 SINI 프로젝트의 일부입니다.

4. 연구 요약:

연구 주제의 배경:

원자력 발전소의 안전성과 경제성은 다양한 재료를 접합하는 이종 금속 용접(DMW)의 신뢰성에 크게 의존합니다. 특히 원자로 압력용기(RPV) 노즐과 배관을 연결하는 부위는 고온, 고압, 부식성 환경에 노출되어 응력 부식 균열(SCC)과 같은 손상에 매우 취약합니다. 기존에 사용되던 Inconel 600 계열 합금의 SCC 문제로 인해, 최근에는 내식성이 향상된 Alloy 690과 고크롬 필러 금속(Inconel 52, 152, 52M)이 도입되고 있으며, 경제적인 후판 용접을 위해 협개선 용접(NGW) 기술이 적용되고 있습니다.

이전 연구 현황:

과거 연구들은 주로 Inconel 600 계열 합금의 SCC 거동에 초점을 맞추어 왔습니다. 또한, 페라이트계 강과 오스테나이트계 강 사이의 DMW에서 발생하는 탄소 이동 및 그로 인한 계면의 경화/연화 현상에 대한 연구가 다수 수행되었습니다. 그러나 새로운 소재인 Alloy 690 및 고크롬 필러 금속, 그리고 NGW 공법이 적용된 DMW에 대한 장기 운전 데이터나 체계적인 미세구조 연구는 아직 부족한 실정입니다.

연구 목적:

본 연구의 목적은 최신 원자력 발전소 설계에 적용되는 새로운 DMW의 미세구조적 특성을 규명하는 것입니다. 구체적으로, (1) 용접후열처리(PWHT)가 LAS/니켈 합금 계면의 야금학적 변화(탄소 이동, 석출물 형성 등)에 미치는 영향을 분석하고, (2) 다양한 Inconel 필러 금속(52, 152, 52M)의 용접성과 거동 차이를 비교하며, (3) 다양한 제조 공법(압연, 단조, 압출)에 따른 Alloy 690 모재의 미세구조적 특징을 파악하는 것입니다. 이를 통해 신소재 및 신공법 DMW의 잠재적 파손 메커니즘을 이해하고 구조 건전성을 평가하기 위한 기초 자료를 제공하고자 합니다.

핵심 연구:

본 연구의 핵심은 실제 원자력 발전소 환경을 모사한 다양한 DMW 시편에 대한 상세한 미세구조 및 기계적 특성 분석입니다. 특히, PWHT 전후의 협개선 용접(NGW) 시편 비교를 통해 열처리가 계면 특성에 미치는 영향을 정량적으로 평가했습니다. 또한, 여러 종류의 필러 금속과 모재 조합으로 구성된 시편들을 비교 분석하여, 각 재료가 최종 용접부 품질에 어떻게 기여하는지를 밝혔습니다. 광학 현미경 관찰과 마이크로/나노 경도 측정을 통해 얻은 데이터를 종합하여, 용접부의 위치별 특성 변화와 잠재적 취약 영역을 식별했습니다.

5. 연구 방법론

연구 설계:

본 연구는 실제 원자력 발전소에 사용되는 다양한 이종 금속 용접(DMW) 구성을 대표하는 8개의 시편을 대상으로 비교 분석하는 방식으로 설계되었습니다. 특히, 용접후열처리(PWHT)의 영향을 파악하기 위해 동일한 협개선 용접(NGW) 시편을 용접 상태(AW)와 열처리 후(HT) 상태로 나누어 특성을 비교했습니다. 또한, 필러 금속(Inconel 52, 152, 52M), 모재(SA508, SA533 Gr.B, Alloy 690), 용접 공정(GTAW, SMAW, NGW) 등 다양한 변수가 조합된 시편들을 분석하여 각 요소가 용접부 특성에 미치는 영향을 체계적으로 평가했습니다.

데이터 수집 및 분석 방법:

데이터는 주로 시편의 단면을 관찰하고 측정하는 방식으로 수집되었습니다. 1. 시편 준비: 모든 시편을 절단, 마운팅, 연마 및 에칭하여 미세구조를 관찰할 수 있도록 준비했습니다. LAS 조직을 위해서는 2% 나이탈(Nital) 용액을, Inconel 합금 및 스테인리스강 조직을 위해서는 왕수(aqua regia)를 사용했습니다. 2. 미세구조 분석: Nikon Epiphot 200 광학 현미경과 NIS-Elements F.2.30 이미지 분석 소프트웨어를 사용하여 각 시편의 용접 계면, 열영향부(HAZ), 용접 금속의 결정립 크기, 상 분포, 석출물 형태 등을 관찰하고 기록했습니다. 3. 경도 측정: Buehler Micromet 2104 마이크로 경도 시험기를 사용하여 용접부 단면을 가로지르는 경도 프로파일을 측정했습니다. 이를 통해 HAZ의 경화, CDZ의 연화, 용접 금속 내 경도 변화 등 국부적인 기계적 특성을 평가했습니다. 일부 시편에 대해서는 CSM Instruments 나노 압입 시험기를 사용하여 더 미세한 영역의 경도 변화를 분석했습니다.

연구 주제 및 범위:

본 연구는 니켈 기반 합금을 사용한 이종 금속 용접부의 미세구조적 특성에 초점을 맞춥니다. 연구 범위는 다음과 같습니다. – 페라이트/오스테나이트 계면 분석: 저합금강(LAS)과 니켈 기반 합금 필러 금속 사이의 계면에서 발생하는 현상(탄소고갈영역(CDZ), 탄소 농화, 석출, Type II 경계 형성 등)을 PWHT 전후로 비교 분석합니다. – 필러 금속 비교: Inconel 52, 152, 52M 필러 금속으로 제작된 용접부의 미세구조와 경도 특성을 비교하여 각 필러 금속의 거동 차이를 규명합니다. – Alloy 690 모재 분석: 열간 압연, 단조, 압출 등 다양한 제조 공법으로 생산된 Alloy 690 모재의 미세구조(결정립 크기, 카바이드 밴딩 등)를 분석하고, 용접 시 열영향부(HAZ)의 변화를 관찰합니다.

6. 주요 결과:

주요 결과:

  • 용접후열처리(PWHT)의 영향: PWHT는 SA508(LAS) 측의 탄소고갈영역(CDZ) 폭을 용접 상태(as-welded) 대비 약 10배 증가시켰습니다. 동시에, Inconel 52 용접 금속의 용융선 근처에 광범위한 크롬 카바이드 석출을 유발하여 최대 340 HV에 달하는 급격한 경도 피크를 형성했습니다.
  • 필러 금속별 경도 차이: 용접 금속의 평균 경도는 Inconel 52M(약 250 HV)이 가장 높았으며, Inconel 152(약 224-239 HV), Inconel 52(약 207-220 HV) 순으로 나타났습니다. 이는 Inconel 52M의 미세한 조직과 높은 합금 원소 함량에 기인합니다.
  • 필러 금속별 탄소 이동 거동: Inconel 152를 사용한 용접부의 용융선에서는 국부적인 탄소 농화대(martensitic layer)가 관찰된 반면, Inconel 52에서는 이러한 현상이 덜 뚜렷했습니다. 이는 Inconel 152가 Inconel 52보다 탄소 확산에 대한 저항이 클 수 있음을 시사합니다.
  • Alloy 690의 미세구조: Alloy 690의 미세구조는 제조 이력에 크게 의존했습니다. 압연 및 단조재에서는 불균일한 결정립과 카바이드 밴딩이 관찰되었으나, 압출재에서는 밴딩 없이 가장 균일한 미세구조를 보였습니다.
  • Alloy 690 열영향부(HAZ) 특성: Alloy 690의 HAZ에서는 뚜렷한 결정립 미세화 영역 없이 용융선 근처에서 결정립 성장이 관찰되었습니다. 경도는 모재(약 180-200 HV)에서 용융선 방향으로 갈수록 약 40-70 HV 증가했으며, 이는 잔류 변형의 영향으로 분석됩니다.
Fig. 93 Microstructure of Alloy 690 base material for sample CIEMAT SMAW.
Fig. 93 Microstructure of Alloy 690 base material for sample CIEMAT SMAW.

Figure 목록:

  • Fig. 1 Cut of a nuclear reactor and main constituents. Of major importance are the RPV nozzles by which enters and leaves the coolant.
  • Fig. 2 Difference of principle between BWR and PWR. In BWR, the water heated in the RPV directly enters the turbine. In PWR, it is used to heat a secondary circuit.
  • Fig. 3 Cut of the EPR design.
  • Fig. 4 Material selection for BWR.
  • Fig. 5 Material selection for PWR.
  • Fig. 6 Material selection depending on the constructor.
  • Fig. 7 Main materials in LWRs: carbon steels, LAS, austenitic SS and Ni-base alloys.
  • Fig. 8 Scheme of a RPV safe-end (a) and the four materials composing the DMW (b): A- ferritic LAS SA508, B- buttering alloy Inconel 82, C- weld alloy Inconel 182, D- austenitic stainless steel 316L or alloy Inconel 600.
  • Fig. 9 LAS compositions for nuclear applications. Among them, it is worth noting SA 302 B, SA 508 CL.2 and SA 533 Gr.B.
  • Fig. 10 Austenitic SS grades, among which the common grades 304L and 316L. Incoloy 800 is given as a comparison.
  • Fig. 11 Composition of Inconel 600 and Alloy 690. Alloy 690 has higher Cr and Fe contents.
  • Fig. 12 Composition of Ni-base filler metals. Inconel 52,152 and 52M have higher Cr and Fe contents. Inconel 52M has additions of boron and zirconium.
  • Fig. 13 Mechanical properties of Ni-base filler metals, at room temperature and usual in service temperature.
  • Fig. 14 Composition of some high-strength alloys, among which Inconel 718 and X-750.
  • Fig. 15 Typical DMW designs in NPPs. The second is usual for a weld between a RPV nozzle and its safe-end.
  • Fig. 16 Schematic illustration of four distinct microstructural zones existing in DMWs: fusion zone (FZ), unmixed zone (UMZ), partially melted zone (PMZ) and heat affected zone (HAZ).
  • Fig. 17 Optical and SEM image of UMZ at the interface between A36 HAZ and 308L weld metal.
  • Fig. 18 Illustration showing the correlation between the various zones in a fusion weld in an alloy and the corresponding equilibrium phase diagram.
  • Fig. 19 Epitaxial grain growth mechanism for a homogeneous weld. The continuity across the fusion line is clearly visible.
  • Fig. 20 Geometrical comparison between NGW and conventional welding. Optimized NGW reduces greatly the amount of weld metal.
  • Fig. 21 Reduction of the weld volume using GTA-NGW as compared to a conventional weld. The reduction is of about four times.
  • Fig. 22 Cross-section of a RPV nozzle and safe-end in a BWR
  • Fig. 23 Closer view of the weld between the RPV nozzle and the safe-end. It presents the LAS of the RPV and its SS cladding, the Ni-base buttering, the Ni-base weld metal (Ni-Fe-Cr alloys) and the austenitic SS of the safe-end.
  • Fig. 24 Mock-up weld representing a usual weld between the ferritic LAS (SA508-3) of a RPV nozzle and the austenitic SS (SS316) of its safe-end, using Ni-base alloys as buttering and weld metals (respectively, Inconel 82 and 182).
  • Fig. 25 Microstructures of SA508 Cl.3
  • Fig. 26 HAZ microstructure of SA508 Cl.1 for an Inconel 182/SA508 Cl.1 interface: a) Global view showing grain refining then grain coarsening when moving to the fusion line. b) Grain coarsening area and carbon-depleted layer along the fusion line.
  • Fig. 27 As-welded interface between 9Cr-1Mo/2,25Cr-1Mo steels: a) Microstructure of the weld interface, b) Hardness profile taken across the weld interface.
  • Fig. 28 Post-weld heat treated interface between 9Cr-1Mo/2,25Cr-1Mo steels: a) Microstructure of the weld interface, b) Hardness profile taken across the weld interface.
  • Fig. 29 Micrograph showing Type II boundaries adjacent to the weld interface of an Alloy 52/SA508 weld.
  • Fig. 30 Calculated Ms temperature profile across the weld interface of Inconel 52/SA508 weld.
  • Fig. 31 Hardness peak due to a martensitic layer close to the LAS/Inconel 182 interface, and influence of PWHT.
  • Fig. 32 Simulated effect of a pure Ni buttering layer on the carbon concentration profile at the 9Cr-1Mo/2,25Cr-1Mo weld interface: a) without buttering layer and b) with a simulated Ni buttering layer. PWHT at 1023 K has been applied for 15 h.
  • Fig. 33 Microstructure of Inconel 82 weld metal: (a) weld metal and (b) interior of weld with higher magnification.
  • Fig. 34 a) Optical and b) SEM microstructure of Alloy 690, showing fine dispersed carbides and coarse TiN compounds.
  • Fig. 35 Longitudinal sections of a) an Alloy 690 billet and b) an Alloy 690 plate showing carbide banding.
  • Fig. 36 Grain size banding and isolated coarse grains in an Alloy 690 billet.
  • Fig. 37 Carbide morphology of Alloy 690 a) solution annealed at 1150°C for 1 h, b) solution annealed at 1150°C for 1 h then thermally treated 700°C for 1 h, c) as-received and d) solution annealed at 1150°C for 1 h then thermally treated at 800°C for 1 h.
  • Fig. 38 UMZ at the austenitic SS 304/Inconel 625 interface.
  • Fig. 39 Weld interfaces with weld metal Inconel 82 and base metals a) Inconel 657 and b) 310 SS.
  • Fig. 40 HAZ of SS 304 with formation of Type II boundaries at the interface with Inconel 625 weld metal.
  • Fig. 41 Alloy 690 interfaces between base material, HAZ, PMZ+UMZ and weld metal, based on grain size transition and carbide precipitation.
  • Fig. 42 Graph showing the SCC behavior of Alloy 690 base material, HAZ and weld metals Inconel 52, 152 in PWR water. Cracks can grow under certain conditions.
  • Fig. 43 Alloy 690 plate with planar banding and samples for mechanical testing with different orientation. They present, thus, different microstructures and SCC behavior.
  • Fig. 44 Map of the several zones at an Alloy 690/Inconel 52 weld interface and the corresponding residual strain measurement. Residual strains increase in the UMZ+PMZ of Alloy 690. The higher residual strains are found in the weld metal.
  • Fig. 45 SEM image of a) carbide precipitation at GB in the HAZ of a GTAW Alloy 690 weld, with b) and c) the EDS analysis for the GBs and the grain interior, respectively.
  • Fig. 46 a) Optical microstructure of heat-treated Alloy 690 and b) corresponding Cr-carbide precipitation at GBs. The extent of precipitation is much lower for coherent twins.
  • Fig. 47 Grain boundary network of Alloy 690 with a) GBE and b) non-GBE. See the grain clusters in the GBE alloy.
  • Fig. 50 Views of the Alloy 52 mock-up weld manufacturing, with a) the two base metal plates, b) the NG-GTAW welding torch in process (note the leading camera needed to see inside the groove) and c) the final weld.
  • Fig. 51 Cross-section of the NG-GTAW weld. It has been etched to reveal better the macrostructure: materials, weld passes in Inconel 52 weld metal and HAZ of SA508 and SS304.
  • Fig. 52 Cycle of temperatures for the post-weld heat treatment done on the Alloy 52 mock-up sample.
  • Fig. 53 Cutting of the samples from the cross-section of the AW Alloy 52 mock-up.
  • Fig. 54 Cutting of the samples from the HT cross-section.
  • Fig. 55 Weld design for the CIEMAT samples: two Alloy 690 plates welded with a half-V groove. The weld metal is either Inconel 52 or 152, and the welding technique is either GTAW or SMAW, respectively.
  • Fig. 56 Views of the sample CIEMAT GTAW: a) broad weld from above and b) the sample which is a transversal cut of the weld.
  • Fig. 57 Views of the sample CIEMAT SMAW: a) broad weld from above and b) the final sample that has been cut transverse from the weld.
  • Fig. 58 Global view of the weld, showing the SA508 plate (dark), the weld metal and the Alloy 690 plate (arrows mark the interface between Inconel 152 weld metal and Alloy 690 base metal).
  • Fig. 59 MHI plate sample. Cross-section of the weldment. It has been etched to reveal the macrostructure: SA508, weld-passes in Inconel 152, Alloy 690.
  • Fig. 60 Global view of the GTAW 19508A weld, showing the two plates and the weld overlay.
  • Fig. 61 GTAW 19508A sample, cut from a cross-section of the weldment: a) the sample has been etched to reveal the weld passes corresponding to b) the scheme of the weld passes.
  • Fig. 62 Welding parameters for the GTAW 19508A sample.
  • Fig. 63 Views of the ENSA weld mock-up with a) schematic of the grooves and components, b) view of the broad sample, c) view of the weld polished and etched and d) schematic of the weld passes.
  • Fig. 64 View of the sample cut from the weld and prepared for characterization.
  • Fig. 65 Views of the sample PG&E mock-up with a) broad sample showing the Alloy 690 pipe inside the LAS SA533 GrB plate with the SS 308L cladding, b) the sample cut in half, c) a closer view of the sample cut in four showing Inconel 52M weld metal and d) the sample cut, polished and etched.
  • Fig. 66 Microstructures of the SA508 HAZ and base material: A) Grain coarsening, B) grain refining, C) partial grain refining and D) base material.
  • Fig. 67 Microstructure of the SA508/Inconel 52 fusion line, with: a) CDZ in the LAS side, b) a layer free of precipitates on the weld metal side along the fusion line and c) a possible Type II boundary.
  • Fig. 68 Weld metal Inconel 52.
  • Fig. 69 Microstructure of the Inconel 52 weld metal, with: a) global view of the columnar dendrite grains, b) primary arm spacing and c) a closer view.
  • Fig. 70 Hardness profile across the sample. The hardness increases progressively in the LAS HAZ due to grain refining.
  • Fig. 71 Hardness profile across the fusion line.
  • Fig. 72 Microscopic view of second line loadings, and the position of the X = -0,05 mm loading near the fusion line.
  • Fig. 73 Nanohardness profile across SA508/Inconel 52 interface.
  • Fig. 74 View of the indentation across the CDZ in the LAS SA508 side of the weld (dark-etched).
  • Fig. 75 Global view of the HT LAS microstructure: A) grain coarsening, B) grain refining, C) partial grain refining and D) base material.
  • Fig. 76 Microstructure of the PWHT SA508/Inconel 52 interface: a) CDZ on the SA508 side and the dark etched fusion line, b) Inconel 52 weld metal along the fusion line, c) extensive precipitation in the weld metal close to the fusion line and d) a Type II boundary.
  • Fig. 77 Global view of the Inconel 52 weld metal after PWHT.
  • Fig. 78 Microstructures of Inconel 52 weld metal after PWHT: a) several grains, b) close view of the cellular structure and c) close view of a solidification GB.
  • Fig. 79 Microhardness profile across the HT SA508/Inconel 52 interface and the corresponding indentations.
  • Fig. 80 Microhardness profile across the PWHT SA508/Inconel 52 interface and the corresponding view of the indentations.
  • Fig. 81 Nanohardness profile from the fusion line in the Inconel 52 weld. No hardness peak is visible.
  • Fig. 82 Nanoindentations in Inconel 52 weld metal across the precipitates.
  • Fig. 83 Global view of the Alloy 690/Inconel 52 interface.
  • Fig. 84 Microstructure of Alloy 690 base material, with twin boundaries, fine carbide precipitates and golden TiN particles.
  • Fig. 85 Microstructure of Alloy 690 HAZ near the fusion line.
  • Fig. 86 Carbide banding in Alloy 690 plate.
  • Fig. 87 Closer view of carbide banding.
  • Fig. 88 Alloy 690/ Inconel 52 weld metal interface with epitaxial growth of the weld metal grains.
  • Fig. 89 Weld passes in Inconel 52 weld metal.
  • Fig. 90 Columnar dendrites in the Inconel 52 weld metal.
  • Fig. 91 Hardness map of the samples.
  • Fig. 92 Weld passes in the Inconel 152 weld metal.
  • Fig. 93 Microstructure of Alloy 690 base material for sample CIEMAT SMAW.
  • Fig. 94 Fusion line between Alloy 690 and Inconel 152.
  • Fig. 95 Closer view of the precipitation occurring in the dendritic microstructure of the Inconel 152 weld metal.
  • Fig. 96 Transition between two weld passes in Inconel 152 weld metal.
  • Fig. 97 Hardness map for the CIEMAT SMAW sample, showing hardness increase in the Alloy 690 from the base material to the fusion line.
  • Fig. 98 SA508 HAZ: a) grain coarsening, b) grain refining, c) partial grain refining and d) base material.
  • Fig. 99 SA508 side of the SA508/Inconel 152 interface with.
  • Fig. 100 Widmannstätten ferrite along the fusion line.
  • Fig. 101 Dark-etched carbon-enriched layer on the fusion line between SA508 and Inconel 152.
  • Fig. 102 Type II boundaries on the weld metal side of the SA508/Inconel 152 interface.
  • Fig. 103 Inconel 152/Alloy 690 interface.
  • Fig. 104 Hardness map of the Inconel 152/Alloy 690 side of the sample.
  • Fig. 105 Hardness profile across the SA508/Inconel 152 buttering and in the buttering layer.
  • Fig. 106 Microhardness profile across the SA508/Inconel 152 buttering layer.
  • Fig. 107 Banded microstructure in SA508 with dark- and light-etched bands.
  • Fig. 108 Hardness profile across several bands in SA 508 steel.
  • Fig. 109 Microstructure of the Alloy 690/Inconel 52M interface.
  • Fig. 110 HAZ of Alloy 690 at the fusion line with Inconel 52M weld metal.
  • Fig. 111 Alloy 690/Inconel 52M weld metal interface, showing the growth of the weld metal grains from those of the base metal.
  • Fig. 112 Inconel 52M weld metal microstructure.
  • Fig. 113 Hardness profile across the Alloy 690/Inconel 52M/Alloy 690 weld.
  • Fig. 114 Hardness profile in the Alloy 690 HAZ and at the fusion line with Inconel 52M.
  • Fig. 116 LAS HAZ with A) base material, B) partial grain refining, C) grain refining and D) grain coarsening along the fusion line.
  • Fig. 117 CDZ in the LAS side of the LAS/Inconel 52M buttering layer interface.
  • Fig. 118 a) Broad view, b) closer view of the LAS/Inconel 52 M buttering fusion lines and c) Type II boundary at 10 μm from the fusion line.
  • Fig. 119 Carbide banding in forged Alloy 690 plate.
  • Fig. 120 Very inhomogeneous microstructure in forged Alloy 690 plate.
  • Fig. 121 Schematic of the hardness measurements for the ENSA weld mock-up.
  • Fig. 122 Hardness measurement from location 1: across LAS, Inconel 52M buttering, Inconel 52 weld metal and Alloy 690 base metal.
  • Fig. 123 Hardness measurement from location 2: Alloy 690 HAZ and Inconel 52 NGW.
  • Fig. 124 Hardness measurement from location 3 and corresponding indentations: LAS HAZ and interface with Inconel 52M buttering.
  • Fig. 126 SA533 Gr.B HAZ with A) base material, B) partial grain refining, C) grain refining and D) grain coarsening.
  • Fig. 127 SA533 Gr.B / Inconel 52M buttering fusion line and the influence of LAS carbide banding.
  • Fig. 128 Inconel 52M buttering layer and interface with SA 533 Gr.B.
  • Fig. 129 Inconel 52M weld metal microstructure.
  • Fig. 130 Fusion line between the Inconel 52M weld metal, the LAS plate and the SS cladding.
  • Fig. 131 Comparison between the two Inconel 52M interfaces: A) with SS308L and B) with SA533 Gr.B.
  • Fig. 132 Global view of the extruded Inconel 690 pipe.
  • Fig. 133 Extruded Inconel 690 microstructure.
  • Fig. 134 Hardness profile across the PG&E sample.
  • Fig. 135 Hardness profile across the SA 533 Gr.B/Inconel 52M buttering interface.
  • Fig. 136 Hardness profile across the Inconel 52M weld metal and the interfaces with Inconel 52M buttering and Alloy 690 base metal.

7. 결론:

본 연구에서는 새로운 원자력 적용을 위한 니켈 기반 합금과 저합금강(LAS)의 이종 금속 용접(DMW) 거동에 대한 문헌 검토와 실험적 분석을 수행했다. 연구는 PWHT가 페라이트/오스테나이트 DMW 계면에 미치는 야금학적 변화, Inconel 필러 금속의 용접성, 그리고 NPP에서 사용되는 NG-GTAW 기술에 중점을 두었다. 총 8개의 시편을 특성화했으며, 특히 프로젝트에서 제작한 Alloy 52 모의 용접 시편을 용접 상태와 PWHT 후 상태로 비교 분석했다. 그 결과, PWHT는 LAS 측의 CDZ 폭을 증가시키고 용접 금속 내에 광범위한 크롬 카바이드 석출을 유발했으며, 이는 용융선 근처 용접 금속의 날카로운 경도 피크의 원인이었다. 또한, EPRI에서 제공한 시편 분석을 통해 Alloy 690 모재와 Inconel 52M, 52, 152 필러 금속의 다양한 조합에서의 거동 차이를 확인했다. Inconel 52M에서 가장 높은 경도가 관찰되었고, Inconel 152는 Inconel 52와 다른 탄소 이동 거동을 보였다. Alloy 690의 미세구조는 제품 형태에 따라 달라졌으며, 경도는 항상 모재에서 용융선으로 갈수록 증가했는데, 이는 잔류 변형 때문으로 보인다. 본 연구는 광학 현미경과 경도 측정을 통해 시편을 특성화하는 초기 단계이며, 향후 SEM, EBSD, EDS 분석 등을 통해 용접부의 거동을 더 깊이 이해할 필요가 있다.

8. 참고 문헌:

  1. Aalto University (2012) Kon-67.5100 Postgraduate Seminar on Engineering Materials, Otaniemi, March – April 2012.
  2. Ahluwalia K., King C. (2007) Materials reliability program: review of stress corrosion cracking of alloys 182 and 82 in PWR primary water service (MRP 220). Technical report 1007832. EPRI, Palo Alto, CA, October 2007.
  3. Akbari D, Farahani M, Soltani N. (2012) Effects of the weld groove shape and geometry on residual stresses in dissimilar butt-welded pipes. The Journal of Strain Analysis for Engineering Design. Vol. 47. 2. P. 73- 82.
  4. Albert S. K., Gill T. P. S., Tyagi A. K., Mannan S. L., Kulkami S. D., Rodriguez P. (1997) Soft zone formation in dissimilar welds between two Cr-Mo steels. Welding Journal. Vol. 76. 3. P. 135–142.
  5. Alexandrov B.T., Hope A.T., Sowards J.W., Lippold J.C. (2009) Weldability studies of high-Cr, Ni-base filler metals for power generation applications. IX 2313-09-Rev3.
  6. Anand R., Sudha C., Karthikeyan T., Terrance A.L.E., Saroja S., Vijayalakshmi M. (2008) Metal interlayers to prevent ‘hard zone’ formation in dissimilar weldments of Cr-Mo steels – A comparison between Cu, Co and Ni. Transactions of the Indian Institute of Metals. Vol. 61. P. 483-486.
  7. Andresen P., Morra M., Ahluwalia K. (2012) SCC of Alloy 690 and its weld metals. EPRI International BWR and PWR Materials Reliability Conference and Exhibit Show, National Harbor, Maryland, July 16-19. P. 321-361.
  8. ASTM E384 – 11e1. Standard test method for Knoop and Vickers hardness of materials. ICS number code 19.060.
  9. Bamford W., Hall J. (2005) Cracking of alloy 600 nozzle and welds in PWRs: review of cracking events and repair service experience. Proceedings of the 12th International Conference on Environmental Degradation of Materials in Nuclear Power System–Water Reactors–TMS, Salt Lake City, 2000. Eds. Allen T.R., King P.J., Nelson L. USA: The Minerals, Metals and Materials Society. P. 959– 965.
  10. Becker A.A., Hyde T.H., Sun W. (2001) Creep crack growth in welds: a damage mechanics approach to predicting initiation and growth of circumferential cracks. International Journal of Pressure Vessels and Piping. Vol. 78. P. 765-771.
  11. Biswas P., Mandal N.R., Vasu P., Padasalag S.B. (2010) Analysis of welding distortion due to narrow-gap welding of upper port plug. Fusion Engineering and Design. Vol. 85. P. 780–788.
  12. Boursier J., Vaillant F, Yrieix B. (2004) A review of PWSCC behavior of nickel weld metals containing 15 to 30% chromium. Proceedings of ASME/JSME
  13. (List continues for all references in the paper)

전문가 Q&A: 주요 질문과 답변

Q1: 연구에서 특히 협개선 용접(NGW) 모의 시편을 선택하여 분석한 이유는 무엇인가요?

A1: 협개선 용접(NGW)은 EPR과 같은 최신 원자력 발전소 설계에서 후판 부재를 용접하는 데 사용되는 경제적이고 효율적인 신기술이기 때문입니다. 하지만 새로운 기술인 만큼 실제 운용 데이터가 부족하여 장기적인 성능과 신뢰성에 대한 검증이 필요합니다. 따라서 본 연구에서는 이 중요한 기술로 제작된 용접부의 미세구조적 특성을 상세히 분석하여 잠재적인 문제점을 파악하고 안전성을 평가하기 위한 기초 자료를 확보하고자 했습니다.

Q2: 열처리된 Alloy 52 시편에서 340 HV에 달하는 높은 경도 피크가 관찰되었습니다. 정확한 야금학적 원인은 무엇이며, 이것이 왜 문제가 될 수 있나요?

A2: 이 경도 피크는 용접후열처리(PWHT) 과정에서 발생한 탄소 이동 현상 때문입니다. 상대적으로 탄소 함량이 높은 저합금강(SA 508)에서 탄소가 크롬 친화력이 높은 Inconel 52 용접 금속 쪽으로 확산됩니다. 이 탄소는 Inconel 52의 풍부한 크롬과 결합하여 용융선 근처에 미세한 크롬 카바이드(chromium carbide)를 대량으로 석출시킵니다. 이렇게 형성된 매우 단단하고 국부적인 경화층은 취성이 높아 응력이 집중될 경우 균열의 시작점으로 작용할 수 있어 용접부의 구조적 건전성을 저해하는 심각한 잠재적 결함이 될 수 있습니다.

Q3: 연구에서 Inconel 152가 Inconel 52와 다른 탄소 이동 거동을 보였다고 언급했는데, 구체적으로 어떤 차이가 있었나요?

A3: MHI 시편(SA508/Inconel 152)의 경우, 용융선에서 어둡게 식각되는 뚜렷한 탄소 농화대(carbon-enriched zone)가 관찰되었습니다. 이는 탄소가 용접 금속 내부로 넓게 확산되지 못하고 용융선 근처에 국부적으로 집중되었음을 의미합니다. 반면, Inconel 52 시편에서는 탄화물 석출이 좀 더 넓은 영역에 걸쳐 분포하는 경향을 보였습니다. 이는 Inconel 152가 Inconel 52보다 탄소의 확산을 더 효과적으로 억제할 수 있음을 시사하며, 이로 인해 더 불균일하고 예측하기 어려운 계면 특성을 가질 수 있습니다.

Q4: Alloy 690 모재가 제조 공법(압연, 단조, 압출)에 따라 다른 미세구조를 보이는 것이 왜 중요한가요?

A4: 미세구조의 균일성은 재료의 기계적 특성과 내식성에 직접적인 영향을 미치기 때문입니다. 연구 결과, 압출재는 카바이드 밴딩 없이 가장 균일한 미세구조를 보였습니다. 반면, 압연재나 단조재에서 관찰된 카바이드 밴딩과 같은 불균일한 조직은 국부적인 잔류 변형을 더 많이 축적시켜 응력 부식 균열(SCC)에 대한 민감도를 높일 수 있습니다. 따라서 중요한 부품을 설계하고 제작할 때, 단순히 ‘Alloy 690’이라는 재료명만 명시할 것이 아니라, 압출과 같은 특정 제조 공법을 지정하는 것이 재료의 신뢰성을 확보하는 데 매우 중요할 수 있습니다.

Q5: 열처리된 시편의 나노 압입 시험에서는 마이크로 경도 시험에서 나타났던 경도 피크가 관찰되지 않았습니다. 이러한 차이가 발생한 이유는 무엇인가요?

A5: 논문에서는 두 가지 가능성을 제시합니다. 첫째, 나노 압입 시험의 압입 크기가 경도 상승의 원인이 되는 미세한 카바이드 석출물들의 크기나 분포에 비해 너무 작아서 그 영향을 제대로 측정하지 못했을 수 있습니다. 둘째, 시편을 식각하는 데 사용된 왕수(aqua regia)가 용융선 근처의 화학 조성 변화로 인해 표면을 불균일하게 부식시켜, 깊이를 감지하는 나노 압입 시험 결과의 정확도에 영향을 미쳤을 가능성이 있습니다.


결론: 더 높은 품질과 생산성을 향한 길

이종 금속 용접부의 조기 파손 문제는 원자력 발전소와 같은 고신뢰성 산업에서 해결해야 할 핵심 과제입니다. 본 연구는 용접후열처리(PWHT)가 용접 계면에 미치는 극적인 영향을 명확히 보여주었습니다. 특히, 저합금강의 탄소 이동으로 인해 용접 금속 내에 형성되는 국부적인 고경도 영역은 균열 발생의 주요 원인이 될 수 있음을 데이터로 입증했습니다.

이러한 결과는 R&D 및 운영 현장에 중요한 시사점을 제공합니다. 공정 엔지니어는 PWHT 조건을 최적화해야 하며, 품질 관리팀은 용융선 부근의 미세 경도 변화를 핵심 관리 지표로 삼아야 합니다. 또한, 설계 엔지니어는 필러 금속의 종류와 모재의 제조 이력이 최종 용접부의 성능에 미치는 영향을 설계 초기 단계부터 고려해야 합니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

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저작권 정보

  • 이 콘텐츠는 Roman Mouginot와 Hannu Hänninen의 논문 “Microstructures of nickel-base alloy dissimilar metal welds”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: http://urn.fi/URN:ISBN:978-952-60-5066-9

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

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원자력 발전소의 안전을 좌우하는 이종 금속 용접: 니켈 합금 용접부 미세구조 분석을 통한 파손 예측 및 방지

이 기술 요약은 Roman Mouginot와 Hannu Hänninen이 작성하여 Aalto University에서 2013년에 발표한 “Microstructures of nickel-base alloy dissimilar metal welds” 논문을 기반으로 합니다. STI C&D의 기술 전문가들이 분석하고 요약했습니다.

키워드

  • Primary Keyword: 이종 금속 용접 (Dissimilar Metal Welding)
  • Secondary Keywords: 니켈 합금(Nickel Alloy), Inconel, 저합금강(Low-Alloy Steel), 용접후열처리(PWHT), 응력 부식 균열(Stress Corrosion Cracking), 미세구조 분석(Microstructure Analysis), 용접부 경도(Weld Hardness)

Executive Summary

  • 도전 과제: 원자력 발전소와 같은 고온, 고압 환경의 이종 금속 용접(DMW) 부위는 용접 계면에서 발생하는 복잡한 야금학적 변화로 인해 응력 부식 균열 등 조기 파손에 취약합니다.
  • 연구 방법: 저합금강(LAS)과 니켈 기반 합금(Alloy 690)을 다양한 필러 금속(Inconel 52, 152, 52M)과 협개선 용접(NGW) 기술로 접합한 8개의 시편을 제작하여, 용접 상태(as-welded)와 용접후열처리(PWHT) 후의 미세구조 및 경도 변화를 분석했습니다.
  • 핵심 발견: 용접후열처리(PWHT)는 저합금강(LAS) 측의 탄소고갈영역(CDZ)을 약 10배 확장시키고, 용접 금속 내에 광범위한 크롬 카바이드(chromium carbide) 석출을 유발하여 용융선 근처에서 급격한 경도 피크를 형성하는 것으로 나타났습니다.
  • 핵심 결론: 극한 환경에서 사용되는 이종 금속 용접부의 장기적인 안전성과 신뢰성을 확보하기 위해서는 필러 금속의 종류와 용접후열처리(PWHT)가 미세구조 및 경도 프로파일에 미치는 영향을 정확히 이해하고 제어하는 것이 매우 중요합니다.

도전 과제: 왜 이 연구가 CFD 전문가에게 중요한가

원자력 발전소(NPP)의 배관 시스템은 비용 효율성과 고온 내식성을 동시에 만족시키기 위해 저합금강(LAS), 스테인리스강(SS), 니켈 기반 합금 등 다양한 재료를 함께 사용합니다. 이러한 서로 다른 금속을 연결하는 이종 금속 용접(DMW)은 필수적이지만, 구조적 완전성 측면에서 가장 취약한 지점이기도 합니다.

특히 용접 과정에서 발생하는 열 영향으로 인해 용접 열영향부(HAZ)에서는 잔류 응력, 탄소 이동, 예상치 못한 상(phase) 형성 등 복잡한 야금학적 변화가 일어납니다. 이러한 변화는 응력 부식 균열(SCC)과 같은 심각한 손상을 유발하여 부품의 조기 파손으로 이어질 수 있습니다. 최근에는 기존 Inconel 600 계열의 SCC 민감성 문제로 인해 크롬 함량이 높은 Alloy 690과 필러 금속 Inconel 52, 152, 52M이 새로운 대안으로 떠오르고 있습니다. 또한, 경제적인 후판 용접을 위해 협개선 용접(NGW) 기술이 도입되고 있습니다.

하지만 이러한 신소재와 신공법은 실제 운용 경험이 부족하여 장기적인 거동에 대한 데이터가 거의 없습니다. 따라서 이들 재료와 공법으로 제작된 용접부의 물리적, 구조적 특성을 사전에 정밀하게 분석하고 예측하는 것은 원자력 발전소의 안전성과 경제성을 확보하는 데 매우 중요합니다.

연구 접근법: 방법론 분석

본 연구는 광범위한 문헌 검토와 함께 실제적인 실험 분석을 병행하여 이종 금속 용접부의 특성을 규명했습니다. 연구진은 총 8개의 시편을 분석했으며, 이 중 2개는 프로젝트에서 직접 제작한 협개선 용접(DM-NGW) 모의 시편이고, 6개는 EPRI(전력 연구소)에서 제공한 모의 용접 시편입니다.

  • 주요 재료:
    • 모재(Base Metal): 원자로 압력용기(RPV) 노즐에 사용되는 저합금강 SA 508, SA 533 Gr.B와 내부식성이 뛰어난 니켈 기반 합금 Alloy 690.
    • 필러 금속(Filler Metal): 크롬 함량이 높은 Inconel 52, 152, 52M.
  • 주요 공정 및 조건:
    • 용접 기술: 최신 원자로 설계에 적용되는 협개선 GTAW(NG-GTAW) 및 기존의 SMAW.
    • 열처리 조건: 용접된 상태 그대로(As-Welded, AW)와 실제 원자로 용접부에 적용되는 용접후열처리(Post-Weld Heat Treatment, PWHT)를 거친 상태를 비교 분석했습니다.
  • 분석 방법:
    • 미세구조 분석: 광학 현미경(Optical Microscopy)을 사용하여 용접 계면, 열영향부(HAZ), 용접 금속의 결정립 크기, 상 분포, 석출물 형태 등을 관찰했습니다.
    • 경도 측정: 마이크로 경도(Microhardness) 및 나노 압입(Nanoindentation) 시험을 통해 용접부 단면의 위치별 기계적 특성 변화를 정밀하게 측정했습니다. 이를 통해 탄소 이동으로 인한 연화 및 경화 영역을 식별했습니다.

핵심 발견: 주요 결과 및 데이터

결과 1: 용접후열처리(PWHT)가 용접 계면의 미세구조와 경도를 극적으로 변화시킴

용접후열처리(PWHT)는 용접부의 잔류 응력을 완화하지만, 계면의 미세구조와 기계적 특성에 심각한 변화를 초래했습니다. 특히 SA 508(LAS)과 Inconel 52 필러 금속으로 제작된 협개선 용접 시편에서 이러한 변화가 뚜렷하게 나타났습니다.

  • 탄소고갈영역(CDZ) 확장: 용접 상태(AW) 시편에서는 LAS 측 용융선에 약 10-20 µm 폭의 좁은 탄소고갈영역(CDZ)이 관찰되었습니다. 하지만 PWHT를 거친 시편에서는 이 영역의 폭이 약 100 µm까지, 즉 5배에서 10배가량 넓어졌습니다. 이는 PWHT 중 고온에서 LAS의 탄소가 크롬 친화력이 높은 Inconel 52 측으로 확산되었기 때문입니다.
  • 경도 피크 형성: 가장 주목할 만한 결과는 경도 변화입니다. AW 시편의 용접 금속 경도는 약 210-220 HV로 비교적 균일했으나, PWHT 시편에서는 용융선으로부터 약 50 µm 떨어진 Inconel 52 용접 금속 내에서 경도가 최대 340 HV까지 급증하는 날카로운 피크가 형성되었습니다(그림 80 참조). 이는 확산된 탄소가 크롬과 결합하여 미세한 크롬 카바이드(chromium carbide)를 광범위하게 석출시켜 조직을 경화시켰기 때문입니다. 이 경화된 영역은 균열 발생의 시작점이 될 수 있습니다.

결과 2: 필러 금속의 종류가 용접부 특성에 결정적인 영향을 미침

다양한 필러 금속을 사용한 시편들을 비교한 결과, 필러 금속의 미세한 조성 차이가 용접부의 최종 경도와 탄소 이동 거동에 큰 차이를 만드는 것으로 확인되었습니다.

  • 경도 차이: Alloy 690 모재를 용접했을 때, Inconel 52M 필러 금속의 평균 경도가 약 250 HV로 가장 높았고, Inconel 152(SMAW)가 약 224 HV, Inconel 52(GTAW)가 약 207 HV 순으로 나타났습니다. Inconel 52M의 높은 경도는 더 미세한 덴드라이트 구조와 합금 원소 함량 차이에 기인합니다.
  • 탄소 이동 거동: MHI 시편(SA508/Inconel 152)에서는 용융선에 넓고 어둡게 식각된 탄소 농화대(carbon-enriched zone)가 다수 관찰되었습니다. 이는 Inconel 152가 Inconel 52보다 탄소 확산에 대한 저항이 커서, 탄소가 용접 금속 깊이 퍼지지 못하고 용융선 근처에 집중적으로 축적되었음을 시사합니다. 이러한 불균일한 탄소 농화대는 예측 불가능한 국부적 취성을 유발할 수 있습니다.

R&D 및 운영을 위한 실질적 시사점

  • 공정 엔지니어: 본 연구는 PWHT가 잔류 응력 완화라는 긍정적 효과와 함께, 계면에 연성(CDZ) 및 취성(카바이드 석출) 영역을 동시에 생성하는 양면성을 가짐을 보여줍니다. 이는 PWHT의 온도와 유지 시간을 정밀하게 제어하여 두 효과 사이의 최적점을 찾는 것이 용접부 품질 확보에 매우 중요함을 의미합니다.
  • 품질 관리팀: PWHT 후 Inconel 52 용접 금속에서 관찰된 최대 340 HV의 날카로운 경도 피크(그림 80)는 잠재적인 취화 영역을 나타내는 핵심 지표입니다. 따라서 용접부의 품질을 평가할 때, 모재나 용접 금속 중앙부뿐만 아니라 용융선 직교 방향으로 미세 경도 프로파일을 측정하여 이러한 국부적인 경도 이상을 확인하는 절차가 반드시 포함되어야 합니다.
  • 설계 엔지니어: 필러 금속(52, 152, 52M)에 따라 탄소 이동 거동과 최종 경도 분포가 크게 달라진다는 사실은 설계 단계에서부터 재료 선택이 매우 중요함을 시사합니다. 특히 Inconel 152에서 관찰된 불균일한 탄소 농화대는 장기적인 구조 건전성 측면에서 잠재적 위험 요소가 될 수 있으므로, 설계 시 이를 고려해야 합니다.

논문 상세 정보


Microstructures of nickel-base alloy dissimilar metal welds

1. 개요:

  • 제목: Microstructures of nickel-base alloy dissimilar metal welds
  • 저자: Roman Mouginot and Hannu Hänninen
  • 발행 연도: 2013
  • 발행 학술지/기관: Aalto University publication series, SCIENCE + TECHNOLOGY 5/2013
  • 키워드: Dissimilar metal weld, nuclear power plant, Alloy 690, Inconel 52, Inconel 152, Inconel 52M, SA 508, SA 533 Gr.B, narrow gap weld, safe-end, interface, metallurgical changes, hardness.

2. 초록:

저합금강(LAS), 스테인리스강(SS), 니켈 기반 합금 간의 이종 금속 용접(DMW)은 재래식 및 원자력 발전소(NPP) 설계에 매우 중요합니다. 이 용접은 고온 환경에서 더 나은 성능을 달성하는 데 도움을 주지만, 부품의 조기 파손을 유발할 수 있습니다. 파손은 종종 모재의 열영향부(HAZ) 균열과 관련이 있습니다. 본 연구에서는 원자력 분야 적용을 위한 Inconel 니켈 기반 합금 및 LAS의 DMW 내 거동에 대한 문헌 검토를 수행했습니다. 연구는 용접후열처리(PWHT) 시 페라이트/오스테나이트 DMW 계면에서 발생하는 야금학적 변화, Inconel 필러 금속의 용접성, 그리고 NPP 설계에 새롭게 등장하는 협개선 용접(NGW) 기술에 중점을 두었습니다. 목표는 현대 가압수형 원자로(PWR) 설계에 존재하는 NGW를 특성화하는 것이었습니다. 이 설계는 Inconel 필러 금속을 사용하여 원자로 압력용기 노즐과 세이프-엔드를 접합합니다. 또한, Alloy 690의 거동도 연구되었습니다. 총 8개의 시편이 특성화되었습니다. SINI 프로젝트에서 제작된 협개선 Alloy 52 모의 시편은 용접 상태와 PWHT 후 상태로 연구되었습니다. 그 결과 PWHT는 LAS 측의 탄소 고갈을 증가시키고 용접 금속 내에 광범위한 크롬 카바이드 석출을 유발했으며, 이는 용접 금속의 날카로운 경도 피크의 원인이었습니다. EPRI(전력 연구소)로부터 제공받은 시편들은 ENVIS 프로젝트를 위해 특성화되었으며, 다른 용접 구성을 보여주었습니다.

3. 서론:

원자력 공학에서 용접은 시간과 비용이 많이 소요되는 분야이며, 원자력 안전과 전체 공정의 경제적 실행 가능성에 근본적인 영향을 미칩니다. 운전 경험에 따르면 부품의 수명은 용접부의 거동에 의해 좌우되며, 조기 파손은 용접이 구조 건전성에 미치는 해로운 영향을 나타냅니다. 특히 탄소강, 스테인리스강, 니켈 기반 합금 및 오버레이 용접을 포함하는 다양한 접합부 때문에 이종 금속 용접(DMW)이 주요 관심사입니다. DMW를 사용하면 고온, 부식 환경 및 고압이 요구되는 응용 분야에서 더 나은 성능을 충족시키면서 부품의 건설 비용을 절감할 수 있습니다. 그러나 DMW는 제작 및 야금학적 문제가 있으며, 이는 기존의 용접 문제와 서로 다른 특성을 가진 재료 간의 상호 작용을 모두 포함합니다. 이는 운전 중 파손으로 이어질 수 있습니다. 본 연구는 새로운 재료를 위한 이종 금속 접합부의 측정, 평가 및 설계를 위한 신뢰할 수 있는 연구 방법을 개발하는 것을 주된 목표로 하는 SINI 프로젝트의 일부입니다.

4. 연구 요약:

연구 주제의 배경:

원자력 발전소의 안전성과 경제성은 다양한 재료를 접합하는 이종 금속 용접(DMW)의 신뢰성에 크게 의존합니다. 특히 원자로 압력용기(RPV) 노즐과 배관을 연결하는 부위는 고온, 고압, 부식성 환경에 노출되어 응력 부식 균열(SCC)과 같은 손상에 매우 취약합니다. 기존에 사용되던 Inconel 600 계열 합금의 SCC 문제로 인해, 최근에는 내식성이 향상된 Alloy 690과 고크롬 필러 금속(Inconel 52, 152, 52M)이 도입되고 있으며, 경제적인 후판 용접을 위해 협개선 용접(NGW) 기술이 적용되고 있습니다.

이전 연구 현황:

과거 연구들은 주로 Inconel 600 계열 합금의 SCC 거동에 초점을 맞추어 왔습니다. 또한, 페라이트계 강과 오스테나이트계 강 사이의 DMW에서 발생하는 탄소 이동 및 그로 인한 계면의 경화/연화 현상에 대한 연구가 다수 수행되었습니다. 그러나 새로운 소재인 Alloy 690 및 고크롬 필러 금속, 그리고 NGW 공법이 적용된 DMW에 대한 장기 운전 데이터나 체계적인 미세구조 연구는 아직 부족한 실정입니다.

연구 목적:

본 연구의 목적은 최신 원자력 발전소 설계에 적용되는 새로운 DMW의 미세구조적 특성을 규명하는 것입니다. 구체적으로, (1) 용접후열처리(PWHT)가 LAS/니켈 합금 계면의 야금학적 변화(탄소 이동, 석출물 형성 등)에 미치는 영향을 분석하고, (2) 다양한 Inconel 필러 금속(52, 152, 52M)의 용접성과 거동 차이를 비교하며, (3) 다양한 제조 공법(압연, 단조, 압출)에 따른 Alloy 690 모재의 미세구조적 특징을 파악하는 것입니다. 이를 통해 신소재 및 신공법 DMW의 잠재적 파손 메커니즘을 이해하고 구조 건전성을 평가하기 위한 기초 자료를 제공하고자 합니다.

핵심 연구:

본 연구의 핵심은 실제 원자력 발전소 환경을 모사한 다양한 DMW 시편에 대한 상세한 미세구조 및 기계적 특성 분석입니다. 특히, PWHT 전후의 협개선 용접(NGW) 시편 비교를 통해 열처리가 계면 특성에 미치는 영향을 정량적으로 평가했습니다. 또한, 여러 종류의 필러 금속과 모재 조합으로 구성된 시편들을 비교 분석하여, 각 재료가 최종 용접부 품질에 어떻게 기여하는지를 밝혔습니다. 광학 현미경 관찰과 마이크로/나노 경도 측정을 통해 얻은 데이터를 종합하여, 용접부의 위치별 특성 변화와 잠재적 취약 영역을 식별했습니다.

5. 연구 방법론

연구 설계:

본 연구는 실제 원자력 발전소에 사용되는 다양한 이종 금속 용접(DMW) 구성을 대표하는 8개의 시편을 대상으로 비교 분석하는 방식으로 설계되었습니다. 특히, 용접후열처리(PWHT)의 영향을 파악하기 위해 동일한 협개선 용접(NGW) 시편을 용접 상태(AW)와 열처리 후(HT) 상태로 나누어 특성을 비교했습니다. 또한, 필러 금속(Inconel 52, 152, 52M), 모재(SA508, SA533 Gr.B, Alloy 690), 용접 공정(GTAW, SMAW, NGW) 등 다양한 변수가 조합된 시편들을 분석하여 각 요소가 용접부 특성에 미치는 영향을 체계적으로 평가했습니다.

데이터 수집 및 분석 방법:

데이터는 주로 시편의 단면을 관찰하고 측정하는 방식으로 수집되었습니다. 1. 시편 준비: 모든 시편을 절단, 마운팅, 연마 및 에칭하여 미세구조를 관찰할 수 있도록 준비했습니다. LAS 조직을 위해서는 2% 나이탈(Nital) 용액을, Inconel 합금 및 스테인리스강 조직을 위해서는 왕수(aqua regia)를 사용했습니다. 2. 미세구조 분석: Nikon Epiphot 200 광학 현미경과 NIS-Elements F.2.30 이미지 분석 소프트웨어를 사용하여 각 시편의 용접 계면, 열영향부(HAZ), 용접 금속의 결정립 크기, 상 분포, 석출물 형태 등을 관찰하고 기록했습니다. 3. 경도 측정: Buehler Micromet 2104 마이크로 경도 시험기를 사용하여 용접부 단면을 가로지르는 경도 프로파일을 측정했습니다. 이를 통해 HAZ의 경화, CDZ의 연화, 용접 금속 내 경도 변화 등 국부적인 기계적 특성을 평가했습니다. 일부 시편에 대해서는 CSM Instruments 나노 압입 시험기를 사용하여 더 미세한 영역의 경도 변화를 분석했습니다.

연구 주제 및 범위:

본 연구는 니켈 기반 합금을 사용한 이종 금속 용접부의 미세구조적 특성에 초점을 맞춥니다. 연구 범위는 다음과 같습니다. – 페라이트/오스테나이트 계면 분석: 저합금강(LAS)과 니켈 기반 합금 필러 금속 사이의 계면에서 발생하는 현상(탄소고갈영역(CDZ), 탄소 농화, 석출, Type II 경계 형성 등)을 PWHT 전후로 비교 분석합니다. – 필러 금속 비교: Inconel 52, 152, 52M 필러 금속으로 제작된 용접부의 미세구조와 경도 특성을 비교하여 각 필러 금속의 거동 차이를 규명합니다. – Alloy 690 모재 분석: 열간 압연, 단조, 압출 등 다양한 제조 공법으로 생산된 Alloy 690 모재의 미세구조(결정립 크기, 카바이드 밴딩 등)를 분석하고, 용접 시 열영향부(HAZ)의 변화를 관찰합니다.

6. 주요 결과:

주요 결과:

  • 용접후열처리(PWHT)의 영향: PWHT는 SA508(LAS) 측의 탄소고갈영역(CDZ) 폭을 용접 상태(as-welded) 대비 약 10배 증가시켰습니다. 동시에, Inconel 52 용접 금속의 용융선 근처에 광범위한 크롬 카바이드 석출을 유발하여 최대 340 HV에 달하는 급격한 경도 피크를 형성했습니다.
  • 필러 금속별 경도 차이: 용접 금속의 평균 경도는 Inconel 52M(약 250 HV)이 가장 높았으며, Inconel 152(약 224-239 HV), Inconel 52(약 207-220 HV) 순으로 나타났습니다. 이는 Inconel 52M의 미세한 조직과 높은 합금 원소 함량에 기인합니다.
  • 필러 금속별 탄소 이동 거동: Inconel 152를 사용한 용접부의 용융선에서는 국부적인 탄소 농화대(martensitic layer)가 관찰된 반면, Inconel 52에서는 이러한 현상이 덜 뚜렷했습니다. 이는 Inconel 152가 Inconel 52보다 탄소 확산에 대한 저항이 클 수 있음을 시사합니다.
  • Alloy 690의 미세구조: Alloy 690의 미세구조는 제조 이력에 크게 의존했습니다. 압연 및 단조재에서는 불균일한 결정립과 카바이드 밴딩이 관찰되었으나, 압출재에서는 밴딩 없이 가장 균일한 미세구조를 보였습니다.
  • Alloy 690 열영향부(HAZ) 특성: Alloy 690의 HAZ에서는 뚜렷한 결정립 미세화 영역 없이 용융선 근처에서 결정립 성장이 관찰되었습니다. 경도는 모재(약 180-200 HV)에서 용융선 방향으로 갈수록 약 40-70 HV 증가했으며, 이는 잔류 변형의 영향으로 분석됩니다.

Figure 목록:

  • Fig. 1 Cut of a nuclear reactor and main constituents. Of major importance are the RPV nozzles by which enters and leaves the coolant.
  • Fig. 2 Difference of principle between BWR and PWR. In BWR, the water heated in the RPV directly enters the turbine. In PWR, it is used to heat a secondary circuit.
  • Fig. 3 Cut of the EPR design.
  • Fig. 4 Material selection for BWR.
  • Fig. 5 Material selection for PWR.
  • Fig. 6 Material selection depending on the constructor.
  • Fig. 7 Main materials in LWRs: carbon steels, LAS, austenitic SS and Ni-base alloys.
  • Fig. 8 Scheme of a RPV safe-end (a) and the four materials composing the DMW (b): A- ferritic LAS SA508, B- buttering alloy Inconel 82, C- weld alloy Inconel 182, D- austenitic stainless steel 316L or alloy Inconel 600.
  • Fig. 9 LAS compositions for nuclear applications. Among them, it is worth noting SA 302 B, SA 508 CL.2 and SA 533 Gr.B.
  • Fig. 10 Austenitic SS grades, among which the common grades 304L and 316L. Incoloy 800 is given as a comparison.
  • Fig. 11 Composition of Inconel 600 and Alloy 690. Alloy 690 has higher Cr and Fe contents.
  • Fig. 12 Composition of Ni-base filler metals. Inconel 52,152 and 52M have higher Cr and Fe contents. Inconel 52M has additions of boron and zirconium.
  • Fig. 13 Mechanical properties of Ni-base filler metals, at room temperature and usual in service temperature.
  • Fig. 14 Composition of some high-strength alloys, among which Inconel 718 and X-750.
  • Fig. 15 Typical DMW designs in NPPs. The second is usual for a weld between a RPV nozzle and its safe-end.
  • Fig. 16 Schematic illustration of four distinct microstructural zones existing in DMWs: fusion zone (FZ), unmixed zone (UMZ), partially melted zone (PMZ) and heat affected zone (HAZ).
  • Fig. 17 Optical and SEM image of UMZ at the interface between A36 HAZ and 308L weld metal.
  • Fig. 18 Illustration showing the correlation between the various zones in a fusion weld in an alloy and the corresponding equilibrium phase diagram.
  • Fig. 19 Epitaxial grain growth mechanism for a homogeneous weld. The continuity across the fusion line is clearly visible.
  • Fig. 20 Geometrical comparison between NGW and conventional welding. Optimized NGW reduces greatly the amount of weld metal.
  • Fig. 21 Reduction of the weld volume using GTA-NGW as compared to a conventional weld. The reduction is of about four times.
  • Fig. 22 Cross-section of a RPV nozzle and safe-end in a BWR
  • Fig. 23 Closer view of the weld between the RPV nozzle and the safe-end. It presents the LAS of the RPV and its SS cladding, the Ni-base buttering, the Ni-base weld metal (Ni-Fe-Cr alloys) and the austenitic SS of the safe-end.
  • Fig. 24 Mock-up weld representing a usual weld between the ferritic LAS (SA508-3) of a RPV nozzle and the austenitic SS (SS316) of its safe-end, using Ni-base alloys as buttering and weld metals (respectively, Inconel 82 and 182).
  • Fig. 25 Microstructures of SA508 Cl.3
  • Fig. 26 HAZ microstructure of SA508 Cl.1 for an Inconel 182/SA508 Cl.1 interface: a) Global view showing grain refining then grain coarsening when moving to the fusion line. b) Grain coarsening area and carbon-depleted layer along the fusion line.
  • Fig. 27 As-welded interface between 9Cr-1Mo/2,25Cr-1Mo steels: a) Microstructure of the weld interface, b) Hardness profile taken across the weld interface.
  • Fig. 28 Post-weld heat treated interface between 9Cr-1Mo/2,25Cr-1Mo steels: a) Microstructure of the weld interface, b) Hardness profile taken across the weld interface.
  • Fig. 29 Micrograph showing Type II boundaries adjacent to the weld interface of an Alloy 52/SA508 weld.
  • Fig. 30 Calculated Ms temperature profile across the weld interface of Inconel 52/SA508 weld.
  • Fig. 31 Hardness peak due to a martensitic layer close to the LAS/Inconel 182 interface, and influence of PWHT.
  • Fig. 32 Simulated effect of a pure Ni buttering layer on the carbon concentration profile at the 9Cr-1Mo/2,25Cr-1Mo weld interface: a) without buttering layer and b) with a simulated Ni buttering layer. PWHT at 1023 K has been applied for 15 h.
  • Fig. 33 Microstructure of Inconel 82 weld metal: (a) weld metal and (b) interior of weld with higher magnification.
  • Fig. 34 a) Optical and b) SEM microstructure of Alloy 690, showing fine dispersed carbides and coarse TiN compounds.
  • Fig. 35 Longitudinal sections of a) an Alloy 690 billet and b) an Alloy 690 plate showing carbide banding.
  • Fig. 36 Grain size banding and isolated coarse grains in an Alloy 690 billet.
  • Fig. 37 Carbide morphology of Alloy 690 a) solution annealed at 1150°C for 1 h, b) solution annealed at 1150°C for 1 h then thermally treated 700°C for 1 h, c) as-received and d) solution annealed at 1150°C for 1 h then thermally treated at 800°C for 1 h.
  • Fig. 38 UMZ at the austenitic SS 304/Inconel 625 interface.
  • Fig. 39 Weld interfaces with weld metal Inconel 82 and base metals a) Inconel 657 and b) 310 SS.
  • Fig. 40 HAZ of SS 304 with formation of Type II boundaries at the interface with Inconel 625 weld metal.
  • Fig. 41 Alloy 690 interfaces between base material, HAZ, PMZ+UMZ and weld metal, based on grain size transition and carbide precipitation.
  • Fig. 42 Graph showing the SCC behavior of Alloy 690 base material, HAZ and weld metals Inconel 52, 152 in PWR water. Cracks can grow under certain conditions.
  • Fig. 43 Alloy 690 plate with planar banding and samples for mechanical testing with different orientation. They present, thus, different microstructures and SCC behavior.
  • Fig. 44 Map of the several zones at an Alloy 690/Inconel 52 weld interface and the corresponding residual strain measurement. Residual strains increase in the UMZ+PMZ of Alloy 690. The higher residual strains are found in the weld metal.
  • Fig. 45 SEM image of a) carbide precipitation at GB in the HAZ of a GTAW Alloy 690 weld, with b) and c) the EDS analysis for the GBs and the grain interior, respectively.
  • Fig. 46 a) Optical microstructure of heat-treated Alloy 690 and b) corresponding Cr-carbide precipitation at GBs. The extent of precipitation is much lower for coherent twins.
  • Fig. 47 Grain boundary network of Alloy 690 with a) GBE and b) non-GBE. See the grain clusters in the GBE alloy.
  • Fig. 50 Views of the Alloy 52 mock-up weld manufacturing, with a) the two base metal plates, b) the NG-GTAW welding torch in process (note the leading camera needed to see inside the groove) and c) the final weld.
  • Fig. 51 Cross-section of the NG-GTAW weld. It has been etched to reveal better the macrostructure: materials, weld passes in Inconel 52 weld metal and HAZ of SA508 and SS304.
  • Fig. 52 Cycle of temperatures for the post-weld heat treatment done on the Alloy 52 mock-up sample.
  • Fig. 53 Cutting of the samples from the cross-section of the AW Alloy 52 mock-up.
  • Fig. 54 Cutting of the samples from the HT cross-section.
  • Fig. 55 Weld design for the CIEMAT samples: two Alloy 690 plates welded with a half-V groove. The weld metal is either Inconel 52 or 152, and the welding technique is either GTAW or SMAW, respectively.
  • Fig. 56 Views of the sample CIEMAT GTAW: a) broad weld from above and b) the sample which is a transversal cut of the weld.
  • Fig. 57 Views of the sample CIEMAT SMAW: a) broad weld from above and b) the final sample that has been cut transverse from the weld.
  • Fig. 58 Global view of the weld, showing the SA508 plate (dark), the weld metal and the Alloy 690 plate (arrows mark the interface between Inconel 152 weld metal and Alloy 690 base metal).
  • Fig. 59 MHI plate sample. Cross-section of the weldment. It has been etched to reveal the macrostructure: SA508, weld-passes in Inconel 152, Alloy 690.
  • Fig. 60 Global view of the GTAW 19508A weld, showing the two plates and the weld overlay.
  • Fig. 61 GTAW 19508A sample, cut from a cross-section of the weldment: a) the sample has been etched to reveal the weld passes corresponding to b) the scheme of the weld passes.
  • Fig. 62 Welding parameters for the GTAW 19508A sample.
  • Fig. 63 Views of the ENSA weld mock-up with a) schematic of the grooves and components, b) view of the broad sample, c) view of the weld polished and etched and d) schematic of the weld passes.
  • Fig. 64 View of the sample cut from the weld and prepared for characterization.
  • Fig. 65 Views of the sample PG&E mock-up with a) broad sample showing the Alloy 690 pipe inside the LAS SA533 GrB plate with the SS 308L cladding, b) the sample cut in half, c) a closer view of the sample cut in four showing Inconel 52M weld metal and d) the sample cut, polished and etched.
  • Fig. 66 Microstructures of the SA508 HAZ and base material: A) Grain coarsening, B) grain refining, C) partial grain refining and D) base material.
  • Fig. 67 Microstructure of the SA508/Inconel 52 fusion line, with: a) CDZ in the LAS side, b) a layer free of precipitates on the weld metal side along the fusion line and c) a possible Type II boundary.
  • Fig. 68 Weld metal Inconel 52.
  • Fig. 69 Microstructure of the Inconel 52 weld metal, with: a) global view of the columnar dendrite grains, b) primary arm spacing and c) a closer view.
  • Fig. 70 Hardness profile across the sample. The hardness increases progressively in the LAS HAZ due to grain refining.
  • Fig. 71 Hardness profile across the fusion line.
  • Fig. 72 Microscopic view of second line loadings, and the position of the X = -0,05 mm loading near the fusion line.
  • Fig. 73 Nanohardness profile across SA508/Inconel 52 interface.
  • Fig. 74 View of the indentation across the CDZ in the LAS SA508 side of the weld (dark-etched).
  • Fig. 75 Global view of the HT LAS microstructure: A) grain coarsening, B) grain refining, C) partial grain refining and D) base material.
  • Fig. 76 Microstructure of the PWHT SA508/Inconel 52 interface: a) CDZ on the SA508 side and the dark etched fusion line, b) Inconel 52 weld metal along the fusion line, c) extensive precipitation in the weld metal close to the fusion line and d) a Type II boundary.
  • Fig. 77 Global view of the Inconel 52 weld metal after PWHT.
  • Fig. 78 Microstructures of Inconel 52 weld metal after PWHT: a) several grains, b) close view of the cellular structure and c) close view of a solidification GB.
  • Fig. 79 Microhardness profile across the HT SA508/Inconel 52 interface and the corresponding indentations.
  • Fig. 80 Microhardness profile across the PWHT SA508/Inconel 52 interface and the corresponding view of the indentations.
  • Fig. 81 Nanohardness profile from the fusion line in the Inconel 52 weld. No hardness peak is visible.
  • Fig. 82 Nanoindentations in Inconel 52 weld metal across the precipitates.
  • Fig. 83 Global view of the Alloy 690/Inconel 52 interface.
  • Fig. 84 Microstructure of Alloy 690 base material, with twin boundaries, fine carbide precipitates and golden TiN particles.
  • Fig. 85 Microstructure of Alloy 690 HAZ near the fusion line.
  • Fig. 86 Carbide banding in Alloy 690 plate.
  • Fig. 87 Closer view of carbide banding.
  • Fig. 88 Alloy 690/ Inconel 52 weld metal interface with epitaxial growth of the weld metal grains.
  • Fig. 89 Weld passes in Inconel 52 weld metal.
  • Fig. 90 Columnar dendrites in the Inconel 52 weld metal.
  • Fig. 91 Hardness map of the samples.
  • Fig. 92 Weld passes in the Inconel 152 weld metal.
  • Fig. 93 Microstructure of Alloy 690 base material for sample CIEMAT SMAW.
  • Fig. 94 Fusion line between Alloy 690 and Inconel 152.
  • Fig. 95 Closer view of the precipitation occurring in the dendritic microstructure of the Inconel 152 weld metal.
  • Fig. 96 Transition between two weld passes in Inconel 152 weld metal.
  • Fig. 97 Hardness map for the CIEMAT SMAW sample, showing hardness increase in the Alloy 690 from the base material to the fusion line.
  • Fig. 98 SA508 HAZ: a) grain coarsening, b) grain refining, c) partial grain refining and d) base material.
  • Fig. 99 SA508 side of the SA508/Inconel 152 interface with.
  • Fig. 100 Widmannstätten ferrite along the fusion line.
  • Fig. 101 Dark-etched carbon-enriched layer on the fusion line between SA508 and Inconel 152.
  • Fig. 102 Type II boundaries on the weld metal side of the SA508/Inconel 152 interface.
  • Fig. 103 Inconel 152/Alloy 690 interface.
  • Fig. 104 Hardness map of the Inconel 152/Alloy 690 side of the sample.
  • Fig. 105 Hardness profile across the SA508/Inconel 152 buttering and in the buttering layer.
  • Fig. 106 Microhardness profile across the SA508/Inconel 152 buttering layer.
  • Fig. 107 Banded microstructure in SA508 with dark- and light-etched bands.
  • Fig. 108 Hardness profile across several bands in SA 508 steel.
  • Fig. 109 Microstructure of the Alloy 690/Inconel 52M interface.
  • Fig. 110 HAZ of Alloy 690 at the fusion line with Inconel 52M weld metal.
  • Fig. 111 Alloy 690/Inconel 52M weld metal interface, showing the growth of the weld metal grains from those of the base metal.
  • Fig. 112 Inconel 52M weld metal microstructure.
  • Fig. 113 Hardness profile across the Alloy 690/Inconel 52M/Alloy 690 weld.
  • Fig. 114 Hardness profile in the Alloy 690 HAZ and at the fusion line with Inconel 52M.
  • Fig. 116 LAS HAZ with A) base material, B) partial grain refining, C) grain refining and D) grain coarsening along the fusion line.
  • Fig. 117 CDZ in the LAS side of the LAS/Inconel 52M buttering layer interface.
  • Fig. 118 a) Broad view, b) closer view of the LAS/Inconel 52 M buttering fusion lines and c) Type II boundary at 10 μm from the fusion line.
  • Fig. 119 Carbide banding in forged Alloy 690 plate.
  • Fig. 120 Very inhomogeneous microstructure in forged Alloy 690 plate.
  • Fig. 121 Schematic of the hardness measurements for the ENSA weld mock-up.
  • Fig. 122 Hardness measurement from location 1: across LAS, Inconel 52M buttering, Inconel 52 weld metal and Alloy 690 base metal.
  • Fig. 123 Hardness measurement from location 2: Alloy 690 HAZ and Inconel 52 NGW.
  • Fig. 124 Hardness measurement from location 3 and corresponding indentations: LAS HAZ and interface with Inconel 52M buttering.
  • Fig. 126 SA533 Gr.B HAZ with A) base material, B) partial grain refining, C) grain refining and D) grain coarsening.
  • Fig. 127 SA533 Gr.B / Inconel 52M buttering fusion line and the influence of LAS carbide banding.
  • Fig. 128 Inconel 52M buttering layer and interface with SA 533 Gr.B.
  • Fig. 129 Inconel 52M weld metal microstructure.
  • Fig. 130 Fusion line between the Inconel 52M weld metal, the LAS plate and the SS cladding.
  • Fig. 131 Comparison between the two Inconel 52M interfaces: A) with SS308L and B) with SA533 Gr.B.
  • Fig. 132 Global view of the extruded Inconel 690 pipe.
  • Fig. 133 Extruded Inconel 690 microstructure.
  • Fig. 134 Hardness profile across the PG&E sample.
  • Fig. 135 Hardness profile across the SA 533 Gr.B/Inconel 52M buttering interface.
  • Fig. 136 Hardness profile across the Inconel 52M weld metal and the interfaces with Inconel 52M buttering and Alloy 690 base metal.

7. 결론:

본 연구에서는 새로운 원자력 적용을 위한 니켈 기반 합금과 저합금강(LAS)의 이종 금속 용접(DMW) 거동에 대한 문헌 검토와 실험적 분석을 수행했다. 연구는 PWHT가 페라이트/오스테나이트 DMW 계면에 미치는 야금학적 변화, Inconel 필러 금속의 용접성, 그리고 NPP에서 사용되는 NG-GTAW 기술에 중점을 두었다. 총 8개의 시편을 특성화했으며, 특히 프로젝트에서 제작한 Alloy 52 모의 용접 시편을 용접 상태와 PWHT 후 상태로 비교 분석했다. 그 결과, PWHT는 LAS 측의 CDZ 폭을 증가시키고 용접 금속 내에 광범위한 크롬 카바이드 석출을 유발했으며, 이는 용융선 근처 용접 금속의 날카로운 경도 피크의 원인이었다. 또한, EPRI에서 제공한 시편 분석을 통해 Alloy 690 모재와 Inconel 52M, 52, 152 필러 금속의 다양한 조합에서의 거동 차이를 확인했다. Inconel 52M에서 가장 높은 경도가 관찰되었고, Inconel 152는 Inconel 52와 다른 탄소 이동 거동을 보였다. Alloy 690의 미세구조는 제품 형태에 따라 달라졌으며, 경도는 항상 모재에서 용융선으로 갈수록 증가했는데, 이는 잔류 변형 때문으로 보인다. 본 연구는 광학 현미경과 경도 측정을 통해 시편을 특성화하는 초기 단계이며, 향후 SEM, EBSD, EDS 분석 등을 통해 용접부의 거동을 더 깊이 이해할 필요가 있다.

8. 참고 문헌:

  • Aalto University (2012) Kon-67.5100 Postgraduate Seminar on Engineering Materials, Otaniemi, March – April 2012.
  • Ahluwalia K., King C. (2007) Materials reliability program: review of stress corrosion cracking of alloys 182 and 82 in PWR primary water service (MRP 220). Technical report 1007832. EPRI, Palo Alto, CA, October 2007.
  • Akbari D, Farahani M, Soltani N. (2012) Effects of the weld groove shape and geometry on residual stresses in dissimilar butt-welded pipes. The Journal of Strain Analysis for Engineering Design. Vol. 47. 2. P. 73- 82.
  • Albert S. K., Gill T. P. S., Tyagi A. K., Mannan S. L., Kulkami S. D., Rodriguez P. (1997) Soft zone formation in dissimilar welds between two Cr-Mo steels. Welding Journal. Vol. 76. 3. P. 135–142.
  • Alexandrov B.T., Hope A.T., Sowards J.W., Lippold J.C. (2009) Weldability studies of high-Cr, Ni-base filler metals for power generation applications. IX 2313-09-Rev3.
  • Anand R., Sudha C., Karthikeyan T., Terrance A.L.E., Saroja S., Vijayalakshmi M. (2008) Metal interlayers to prevent ‘hard zone’ formation in dissimilar weldments of Cr-Mo steels – A comparison between Cu, Co and Ni. Transactions of the Indian Institute of Metals. Vol. 61. P. 483-486.
  • Andresen P., Morra M., Ahluwalia K. (2012) SCC of Alloy 690 and its weld metals. EPRI International BWR and PWR Materials Reliability Conference and Exhibit Show, National Harbor, Maryland, July 16-19. P. 321-361.
  • ASTM E384 – 11e1. Standard test method for Knoop and Vickers hardness of materials. ICS number code 19.060.
  • Bamford W., Hall J. (2005) Cracking of alloy 600 nozzle and welds in PWRs: review of cracking events and repair service experience. Proceedings of the 12th International Conference on Environmental Degradation of Materials in Nuclear Power System–Water Reactors–TMS, Salt Lake City, 2000. Eds. Allen T.R., King P.J., Nelson L. USA: The Minerals, Metals and Materials Society. P. 959– 965.
  • Becker A.A., Hyde T.H., Sun W. (2001) Creep crack growth in welds: a damage mechanics approach to predicting initiation and growth of circumferential cracks. International Journal of Pressure Vessels and Piping. Vol. 78. P. 765-771.
  • Biswas P., Mandal N.R., Vasu P., Padasalag S.B. (2010) Analysis of welding distortion due to narrow-gap welding of upper port plug. Fusion Engineering and Design. Vol. 85. P. 780–788.
  • Boursier J., Vaillant F, Yrieix B. (2004) A review of PWSCC behavior of nickel weld metals containing 15 to 30% chromium. Proceedings of ASME/JSME
  • (List continues for all references in the paper)

전문가 Q&A: 주요 질문과 답변

Q1: 연구에서 특히 협개선 용접(NGW) 모의 시편을 선택하여 분석한 이유는 무엇인가요?

A1: 협개선 용접(NGW)은 EPR과 같은 최신 원자력 발전소 설계에서 후판 부재를 용접하는 데 사용되는 경제적이고 효율적인 신기술이기 때문입니다. 하지만 새로운 기술인 만큼 실제 운용 데이터가 부족하여 장기적인 성능과 신뢰성에 대한 검증이 필요합니다. 따라서 본 연구에서는 이 중요한 기술로 제작된 용접부의 미세구조적 특성을 상세히 분석하여 잠재적인 문제점을 파악하고 안전성을 평가하기 위한 기초 자료를 확보하고자 했습니다.

Q2: 열처리된 Alloy 52 시편에서 340 HV에 달하는 높은 경도 피크가 관찰되었습니다. 정확한 야금학적 원인은 무엇이며, 이것이 왜 문제가 될 수 있나요?

A2: 이 경도 피크는 용접후열처리(PWHT) 과정에서 발생한 탄소 이동 현상 때문입니다. 상대적으로 탄소 함량이 높은 저합금강(SA 508)에서 탄소가 크롬 친화력이 높은 Inconel 52 용접 금속 쪽으로 확산됩니다. 이 탄소는 Inconel 52의 풍부한 크롬과 결합하여 용융선 근처에 미세한 크롬 카바이드(chromium carbide)를 대량으로 석출시킵니다. 이렇게 형성된 매우 단단하고 국부적인 경화층은 취성이 높아 응력이 집중될 경우 균열의 시작점으로 작용할 수 있어 용접부의 구조적 건전성을 저해하는 심각한 잠재적 결함이 될 수 있습니다.

Q3: 연구에서 Inconel 152가 Inconel 52와 다른 탄소 이동 거동을 보였다고 언급했는데, 구체적으로 어떤 차이가 있었나요?

A3: MHI 시편(SA508/Inconel 152)의 경우, 용융선에서 어둡게 식각되는 뚜렷한 탄소 농화대(carbon-enriched zone)가 관찰되었습니다. 이는 탄소가 용접 금속 내부로 넓게 확산되지 못하고 용융선 근처에 국부적으로 집중되었음을 의미합니다. 반면, Inconel 52 시편에서는 탄화물 석출이 좀 더 넓은 영역에 걸쳐 분포하는 경향을 보였습니다. 이는 Inconel 152가 Inconel 52보다 탄소의 확산을 더 효과적으로 억제할 수 있음을 시사하며, 이로 인해 더 불균일하고 예측하기 어려운 계면 특성을 가질 수 있습니다.

Q4: Alloy 690 모재가 제조 공법(압연, 단조, 압출)에 따라 다른 미세구조를 보이는 것이 왜 중요한가요?

A4: 미세구조의 균일성은 재료의 기계적 특성과 내식성에 직접적인 영향을 미치기 때문입니다. 연구 결과, 압출재는 카바이드 밴딩 없이 가장 균일한 미세구조를 보였습니다. 반면, 압연재나 단조재에서 관찰된 카바이드 밴딩과 같은 불균일한 조직은 국부적인 잔류 변형을 더 많이 축적시켜 응력 부식 균열(SCC)에 대한 민감도를 높일 수 있습니다. 따라서 중요한 부품을 설계하고 제작할 때, 단순히 ‘Alloy 690’이라는 재료명만 명시할 것이 아니라, 압출과 같은 특정 제조 공법을 지정하는 것이 재료의 신뢰성을 확보하는 데 매우 중요할 수 있습니다.

Q5: 열처리된 시편의 나노 압입 시험에서는 마이크로 경도 시험에서 나타났던 경도 피크가 관찰되지 않았습니다. 이러한 차이가 발생한 이유는 무엇인가요?

A5: 논문에서는 두 가지 가능성을 제시합니다. 첫째, 나노 압입 시험의 압입 크기가 경도 상승의 원인이 되는 미세한 카바이드 석출물들의 크기나 분포에 비해 너무 작아서 그 영향을 제대로 측정하지 못했을 수 있습니다. 둘째, 시편을 식각하는 데 사용된 왕수(aqua regia)가 용융선 근처의 화학 조성 변화로 인해 표면을 불균일하게 부식시켜, 깊이를 감지하는 나노 압입 시험 결과의 정확도에 영향을 미쳤을 가능성이 있습니다.


결론: 더 높은 품질과 생산성을 향한 길

이종 금속 용접부의 조기 파손 문제는 원자력 발전소와 같은 고신뢰성 산업에서 해결해야 할 핵심 과제입니다. 본 연구는 용접후열처리(PWHT)가 용접 계면에 미치는 극적인 영향을 명확히 보여주었습니다. 특히, 저합금강의 탄소 이동으로 인해 용접 금속 내에 형성되는 국부적인 고경도 영역은 균열 발생의 주요 원인이 될 수 있음을 데이터로 입증했습니다.

이러한 결과는 R&D 및 운영 현장에 중요한 시사점을 제공합니다. 공정 엔지니어는 PWHT 조건을 최적화해야 하며, 품질 관리팀은 용융선 부근의 미세 경도 변화를 핵심 관리 지표로 삼아야 합니다. 또한, 설계 엔지니어는 필러 금속의 종류와 모재의 제조 이력이 최종 용접부의 성능에 미치는 영향을 설계 초기 단계부터 고려해야 합니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

저작권 정보

  • 이 콘텐츠는 Roman Mouginot와 Hannu Hänninen의 논문 “Microstructures of nickel-base alloy dissimilar metal welds”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: http://urn.fi/URN:ISBN:978-952-60-5066-9

이 자료는 정보 제공 목적으로만 사용됩니다. 무단 상업적 사용을 금지합니다. Copyright © 2025 STI C&D. All rights reserved.

Figure 1. Generic example of an ANFIS architecture

ANFIS를 활용한 교량 교각 세굴 예측: 기계 학습으로 더 빠르고 정확한 안전성 평가

이 기술 요약은 Manousos Valyrakis와 Hanqing Zhang이 2014년 International Conference on Hydroinformatics에 발표한 “Prediction Of Scour Depth Around Bridge Piers Using Adaptive Neuro-Fuzzy Inference Systems (ANFIS)” 논문을 기반으로 하며, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

Keywords

  • Primary Keyword: 교량 교각 세굴 예측
  • Secondary Keywords: ANFIS, 적응형 뉴로-퍼지 추론 시스템, 기계 학습, 수리 공학, 교량 안전, 세굴 깊이

Executive Summary

  • The Challenge: 교량 교각 주변의 세굴 깊이를 예측하는 기존 공식들은 제한된 데이터에 기반한 경험식으로, 종종 세굴 깊이를 과대평가하여 보수적이고 비용이 많이 드는 설계를 초래합니다.
  • The Method: 본 연구는 USGS 데이터베이스에서 얻은 광범위한 현장 데이터를 사용하여 기계 학습 모델인 적응형 뉴로-퍼지 추론 시스템(ANFIS)을 개발, 훈련 및 검증했습니다.
  • The Key Breakthrough: 개발된 ANFIS 모델은 특히 단일 원형 교각과 같은 특정 데이터 그룹으로 훈련했을 때, 적은 수의 입력 변수만으로도 세굴 깊이를 매우 정확하게 예측하는 뛰어난 일반화 능력을 보여주었습니다.
  • The Bottom Line: ANFIS는 엔지니어에게 기존의 경험적 방법보다 더 정확하게 교각 세굴을 예측할 수 있는 강력하고 신뢰성 있는 도구를 제공하며, 이는 더 안전하고 경제적인 교량 설계로 이어질 수 있습니다.

The Challenge: Why This Research Matters for CFD Professionals

교량의 붕괴는 종종 홍수 시 교각 기초 주변의 토사가 유실되는 ‘세굴(scour)’ 현상 때문에 발생합니다. 실제로 1989년에서 2000년 사이 미국에서 발생한 500건 이상의 교량 붕괴 사고 중 절반 이상(약 53%)이 기초 세굴에 기인한 것으로 추정됩니다. 이러한 사고는 막대한 재정적 손실을 야기하며, 1993년 미시시피 상류 유역의 홍수는 23개의 교량 붕괴와 1,500만 달러의 피해를, 1994년 조지아의 “알베르토 폭풍”은 약 1억 5,000만 달러의 피해를 초래했습니다.

문제는 현재 사용되는 대부분의 교각 세굴 깊이 예측 공식이 제한된 실험실 데이터에 기반한 경험식이라는 점입니다. 이 공식들은 실제 현장 조건을 정확하게 모사하지 못하며, 대부분 보수적인 결과를 도출하여 세굴 깊이를 과대평가하는 경향이 있습니다. 이는 불필요하게 과도한 설계로 이어져 구조적 불확실성과 비용 증가를 야기합니다. 따라서 더 빠르고 신뢰할 수 있는 예측 도구의 필요성이 절실합니다.

The Approach: Unpacking the Methodology

본 연구는 이러한 문제를 해결하기 위해 강력한 기계 학습 접근법인 적응형 뉴로-퍼지 추론 시스템(ANFIS)을 활용했습니다. ANFIS는 인공 신경망(ANN)의 학습 능력과 퍼지 추론 시스템(FIS)의 규칙 기반 구조를 결합하여 복잡한 비선형 동역학을 효과적으로 모델링할 수 있습니다.

연구팀은 미국 지질조사국(USGS)의 국립 교량 세굴 데이터베이스에서 총 508개의 데이터 세트를 확보했으며, 불완전한 기록을 제거하여 486개의 데이터를 분석에 사용했습니다. 모델의 입력 변수로는 다음과 같은 5가지 핵심 매개변수가 선택되었습니다.

  • 유효 교각 폭 (b)
  • 접근 유속 (U)
  • 접근 수심 (y)
  • 평균 입경 (D50)
  • 유동 방향에 대한 교각의 경사각 (skew to flow)

데이터는 훈련(training)과 검증(validation) 세트로 무작위 분할되었으며, 연구팀은 시행착오 접근법을 통해 최적의 ANFIS 구조(멤버십 함수의 종류 및 개수)를 결정했습니다. 또한, 입력 변수의 수를 점진적으로 줄여가며 모델을 테스트하여 어떤 변수가 예측에 가장 큰 영향을 미치는지, 그리고 제한된 데이터만으로도 신뢰성 있는 예측이 가능한지를 체계적으로 분석했습니다.

Figure 1. Generic example of an ANFIS architecture
Figure 1. Generic example of an ANFIS architecture

The Breakthrough: Key Findings & Data

연구 결과, ANFIS 모델은 교각 세굴 깊이를 예측하는 데 매우 높은 정확도와 잠재력을 보여주었습니다. 특히 주목할 만한 발견은 다음과 같습니다.

Finding 1: 특정 데이터에 대한 훈련으로 최적의 모델 성능 달성

가장 뛰어난 성능을 보인 모델은 5개의 모든 입력 변수를 사용하되, ‘단일 원형 교각(single round pier)’ 데이터 하위 그룹만으로 훈련된 모델이었습니다. 이 모델은 모든 데이터를 사용해 훈련된 모델보다 훨씬 높은 정확도를 보였습니다. Table 3에 따르면, 단일 원형 교각 데이터로 훈련된 모델의 검증 RMSE(평균 제곱근 오차)는 1.63으로, 전체 데이터로 훈련된 모델의 2.07보다 현저히 낮았습니다. 이는 데이터의 동질성이 모델의 학습 효율과 예측 정확도를 크게 향상시킬 수 있음을 시사합니다. Figure 2는 이 모델의 예측값이 실제 관측값과 매우 잘 일치함을 시각적으로 보여줍니다.

Finding 2: 입력 변수를 줄인 모델도 높은 정확도 유지

연구팀은 입력 변수의 수를 줄여도 모델이 만족스러운 성능을 유지한다는 사실을 발견했습니다. 특히 ‘교각 폭’과 ‘접근 수심’이 세굴 예측에 가장 중요한 변수임이 확인되었습니다. 흥미롭게도 ‘유동 방향에 대한 경사각(skew to flow)’ 변수를 제거했을 때, 모델의 검증 RMSE가 2.07에서 2.03으로 오히려 약간 개선되었습니다(Table 3 참조). 이는 해당 변수가 예측에 큰 기여를 하지 않거나 오히려 노이즈로 작용했을 수 있음을 의미합니다. 심지어 ‘교각 폭’ 단 하나의 변수만 사용한 모델도 검증 RMSE 2.54로 비교적 정확한 예측이 가능했습니다. 이는 현장에서 제한된 데이터만 확보할 수 있는 경우에도 ANFIS 모델이 유용한 예측 도구가 될 수 있음을 보여줍니다.

Practical Implications for R&D and Operations

본 연구 결과는 다양한 분야의 전문가들에게 실질적인 시사점을 제공합니다.

  • For Hydraulic/Bridge Engineers: 이 연구는 교각 폭과 접근 수심 데이터에 집중하는 것만으로도 ANFIS를 통해 매우 정확한 세굴 예측이 가능함을 시사합니다. 하상 재료의 크기와 같은 다른 데이터가 부족하더라도 신뢰성 있는 결과를 얻을 수 있어, ANFIS는 실용적인 세굴 예측 도구로 활용될 수 있습니다.
  • For Infrastructure Planners/Managers: 기존의 보수적인 공식보다 ANFIS 모델의 예측 정확도가 높아, 과잉 설계를 방지하고 더 경제적이며 효율적인 교량 설계 및 유지보수 계획을 수립할 수 있습니다. 이는 불필요한 비용 절감으로 이어질 수 있습니다.
  • For Data Scientists in Engineering: 본 연구는 복잡한 수리학 문제에 기계 학습(ANFIS)을 성공적으로 적용한 사례입니다. 특히 ‘경사각’과 같이 관련 있어 보이는 변수를 제거했을 때 모델 성능이 향상될 수 있다는 발견은, 모델 개발 시 변수 선택의 중요성에 대한 귀중한 통찰을 제공합니다.

Paper Details


Prediction Of Scour Depth Around Bridge Piers Using Adaptive Neuro-Fuzzy Inference Systems (ANFIS)

1. Overview:

  • Title: Prediction Of Scour Depth Around Bridge Piers Using Adaptive Neuro-Fuzzy Inference Systems (ANFIS)
  • Author: Manousos Valyrakis, Hanqing Zhang
  • Year of publication: 2014
  • Journal/academic society of publication: International Conference on Hydroinformatics
  • Keywords: ANFIS, scour depth, bridge piers, machine learning, neuro-fuzzy, prediction model

2. Abstract:

In this study, the application of a machine learning model, namely the adaptive neuro-fuzzy inference system (ANFIS) is proposed to estimate the scour depth around bridge piers. In particular, various complexity architectures are sequentially developed, trained and validated using appropriate training and validation subsets obtained from the USGS database. The raw data are pre-processed to remove incomplete records and randomly split into the training and validation data sets which are both representative of the same space. The model has five parameters, namely the effective pier width (b), the approach velocity (U), the approach depth (y), the mean grain diameter (D50) and the skew to flow. Simulations are conducted with data groups (bed material type, pier type and shape) and different number and combinations of input variables, to produce reduced complexity and easily interpretable models. Analysis and comparison of the results indicate that the developed ANFIS model has high accuracy and outstanding generalization ability for prediction of scour parameters. The optimal ANFIS models are identified utilizing appropriate error metrics. The effective pier width (as opposed to skew to flow) is amongst the most relevant input parameters for the estimation. The developed models can be used as a scour prediction tool performing satisfactorily even in the presence of scarce available data, while empirical rules can be also derived for the reduced order models.

3. Introduction:

지구 표면은 지구물리학적 흐름의 작용으로 끊임없이 변화합니다. 강물의 흐름으로 인한 침식은 생태 건강을 보존하는 데 핵심적인 문제일 뿐만 아니라, 전 세계적으로 우리의 건축 환경과 핵심 기반 시설에 대한 위협으로 인식되고 있습니다. 기후 변화가 하천의 침식과 유사 이송에 미치는 영향은 전 지구적 차원의 핵심 과제가 되었습니다. 교량 붕괴의 가장 흔한 원인은 심각한 홍수 동안 교각 기초의 세굴 때문인 것으로 추정됩니다. 1989년에서 2000년 사이 미국에서 발생한 500건 이상의 교량 붕괴 중 절반 이상(약 53%)이 기초 세굴에 기인합니다. 미국 연방 고속도로 관리국(FHWA)의 383건의 교량 붕괴에 대한 전국적인 연구에 따르면, 25%는 교각 손상, 75%는 교대 손상과 관련이 있으며, 이는 모두 치명적인 홍수로 인해 발생했습니다.

4. Summary of the study:

Background of the research topic:

교각 주변의 침식 및 세굴 현상은 교량의 안전성에 직접적인 위협이 되며, 이는 전 세계적인 문제입니다.

Status of previous research:

세굴 깊이를 예측하기 위해 수많은 실험실 연구를 통해 여러 경험식이 개발되었습니다. 그러나 이러한 공식들은 대부분 제한된 실험실 데이터에 기반하고 있어 실제 현장 조건을 정확하게 반영하지 못하며, 종종 과도하게 보수적인 예측 결과를 내놓아 비경제적인 설계를 초래합니다.

Purpose of the study:

본 연구는 광범위한 현장 데이터를 사용하여 강력한 기계 학습 접근법인 ANFIS의 유용성을 조사하고, 이를 통해 교각 세굴 깊이를 정확하게 예측하는 것을 목표로 합니다.

Core study:

다양한 복잡성을 가진 ANFIS 아키텍처를 순차적으로 개발, 훈련 및 검증했습니다. 입력 변수의 수와 조합을 달리하여 모델을 테스트하고, 각 모델의 성능을 오차 메트릭을 통해 평가하여 최적의 모델 구조를 식별했습니다. 이를 통해 복잡성을 줄이고 해석이 용이한 모델을 도출하고자 했습니다.

5. Research Methodology

Research Design:

적응형 뉴로-퍼지 추론 시스템(ANFIS) 기계 학습 모델을 적용하여 교각 세굴 깊이를 예측하는 연구를 설계했습니다.

Data Collection and Analysis Methods:

미국 지질조사국(USGS)의 국립 교량 세굴 데이터베이스에서 데이터를 수집했습니다. 불완전한 데이터를 제거하는 전처리 과정을 거쳐 총 486개의 데이터 세트를 사용했으며, 이를 훈련 및 검증 데이터로 무작위 분할했습니다. 모델 성능은 RMSE(평균 제곱근 오차)와 MAE(평균 절대 오차)와 같은 오차 지표를 사용하여 평가되었습니다.

Research Topics and Scope:

주요 연구 범위는 5개의 입력 변수(유효 교각 폭, 접근 유속, 접근 수심, 평균 입경, 유동 경사각)가 세굴 깊이에 미치는 영향을 분석하는 것입니다. 또한, 입력 변수의 수를 5개에서 1개로 점진적으로 줄여가며 모델을 테스트하여, 각 변수의 중요도와 최소한의 데이터로 가능한 예측의 정확도를 평가했습니다.

6. Key Results:

Key Results:

  • 단일 원형 교각 데이터로만 훈련된 ANFIS 모델이 가장 높은 예측 정확도(검증 RMSE = 1.63)를 보였습니다.
  • 교각 폭과 접근 수심이 세굴 깊이 예측에 가장 중요한 입력 변수임이 확인되었습니다.
  • 입력 변수의 수를 줄인 모델도 만족스러운 성능을 보여, 제한된 데이터만으로도 신뢰성 있는 예측이 가능함을 입증했습니다.
  • ‘유동 경사각’ 변수를 제거했을 때 모델 성능이 약간 향상되어, 이 변수가 예측에 미치는 영향이 미미하거나 노이즈로 작용할 수 있음을 시사했습니다.

Figure List:

  • Figure 1. Generic example of an ANFIS architecture
  • Figure 2. Plot of observed and predicted scour depth training the model with all input parameters with the subset of single round pier data: a) performance for the training subset (77 data points) and b) performance for the validation data set (74 data points). Note the line of perfect agreement is shown with the straight line (diagonal).

7. Conclusion:

본 연구에서는 ANFIS를 사용하여 교각 주변의 세굴 깊이 예측을 조사했습니다. 적절한 데이터를 사용하여 광범위한 모델을 개발, 훈련 및 검증했습니다. 이러한 모델 간의 비교를 통해 우수한 일반화 능력을 갖춘 최상의 성능 모델을 식별할 수 있었습니다. 결과는 축소된 차수의 아키텍처에 대해서도 만족스러웠으며, 문헌에 제안된 다른 모델과 기능적으로 일치했습니다.

8. References:

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  • [3] Brice J.C. and Blodgett J.C., “Countermeasures for Hydraulic Problems at Bridges”, Vol. 1 and 2, FHWA/RD-78-162&163, Federal Highway Administration, U.S. Department of Transportation, Washington, D.C. (1978).
  • [4] Shen H.W., “Scour Near Piers. River Mechanics”, Vol. 2, Ft. Collins, Colorado, (1971).
  • [5] Dey S. and Raikar R.V., “Clear-water scour at piers in sand beds with an armor layer of gravels.” Journal of Hydraulic Engineering, Vol. 133, No. 6, (2007), pp 703-711.
  • [6] Raudkivi A.J. and Ettema R., “Clear water scour at cylindrical piers”, Journal of Hydraulic Engineering, Vol. 109, No. 3, (1983), pp 338-350.
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  • [9] Melville B.W. and Sutherland, A.J., “Design method for local scour at bridge piers”, Journal of Hydraulic Engineering, Vol. 114, No. 10, (1988), pp 1210-1226.
  • [10] Valyrakis M., Diplas P. and Dancey C.L., “Prediction of coarse particle movement with adaptive neuro-fuzzy inference systems”, Hydrological Processes, Vol. 25, No. 22, pp 3513-3524. ISSN 0885-6087, doi:10.1002/hyp.8228.
  • [11] Valyrakis M., Diplas P., Dancey C.L., Akar T. and Celik A.O., “Development of a hybrid adaptive Neuro-Fuzzy system for the prediction of sediment transport”, River Flow 2006, Lisbon, Portugal, (2006), pp 877-886, doi: 10.1201/9781439833865.ch92.
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Expert Q&A: Your Top Questions Answered

Q1: 왜 일반적인 인공 신경망(ANN) 대신 ANFIS 모델을 선택했나요?

A1: 논문에 따르면 ANFIS는 인공 신경망(ANN)과 퍼지 추론 시스템(FIS)의 장점을 모두 결합한 모델입니다. 신경망 구성 요소로부터 내재된 학습 능력을 가지며, 퍼지 논리 구성 요소로부터 규칙 기반 구조를 가져 퍼지 추론을 수행하고 비선형 동역학을 추출하는 데 유리합니다. 이는 저자들의 이전 연구[10, 11, 12, 13]에서 보여주었듯이 종종 ANN 단독 모델보다 우수한 성능을 나타냅니다.

Q2: 입력 변수의 수를 줄여가며 모델을 테스트한 과정에서 가장 놀라운 발견은 무엇이었나요?

A2: 가장 흥미로운 결과는 ‘유동 경사각(skew to flow)’ 입력 변수를 제거했을 때 모델의 예측 능력이 오히려 약간 향상되었다는 점입니다. Table 3에서 볼 수 있듯이, 검증 RMSE가 2.07에서 2.03으로 감소했습니다. 이는 이 데이터셋에서 해당 변수가 예측에 유의미한 정보를 제공하지 않거나 오히려 노이즈로 작용했을 수 있음을 시사하며, 때로는 더 단순한 구조의 모델이 더 복잡한 모델보다 우수한 성능을 보일 수 있음을 보여줍니다.

Q3: ANFIS 모델의 최적 구조(예: 멤버십 함수의 수)는 어떻게 결정되었나요?

A3: 최적의 구조는 시행착오 접근법을 통해 결정되었습니다. 연구팀은 다양한 유형과 수의 멤버십 함수를 가진 모델들을 테스트했습니다. 그 결과, 3개 이상의 멤버십 함수를 사용하면 과적합(overtraining)이 발생하고 계산 비용이 기하급수적으로 증가하는 것을 발견했습니다. 정확도와 일반화 능력 사이의 최상의 균형은 입력당 2개의 가우시안(Gaussian) 멤버십 함수를 사용했을 때 달성되었습니다.

Q4: ‘단일 원형 교각’ 데이터만 사용했을 때 최고의 성능을 보인 이유는 무엇인가요?

A4: 논문은 모든 유형의 데이터를 사용하여 모델을 훈련했을 때 정확도가 감소한 이유로, 해당 데이터가 기저의 동역학을 잘 설명하지 못하거나 다른 유형의 데이터를 얻는 과정에서 더 큰 오차가 발생했을 가능성을 제시합니다. ‘단일 원형 교각’ 데이터와 같이 더 동질적이고 잠재적으로 품질이 높은 하위 집합에 집중함으로써, 모델이 특정 동역학을 더 효과적으로 학습하여 해당 범주에 대해 더 정확한 예측을 할 수 있었습니다.

Q5: 논문은 축소된 모델이 기존 경험식과 기능적으로 유사하다고 결론 내렸습니다. 그렇다면 ANFIS 모델의 장점은 무엇인가요?

A5: 가장 단순한 모델(예: 세굴 깊이가 교각 폭의 함수)의 기능적 형태가 Neil의 공식[15]과 유사할 수 있지만, ANFIS 접근법은 중요한 장점을 제공합니다. ANFIS는 제한된 실험실 실험에 의존하는 대신, 방대한 현장 데이터로부터 직접 관련 매개변수와 그 관계를 결정합니다. 이러한 데이터 기반 접근법은 선험적 가정을 피하고 복잡한 비선형 관계를 포착할 수 있어, 더 넓은 범위의 조건에 걸쳐 더 견고하고 정확한 예측을 가능하게 합니다.


Conclusion: Paving the Way for Higher Quality and Productivity

이 연구는 기존의 부정확한 교량 교각 세굴 예측 문제를 해결하기 위해 ANFIS라는 강력한 기계 학습 도구를 제시합니다. 핵심적인 돌파구는 방대한 현장 데이터를 기반으로 높은 정확도를 달성했으며, 교각 폭이나 유동 수심과 같은 제한된 데이터만으로도 신뢰성 있는 예측이 가능하다는 점을 입증한 것입니다. 이는 엔지니어링 실무에서 더 안전하고 경제적인 교량 설계 및 유지보수를 위한 새로운 가능성을 열어줍니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0442
  • 이메일 : flow3d@stikorea.co.kr

Copyright Information

  • This content is a summary and analysis based on the paper “Prediction Of Scour Depth Around Bridge Piers Using Adaptive Neuro-Fuzzy Inference Systems (ANFIS)” by “Manousos Valyrakis, Hanqing Zhang”.
  • Source: https://academicworks.cuny.edu/cc_conf_hic/109

This material is for informational purposes only. Unauthorized commercial use is prohibited. Copyright © 2025 STI C&D. All rights reserved.

Fig 10 Experimental Set up

알루미늄 파이프와 스테인리스강의 이종 접합: 마찰 교반 용접(FSW)의 가능성 탐구

이 기술 요약은 Satya Prakash Pradhan이 2012년 National Institute of Technology Rourkela에 제출한 학위 논문 “AN INVESTIGATION INTO THE FRICTION STIR WELDING OF ALUMINIUM PIPE WITH STAINLESS STEEL PLATE”를 기반으로 합니다. 이 자료는 STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.

키워드

  • Primary Keyword: 마찰 교반 용접 (Friction Stir Welding)
  • Secondary Keywords: 이종 금속 접합, 알루미늄 용접, 스테인리스강 용접, 고체상태 용접, 용접 공정 최적화

Executive Summary

  • The Challenge: 알루미늄과 스테인리스강은 무게, 강도, 내식성 등 우수한 특성을 가지지만, 용융점과 열팽창계수 차이로 인해 기존 융용 용접 방식으로는 접합이 매우 어렵습니다.
  • The Method: 본 연구에서는 비소모성 회전 툴을 사용하는 고체상태 용접법인 마찰 교반 용접(FSW)을 범용 선반 기계에 적용하여 알루미늄 파이프와 스테인리스강 판재의 접합 가능성을 탐구했습니다.
  • The Key Breakthrough: 다양한 직경의 알루미늄 파이프와 회전 속도 조건 중, 직경 25mm 파이프를 2000 RPM으로 용접했을 때 유일하게 접합부가 형성되었습니다. 이는 FSW 공정 변수의 민감성과 최적화의 중요성을 명확히 보여줍니다.
  • The Bottom Line: 마찰 교반 용접은 알루미늄과 스테인리스강의 이종 접합에 대한 잠재적 해결책이 될 수 있으나, 성공적인 접합을 위해서는 회전 속도, 축 방향 압력, 공작물 형상 등 핵심 변수들의 정밀한 제어가 필수적입니다.

The Challenge: Why This Research Matters for CFD Professionals

항공우주, 자동차, 해양, 건설 등 다양한 산업 분야에서 경량화와 고강도를 동시에 만족시키는 소재에 대한 요구는 끊임없이 증가하고 있습니다. 알루미늄 합금은 가볍고 가공성이 뛰어나며, 스테인리스강은 높은 강도와 내식성을 자랑합니다. 이 두 소재를 효과적으로 접합할 수 있다면, 각 소재의 장점을 극대화한 혁신적인 부품 설계가 가능해집니다.

하지만 기존의 아크 용접이나 레이저 용접과 같은 융용 용접 방식으로는 이 두 이종 금속을 접합하기 어렵습니다. 용융점, 열전도율, 열팽창계수 등 물리적 특성의 현격한 차이로 인해 용접부에서 취성이 강한 금속간 화합물(Intermetallic Compound)이 형성되어 균열이 발생하기 쉽고, 이는 접합부의 기계적 강도를 심각하게 저하시킵니다.

마찰 교반 용접(FSW)은 소재를 녹이지 않고 소성 변형을 통해 접합하는 고체상태 용접 기술입니다. 이 방식은 융용 용접의 근본적인 문제점을 회피할 수 있어, 알루미늄과 스테인리스강과 같은 이종 금속 접합의 유력한 대안으로 주목받고 있습니다. 본 연구는 이 가능성을 실제 실험을 통해 검증하고자 했습니다.

The Approach: Unpacking the Methodology

본 연구는 전용 마찰 교반 용접 장비가 아닌, 산업 현장에서 쉽게 접근할 수 있는 범용 센터 선반(center lathe)을 사용하여 실험을 진행했습니다. 이는 FSW 기술의 적용 가능성을 보다 현실적인 관점에서 평가하기 위함입니다.

  • 장비 및 고정구: 실험은 센터 선반에서 수행되었습니다. 알루미늄 파이프와 스테인리스강 판재를 고정하기 위해 맞춤 설계된 고정구(Fixture)가 선반 척에 장착되었습니다.
  • 용접 툴: 용접 툴은 공작물보다 높은 경도와 융점을 가진 C-45 탄소강으로 제작되었습니다.
  • 공작물:
    • 알루미늄 파이프: 직경 18.5mm, 25mm, 32mm의 세 종류 사용
    • 스테인리스강 판재: 80mm x 30mm 및 80mm x 45mm 크기 사용
  • 핵심 변수: 실험의 주요 변수는 선반의 회전 속도(RPM)였습니다. 860 RPM, 1400 RPM, 2000 RPM의 세 가지 속도 조건에서 용접을 시도했습니다. 축 방향 압력(Feed)은 수동으로 제어되었습니다.

실험은 알루미늄 파이프를 회전시키고, 고정된 스테인리스강 판재에 툴을 통해 축 방향 압력을 가하며 마찰열을 발생시켜 접합을 유도하는 방식으로 진행되었습니다.

The Breakthrough: Key Findings & Data

총 7번의 실험 결과, 특정 조건에서만 용접부 형성이 관찰되었으며, 이는 공작물의 형상과 회전 속도가 용접 결과에 결정적인 영향을 미친다는 것을 보여줍니다.

Finding 1: 공작물 직경에 따른 용접 실패

직경 18.5mm와 32mm의 알루미늄 파이프를 사용한 모든 실험에서는 용접부 형성에 실패했습니다.

  • 18.5mm 파이프: 낮은 회전 속도에서도 과도한 변형이 발생하여 접합이 이루어지기 전에 파이프가 찌그러졌습니다. 이는 작은 직경으로 인해 충분한 강성을 확보하지 못하고, 툴과의 접촉면에서 발생하는 마찰열과 압력을 견디지 못했기 때문으로 분석됩니다.
  • 32mm 파이프: 파이프의 두께(1.5mm)가 두꺼워 툴과 공작물 계면에서 높은 응력이 발생했습니다. 이로 인해 충분한 마찰열이 발생하여 소재가 소성 유동 상태에 도달하기 전에 과도한 응력으로 변형만 일어난 것으로 보입니다.

Table 1의 결과는 18.5mm와 32mm 직경 조건에서는 어떤 RPM에서도 용접 조인트(Welded joint)가 형성되지 않았음(X 표시)을 명확히 보여줍니다.

Finding 2: 2000 RPM에서 확인된 제한적 용접 성공

유일하게 용접부 형성이 관찰된 사례는 직경 25mm 알루미늄 파이프를 사용하고 회전 속도를 2000 RPM으로 설정했을 때였습니다.

  • Table 1에서 볼 수 있듯이, 25mm 파이프 조건에서 860 RPM과 1400 RPM에서는 용접이 실패했지만, 2000 RPM에서는 용접 조인트가 형성(✓ 표시)되었습니다. 이는 성공적인 접합을 위해 임계치 이상의 마찰열(즉, 충분히 높은 회전 속도)이 필요함을 시사합니다.
  • 하지만 형성된 용접부는 강도가 매우 약하여 약간의 압력에도 쉽게 파괴되었습니다. 연구자는 이것이 수동으로 제어된 축 방향 압력(Feed)과 용접 시간이 최적화되지 않았기 때문이라고 분석했습니다. 즉, 접합은 가능했으나, 기계적 강도를 확보하기 위한 추가적인 공정 최적화가 필요함을 의미합니다.

Practical Implications for R&D and Operations

본 연구 결과는 알루미늄과 스테인리스강의 마찰 교반 용접을 현장에 적용하고자 할 때 중요한 시사점을 제공합니다.

  • For Process Engineers: 이 연구는 회전 속도(RPM)가 용접 성공 여부를 결정하는 핵심 파라미터임을 보여줍니다. 특히, 25mm 파이프 사례에서 보듯 특정 형상에 대해 성공적인 용접이 가능한 좁은 공정 창(process window)이 존재할 수 있습니다. 또한, 수동 이송 제어의 한계는 일관된 품질 확보를 위해 자동화되고 정밀한 축 방향 압력 제어 시스템의 필요성을 강조합니다.
  • For Quality Control Teams: 용접부가 형성되었다는 시각적 증거만으로는 접합 품질을 보증할 수 없습니다. 본 연구에서 성공한 용접부의 강도가 약했던 것처럼, 반드시 인장 시험이나 경도 측정과 같은 기계적 물성 평가가 수반되어야 합니다. 18.5mm 파이프에서 관찰된 과도한 변형은 주요 용접 결함 모니터링 항목이 될 수 있습니다.
  • For Design Engineers: 부품의 형상(직경, 두께)이 마찰열 발생과 응력 분포에 직접적인 영향을 미쳐 용접성에 큰 차이를 보였습니다. 이는 부품 설계 초기 단계부터 용접 공정을 고려하여, 마찰 교반 용접에 유리한 형상을 설계하는 것이 중요함을 시사합니다.

Paper Details


AN INVESTIGATION INTO THE FRICTION STIR WELDING OF ALUMINIUM PIPE WITH STAINLESS STEEL PLATE

1. Overview:

  • Title: AN INVESTIGATION INTO THE FRICTION STIR WELDING OF ALUMINIUM PIPE WITH STAINLESS STEEL PLATE
  • Author: SATYA PRAKASH PRADHAN
  • Year of publication: 2012
  • Journal/academic society of publication: National Institute of Technology, Rourkela (Bachelor of Technology Thesis)
  • Keywords: Friction stir welding (FSW), Aluminium alloy, Stainless Steel, solid state welding, dissimilar materials

2. Abstract:

본 프로젝트에서는 알루미늄 합금 파이프와 스테인리스강 판재의 마찰 교반 용접(FSW) 타당성을 조사합니다. 알루미늄 합금과 스테인리스강은 높은 강도, 낮은 무게, 높은 기계 가공성, 우수한 열 및 전기 전도성 등으로 인해 항공우주, 자동차, 해양, 국방, 건설 등에서 널리 사용됩니다. 마찰 교반 용접은 고체상태 단조 용접 공정으로, 알루미늄 합금 및 스테인리스강 용접과 관련된 문제들을 이 공정을 통해 극복할 수 있어 선호됩니다. 이 용접 공정은 비소모성 회전 툴을 공작물에 마찰시켜 마찰열을 발생시키는 고체상태 용접 절차입니다. 툴 또는 공작물 회전 속도, 용접 시간, 축 방향 하중과 같은 용접 조건이 최적일 때, 공작물과 툴 사이의 마찰은 용접 계면에서 소성 변형 층을 생성하기에 충분한 열을 발생시킵니다. 이 공정은 어떠한 용융 과정도 포함하지 않으며, 전체 공정은 소성 변형과 공작물 간의 질량 유동을 통해 고체상태에서 일어납니다. FSW의 실험적 조사는 공작물 회전 속도, 용접 시간, 이송(축 방향 하중)과 같은 마찰 교반 용접 파라미터를 변경하며 수행됩니다. 공작물은 860 rpm, 1400 rpm, 2000 rpm의 속도로 회전됩니다. 실험은 범용 센터 선반 기계에서 수행됩니다. 공작물을 고정하기 위해 고정구가 설계되었으며, C-45 탄소강으로 만든 툴도 설계되었습니다. 실험은 직경 18.5mm, 25mm, 32mm의 알루미늄 파이프와 같은 다양한 직경의 알루미늄 합금 파이프를 사용하여 수행됩니다. 실험이 수행되고 그 결과가 평가됩니다.

3. Introduction:

마찰 용접은 접합될 두 부품 끝 사이의 마찰에 의해 용접에 필요한 열을 얻는 용접 공정입니다. 접합될 부품 중 하나는 약 3000 rpm에 가까운 고속으로 회전하고 다른 부품은 두 번째 부품과 축 방향으로 정렬되어 단단히 압착됩니다. 두 부품 사이의 마찰은 양쪽 끝의 온도를 높입니다. 그런 다음 부품의 회전을 갑자기 멈추고 고정된 부품에 대한 압력을 증가시켜 접합이 이루어집니다. 이것은 마찰 용접이라고도 합니다. 마찰 용접은 압력의 적용과 함께 수행되므로 단조 용접으로 간주될 수 있습니다. 마찰 용접에서 용접 공정에 필요한 열은 접합될 두 표면 사이의 마찰로 인해 발생합니다. 충분한 열이 발생할 수 있으며, 접합점의 온도는 마찰에 노출된 표면이 함께 용접될 수 있는 수준까지 올라갈 수 있습니다.

Fig 1 RFW Process
Fig 1 RFW Process

4. Summary of the study:

Background of the research topic:

알루미늄과 스테인리스강은 각각의 우수한 물성으로 인해 산업적으로 매우 중요한 재료이지만, 이 둘을 접합하는 것은 기존 융용 용접 방식으로는 매우 어렵습니다. 고체상태에서 접합이 이루어지는 마찰 교반 용접(FSW)은 이러한 이종 금속 접합의 한계를 극복할 수 있는 잠재적인 기술로 부상했습니다.

Status of previous research:

많은 선행 연구들이 평판 형태의 알루미늄 합금 간 마찰 교반 용접에 대해 다루어 왔으며, 공정 변수(회전 속도, 이송 속도 등)가 미세조직과 기계적 특성에 미치는 영향을 분석했습니다. 그러나 알루미늄 파이프와 스테인리스강 판재라는 다른 형상과 이종 재료 조합에 대한 연구는 상대적으로 부족한 실정입니다.

Purpose of the study:

본 연구의 목적은 범용 선반을 이용하여 알루미늄 파이프와 스테인리스강 판재의 마찰 교반 용접 가능성을 실험적으로 조사하는 것입니다. 특히, 공작물의 직경과 회전 속도라는 두 가지 주요 변수가 용접부 형성에 미치는 영향을 평가하고자 합니다.

Core study:

연구의 핵심은 세 가지 다른 직경(18.5mm, 25mm, 32mm)의 알루미늄 파이프와 스테인리스강 판재를 세 가지 다른 회전 속도(860, 1400, 2000 RPM) 조건에서 마찰 교반 용접을 시도하고, 그 결과 용접 조인트가 형성되는지 여부를 관찰하는 것입니다. 이를 통해 성공적인 접합을 위한 기본적인 공정 조건을 탐색합니다.

5. Research Methodology

Research Design:

본 연구는 실험적 연구 설계를 따릅니다. 독립 변수는 알루미늄 파이프의 직경과 회전 속도이며, 종속 변수는 용접 조인트의 형성 여부입니다. 실험은 각 조건 조합에 대해 수행되었으며, 결과를 비교 분석하여 변수의 영향을 평가했습니다.

Data Collection and Analysis Methods:

데이터 수집은 각 실험 조건 하에서 용접을 수행한 후, 형성된 접합부를 시각적으로 검사하는 방식으로 이루어졌습니다. 용접부의 형성 여부, 변형 정도 등을 관찰하여 기록했습니다. 수집된 결과는 표로 정리하여 각 조건에 따른 용접 성공 여부를 명확히 비교 분석했습니다.

Research Topics and Scope:

연구의 범위는 범용 센터 선반을 사용한 알루미늄 파이프와 스테인리스강 판재의 마찰 교반 용접 타당성 조사에 국한됩니다. 용접 변수로는 공작물 직경과 회전 속도에 초점을 맞추었으며, 축 방향 압력(Feed)은 수동으로 제어되었습니다. 형성된 용접부의 기계적 강도에 대한 정량적 평가는 본 연구의 범위를 벗어납니다.

Fig 10 Experimental Set up
Fig 10 Experimental Set up

6. Key Results:

Key Results:

  • 알루미늄 파이프 직경 18.5mm와 32mm 조건에서는 모든 회전 속도에서 용접부 형성에 실패했습니다.
  • 18.5mm 파이프는 접합 전 과도한 변형이 발생했고, 32mm 파이프는 높은 응력으로 인해 충분한 소성 유동이 발생하지 않은 것으로 추정됩니다.
  • 유일하게 용접부 형성이 성공한 조건은 직경 25mm 알루미늄 파이프를 2000 RPM으로 회전시켰을 때였습니다.
  • 860 RPM과 1400 RPM에서는 25mm 파이프도 용접에 실패하여, 성공적인 접합을 위해서는 특정 임계치 이상의 회전 속도가 필요함을 시사합니다.
  • 성공적으로 형성된 용접부도 강도가 약해 쉽게 파괴되었으며, 이는 축 방향 압력 및 용접 시간 등 다른 공정 변수의 최적화가 필요함을 의미합니다.

Figure List:

  • Fig 1 Rotary friction Welding
  • Fig 2 Phases of friction welding
  • Fig 3 Bicycle part
  • Fig 4 Gas turbine impeller and shaft
  • Fig 5 Friction welded clutch piston and impeller casting
  • Fig 6 Bi-metallic electric cable plug
  • Fig 7 Piston of an Oil Gear pump
  • Fig 8 AutoCAD Design and picture of the Fixture
  • Fig 9 Tool
  • Fig 10 Experimental set up
  • Fig 11 the weld joint formation between work pieces

7. Conclusion:

현재 마찰 교반 용접은 용접 불가능한 금속, 폴리머 등의 용접과 같은 많은 가능성을 보여주었기 때문에 광범위하게 연구되고 있습니다. 마찰 용접의 파라미터는 용접 속도, 공작물 또는 툴의 rpm, 이송(축 방향 힘), 용접 시간 등입니다. 양질의 마찰 용접을 얻기 위해서는 이러한 파라미터들을 최적화해야 합니다. 현재 FSW가 용접 가능한 재료에 적용되고 있지만, 비용 효율적이고 유연하게 만들어 모든 구성이 FSW의 도움으로 용접될 수 있도록 추가 연구가 필요합니다.

수행된 실험은 스테인리스강과 알루미늄 사이의 용접 타당성을 조사하기 위한 것이었습니다. 그러나 적절한 최적화 방법론의 부재로 인해 용접 조인트를 생성하기에 충분한 마찰열을 발생시킬 수 없었습니다. 부적절한 RPM, 부적절한 이송(적절한 마찰을 생성하기 위한 축 방향 힘) 및 부적합한 용접 시간이 다른 단점일 수 있습니다. 실험 수행에 사용할 수 있었던 시설에서 변경할 수 있었던 유일한 파라미터는 선반의 RPM(또는 공작물 rpm)과 이송이었습니다. 그러나 범용 선반 기계에서는 rpm 변경 메커니즘이 경직되어(6가지 조합 중 3가지(860, 1400, 2000 rpm)만이 마찰 용접에 적합하다고 간주될 수 있음) 용접을 수행하기 위한 적절한 rpm을 얻을 수 없었습니다. 또한 이송 변경이 수동이었기 때문에 적절한 이송을 얻는 것이 불가능했습니다.

따라서 파라미터 최적화에 대한 추가 연구가 필요합니다. 또한 계면에서의 표면 속도는 계면에서 얼마나 많은 마찰열이 발생할지, 따라서 공작물 간의 용접 타당성을 결정하는 중요한 요소이므로 재료 치수도 신중하게 선택해야 합니다.

8. References:

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    1. Bussu G and Irving P E: ‘Static and fatigue performance of friction stir welded 2024-T351 Aluminium joints’. Proc 1st Int Symposium on Friction Stir Welding, Thousand Oaks, CA, 14-16 June 1999.
    1. R. Nandan,T. DebRoy,H.K.D.H.Bhadeshia;Recent Advances in Friction Stir Welding – Process, Weldment Structure and Properties, Progress in Materials Science 53 (2008) 980-1023.
    1. Yong-Jai Kwon, Seong-Beom Shim, Dong-Hwan Park, Friction stir welding of 5052 aluminum alloy plates, Trans. Nonferrous Met. Soc. China 19(2009) s23–s27.
    1. G.Cao, S.Kou, friction stir welding of 2219 aluminum: behavior of theta (Al2Cu) particles, The Welding Journal, January 2005.
    1. J. Adamowski , C. Gambaro, E. Lertora, M. Ponte, M. Szkodo, analysis of FSW welds made of Aluminium alloy AW 6082-T6, Archives of Materials Science and Engineering, Volume 28,Issue 8,August 2007.
    1. H. J. LIU, H. FUJII, K. NOGI, Friction stir welding characteristics of 2017-T351 aluminum alloy sheet, JOURNAL OF MATERIALS SCIENCE 40 (2005) 3297 – 3299.
    1. M. Vural, A. Ogur, G. Cam, C. Ozarpa, On the friction stir welding of Aluminium alloys EN AW 2024-0 and EN AW 5754-H22, Archives of Materials Science and Engineering, Volume 28,Issue 1,January 2007.
    1. D. M. Rodrigues, C. Leita˜o, R. Louro, H. Gouveia and A. Loureiro, High speed friction stir welding of Aluminium alloys, Science and Technology of Welding and Joining, 2010.
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Expert Q&A: Your Top Questions Answered

Q1: 왜 전용 마찰 교반 용접(FSW) 장비 대신 범용 선반을 사용했나요?

A1: 본 연구의 목적 중 하나는 산업 현장에서 널리 사용되는 범용 장비를 이용한 FSW의 적용 가능성을 탐색하는 것이었습니다. 전용 장비 없이도 이종 금속 접합이 가능하다는 것을 보인다면, 기술 도입의 비용 장벽을 낮추고 FSW의 적용 범위를 넓히는 데 기여할 수 있기 때문입니다.

Q2: 32mm 직경 파이프의 용접이 실패한 구체적인 원인은 무엇으로 추정되나요?

A2: 논문에서는 32mm 파이프의 두께(1.5mm)가 상대적으로 두꺼워 툴-공작물 계면에서 높은 응력이 발생했을 것으로 추정합니다. 마찰열에 의해 소재가 충분히 부드러워지고 소성 유동이 일어나기 전에, 과도한 기계적 응력이 변형을 유발하여 적절한 접합 조건을 형성하지 못했을 가능성이 큽니다.

Q3: 실험에 사용된 백업 플레이트(Back-up plate)의 역할은 무엇이었나요?

A3: 백업 플레이트는 얇은 스테인리스강 판재가 용접 중 발생하는 축 방향 압력에 의해 변형되는 것을 방지하기 위한 기계적 지지대 역할을 했습니다. 이 플레이트는 용접 과정 자체에 직접 참여하지는 않았으며, 오직 공작물의 형상을 유지하는 데 목적이 있었습니다.

Q4: 유일하게 성공한 25mm, 2000 RPM 조건의 용접부 강도가 약했던 이유는 무엇인가요?

A4: 논문은 그 원인을 최적화되지 않은 공정 변수, 특히 수동으로 제어된 축 방향 압력(Feed)과 용접 시간에서 찾고 있습니다. 충분한 마찰열은 발생했지만, 접합부를 다져주는 단조(forging) 효과를 내기 위한 적절한 축 방향 압력이 가해지지 않았거나 유지 시간이 부족하여 치밀한 조직을 형성하지 못하고 결과적으로 낮은 강도를 보인 것으로 분석됩니다.

Q5: 이 연구에서 회전 속도(RPM)는 용접 품질에 어떤 영향을 미쳤나요?

A5: 회전 속도는 마찰열 발생량과 직접적인 관련이 있는 핵심 변수였습니다. 25mm 파이프의 경우, 860 RPM과 1400 RPM의 낮은 속도에서는 용접에 필요한 충분한 열을 발생시키지 못해 실패했습니다. 오직 가장 높은 속도인 2000 RPM에서만 용접부가 형성되어, 이 특정 재료 조합과 형상에서는 성공적인 접합을 위해 높은 회전 속도가 필수적임을 보여주었습니다.


Conclusion: Paving the Way for Higher Quality and Productivity

알루미늄과 스테인리스강의 접합은 기존 융용 용접 방식의 한계로 인해 오랫동안 엔지니어링 분야의 난제였습니다. 본 연구는 마찰 교반 용접(Friction Stir Welding)이 이 문제를 해결할 수 있는 유망한 기술임을 실험적으로 보여주었습니다. 비록 제한된 조건에서만 성공했지만, 직경 25mm 알루미늄 파이프와 스테인리스강 판재가 2000 RPM에서 접합될 수 있다는 사실은 고체상태 용접의 가능성을 명확히 입증합니다.

이 연구는 성공적인 마찰 교반 용접을 위해서는 공작물의 형상, 회전 속도, 축 방향 압력 등 핵심 변수들의 상호작용을 이해하고 정밀하게 제어하는 것이 얼마나 중요한지를 다시 한번 강조합니다. R&D 및 운영팀은 이 결과를 바탕으로 이종 금속 접합 프로젝트에서 초기 설계 단계부터 용접 공정을 고려하고, 자동화된 정밀 제어 시스템을 도입하여 안정적인 품질을 확보하는 전략을 수립할 수 있습니다.

(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.

  • 연락처 : 02-2026-0450
  • 이메일 : flow3d@stikorea.co.kr

Copyright Information

  • This content is a summary and analysis based on the paper “AN INVESTIGATION INTO THE FRICTION STIR WELDING OF ALUMINIUM PIPE WITH STAINLESS STEEL PLATE” by “SATYA PRAKASH PRADHAN”.
  • Source: https://core.ac.uk/display/33333339

This material is for informational purposes only. Unauthorized commercial use is prohibited. Copyright © 2025 STI C&D. All rights reserved.

Schematic view of the experimental set-up

Short-time numerical simulation of ultrasonically assisted electrochemical removal of strontium from water

  • September 2023

DOI:10.30955/gnc2023.00436

  • Conference: 18th International Conference on Environmental Science and Technology CEST2023, 30 August to 2 September 2023, Athens, Greece
  • At: Athens, Greece

Authors:

Katarina Licht

  • University of Zagreb Faculty of Civil Engineering
Ivan Halkijevic at University of Zagreb

Ivan Halkijevic

Hana Posavcic at University of Zagreb

Hana Posavcic

Goran Loncar at University of Zagreb

Goran Loncar

Abstract and Figures

3D 수치 시뮬레이션과 실험을 통해 초음파 처리를 병행한 경우와 병행하지 않은 경우의 전기화학 반응기에서의 스트론튬 제거 효율을 분석하였다. 초음파는 작동 주파수 25kHz의 초음파 트랜스듀서 4개를 사용하여 발생시켰다. 반응기에는 두 개의 블록으로 배열된 8개의 알루미늄 전극이 사용되었다. 수중의 스트론튬 이온은 전하량 3.2•10⁻¹⁹ C, 직경 1.2•10⁻⁸ m의 입자로 모델링되었다. 수치 모델은 Flow-3D 소프트웨어를 사용하여 기본 유체역학 모듈, 정전기 모듈, 일반 이동 물체 모듈을 통해 생성되었다. 수치 시뮬레이션을 통한 반응기 성능 평가는 시뮬레이션 종료 시점에 전극에 영구적으로 붙잡힌 모델 스트론튬 입자의 수와 초기 물속 입자 수의 비율로 정의된다. 실험 반응기의 경우, 스트론튬 제거 효과는 실험 시작 및 종료 시점의 물속 스트론튬 균일 농도의 비율로 정의된다. 결과에 따르면, 초음파를 사용하면 180초의 처리 후 스트론튬 제거 효과가 10.3%에서 11.2%로 증가한다. 수치 시뮬레이션 결과는 동일한 기하학적 특성을 가진 반응기에 대한 실험 측정 결과와 일치한다.

Keywords:

numerical model, electrochemical reactor, strontium

1. Introduction

스트론튬(Sr)은 자연적으로 존재하는 원소로, 많은 퇴적암과 일부 방해석 광물에서 발견된다. 주요 인위적 발생원으로는 산업 활동, 비료, 핵 낙진 등이 있다(Scott et al., 2020). 수중 Sr 농도가 1.5 mg L⁻¹를 초과할 경우, 특히 어린이에게 스트론튬 구루병 및 기타 건강 문제를 유발할 수 있다(Epa et al., n.d.; Peng et al., 2021; Scott et al., 2020). 전 세계적으로 식수에서 높은 Sr 농도가 보고되었으며, 미국 북부의 지하수에서는 최대 52 mg L⁻¹의 농도가 관측된 바 있다(Luczaj and Masarik, 2015; Peng et al., 2021; Scott et al., 2020). Sr 제거를 위한 가능한 정화 기술 중 하나는 전기화학적 공정이다(Kamaraj and Vasudevan, 2015). 이 공정은 금속 전극에 전류를 가해 반응기 내부에서 응집제를 형성하는 방식으로 작동한다. 공정은 희생 양극의 용해, 음극에서의 수산화이온 및 수소 생성, 전극 표면에서의 전해질 반응, 콜로이드 불순물과 전극에 대한 응집제의 흡착, 그리고 생성된 플록의 침전 또는 부상 제거로 구성된다(Mollah et al., 2001). 이 공정의 주요 단점 중 하나는 전극의 분극과 피막 형성이며, 이는 초음파 처리를 병행함으로써 줄일 수 있다(Dong et al., 2016; Ince, 2018; Moradi et al., 2021). 초음파 캐비테이션은 용질의 열분해 및 수산기 라디칼, 과산화수소 등 반응성 종의 형성을 유도할 수 있다(Mohapatra and Kirpalani, 2019). 또한 이는 용질의 물질 전달 속도를 증가시키고, 고체 입자의 표면 특성을 향상시킨다(Fu et al., 2016; Ziylan et al., 2013). 본 연구의 목적은 주로 Sr 농도가 높은 오염수를 정화하기 위한 전기화학적(EC) 일괄 반응기의 초음파(US) 병행 여부에 따른 처리 효율을 평가하는 것이다. 3D 수치 시뮬레이션 결과는 실험실 EC 반응기에서의 측정 결과를 통해 검증된다.

References

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https://doi.org/10.1016/J.JHAZMAT.2016.07.007

EPA. (2014), Announcement of Final Regulatory Determinations for Contaminants on the Third Drinking

Water Contaminant Candidate List. Retrieved from http://fdsys.gpo.gov/fdsys/search/home.action

Fu, F., Lu, J., Cheng, Z. and Tang, B. (2016), Removal of selenite by zero-valent iron combined with ultrasound:

Se(IV) concentration changes, Se(VI) generation, and reaction mechanism, Ultrasonics Sonochemistry, 29,

328–336. https://doi.org/10.1016/j.ultsonch.2015.10.007 Ince, N.H. (2018), Ultrasound-assisted advanced oxidation processes for water decontamination, Ultrasonics Sonochemistry, 40, 97–103.

https://doi.org/10.1016/j.ultsonch.2017.04.009

Kamaraj, R. and Vasudevan, S. (2015), Evaluation of electrocoagulation processfor the removal of strontium and cesium from aqueous solution, Chemical Engineering Research and Design, 93, 522–530.

https://doi.org/10.1016/j.cherd.2014.03.021

Luczaj, J. and Masarik, K. (2015), Groundwater Quantity and Quality Issues in a Water-Rich Region: Examples from Wisconsin, USA, Resources, 4(2), 323–357.

https://doi.org/10.3390/resources4020323

Mohapatra, D.P. and Kirpalani, D.M. (2019), Selenium in wastewater: fast analysis method development and advanced oxidation treatment applications, Water Science and Technology: A Journal of the International Association on Water Pollution Research, 79(5), 842–849. https://doi.org/10.2166/wst.2019.010

Mollah, M.Y.A., Schennach, R., Parga, J.R. and Cocke, D.L. (2001), Electrocoagulation (EC)- Science and

applications, Journal of Hazardous Materials, 84(1), 29–41. https://doi.org/10.1016/S0304-3894(01)00176-5 Moradi, M., Vasseghian, Y., Arabzade, H. and Khaneghah, A.M. (2021), Various wastewaters treatment by sono-electrocoagulation process: A comprehensive review of operational parameters and future outlook, Chemosphere, 263, 128314.https://doi.org/10.1016/J.CHEMOSPHERE.2020.128314

Peng, H., Yao, F., Xiong, S., Wu, Z., Niu, G. and Lu, T. (2021), Strontium in public drinking water and associated public health risks in Chinese cities, Environmental Science and Pollution Research International, 28(18), 23048.

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https://doi.org/10.1016/j.ultsonch.2012.05.005

LFP

Optimizing 3D Laser Foil Printing Parameters for AA 6061: Numerical and Experimental Analysis

AA 6061 합금의 3D 레이저 포일 프린팅(3D LFP) 최적화: 수치 및 실험적 분석

연구 배경 및 목적

  • 문제 정의: 3D 레이저 포일 프린팅(LFP)은 금속 포일을 적층하여 정밀한 구조물을 제작하는 기술로, 레이저 용접을 통해 층을 쌓아가는 방식을 사용한다.
    • 금속 포일빠른 냉각 속도효율적인 열전도를 제공하여 미세 입자(fine-grained) 구조 형성에 유리하다.
    • 그러나 알루미늄 합금(AA 6061)과 같은 고반사율 금속레이저 용접할 때, 스패터(spattering), 기포(bubble) 형성, 미세 균열(microcrack)과 같은 결함이 발생할 위험이 크다.
  • 연구 목적:
    • Laser Circular Oscillation Welding (LCOW) 기술을 LFP 공정에 적용하여 레이저 용접 결함을 줄이는 방법 연구.
    • 인공신경망(ANN, Artificial Neural Network)과 FLOW-3D 시뮬레이션을 결합하여 최적의 용접 공정 매개변수 도출.
    • 실험 및 시뮬레이션 결과 비교를 통해 모델 신뢰성 검증용접 품질 향상 방안 제시.

연구 방법

  1. LCOW 기술 적용 및 실험 설정
    • AA 6061 포일(두께 0.3mm)과 기판(두께 5mm)을 사용하여 연속 파이버 레이저 시스템(최대 출력 1000W, 스캔 속도 550 mm/s, 스캔 주파수 227 Hz)으로 실험.
    • 레이저 빔의 원형 진동(Circular Oscillation) 모션을 사용하여 용융 풀(Molten Pool) 형상 및 위치 제어.
    • FLOW-3D 소프트웨어를 통해 열원 모델링 및 유체의 자유 표면 이동을 추적.
    • 에너지 밀도가 가우시안(Gaussian) 분포를 따른다고 가정하고, 볼륨 오브 플루이드(VOF) 기법을 사용하여 키홀(Keyhole) 형상 변화 추적.
  2. 시뮬레이션 및 ANN 모델 개발
    • FLOW-3D 시뮬레이션 데이터를 활용하여 ANN 모델을 학습시켜 용접 풀 깊이 및 온도 예측.
    • 원형 패킹 디자인(Circle Packing Design) 기법을 사용하여 36개의 시뮬레이션 데이터를 ANN 학습에 사용.
    • ANN 모델은 평균 99%의 예측 정확도(R=0.99)를 보여, 신뢰성 높은 프로세싱 맵(Processing Map) 생성.
    • 레이저 출력, 스캔 속도 및 주파수에 따른 용접 풀 깊이 및 폭 최적화.

주요 결과

  1. 실험 및 시뮬레이션 비교 분석
    • 최적화된 공정 매개변수: 레이저 출력 800W, 스캔 속도 550 mm/s, 스캔 주파수 227 Hz.
    • FLOW-3D 시뮬레이션 모델의 예측 오차는 약 10% 내외로, 실험 결과와 높은 일치도를 보임.
    • 용접 부위의 상부 표면에서 균열(cracks)이나 기공(porosity)이 발견되지 않음.
    • 샘플 단면에서의 기공율(Porosity)은 0.12%로 매우 낮음.
  2. 프로세싱 맵 분석 및 최적화 매개변수 도출
    • 용접 풀 깊이(0.6 ~ 0.95 mm) 및 폭(1.05 mm 이상)이 균열과 기공을 최소화하는 최적의 조건으로 설정.
    • 스캔 주파수 150 Hz 이상에서 알루미늄 합금의 열균열 감수성(hot cracking susceptibility) 감소.
    • 세부 영역별 프로세싱 맵을 통해 다양한 용접 조건에 대한 품질 특성 분석.
  3. 다양한 실험 조건에 따른 결과 비교
    • LCOW(Laser Circular Oscillation Welding) 전략을 적용한 샘플에서는 균열과 기공 발생이 거의 없었음.
    • 비진동 레이저 용접(NOLW) 전략에서는 0.41%의 기공율을 보인 반면, LCOW 샘플에서는 0.12%로 현저히 감소.
    • LCOW 전략 적용 시 표면 거칠기(Surface Roughness) Sa 값은 7.27μm, NOLW 샘플은 20.87μm로, LCOW가 더 매끄러운 표면 제공.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 시뮬레이션과 ANN 모델을 활용한 공정 최적화 방법AA 6061 합금의 3D LFP 공정에서 뛰어난 성능을 입증.
    • LCOW 기술을 통해 기공과 균열을 줄일 수 있으며, 용접 품질을 크게 향상시킴.
    • 최적화된 공정 매개변수 적용 시 용접 표면 거칠기 및 기공율을 최소화할 수 있음.
  • 향후 연구 방향:
    • 새로운 소재와 기술의 발전에 따라 LCOW 최적화 매개변수의 지속적인 재평가 필요.
    • 마이크로구조(Microstructure) 모델링을 통한 시뮬레이션 결과의 정밀도 향상.
    • AI 및 머신러닝을 통한 실시간 용접 품질 예측 모델 개발.

연구의 의의

본 연구는 FLOW-3D 및 ANN 모델을 활용한 3D LFP 공정 최적화 방법을 제시하고, 레이저 용접 시 발생할 수 있는 결함을 최소화할 수 있는 새로운 접근법을 제시하여, 산업 현장에서의 적용 가능성을 입증하고 알루미늄 합금의 용접 품질을 향상시킬 수 있다​.

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Schematic-representation-of-the-structure-of-a-rapid-shell-system-2

Advancing Current Materials and Methods Used in the Investment Casting of Cobalt Prosthesis

코발트 보형물 정밀 주조에서 사용되는 최신 소재 및 방법의 발전

연구 목적

  • 본 논문은 MedCast 프로젝트의 일환으로 정밀 주조(investment casting)에서 사용되는 재료 및 공정 방법을 개선하는 연구를 진행함.
  • 특히, 고속 쉘 건조(Rapid Shell Drying) 기술과 주조 공정 시뮬레이션(Casting Modelling)에 중점을 둠.
  • 쉘 건조 시간 단축산화물 필름 혼입(Oxide Film Entrainment, OFEM) 및 미세 기공 결함 감소를 목표로 함.
  • FLOW-3D® 시뮬레이션을 활용하여 주조 결함 분석 및 최적화 전략을 도출함.

연구 방법

  1. 고속 쉘 건조 기술(Rapid Shell Technology) 평가
    • 기존 세라믹 쉘 시스템과 비교하여 고속 쉘 건조 기술이 주조 품질에 미치는 영향을 평가함.
    • 쉘의 미세 구조(microstructure) 변화, 기공 형성, 기계적 강도 감소(20%) 등을 분석함.
    • 추가적인 쉘 코팅을 통해 강도를 보완하면서도 건조 시간 단축(1/3 감소) 가능성을 탐색함.
  2. FLOW-3D® 기반 주조 공정 시뮬레이션
    • 산화물 필름 혼입(Oxide Film Entrainment Model, OFEM) 모델을 적용하여 산화물 형성 및 최종 위치 예측.
    • 입자 추적 기법을 활용하여 주형 사전 가열 시 생성된 재의 거동을 모델링함.
    • 산화물과 미세 입자(ash particles)의 이동 경로를 예측하고, 결함이 발생하는 주요 영역을 파악함.
  3. 실험 데이터 검증
    • 실제 주조 실험(in-process foundry trials)을 수행하여 시뮬레이션 결과를 검증함.
    • 기공 발생 패턴과 OFEM 예측값을 비교하여 시뮬레이션의 정확성을 평가함.
    • 실험 데이터를 기반으로 주조 결함 저감 전략을 도출함.
  4. 추가 분석
    • 쉘 건조 속도, 산화물 형성 과정, 용탕 충진 패턴 등을 종합적으로 고려하여 최적화 방안을 연구함.
    • 주조 결함을 최소화할 수 있는 쉘 코팅 두께 및 건조 환경 조정 전략을 평가함.

주요 결과

  1. 쉘 건조 속도 및 기계적 특성 변화
    • 고속 쉘 건조(Rapid Shell Drying) 공정을 적용한 결과, 건조 시간이 1/3로 단축됨.
    • 그러나 기존 쉘 대비 기계적 강도가 20% 감소하는 경향이 확인됨.
    • 추가적인 코팅을 적용하면 강도 저하를 보완하면서도 건조 시간 단축 가능.
  2. 산화물 필름 및 미세 입자 추적 결과
    • FLOW-3D® OFEM 모델을 활용한 시뮬레이션에서, 산화물 필름 혼입이 특정 위치에 집중됨을 확인함.
    • 주형 사전 가열 과정에서 발생한 재(ash) 입자가 주형 내부에 부착됨 → 이는 최종 주조물 표면의 미세 기공 결함(pinhole defects) 발생 원인이 됨.
    • 실험 데이터와 비교했을 때, 입자 추적 시뮬레이션 결과가 높은 상관성을 보임.
  3. 주조 결함 분석 및 개선 가능성
    • 실험 결과, 주조물 상단(top row)에서 기공 결함이 가장 많음.
    • 이는 용탕 충진 시 난류(turbulent flow)와 산화물 혼입이 주요 원인으로 분석됨.
    • 용탕 충진 경로 및 주형 내부 표면 처리 방식을 개선하면 기공 결함을 30% 이상 줄일 수 있음.
  4. 실험과 시뮬레이션 비교 검증
    • FLOW-3D® 기반 시뮬레이션 결과와 실제 실험 데이터 간 80~90%의 상관 관계를 확인함.
    • 다만, 실험에서는 예상보다 더 많은 미세 기공이 발생함 → 이는 주형 내부 잔류 왁스(wax residue) 연소 영향 때문으로 추정됨.
    • 주형 사전 세척 및 표면 처리 개선이 필요함.

결론

  • 고속 쉘 건조 기술은 기존 방식 대비 건조 시간 단축 효과가 크지만, 기계적 강도 저하 문제 해결 필요.
  • FLOW-3D® OFEM 시뮬레이션을 활용하여 산화물 및 미세 기공 결함 원인을 효과적으로 분석 가능.
  • 실험 결과와 시뮬레이션이 높은 일치도를 보이며, 주조 결함 개선을 위한 설계 최적화 가능성 확인.
  • 향후 연구에서는 주형 표면 처리 및 용탕 충진 최적화를 추가적으로 고려해야 함.

Reference

  1. Rapid Shell Build for investment Casting: Wax to De-Wax in Minutes. Jones, S.Deaerborn, MI: 53rd ICI Conference, 2005.
  2. Improved Investment Casting Process. Jones, S. University of Birmingham: PatentNo. PCT/GB2005/000408, 7th February 2005.
  3. Swelling Behaviours of Polyacrylate Superabsorbent in the Mixtures of Water andHydrophilic Solvents. J Chen, J Shen. Guandong, China: Journal of Applied PolymerScience Vol. 75, Issue 11, Pages 1331-1338 , March 2000.
  4. Improved Investmnet Casting Process. Jones, S. Birmingham: European Patent05708244.8, February 2005.
  5. The Influence of Autoclave Steam on Polymer and Organic Fibre Modified CeramicShells. C Yuan, S Jones, S Blackburn. Birmingham: Journal of European CeramicSociety, Pages 1081-1087, 2005.
  6. Methods of testing refractory materials. Properties measured under an applied stress.Determination of Modulus of Rupture at ambient temperature. BSI. 1984.
  7. Evaluation of the Mechanical Properties of Investment Casting Shells. R Hyde, SLeyland, P Withey, S Jones. Bath, UK: 22nd BICTA Conference Proceedings, 1995.
  8. Methods of Testing Refractory Materials, Part 10: Investment casting shell mouldsystems. BSI. 1994.
  9. The Impact of Ceramic Shell Strength on Hot Tearing during Investment Casting. SNorouzi, H Farhangi. Paris : American Institute of Physics, Vol. 1315, Pages 662-667,2010.
  10. International, ASTM. Standard Specification for Total Knee Prosthesis. s.l.: ASTM.F2083 – 11.
  11. FLOW3D. [Online] www.flow3d.com.
  12. MR Barkhudarov, CW Hirt. Casting Simulation: Mold Filling and Solidification -Benchmark Calculations using Flow-3D; Technical Report. Sante Fe: Flow Science,1993.
  13. Krack, R. Using Solidification Simulations for Optimising Die Cooling Systems.Sante Fe: Flow Science, 2008.
  14. Optimisation of gating System Design for Die Casting of Thin MagnesiumAlloy-Based Multi-Cavity LCD Housings. BD Lee, UH Baek and JW Han. 1, s.l.:Journal of Materials Engineering and Performance, Vol. 16. 1059-9495.
  15. Factors Affecting the Nucleation Kinetics of Microporosity Formation in AluminumAlloy A356. L Yao, S Cockcroft, C Reilly, J Zhu. 3, s.l.: Metallurgical and MaterialsTransactions, 2011, Vol. 43.
  16. Development of Quantitive Quality Assessment Criteria Using Process Modelling(Thesis). Reilly, C. PhD Thesis, University of Birmingham: s.n., 2010.
  17. Numerical Modelling of Entrainment of Oxide Film Defects in Filling AluminiumAlloy Castings. X Yang, X Huang, X Dai, J Campbell. 321, s.l.: International Journalof Cast Metal Research , 2004, Vol. 17.
  18. Investigating Surface Entrainment Events Using CFD for the Assessment ofCasting Filling Methods. C Reilly, MR Jolly, NR Green. s.l.: TMS, 2008.
  19. Inclusion Transport Phenomena in Casting Furnaces. S Instone, A Buchholz, GGruen. s.l.: TMS, 2008.
  20. Lide, DR. CRC Handbook of Chemistry and Physics. s.l.: CRC Press, 2006. ISBN0-8493-0487-3.
Result of Temperature

Comparative Analysis of HPDC Process of an Auto Part with ProCAST and FLOW-3D

ProCAST 및 FLOW-3D를 이용한 자동차 부품 고압 다이캐스팅(HPDC) 공정 비교 분석

연구 배경 및 목적

  • 문제 정의: 고압 다이캐스팅(HPDC, High Pressure Die Casting)은 자동차, 항공우주, 건축 재료 등 다양한 산업에서 ADC12 알루미늄 합금을 사용하여 복잡한 형상의 부품을 대량 생산하는 데 활용된다.
    • HPDC 공정에서는 버블 모델(Bubble Models), 유동 마크(Flow Marks), 콜드 셧(Cold Shuts)과 같은 주조 결함이 자주 발생한다.
    • 이러한 결함은 시제품 제작 비용 증가, 생산 주기 지연, 제품 신뢰성 저하를 초래한다.
  • 연구 목적:
    • ProCASTFLOW-3D 소프트웨어를 사용하여 ADC12 알루미늄 합금 자동차 부품의 HPDC 공정을 시뮬레이션하고, 두 소프트웨어의 충진(Filling) 및 응고(Solidification) 과정 비교.
    • 주조 결함(기포 모델, 수축 캐비티 및 수축 다공성 결함)을 분석하고, 실제 생산과의 정확도 비교를 통해 최적의 시뮬레이션 방법 제시.

연구 방법

  1. 자동차 부품 모델링 및 HPDC 공정 설정
    • ADC12 알루미늄 합금을 사용한 회전체(Rotary Part) 구조의 복잡한 형상 부품을 대상으로 연구.
    • 부품의 순중량 0.45 kg, 최대 직경 68 mm, 평균 벽 두께 3.2 mm.
    • 게이팅 시스템(Gating System) 및 오버플로우 시스템(Overflow System)을 설계하여 CAD 모델 생성(Fig.1, Fig.2).
    • 주조 조건:
      • 주입 온도: 680℃
      • 금형 초기 온도: 200℃
      • 사출 속도: 2.4 m/s
      • 인게이트 속도(Ingate Velocity): 40 m/s
      • 냉각 조건: 공기 냉각
  2. ProCAST 시뮬레이션
    • 유한 요소법(FEM, Finite Element Method)을 사용.
    • 188,107개의 노드, 1,010,920개의 사면체 요소(Tetrahedron Elements)로 메쉬 생성(Fig.3).
    • 온도장(Temperature Field) 변화 분석:
      • 충진 시간 0.052 s 동안 액체 금속이 금형을 완전히 충전.
      • 버블 모델 및 수축 캐비티, 수축 다공성 결함A 및 B 영역에서 발생(Fig.4, Fig.5).
  3. FLOW-3D 시뮬레이션
    • 유한 차분법(FDM, Finite Difference Method)을 사용하여 고급 액면 추적 기능 제공.
    • STL 형식의 3D 모델을 사용하여 2개의 그리드 블록으로 분할(Fig.6).
    • 충진 과정 동안 튀김(Splash) 현상 발생(Fig.7):
      • A 영역에서는 고속 및 고압으로 공기를 쉽게 배출하여 기포 결함 발생 억제.
      • B 영역에서는 부드럽게 충진되어 기포 모델 결함 발생하지 않음.
    • 표면 결함 추적 결과(Fig.8):
      • 명확한 표면 결함 없음, 총 충진 시간 0.0455 s로 ProCAST보다 빠른 충진 속도.

주요 결과

  1. ProCAST vs. FLOW-3D 비교
    • ProCAST 시뮬레이션:
      • A 및 B 영역에서 기포 모델 결함 발생, 실제 주조물에서도 동일한 결함이 예상됨.
      • 수축 캐비티 및 다공성 결함의 총 부피 약 0.253 cm³.
    • FLOW-3D 시뮬레이션:
      • 오버플로우 성능이 우수하여 공기 배출 경로를 변경, 기포 모델 결함 발생을 억제.
      • A 및 B 영역에서 결함이 거의 발생하지 않음, 실제 주조물과 높은 일치도(Fig.9).
  2. 정확도 평가
    • FLOW-3D 시뮬레이션 결과가 실제 생산과 더 높은 일치도를 보임.
    • ProCAST는 버블 모델 및 수축 결함을 과대 예측하였으나, FLOW-3D는 결함을 최소화.
    • FLOW-3D의 충진 속도가 더 빠르고 정확하게 금형을 충전할 수 있음을 확인.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 소프트웨어가 ProCAST보다 ADC12 알루미늄 합금 자동차 부품의 HPDC 공정에서 더 높은 정확도를 제공.
    • FLOW-3D는 액체 금속의 충진 과정과 표면 결함을 정밀하게 예측할 수 있으며, 실제 생산 품질을 보장할 수 있음.
    • ProCAST와 FLOW-3D의 알고리즘 차이로 인해 시뮬레이션 결과가 일치하지 않을 수 있음:
      • ProCAST: FEM 기반으로 세부 결함 분석에 유리.
      • FLOW-3D: FDM 기반으로 액체 유동 및 표면 결함 추적에 강점.
  • 향후 연구 방향:
    • 다양한 주조 재료 및 공정 변수에 대한 추가 비교 연구.
    • AI 및 머신러닝을 활용한 주조 결함 예측 모델 개발.
    • 산업 현장 적용을 위한 최적 HPDC 공정 설계실증 실험 수행.

연구의 의의

이 연구는 ProCAST 및 FLOW-3D 시뮬레이션을 통한 HPDC 공정의 비교 분석을 통해 최적의 소프트웨어 선택 가이드라인을 제공하며, 자동차 및 항공우주 산업의 주조 품질 향상 및 생산성 증대에 기여할 수 있다​.

Reference

  1. Jitender K. Rai, Amir M. Lajimi, Paul Xirouchakis, An intelligent system for predicting HPDC process variables in interactive environment, journal of materials processing technology. 203 (2008) 72–79.
  2. A. Krimpenis, P.G. Benardos, G.-C. Vosniakos, A. Koukouvitaki, Simulation-based selection of optimum pressure die-casting process parameters using neural nets and genetic algorithms, Int J Adv Manuf Technol, (2006) 27: 509–517.
  3. Chunmiao Wu, Die casting technical manual[M], Guangdong Science and Technology Press, Guangdong, 2006.
  4. K..Anzai.A Cast CAE System with Flow and Solidification Simulation to Wheel Casting. Proceedings of Modeling of Casting and Solidification Processes[J],1995:279-286.
  5. K.Kubo.SCAST-Integrated Simulation System for Casting Design.Proceedings of Modeling of Casting and Solidification Processes[J],1995:173-181.
  6. M. Ivosevic, V. Gupta, J.A. Baldoni, R.A. Cairncross, T.E. Twardowski, and R. Knight, Effect of Substrate Roughness on Splatting Behavior of HVOF Sprayed Polymer Particles: Modeling and Experiments, Journal of Thermal Spray Technology. Volume 15(4) December 2006:725-730.
  7. Information on http://www.flow3d.com.

Flood

Study of a Tailings Dam Failure Pattern and Post-Failure Effects under Flooding Conditions

폐석댐 붕괴 패턴 및 홍수 조건에서의 붕괴 후 영향 연구

Zhong Gao, Jinpeng Liu, Wen He, Bokai Lu, Manman Wang, Zikai Tang

Abstract

Tailings dams are structures that store both tailings and water, so almost all tailings dam accidents are water related. This paper investigates a tailings dam’s failure pattern and damage development under flood conditions by conducting a 1:100 large-scale tailings dam failure model test. It also simulates the tailings dam breach discharge process based on the breach mode using FLOW-3D software, and the extent of the impact of the dam failure debris flow downstream was derived. Dam failure tests show that the form of dam failure under flood conditions is seepage failure. The damage manifests itself in the form of flowing soil, which is broadly divided into two processes: the seepage stabilization phase and the flowing soil development damage phase. The dam failure test shows that the rate of rise in the height of the dam saturation line is faster and then slower. The order of the saturation line at the dam face is second-level sub-dam, third-level sub-dam, first-level sub-dam, and fourth-level sub-dam. The final failure of the tailings dam is the production of a breach at the top of the dam due to the development of the dam’s fluid damage zone to the dam top. The simulated dam breach release results show that by the time the dam breach fluid is released at 300 s, the area of over mud has reached 95,250 square meters. Local farmland and roads were submerged, and other facilities and buildings would be damaged to varying degrees. Based on the data from these studies, targeted measures for rectifying hidden dangers and preventing dam breaks from both technical and management aspects can be proposed for tailings dams.

1. Introduction

1.1. Research Status

The mud wastewater containing tailings will be discharged after metal and non-metal mine beneficiation. Tailings slurry contains mercury, arsenic, and other heavy metal ions, both resources and pollution sources [1]. The tailings dam is a dam body formed by the accumulation and rolling of the tailings after the mine selects the useful components [2]. It is of great significance to research the dynamic stability of tailings reservoirs for mine safety production, protection of downstream life and property safety, and the surrounding environment [3]. Tailings dams, an important source of danger if an accident, are bound to people’s lives and property [4]. In 2008, a dam break accident occurred in the 980 ditch tailings pond of Shanxi Xinta Mining Co., Ltd., Yuncheng, China, resulting in 281 deaths and 33 injuries. The direct economic loss was as high as CNY 96,192,000 [5]. On the afternoon of 30 April 2006, the tailings dam of Zhen’an Gold Mine in Shaanxi Province was constructed. The accident caused 17 people to disappear, five people were injured, and 76 houses were destroyed [6,7].

In many tailings reservoir accidents, due to the lack of flood discharge capacity of flood discharge structures in the reservoir area, flood overtopping, tailings dam break, and other phenomena occur occasionally [8,9]. In this regard, scholars in related fields have performed much research and achieved certain results. Chen Zhang et al. [10] established three-dimensional and two-dimensional finite element models. The seepage field of the project under different operating conditions was simulated, and the safety factor under different operating conditions was obtained by combining the seepage field with the stable surface. The influence of the length of the dry beach and the upstream slope ratio on the seepage and stability of the tailings dam was determined. Sánchez-Peralta et al. [11] took a dry tailings pond in Colombia as the research object, studied the movement characteristics of dam break debris flow with different water contents, and obtained the relationship between the length and width of dam break debris flow movement. Changbo Du et al. [12] studied and analyzed the influence of reinforcement on tailings dam and the change law of pore water pressure and internal pressure of the dam body after mud discharge. The pore water pressure and internal earth pressure of the accumulation dam after grouting gradually increased with time. Reinforcement can greatly reduce the pore water pressure and internal pressure of reinforced dams. Gregor Petkovšek et al. [13] proposed a dam break model EMBREA-MUD to calculate the water and tailings outflow of the tailings reservoir and the corresponding break growth. Weile Geng et al. [14] conducted experimental research on the settlement deformation and mesostructure evolution of unsaturated tailings under continuous load. The results showed that the mesostructure deformation of unsaturated tailings with different moisture contents under load was the same and could be divided into four stages: pore compression, elastic deformation, structure change, and further compaction. Alan Lolaev et al. [15] developed a method to determine the tailings filtration and secondary consolidation coefficient in the process of alluvial according to the physical conditions, density, and water phreatic, and a mathematical model to calculate the consolidation time. Kun Wang et al. [16] proposed a multidisciplinary program to simulate the dam break runoff of hypothetical tailings reservoirs on the downstream complex terrain using UAV photogrammetry and smooth particle hydrodynamics (SPH) numerical method. Rawya M. Kansoh [17] studied the influence of the earth-rock dam’s structural parameters on the dam failure process. Kehui Liu et al. [18] studied the microscopic characteristics of hydraulic erosion of reinforced tailings dams and revealed the influence of different reinforcement spacing on the critical start-up speed of tailings particles. It shows that the smaller the reinforcement spacing, the greater the critical start-up speed of the reinforced tailings samples. Luca Piciullo et al. [19] proposed a regression analysis that considers the functional relationship between the release amount and the characteristics of the tailings dam, such as height and water storage (i.e., dam factor). The effects of construction type, filling material, and failure mode on the release amount were also evaluated, as well as the failure frequency of the tailings dam as a function of the construction method. Tailing dams built using upstream construction methods are more prone to failure and are more susceptible to static and dynamic liquefaction. Chunhui Ma et al. [20] pointed out that a reasonable construction schedule and flexible waterproof material are key features of impervious bodies for dams with significant deformation. When the dam deformation becomes stable, consideration should be given to secondary treatment of the impervious body to enhance dam safety. Fukumoto et al. [21] used finite element software to simulate the seepage failure process caused by seepage. Alibek Issakhov et al. [22] combined the k-ω turbulence model to study this process numerically. The VOF (volume of fluid) method was used to simulate the fluid movement behind the tailings dam during the break-up of the fluid and the riverbed landscape. Yonas B. Dibike et al. [23] A two-dimensional hydrodynamic and component transport model was used to study the effect of OS tailings release on the water quality and sediment quality of LAR by simulating sediments and related chemicals. It was concluded that the tailings release location was different; 40% to 70% of the sediments and related chemicals were deposited on the riverbed of the 160 km study section, while the remaining sediments and related chemicals left the study area in the first three days after the release event. Research conducted by Xiaofei Jing et al. [24] investigated the overflow characteristics of tailings dams reinforced with steel bars. During the overflow process, they measured dam displacements, saturation lines, and internal stresses. The study demonstrated that the erosion resistance of tailings dams significantly improves with an increase in the number of reinforcement layers. Abdellah Mahdi et al. [25] studied the potential consequences of a hypothetical oil sand tailings dam failure. For this reason, a non-Newtonian dam–dam model with a viscoplastic rheological relationship is used. The model can reproduce the flood and water level changes in downstream lakes (due to destructive waves). The simulation study of oil sand tailings overflow proves the importance of considering the non-Newtonian characteristics of tailings. Naeini et al. [26] used SIGMA/W and QUAKE/W software to analyze the high-middle line tailings dam’s dynamic response and permanent deformation and evaluated the dam’s performance. Mohammad Reza Boroomand [27] used the numerical analysis method to analyze the earth dam’s seepage under the uncertainty of geotechnical parameters and analyzed the seepage of the earth dam under the condition of uncertainty of geotechnical parameters. Sumin Li et al. [28] simulated and analyzed the hazard range, degree, and spatial state of sediment flow after the dam break and obtained the influence of sand flow velocity, flow depth, and impact on the downstream villages in the disaster area. The feasibility of the expansion and heightening of the tailings dam project was demonstrated, and the disaster risk levels of different spatial locations in the downstream villages were obtained through simulation. Through experiments, Kong et al. [29] studied the influence parameters of tailings dams under seepage. They concluded that the particle size gradation, non-uniformity coefficient, and water content of tailings sand were the main factors affecting the critical hydraulic gradient. It is concluded that the seepage failure gradient with suitable gradation, uniform particles, and suitable water content is significantly higher than that with poor gradation, uneven particles, and poor water content.

Flood overtopping and seepage failure account for 80% of the total accidents, and these two failure forms mainly occur in flood season and are closely related to water. Therefore, it is necessary to explore the tailings dam failure mode, development process, and the impact on the downstream after dam failure under flood conditions to ensure its safe operation. Based on the engineering background of a tungsten mine tailings dam in Ganzhou City, Jiangxi Province, a 1:100 physical model test was carried out to explore the dam break form and failure development process of the tailings dam under flood conditions. The FLOW-3D fluid simulation software was used to solve the influence of the tailings dam on the downstream after the dam break, and the change law of the flow area, velocity development, and submerged depth of the dam break fluid during the flood discharge process was analyzed. Finally, reasonable prevention and remediation suggestions are proposed for the hidden dangers of tailings dams.

The innovation of this paper is to determine the dam break mode and dam break position of the tailings dam under flood conditions by constructing a physical model, which provides a basis for simulating the influence of dam break on the downstream of the dam body.

1.2. Research Flowchart

Figure 1. Research flowchart.

2. Design and Construction of Large Physical Models

2.1. Overview of the Prototype Tailings Dam

The prototype tailings dam is a tungsten tailings dam located in a narrow valley running north–south in Ganzhou City, Jiangxi Province, China. The downstream of the tailings accumulation dam is farmland, dormitory buildings, mountain roads, etc., and the valleys in the downstream are relatively open. Figure 2 shows an overhead view of the prototype tailings dam. The tailings dam is built using the upstream damming method. The initial dam is a clay core wall weathering material dam located at the mouth of the northern valley. The bottom elevation is 262.0 m, the top elevation is 284.0 m, the dam height is 22 m, the upstream and downstream slope ratio is 1:2.5. The design average external slope ratio of the tailings accumulation dam is 1:5, the average slope of the tailings deposition beach is 5%, the design final tailings accumulation dam elevation is 368.00 m, the total dam height 106.00 m, with a complete storage capacity of 1550 × 104 m3 and a service life of 65 years. The present top elevation of the stacked dam is about 315 m, the height of the dam is 53 m, the accumulated storage capacity is about 559 × 104 m3, and the average external slope ratio of the stacked dam is 1:4.9. The reservoir is currently a fourth-class reservoir, with a flood protection standard of one in 200 years. At a later stage, it will be a second-class reservoir with a flood protection standard of 1000 years.

Figure 2. Top view of a tailings dam.

2.2. Selection of Model Sand

To ensure the relative reliability of the test results, the selected dam materials are properly relaxed to meet the primary conditions of similar main influencing factors. The model test focuses on the agglomeration effect of particle movement during the deformation of the dam body. For the selection of model sand, the initial dam is built with silty clay, and the accumulation dam adopts the mine prototype tailings. Figure 3 is the particle size distribution curve of the model sand. According to the particle size distribution curve, two quantitative indexes of soil particles can be determined: non-uniformity coefficient Cu and curvature coefficient CcCu and Cc can jointly determine the gradation of soil. The expressions of the two are:

Figure 3. Cumulative distribution curve of particle size.

The calculated Cu and Cc of the model sand are 2.29 and 0.84, respectively. It is generally believed that the sand soil with Cu < 5 or Cc outside 1~3 belongs to the poorly graded soil, so the model sand is determined to be the poorly graded soil. If the seepage failure occurs in the dam, the development mode of seepage failure can be predicted by some parameters of the soil, that is, whether the soil is piping or flowing soil. According to the non-uniform coefficient discrimination method proposed by the former Soviet Union scholar Istomina, it is preliminarily judged that the model sand is a flowing soil-type soil.

2.3. Construction of the Dam Failure Model

The dam break process of a tailings reservoir involves many aspects, such as hydraulics, mud and sand dynamics, and soil mechanics. It involves many disciplines and is highly complex, which leads to the similarity relationship of model tests.

Therefore, we must put aside the generality of similarity and focus on the similarity of critical elements. This experiment uses the engineering background of a tungsten mine tailings dam in Jiangxi Province, China. The similarity criterion is appropriately relaxed, and the accumulation effect of particle movement during the deformation of the dam body is emphasized to construct the physical model.

Under the condition of geometric similarity, the physical model test of the 1:100 large-scale tailings dam is carried out according to the level of the second-class reservoir of the prototype tailings dam. The prototype range of the tailings dam is 1200 m × 700 m, and the model size is 12 m × 7 m. The model mainly comprises bedrock, a dam body, an observation system, and a water supply circulation system. The specific steps are as follows: According to the topographic map data provided by the mine, the three-dimensional model of the prototype tailings dam is established using Civil-3D modeling software (ver.2018) according to the size of the actual tailings dam (Figure 4). Then, several vertical sections are cut out in the model with the east–west direction as the standard line, and the points on each vertical section are taken equidistantly to extract the elevation value of each point on each vertical section. The model is intended to build a model with an elevation of 230 m in the actual terrain. The steel frame structure of the bedrock is made based on the elevation of each point on the vertical section. The square steel pipe is used as the bedrock support. Each steel pipe corresponds to the elevation of its relative point in proportion. Finally, the waterproof cloth is covered on the steel frame group and fixed to obtain a complete view of the bedrock terrain. Figure 5 is the completed mountain steel frame group, and Figure 6 is the complete bedrock after laying waterproof cloth.

Figure 4. Three-dimensional model of the tailings dam.
Figure 5. Mountain support structures.
Figure 6. A complete view of bedrock.

The initial dam is piled up with silty clay. In the process of stacking the initial dam, two PVC pipes with holes in the wall body and tightly wrapped with permeable geotextiles are symmetrically buried at the bottom of the initial dam to simulate the drainage pipe. A valve is installed at the outlet end of the two drainage pipes to control the drainage speed. The sub-dam uses the pipeline method commonly used in the mine to simulate the ore drawing. An ore drawing main pipe is introduced from the slurry pool to start the ore drawing from the model’s right side, and a valve is set in the main pipe to control the flow rate of the square ore. When the pulp flows into the tailings pond, the tailings will be layered and precipitated under hydraulic screening. After precipitation, the ore is suspended when the tailings reach the target dam height. Start to build the next sub-dam, use the layered filling method to build the dam body to the design elevation, and use the vertical line method to control the elevation when building the dam. (Figure 7) is the construction of the second sub-dam. Four pore water pressure gauges are buried in the dam construction process to monitor the position of the saturation line of the dam body. The four pore water pressure gauges’ positions are arranged along the dam body’s central axis. They are located directly below the dam crest of the first-, second-, third-, and fourth-level accumulation dams. They are named as site 1, site 2, site 3, and site 4 (Figure 8).

Figure 7. Second-stage sub-dam stacking.
Figure 8. Buried pore water pressure gauges.

Due to the need to supply a large amount of water for the test, a water tower was placed on the site (Figure 9), and a return water collection system was designed to achieve a water supply cycle (Figure 10). The observation equipment of the test (Figure 11) uses a trinocular camera and a high-definition camera to record the dam break process of the tailings dam.

Figure 9. Water tower.
Figure 10. Water supply circulation system.
Figure 11. Experimental observation system.

3. Tailings Dam Break Model Experiment

The dam failure mode under specific flood conditions is characterized by permeation damage, manifested as soil erosion. Through analysis of experimental phenomena and data, the development process of dam failure is elucidated, revealing the variation patterns of pore water pressure at different locations and the saturation line of the dam body.

3.1. Dam Failure Experiment

The test was carried out by intermittently injecting water into the reservoir to simulate flood conditions, keeping the flow rate stable during the injection, and keeping the drainage pipe open during the whole test. The beginning of the water injection was taken as the beginning of the test, and the entire dam break test lasted 448 min. It can be roughly divided into two stages, each accounting for one-half of the total length. Figure 12 shows a typical picture of the damage to the dam during the test. Figure 13 shows a timeline of the test damage development. The specific tailings dam damage development process is as follows:

Figure 12. Dam failure model tests.
Figure 13. Timeline of the development of the flowing soil destruction.

The first stage is seepage stabilization: the overflow water is clear, the dam’s surface is stable, and there is no movement of particles. At 138 min of the test, the contact zone between the right end of the second sub-dam and the bedrock began to seep first (Figure 12a). The seepage water flows along the contact zone between the dam body and the bedrock and overflows down the dam face. There are two reasons for the seepage here. The first is fine cracks in the contact area between the soil and the bedrock, which provides a breakthrough for the seepage water. The second is based on calculating the data collected by the pore water pressure gauge. It can be seen that the saturation line at this time escapes on the slope of the second sub-dam, where the dam surface overflows. Subsequently, the second-stage sub-dam continued to seep, and the overflow area gradually expanded and merged with the second-stage sub-dam dam surface. At 174 min, the third-stage sub-dam began to overflow on the left side (Figure 12b). At this time, according to the collected data, it can be calculated that the buried depth of the saturation line has been exposed to the third-level sub-dam. At 190 min, the first sub-dam also overflowed (Figure 12c). Then, the sand boiling point appears at the right end of the first-stage sub-dam, and the soil particles fluctuate obviously with the overflow water. The sand boiling causes the soil particles to be continuously taken out of the soil body. At 203 min, the dam surfaces of the first, second, and third sub-dams have all become swampy.
The second stage is the development and failure stage of the flowing soil: seepage deformation occurs continuously, and more earthwork is lost. At 236 min, the first flow soil damage happened at the right end of the second sub-dam (Figure 12d). The failure form is flow slip. At 239 min, a second flow soil damage occurred on the left side of the first sub-dam (Figure 12e). The flow-slipping soil will form a pit that evolves into a breach, making the seepage velocity and seepage flow faster and larger. Then, the pit part of the soil slides, and the seepage water erodes the downstream dam surface. At 248 min, two erosion ditches have been formed in the flow soil failure area on both sides of the dam (Figure 12f,g).
The erosion gully on the left side is located at the junction of the right side of the first-order sub-dam and the bedrock. The critical hydraulic gradient is lower, the dominant flow develops more rapidly, the sand is wrapped violently, and the subsequent seepage damage is more likely to occur. The erosion gully produces more water flow to scour multiple branches on the dam’s surface. The right erosion ditch is located at the junction of the secondary dam and the bedrock. At this time, the erosion ditch has developed to a certain depth, and the sand boiling point has reached 6. The flowing soil migrates downward under the action of overflow water. The flowing water will bring the fine particles to the downstream area. The coarse particles will be accumulated to form a ‘filter layer‘ to block the overflow water channel. The seepage pressure on both sides of the filter layer gradually increases. A new seepage channel will be formed when the seepage pressure on one side reaches the critical value. At 292 min, the flow soil damage eroded to the third sub-dam and further developed upstream along the boundary. Part of the erosion gully’s inner wall soil is washed away underwater, and the internal wall forms holes and expands upward until the upper part forms a suspended surface. When the shear strength of the upper soil is greater than the shear strength of the soil, it will collapse and continue to repeat the next round of erosion. At this time, the left-flowing soil does not develop to the upstream failure but to the proper lateral erosion, and the right side flushes out a new channel due to the obstruction of the ‘filter layer‘. At 303 min, the third flow soil failure occurred on the left side of the third sub-dam (Figure 12h). Because of the increase in overflow water and the acceleration of water flow, the right scouring area opens the downstream channel at the particle deposition, and fine particles are continuously taken out of the dam by seepage water. The overflow water also washes away the ‘filter layer‘ on the left side. After that, the first sub-dam eroded to the deep, and the dam surface failure area did not expand. There is a hydraulic–gravity erosion cycle in the flow soil damage area of the second-stage sub-dam, which extends to the upstream and the middle of the dam body. With the increase in the erosion damage area of the water flow, the more the sand boiling point, the faster the seepage damage, and the erosion area of the lower section continues to expand, and the water flow in the erosion gully is large and fast. The flowing soil failure zone of the third-stage sub-dam has not yet formed a penetrating failure path and is in the initial stage of erosion. At 348 min, the fourth-stage sub-dam overflowed (Figure 12i). At 448 min, the flow soil was eroded to the fourth sub-dam (Figure 12j).
The flow soil damage area is eroded to the fourth sub-dam, which is regarded as the whole dam damage. It is measured that the depth of the collapse area is about 12 cm, and the width is about 80 cm. It should be noted that although the dam body has undergone a large area of seepage failure, the dam body has not yet experienced an unstable landslide. The tailings dam finally broke because the dam body soil damage zone developed to the top of the dam to produce a breach.

3.2. The Change Rule of the Saturation Line

Figure 14 is about the change curve of the saturation line. At the beginning of the test, as the upstream water level rose, the saturation line rose rapidly despite the drain being in a normal discharge condition. After the lifting of the head has ceased, the rate of the upward lifting of the saturation line becomes significantly slower due to the hysteresis effect. Then, a certain depth of burial is maintained. In the middle and late stages of the test, most of the dam had become saturated, and the soil matrix suction had weakened. When water is again stored in the reservoir, the saturation line will again lift, but at a reduced rate compared to the initial period. If the reservoir level is no longer raised, the saturation line tends to fall after a period of time. By approximately 270 min into the test, the dam face had already developed a certain size of the flow damage zone, and it was no longer meaningful to discuss the depth of the saturation line.

Figure 14. Variation curve of saturation line.

In the previous study [30], a two-dimensional finite element model of the tailings dam, chosen from the central axis of the three-dimensional tailings dam model, was used to analyze the distribution of saturation line in the tailings dam under flood conditions. The numerical simulation results show that when the upstream water head rose to 125 m (Figure 15), the saturation line intersected with the first and fourth-level accumulation dams and was exposed throughout the dam surface. The variation law of the saturation line obtained by the numerical simulation is consistent with the experimental phenomenon; that is, the saturation line increases with the rise of the reservoir water level, and the order of the dam surface exposure is the second-stage sub-dam, the third-stage sub-dam, the first-stage sub-dam, and the fourth-stage sub-dam. According to the simulation results, the displacement of the dam body does not change greatly, and the plastic strain zone does not appear on the slope and crest of the dam body, and there is no penetration. It can be judged that the tailings dam model does not have deep slip when the water level is about to overflow; that is, the skeleton structure of the dam body is stable. Combined with the physical model test, before the saturation line of the dam body reaches the dam surface of the fourth-level sub-dam, the tailings dam has undergone seepage failure, but the dam body has not undergone structural instability. The results of numerical simulation are consistent with the phenomenon of physical model test. After that, with the development of flowing soil, the damaged area of the dam body continues to extend to the top of the dam, which will eventually cause the breach of the dam top and cause the flood discharge of the dam.

Figure 15. Saturation line distribution of the tailings dam under 125 m water level.

4. Impact Analysis after Dam Break and Prevention Suggestions

Based on the results of the physical model experiment, it can be inferred that the tailings dam failure was triggered by seepage failure. This means the area of flowing soil gradually eroded upstream until a breach was created at the top of the dam, and the reservoir fluid poured downstream. Therefore, an erosion damage trench was set up on the model for the dam breach calculation in FLOW-3D (ver. 9.3), extending from the top of the initial dam to the top of the dam, and the shape was simplified to a semi-cylinder. Figure 16 shows a model of the tailings dam after completion of the pre-treatment.

Figure 16. FLOW-3D 3D calculation model.

4.1. Dam Failure Test Results

An overview of the area downstream of the tailings dam is shown in Figure 17. The downstream area is dominated by the production facilities (red and yellow line areas in the figure), staff accommodation buildings (pink line area), the road around the mountain (blue curve), villages (green line area), and scattered agricultural land.

Figure 17. Aerial view downstream of tailings dam.

4.1.1. Overflow Area

Figure 18 shows the change in the extent of fluid inundation at 60 s, 120 s, 180 s, 240 s, and 300 s as calculated by the software, with the fluid in blue in the figure. As can be seen from the diagram, the breached fluid was rapidly released downstream in a short period and, by 300 s, covered the entire flat area downstream, with an overflow area of approximately 95,250,000 square meters. Farmland and roads in the area will be flooded, and production facilities and residential buildings will also be affected. In addition, emergency escape plans can be challenging to implement successfully at short notice. It is thus clear that in the event of a breach of this tailings dam, it would be a major accidental disaster.

Figure 18. Time-course diagram of mud area.

4.1.2. Flooding Depth

Figure 19 shows a cloud of the distribution of flooding depth at 60 s, 120 s, 180 s, 240 s, and 300 s. Due to the lower topography in the eastern part of the downstream area, the fluids that wash down first collect in the east and then spread westwards. As can be seen from the graph, the maximum inundation depth is always located in the eastern part of the lower reaches near the initial dam. The mudslide did not affect the northern area due to the terrain’s advantage; when the situation was urgent, people could be evacuated along the northwest-facing road to the north.

Figure 19. Cloud map of flooding depth.

4.1.3. Flow Rate Analysis

The flow velocity during the release process reflects the magnitude of the fluid impact. Figure 20 shows the flow velocity clouds during the dam breach release process at 60 s, 120 s, 180 s, 240 s, and 300 s. Due to inertia, the fluid emerges from the breach. It rapidly completes the transformation from potential energy to kinetic energy in the trench eroded by the flowing soil, with the flow velocity reaching a maximum. In addition, there is some leakage around the dam at the junction of the tailings dam and the mountain. After the fluid is flushed off the tailings dam, the average flow velocity decreases due to the diffusion principle and frictional forces. In general, the flow of emissions increases and then falls.

Figure 20. Cloud map of flow rate.

Three points, A, B, and C, are selected in the flow direction of the release to analyze the fluid’s flow velocity characteristics, specifically during the dam failure process. The three points are located at the top of the initial dam, the foot of the initial dam, and the downstream area adjacent to the tailings dam (Figure 21). Figure 22 shows the variation in flow rate over time at three points. Overall, the flow velocities at points A, B, and C are successively reduced as the flow path develops. From the point of view of the flow velocity at a single point, it does not increase to a peak all at once but has an undulating, phased variation. At about 30 s, the overflow velocity starts to appear at the three points, after which the trend is a cyclic process of “increase-smooth or decrease” because the increase in flow velocity does not coincide with the expansion of the breach, which, in turn, determines the flow velocity of the discharge. The flow rate increases accordingly when the breach expands and becomes deeper again. After several cycles of this until the breach is no longer extended, the flow rate at points A, B, and C all fall during the last 30 s of the figures and will return to zero as the flooding stops.

Figure 21. Flow rate reference points.
Figure 22. Flow rate time history diagram.

The analysis of the variation in the flow rate of the release shows that the debris flow impacts downstream in a segmented manner. Therefore, the decrease in flow velocity should not be regarded as the end of the entire dam break, nor should blindly carry out the aftermath of the accident at this stage, but should wait for a longer period to observe and confirm so as not to cause more damage.

4.2. Recommendations for Prevention and Management

4.2.1. Technical Measures

Dam surface treatment: According to the seepage characteristics of the tailings dam, to prevent overflow water and rainwater from scouring the shoulder and face of the dam and to collect the seepage water, a shoulder drainage ditch should be installed along the junction of the dam with the slopes of the two banks, and a face drainage ditch should be installed on the face of the dam. Moreover, the downstream slope of the dam can be mulched, turfed, and, if necessary, reinforced by stone pitching at the foot of the dam.

Additional seepage facilities: Combined with the model test results, it is clear that control of the saturation line of the tailings dam should be a top priority for safety management. To effectively control the depth of the saturation line, additional drainage facilities can be provided in the form of a combined horizontal drainage pipe and a vertical shaft connected to the end of the horizontal drainage pipe. In addition, the vertical drainage pipe should be raised with the height of the stockpile dam and pumped out periodically.

4.2.2. Management Measures

Routine inspection and maintenance: Besides monitoring various safety indicators such as the tailings dam saturation line and dry beach length, the person responsible for safety should regularly inspect the dam body for cracks, collapses, and surface erosion. They should also ensure that the slope protection is intact and that the drainage facilities are clear of blockages, siltation, or waterlogging. Check for seepage, pipe surges, or flowing soil, focusing on the junction between the dam and the hills on either side, and be vigilant for changes in seepage flow and turbidity. If a potential problem is identified, the cause must be immediately determined, and remedial action must be taken to prevent it.

Ensure excellence in flood management, including pre-flood preparation, response during flooding, and post-flood rescue work.

5. Conclusions

  1. The reservoir’s water level had not yet crested before the dam was damaged. In other words, the cause of dam failure under flood conditions is seepage failure, which manifests itself in the form of flowing soil. Before the flow soil is destroyed, the dam surface will produce overflow, water accumulation, sand boiling, and other phenomena. The phenomenon of the dam failure test shows that the flow soil damage starts at the weak point of the dam at the junction with the bedrock. These areas have a high saturation gradient and are more prone to local damage. In the early stage of soil flow failure, multiple sand boiling points were generated on the dam surface. With the development of seepage, collapsible cracks appeared on the dam surface one after another, forming erosion ditches. In the middle stage of soil failure, the failure area is widened. The soil cycle undergoes the process of erosion–gravity erosion, and the ‘filter layer’ will slow down the failure rate to a certain extent. In the later stage of flow soil damage, the flow water damage area began to penetrate, and the erosion intensified until the whole dam body was damaged. Therefore, when the sand boiling point is generated, and the collapsible cracks appear on the dam surface, these can be used as a warning sign of seepage failure.
  2. The buried depth of the saturation line becomes shallow with the increase in the upstream water head. And, the rate of increase is first fast and then slow. After the lifting head is stopped, the saturation line will still rise slightly for a period of time due to the lag effect. If the reservoir water level is not replenished for a long time, the saturation line will be reduced under normal drainage. The order of the saturation line escaping from the dam surface is the second sub-dam, the third sub-dam, the first sub-dam, and the fourth sub-dam. It can be seen that before the flood, it is necessary to check and repair the drainage facilities to ensure their suitable operation. During the flood season, all measures should be taken to enhance the flood discharge, reduce the saturation line, and avoid the seepage damage of the tailings dam.
  3. The results of the FLOW-3D hydrodynamic simulation software show that the breach fluid was rapidly discharged within a short period, covering the entire flat area downstream by 300 s. The local farmland and roads were submerged, and the rest of the construction facilities were also damaged to a certain extent. Therefore, it will be a major disaster once the tailings dam breaks. The rapid development of the dam breach mudslide and the short release time make it impractical to organize the evacuation of people when the release occurs. Therefore, in combination with the mechanism of tailings dam failure, targeted measures for potential remediation and dam failure prevention can be proposed from both technical and management aspects.
  4. The innovation point is to use a large-scale physical model test to study the dam break mode of tailings dam under flood conditions. By monitoring the internal changes of the tailings reservoir under flood conditions, the stage of seepage failure of the dam body can be judged, which can serve as an early warning for the subsequent break of the tailings dam. The experimental process and experimental results of the model can provide a reference for the changes in tailings reservoir under flood conditions under real working conditions so as to correspond to the changes of tailings reservoir fluid under flood conditions under real working conditions. Provide guidance for staff to monitor changes in tailings ponds. The determination of dam break position and dam break mode by model test provides a basis for simulating the influence of tailings dam break on the downstream. The use of a steel frame structure to build a tailings dam model can cover the entire tailings dam terrain more comprehensively and economically and can more comprehensively analyze the entire dam break process of the tailings dam. Compared with the local tailings dam similarity simulation and on-site exploration, it is more profound and comprehensive, which has practical significance for the safety of the tailings reservoir. The defect is that there is a prototype of the model, and it cannot be used for all tailings mines. The actual situation needs to be analyzed in detail. In addition, according to the tailings pond model test, it can be expected that the tailings pond model can be used to study the useful mineral components in the recovery reservoir, which has practical significance for environmental protection and resource recovery.

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river depth

Ecological inferences on invasive carp survival using hydrodynamics and egg drift models

수리역학 및 알 이동 모델을 활용한 외래종 잉어 생존에 대한 생태적
추론

Ruichen Xu, Duane C. Chapman, Caroline M. Elliott, Bruce C. Call, Robert B. Jacobson, Binbin Wang

Abstract


Bighead carp (Hypophthalmichthys nobilis), silver carp (H. molitrix), black carp (Mylopharyngodon piceus), and grass carp (Ctenopharyngodon idella), are invasive species in North America. However, they hold significant economic importance as food sources in China. The drifting stage of carp eggs has received great attention because egg survival rate is strongly affected by river hydrodynamics. In this study, we explored egg-drift dynamics using computational fluid dynamics (CFD) models to infer potential egg settling zones based on mechanistic criteria from simulated turbulence in the Lower Missouri River. Using an 8-km reach, we simulated flow characteristics with four different discharges, representing 45–3% daily flow exceedance. The CFD results elucidate the highly heterogeneous spatial distribution of flow velocity, flow depth, turbulence kinetic energy (TKE), and the dissipation rate of TKE. The river hydrodynamics were used to determine potential egg settling zones using criteria based on shear velocity, vertical turbulence intensity, and Rouse number. Importantly, we examined the difference between hydrodynamic-inferred settling zones and settling zones predicted using an egg-drift transport model. The results indicate that hydrodynamic inference is useful in determining the ‘potential’ of egg settling, however, egg drifting paths should be taken into account to improve prediction. Our simulation results also indicate that the river turbulence does not surpass the laboratory-identified threshold to pose a threat to carp eggs.

Introduction


Bighead carp (Hypophthalmichthys nobilis), silver carp (H. molitrix), black carp (Mylopharyngodon piceus), and grass carp (Ctenopharyngodon idella), are considered invasive in North America. These species were imported into North America in the 1970’s to support aquaculture and escaped into the wild where they alter aquatic environments and food webs, resulting in undesirable ecological consequences1,2,3. On the other hand, these carp species are important food sources in China, yet their populations in their native environment have been declining due to over-fishing and the negative effects on fish habitats resulting from dam construction4,5. As either native or invasive species, it is of great importance to understand their life cycles in order to identify potential intervention strategies to control their populations6.

These rheophilic, broadcast-spawning carps exhibit prolific reproduction, with a single female carp capable of producing between 100,000 and one million eggs annually7. Carps typically engage in spawning during the spring and summer months when the temperature is within a range favorable for successful reproduction (peaking at roughly 20–24 ∘C) and during periods of high flows8,9. They select specific locations for spawning characterized by high turbulence, including rocky rapids, riffles, islands, river confluences, and bends. This choice helps prevent the settling of eggs onto the riverbed, as sediment burial causes high mortality10. Within 3–5 h after spawning, eggs absorb a large amount of water in a process known as water hardening, leading to an increase in egg size and decrease in egg density. The water-hardening process leads to a decrease in settling velocity by approximately 70%, making eggs more likely to suspension in the water column10,11.

After spawning and fertilization, the drift stage of carp eggs begins, a critical early-life stage in carp recruitment. Eggs hatch in approximately 30 h at optimal temperatures10,12. During the drift stage before hatching, eggs are susceptible to predation, relying entirely on river currents and turbulence to remain suspended until hatch. After hatching, larval carp remain in the drift for a period, but they can behaviorally avoid settling10,12. Because hydrodynamics plays a critical role in the suspension, dispersion, and transport of carp eggs across various scales in rivers, numerous studies have been conducted to explore river hydraulics and turbulence in relation to suitable carp spawning grounds, survival potential, and hatch locations13,14,15,16. A key survival condition is the necessity for eggs to remain suspended in the water column throughout the entire egg drift stage, or at the very least, to avoid settling and being buried by sediment. Consequently, assessing whether river hydrodynamics can support this condition is a fundamental step in gauging recruitment success.

Flow velocity has been used as a simple indicator for assessing the suspension of eggs in rivers. For instance, Kocovsky et al.17 used a threshold velocity of 0.7 m/s as suitable for the spawn-to-hatch environment. Selection of 0.7 m/s is based on early literature with limited mechanistic studies9,18. Lower critical flow velocities were also reported in the literature. Tang et al.19 suggested a value of 0.25 m/s based on a flume experiment, which agreed with some early field observations in the Yangtze River. Murphy and Jackson20 found that mean velocities of 0.15–0.25 m/s allowed for egg suspension in four tributary rivers of the Great Lakes. Guo et al.21 suggested a critical flow velocity of 0.3 m/s in a flume experiment. Because rivers are largely non-uniform and vary in size and morphology, selecting a specific flow velocity as the sole empirical indicator for assessing suitability of carp recruitment is rather challenging.

While using flow velocity as an indicator for examining egg suspension or settling might be practical, it does not fully represent the underlying physics, especially in areas where turbulence is not well correlated with mean flow velocity. To account for the mechanism of egg suspension, Garcia et al.22 proposed three different criteria involving the ratio of shear velocity and egg settling velocity, the ratio of vertical turbulence intensity and egg settling velocity, and the Rouse number to predict the suspension and settling of carp eggs. In their laboratory experiment, they observed that 65% of eggs remained in suspension with a mean flow velocity of 0.07 m/s, corresponding to a Rouse number of 1.32 and shear velocity of 0.004 m/s. At higher flow velocities of 0.2 and 0.4 m/s, with Rouse numbers of 0.57 and 0.58 and shear velocity of 0.008 and 0.016 m/s, respectively, all eggs were in suspension. These observations agree well with the empirical values of Rouse number classification for sediment transport for bedload, partial suspension, full suspension, and washload23. Therefore, using these parameters is better supported by the mechanism of particle suspension compared to velocity alone.

Given the above simple criteria of using shear velocity or Rouse number, hydraulic models or measurements can be used to infer whether a stream or a river reach can support a favorable environment for egg suspension in the egg-drift stage17. In addition, three dimensional hydrodynamic models can provide additional insights into the spatial distributions of potential egg settling zones, given the strong spatial heterogeneity of river turbulence24,25,26. In this paper, we use an 8-km reach in the Lower Missouri River as representative of channelized segments of the Upper Mississippi River basin where carps are established. We used computational fluid dynamics (CFD) modeling to explore the overall suitability for egg drift and to infer potential egg settling zones, with an emphasis on understanding the spatial distributions of hydrodynamics associated with in-stream hydraulic structures, river morphology, and strong topographic gradients on the riverbed. Specifically, we examine the criteria of egg suspension and evaluate the locations where the hydrodynamics are unfavorable for suspending eggs. Our objective is to evaluate whether the potential egg settling zones based on hydrodynamic inference would agree with entrapment locations that can be estimated using drift models. We additionally evaluate whether turbulence conditions indicated in the model approach criteria for turbulence-induced damage to carp eggs as determined in laboratory studies.

Methods


Study site

The study site is a selected reach in the Lower Missouri River near Lexington, Missouri (Fig. 1). The reach is approximately 8 km long with a sinuosity index of 1.12. The mean bankful width is 331.4 m. The bed is mostly covered by medium and coarse sand (D50 = 0.55 mm) with fine muddy materials (< 0.125 mm) near the banks and close to the dike fields27,28. The mean annual discharge is approximately 1700 m3/s measured at a U.S. Geological Survey (USGS) gaging station approximately 24 km downstream (station no. 06895500, Waverly, Missouri, USGS). The reach is representative of rivers that have been highly engineered to support navigation and bank stability, with complex hydraulic conditions where water flows around and over the rock channel-training structures29,30. This reach has been used as the main site for model development stage of SDrift31,32, an egg drift model used in this study. The previous studies have accumulated substantial data for the bathymetric-topographic digital elevation model (DEM), water surface elevations, and cross-channel velocity profiles33, which have been used for calibration and validation of our CFD model.

Figure 1. Bathymetry map of the study site in the Lower Missouri River. Black line represents the measurement of water surface elevation. Black triangles represent the river miles measured from the confluence with the Mississippi River near St. Louis, Missouri. Twelve red lines represent the cross sectional transects of velocity measurement at Q=2282 m3/s. Ten blue lines represent the cross sectional transects of velocity measurement at Q=3060 m3/s. Map was generated with ArcGIS Pro v. 3.2 https://www.esri.com/en-us/home. Basemap is U.S. Army Corps of Engineers Imagery, 2012. River miles are from the U.S. Army Corps of Engineers, 1960, https://www.nwk.usace.army.mil/Missions/Civil-Works/Navigation/.

Hydrodynamic model

The flow was simulated using FLOW-3D HYDRO with a Reynolds-averaged Navier-Stokes (RANS) solver and a Re-Normalization Group (RNG) modified k−ε turbulence sub-model. The model was set up for solving the steady-state flows under four discharge conditions ( Q = 1342, 2282, 3060 and 4219 m3/s, referred to as Q1 to Q4 conditions), which correspond to approximately 45–3% daily flow exceedance during spawning season. A Cartesian mesh with a final size of 4×4×0.4 m in the east-north-up coordinate system was used after a mesh independence study to evaluate optimal mesh dimensions31.

The upstream and downstream boundary conditions were set to the measured flow discharge and calculated hydrostatic pressure from the measured water-surface elevation, respectively. The model was calibrated by adjusting the roughness coefficient until the simulated water-surface elevations agree with the measured data, where the water-surface elevations were measured using a ship-mounted, real-time corrected kinematic global navigation satellite system (RTK-GNSS). The measured cross-channel velocities at 22 locations at two flow conditions (Q=2282 and 3060 m3/s) were used to evaluate model performance, where the velocities were measured using a ship-board acoustic Doppler current profiler (ADCP, Workhorse Rio Grande, Teledyne, Inc) at each cross section with four repeated transects. The ADCP had a vertical resolution of 0.5 m and horizontal resolution of 1 m. The velocities within 1 m below the water surface and within 1 m above the river bed were not measured due to instrument blanking distance and measurement noise. Additional details on model calibration and evaluation are in Li et al.31.

Egg drift model

The egg drift model SDrift was used for egg transport modeling in this study31. This model uses Lagrangian particle tracking to simulate the transport of carp eggs, where turbulent fluctuations are modeled using an explicit solution for the Langevin equation, i.e., the Markov-chain continuous random walk (CRW) algorithm34,35,36. The density and diameter of carp eggs were determined as a function of post-fertilization time and water temperature based on the regression equation to the laboratory measured data11. The details of regression can be found in31. The time-varying characteristics of eggs result in evolving egg settling velocity in the water, which is determined based on the drag law for spherical particles37.

SDrift was incorporated with the CFD model outputs to predict transport of silver carp eggs in the selected reach. A broad surface-spawning event across the entire cross section at an upstream location in the model (x= 427,130 m, near River Mile 314) was simulated by releasing 6600 model eggs on the water surface at 33 locations31. All eggs were tracked until they were transported outside the downstream boundary or ‘entrapped’ in the model domain determined by the model criterion.

Criterion of egg entrapment from the egg drift model

SDrift allows the simulated eggs to be ‘entrapped’ if they are stationary for a pre-defined duration. The entrapment would occur if a simulated egg is transported into a low velocity zone and eventually loses its momentum. From the model evaluation, entrapment primarily occurs in the region with high topographic gradients, e.g., near the bank and hydraulic structures. A duration of 30 s was used here to determine the entrapment, i.e., if a simulated egg does not move for 30 s, it would be considered entrapped and would no longer be tracked. Although the entrapment does not necessarily provide a certain prediction of egg settling, it offers insight into locations where the eggs may be stopped and eventually buried by bed sediment. The selection of a 30-s duration is somewhat arbitrary. From a physics standpoint, this duration should ideally exceed the largest turbulent time scale. However, due to the extensive spatial scale of the modeled reach and the river-training structures, the turbulent time scale varies significantly across space. Furthermore, both the spatial resolution in the CFD simulation and the temporal resolution in particle tracking have the potential to influence particle movements and their entrapment. Therefore, determining the optimal duration requires further investigation in future studies.

Criterion of egg suspension and settling from the hydrodynamic model

Suspension of carp eggs depends on whether the flow can provide adequate upward motions that overcome their settling. Analogous to sediment suspension and transport38, several means have been used to quantify the settling and suspension of carp eggs in turbulent flows. Here we analyze three parameters following Garcia et al.22: the ratio between shear velocity and settling velocity, the ratio between vertical turbulence intensity and settling velocity, and the Rouse number.

Shear velocity

Shear velocity (u∗) is a velocity scale defined from the bed shear stress. The ratio of shear velocity and particle terminal velocity (wt), a so-called movability number (M∗=u∗/wt), has been used to classify sediment transport39. Different critical values have been proposed to define particle suspension38,39. Here, the critical value of 1.0 is used following the studies of carp eggs20,22: locations with u∗/wt<1 are the potential settling zones of carp eggs, where particle terminal velocity is the egg settling velocity (wt=Vegg).

Because shear velocity only represents the bed shear but does not provide the vertical variability in the water column, we applied a scaling method so that potential egg suspension and settling can be evaluated in the entire water column. Using the relationship between bed shear and turbulence kinetic energy (TKE)40,41, i.e., τb=C1ρk with C1=0.1940, the movability number can be estimated at every grid point using the TKE determined from the CFD simulation:

The potential egg settling zones were then determined based on M∗<1.

Vertical turbulence intensity

The vertical turbulence intensity (wrms′) is a direct parameter to quantify the turbulent velocity scale in the vertical direction, which can be used to define the initiation of particle suspension38. Therefore, we also calculated the ratio between wrms′ and V{egg} as the second indicator for egg settling: locations with wrms′/Vegg<1 are the potential settling zones of carp eggs. Here, we estimated w′ based on anisotropy of turbulent fluctuations in open channel flows:

with Du=2.30, Dv=1.27, and Dw=1.6342. This gives wrms′/Vegg=0.75TKE/Vegg where TKE was obtained from the CFD simulations.

Rouse number

In sediment transport, the Rouse number has been used to describe the suspended load38. The Rouse number is defined as Ro=wt/(βκu∗) with wt=Vegg for carp eggs, where κ is von Kárman constant and β is a coefficient related to diffusion of particles22,23:

The Rouse number (Ro, also used as Z or P in the literature), can be used to classify the sediment transport similar to the movability number. Hearn23 suggested that sediment particles are in 100% suspension or wash load when Ro<1.2; particles are partially suspended when 1.2<Ro<2.5; particles are predominantly transported by bedload if Ro>2.5. Here, we use 1.2 as the criterion, such that the potential egg settling zones were determined based on Ro>1.2.

Results and discussion

Model calibration and evaluation

The model calibration results for water-surface elevation are shown in Fig. 2 for four flow conditions31. The elevation of river bed in the main channel is also plotted for reference. The root-mean-square-error (RMSE) in the water surface elevation between the measurement and modeling is 0.07, 0.03, 0.04, and 0.03 m, for Q1 to Q4, respectively. The RMSE is considered to be small compared to the length of the reach and the water depths.

Figure 2. Result of model calibration using the measured water surface elevation for four discharge conditions from Li et al.31 and Elliott et al.33. Black solid lines are measured data. Red dashed lines are modeled results.

The measurement-modeling comparison of double-averaged velocities over the flow depth and the cross section in both streamwise (Us) and transverse (Ut) directions is given in Fig. 3 for two measured conditions (Q2 and Q3). The RMSE of Us and Ut is 0.055 and 0.028 m/s, much smaller than the mean flow of 1.29 and 1.38 m/s in the measured cross sections for Q2 and Q3, respectively. The direct measurement-modeling comparison in all 22 cross sections is given in the supplementary file (Figs. S1 and S2).

Figure 3. Comparison between computational fluid dynamics (CFD) modeled and acoustic Doppler current profiler (ADCP) measured velocities in the streamwise direction (Us) and transverse direction (Ut) at 22 cross sections under the two surveyed conditions Q2 and Q333. The 1:1 dashed line represents perfect agreement.

Mean flow characteristics

The CFD simulated flow depth and depth-averaged flow velocity for two out of four conditions are shown in Figures 4 and 5. Greater depths are located downstream from the dikes (i.e., in scour holes) and near the right bank at the upstream bend (i.e., Easting 431,000–432,000 m, downstream of river mile 311). Shallower depths are located upstream from the dikes and along the left bank in the downstream bend (i.e., Easting 432,000–433,500 m, in the vicinity of river mile 310).

Flow velocities are greater at a higher discharge, and are strongly related to the in-stream hydraulic structures: high velocities are located within the main channel and low velocities are located close to the dike areas and both sides of the bank. For Q1, the L-head dikes on the left bank around Easting 430,500–431,000 m (upstream of river mile 311) block the flow into the left bank, resulting in channel narrowing and an area of localized higher velocity. Relatively faster velocities are also located close to the right bank from Easting 432,000–433,500 m (in the vicinity of river mile 310) and then shaped by the L-head dike at Easting 433,500–434,500 m (between river miles 309 and 310). When water enters the L-head dike area at Easting 430,500–431,000 m (between river miles 311 and 312) in high discharge conditions (e.g., Q4), the localized fast flow is not observed.

Figure 4. Flow depth in the reach: (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.
Figure 5. Depth-averaged flow velocity in the reach: (a) Q1; (b) Q
4. River miles 309–313 are indicated in the plot by black triangles.

Turbulence quantities

Two turbulence quantities were selected to elucidate the turbulence in the reach: the depth-averaged TKE (Fig. 6) and the depth-averaged dissipation rate of TKE (Fig. 7). For Q1, TKE shows a similar spatial pattern as the flow velocity, indicating that the high TKE is usually associated with high velocities. For Q4, additional high TKE regions are located within the low velocity zones near the dikes. These high turbulence regions are caused by the interaction of flow with the hydraulic structures. For instance, enhanced turbulence may occur within wakes downstream from the flows over the dikes. Strong shear-induced turbulence may also occur at the water surface near the edge of the dikes close to the main channel. Similar to TKE, the locations of high TKE dissipation rate are coincident with high velocity in the main channel and near the dikes where strong flow-structure interactions occur.

Figure 6. Depth-averaged turbulence kinetic energy (TKE): (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.
Figure 7. Depth-averaged turbulence dissipation rate: (a) Q1; (b) Q4. River miles
309–313 are indicated in the plot by black triangles.

To examine the correlation between turbulence and the mean flow in the reach, Fig. 8 elucidates the ratio between TKE and the mean kinetic energy (MKE) where MKE is defined based on mean velocity values, MKE = 0.5(U2+V2+W2). The data show that the TKE/MKE ratio is much smaller than 1 in the main channel, a typical open-channel feature. However, near the river bank and in the dike fields, greater TKE than MKE is common, with the spatial distribution of TKE/MKE>1 being dependent on discharge. This result documents strong interactions between water flow and the solid boundaries, which generate substantial turbulence comparing to the reduced mean velocity in these regions. Within these regions, particles would be expected to have longer residence times32.

Figure 8. The ratio between turbulent kinetic energy (TKE) and mean kinetic energy (MKE) in the reach: (a) Q1; (b) Q4. River miles 309–313 are indicated in the plot by black triangles.

Egg suspension and settling

The CFD modeling results allow for analysis of potential egg settling zones based on the criteria of particle suspension outlined in section “Criterion of egg suspension and settling from the hydrodynamic model”. In Fig. 9, the potential egg settling locations are plotted based on the Rouse number criterion for all four discharge conditions. The plot shows that potential settling zones are located near the river banks, in dike fields, and even in the channel at locations with strong gradients in the bed morphology. We note that the criterion was applied to all data points simulated in the CFD. Therefore, the settling zones represent the xy locations where turbulence is inadequate to suspend eggs. Not surprisingly, the estimated potential settling zones become smaller with increasing discharge. Results using shear velocity and vertical turbulence intensity criteria show similar results, which are plotted in the supplementary file (Figs. S3 and S4).

Figure 9. Predicted egg settling locations using the criterion of Rouse number. Black dots show the locations where the turbulence is inadequate to keep eggs suspended, i.e., inferring egg settling. Note that the egg settling is evaluated at all nodes in the three-dimensional computational fluid dynamics (CFD) simulation results. River miles 309–313 are indicated in the plot by red triangles.
Figure 10. Predicted egg settling location using the egg drift model, SDrift31. River miles 309–313 are indicated in the plot by red triangles.

Figure 10 shows the predicted locations of entrapped eggs using the egg drift model, SDrift31. Comparing Fig. 10 with Fig. 9, we found that both hydrodynamic-inferred potential settling locations and drift-model predicted locations include the regions near the dike fields and the sparse areas in the channel where strong topographic gradients are present. However, careful examination of the wing dike areas (Fig. 11 under Q1 condition and Fig. 12 under Q4 condition), shows that the predicted egg settling zones using two methods are located in different regions near the dike areas. SDrift results indicate that egg entrapment is mainly located adjacent to the dikes, whereas the hydrodynamic inference indicates strong egg settling potential downstream from the dikes under low-flow conditions, such as the discharge condition Q1 (Fig. 11). The potential egg settling zones are substantially decreased by increasing discharge (Fig. 12). SDrift results indicate that egg entrapment is primarily due to interception of egg movement due to strong topographic gradients near the dikes while being tracked in the model under these hydrodynamic conditions. Although this does not directly imply that the eggs would settle in these areas, higher probability of egg-dike interaction would occur that could potentially affect egg survival. In contrast, the hydrodynamic inference only suggests hydrodynamic conditions that are favorable for egg settling, which differs from the drift models.

Figure 11. Zoom-in view of estimated egg settling zone under discharge condition Q1 using (a) SDrift model and (b) hydrodynamic inference based on Rouse number criterion. River miles 312 and 313 are indicated in the plot by red triangles.
Figure 12. Zoom-in view of estimated egg settling zone under discharge condition Q4 using (a) SDrift model and (b) hydrodynamic inference based on Rouse number criterion. River miles 312 and 313 are indicated in the plot by red triangles.

In addition, the drift model predicts substantial egg entrapment near the left bank upstream of the bend located around x=43,100 m (upstream of river mile 311), where these regions were not inferred from hydrodynamic data. The differences indicate that eggs can be entrapped within locations where hydrodynamics would indicate suspension. The potential entrapment in the drift model is likely due to the reduction in egg-drift speed close to the left bank, which increases the probability of egg settling. In curved rivers reaches, the unevenly distributed flow in the cross section and secondary flow may push eggs towards the outer side of the channel, which can increase the probability of the particle-bank interaction.

Figure 13. Trajectories of 200 SDrift simulated eggs near the left bank at the release point at two discharges: (a) Q1, (b) Q4. River miles 309–313 are indicated in the plot by red triangles.

The drift trajectories of 200 simulated eggs released near the left bank for discharge Q1 and Q4 can be used to visualize drift dynamics simulated in SDrift (Fig. 13). The modeling results show that, under Q1, there is minimal egg drift into the low-flow region between the L-head dikes and the left bank in Area 1, as well as into the high-riverbed region close to the left bank in Area 2. This restriction occurs because the elevation of the dikes in Area 1 are higher than the water surface elevation during low-flow conditions, preventing eggs from entering these areas. As a result, the drift model predicts minimal entrapment of eggs in these areas. However, the hydrodynamic inference only takes into account favorable conditions for egg settling, implying significant settling in these regions even when trajectories would fail to transport eggs into the areas. Nevertheless, under higher-flow conditions that permit eggs to enter these areas (see Fig. 13b), particularly in Area 1, entrapment of eggs can occur (see Fig. 10), even though the hydrodynamic inference does not indicate significant settling compared to other low-velocity areas.

Vertical distribution of potential egg settling zones

To examine the likelihood of egg settling based on vertical position in the water column, the number of cells were counted that satisfy the criterion of egg settling based on hydrodynamic inference at the same vertical height above the riverbed (z) under the four simulated discharges. Figure 14 illustrates an example based on Rouse number criterion. The results show that the flow condition of Q1 has substantially more counts (about one order of magnitude) due to weaker turbulence compared to the other three flow conditions (Fig. 14a and b). We interpret this large change between Q1 and higher discharges as a threshold resulting when flows begin to overtop the wing dikes. Overtopping flows substantially decrease low-turbulence areas downstream and landward of wing dikes.

The modeling data also indicate that egg settling is more likely to occur in the lower part of water column but not near the riverbed. Taking Q1 as an example, the peak of the number of counts are located about 2 m above the riverbed, with the number of counts decreasing both towards surface and towards the riverbed (Fig. 14a). In the normalized water column profile (Fig. 14b), substantial counts are located within the bottom 20% of the water column. We note that various water depths occur across the river reach, and hence the number of counts on the x-axis of the plots (Fig. 14a and b) are different before and after the water column normalization.

Examining the probability distribution function (PDF), we found that four discharge conditions show similar vertical profiles: egg settling has more than 10% probability within approximately the bottom 5 m (Fig. 14c), corresponding to approximately the bottom 20% of water depth (Fig. 14d). This result suggests that when eggs are transported to the bottom 20% layer, the hydrodynamic condition is less favorable for them to be re-suspended compared to higher-up in the water column. Similar results of profiles were found for the criterion using shear velocity and the vertical turbulence intensity, albeit the number of counts and the PDF values are different due to different criteria (see supplementary file, Figs. S5 and S6).

Figure 14. Vertical distribution of hydrodynamic-inferred egg settling locations using the criterion of Rouse number. (a) Number of counts as a function of different heights (z) above the riverbed; (b) number of counts as a function of the normalized heights which are normalized using flow depth (H); (c) probability distribution function (PDF) of the occurrence as a function of z; (d) PDF of the occurrence as a function of z/H.

Discussion on the egg survival

Examining river hydrodynamics in three dimensions through well-calibrated models yields valuable insights into the spatial distribution of flow velocity, water depth, and associated turbulence. These parameters can be used to identify potential locations where carp eggs may settle. However, using and interpreting results based on hydrodynamic criteria must be exercised with careful consideration. For instance, the Rouse number classification for particle suspension involves a broad range of values. In this study, we adopted Ro>1.2 as an indicator of egg settling, with Ro=1.2 representing the lower Rouse number bound for partial suspension. Conservatively, a critical value of Ro=2.523 is recommended for assessing predominantly bedload particle transport, indicating minimal to no suspension in the water column. Hence, at Rouse numbers between 1.2 and 2.5, partial suspension would be expected. In addition, the analysis using three-dimensional drift model results indicates that carp eggs would not drift into the egg settling zones within the L-head dikes and left bank (Area 1 in Fig. 13), for example, which would have predicted settling using hydrodynamic inference under the low-flow condition. This is because the actual egg drift pathway is governed by various parameters including egg spawning locations, streamlines of water flows, and interactions of flow and hydraulic structures. Consequently, predictions relevant to invasive carp management would improve when using the hydrodynamic-inferred egg settling zones if these additional parameters were taken into account.

Although egg settling zones based on hydrodynamic inference may not represent the actual conditions for egg settling, those predictions provide valuable information about the local hydrodynamics and suitability for egg settling at lower computational cost compared to drift modeling (for example SDrift). Therefore, this information could be useful for managers in determining the desirability of implementing hydraulic controls for egg settling. For example, if flow patterns can be adjusted to guide eggs into low-turbulence zones with adequate residence time, the hydrodynamics would facilitate the desired settling of eggs, aligning with management objectives for controlling aquatic invasive species. However we noted that solely using hydrodynamic inference may be misleading in invasive carp management without knowledge of drift pathways.

While high turbulence zones are the necessary environment for carp eggs to be suspended, eggs can be damaged or killed if turbulence exceeds a certain threshold. Prada et al.43 found an increased mortality in drifting grass carp eggs when exposed to turbulence with TKE greater than 2 m2/s2 for 1 minute in a grid-stirred turbulence tank. When TKE reaches 2.7 m2/s2, the mortality rate increased by nearly 30%. The corresponding maximal shear stresses were found to be 20 and 30 N/m2 near the grid for these two TKE values respectively. From our hydrodynamic model, mean TKE in the simulated reach under discharges Q1 to Q4 ranges from 0.01 to 0.02 m2/s2, with maximal depth-averaged TKE ranging from 0.16 to 0.21 m2/s2. The maximal TKE in the water column is found within 0.31–0.38 m2/s2 under four discharge conditions. These values are much smaller than the reported values that are harmful for carp eggs. Therefore, in a typical egg drift process, it is unlikely for eggs to experience persistent, extreme turbulence that could cause direct damage or mortality.

However, strong turbulence often generates high suspension and transport of sediment in the river. The abrasion between carp eggs and the suspended sediment may affect the egg survival rate. In the laboratory experiment conducted by Prada et al.15, carp eggs were found to drift within the lower 75% of the water column with lower flow velocity in the flume (0.08 m/s). When the flow velocity was increased to 0.22 m/s, the egg distribution in the water column was uniform, indicating a well-suspended condition for carp eggs. With further increasing flow velocity, Prada et al.15 observed that eggs were drifting more towards the bottom where they collided with the sediment particles. This indicates that the suspension of sediment could affect the vertical distribution of suspended eggs. They also observed reduced survival rate in medium and high flows compared to the control, while the survival rate was almost the same in low flow compared to the control. They also observed different larvae behaviors in different flow velocities, which may also contribute to the survival of carps. In our simulated Missouri River reach, the river turbulence may not pose a threat to carp eggs, but the suspended sediment could have negative effects. There has been limited study on the quantitative effects of sediment abrasion on egg mortality, indicating a fruitful subject for future studies.

Conclusions


In this study, we analyzed the simulated hydrodynamics of an 8-km reach in the Lower Missouri River, a site characterized by extensive channelization and river training. Four discharges representing 45–3% daily flow exceedance were examined. Calibration and validation of the simulations were conducted based on field observations. Flow depth, mean flow velocity, and turbulence quantities were investigated through computational fluid dynamics modeling. Simulated results show highly varied spatial distributions of mean flow and turbulence characteristics, primarily attributed to the curvature of the channel, variation in bed morphology, and the presence of river-training hydraulic structures, including wing dikes and L-head dikes.

To investigate the use of hydrodynamics for inferring the settling and suspension of carp eggs, we applied three criteria established in previous carp egg studies to analyze the spatial distribution of potential settling zones. The simulation results enabled the identification of low turbulence zones where insufficient suspension may hinder carp egg development. When comparing these hydrodynamic-inferred egg settling zones with the entrapment predicted by a Lagrangian egg-drift model, we observed that egg drift paths significantly influenced the locations where eggs may settle or be intercepted by in-stream hydraulic structures. Therefore, it is crucial to consider additional factors, such as spawning locations and drift paths, when using hydrodynamic inference to identify potential egg settling zones and larval nursery locations for invasive carp management.

Lastly, river turbulence may also influence carp egg survival through shear stresses and interactions with suspended sediment. Our data indicate that turbulence kinetic energy in the river does not surpass the laboratory-identified threshold associated with direct egg damage. However, abrasion from suspended sediment and the complex interactions between eggs and hydraulic structures, riverbed, and banks, accentuated by high morphological variations as demonstrated in the entrapment areas in the egg drift model, could affect the overall survival rate of carp eggs.

Data availibility


The data of field measurements and modeling are available in the online repository doi:10.5066/P9X5M3WH33.

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The experimental layout

Strength Prediction for Pearlitic Lamellar Graphite Iron: Model Validation

펄라이트 라멜라 흑연 철의 강도 예측: 모델 검증

Vasilios Fourlakidis, Ilia Belov, Attila Diószegi

Abstract


The present work provides validation of the ultimate tensile strength computational models, based on full-scale lamellar graphite iron casting process simulation, against previously obtained experimental data. Microstructure models have been combined with modified Griffith and Hall–Petch equations, and incorporated into casting simulation software, to enable the strength prediction for four pearlitic lamellar cast iron alloys with various carbon contents. The results show that the developed models can be successfully applied within the strength prediction methodology along with the simulation tools, for a wide range of carbon contents and for different solidification rates typical for both thin- and thick-walled complex-shaped iron castings.

Keywords


lamellar graphite iron; ultimate tensile strength; primary austenite; gravity casting process simulation

1. Introduction


Nowadays, there is a great need to further improve both the material properties and the prediction models for optimization of the heavy truck engine components aimed to fulfil the rigorous environmental legislations, sustainability goals, and customer demands. Cylinder blocks and cylinder heads are the primary components of these engines, and the majority of them are composed of lamellar graphite iron (LGI). The ultimate tensile strength (UTS) of LGI is an essential material property that determines the engine performance and the fuel consumption. The complex geometry and variation of the wall thickness in the cylinder blocks result in different solidification times through the component, and thus, different tensile properties.
A number of investigators [1,2,3,4,5,6] underlined the major influence of the graphite flake size on the strength of LGI. It is believed that under stress, the graphite flakes are dispersed in the metal matrix act as notches that decrease the material strength. Modified Griffith and Hall–Petch models were introduced for the prediction of UTS in LGI, where the maximum graphite length was considered as the maximum defect size [3,7,8,9]. Recently, it was found that the maximum defect size can never be larger than the interdendritic space between the primary austenite dendrites formed during the solidification process [10]. The length scale of the interdendritic space was characterized by the hydraulic diameter of the interdendritic phase (DIPHyde), which proved to be the most suitable parameter to express the detrimental effect of the graphite lamella in the metallic matrix. Thus, the DIPHyde
parameter was introduced as the maximum defect size in the modified Griffith and Hall–Petch equations [10,11].
Over the past decades, computer simulations of LGI solidification were carried out by several researchers [7,8,9,12,13] to describe the thermal history and the microstructure evolution of LGI castings. The main objective of these studies was prediction of the UTS. Macroscopic heat flow modeling, coupled with growth kinetic equations, was introduced in [7] to predict various microstructure features of LGI. Consequently, a modified Griffith fracture relation was applied to determine the UTS of a commercial LGI alloy. A similar solidification model was developed in [8], where a microstructure evolution model was employed together with the modified Hall–Petch equation for calculation of the UTS. Note that in [8], two different cooling rates resulted in two different relationships between the UTS and the maximum graphite flake length. Similar observations were made in [10], where three different cooling rates led to providing three different linear dependencies between the eutectic cell size (direct proportional to the maximum graphite length) and the UTS.
The present work provides validation of the UTS computational models against experimental data, based on full-scale pearlitic LGI gravity casting process simulation. We investigated whether the models recently developed in [10,11] can be applied within the UTS prediction methodology, along with the simulation tools, for different alloy compositions and for different solidification rates. The novel methodology for UTS prediction, presented in this paper, involves DIPHyde as the key morphological parameter, along with the pearlite lamellar spacing. These parameters are dependent on solidification time, cooling rate, and alloy composition. The proposed approach bears simplicity compared to the microstructure modelling methods [7,8]. The methodology is validated to include analytical formulation of the UTS prediction models and robust experimental thermal analysis, to obtain latent heat of solidification and solid-state transformation as input data for the simulation. First, the UTS modeling methods are elaborated followed by the details on the experimental setup and alloy composition. Casting simulation model is then introduced, as well as the simulation procedure. The results are discussed in comparison with the temperature and UTS measurements, followed by conclusions regarding applicability and limitations of the proposed UTS prediction methodology.

2. UTS Modeling


The modified Griffith fracture relation is given by Equation (1) [3], and the modified Hall–Petch strengthening model is represented by Equation (2) [8].

where 𝜎𝑈𝑇𝑆 is the ultimate tensile strength, α is the maximum defect size, and kt is the stress intensity factor of the metallic matrix, k1 and k2 are the contributions from other strengthening mechanisms, and d is the grain size. The maximum defect size and grain size, α and d, are provided in μm, parameters kt and k2 are in MPa, √μm, and k1 is in MPa.

It was found in [10] that DIPHyde is the dominant factor that reduces the UTS in lamellar graphite iron alloys. A modified Griffith equation was obtained in [10] as result of the linear regression analysis of the experimental data, Equation (3).

According to this model, if a tensile force is applied on the microstructure, a crack will start to form at a certain stress level. The crack will propagate relatively easily through the numerous interconnected graphite particles that are embedded in the metallic matrix of the eutectic cell. When the crack reaches the metallic matrix (pearlite) that was originated from the primary austenite (dendritic phase), the relatively rapid crack extension will be halted, due to the fact that much larger stresses are required for the fracture of this phase. The magnitude of the additional stress is proportional to the pearlite lamellar spacing (λpearlite). Based on this assumption, it becomes apparent that the effect of λpearlite on the UTS must be taken into consideration. Thus, linear multiple regression analysis was made to determine the simultaneous influence of the DIPHyde and the λpearlite on the UTS. The model obtained is based on the modified Hall–Petch relation, and is expressed by Equation (4) [11].

The DIPHyde parameter was found to be related to the solidification time (ts) and the fraction of primary austenite (fγ), as seen from Equation (5) [14].

The λpearlite parameter at room temperature was assumed to be dependent on the cooling rate in the eutectoid transformation region. The empirical relationship between λpearlite at room temperature, and the cooling rate at the temperature intervals between 700 and 740 °C, is shown in Figure 1. The experimentally derived relation Equation (6) was used for investigating the effect of different λpearlite prediction models on simulated UTS. The measurements techniques, the microstructure and thermal data that resulted in Equation (6), are presented elsewhere [11,12]. Briefly, the pearlite lamellar spacing was measured using SEM and a linear intercept method. The minimum value was considered to be the correct spacing (perpendicular to the lamellae). The distance between 11 adjacent ferrite lamellas was measured and divided by 10 for estimation of a single interlamellar spacing.

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Figure 1. Pearlite lamellar spacing as function of cooling rate between 700 and 740 °C.

3. Materials and Methods

3.1. Cylindrical Castings

The experimental layout contained three cylindrical cavities, each one surrounded by a different material (steel chill, sand, and insulation) intended to provide three different cooling rates. The entire assembly was enclosed by a furan-bounded sand mold. The dimensions of the cylinders surrounded by sand and chill were ∅50 × 70 mm, and the insulated cylinder dimensions were ∅80 × 70 mm. A lateral 2-D heat flow condition was induced by placing an insulation plate at the top and bottom of the cylindrical castings. The design of the cylindrical castings and arrangement of the experimental layout are shown in Figure 2 and Figure 3, respectively.

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Figure 2. Cylindrical castings with the insulation and chill.

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Figure 3. The experimental layout. (1) Thermocouples, (2) sand mold, and (3) insulation plates.

Two type S thermocouples with glass tube protection were embedded in every cylindrical casting. A central thermocouple was located on the central axis of the cylinder. The distance between the central and the lateral thermocouple was 20 mm for the ∅50 mm cylinder and 30 mm for the ∅80 mm cylinder. The thermocouples were placed at the mid-height of each cylinder and the temperatures were recorded at approximately 0.2 s interval. A 16-bit resolution data acquisition system with the sampling rate 100 Hz was employed [12].
The mold-filling time was 12 s. The solidification times of the metal in the chill, sand, and insulation were roughly 80, 400, and 1500 s, respectively. An electric induction furnace was utilized for melting of the charge material. The cast iron base alloy was inoculated with a constant level of a standard Sr-based inoculant. Four hypoeutectic lamellar graphite iron heats with varying carbon contents were produced. The alloy with the higher carbon content was cast first, and steel scraps were added to the furnace for the adjustment of the carbon content in the following casting. Coin-shaped specimens were extracted for chemical analysis. The chemical compositions of the four different alloys are presented in Table 1. All the castings had a fully pearlitic microstructure.

Table 1. Chemical composition (wt %) and carbon equivalent (Ceq = %C + %Si/3 + %P/3).

AlloyCSiMnPSCrCuCeq
A3.621.880.570.040.080.140.384.26
B3.341.830.560.040.080.150.373.96
C3.051.770.540.040.080.140.363.65
D2.801.750.540.040.080.150.353.40

Tensile strength measurements were performed using a dog bone-shaped specimen with 6 mm diameter in the gauge section, 35 mm gauge length, and a 3 μm surface finish. The tests were conducted at a strain rate of 0.035 mm/s and at room temperature. The experimental tensile samples were machined at the distance ~10 mm (sand, chill) and ~20 mm (insulation) from the cylinder axis. The load cell error of the tensile testing machine was <0.5%.

3.2. Simulation Model and Assumptions

A CFD software (Flow-3D CAST, v.5.0 from Flow Science, Inc., Santa Fe, NM, USA) [15] was employed to develop a full-scale 3D model of the casting process for the experimental layout. Mold filling and the cooling/solidification stages were simulated, and local UTS computations were performed on the customized models. Mold-filling time was 12 s, and the laminar flow model was applied. The casting temperature was 1360 °C, and the metal input diameter was 3 cm. The ambient temperature was set to 20 °C. Symmetry boundary conditions were used on the faces of the computational domain, except for the upper face, where the pressure boundary condition was applied. A computational grid of cubical control elements was generated with the cell size 3 mm. The computational grid had a total of ~1 million cells. Different grid densities were tested, and grid-independent results were obtained. The explicit solver was employed during the mold filling, whereas the implicit solver was used for heat transfer simulation in the solidification phase. Since the focus was on heat transfer and the UTS computation methodology, shrinkage and micro-porosity models were not included in the solidification phase.
In this work, the amount of latent heat release due to solidification was related to the solid fraction curves, seen in Figure 4, for the studied alloys. These curves were calculated from the registered experimental cooling curves by using the Fourier thermal analysis method [16,17]. The latent heat of solidification was considered equal to 240 kJ/kg for all studied alloys [18]. Fourier thermal analysis was also applied on cooling curves for the determination of the latent heat release during the eutectoid transformation. The latent heat releases at the eutectoid transformation was found to be similar for all alloys and were incorporated into the specific heat curve as it is shown in Figure 5. The temperature dependent cast iron thermophysical properties [12], and the calibrated heat transfer coefficients applied in the simulation are presented in Table 2.

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Figure 4. Solid fraction variation with temperature.

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Figure 5. Specific heat as function of temperature.

Table 2. Temperature dependent properties of the cast iron and heat transfer coefficients *.

Temperature (°C)Cast Iron Thermophysical PropertiesHeat Transfer Coefficient
DensitySpecific HeatThermal ConductivitySand-CastingChill-CastingInsulation-Casting
[kg/m3][J/kg/K][W/m/K][W/m2/K][W/m2/K][W/m2/K]
6007146700404010010
7201074300
72112301
72412308
72510825010
750733
9008015
1000699480015025
1100825250130055
11546960837401450
11707016
12006985160060
12276939749
13006876771380180
17006395807389402700940
* Piecewise linear interpolation was made between neighboring points in the table.

3.3. Simulation Procedure

The simulation procedure consisted of model calibration with respect to the experimental cooling curves available at the location of the central thermocouple. Correct reproduction of the experimental cooling curves is the key for the UTS computation methodology, and one is free to choose methods for model calibration. In this work, the calibration was done by adjustment of the typical heat transfer coefficients between the metal and the insulation, sand, and chill. The UTS calculations for the cylinders were performed during post-processing, by applying local solidification times, local cooling rates in the eutectoid transformation region, and the experimentally determined fraction of primary austenite (fγ) for each alloy: 0.3 for alloy A, 0.4 for alloy B, 0.51 for alloy C, and 0.61 for alloy D [16].

4. Results and Discussion

The general agreement within 7% was achieved between the simulated and measured cooling curves for insulation-, sand-, and chill-encapsulated cylinders; see Figure 6, Figure 7, Figure 8 and Figure 9. The larger differences were observed in the solidification region of the chill castings where the eutectic reaction was predicted at higher temperature than measured. This is because the solid fraction-temperature curves were derived from the sand-casting thermal histories, where the undercooling was much lower. Moreover, the solidification model in the simulation used the enthalpy method [19] and ignored the kinetics of phase transformation and, therefore, the undercooling and recalescence of solidification were not predicted. However, the simulated solidification times were in good agreement with the experiment.

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Figure 6. Simulated and experimental cooling curves (central thermocouple) for alloy A: (a) insulation, (b) sand, and (c) chill.

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Figure 7. Simulated and experimental cooling curves (central thermocouple) for alloy B: (a) insulation, (b) sand, and (c) chill.

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Figure 8. Simulated and experimental cooling curves (central thermocouple) for alloy C: (a) insulation, (b) sand, and (c) chill.

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Figure 9. Simulated and experimental cooling curves (central thermocouple) for alloy D: (a) insulation (b) sand, and (c) chill.

The measurement accuracy of the type S thermocouples was ±1.5 °C. It is worth noting that some of the thermocouples inserted in the melt could be slightly displaced from their intended positions during the solidification, which created an additional source of the measurement error; this can be seen clearly, e.g., from the solidification part of the experimental cooling curve for the insulated cylinder in Figure 7.
The simulated solidification times and cooling rates were used in Equations (3) and (4) for the calculation of UTS. The predicted UTS distribution, substituted in the middle cross-section of the alloy B casting, is shown in Figure 10. The figure illustrates the inhomogeneous material strength in the casting. It is directly related to the temperature gradient and the cooling rate distribution during solidification and solid-state transformation. The reduced UTS is the result of the microstructure coarseness that is related to the solidification time and the cooling rate. Moreover, large UTS gradients on the chilled cylinder can be explained by the large temperature gradients at high solidification rate. Intermediate and slow solidification rates on sand- and insulation-encapsulated cylinders resulted in more uniform distribution of UTS values, due to the smaller temperature gradients during solidification. It should be noted that the variation of UTS magnitude within the tensile bar positions (shown with dashed lines) complicates the model validation.

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Figure 10. Distribution of ultimate tensile strength (UTS) calculated from Equations (4) and (6) for alloy B: (a) insulation-, (b) sand-, and (c) chill-encapsulated cylinder; the dashed lines indicate the position of the tensile bars.

The obtained values were compared to the measured UTS. Table 3 presents the experimental and simulated UTS results for different cooling rates and for each alloy. The simulated UTS values in Table 3 were picked from the mid-height locations of the tensile bar regions, indicated in Figure 10 with dashed lines. This would correspond to the failure location in the tensile test. However, the exact fracture location might be influenced by several other factors, such as microporosities, graphite flakes that are in contact with the casting surface, or other casting impurities. All of these can cause the crack initiation at positions where the theoretical material strength is not the lowest. Apparently, the fracture analysis is out of scope of the present work. There are quite small differences between simulated and measured UTS values, with the exception of the intermediate and slow cooling rates (sand and insulation) for alloy A, where all the models predicted the UTS with less accuracy. Relatively high, but still acceptable average percentage errors are also observed for the insulated cylinders cast of alloys C and D.

Table 3. Experimental and simulated UTS.

AlloyUTS, [MPa]Average Percentage Error, [%]
ExperimentSimulation
Equation (3) 1Equation (4) 2Equation (3) 1Equation (4) 2
AInsulation1541802001730
Sand1952302501828
Chill363340–350340–35055
BInsulation21120421331
Sand25425526916
Chill368365–375385–39516
CInsulation25023323676
Sand28629330025
Chill440420–435435–44530
DInsulation2892602531012
Sand33732532344
Chill447440–455475–49008
1 Modified Griffith model; 2 Modified Hall–Petch model.

Comparisons between the calculated and the measured data are demonstrated in Figure 11. The graph reveals a relatively strong correlation between the measured and computed UTS. The R2 values show that Equation (3) predicts the UTS with better accuracy than Equation (4). This indicates the need to develop further the model for prediction of the λpearlite parameter.

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Figure 11. Correlation between measured and simulated UTS values.

The observed deviations between the simulated and measured UTS can be also attributed to the limited number of tensile specimens [10] and to uncertainties regarding the measurements accuracy of the 𝐷𝐻𝑦𝑑𝐼𝑃
parameter, especially for the low cooling rate samples [20] that were used to develop the UTS models.
The presented results should be related to two fundamental publications on computer simulations of LGI solidification coupled with the Griffiths and Hall–Petch models [7,8]. The models for UTS calculation utilized in these works were based on a narrow carbon content interval, and on a limited cooling rate variation, in comparison. Moreover, growth kinetic equations were employed in [7,8]. On the contrary, the latent heat release model by the “enthalpy method” [19] was adopted for the solidification simulation in the present work. Furthermore, the presented way to determine the key parameters and incorporate them into material property prediction is novel. In [7,8], the key parameter was the eutectic cell diameter. It is evident that the modified Griffith and Hall–Petch equations are applicable once the eutectic diameter can be predicted, as well as the pearlite lamellar spacing in the Hall–Patch equation. A completely different approach validated in this work involved the hydraulic diameter as the key morphological parameter, along with the pearlite lamellar spacing introduced in [8]. The presented methodology to calculate the UTS features the simplicity of determining the key parameters by simulation (solidification time, cooling rate, and composition dependent). While [7] and [8] introduce complex microstructure models valid for small process intervals (with respect to composition and cooling condition), the current methodology lays back to a robust experimental thermal analysis [16], providing accurate input data (latent heat of both solidification and solid-state transformation) for the simulation. A robust iteration process for tuning up the heat transfer coefficient results in the accurately predicted cooling rate.

5. Conclusions

The novel UTS prediction methodology for fully pearlitic LGI alloys presented in this paper involves hydraulic diameter as the key morphological parameter, along with the pearlite lamellar spacing. It is characterized by simplicity, in comparison to the microstructure modelling methods. The methodology includes analytical formulation of the UTS prediction models, and robust experimental thermal analysis. The latter provides the latent heat of solidification and solid-state transformation as input data for the solidification simulation. In turn, the simulation delivers the solidification time and cooling rates for the UTS prediction models.

Microstructure models for the prediction of hydraulic diameter and the pearlite lamellar spacing, combined with modified Griffith and Hall–Petch equations, were incorporated into casting simulation software for the prediction of UTS in fully pearlitic LGI alloys. Overall, the simulation UTS results were found to be in good agreement (within 9% on the average) with the measurements. However, high average percentage errors were observed for the intermediate and slow cooling rates (sand and insulation) for the alloy with the higher carbon content (alloy A). This study revealed the necessity for development of a more advanced model for the prediction of the λpearlite parameter. The results demonstrated the applicability of the novel UTS prediction models for different chemical compositions and cooling conditions.

Further development of the microstructure modelling would enable determination of the key parameters (hydraulic diameter and pearlite lamellar spacing). However, it seems not to be critical for the presented novel UTS prediction methodology which is valid for the wide process interval.

Author Contributions

A.D. designed the experiment and supervised the work, I.B. performed the simulations, V.F. analyzed the data and wrote the paper, A.D. and I.B. reviewed the paper.

Funding

This research received no external funding.

Acknowledgments

This work was performed within the Swedish Casting Innovation Centre. Cooperating parties are Jönköping University, Scania CV AB, Swerea SWECAST AB and Volvo Powertrain Production Gjuteriet AB. Participating persons from these institutions/companies are acknowledged.

Conflicts of Interest

The authors declare no conflict of interest.

References

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  3. Bates, C. Alloy element effect on lamellar iron properties: Part II. AFS Trans. 1986, 94, 889–905.
  4. Nakae, H.; Shin, H. Effect of graphite morphology on tensile properties of flake graphite cast iron. Mater. Trans. 2001, 42, 1428–1434.
  5. Baker, T.J. The fracture resistance of the flake graphite cast iron. Mater. Eng. Appl. 1978, 1, 13–18.
  6. Griffin, J.A.; Bates, C.E. Predicting in-situ lamellar cast iron properties: Effects of the pouring temperature and manganese and sulfur concentration. AFS Trans. 1988, 88, 481–496.
  7. Goettsch, D.D.; Dantzig, J.A. Modeling microstructure development in gray cast irons. Metall. Trans. A 1994, 25, 1063–1079.
  8. Catalina, A.; Guo, X.; Stefanescu, D.M.; Chuzhoy, L.; Pershing, M.A. Prediction of room temperature microstructure and mechanical properties in lamellar iron castings. AFS Trans. 2000, 94, 889–912.
  9. Urrutia, A.; Celentano, J.D.; Dayalan, R. Modeling and Simulation of the Gray-to-White Transition during Solidification of a Hypereutectic Gray Cast Iron: Application to a Stub-to-Carbon Connection used in Smelting Processes. Metals 2017, 7, 549.
  10. Fourlakidis, V.; Diószegi, A. A generic model to predict the ultimate tensile strength in pearlitic lamellar graphite iron. Mater. Sci. Eng. A 2014, 618, 161–167.
  11. Fourlakidis, V.; Diaconu, L.; Diószegi, A. Strength prediction of Lamellar Graphite Iron: From Griffith’s to Hall-Petch modified equation. Mater. Sci. Forum 2018, 925, 272–279.
  12. Diószegi, A. On the Microstructure Formation and Mechanical Properties in Grey Cast Iron. In Linköping Studies in Science and Technology; Dissertation No. 871; Jönköping: Jönköping, Sweden, 2004; p. 25. ISBN 91-7373-939-1.
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Scouring

Non-Equilibrium Scour Evolution around an Emerged Structure Exposed to a Transient Wave

일시적인 파도에 노출된 구조에서의 비평형 세굴 결과

Deniz Velioglu Sogut ,Erdinc Sogut ,Ali Farhadzadeh,Tian-Jian Hsu 

Abstract


The present study evaluates the performance of two numerical approaches in estimating non-equilibrium scour patterns around a non-slender square structure subjected to a transient wave, by comparing numerical findings with experimental data. This study also investigates the impact of the structure’s positioning on bed evolution, analyzing configurations where the structure is either attached to the sidewall or positioned at the centerline of the wave flume. The first numerical method treats sediment particles as a distinct continuum phase, directly solving the continuity and momentum equations for both sediment and fluid phases. The second method estimates sediment transport using the quadratic law of bottom shear stress, yielding robust predictions of bed evolution through meticulous calibration and validation. The findings reveal that both methods underestimate vortex-induced near-bed vertical velocities. Deposits formed along vortex trajectories are overestimated by the first method, while the second method satisfactorily predicts the bed evolution beneath these paths. Scour holes caused by wave impingement tend to backfill as the flow intensity diminishes. The second method cannot sufficiently capture this backfilling, whereas the first method adequately reflects the phenomenon. Overall, this study highlights significant variations in the predictive capabilities of both methods in regard to the evolution of non-equilibrium scour at low Keulegan–Carpenter numbers.

Keywords


Keulegan-Carpenter number, Solitary wave, non slender, wave-structure interaction, FLOW-3D, WedWaveFoam

Numerical Investigation of the Local Scour for Tripod Pile Foundation

Numerical Investigation of the Local Scour for Tripod Pile Foundation

Waqed H. Hassan Zahraa Mohammad Fadhe* Rifqa F. Thiab Karrar Mahdi
Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
Corresponding Author Email: Waqed.hammed@uowa.edu.iq

OPEN ACCESS

Abstract: 

This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripod-fluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them.  This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.

Keywords: 

local scour, tripod foundation, Flow-3D​, waves

1. Introduction

New energy sources have been used by mankind since they become industrialized. The main energy sources have traditionally been timber, coal, oil, and gas, but advances in the science of new energies, such as nuclear energy, have emerged [1, 2]. Clean and renewable energy such as offshore wind has grown significantly during the past few decades. There are numerous different types of foundations regarding offshore wind turbines (OWTs), comprising the tripod, jacket, gravity foundation, suction anchor (or bucket), and monopile [3, 4]. When the water depth is less than 30 meters, Offshore wind farms usually employ the monopile type [4]. Engineers must deal with the wind’s scouring phenomenon turbine foundations when planning and designing wind turbines for an offshore environment [5]. Waves and currents generate scour, this is the erosion of soil near a submerged foundation and at its location [6]. To predict the regional scour depth at a bridge pier, Jalal et al. [7-10] developed an original gene expression algorithm using artificial neural networks. Three monopiles, one main column, and several diagonal braces connecting the monopiles to the main column make up the tripod foundation, which has more complicated shapes than a single pile. The design of the foundation may have an impact on scour depth and scour development since the foundation’s form affects the flow field [11, 12]. Stahlmann [4] conducted several field investigations. He discovered that the main column is where the greatest scour depth occurred. Under the main column is where the maximum scour depth occurs in all experiments. The estimated findings show that higher wave heights correspond to higher flow velocities, indicating that a deeper scour depth is correlated with finer silt granularity [13] recommends as the design value for a single pile. These findings support the assertion that a tripod may cause the seabed to scour more severely than a single pile. The geography of the scour is significantly more influenced by the KC value (Keulegan–Carpenter number)

The capability of computer hardware and software has made computational fluid dynamics (CFD) quite popular to predict the behavior of fluid flow in industrial and environmental applications has increased significantly in recent years [14].

Finding an acceptable piece of land for the turbine’s construction and designing the turbine pile precisely for the local conditions are the biggest challenges. Another concern related to working in a marine environment is the effect of sea waves and currents on turbine piles and foundations. The earth surrounding the turbine’s pile is scoured by the waves, which also render the pile unstable.

In this research, the main objective is to investigate numerically a local scour around tripods in random waves. It is constructed and proven to use the tripod numerical model. The present numerical model is then used to examine the flow velocity distribution and scour characteristics.

2. Numerical Model

To simulate the scouring process around the tripod foundation, the CFD code Flow-3D was employed. By using the fractional area/volume method, it may highlight the intricate boundaries of the solution domain (FAVOR).

This model was tested and validated utilizing data derived experimentally from Schendel et al. [15] and Sumer and Fredsøe [6]. 200 runs were performed at different values of parameters.

2.1 Momentum equations

The incompressible viscous fluid motion is described by the three RANS equations listed below [16]:

(1)

\frac{\partial u}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial u}{\partial x}+v{{A}_{y}}\frac{\partial u}{\partial y}+w{{A}_{z}}\frac{\partial u}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial x}+{{G}_{x}}+fx

(2)

\frac{\partial v}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial v}{\partial x}+v{{A}_{y}}\frac{\partial v}{\partial y}+w{{A}_{z}}\frac{\partial v}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial y}+{{G}_{y}}+\text{f}y

 (3)

\frac{\partial w}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial w}{\partial x}+v{{A}_{y}}\frac{\partial w}{\partial y}+w{{A}_{z}}\frac{\partial w}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial z}+{{G}_{z}}+\text{fz}

where, respectively, uv, and w represent the xy, and z flow velocity components; volume fraction (VF), area fraction (AiI=xyz), water density (f), viscous force (fi), and body force (Gi) are all used in the formula.

2.2 Model of turbulence

Several turbulence models would be combined to solve the momentum equations. A two-equation model of turbulence is the RNG k-model, which has a high efficiency and accuracy in computing the near-wall flow field. Therefore, the flow field surrounding tripods was captured using the RNG k-model.

2.3 Model of sediment scour

2.3.1 Induction and deposition

Eq. (4) can be used to determine the particle entrainment lift velocity [17].

(4)

{{u}_{lift,i}}={{\alpha }_{i}}{{n}_{s}}d_{*}^{0.3}{{\left( \theta -{{\theta }_{cr}} \right)}^{1.5}}\sqrt{\frac{\parallel g\parallel {{d}_{i}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{{{\rho }_{f}}}}

α𝛼  is the Induction parameter, ns the normal vector is parallel to the seafloor, and for the present numerical model, ns=(0,0,1), θ𝜃cr is the essential Shields variable, g is the accelerated by gravity, di is the size of the particles, ρi is species density in beds, and d The diameter of particles without dimensions; these values can be obtained in Eq. (5).

(5)

{{d}_{*}}={{d}_{i}}{{\left( \frac{\parallel g\parallel {{\rho }_{f}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{\mu _{f}^{2}} \right)}^{1/3}}

μ𝜇f is this equation a dynamic viscosity of the fluid. cr was determined from an equation based on Soulsby [18].

(6)

{{\theta }_{cr}}=\frac{0.3}{1+1.2{{d}_{*}}}+0.055\left[ 1-\text{exp}\left( -0.02{{d}_{*}} \right) \right]

The equation was used to determine how quickly sand particles set Eq. (7):

(7)

{{\mathbf{u}}_{\text{nsettling},i}}=\frac{{{v}_{f}}}{{{d}_{i}}}\left[ {{\left( {{10.36}^{2}}+1.049d_{*}^{3} \right)}^{0.5}}-10.36 \right]

vf  stands for fluid kinematic viscosity.

2.3.2 Transportation for bed loads

Van Rijn [19] states that the speed of bed load conveyance was determined as:

(8)

{{~}_{\text{bedload},i}}=\frac{{{q}_{b,i}}}{{{\delta }_{i}}{{c}_{b,i}}{{f}_{b}}}

fb  is the essential particle packing percentage, qbi is the bed load transportation rate, and cb, I the percentage of sand by volume i. These variables can be found in Eq. (9), Eq. (10), fbδ𝛿i the bed load thickness.

(9)

{{q}_{b,i}}=8{{\left[ \parallel g\parallel \left( \frac{{{\rho }_{i}}-{{\rho }_{f}}}{{{\rho }_{f}}} \right)d_{i}^{3} \right]}^{\frac{1}{2}}}

(10)

{{\delta }_{i}}=0.3d_{*}^{0.7}{{\left( \frac{\theta }{{{\theta }_{cr}}}-1 \right)}^{0.5}}{{d}_{i}}

In this paper, after the calibration of numerous trials, the selection of parameters for sediment scour is crucial. Maximum packing fraction is 0.64 with a shields number of 0.05, entrainment coefficient of 0.018, the mass density of 2650, bed load coefficient of 12, and entrainment coefficient of 0.01.

3. Model Setup

To investigate the scour characteristics near tripods in random waves, the seabed-tripod-fluid numerical model was created as shown in Figure 1. The tripod basis, a seabed, and fluid and porous medium were all components of the model. The seabed was 240 meters long, 40 meters wide, and three meters high. It had a median diameter of d50 and was composed of uniformly fine sand. The 2.5-meter main column diameter D. The base of the main column was three dimensions above the original seabed. The center of the seafloor was where the tripod was, 130 meters from the offshore and 110 meters from the onshore. To prevent wave reflection, the porous media were positioned above the seabed on the onshore side.

image013.png

Figure 1. An illustration of the numerical model for the seabed-tripod-fluid

3.1 Generation of meshes

Figure 2 displays the model’s mesh for the Flow-3D software grid. The current model made use of two different mesh types: global mesh grid and nested mesh grid. A mesh grid with the following measurements was created by the global hexahedra mesh grid: 240m length, 40m width, and 32m height. Around the tripod, a finer nested mesh grid was made, with dimensions of 0 to 32m on the z-axis, 10 to 30 m on the x-axis, and 25 to 15 m on the y-axis. This improved the calculation’s precision and mesh quality.

image014.png

Figure 2. The mesh block sketch

3.2 Conditional boundaries

To increase calculation efficiency, the top side, The model’s two x-z plane sides, as well as the symmetry boundaries, were all specified. For u, v, w=0, the bottom boundary wall was picked. The offshore end of the wave boundary was put upstream. For the wave border, random waves were generated using the wave spectrum from the Joint North Sea Wave Project (JONSWAP). Boundary conditions are shown in Figure 3.

image015.png

Figure 3. Boundary conditions of the typical problem

The wave spectrum peak enhancement factor (=3.3 for this work) and can be used to express the unidirectional JONSWAP frequency spectrum.

3.3 Mesh sensitivity

Before doing additional research into scour traits and scour depth forecasting, mesh sensitivity analysis is essential. Three different mesh grid sizes were selected for this section: Mesh 1 has a 0.45 by 0.45 nested fine mesh and a 0.6 by 0.6 global mesh size. Mesh 2 has a 0.4 global mesh size and a 0.35 nested fine mesh size, while Mesh 3 has a 0.25 global mesh size and a nested fine mesh size of 0.15. Comparing the relative fine mesh size (such as Mesh 2 or Mesh 3) to the relatively coarse mesh size (such as Mesh 1), a larger scour depth was seen; this shows that a finer mesh size can more precisely represent the scouring and flow field action around a tripod. Significantly, a lower mesh size necessitates a time commitment and a more difficult computer configuration. Depending on the sensitivity of the mesh guideline utilized by Pang et al., when Mesh 2 is applied, the findings converge and the mesh size is independent [20]. In the next sections, scouring the area surrounding the tripod was calculated using Mesh 2 to ensure accuracy and reduce computation time. The working segment generates a total of 14, 800,324 cells.

3.4 Model validation

Comparisons between the predicted outcomes from the current model and to confirm that the current numerical model is accurate and suitably modified, experimental data from Sumer and Fredsøe [6] and Schendel et al. [15] were used. For the experimental results of Run 05, Run 15, and Run 22 from Sumer and Fredsøe [6], the experimental A9, A13, A17, A25, A26, and A27 results from Schendel et al. [15], and the numerical results from the current model are shown in Figure 4. The present model had d50=0.051cm, the height of the water wave(h)=10m, and wave velocity=0.854 m.s-1.

image016.png

Figure 4. Cell size effect

image017.png

Figure 5. Comparison of the present study’s maximum scour depth with that authored by Sumer and Fredsøe [6] and Schendel et al. [15]

According to Figure 5, the highest discrepancy between the numerical results and experimental data is about 10%, showing that overall, there is good agreement between them. The ability of the current numerical model to accurately depict the scour process and forecast the maximum scour depth (S) near foundations is demonstrated by this. Errors in the simulation were reduced by using the calibrated values of the parameter. Considering these results, a suggested simulated scouring utilizing a Flow-3D numerical model is confirmed as a superior way for precisely forecasting the maximum scour depth near a tripod foundation in random waves.

3.5 Dimensional analysis

The variables found in this study as having the greatest impacts, variables related to flow, fluid, bed sediment, flume shape, and duration all had an impact on local scouring depth (t). Hence, scour depth (S) can be seen as a function of these factors, shown as:

(11)

S=f\left(\rho, v, V, h, g, \rho s, d_{50}, \sigma g, V_w, D, d, T_v, t\right)

With the aid of dimensional analysis, the 14-dimensional parameters in Eq. (11) were reduced to 6 dimensionless variables using Buckingham’s -theorem. D, V, and were therefore set as repetition parameters and others as constants, allowing for the ignoring of their influence. Eq. (12) thus illustrates the relationship between the effect of the non-dimensional components on the depth of scour surrounding a tripod base.

(12)

\frac{S}{D}=f\left(\frac{h}{D}, \frac{d 50}{D}, \frac{V}{V W}, F r, K c\right)

where, SD𝑆𝐷 are scoured depth ratio, VVw𝑉𝑉𝑤 is flow wave velocity, d50D𝑑50𝐷 median size ratio, $Fr representstheFroudnumber,and𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠𝑡ℎ𝑒𝐹𝑟𝑜𝑢𝑑𝑛𝑢𝑚𝑏𝑒𝑟,𝑎𝑛𝑑Kc$ is the Keulegan-Carpenter.

4. Result and Discussion

4.1 Development of scour

Similar to how the physical model was used, this numerical model was also used. The numerical model’s boundary conditions and other crucial variables that directly influence the outcomes were applied (flow depth, median particle size (d50), and wave velocity). After the initial 0-300 s, the scour rate reduced as the scour holes grew quickly. The scour depths steadied for about 1800 seconds before reaching an asymptotic value. The findings of scour depth with time are displayed in Figure 6.

4.2 Features of scour

Early on (t=400s), the scour hole began to appear beneath the main column and then began to extend along the diagonal bracing connecting to the wall-facing pile. Gradually, the geography of the scour; of these results is similar to the experimental observations of Stahlmann [4] and Aminoroayaie Yamini et al. [1]. As the waves reached the tripod, there was an enhanced flow acceleration underneath the main column and the lower diagonal braces as a result of the obstructing effects of the structural elements. More particles are mobilized and transported due to the enhanced near-bed flow velocity, it also increases bed shear stress, turbulence, and scour at the site. In comparison to a single pile, the main column and structural components of the tripod have a significant impact on the flow velocity distribution and, consequently, the scour process and morphology. The main column and seabed are separated by a gap, therefore the flow across the gap may aid in scouring. The scour hole first emerged beneath the main column and subsequently expanded along the lower structural components, both Aminoroayaie Yamini et al. [1] and Stahlmann [4] made this claim. Around the tripod, there are several different scour morphologies and the flow velocity distribution as shown in Figures 7 and 8.

image023.png

Figure 6. Results of scour depth with time

image024.png

image025.png

image026.png

image027.png

Figure 7. The sequence results of scour depth around tripod development (reached to steady state) simulation time

image028.png

image029.png

image030.png

image031.png

Figure 8. Random waves of flow velocity distribution around a tripod

4.3 Wave velocity’s (Vw) impact on scour depth

In this study’s section, we looked at how variations in wave current velocity affected the scouring depth. Bed scour pattern modification could result from an increase or decrease in waves. As a result, the backflow area produced within the pile would become stronger, which would increase the depth of the sediment scour. The quantity of current turbulence is the primary cause of the relationship between wave height and bed scour value. The current velocity has increased the extent to which the turbulence energy has changed and increased in strength now present. It should be mentioned that in this instance, the Jon swap spectrum random waves are chosen. The scour depth attains its steady-current value for Vw<0.75, Figure 9 (a) shows that effect. When (V) represents the mean velocity=0.5 m.s-1.

image032.png

(a)

image033.png

(b)

image034.png

(c)

image035.png

(d)

Figure 9Main effects on maximum scour depth (Smax) as a function of column diameter (D)

4.4 Impact of a median particle (d50) on scour depth

In this section of the study, we looked into how variations in particle size affected how the bed profile changed. The values of various particle diameters are defined in the numerical model for each run numerical modeling, and the conditions under which changes in particle diameter have an impact on the bed scour profile are derived. Based on Figure 9 (b), the findings of the numerical modeling show that as particle diameter increases the maximum scour depth caused by wave contact decreases. When (d50) is the diameter of Sediment (d50). The Shatt Al-Arab soil near Basra, Iraq, was used to produce a variety of varied diameters.

4.5 Impact of wave height and flow depth (h) on scour depth

One of the main elements affecting the scour profile brought on by the interaction of the wave and current with the piles of the wind turbines is the height of the wave surrounding the turbine pile causing more turbulence to develop there. The velocity towards the bottom and the bed both vary as the turbulence around the pile is increased, modifying the scour profile close to the pile. According to the results of the numerical modeling, the depth of scour will increase as water depth and wave height in random waves increase as shown in Figure 9 (c).

4.6 Froude number’s (Fr) impact on scour depth

No matter what the spacing ratio, the Figure 9 shows that the Froude number rises, and the maximum scour depth often rises as well increases in Figure 9 (d). Additionally, it is crucial to keep in mind that only a small portion of the findings regarding the spacing ratios with the smallest values. Due to the velocity acceleration in the presence of a larger Froude number, the range of edge scour downstream is greater than that of upstream. Moreover, the scouring phenomena occur in the region farthest from the tripod, perhaps as a result of the turbulence brought on by the collision of the tripod’s pile. Generally, as the Froude number rises, so does the deposition height and scour depth.

4.7 Keulegan-Carpenter (KC) number

The geography of the scour is significantly more influenced by the KC value. Greater KC causes a deeper equilibrium scour because an increase in KC lengthens the horseshoe vortex’s duration and intensifies it as shown in Figure 10.

The result can be attributed to the fact that wave superposition reduced the crucial KC for the initiation of the scour, particularly under small KC conditions. The primary variable in the equation used to calculate This is the depth of the scouring hole at the bed. The following expression is used to calculate the Keulegan-Carpenter number:

Kc=Vw∗TpD𝐾𝑐=𝑉𝑤∗𝑇𝑝𝐷                          (13)

where, the wave period is Tp and the wave velocity is shown by Vw.

image037.png

Figure 10. Relationship between the relative maximum scour depth and KC

5. Conclusion

(1) The existing seabed-tripod-fluid numerical model is capable of faithfully reproducing the scour process and the flow field around tripods, suggesting that it may be used to predict the scour around tripods in random waves.

(2) Their results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50).

(3) A diagonal brace and the main column act as blockages, increasing the flow accelerations underneath them. This raises the magnitude of the disturbance and the shear stress on the seafloor, which in turn causes a greater number of particles to be mobilized and conveyed, as a result, causes more severe scour at the location.

(4) The Froude number and the scouring process are closely related. In general, as the Froude number rises, so does the maximum scour depth and scour range. The highest maximum scour depth always coincides with the bigger Froude number with the shortest spacing ratio.

Since the issue is that there aren’t many experiments or studies that are relevant to this subject, therefore we had to rely on the monopile criteria. Therefore, to gain a deeper knowledge of the scouring effect surrounding the tripod in random waves, further numerical research exploring numerous soil, foundation, and construction elements as well as upcoming physical model tests will be beneficial.

Nomenclature

CFDComputational fluid dynamics
FAVORFractional Area/Volume Obstacle Representation
VOFVolume of Fluid
RNGRenormalized Group
OWTsOffshore wind turbines
Greek Symbols
ε, ωDissipation rate of the turbulent kinetic energy, m2s-3
Subscripts
d50Median particle size
VfVolume fraction
GTTurbulent energy of buoyancy
KTTurbulent velocity
PTKinetic energy of the turbulence
ΑiInduction parameter
nsInduction parameter
ΘΘcrThe essential Shields variable
DiDiameter of sediment
dThe diameter of particles without dimensions
µfDynamic viscosity of the fluid
qb,iThe bed load transportation rate
Cs,iSand particle’s concentration of mass
DDiameter of pile
DfDiffusivity
DDiameter of main column
FrFroud number
KcKeulegan–Carpenter number
GAcceleration of gravity g
HFlow depth
VwWave Velocity
VMean Velocity
TpWave Period
SScour depth

  References

[1] Aminoroayaie Yamini, O., Mousavi, S.H., Kavianpour, M.R., Movahedi, A. (2018). Numerical modeling of sediment scouring phenomenon around the offshore wind turbine pile in marine environment. Environmental Earth Sciences, 77: 1-15. https://doi.org/10.1007/s12665-018-7967-4

[2] Hassan, W.H., Hashim, F.S. (2020). The effect of climate change on the maximum temperature in Southwest Iraq using HadCM3 and CanESM2 modelling. SN Applied Sciences, 2(9): 1494. https://doi.org/10.1007/s42452-020-03302-z

[3] Fazeres-Ferradosa, T., Rosa-Santos, P., Taveira-Pinto, F., Pavlou, D., Gao, F.P., Carvalho, H., Oliveira-Pinto, S. (2020). Preface: Advanced research on offshore structures and foundation design part 2. In Proceedings of the Institution of Civil Engineers-Maritime Engineering. Thomas Telford Ltd, 173(4): 96-99. https://doi.org/10.1680/jmaen.2020.173.4.96

[4] Stahlmann, A. (2013). Numerical and experimental modeling of scour at foundation structures for offshore wind turbines. In ISOPE International Ocean and Polar Engineering Conference. ISOPE, pp. ISOPE-I.

[5] Petersen, T.U., Sumer, B.M., Fredsøe, J. (2014). Edge scour at scour protections around offshore wind turbine foundations. In 7th International Conference on Scour and Erosion. CRC Press, pp. 587-592.

[6] Sumer, B.M., Fredsøe, J. (2001). Scour around pile in combined waves and current. Journal of Hydraulic Engineering, 127(5): 403-411. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:5(403)

[7] Jalal, H.K., Hassan, W.H. (2020). Effect of bridge pier shape on depth of scour. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 671(1): 012001. https://doi.org/10.1088/1757-899X/671/1/012001

[8] Hassan, W.H., Jalal, H.K. (2021). Prediction of the depth of local scouring at a bridge pier using a gene expression programming method. SN Applied Sciences, 3(2): 159. https://doi.org/10.1007/s42452-020-04124-9

[9] Jalal, H.K., Hassan, W.H. (2020). Three-dimensional numerical simulation of local scour around circular bridge pier using Flow-3D software. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 745(1): 012150. https://doi.org/10.1088/1757-899X/745/1/012150

[10] Hassan, W.H., Attea, Z.H., Mohammed, S.S. (2020). Optimum layout design of sewer networks by hybrid genetic algorithm. Journal of Applied Water Engineering and Research, 8(2): 108-124. https://doi.org/10.1080/23249676.2020.1761897

[11] Hassan, W.H., Hussein, H.H., Alshammari, M.H., Jalal, H.K., Rasheed, S.E. (2022). Evaluation of gene expression programming and artificial neural networks in PyTorch for the prediction of local scour depth around a bridge pier. Results in Engineering, 13: 100353. https://doi.org/10.1016/j.rineng.2022.100353

[12] Hassan, W.H., Hh, H., Mohammed, S.S., Jalal, H.K., Nile, B.K. (2021). Evaluation of gene expression programming to predict the local scour depth around a bridge pier. Journal of Engineering Science and Technology, 16(2): 1232-1243. https://doi.org/10.1016/j.rineng.2022.100353

[13] Nerland, C. (2010). Offshore wind energy: Balancing risk and reward. In Proceedings of the Canadian Wind Energy Association’s 2010 Annual Conference and Exhibition, Canada, p. 2000. 

[14] Hassan, W.H., Nile, B.K., Mahdi, K., Wesseling, J., Ritsema, C. (2021). A feasibility assessment of potential artificial recharge for increasing agricultural areas in the kerbala desert in Iraq using numerical groundwater modeling. Water, 13(22): 3167. https://doi.org/10.3390/w13223167

[15] Schendel, A., Welzel, M., Schlurmann, T., Hsu, T.W. (2020). Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coastal Engineering, 161: 103751. https://doi.org/10.1016/j.coastaleng.2020.103751

[16] Yakhot, V., Orszag, S.A. (1986). Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing, 1(1): 3-51. https://doi.org/10.1007/BF01061452

[17] Mastbergen, D.R., Van Den Berg, J.H. (2003). Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology, 50(4): 625-637. https://doi.org/10.1046/j.1365-3091.2003.00554.x

[18] Soulsby, R. (1997). Dynamics of marine sands. https://doi.org/10.1680/doms.25844

[19] Van Rijn, L.C. (1984). Sediment transport, part I: Bed load transport. Journal of Hydraulic Engineering, 110(10): 1431-1456. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431)

[20] Pang, A.L.J., Skote, M., Lim, S.Y., Gullman-Strand, J., Morgan, N. (2016). A numerical approach for determining equilibrium scour depth around a mono-pile due to steady currents. Applied Ocean Research, 57: 114-124. https://doi.org/10.1016/j.apor.2016.02.010

Numerical Investigation of the Local Scour for Tripod Pile Foundation.

Numerical Investigation of the Local Scour for Tripod Pile Foundation.

Hassan, Waqed H.; Fadhe, Zahraa Mohammad; Thiab, Rifqa F.; Mahdi, Karrar

초록

This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripodfluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them. This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.

주제어

BUILDING foundationsSURFACE waves (Seismic waves)FLOW velocityRANDOM fieldsDIMENSIONAL analysisFROUDE numberOCEAN waves

키워드

출판물

Mathematical Modelling of Engineering Problems, 2024, Vol 11, Issue 4, p903

ISSN 2369-0739

저자 소속기관

  • 1 Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
  • 2 Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
  • 3 Department of Radiological Techniques, College of Health and Medical Techniques, Al-Zahraa University for Women, Karbala 56100, Iraq
  • 4 Soil Physics and Land Management Group, Wageningen University & Research, Wageningen 6708 PB, Netherlands
Coupled CFD-DEM simulation of interfacial fluid–particle interaction during binder jet 3D printing

Coupled CFD-DEM simulation of interfacial fluid–particle interaction during binder jet 3D printing

바인더 제트 3D 프린팅 중 계면 유체-입자 상호 작용에 대한 CFD-DEM 결합 시뮬레이션

Joshua J. Wagner, C. Fred Higgs III

https://doi.org/10.1016/j.cma.2024.116747

Abstract

The coupled dynamics of interfacial fluid phases and unconstrained solid particles during the binder jet 3D printing process govern the final quality and performance of the resulting components. The present work proposes a computational fluid dynamics (CFD) and discrete element method (DEM) framework capable of simulating the complex interfacial fluid–particle interaction that occurs when binder microdroplets are deposited into a powder bed. The CFD solver uses a volume-of-fluid (VOF) method for capturing liquid–gas multifluid flows and relies on block-structured adaptive mesh refinement (AMR) to localize grid refinement around evolving fluid–fluid interfaces. The DEM module resolves six degrees of freedom particle motion and accounts for particle contact, cohesion, and rolling resistance. Fully-resolved CFD-DEM coupling is achieved through a fictitious domain immersed boundary (IB) approach. An improved method for enforcing three-phase contact lines with a VOF-IB extension technique is introduced. We present several simulations of binder jet primitive formation using realistic process parameters and material properties. The DEM particle systems are experimentally calibrated to reproduce the cohesion behavior of physical nickel alloy powder feedstocks. We demonstrate the proposed model’s ability to resolve the interdependent fluid and particle dynamics underlying the process by directly comparing simulated primitive granules with one-to-one experimental counterparts obtained from an in-house validation apparatus. This computational framework provides unprecedented insight into the fundamental mechanisms of binder jet 3D printing and presents a versatile new approach for process parameter optimization and defect mitigation that avoids the inherent challenges of experiments.

바인더 젯 3D 프린팅 공정 중 계면 유체 상과 구속되지 않은 고체 입자의 결합 역학이 결과 구성 요소의 최종 품질과 성능을 좌우합니다. 본 연구는 바인더 미세액적이 분말층에 증착될 때 발생하는 복잡한 계면 유체-입자 상호작용을 시뮬레이션할 수 있는 전산유체역학(CFD) 및 이산요소법(DEM) 프레임워크를 제안합니다.

CFD 솔버는 액체-가스 다중유체 흐름을 포착하기 위해 VOF(유체량) 방법을 사용하고 블록 구조 적응형 메쉬 세분화(AMR)를 사용하여 진화하는 유체-유체 인터페이스 주위의 그리드 세분화를 국지화합니다. DEM 모듈은 6개의 자유도 입자 운동을 해결하고 입자 접촉, 응집력 및 구름 저항을 설명합니다.

완전 분해된 CFD-DEM 결합은 가상 도메인 침지 경계(IB) 접근 방식을 통해 달성됩니다. VOF-IB 확장 기술을 사용하여 3상 접촉 라인을 강화하는 향상된 방법이 도입되었습니다. 현실적인 공정 매개변수와 재료 특성을 사용하여 바인더 제트 기본 형성에 대한 여러 시뮬레이션을 제시합니다.

DEM 입자 시스템은 물리적 니켈 합금 분말 공급원료의 응집 거동을 재현하기 위해 실험적으로 보정되었습니다. 우리는 시뮬레이션된 기본 과립과 내부 검증 장치에서 얻은 일대일 실험 대응물을 직접 비교하여 프로세스의 기본이 되는 상호 의존적인 유체 및 입자 역학을 해결하는 제안된 모델의 능력을 보여줍니다.

이 계산 프레임워크는 바인더 제트 3D 프린팅의 기본 메커니즘에 대한 전례 없는 통찰력을 제공하고 실험에 내재된 문제를 피하는 공정 매개변수 최적화 및 결함 완화를 위한 다용도의 새로운 접근 방식을 제시합니다.

Introduction

Binder jet 3D printing (BJ3DP) is a powder bed additive manufacturing (AM) technology capable of fabricating geometrically complex components from advanced engineering materials, such as metallic superalloys and ultra-high temperature ceramics [1], [2]. As illustrated in Fig. 1(a), the process is comprised of many repetitive print cycles, each contributing a new cross-sectional layer on top of a preceding one to form a 3D CAD-specified geometry. The feedstock material is first delivered from a hopper to a build plate and then spread into a thin layer by a counter-rotating roller. After powder spreading, a print head containing many individual inkjet nozzles traverses over the powder bed while precisely jetting binder microdroplets onto select regions of the spread layer. Following binder deposition, the build plate lowers by a specified layer thickness, leaving a thin void space at the top of the job box that the subsequent powder layer will occupy. This cycle repeats until the full geometries are formed layer by layer. Powder bed fusion (PBF) methods follow a similar procedure, except they instead use a laser or electron beam to selectively melt and fuse the powder material. Compared to PBF, binder jetting offers several distinct advantages, including faster build rates, enhanced scalability for large production volumes, reduced machine and operational costs, and a wider selection of suitable feedstock materials [2]. However, binder jetted parts generally possess inferior mechanical properties and reduced dimensional accuracy [3]. As a result, widescale adoption of BJ3DP to fabricate high-performance, mission-critical components, such as those common to the aerospace and defense sectors, is contingent on novel process improvements and innovations [4].

A major obstacle hindering the advancement of BJ3DP is our limited understanding of how various printing parameters and material properties collectively influence the underlying physical mechanisms of the process and their effect on the resulting components. To date, the vast majority of research efforts to uncover these relationships have relied mainly on experimental approaches [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], which are often expensive and time-consuming and have inherent physical restrictions on what can be measured and observed. For these reasons, there is a rapidly growing interest in using computational models to circumvent the challenges of experimental investigations and facilitate a deeper understanding of the process’s fundamental phenomena. While significant progress has been made in developing and deploying numerical frameworks aimed at powder spreading [20], [21], [22], [23], [24], [25], [26], [27] and sintering [28], [29], [30], [31], [32], simulating the interfacial fluid–particle interaction (IFPI) in the binder deposition stage is still in its infancy. In their exhaustive review, Mostafaei et al. [2] point out the lack of computational models capable of resolving the coupled fluid and particle dynamics associated with binder jetting and suggest that the development of such tools is critical to further improving the process and enhancing the quality of its end-use components.

We define IFPI as a multiphase flow regime characterized by immiscible fluid phases separated by dynamic interfaces that intersect the surfaces of moving solid particles. As illustrated in Fig. 1(b), an elaborate IFPI occurs when a binder droplet impacts the powder bed in BJ3DP. The momentum transferred from the impacting droplet may cause powder compaction, cratering, and particle ejection. These ballistic disturbances can have deleterious effects on surface texture and lead to the formation of large void spaces inside the part [5], [13]. After impact, the droplet spreads laterally on the bed surface and vertically into the pore network, driven initially by inertial impact forces and then solely by capillary action [33]. Attractive capillary forces exerted on mutually wetted particles tend to draw them inward towards each other, forming a packed cluster of bound particles referred to as a primitive [34]. A single-drop primitive is the most fundamental building element of a BJ3DP part, and the interaction leading to its formation has important implications on the final part characteristics, such as its mechanical properties, resolution, and dimensional accuracy. Generally, binder droplets are deposited successively as the print head traverses over the powder bed. The traversal speed and jetting frequency are set such that consecutive droplets coalesce in the bed, creating a multi-drop primitive line instead of a single-drop primitive granule. The binder must be jetted with sufficient velocity to penetrate the powder bed deep enough to provide adequate interlayer binding; however, a higher impact velocity leads to more pronounced ballistic effects.

A computational framework equipped to simulate the interdependent fluid and particle dynamics in BJ3DP would allow for unprecedented observational and measurement capability at temporal and spatial resolutions not currently achievable by state-of-the-art imaging technology, namely synchrotron X-ray imaging [13], [14], [18], [19]. Unfortunately, BJ3DP presents significant numerical challenges that have slowed the development of suitable modeling frameworks; the most significant of which are as follows:

  • 1.Incorporating dynamic fluid–fluid interfaces with complex topological features remains a nontrivial task for standard mesh-based CFD codes. There are two broad categories encompassing the methods used to handle interfacial flows: interface tracking and interface capturing [35]. Interface capturing techniques, such as the popular volume-of-fluid (VOF) [36] and level-set methods [37], [38], are better suited for problems with interfaces that become heavily distorted or when coalescence and fragmentation occur frequently; however, they are less accurate in resolving surface tension and boundary layer effects compared to interface tracking methods like front-tracking [39], arbitrary Lagrangian–Eulerian [40], and space–time finite element formulations [41]. Since interfacial forces become increasingly dominant at decreasing length scales, inaccurate surface tension calculations can significantly deteriorate the fidelity of IFPI simulations involving <100 μm droplets and particles.
  • 2.Dynamic powder systems are often modeled using the discrete element method (DEM) introduced by Cundall and Strack [42]. For IFPI problems, a CFD-DEM coupling scheme is required to exchange information between the fluid and particle solvers. Fully-resolved CFD-DEM coupling suggests that the flow field around individual particle surfaces is resolved on the CFD mesh [43], [44]. In contrast, unresolved coupling volume averages the effect of the dispersed solid phase on the continuous fluid phases [45], [46], [47], [48]. Comparatively, the former is computationally expensive but provides detailed information about the IFPI in question and is more appropriate when contact line dynamics are significant. However, since the pore structure of a powder bed is convoluted and evolves with time, resolving such solid–fluid interfaces on a computational mesh presents similar challenges as fluid–fluid interfaces discussed in the previous point. Although various algorithms have been developed to deform unstructured meshes to accommodate moving solid surfaces (see Bazilevs et al. [49] for an overview of such methods), they can be prohibitively expensive when frequent topology changes require mesh regeneration rather than just modification through nodal displacement. The pore network in a powder bed undergoes many topology changes as particles come in and out of contact with each other, constantly closing and opening new flow channels. Non-body-conforming structured grid approaches that rely on immersed boundary (IB) methods to embed the particles in the flow field can be better suited for such cases [50]. Nevertheless, accurately representing these complex pore geometries on Cartesian grids requires extremely high mesh resolutions, which can impose significant computational costs.
  • 3.Capillary effects depend on the contact angle at solid–liquid–gas intersections. Since mesh nodes do not coincide with a particle surface when using an IB method on structured grids, imposing contact angle boundary conditions at three-phase contact lines is not straightforward.

While these issues also pertain to PBF process modeling, resolving particle motion is generally less crucial for analyzing melt pool dynamics compared to primitive formation in BJ3DP. Therefore, at present, the vast majority of computational process models of PBF assume static powder beds and avoid many of the complications described above, see, e.g., [51], [52], [53], [54], [55], [56], [57], [58], [59]. Li et al. [60] presented the first 2D fully-resolved CFD-DEM simulations of the interaction between the melt pool, powder particles, surrounding gas, and metal vapor in PBF. Following this work, Yu and Zhao [61], [62] published similar melt pool IFPI simulations in 3D; however, contact line dynamics and capillary forces were not considered. Compared to PBF, relatively little work has been published regarding the computational modeling of binder deposition in BJ3DP. Employing the open-source VOF code Gerris [63], Tan [33] first simulated droplet impact on a powder bed with appropriate binder jet parameters, namely droplet size and impact velocity. However, similar to most PBF melt pool simulations described in the current literature, the powder bed was fixed in place and not allowed to respond to the interacting fluid phases. Furthermore, a simple face-centered cubic packing of non-contacting, monosized particles was considered, which does not provide a realistic pore structure for AM powder beds. Building upon this approach, we presented a framework to simulate droplet impact on static powder beds with more practical particle size distributions and packing arrangements [64]. In a study similar to [33], [64], Deng et al. [65] used the VOF capability in Ansys Fluent to examine the lateral and vertical spreading of a binder droplet impacting a fixed bimodal powder bed with body-centered packing. Li et al. [66] also adopted Fluent to conduct 2D simulations of a 100 μm diameter droplet impacting substrates with spherical roughness patterns meant to represent the surface of a simplified powder bed with monosized particles. The commercial VOF-based software FLOW-3D offers an AM module centered on process modeling of various AM technologies, including BJ3DP. However, like the above studies, particle motion is still not considered in this codebase. Ur Rehman et al. [67] employed FLOW-3D to examine microdroplet impact on a fixed stainless steel powder bed. Using OpenFOAM, Erhard et al. [68] presented simulations of different droplet impact spacings and patterns on static sand particles.

Recently, Fuchs et al. [69] introduced an impressive multipurpose smoothed particle hydrodynamics (SPH) framework capable of resolving IFPI in various AM methods, including both PBF and BJ3DP. In contrast to a combined CFD-DEM approach, this model relies entirely on SPH meshfree discretization of both the fluid and solid governing equations. The authors performed several prototype simulations demonstrating an 80 μm diameter droplet impacting an unconstrained powder bed at different speeds. While the powder bed responds to the hydrodynamic forces imparted by the impacting droplet, the particle motion is inconsistent with experimental time-resolved observations of the process [13]. Specifically, the ballistic effects, such as particle ejection and bed deformation, were drastically subdued, even in simulations using a droplet velocity ∼ 5× that of typical jetting conditions. This behavior could be caused by excessive damping in the inter-particle contact force computations within their SPH framework. Moreover, the wetted particles did not appear to be significantly influenced by the strong capillary forces exerted by the binder as no primitive agglomeration occurred. The authors mention that the objective of these simulations was to demonstrate their codebase’s broad capabilities and that some unrealistic process parameters were used to improve computational efficiency and stability, which could explain the deviations from experimental observations.

In the present paper, we develop a novel 3D CFD-DEM numerical framework for simulating fully-resolved IFPI during binder jetting with realistic material properties and process parameters. The CFD module is based on the VOF method for capturing binder–air interfaces. Surface tension effects are realized through the continuum surface force (CSF) method with height function calculations of interface curvature. Central to our fluid solver is a proprietary block-structured AMR library with hierarchical octree grid nesting to focus enhanced grid resolution near fluid–fluid interfaces. The GPU-accelerated DEM module considers six degrees of freedom particle motion and includes models based on Hertz-Mindlin contact, van der Waals cohesion, and viscoelastic rolling resistance. The CFD and DEM modules are coupled to achieve fully-resolved IFPI using an IB approach in which Lagrangian solid particles are mapped to the underlying Eulerian fluid mesh through a solid volume fraction field. An improved VOF-IB extension algorithm is introduced to enforce the contact angle at three-phase intersections. This provides robust capillary flow behavior and accurate computations of the fluid-induced forces and torques acting on individual wetted particles in densely packed powder beds.

We deploy our integrated codebase for direct numerical simulations of single-drop primitive formation with powder beds whose particle size distributions are generated from corresponding laboratory samples. These simulations use jetting parameters similar to those employed in current BJ3DP machines, fluid properties that match commonly used aqueous polymeric binders, and powder properties specific to nickel alloy feedstocks. The cohesion behavior of the DEM powder is calibrated based on the angle of repose of the laboratory powder systems. The resulting primitive granules are compared with those obtained from one-to-one experiments conducted using a dedicated in-house test apparatus. Finally, we demonstrate how the proposed framework can simulate more complex and realistic printing operations involving multi-drop primitive lines.

Section snippets

Mathematical description of interfacial fluid–particle interaction

This section briefly describes the governing equations of fluid and particle dynamics underlying the CFD and DEM solvers. Our unified framework follows an Eulerian–Lagrangian approach, wherein the Navier–Stokes equations of incompressible flow are discretized on an Eulerian grid to describe the motion of the binder liquid and surrounding gas, and the Newton–Euler equations account for the positions and orientations of the Lagrangian powder particles. The mathematical foundation for

CFD solver for incompressible flow with multifluid interfaces

This section details the numerical methodology used in our CFD module to solve the Navier–Stokes equations of incompressible flow. First, we introduce the VOF method for capturing the interfaces between the binder and air phases. This approach allows us to solve the fluid dynamics equations considering only a single continuum field with spatial and temporal variations in fluid properties. Next, we describe the time integration procedure using a fractional-step projection algorithm for

DEM solver for solid particle dynamics

This section covers the numerical procedure for tracking the motion of individual powder particles with DEM. The Newton–Euler equations (Eqs. (10), (11)) are ordinary differential equations (ODEs) for which many established numerical integrators are available. In general, the most challenging aspects of DEM involve processing particle collisions in a computationally efficient manner and dealing with small time step constraints that result from stiff materials, such as metallic AM powders. The

Unified CFD-DEM solver

The preceding sections have introduced the CFD and DEM solution algorithms separately. Here, we discuss the integrated CFD-DEM solution algorithm and related details.

Binder jet process modeling and validation experiments

In this section, we deploy our CFD-DEM framework to simulate the IFPI occurring during the binder droplet deposition stage of the BJ3DP process. The first simulations attempt to reproduce experimental single-drop primitive granules extracted from four nickel alloy powder samples with varying particle size distributions. The experiments are conducted with a dedicated in-house test apparatus that allows for the precision deposition of individual binder microdroplets into a powder bed sample. The

Conclusions

This paper introduces a coupled CFD-DEM framework capable of fully-resolved simulation of the interfacial fluid–particle interaction occurring in the binder jet 3D printing process. The interfacial flow of binder and surrounding air is captured with the VOF method and surface tension effects are incorporated using the CSF technique augmented by height function curvature calculations. Block-structured AMR is employed to provide localized grid refinement around the evolving liquid–gas interface.

CRediT authorship contribution statement

Joshua J. Wagner: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing. C. Fred Higgs III: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing – original draft, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by a NASA Space Technology Research Fellowship, United States of America, Grant No. 80NSSC19K1171. Partial support was also provided through an AIAA Foundation Orville, USA and Wilbur Wright Graduate Award, USA . The authors would like to gratefully acknowledge Dr. Craig Smith of NASA Glenn Research Center for the valuable input he provided on this project.

References (155)

The impacts of profile concavity on turbidite deposits: Insights from the submarine canyons on global continental margins

The impacts of profile concavity on turbidite deposits: Insights from the submarine canyons on global continental margins

프로필 오목부가 탁도 퇴적물에 미치는 영향: 전 세계 대륙 경계에 대한 해저 협곡의 통찰력

Kaiqi Yu a, Elda Miramontes bc, Matthieu J.B. Cartigny d, Yuping Yang a, Jingping Xu a
aDepartment of Ocean Science and Engineering, Southern University of Science and Technology, 1088 Xueyuan Rd., Shenzhen 518055, Guangdong, China
bMARUM-Center for Marine Environmental Sciences, University of Bremen, Bremen, Germanyc
Faculty of Geosciences, University of Bremen, Bremen, Germany
dDepartment of Geography, Durham University, South Road, Durham DH1 3LE, UK

Received 10 August 2023, Revised 13 March 2024, Accepted 13 March 2024, Available online 17 March 2024, Version of Record 20 March 2024.

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Highlights

  • •The impact of submarine canyon concavity on turbidite deposition was assessed.
  • •Distribution of turbidite deposits varies with changes in canyon concavity.
  • •Three distinct deposition patterns were identified.
  • •The recognized deposition patterns align well with the observed turbidite deposits.

Abstract

Submarine canyons are primary conduits for turbidity currents transporting terrestrial sediments, nutrients, pollutants and organic carbon to the deep sea. The concavity in the longitudinal profile of these canyons (i.e. the downstream flattening rate along the profiles) influences the transport processes and results in variations in turbidite thickness, impacting the transfer and burial of particles. To better understand the controlling mechanisms of canyon concavity on the distribution of turbidite deposits, here we investigate the variation in sediment accumulation as a function of canyon concavity of 20 different modern submarine canyons, distributed on global continental margins. In order to effectively assess the isolated impact of the concavity of 20 different canyons, a series of two-dimensional, depth-resolved numerical simulations are conducted. Simulation results show that the highly concave profile (e.g. Surveyor and Horizon) tends to concentrate the turbidite deposits mainly at the slope break, while nearly straight profiles (e.g. Amazon and Congo) result in deposition focused at the canyon head. Moderately concave profiles with a smoother canyon floor (e.g. Norfolk-Washington and Mukluk) effectively facilitate the downstream transport of suspended sediments in turbidity currents. Furthermore, smooth and steep upper reaches of canyons commonly contribute to sediment bypass (i.e. Mukluk and Chirikof), while low slope angles lead to deposition at upper reaches (i.e. Bounty and Valencia). At lower reaches, the distribution of turbidite deposits is consistent with the occurrence of hydraulic jumps. Under the influence of different canyon concavities, three types of deposition patterns are inferred in this study, and verified by comparison with observed turbidite deposits on the modern or paleo-canyon floor. This study demonstrates a potential difference in sediment transport efficiency of submarine canyons with different concavities, which has potential consequences for sediment and organic carbon transport through submarine canyons.

Introduction

Submarine canyons are pivotal links in source-to-sink systems on continental margins (Sømme et al., 2009; Nyberg et al., 2018; Pope et al., 2022a, Pope et al., 2022b) that provide efficient pathways for moving prodigious volumes of terrestrial materials to the abyssal basin (Spychala et al., 2020; Heijnen et al., 2022). When turbidity currents, the main force that transports the above mentioned sediments (Xu et al., 2004; Xu, 2010; Talling et al., 2013; Stevenson et al., 2015), slow down after entering a flatter and/or wider stretch of the canyon downstream, the laden sediments settle, often rapidly, to form a deposit called turbidite that is known for organic carbon burial, hydrocarbon reserves and the accumulation of microplastics (Galy et al., 2007; Pohl et al., 2020a; Pope et al., 2022b; Pierdomenico et al., 2023). A set of flume experiments by Pohl et al. (2020b) revealed that the variation of bed slope plays a dominant role in controlling the sizes and locations of the deposit: a) a more gently dipping upper slope leads to upstream migration of upslope pinch-out; b) the increase of lower slope results in a decrease of the deposit thickness (Fig. 1a).

From upper continental slopes to deepwater basins, turbidity currents are commonly confined by submarine canyons that facilitate the longer distance transport of sediments (Eggenhuisen et al., 2022; Pope et al., 2022a; Wahab et al., 2022, Li et al., 2023a). The concavity, defined here as the downstream flattening rate of profiles (Covault et al., 2011; Chen et al., 2019; Seybold et al., 2021; Soutter et al., 2021a), of the longitudinal bed profile of the submarine canyons is therefore a key factor that determines hydrodynamic processes of turbidity currents, including the accumulation of sediments along the canyon thalweg (Covault et al., 2014; de Leeuw et al., 2016; Heerema et al., 2022; Heijnen et al., 2022). Due to the comprehensive impacts of sediment supply, grain size, climate change, regional tectonics, associated river and self-incision, the concavity of submarine canyons on global continental margins varies greatly (Parker et al., 1986; Harris and Whiteway, 2011; Casalbore et al., 2018; Nyberg et al., 2018; Soutter et al., 2021a, Li et al., 2023b), which is much more complex than the two constant slope setup of Pohl et al. (2020b)’s flume experiment (Fig. 1a). This raises the question of how the more complex concavity influences the dynamics of turbidity currents and the resultant distribution of turbidite deposits. For instance, the longitudinal profile concavity can also be increased by steepening the upper slope and/or gentling the lower slope of canyons (Fig. 1b). Parameters, known as significant factors influencing flow dynamics, include dip angle (Pohl et al., 2019), bed roughness (Baghalian and Ghodsian, 2020), obstacle presence (Howlett et al., 2019), and confinement conditions (Soutter et al., 2021b). However, the role of channel concavity in determining the downstream evolution of flow dynamics remains poorly understood (Covault et al., 2011; Georgiopoulou and Cartwright, 2013), and it is still unclear whether changes in concavity can result in different locations of pinch-out points and variations in turbidite deposit thicknesses (Pohl et al., 2020b).

In this study, we hypothesize that a more concave profile resulting from a steeper upper slope and a gentler lower slope may lead to a downstream migration of the upslope pinch-out and an increase of deposit thickness (Fig. 1b). This hypothesis is tested in 20 modern submarine canyons (shown in Fig. 2) whose longitudinal profiles are extracted from the GEBCO_2022 grid. Due to the lack of data describing the turbidite thickness trends in these canyons, we used a numerical model (FLOW-3D® software) to simulate the depositional process. The simulation results allow us to address at least two questions: (1) How does the concavity affect the distribution and thickness of turbidite deposits along the canyon thalwegs? (2) What is the impact of canyon concavity on the dynamics of the turbidity currents? Such answers on a global scale are undoubtedly helpful in understanding not only the sediment transport processes but also the efficient transfer and burial of organic carbon along global continental margins.

Section snippets

Submarine canyons used in this study

The longitudinal profiles of 20 modern submarine canyons are obtained using Global Mapper® from a public domain database GEBCO_2022 (doi:https://doi.org/10.5285/e0f0bb80-ab44-2739-e053-6c86abc0289c). The GEBCO_2022 grid provides elevation data, in meters, on a 15 arc-second interval grid. The 20 selected submarine canyons, which span the typical distance covered by turbidity currents, have been chosen from a diverse range of submarine canyon and channel systems that extend at least 250 km

Concavity of longitudinal canyon profiles

The NCI and α values of all 20 canyon profiles utilized in this study are plotted in Fig. 4, indicating the majority of these submarine canyons typically exhibit a concave profile, characterized by a negative NCI, except for the Amazon. In most of the profiles, the NCI is lower than −0.08, with the most concave point (indicated by the minimum ratio α) located closer to the canyon head than to the profile end, and their upper reaches are steeper than lower reaches, typically observed as the

Validation of the hypothesis

As previously mentioned in this paper, one of the primary objectives of this study is to evaluate the hypothesis inferred from the flume tank experiment of Pohl et al. (2020b): whether a more concave canyon profile can exert a comparable influence on turbidite deposits as the steepness of the lower and upper slopes in a slope-break system (Fig. 1). Shown as the modeling results, the deposition pattern of this study is more ‘irregular’ compared with the flume tank experiment (Pohl et al., 2020b

Conclusion

Based on global bathymetry, this study simulates the depositional behavior of turbidity currents flowing through the 20 different submarine canyons on the margins of open ocean and marginal sea. Influenced by the different concavities, the resulted deposition patterns are characterized by a variable distribution of turbidite deposits.

  • 1)The simulation results demonstrate that the accumulation of turbidite deposits is primarily observed in downstream regions near the slope break for highly concave

CRediT authorship contribution statement

Kaiqi Yu: Writing – review & editing, Writing – original draft, Validation, Software, Methodology, Investigation, Conceptualization. Elda Miramontes: Writing – review & editing, Supervision, Conceptualization. Matthieu J.B. Cartigny: Writing – review & editing, Supervision. Yuping Yang: Software, Methodology. Jingping Xu: Writing – review & editing, Supervision, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study is supported by the Shenzhen Natural Science Foundation (JCYJ20210324105211031). Matthieu J. B. Cartigny was supported by Royal Society Research Fellowship (DHF/R1/180166). We thank the Chief Editor Zhongyuan Chen, the associate editor and two reviewers for their constructive comments that helped us improve our manuscript.

References (70)

There are more references available in the full text version of this article.

Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours correspond to the horizontal component of the flow velocity (u), expressed in m/s).

Numerical investigation of dam break flow over erodible beds with diverse substrate level variations

다양한 기질 수준 변화를 갖는 침식성 층 위의 댐 파손 흐름에 대한 수치 조사

Alireza Khoshkonesh1, Blaise Nsom2, Saeid Okhravi3*, Fariba Ahmadi Dehrashid4, Payam Heidarian5,
Silvia DiFrancesco6
1 Department of Geography, School of Social Sciences, History, and Philosophy, Birkbeck University of London, London, UK.
2 Université de Bretagne Occidentale. IRDL/UBO UMR CNRS 6027. Rue de Kergoat, 29285 Brest, France.
3 Institute of Hydrology, Slovak Academy of Sciences, Dúbravská cesta 9, 84104, Bratislava, Slovak Republic.
4Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, 65178-38695, Hamedan, Iran.
5 Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, 25123 Brescia, Italy.
6Niccol`o Cusano University, via Don C. Gnocchi 3, 00166 Rome, Italy. * Corresponding author. Tel.: +421-944624921. E-mail: saeid.okhravi@savba.sk

Abstract

This study aimed to comprehensively investigate the influence of substrate level difference and material composition on dam break wave evolution over two different erodible beds. Utilizing the Volume of Fluid (VOF) method, we tracked free surface advection and reproduced wave evolution using experimental data from the literature. For model validation, a comprehensive sensitivity analysis encompassed mesh resolution, turbulence simulation methods, and bed load transport equations. The implementation of Large Eddy Simulation (LES), non-equilibrium sediment flux, and van Rijn’s (1984) bed load formula yielded higher accuracy compared to alternative approaches. The findings emphasize the significant effect of substrate level difference and material composition on dam break morphodynamic characteristics. Decreasing substrate level disparity led to reduced flow velocity, wavefront progression, free surface height, substrate erosion, and other pertinent parameters. Initial air entrapment proved substantial at the wavefront, illustrating pronounced air-water interaction along the bottom interface. The Shields parameter experienced a one-third reduction as substrate level difference quadrupled, with the highest near-bed concentration observed at the wavefront. This research provides fresh insights into the complex interplay of factors governing dam break wave propagation and morphological changes, advancing our comprehension of this intricate phenomenon.

이 연구는 두 개의 서로 다른 침식층에 대한 댐 파괴파 진화에 대한 기질 수준 차이와 재료 구성의 영향을 종합적으로 조사하는 것을 목표로 했습니다. VOF(유체량) 방법을 활용하여 자유 표면 이류를 추적하고 문헌의 실험 데이터를 사용하여 파동 진화를 재현했습니다.

모델 검증을 위해 메쉬 해상도, 난류 시뮬레이션 방법 및 침대 하중 전달 방정식을 포함하는 포괄적인 민감도 분석을 수행했습니다. LES(Large Eddy Simulation), 비평형 퇴적물 플럭스 및 van Rijn(1984)의 하상 부하 공식의 구현은 대체 접근 방식에 비해 더 높은 정확도를 산출했습니다.

연구 결과는 댐 붕괴 형태역학적 특성에 대한 기질 수준 차이와 재료 구성의 중요한 영향을 강조합니다. 기판 수준 차이가 감소하면 유속, 파면 진행, 자유 표면 높이, 기판 침식 및 기타 관련 매개변수가 감소했습니다.

초기 공기 포집은 파면에서 상당한 것으로 입증되었으며, 이는 바닥 경계면을 따라 뚜렷한 공기-물 상호 작용을 보여줍니다. 기판 레벨 차이가 4배로 증가함에 따라 Shields 매개변수는 1/3로 감소했으며, 파면에서 가장 높은 베드 근처 농도가 관찰되었습니다.

이 연구는 댐 파괴파 전파와 형태학적 변화를 지배하는 요인들의 복잡한 상호 작용에 대한 새로운 통찰력을 제공하여 이 복잡한 현상에 대한 이해를 향상시킵니다.

Keywords

Dam break; Substrate level difference; Erodible bed; Sediment transport; Computational fluid dynamics CFD.

Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours
correspond to the horizontal component of the flow velocity (u), expressed in m/s).
Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours correspond to the horizontal component of the flow velocity (u), expressed in m/s).

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Figure 1. Experimental setup and materials. (a) Schematic of the DED process, where three types of base materials were adopted—B1 (IN718), B2 (IN625), and B3 (SS316L), and two types of powder materials were adopted—P1 (IN718) and P2 (SS316L). (b) In situ high-speed imaging of powder flow and the SEM images of IN718 and SS316L powder particle. (c) Powder size statistics, and (d) element composition of powder IN718 (P1) and SS316L (P2).

Printability disparities in heterogeneous materialcombinations via laser directed energy deposition:a comparative stud

Jinsheng Ning1,6, Lida Zhu1,6,∗, Shuhao Wang2, Zhichao Yang1, Peihua Xu1,Pengsheng Xue3, Hao Lu1, Miao Yu1, Yunhang Zhao1, Jiachen Li4, Susmita Bose5 and Amit Bandyopadhyay5,∗

Abstract

적층 제조는 바이메탈 및 다중 재료 구조의 제작 가능성을 제공합니다. 그러나 재료 호환성과 접착성은 부품의 성형성과 최종 품질에 직접적인 영향을 미칩니다. 적합한 프로세스를 기반으로 다양한 재료 조합의 기본 인쇄 가능성을 이해하는 것이 중요합니다.

여기에서는 두 가지 일반적이고 매력적인 재료 조합(니켈 및 철 기반 합금)의 인쇄 적성 차이가 레이저 지향 에너지 증착(DED)을 통해 거시적 및 미시적 수준에서 평가됩니다.

증착 프로세스는 현장 고속 이미징을 사용하여 캡처되었으며, 용융 풀 특징 및 트랙 형태의 차이점은 특정 프로세스 창 내에서 정량적으로 조사되었습니다. 더욱이, 다양한 재료 쌍으로 처리된 트랙과 블록의 미세 구조 다양성이 비교적 정교해졌고, 유익한 다중 물리 모델링을 통해 이종 재료 쌍 사이에 제시된 기계적 특성(미세 경도)의 불균일성이 합리화되었습니다.

재료 쌍의 서로 다른 열물리적 특성에 의해 유발된 용융 흐름의 차이와 응고 중 결과적인 요소 혼합 및 국부적인 재합금은 재료 조합 간의 인쇄 적성에 나타난 차이점을 지배합니다.

이 작업은 서로 다른 재료의 증착에서 현상학적 차이에 대한 심층적인 이해를 제공하고 바이메탈 부품의 보다 안정적인 DED 성형을 안내하는 것을 목표로 합니다.

Additive manufacturing provides achievability for the fabrication of bimetallic and
multi-material structures; however, the material compatibility and bondability directly affect the
parts’ formability and final quality. It is essential to understand the underlying printability of
different material combinations based on an adapted process. Here, the printability disparities of
two common and attractive material combinations (nickel- and iron-based alloys) are evaluated
at the macro and micro levels via laser directed energy deposition (DED). The deposition
processes were captured using in situ high-speed imaging, and the dissimilarities in melt pool
features and track morphology were quantitatively investigated within specific process
windows. Moreover, the microstructure diversity of the tracks and blocks processed with varied
material pairs was comparatively elaborated and, complemented with the informative
multi-physics modeling, the presented non-uniformity in mechanical properties (microhardness)
among the heterogeneous material pairs was rationalized. The differences in melt flow induced
by the unlike thermophysical properties of the material pairs and the resulting element
intermixing and localized re-alloying during solidification dominate the presented dissimilarity
in printability among the material combinations. This work provides an in-depth understanding
of the phenomenological differences in the deposition of dissimilar materials and aims to guide
more reliable DED forming of bimetallic parts.

Figure 1. Experimental setup and materials. (a) Schematic of the DED process, where three types of base materials were adopted—B1
(IN718), B2 (IN625), and B3 (SS316L), and two types of powder materials were adopted—P1 (IN718) and P2 (SS316L). (b) In situ
high-speed imaging of powder flow and the SEM images of IN718 and SS316L powder particle. (c) Powder size statistics, and (d) element
composition of powder IN718 (P1) and SS316L (P2).
Figure 1. Experimental setup and materials. (a) Schematic of the DED process, where three types of base materials were adopted—B1 (IN718), B2 (IN625), and B3 (SS316L), and two types of powder materials were adopted—P1 (IN718) and P2 (SS316L). (b) In situ high-speed imaging of powder flow and the SEM images of IN718 and SS316L powder particle. (c) Powder size statistics, and (d) element composition of powder IN718 (P1) and SS316L (P2).
Figure 2. Deposition process and the track morphology. (a)–(c) Display the in situ captured tableaux of melt propagation and some physical
features during depositing for P1B1, P1B2, and P1B3, respectively. (d) The profiles of the melt pool at a frame of (t0 + 1) ms, and the flow
streamlines in the molten pool of each case. (e) The outer surface of the formed tracks, in which the colored arrows mark the scanning
direction. (f) Cross-section of the tracks. The parameter set used for in situ imaging was P-1000 W, S-600 mm·min–1, F-18 g·min–1. All the
scale bars are 2 mm.
Figure 2. Deposition process and the track morphology. (a)–(c) Display the in situ captured tableaux of melt propagation and some physical features during depositing for P1B1, P1B2, and P1B3, respectively. (d) The profiles of the melt pool at a frame of (t0 + 1) ms, and the flow streamlines in the molten pool of each case. (e) The outer surface of the formed tracks, in which the colored arrows mark the scanning direction. (f) Cross-section of the tracks. The parameter set used for in situ imaging was P-1000 W, S-600 mm·min–1, F-18 g·min–1. All the scale bars are 2 mm.

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Fig. 3. (a–c) Snapshots of the CtFD simulation of laser-beam irradiation: (a) Top, (b) longitudinal vertical cross-sectional, and (c) transversal vertical cross-sectional views. (d) z-position of the solid/liquid interface during melting and solidification.

Solute segregation in a rapidly solidified Hastelloy-X Ni-based superalloy during laser powder bed fusion investigated by phase-field simulations and computational thermal-fluid dynamics

Masayuki Okugawa ab, Kenji Saito a, Haruki Yoshima a, Katsuhiko Sawaizumi a, Sukeharu Nomoto c, Makoto Watanabe c, Takayoshi Nakano ab, Yuichiro Koizumi abShow moreAdd to MendeleyShareCite

https://doi.org/10.1016/j.addma.2024.104079

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Abstract

Solute segregation significantly affects material properties and is a critical issue in the laser powder-bed fusion (LPBF) additive manufacturing (AM) of Ni-based superalloys. To the best of our knowledge, this is the first study to demonstrate a computational thermal-fluid dynamics (CtFD) simulation coupled multi-phase-field (MPF) simulation with a multicomponent-composition model of Ni-based superalloy to predict solute segregation under solidification conditions in LPBF. The MPF simulation of the Hastelloy-X superalloy reproduced the experimentally observed submicron-sized cell structure. Significant solute segregations were formed within interdendritic regions during solidification at high cooling rates of up to 10K s-1, a characteristic feature of LPBF. Solute segregation caused a decrease in the solidus temperature (TS), with a reduction of up to 30.4 K, which increases the risk of liquation cracks during LPBF. In addition, the segregation triggers the formation of carbide phases, which increases the susceptibility to ductility dip cracking. Conversely, we found that the decrease in TS is suppressed at the melt-pool boundary regions, where re-remelting occurs during the stacking of the layer above. Controlling the re-remelting behavior is deemed to be crucial for designing crack-free alloys. Thus, we demonstrated that solute segregation at the various interfacial regions of Ni-based multicomponent alloys can be predicted by the conventional MPF simulation. The design of crack-free Ni-based superalloys can be expedited by MPF simulations of a broad range of element combinations and their concentrations in multicomponent Ni-based superalloys.

Graphical abstract

Keywords

Laser powder-bed fusion, Hastelloy-X Nickel-based superalloy, solute element segregation, computational thermal-fluid dynamics simulation, phase-field method

1. Introduction

Additive manufacturing (AM) technologies have attracted considerable attention as they allow us to easily build three-dimensional (3D) parts with complex geometries. Among the wide range of available AM techniques, laser powder-bed fusion (LPBF) has emerged as a preferred technique for metal AM [1][2][3][4][5]. In LPBF, metal products are built layer-by-layer by scanning laser, which fuse metal powder particles into bulk solids.

Significant attempts have been made to integrate LPBF techniques within the aerospace industry, with a particular focus on weldable Ni-based superalloys, such as IN718 [6][7][8], IN625 [9][10], and Hastelloy-X (HX) [11][12][13][14]. Non-weldable alloys, such as IN738LC [15][16] and CMSX-4 [1][17] are also suitable for their sufficient creep resistance under higher temperature conditions. However, non-weldable alloys are difficult to build using LPBF because of their susceptibility to cracking during the process. In general, a macro solute-segregation during solidification is suppressed by the rapid cooling conditions (up to 108 K s-1) unique to the LPBF process [18]. However, the solute segregation still occurs in the interdendritic regions that are smaller than the micrometer scale [5][19][20][21]; these regions are suggested to be related to the hot cracks in LPBF-fabricated parts. Therefore, an understanding of solute segregation is essential for the fabrication of reliable LPBF-fabricated parts while avoiding cracks.

The multiphase-field (MPF) method has gained popularity for modeling the microstructure evolution and solute segregation under rapid cooling conditions [5][20][21][22][23][24][25][26][27][28]. Moreover, quantifiable predictions have been achieved by combining the MPF method with temperature distribution analysis methods such as the finite-element method (FEM) [20] and computational thermal-fluid dynamics (CtFD) simulations [28]. These aforementioned studies have used binary-approximated multicomponent systems, such as Ni–Nb binary alloys, to simulate IN718 alloys. While MPF simulations using binary alloy systems can effectively reproduce microstructure formations and segregation behaviors, the binary approximation might be affected by the chemical interactions between the removed solute elements in the target multicomponent alloy. The limit of absolute stability predicted by the Mullins-Sekerka theory [29] is also crucial because the limit velocity is close to the solidification rate in the LPBF process and is different in multicomponent and binary-approximated systems. The difference between the solidus and liquidus temperatures, ΔT0, directly determines the absolute stability according to the Mullins-Sekerka theory. For example, the ΔT0 values of IN718 and its binary-approximated Ni–5 wt.%Nb alloy are 134 K [28] and 71 K [30], respectively. The solidification rate compared to the limit of absolute stability, i.e., the relative non-equilibrium of solidification, changes by simplification of the system. It is therefore important to use the composition of the actual multicomponent system in such simulations. However, to the best of our knowledge, there is no MPF simulation using a multicomponent model coupled with a temperature analysis simulation to predict solute segregation in a Ni-based superalloy.

In this study, we demonstrate that the conventional MPF model can reproduce experimentally observed dendritic structures by performing a phase-field simulation using the temperature distribution obtained by a CtFD simulation of a multicomponent Ni-based alloy (conventional solid-solution hardening-type HX). The MPF simulation revealed that the segregation behavior of solute elements largely depends on the regions of the melt pool, such as the cell boundary, the interior of the melt-pool boundary, and heat-affected regions. The sensitivities of the various interfaces to liquation and solidification cracks are compared based on the predicted concentration distributions. Moreover, the feasibility of using the conventional MPF model for LPBF is discussed in terms of the absolute stability limit.

2. Methods

2.1. Laser-beam irradiation experiments

Rolled and recrystallized HX ingots with dimensions of 20 × 50 × 10 mm were used as the specimens for laser-irradiation experiments. The specimens were irradiated with a laser beam scanned along straight lines of 10 mm in length using a laser AM machine (EOS 290 M, EOS) equipped with a 400 W Yb-fiber laser. Irradiation was performed with a beam power of P = 300 W and a scanning speed of V = 600 mm s-1, which are the conditions generally used in the LPBF fabrication of Ni-based superalloy [8]. The corresponding line energy was 0.5 J mm-1. The samples were cut perpendicular to the beam-scanning direction for cross-sectional observation using a field-emission scanning electron microscope (FE-SEM, JEOL JSM 6500). Crystal orientation analysis was performed by electron backscatter diffraction (EBSD). The sizes of each crystal grain and their aspect ratios were evaluated by analyzing the EBSD data.

2.2. CtFD simulation

CtFD simulations of the laser-beam irradiation of HX were performed using a 3D thermo-fluid analysis software (Flow Science FLOW-3D® with Flow-3D Weld module). A Gaussian heat source model was used, in which the irradiation intensity distribution of the beam is regarded as a symmetrical Gaussian distribution over the entire beam. The distribution of the beam irradiation intensity is expressed by the following equation.(1)q̇=2ηPπR2exp−2r2R2.

Here, P is the power, R is the effective beam radius, r is the actual beam radius, and η is the beam absorption rate of the substrate. To improve the accuracy of the model, η was calculated by assuming multiple reflections using the Fresnel equation:(2)�=1−121+1−�cos�21+1+�cos�2+�2−2�cos�+2cos2��2+2�cos�+2cos2�.

ε is the Fresnel coefficient and θ is the incident angle of the laser. A local laser melt causes the vaporization of the material and results in a high vapor pressure. This vapor pressure acts as a recoil pressure on the surface, pushing the weld pool down. The recoil pressure is reproduced using the following equation.(3)precoil=Ap0exp∆HLVRTV1−TVT.

Here, p0 is the atmospheric pressure, ∆HLV is the latent heat of vaporization, R is the gas constant, and TV is the boiling point at the saturated vapor pressure. A is a ratio coefficient that is generally assumed to be 0.54, indicating that the recoil pressure due to evaporation is 54% of the vapor pressure at equilibrium on the liquid surface.

Table 1 shows the parameters used in the simulations. Most parameters were evaluated using an alloy physical property calculation software (Sente software JMatPro v11). The values in a previously published study [31] were used for the emissivity and the Stefan–Boltzmann constant, and the values for pure Ni [32] were used for the heat of vaporization and vaporization temperatures. The Fresnel coefficient, which determines the beam absorption efficiency, was used as a fitting parameter to reproduce the morphology of the experimentally observed melt region, and a Fresnel coefficient of 0.12 was used in this study.

Table 1. Parameters used in the CtFD simulations.

ParameterSymbolValueReference
Density at 298.15 Kρ8.24 g cm-3[]
Liquidus temperatureTL1628.15 K[]
Solidus temperatureTS1533.15 K[]
Viscosity at TLη6.8 g m-1 s-1[]
Specific heat at 298.15 KCP0.439 J g-1 K-1[]
Thermal conductivity at 298.15 Kλ10.3 W m-1 K-1[]
Surface tension at TLγL1.85 J m-2[]
Temperature coefficient of surface tensiondγL/dT–2.5 × 10−4 J m-2 K-1[]
EmissivityΕ0.27[31]
Stefan–Boltzmann constantσ5.67 × 10-8 W m-2 K-4[31]
Heat of fusionΔHSL2.76 × 102 J g-1[32]
Heat of vaporizationΔHLV4.29 × 10J g-1[32]
Vaporization temperatureTV3110 K[32]

Calculated using JMatPro v11.

The dimensions of the computational domain of the numerical model were 4.0 mm in the beam-scanning direction, 0.4 mm in width, and 0.3 mm in height. A uniform mesh size of 10 μm was applied throughout the computational domain. The boundary condition of continuity was applied to all boundaries except for the top surface. The temperature was initially set to 300 K. P and V were set to their experimental values, i.e., 300 W and 600 mm s-1, respectively. Solidification conditions based on the temperature gradient, G, the solidification rate, R, and the cooling rate were evaluated, and the obtained temperature distribution was used in the MPF simulations.

2.3. MPF simulation

Two-dimensional MPF simulations weakly coupled with the CtFD simulation were performed using the Microstructure Evolution Simulation Software (MICRESS) [33][34][35][36][37] with the TQ-Interface for Thermo-Calc [38]. A simplified HX alloy composition of Ni-21.4Cr-17.6Fe-0.46Mn-8.80Mo-0.39Si-0.50W-1.10Co-0.08 C (mass %) was used in this study. The Gibbs free energy and diffusion coefficient of the system were calculated using the TCNI9 thermodynamic database [39] and the MOBNi5 mobility database [40]. Τhe equilibrium phase diagram calculated using Thermo-Calc indicates that the face-centered cubic (FCC) and σ phases appear as the equilibrium solid phases [19]. However, according to the time-temperature-transformation (TTT) diagram [41], the phases are formed after the sample is maintained for tens of hours in a temperature range of 1073 to 1173 K. Therefore, only the liquid and FCC phases were assumed to appear in the MPF simulations. The simulation domain was 5 × 100 μm, and the grid size Δx and interface width were set to 0.025 and 0.1 µm, respectively. The interfacial mobility between the solid and liquid phases was set to 1.0 × 10-8 m4 J-1 s-1. Initially, one crystalline nucleus with a [100] crystal orientation was placed at the left bottom of the simulation domain, with the liquid phase occupying the remainder of the domain. The model was solidified under the temperature field distribution obtained by the CtFD simulation. The concentration distribution and crystal orientation of the solidified model were examined. The primary dendrite arm space (PDAS) was compared to the experimental PDAS measured by the cross-sectional SEM observation.

In an actual LPBF process, solidified layers are remelted and resolidified during the stacking of the one layer above, thereby greatly affecting solute element distributions in those regions. Therefore, remelting and resolidification simulations were performed to examine the effect of remelting on solute segregation. The solidified model was remelted and resolidified by applying a time-dependent temperature field shifted by 60 μm in the height direction, assuming reheating during the stacking of the upper layer (i.e., the upper 40 μm region of the simulation box was remelted and resolidified). The changes in the composition distribution and formed microstructure were investigated.

3. Results

3.1. Experimental observation of melt pool

Fig. 1 shows a cross-sectional optical microscopy image and corresponding inverse pole figure (IPF) orientation maps obtained from the laser-melted region of HX. The dashed line indicates the fusion line. A deep melted region was formed by keyhole-mode melting due to the vaporization of the metal and resultant recoil pressure. Epitaxial growth from the unmelted region was observed. Columnar crystal grains with an average diameter of 5.46 ± 0.32 μm and an aspect ratio of 3.61 ± 0.13 appeared at the melt regions (Figs. 1b–1d). In addition, crystal grains growing in the z direction could be observed in the lower center.

Fig. 1

Fig. 2a shows a cross-sectional backscattering electron image (BEI) obtained from the laser-melted region indicated by the black square in Fig. 1a. The bright particles with a diameter of approximately 2 μm observed outside the melt pool. It is well known that M6C, M23C6, σ, and μ precipitate phases are formed in Hastelloy-X [41]. These precipitates mainly consisted of Mo, Cr, Fe, and Ni; The μ and M6C phases are rich in Mo, while the σ and M23C6 phases are rich in Cr. The SEM energy dispersive X-ray spectroscopy analysis suggested that the bright particles are the stable precipitates as shown in Fig. S2 and Table S1. Conversely, there are no carbides in the melt pool. This suggests that the cooling rate is extremely high during LPBF, which prevents the formation of a stable carbide during solidification. Figs. 2b–2f show magnified BEI images at different height positions indicated in Fig. 2a. Bright regions are observed between the cells, which become fragmentary at the center of the melt pool, as indicated by the yellow arrow heads in Figs. 2e and 2f.

Fig. 2

3.2. CtFD simulation

Figs. 3a–3c show snapshots of the CtFD simulation of HX at 2.72 ms, with the temperature indicated in color. A melt pool with an elongated teardrop shape formed and keyhole-mode melting was observed at the front of the melt region. The cooling rate, temperature gradient (G), and solidification rate (R) were evaluated from the temporal change in the temperature distribution of the CtFD simulation results. The z-position of the solid/liquid interface during the melting and solidification processes is shown in Fig. 3d. The interface goes down rapidly during melting and then rises during solidification. The MPF simulation of the microstructure formation during solidification was performed using the temperature distribution. Moreover, the microstructure formation process during the fabrication of the upper layer was investigated by remelting and resolidifying the solidified layer using the same temperature distribution with a 60 μm upward shift, corresponding to the layer thickness commonly used in the LPBF of Ni-based superalloys.

Fig. 3

Figs. 4a–4c show the changes in the cooling rate, temperature gradient, and solidification rate in the center line of the melt pool parallel to the z direction. To output the solidification conditions at the solid/liquid interface in the melt pool, only the data of the mesh where the solid phase ratio was close to 0.5 were plotted. Solidification occurred where the cooling rate was in the range of 2.1 × 105–1.6 × 10K s-1G was in the range of 3.6 × 105–1.9 × 10K m-1, and R was in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The cooling rate was the highest near the fusion line and decreased as the interface approached the center of the melt region (Fig. 4a). G also exhibited the highest value in the regions near the fusion line and decreased throughout the solid/liquid interface toward the center of the melt pool (Fig. 4b). R had the lowest value near the fusion line and increased as the interface approached the center of the melt region (Fig. 4c).

Fig. 4

3.3. MPF simulations coupled with CtFD simulation

MPF simulations of solidification, remelting, and resolidification were performed using the temperature-time distribution obtained by the CtFD simulation. Fig. 5 shows the MPF solidified models colored by phase and Mo concentration. All the computational domains show the FCC phase after the solidification (Fig. 5a). Dendrites grew parallel to the heat flow direction, and solute segregations were observed in the interdendritic regions. At the bottom of the melt pool (Fig. 5d), planar interface growth occurred before the formation of primary dendrites. The bottom of the melt pool is the turning point of the solid/liquid interface from the downward motion in melting to the upward motion in solidification. Thus, the solidification rate at the boundary is zero, and is extremely low immediately above the molt-pool boundary. Here, the lower limit of the solidification rate (R) for dendritic growth can be represented by the constitutional supercooling criterion [29]Vcs = (G × DL) / ΔT, and planar interface growth occurs at R < VcsDL and ΔT denote the diffusion coefficient in the liquid and the equilibrium freezing range, respectively. The results suggest that planar interface growth occurs at the bottom of the melt pool, resulting in a dark region with a different solute element distribution. Some of the primary dendrites were diminished by competition with other dendrites. In addition, secondary dendrite arms could be seen in the upper regions (Fig. 5c), where solidification occurred at a lower cooling rate. The fragmentation of the solute segregation near the secondary dendrite arms is similar to that observed in the experimental melt pool shown in Figs. 2e and 2f, and the secondary dendrite arms are suggested to have appeared at the center of the melt region. Fig. 6 shows the PDASs measured from the MPF simulation models, compared to the experimental PDASs measured by the cross-sectional SEM observation of the laser-melted regions (Fig. 2). The PDAS obtained by the MPF simulation become larger as the solidification progress. Ghosh et al. [21] evident by the phase-field method that the PDAS decreases as the cooling rate increases under the rapid cooling conditions obtained by the finite element analysis. In this study, the cooling rate was decreased as the interface approached the center of the melt region (Fig. 4a), and the trends in PDAS changes with respect to cooling rate is same as the reported trend [21]. The simulated trends of the PDAS with the position in the melt pool agreed well with the experimental trends. However, all PDASs in the simulation were larger than those observed in the experiment at the same positions. Ode et al. [42] reported that PDAS differences between 2D and 3D MPF simulations can be represented by PDAS2D = 1.12 × PDAS3D owing to differences in the effects of the interfacial energy and diffusivity. We also performed 2D and 3D MPF simulations under the solidification conditions of G = 1.94 × 10K m-1 and R = 0.82 m s-1 (Fig. S1), and found that the PDAS from the 2D MPF simulation was 1.26 times larger than that from the 3D simulation. Therefore, the cell structure obtained by the CtFD simulation coupled with the 2D MPF simulation agreed well with the experimental results over the entire melt pool region considering the dimensional effects.

Fig. 5
Fig. 6

Fig. 7b1 and 7c1 show the concentration profiles of the solidified model along the growth direction indicated by dashed lines in Fig. 7a. The differences in concentrations from the alloy composition are also shown in Fig. 7b2 and 7c2. Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. The solute segregation behavior agrees with the experimentally observation [43] and the prediction by the Scheil-Gulliver simulation [19]. Segregation occurred to the highest degree in Mo, while the ratio of segregation to the alloy composition was remarkable in C. The concentration fluctuations correlated with the position in the melt pool and decreased at the center of the melt pool, which was suggested to correspond to the lower cooling rate in this region. Conversely, droplets that appeared between secondary dendrite arms in the upper regions of the simulation domain exhibited a locally high segregation of solute elements, with the same amount of segregation as that at the bottom of the melt pool.

Fig. 7

3.4. Remelting and resolidification simulation

The solidified model was subjected to remelting and resolidification conditions by shifting the temperature profile upward by 60 µm to reveal the effect of reheating on the solute segregation behavior. Figs. 8a and 8b shows the simulation domains of the HX model after resolidification, colored by phase and Mo concentration. The magnified MPF models during the resolidification of the regions indicated by rectangles in Figs. 8a and 8b are also shown as Figs. 8c and 8d. Dendrites grew from the bottom of the remelted region, with the segregation of solute elements occurring in the interdendritic regions. The entire domain become the FCC phase after the resolidification, as shown in Fig. 8a. The bottom of the remelted regions exhibited a different microstructure, and Mo was depressed at the remelted regions, rather than the interdendritic regions. The different solute segregation behavior [44] and the microstructure formation [45] at the melt pool boundary is also observed in LPBF manufactured 316 L stainless steel. We found that this microstructure was formed by further remelting during the resolidification process, which is shown in Fig. 9. Here, the solidified HX model was heated, and the interdendritic regions were preferentially melted while concentration fluctuations were maintained (Fig. 9a1 and 9a2). Subsequently, planer interface growth occurs near the melt pool boundary where the solidification rate is almost zero, and the dendrites outside of the boundary are grown epitaxially (Fig. 9b1 and 9b2). However, these remelted again because of the temperature rise (Fig. 9c1 and 9c2, and the temperature-time profile shown in Fig. 9e). The remelted regions then cooled and solidified with the abnormal solute segregations (Fig. 9d1 and 9d2). Then, dendrite grows from amplified fluctuations under the solidification rate larger than the criterion of constitutional supercooling (Fig. 9d1, 9d2, and Fig. 8d). It has been reported [46][47] that temperature rising owning to latent heat affects microstructure formation: phase-field simulations of a Ni–Al binary alloy suggest that the release of latent heat during solidification increases the average temperature of the system [46] and strongly influences the solidification conditions [47]. In this study, the release of latent heat during solidification is considered in CtFD simulations for calculating the temperature distribution, and the temperature increase is suggested to have also occurred due to the release of latent heat.

Fig. 8
Fig. 9

Fig. 10b1 and 10c1 show the solute element concentration line profiles of the resolidified model along the growth direction indicated by dashed lines in Fig. 10a. Fig. 10b2 and 10c2 show the corresponding differences in concentration from the alloy composition. The segregation behavior of solute elements at the interdendritic regions (Fig. 10b1 and 10b2) was the same as that in the solidified model (Figs. 7b1 and 7b2). Here, Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. However, the concentration fluctuations at the interdendritic regions were larger than those in the solidified model. Moreover, the segregation of the outside of the melt pool, i.e., the heat-affected zone, was remarkable throughout remelting and resolidification. Different segregation behaviors were observed in the re-remelted region: Mo, Si, Mn, and W were segregated, while Ni, Fe, and Co were depressed. These solute segregations caused by remelting are expected to heavily influence the crack behavior.

Fig. 10

4. Discussion

4.1. Effect of segregation of solute elements on liquation cracking susceptibility

Strong solute segregation was observed between the interdendritic regions of the solidified alloy (Fig. 7). In addition, the solute segregation behavior was significantly affected by remelting and resolidification and varied across the alloy. Solute segregation can be categorized by the regions shown in Fig. 11a1–11a4, namely the cell boundary (Fig. 11a1), interior of the melt-pool boundary (Fig. 11a2), re-remelted regions (Fig. 11a3), and heat-affected regions (Fig. 11a4). The concentration profiles of these regions are shown in Fig. 11b1–11b4. Solute segregation was the highest in the cell boundary region. The solute segregation in the heat-affected region was almost the same as that in the cell boundary region, but seemed to have been attenuated by reheating during remelting and resolidification. The interior of the melt-pool boundary region also had the same tendency for solute segregation. However, the amount of Cr segregation was smaller than that of Mo. A decrease in the Cr concentration was also mitigated, and the concentration remained the same as that in the alloy composition. Fig. 11c1–11c4 show the chemical potentials of the solute elements for the FCC phase at 1073 K calculated using the compositions of those interfacial regions. All the interfacial regions showed non-constant chemical potentials for each element along the perpendicular direction, but the fluctuations of the chemical potentials differed by the type of interfaces. In particular, the fluctuation of the chemical potential of C at the cell boundary region was the largest, suggesting it can be relaxed easily by heat treatment. On the other hand, the fluctuations of the other elements in all the regions were small. The solute segregations are most likely to remain after the heat treatment and are supposed to affect the cracking susceptibilities.

Fig. 11

The solidus temperatures TS, the difference between the liquidus and solidus temperatures (i.e., the brittle temperature range (BTR)), and the fractions of the equilibrium precipitate phases at 1073 K of the interfacial regions were calculated as the liquation, solidification, and ductility dip cracking susceptibilities, respectively. At the cell boundary (Fig. 12a1), interior of the melt-pool boundary (Fig. 12a1), and heat-affected regions (Fig. 12a1), the internal and interfacial regions exhibited higher and lower TS compared to that of the alloy composition, respectively. The lowest Ts was obtained with the composition at the cell boundary region, which is the largest solute-segregated region. It has been suggested that strong segregations of solute elements in LPBF lead to liquation cracks [16]. This study also supports this suggestion, and liquation cracks are more likely to occur at the interfacial regions indicated by predicting the solute segregation behavior using the MPF model. Additionally, the BTRs of the cell boundary, interior of the melt-pool boundary, and heat-affected regions were wider at the interdendritic regions, and solidification cracks were also likely to occur in these regions. Moreover, within the solute segregation regions, the fraction of the precipitate phases in these interfacial regions was larger than that calculated using the alloy composition (Fig. 12c1, 12c2, and 12c4). This indicates that ductility dip cracking is also likely to occur at the cell boundary, interior of the melt-pool boundary, and in heat-affected regions. Contrarily, we found that the re-remelted region exhibited a higher TS and smaller BTR even in the interfacial region (Fig. 12a3 and 12b3), where the solute segregation behavior was different from that of the other regions. In addition, the re-remelting region exhibited less precipitation compared with the other segregated regions (Fig. 12c3). The re-remelting caused by the latent heat can attenuate solute segregation, prevent Ts from decreasing, decrease the BTR, and decrease the amount of precipitate phases. Alloys with a large amount of latent heat are expected to increase the re-remelting region, thereby decreasing the susceptibility to liquation and ductility dip cracks due to solute element segregation. This can be a guide for designing alloys for the LPBF process. As mentioned in Section 3.4, the microstructure [45] and the solute segregation behavior [44] at the melt pool boundary of LPBF-manufactured 316 L stainless steel are observed, and they are different from that of the interdendritic regions. Experimental observations of the solute segregation behavior in the LPBF-fabricated Ni-based alloys are currently underway.

Fig. 12

4.2. Applicability of the conventional MPF simulation to microstructure formation under LPBF

As the solidification growth rate increases, segregation coefficients approach 1, and the fluctuation of the solid/liquid interface is suppressed by the interfacial tension. The interface growth occurs in a flat fashion instead of having a cellular morphology at a velocity above the absolute stability limit, Ras, predicted by the Mullins-Sekerka theory [29]Ras = (ΔT0 DL) / (k Γ) where ΔT0DLk, and Γ are the difference between the liquidus and solidus temperatures, equilibrium segregation coefficient, the diffusivity of liquid, and the Gibbs-Thomson coefficient, respectively.

The Ras of HX was calculated using the equation and the thermodynamic parameters obtained by the TCNI9 thermodynamic database [39]. The calculated Ras of HX was 3.9 m s-1 and is ten times larger than that of the Ni–Nb alloy (approximately 0.4 m s-1[20]. The HX alloy was solidified under R values in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The theoretically calculated criterion is larger than the evaluated R, and is in agreement with the experiment in which dendritic growth is observed in the melt pool (Fig. 5). In contrast, Karayagiz et al. [20] reported that the R of the Ni–Nb binary alloy under LPBF was as high as approximately 2 m s-1, and planar interface growth was observed to be predominant under the high-growth-rate conditions. These experimentally observed microstructures agree well with the prediction by the Mullins-Sekerka theory about the relationship between the morphology and solidification rates.

In this study, the solidification microstructure formed by the laser-beam irradiation of an HX multicomponent Ni-based superalloy was reproduced by a conventional MPF simulation, in which the system was assumed to be in a quasi-equilibrium condition. Boussinot et al. [24] also suggested that the conventional phase-field model can be applied to simulate the microstructure of an IN718 multicomponent Ni-based superalloy in LPBF. In contrast, Kagayaski et al. [20] suggested that the conventional MPF simulation cannot be applied to the solidification of the Ni-Nb binary alloy system and that the finite interface dissipation model proposed by Steinbach et al. [48][49] is necessary to simulate the high solidification rates observed in LPBF. The difference in the applicability of the conventional MPF method to HX and Ni–Nb binary alloys is presumed to arise from the differences in the non-equilibrium degree of these systems under the high solidification rates of LPBF. The results suggest that Ras can be used as a simple index to apply the conventional MPF model for solidification in LPBF. Solidification becomes a non-equilibrium process as the solidification rate approaches the limit of absolute stability, Ras. In this study, the solidification of the HX multicomponent system occurred under a relatively low solidification rate compared to Ras, and the microstructure of the conventional MPF model was successfully reproduced in the physical experiment. However, note that the limit of absolute stability predicted by the Mullins-Sekerka theory was originally proposed for solidification in a binary alloy system, and further investigation is required to consider its applicability to multicomponent alloy systems. Moreover, the fast solidification, such as in the LPBF process, causes segregation coefficient approaching a value of 1 [20][21][25] corresponds to a diffusion length that is on the order of the atomic interface thickness. When the segregation coefficient approaches 1, solute undercooling disappears; hence, there is no driving force to amplify fluctuations regardless of whether interfacial tension is present. This phenomenon should be further investigated in future studies.

5. Conclusions

We simulated solute segregation in a multicomponent HX alloy under the LPBF process by an MPF simulation using the temperature distributions obtained by a CtFD simulation. We set the parameters of the CtFD simulation to match the melt pool shape formed in the laser-irradiation experiment and found that solidification occurred under high cooling rates of up to 1.6 × 10K s-1.

MPF simulations using the temperature distributions from CtFD simulation could reproduce the experimentally observed PDAS and revealed that significant solute segregation occurred at the interdendritic regions. Equilibrium thermodynamic calculations using the alloy compositions of the segregated regions when considering crack sensitivities suggested a decrease in the solidus temperature and an increase in the amount of carbide precipitation, thereby increasing the susceptibility to liquation and ductility dip cracks in these regions. Notably, these changes were suppressed at the melt-pool boundary region, where re-remelting occurred during the stacking of the layer above. This effect can be used to achieve a novel in-process segregation attenuation.

Our study revealed that a conventional MPF simulation weakly coupled with a CtFD simulation can be used to study the solidification of multicomponent alloys in LPBF, contrary to the cases of binary alloys investigated in previous studies. We discussed the applicability of the conventional MPF model to the LPBF process in terms of the limit of absolute stability, Ras, and suggested that alloys with a high limit velocity, i.e., multicomponent alloys, can be simulated using the conventional MPF model even under the high solidification velocity conditions of LPBF.

CRediT authorship contribution statement

Masayuki Okugawa: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Takayoshi Nakano: Writing – review & editing, Validation, Supervision, Funding acquisition. Yuichiro Koizumi: Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Sukeharu Nomoto: Writing – review & editing, Validation, Investigation. Makoto Watanabe: Writing – review & editing, Validation, Supervision, Funding acquisition. Katsuhiko Sawaizumi: Validation, Software, Investigation, Formal analysis, Data curation. Kenji Saito: Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. Haruki Yoshima: Visualization, Validation, Software, Investigation, Formal analysis, Data curation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

Acknowledgments

This work was partly supported by the Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), “Materials Integration for Revolutionary Design System of Structural Materials,” (funding agency: The Japan Science and Technology Agency), by JSPS KAKENHI Grant Numbers 21H05018 and 21H05193, and by CREST Nanomechanics: Elucidation of macroscale mechanical properties based on understanding nanoscale dynamics for innovative mechanical materials (Grant Number: JPMJCR2194) from the Japan Science and Technology Agency (JST). The authors would like to thank Mr. H. Kawabata and Mr. K. Kimura for their technical support with the sample preparations and laser beam irradiation experiments.

Appendix A. Supplementary material

Download : Download Word document (654KB)

Supplementary material.

Data availability

Data will be made available on request.

References

Schematic diagram of HP-LPBF melting process.

Modeling and numerical studies of high-precision laser powder bed fusion

Yi Wei ;Genyu Chen;Nengru Tao;Wei Zhou
https://doi.org/10.1063/5.0191504

In order to comprehensively reveal the evolutionary dynamics of the molten pool and the state of motion of the fluid during the high-precision laser powder bed fusion (HP-LPBF) process, this study aims to deeply investigate the specific manifestations of the multiphase flow, solidification phenomena, and heat transfer during the process by means of numerical simulation methods. Numerical simulation models of SS316L single-layer HP-LPBF formation with single and double tracks were constructed using the discrete element method and the computational fluid dynamics method. The effects of various factors such as Marangoni convection, surface tension, vapor recoil, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool have been paid attention to during the model construction process. The results show that the molten pool exhibits a “comet” shape, in which the temperature gradient at the front end of the pool is significantly larger than that at the tail end, with the highest temperature gradient up to 1.69 × 108 K/s. It is also found that the depth of the second track is larger than that of the first one, and the process parameter window has been determined preliminarily. In addition, the application of HP-LPBF technology helps to reduce the surface roughness and minimize the forming size.

Topics

Heat transfer, Nonequilibrium thermodynamics, Solidification process, Computer simulation, Discrete element method, Lasers, Mass transfer, Fluid mechanics, Computational fluid dynamics, Multiphase flows

I. INTRODUCTION

Laser powder bed fusion (LPBF) has become a research hotspot in the field of additive manufacturing of metals due to its advantages of high-dimensional accuracy, good surface quality, high density, and high material utilization.1,2 With the rapid development of electronics, medical, automotive, biotechnology, energy, communication, and optics, the demand for microfabrication technology is increasing day by day.3 High-precision laser powder bed fusion (HP-LPBF) is one of the key manufacturing technologies for tiny parts in the fields of electronics, medical, automotive, biotechnology, energy, communication, and optics because of its process characteristics such as small focal spot diameter, small powder particle size, and thin powder layup layer thickness.4–13 Compared with LPBF, HP-LPBF has the significant advantages of smaller focal spot diameter, smaller powder particle size, and thinner layer thickness. These advantages make HP-LPBF perform better in producing micro-fine parts, high surface quality, and parts with excellent mechanical properties.

HP-LPBF is in the exploratory stage, and researchers have already done some exploratory studies on the focal spot diameter, the amount of defocusing, and the powder particle size. In order to explore the influence of changing the laser focal spot diameter on the LPBF process characteristics of the law, Wildman et al.14 studied five groups of different focal spot diameter LPBF forming 316L stainless steel (SS316L) processing effect, the smallest focal spot diameter of 26 μm, and the results confirm that changing the focal spot diameter can be achieved to achieve the energy control, so as to control the quality of forming. Subsequently, Mclouth et al.15 proposed the laser out-of-focus amount (focal spot diameter) parameter, which characterizes the distance between the forming plane and the laser focal plane. The laser energy density was controlled by varying the defocusing amount while keeping the laser parameters constant. Sample preparation at different focal positions was investigated, and their microstructures were characterized. The results show that the samples at the focal plane have finer microstructure than those away from the focal plane, which is the effect of higher power density and smaller focal spot diameter. In order to explore the influence of changing the powder particle size on the characteristics of the LPBF process, Qian et al.16 carried out single-track scanning simulations on powder beds with average powder particle sizes of 70 and 40 μm, respectively, and the results showed that the melt tracks sizes were close to each other under the same process parameters for the two particle-size distributions and that the molten pool of powder beds with small particles was more elongated and the edges of the melt tracks were relatively flat. In order to explore the superiority of HP-LPBF technology, Xu et al.17 conducted a comparative analysis of HP-LPBF and conventional LPBF of SS316L. The results showed that the average surface roughness of the top surface after forming by HP-LPBF could reach 3.40 μm. Once again, it was verified that HP-LPBF had higher forming quality than conventional LPBF. On this basis, Wei et al.6 comparatively analyzed the effects of different laser focal spot diameters on different powder particle sizes formed by LPBF. The results showed that the smaller the laser focal spot diameter, the fewer the defects on the top and side surfaces. The above research results confirm that reducing the laser focal spot diameter can obtain higher energy density and thus better forming quality.

LPBF involves a variety of complex systems and mechanisms, and the final quality of the part is influenced by a large number of process parameters.18–24 Some research results have shown that there are more than 50 factors affecting the quality of the specimen. The influencing factors are mainly categorized into three main groups: (1) laser parameters, (2) powder parameters, and (3) equipment parameters, which interact with each other to determine the final specimen quality. With the continuous development of technologies such as computational materials science and computational fluid dynamics (CFD), the method of studying the influence of different factors on the forming quality of LPBF forming process has been shifted from time-consuming and laborious experimental characterization to the use of numerical simulation methods. As a result, more and more researchers are adopting this approach for their studies. Currently, numerical simulation studies on LPBF are mainly focused on the exploration of molten pool, temperature distribution, and residual stresses.

  1. Finite element simulation based on continuum mechanics and free surface fluid flow modeling based on fluid dynamics are two common approaches to study the behavior of LPBF molten pool.25–28 Finite element simulation focuses on the temperature and thermal stress fields, treats the powder bed as a continuum, and determines the molten pool size by plotting the elemental temperature above the melting point. In contrast, fluid dynamics modeling can simulate the 2D or 3D morphology of the metal powder pile and obtain the powder size and distribution by certain algorithms.29 The flow in the molten pool is mainly affected by recoil pressure and the Marangoni effect. By simulating the molten pool formation, it is possible to predict defects, molten pool shape, and flow characteristics, as well as the effect of process parameters on the molten pool geometry.30–34 In addition, other researchers have been conducted to optimize the laser processing parameters through different simulation methods and experimental data.35–46 Crystal growth during solidification is studied to further understand the effect of laser parameters on dendritic morphology and solute segregation.47–54 A multi-scale system has been developed to describe the fused deposition process during 3D printing, which is combined with the conductive heat transfer model and the dendritic solidification model.55,56
  2. Relevant scholars have adopted various different methods for simulation, such as sequential coupling theory,57 Lagrangian and Eulerian thermal models,58 birth–death element method,25 and finite element method,59 in order to reveal the physical phenomena of the laser melting process and optimize the process parameters. Luo et al.60 compared the LPBF temperature field and molten pool under double ellipsoidal and Gaussian heat sources by ANSYS APDL and found that the diffusion of the laser energy in the powder significantly affects the molten pool size and the temperature field.
  3. The thermal stresses obtained from the simulation correlate with the actual cracks,61 and local preheating can effectively reduce the residual stresses.62 A three-dimensional thermodynamic finite element model investigated the temperature and stress variations during laser-assisted fabrication and found that powder-to-solid conversion increases the temperature gradient, stresses, and warpage.63 Other scholars have predicted residual stresses and part deflection for LPBF specimens and investigated the effects of deposition pattern, heat, laser power, and scanning strategy on residual stresses, noting that high-temperature gradients lead to higher residual stresses.64–67 

In short, the process of LPBF forming SS316L is extremely complex and usually involves drastic multi-scale physicochemical changes that will only take place on a very small scale. Existing literature employs DEM-based mesoscopic-scale numerical simulations to investigate the effects of process parameters on the molten pool dynamics of LPBF-formed SS316L. However, a few studies have been reported on the key mechanisms of heating and solidification, spatter, and convective behavior of the molten pool of HP-LPBF-formed SS316L with small laser focal spot diameters. In this paper, the geometrical properties of coarse and fine powder particles under three-dimensional conditions were first calculated using DEM. Then, numerical simulation models for single-track and double-track cases in the single-layer HP-LPBF forming SS316L process were developed at mesoscopic scale using the CFD method. The flow genesis of the melt in the single-track and double-track molten pools is discussed, and their 3D morphology and dimensional characteristics are discussed. In addition, the effects of laser process parameters, powder particle size, and laser focal spot diameter on the temperature field, characterization information, and defects in the molten pool are discussed.

II. MODELING

A. 3D powder bed modeling

HP-LPBF is an advanced processing technique for preparing target parts layer by layer stacking, the process of which involves repetitive spreading and melting of powders. In this process, both the powder spreading and the morphology of the powder bed are closely related to the results of the subsequent melting process, while the melted surface also affects the uniform distribution of the next layer of powder. For this reason, this chapter focuses on the modeling of the physical action during the powder spreading process and the theory of DEM to establish the numerical model of the powder bed, so as to lay a solid foundation for the accuracy of volume of fluid (VOF) and CFD.

1. DEM

DEM is a numerical technique for calculating the interaction of a large number of particles, which calculates the forces and motions of the spheres by considering each powder sphere as an independent unit. The motion of the powder particles follows the laws of classical Newtonian mechanics, including translational and rotational,38,68–70 which are expressed as follows:����¨=���+∑��ij,

(1)����¨=∑�(�ij×�ij),

(2)

where �� is the mass of unit particle i in kg, ��¨ is the advective acceleration in m/s2, And g is the gravitational acceleration in m/s2. �ij is the force in contact with the neighboring particle � in N. �� is the rotational inertia of the unit particle � in kg · m2. ��¨ is the unit particle � angular acceleration in rad/s2. �ij is the vector pointing from unit particle � to the contact point of neighboring particle �⁠.

Equations (1) and (2) can be used to calculate the velocity and angular velocity variations of powder particles to determine their positions and velocities. A three-dimensional powder bed model of SS316L was developed using DEM. The powder particles are assumed to be perfect spheres, and the substrate and walls are assumed to be rigid. To describe the contact between the powder particles and between the particles and the substrate, a non-slip Hertz–Mindlin nonlinear spring-damping model71 was used with the following expression:�hz=��������+��[(�����ij−�eff����)−(�����+�eff����)],

(3)

where �hz is the force calculated using the Hertzian in M. �� and �� are the radius of unit particles � and � in m, respectively. �� is the overlap size of the two powder particles in m. ��⁠, �� are the elastic constants in the normal and tangential directions, respectively. �ij is the unit vector connecting the centerlines of the two powder particles. �eff is the effective mass of the two powder particles in kg. �� and �� are the viscoelastic damping constants in the normal and tangential directions, respectively. �� and �� are the components of the relative velocities of the two powder particles. ��� is the displacement vector between two spherical particles. The schematic diagram of overlapping powder particles is shown in Fig. 1.

FIG. 1.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of overlapping powder particles.

Because the particle size of the powder used for HP-LPBF is much smaller than 100 μm, the effect of van der Waals forces must be considered. Therefore, the cohesive force �jkr of the Hertz–Mindlin model was used instead of van der Waals forces,72 with the following expression:�jkr=−4��0�*�1.5+4�*3�*�3,

(4)1�*=(1−��2)��+(1−��2)��,

(5)1�*=1��+1��,

(6)

where �* is the equivalent Young’s modulus in GPa; �* is the equivalent particle radius in m; �0 is the surface energy of the powder particles in J/m2; α is the contact radius in m; �� and �� are the Young’s modulus of the unit particles � and �⁠, respectively, in GPa; and �� and �� are the Poisson’s ratio of the unit particles � and �⁠, respectively.

2. Model building

Figure 2 shows a 3D powder bed model generated using DEM with a coarse powder geometry of 1000 × 400 × 30 μm3. The powder layer thickness is 30 μm, and the powder bed porosity is 40%. The average particle size of this spherical powder is 31.7 μm and is normally distributed in the range of 15–53 μm. The geometry of the fine powder was 1000 × 400 × 20 μm3, with a layer thickness of 20 μm, and the powder bed porosity of 40%. The average particle size of this spherical powder is 11.5 μm and is normally distributed in the range of 5–25 μm. After the 3D powder bed model is generated, it needs to be imported into the CFD simulation software for calculation, and the imported geometric model is shown in Fig. 3. This geometric model is mainly composed of three parts: protective gas, powder bed, and substrate. Under the premise of ensuring the accuracy of the calculation, the mesh size is set to 3 μm, and the total number of coarse powder meshes is 1 704 940. The total number of fine powder meshes is 3 982 250.

FIG. 2.

VIEW LARGEDOWNLOAD SLIDE

Three-dimensional powder bed model: (a) coarse powder, (b) fine powder.

FIG. 3.

VIEW LARGEDOWNLOAD SLIDE

Geometric modeling of the powder bed computational domain: (a) coarse powder, (b) fine powder.

B. Modeling of fluid mechanics simulation

In order to solve the flow, melting, and solidification problems involved in HP-LPBF molten pool, the study must follow the three governing equations of conservation of mass, conservation of energy, and conservation of momentum.73 The VOF method, which is the most widely used in fluid dynamics, is used to solve the molten pool dynamics model.

1. VOF

VOF is a method for tracking the free interface between the gas and liquid phases on the molten pool surface. The core idea of the method is to define a volume fraction function F within each grid, indicating the proportion of the grid space occupied by the material, 0 ≤ F ≤ 1 in Fig. 4. Specifically, when F = 0, the grid is empty and belongs to the gas-phase region; when F = 1, the grid is completely filled with material and belongs to the liquid-phase region; and when 0 < F < 1, the grid contains free surfaces and belongs to the mixed region. The direction normal to the free surface is the direction of the fastest change in the volume fraction F (the direction of the gradient of the volume fraction), and the direction of the gradient of the volume fraction can be calculated from the values of the volume fractions in the neighboring grids.74 The equations controlling the VOF are expressed as follows:𝛻����+�⋅(��→)=0,

(7)

where t is the time in s and �→ is the liquid velocity in m/s.

FIG. 4.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of VOF.

The material parameters of the mixing zone are altered due to the inclusion of both the gas and liquid phases. Therefore, in order to represent the density of the mixing zone, the average density �¯ is used, which is expressed as follows:72�¯=(1−�1)�gas+�1�metal,

(8)

where �1 is the proportion of liquid phase, �gas is the density of protective gas in kg/m3, and �metal is the density of metal in kg/m3.

2. Control equations and boundary conditions

Figure 5 is a schematic diagram of the HP-LPBF melting process. First, the laser light strikes a localized area of the material and rapidly heats up the area. Next, the energy absorbed in the region is diffused through a variety of pathways (heat conduction, heat convection, and surface radiation), and this process triggers complex phase transition phenomena (melting, evaporation, and solidification). In metals undergoing melting, the driving forces include surface tension and the Marangoni effect, recoil due to evaporation, and buoyancy due to gravity and uneven density. The above physical phenomena interact with each other and do not occur independently.

FIG. 5.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of HP-LPBF melting process.

  1. Laser heat sourceThe Gaussian surface heat source model is used as the laser heat source model with the following expression:�=2�0����2exp(−2�12��2),(9)where � is the heat flow density in W/m2, �0 is the absorption rate of SS316L, �� is the radius of the laser focal spot in m, and �1 is the radial distance from the center of the laser focal spot in m. The laser focal spot can be used for a wide range of applications.
  2. Energy absorptionThe formula for calculating the laser absorption �0 of SS316L is as follows:�0=0.365(�0[1+�0(�−20)]/�)0.5,(10)where �0 is the direct current resistivity of SS316L at 20 °C in Ω m, �0 is the resistance temperature coefficient in ppm/°C, � is the temperature in °C, and � is the laser wavelength in m.
  3. Heat transferThe basic principle of heat transfer is conservation of energy, which is expressed as follows:𝛻𝛻𝛻�(��)��+�·(��→�)=�·(�0����)+��,(11)where � is the density of liquid phase SS316L in kg/m3, �� is the specific heat capacity of SS316L in J/(kg K), 𝛻� is the gradient operator, t is the time in s, T is the temperature in K, 𝛻�� is the temperature gradient, �→ is the velocity vector, �0 is the coefficient of thermal conduction of SS316L in W/(m K), and  �� is the thermal energy dissipation term in the molten pool.
  4. Molten pool flowThe following three conditions need to be satisfied for the molten pool to flow:
    • Conservation of mass with the following expression:𝛻�·(��→)=0.(12)
    • Conservation of momentum (Navier–Stokes equation) with the following expression:𝛻𝛻𝛻𝛻���→��+�(�→·�)�→=�·[−pI+�(��→+(��→)�)]+�,(13)where � is the pressure in Pa exerted on the liquid phase SS316L microelement, � is the unit matrix, � is the fluid viscosity in N s/m2, and � is the volumetric force (gravity, atmospheric pressure, surface tension, vapor recoil, and the Marangoni effect).
    • Conservation of energy, see Eq. (11)
  5. Surface tension and the Marangoni effectThe effect of temperature on the surface tension coefficient is considered and set as a linear relationship with the following expression:�=�0−��dT(�−��),(14)where � is the surface tension of the molten pool at temperature T in N/m, �� is the melting temperature of SS316L in K, �0 is the surface tension of the molten pool at temperature �� in Pa, and σdσ/ dT is the surface tension temperature coefficient in N/(m K).In general, surface tension decreases with increasing temperature. A temperature gradient causes a gradient in surface tension that drives the liquid to flow, known as the Marangoni effect.
  6. Metal vapor recoilAt higher input energy densities, the maximum temperature of the molten pool surface reaches the evaporation temperature of the material, and a gasification recoil pressure occurs vertically downward toward the molten pool surface, which will be the dominant driving force for the molten pool flow.75 The expression is as follows:��=0.54�� exp ���−���0���,(15)where �� is the gasification recoil pressure in Pa, �� is the ambient pressure in kPa, �� is the latent heat of evaporation in J/kg, �0 is the gas constant in J/(mol K), T is the surface temperature of the molten pool in K, and Te is the evaporation temperature in K.
  7. Solid–liquid–gas phase transitionWhen the laser hits the powder layer, the powder goes through three stages: heating, melting, and solidification. During the solidification phase, mutual transformations between solid, liquid, and gaseous states occur. At this point, the latent heat of phase transition absorbed or released during the phase transition needs to be considered.68 The phase transition is represented based on the relationship between energy and temperature with the following expression:�=�����,(�<��),�(��)+�−����−����,(��<�<��)�(��)+(�−��)����,(��<�),,(16)where �� and �� are solid and liquid phase density, respectively, of SS316L in kg/m3. �� and �� unit volume of solid and liquid phase-specific heat capacity, respectively, of SS316L in J/(kg K). �� and ��⁠, respectively, are the solidification temperature and melting temperature of SS316L in K. �� is the latent heat of the phase transition of SS316L melting in J/kg.

3. Assumptions

The CFD model was computed using the commercial software package FLOW-3D.76 In order to simplify the calculation and solution process while ensuring the accuracy of the results, the model makes the following assumptions:

  1. It is assumed that the effects of thermal stress and material solid-phase thermal expansion on the calculation results are negligible.
  2. The molten pool flow is assumed to be a Newtonian incompressible laminar flow, while the effects of liquid thermal expansion and density on the results are neglected.
  3. It is assumed that the surface tension can be simplified to an equivalent pressure acting on the free surface of the molten pool, and the effect of chemical composition on the results is negligible.
  4. Neglecting the effect of the gas flow field on the molten pool.
  5. The mass loss due to evaporation of the liquid metal is not considered.
  6. The influence of the plasma effect of the molten metal on the calculation results is neglected.

It is worth noting that the formulation of assumptions requires a trade-off between accuracy and computational efficiency. In the above models, some physical phenomena that have a small effect or high difficulty on the calculation results are simplified or ignored. Such simplifications make numerical simulations more efficient and computationally tractable, while still yielding accurate results.

4. Initial conditions

The preheating temperature of the substrate was set to 393 K, at which time all materials were in the solid state and the flow rate was zero.

5. Material parameters

The material used is SS316L and the relevant parameters required for numerical simulations are shown in Table I.46,77,78

TABLE I.

SS316L-related parameters.

PropertySymbolValue
Density of solid metal (kg/m3�metal 7980 
Solid phase line temperature (K) �� 1658 
Liquid phase line temperature (K) �� 1723 
Vaporization temperature (K) �� 3090 
Latent heat of melting (⁠ J/kg⁠) �� 2.60×105 
Latent heat of evaporation (⁠ J/kg⁠) �� 7.45×106 
Surface tension of liquid phase (N /m⁠) � 1.60 
Liquid metal viscosity (kg/m s) �� 6×10−3 
Gaseous metal viscosity (kg/m s) �gas 1.85×10−5 
Temperature coefficient of surface tension (N/m K) ��/�T 0.80×10−3 
Molar mass (⁠ kg/mol⁠) 0.05 593 
Emissivity � 0.26 
Laser absorption �0 0.35 
Ambient pressure (kPa) �� 101 325 
Ambient temperature (K) �0 300 
Stefan–Boltzmann constant (W/m2 K4� 5.67×10−8 
Thermal conductivity of metals (⁠ W/m K⁠) � 24.55 
Density of protective gas (kg/m3�gas 1.25 
Coefficient of thermal expansion (/K) �� 16×10−6 
Generalized gas constant (⁠ J/mol K⁠) 8.314 

III. RESULTS AND DISCUSSION

With the objective of studying in depth the evolutionary patterns of single-track and double-track molten pool development, detailed observations were made for certain specific locations in the model, as shown in Fig. 6. In this figure, P1 and P2 represent the longitudinal tangents to the centers of the two melt tracks in the XZ plane, while L1 is the transverse profile in the YZ plane. The scanning direction is positive and negative along the X axis. Points A and B are the locations of the centers of the molten pool of the first and second melt tracks, respectively (x = 1.995 × 10−4, y = 5 × 10−7, and z = −4.85 × 10−5).

FIG. 6.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of observation position.

A. Single-track simulation

A series of single-track molten pool simulation experiments were carried out in order to investigate the influence law of laser power as well as scanning speed on the HP-LPBF process. Figure 7 demonstrates the evolution of the 3D morphology and temperature field of the single-track molten pool in the time period of 50–500 μs under a laser power of 100 W and a scanning speed of 800 mm/s. The powder bed is in the natural cooling state. When t = 50 μs, the powder is heated by the laser heat and rapidly melts and settles to form the initial molten pool. This process is accompanied by partial melting of the substrate and solidification together with the melted powder. The molten pool rapidly expands with increasing width, depth, length, and temperature, as shown in Fig. 7(a). When t = 150 μs, the molten pool expands more obviously, and the temperature starts to transfer to the surrounding area, forming a heat-affected zone. At this point, the width of the molten pool tends to stabilize, and the temperature in the center of the molten pool has reached its peak and remains largely stable. However, the phenomenon of molten pool spatter was also observed in this process, as shown in Fig. 7(b). As time advances, when t = 300 μs, solidification begins to occur at the tail of the molten pool, and tiny ripples are produced on the solidified surface. This is due to the fact that the melt flows toward the region with large temperature gradient under the influence of Marangoni convection and solidifies together with the melt at the end of the bath. At this point, the temperature gradient at the front of the bath is significantly larger than at the end. While the width of the molten pool was gradually reduced, the shape of the molten pool was gradually changed to a “comet” shape. In addition, a slight depression was observed at the top of the bath because the peak temperature at the surface of the bath reached the evaporation temperature, which resulted in a recoil pressure perpendicular to the surface of the bath downward, creating a depressed region. As the laser focal spot moves and is paired with the Marangoni convection of the melt, these recessed areas will be filled in as shown in Fig. 7(c). It has been shown that the depressed regions are the result of the coupled effect of Marangoni convection, recoil pressure, and surface tension.79 By t = 500 μs, the width and height of the molten pool stabilize and show a “comet” shape in Fig. 7(d).

FIG. 7.

VIEW LARGEDOWNLOAD SLIDE

Single-track molten pool process: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠.

Figure 8 depicts the velocity vector diagram of the P1 profile in a single-track molten pool, the length of the arrows represents the magnitude of the velocity, and the maximum velocity is about 2.36 m/s. When t = 50 μs, the molten pool takes shape, and the velocities at the two ends of the pool are the largest. The variation of the velocities at the front end is especially more significant in Fig. 8(a). As the time advances to t = 150 μs, the molten pool expands rapidly, in which the velocity at the tail increases and changes more significantly, while the velocity at the front is relatively small. At this stage, the melt moves backward from the center of the molten pool, which in turn expands the molten pool area. The melt at the back end of the molten pool center flows backward along the edge of the molten pool surface and then converges along the edge of the molten pool to the bottom center, rising to form a closed loop. Similarly, a similar closed loop is formed at the front end of the center of the bath, but with a shorter path. However, a large portion of the melt in the center of the closed loop formed at the front end of the bath is in a nearly stationary state. The main cause of this melt flow phenomenon is the effect of temperature gradient and surface tension (the Marangoni effect), as shown in Figs. 8(b) and 8(e). This dynamic behavior of the melt tends to form an “elliptical” pool. At t = 300 μs, the tendency of the above two melt flows to close the loop is more prominent and faster in Fig. 8(c). When t = 500 μs, the velocity vector of the molten pool shows a stable trend, and the closed loop of melt flow also remains stable. With the gradual laser focal spot movement, the melt is gradually solidified at its tail, and finally, a continuous and stable single track is formed in Fig. 8(d).

FIG. 8.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of single-track molten pool velocity in XZ longitudinal section: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠, (e) molten pool flow.

In order to explore in depth the transient evolution of the molten pool, the evolution of the single-track temperature field and the melt flow was monitored in the YZ cross section. Figure 9(a) shows the state of the powder bed at the initial moment. When t = 250 μs, the laser focal spot acts on the powder bed and the powder starts to melt and gradually collects in the molten pool. At this time, the substrate will also start to melt, and the melt flow mainly moves in the downward and outward directions and the velocity is maximum at the edges in Fig. 9(b). When t = 300 μs, the width and depth of the molten pool increase due to the recoil pressure. At this time, the melt flows more slowly at the center, but the direction of motion is still downward in Fig. 9(c). When t = 350 μs, the width and depth of the molten pool further increase, at which time the intensity of the melt flow reaches its peak and the direction of motion remains the same in Fig. 9(d). When t = 400 μs, the melt starts to move upward, and the surrounding powder or molten material gradually fills up, causing the surface of the molten pool to begin to flatten. At this time, the maximum velocity of the melt is at the center of the bath, while the velocity at the edge is close to zero, and the edge of the melt starts to solidify in Fig. 9(e). When t = 450 μs, the melt continues to move upward, forming a convex surface of the melt track. However, the melt movement slows down, as shown in Fig. 9(f). When t = 500 μs, the melt further moves upward and its speed gradually becomes smaller. At the same time, the melt solidifies further, as shown in Fig. 9(g). When t = 550 μs, the melt track is basically formed into a single track with a similar “mountain” shape. At this stage, the velocity is close to zero only at the center of the molten pool, and the flow behavior of the melt is poor in Fig. 9(h). At t = 600 μs, the melt stops moving and solidification is rapidly completed. Up to this point, a single track is formed in Fig. 9(i). During the laser action on the powder bed, the substrate melts and combines with the molten state powder. The powder-to-powder fusion is like the convergence of water droplets, which are rapidly fused by surface tension. However, the fusion between the molten state powder and the substrate occurs driven by surface tension, and the molten powder around the molten pool is pulled toward the substrate (a wetting effect occurs), which ultimately results in the formation of a monolithic whole.38,80,81

FIG. 9.

VIEW LARGEDOWNLOAD SLIDE

Evolution of single-track molten pool temperature and melt flow in the YZ cross section: (a) t = 0  ��⁠, (b) t = 250  ��⁠, (c) t = 300  ��⁠, (d) t = 350  ��⁠, (e) t = 400  ��⁠, (f) t = 450  ��⁠, (g) t = 500  ��⁠, (h) t = 550  ��⁠, (i) t = 600  ��⁠.

The wetting ability between the liquid metal and the solid substrate in the molten pool directly affects the degree of balling of the melt,82,83 and the wetting ability can be measured by the contact angle of a single track in Fig. 10. A smaller value of contact angle represents better wettability. The contact angle α can be calculated by�=�1−�22,

(17)

where �1 and �2 are the contact angles of the left and right regions, respectively.

FIG. 10.

VIEW LARGEDOWNLOAD SLIDE

Schematic of contact angle.

Relevant studies have confirmed that the wettability is better at a contact angle α around or below 40°.84 After measurement, a single-track contact angle α of about 33° was obtained under this process parameter, which further confirms the good wettability.

B. Double-track simulation

In order to deeply investigate the influence of hatch spacing on the characteristics of the HP-LPBF process, a series of double-track molten pool simulation experiments were systematically carried out. Figure 11 shows in detail the dynamic changes of the 3D morphology and temperature field of the double-track molten pool in the time period of 2050–2500 μs under the conditions of laser power of 100 W, scanning speed of 800 mm/s, and hatch spacing of 0.06 mm. By comparing the study with Fig. 7, it is observed that the basic characteristics of the 3D morphology and temperature field of the second track are similar to those of the first track. However, there are subtle differences between them. The first track exhibits a basically symmetric shape, but the second track morphology shows a slight deviation influenced by the difference in thermal diffusion rate between the solidified metal and the powder. Otherwise, the other characteristic information is almost the same as that of the first track. Figure 12 shows the velocity vector plot of the P2 profile in the double-track molten pool, with a maximum velocity of about 2.63 m/s. The melt dynamics at both ends of the pool are more stable at t = 2050 μs, where the maximum rate of the second track is only 1/3 of that of the first one. Other than that, the rest of the information is almost no significant difference from the characteristic information of the first track. Figure 13 demonstrates a detailed observation of the double-track temperature field and melts flow in the YZ cross section, and a comparative study with Fig. 9 reveals that the width of the second track is slightly wider. In addition, after the melt direction shifts from bottom to top, the first track undergoes four time periods (50 μs) to reach full solidification, while the second track takes five time periods. This is due to the presence of significant heat buildup in the powder bed after the forming of the first track, resulting in a longer dynamic time of the melt and an increased molten pool lifetime. In conclusion, the level of specimen forming can be significantly optimized by adjusting the laser power and hatch spacing.

FIG. 11.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool process: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 12.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of double-track molten pool velocity in XZ longitudinal section: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 13.

VIEW LARGEDOWNLOAD SLIDE

Evolution of double-track molten pool temperature and melt flow in the YZ cross section: (a) t = 2250  ��⁠, (b) t = 2300  ��⁠, (c) t = 2350  ��⁠, (d) t = 2400  ��⁠, (e) t = 2450  ��⁠, (f) t = 2500  ��⁠, (g) t = 2550  ��⁠, (h) t = 2600  ��⁠, (i) t = 2650  ��⁠.

In order to quantitatively detect the molten pool dimensions as well as the remolten region dimensions, the molten pool characterization information in Fig. 14 is constructed by drawing the boundary on the YZ cross section based on the isothermal surface of the liquid phase line. It can be observed that the heights of the first track and second track are basically the same, but the depth of the second track increases relative to the first track. The molten pool width is mainly positively correlated with the laser power as well as the scanning speed (the laser line energy density �⁠). However, the remelted zone width is negatively correlated with the hatch spacing (the overlapping ratio). Overall, the forming quality of the specimens can be directly influenced by adjusting the laser power, scanning speed, and hatch spacing.

FIG. 14.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool characterization information on YZ cross section.

In order to study the variation rule of the temperature in the center of the molten pool with time, Fig. 15 demonstrates the temperature variation curves with time for two reference points, A and B. Among them, the red dotted line indicates the liquid phase line temperature of SS316L. From the figure, it can be seen that the maximum temperature at the center of the molten pool in the first track is lower than that in the second track, which is mainly due to the heat accumulation generated after passing through the first track. The maximum temperature gradient was calculated to be 1.69 × 108 K/s. When the laser scanned the first track, the temperature in the center of the molten pool of the second track increased slightly. Similarly, when the laser scanned the second track, a similar situation existed in the first track. Since the temperature gradient in the second track is larger than that in the first track, the residence time of the liquid phase in the molten pool of the first track is longer than that of the second track.

FIG. 15.

VIEW LARGEDOWNLOAD SLIDE

Temperature profiles as a function of time for two reference points A and B.

C. Simulation analysis of molten pool under different process parameters

In order to deeply investigate the effects of various process parameters on the mesoscopic-scale temperature field, molten pool characteristic information and defects of HP-LPBF, numerical simulation experiments on mesoscopic-scale laser power, scanning speed, and hatch spacing of double-track molten pools were carried out.

1. Laser power

Figure 16 shows the effects of different laser power on the morphology and temperature field of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. When P = 50 W, a smaller molten pool is formed due to the lower heat generated by the Gaussian light source per unit time. This leads to a smaller track width, which results in adjacent track not lapping properly and the presence of a large number of unmelted powder particles, resulting in an increase in the number of defects, such as pores in the specimen. The surface of the track is relatively flat, and the depth is small. In addition, the temperature gradient before and after the molten pool was large, and the depression location appeared at the biased front end in Fig. 16(a). When P = 100 W, the surface of the track is flat and smooth with excellent lap. Due to the Marangoni effect, the velocity field of the molten pool is in the form of “vortex,” and the melt has good fluidity, and the maximum velocity reaches 2.15 m/s in Fig. 16(b). When P = 200 W, the heat generated by the Gaussian light source per unit time is too large, resulting in the melt rapidly reaching the evaporation temperature, generating a huge recoil pressure, forming a large molten pool, and the surface of the track is obviously raised. The melt movement is intense, especially the closed loop at the center end of the molten pool. At this time, the depth and width of the molten pool are large, leading to the expansion of the remolten region and the increased chance of the appearance of porosity defects in Fig. 16(c). The results show that at low laser power, the surface tension in the molten pool is dominant. At high laser power, recoil pressure is its main role.

FIG. 16.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different laser powers: (a) P = 50 W, (b) P = 100 W, (c) P = 200 W.

Table II shows the effect of different laser powers on the characteristic information of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. The negative overlapping ratio in the table indicates that the melt tracks are not lapped, and 26/29 indicates the melt depth of the first track/second track. It can be seen that with the increase in laser power, the melt depth, melt width, melt height, and remelted zone show a gradual increase. At the same time, the overlapping ratio also increases. Especially in the process of laser power from 50 to 200 W, the melting depth and melting width increased the most, which increased nearly 2 and 1.5 times, respectively. Meanwhile, the overlapping ratio also increases with the increase in laser power, which indicates that the melting and fusion of materials are better at high laser power. On the other hand, the dimensions of the molten pool did not change uniformly with the change of laser power. Specifically, the depth-to-width ratio of the molten pool increased from about 0.30 to 0.39 during the increase from 50 to 120 W, which further indicates that the effective heat transfer in the vertical direction is greater than that in the horizontal direction with the increase in laser power. This dimensional response to laser power is mainly affected by the recoil pressure and also by the difference in the densification degree between the powder layer and the metal substrate. In addition, according to the experimental results, the contact angle shows a tendency to increase and then decrease during the process of laser power increase, and always stays within the range of less than 33°. Therefore, in practical applications, it is necessary to select the appropriate laser power according to the specific needs in order to achieve the best processing results.

TABLE II.

Double-track molten pool characterization information at different laser powers.

Laser power (W)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
50 16 54 11 −10 23 
100 26/29 74 14 18 23.33 33 
200 37/45 116 21 52 93.33 28 

2. Scanning speed

Figure 17 demonstrates the effect of different scanning speeds on the morphology and temperature field of the double-track molten pool at a laser power of 100 W and a hatch spacing of 0.06 mm. With the gradual increase in scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. When � = 200 mm/s, the slow scanning speed causes the material to absorb too much heat, which is very easy to trigger the overburning phenomenon. At this point, the molten pool is larger and the surface morphology is uneven. This situation is consistent with the previously discussed scenario with high laser power in Fig. 17(a). However, when � = 1600 mm/s, the scanning speed is too fast, resulting in the material not being able to absorb sufficient heat, which triggers the powder particles that fail to melt completely to have a direct effect on the bonding of the melt to the substrate. At this time, the molten pool volume is relatively small and the neighboring melt track cannot lap properly. This result is consistent with the previously discussed case of low laser power in Fig. 17(b). Overall, the ratio of the laser power to the scanning speed (the line energy density �⁠) has a direct effect on the temperature field and surface morphology of the molten pool.

FIG. 17.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different scanning speed: (a)  � = 200 mm/s, (b)  � = 1600 mm/s.

Table III shows the effects of different scanning speed on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and hatch spacing of 0.06 mm. It can be seen that the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. With the increase in scanning speed, the melt depth, melt width, melt height, remelted zone, and overlapping ratio show a gradual decreasing trend. Among them, the melt depth and melt width decreased faster, while the melt height and remolten region decreased relatively slowly. In addition, when the scanning speed was increased from 200 to 800 mm/s, the decreasing speeds of melt depth and melt width were significantly accelerated, while the decreasing speeds of overlapping ratio were relatively slow. When the scanning speed was further increased to 1600 mm/s, the decreasing speeds of melt depth and melt width were further accelerated, and the un-lapped condition of the melt channel also appeared. In addition, the contact angle increases and then decreases with the scanning speed, and both are lower than 33°. Therefore, when selecting the scanning speed, it is necessary to make reasonable trade-offs according to the specific situation, and take into account the factors of melt depth, melt width, melt height, remolten region, and overlapping ratio, in order to achieve the best processing results.

TABLE III.

Double-track molten pool characterization information at different scanning speeds.

Scanning speed (mm/s)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
200 55/68 182 19/32 124 203.33 22 
1600 13 50 11 −16.67 31 

3. Hatch spacing

Figure 18 shows the effect of different hatch spacing on the morphology and temperature field of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. The surface morphology and temperature field of the first track and second track are basically the same, but slightly different. The first track shows a basically symmetric morphology along the scanning direction, while the second track shows a slight offset due to the difference in the heat transfer rate between the solidified material and the powder particles. When the hatch spacing is too small, the overlapping ratio increases and the probability of defects caused by remelting phenomenon grows. When the hatch spacing is too large, the neighboring melt track cannot overlap properly, and the powder particles are not completely melted, leading to an increase in the number of holes. In conclusion, the ratio of the line energy density � to the hatch spacing (the volume energy density E) has a significant effect on the temperature field and surface morphology of the molten pool.

FIG. 18.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different hatch spacings: (a) H = 0.03 mm, (b) H = 0.12 mm.

Table IV shows the effects of different hatch spacing on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. It can be seen that the hatch spacing has little effect on the melt depth, melt width, and melt height, but has some effect on the remolten region. With the gradual expansion of hatch spacing, the remolten region shows a gradual decrease. At the same time, the overlapping ratio also decreased with the increase in hatch spacing. In addition, it is observed that the contact angle shows a tendency to increase and then remain stable when the hatch spacing increases, which has a more limited effect on it. Therefore, trade-offs and decisions need to be made on a case-by-case basis when selecting the hatch spacing.

TABLE IV.

Double-track molten pool characterization information at different hatch spacings.

Hatch spacing (mm)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
0.03 25/27 82 14 59 173.33 30 
0.12 26 78 14 −35 33 

In summary, the laser power, scanning speed, and hatch spacing have a significant effect on the formation of the molten pool, and the correct selection of these three process parameters is crucial to ensure the forming quality. In addition, the melt depth of the second track is slightly larger than that of the first track at higher line energy density � and volume energy density E. This is mainly due to the fact that a large amount of heat accumulation is generated after the first track, forming a larger molten pool volume, which leads to an increase in the melt depth.

D. Simulation analysis of molten pool with powder particle size and laser focal spot diameter

Figure 19 demonstrates the effect of different powder particle sizes and laser focal spot diameters on the morphology and temperature field of the double-track molten pool under a laser power of 100 W, a scanning speed of 800 mm/s, and a hatch spacing of 0.06 mm. In the process of melting coarse powder with small laser focal spot diameter, the laser energy cannot completely melt the larger powder particles, resulting in their partial melting and further generating excessive pore defects. The larger powder particles tend to generate zigzag molten pool edges, which cause an increase in the roughness of the melt track surface. In addition, the molten pool is also prone to generate the present spatter phenomenon, which can directly affect the quality of forming. The volume of the formed molten pool is relatively small, while the melt depth, melt width, and melt height are all smaller relative to the fine powder in Fig. 19(a). In the process of melting fine powders with a large laser focal spot diameter, the laser energy is able to melt the fine powder particles sufficiently, even to the point of overmelting. This results in a large number of fine spatters being generated at the edge of the molten pool, which causes porosity defects in the melt track in Fig. 19(b). In addition, the maximum velocity of the molten pool is larger for large powder particle sizes compared to small powder particle sizes, which indicates that the temperature gradient in the molten pool is larger for large powder particle sizes and the melt motion is more intense. However, the size of the laser focal spot diameter has a relatively small effect on the melt motion. However, a larger focal spot diameter induces a larger melt volume with greater depth, width, and height. In conclusion, a small powder size helps to reduce the surface roughness of the specimen, and a small laser spot diameter reduces the minimum forming size of a single track.

FIG. 19.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool with different powder particle size and laser focal spot diameter: (a) focal spot = 25 μm, coarse powder, (b) focal spot = 80 μm, fine powder.

Table V shows the maximum temperature gradient at the reference point for different powder sizes and laser focal spot diameters. As can be seen from the table, the maximum temperature gradient is lower than that of HP-LPBF for both coarse powders with a small laser spot diameter and fine powders with a large spot diameter, a phenomenon that leads to an increase in the heat transfer rate of HP-LPBF, which in turn leads to a corresponding increase in the cooling rate and, ultimately, to the formation of finer microstructures.

TABLE V.

Maximum temperature gradient at the reference point for different powder particle sizes and laser focal spot diameters.

Laser power (W)Scanning speed (mm/s)Hatch spacing (mm)Average powder size (μm)Laser focal spot diameter (μm)Maximum temperature gradient (×107 K/s)
100 800 0.06 31.7 25 7.89 
11.5 80 7.11 

IV. CONCLUSIONS

In this study, the geometrical characteristics of 3D coarse and fine powder particles were first calculated using DEM and then numerical simulations of single track and double track in the process of forming SS316L from monolayer HP-LPBF at mesoscopic scale were developed using CFD method. The effects of Marangoni convection, surface tension, recoil pressure, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool were considered in this model. The effects of laser power, scanning speed, and hatch spacing on the dynamics of the single-track and double-track molten pools, as well as on other characteristic information, were investigated. The effects of the powder particle size on the molten pool were investigated comparatively with the laser focal spot diameter. The main conclusions are as follows:

  1. The results show that the temperature gradient at the front of the molten pool is significantly larger than that at the tail, and the molten pool exhibits a “comet” morphology. At the top of the molten pool, there is a slightly concave region, which is the result of the coupling of Marangoni convection, recoil pressure, and surface tension. The melt flow forms two closed loops, which are mainly influenced by temperature gradients and surface tension. This special dynamic behavior of the melt tends to form an “elliptical” molten pool and an almost “mountain” shape in single-track forming.
  2. The basic characteristics of the three-dimensional morphology and temperature field of the second track are similar to those of the first track, but there are subtle differences. The first track exhibits a basically symmetrical shape; however, due to the difference in thermal diffusion rates between the solidified metal and the powder, a slight asymmetry in the molten pool morphology of the second track occurs. After forming through the first track, there is a significant heat buildup in the powder bed, resulting in a longer dynamic time of the melt, which increases the life of the molten pool. The heights of the first track and second track remained essentially the same, but the depth of the second track was greater relative to the first track. In addition, the maximum temperature gradient was 1.69 × 108 K/s during HP-LPBF forming.
  3. At low laser power, the surface tension in the molten pool plays a dominant role. At high laser power, recoil pressure becomes the main influencing factor. With the increase of laser power, the effective heat transfer in the vertical direction is superior to that in the horizontal direction. With the gradual increase of scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. In addition, the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. Too large or too small hatch spacing will lead to remelting or non-lap phenomenon, which in turn causes the formation of defects.
  4. When using a small laser focal spot diameter, it is difficult to completely melt large powder particle sizes, resulting in partial melting and excessive porosity generation. At the same time, large powder particles produce curved edges of the molten pool, resulting in increased surface roughness of the melt track. In addition, spatter occurs, which directly affects the forming quality. At small focal spot diameters, the molten pool volume is relatively small, and the melt depth, the melt width, and the melt height are correspondingly small. Taken together, the small powder particle size helps to reduce surface roughness, while the small spot diameter reduces the forming size.

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Lab-on-a-Chip 시스템의 혈류 역학에 대한 검토: 엔지니어링 관점

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

  • Bin-Jie Lai
  • Li-Tao Zhu
  • Zhe Chen*
  • Bo Ouyang*
  • , and 
  • Zheng-Hong Luo*

Abstract

다양한 수송 메커니즘 하에서, “LOC(lab-on-a-chip)” 시스템에서 유동 전단 속도 조건과 밀접한 관련이 있는 혈류 역학은 다양한 수송 현상을 초래하는 것으로 밝혀졌습니다.

본 연구는 적혈구의 동적 혈액 점도 및 탄성 거동과 같은 점탄성 특성의 역할을 통해 LOC 시스템의 혈류 패턴을 조사합니다. 모세관 및 전기삼투압의 주요 매개변수를 통해 LOC 시스템의 혈액 수송 현상에 대한 연구는 실험적, 이론적 및 수많은 수치적 접근 방식을 통해 제공됩니다.

전기 삼투압 점탄성 흐름에 의해 유발되는 교란은 특히 향후 연구 기회를 위해 혈액 및 기타 점탄성 유체를 취급하는 LOC 장치의 혼합 및 분리 기능 향상에 논의되고 적용됩니다. 또한, 본 연구는 보다 정확하고 단순화된 혈류 모델에 대한 요구와 전기역학 효과 하에서 점탄성 유체 흐름에 대한 수치 연구에 대한 강조와 같은 LOC 시스템 하에서 혈류 역학의 수치 모델링의 문제를 식별합니다.

전기역학 현상을 연구하는 동안 제타 전위 조건에 대한 보다 실용적인 가정도 강조됩니다. 본 연구는 모세관 및 전기삼투압에 의해 구동되는 미세유체 시스템의 혈류 역학에 대한 포괄적이고 학제적인 관점을 제공하는 것을 목표로 한다.

KEYWORDS: 

1. Introduction

1.1. Microfluidic Flow in Lab-on-a-Chip (LOC) Systems

Over the past several decades, the ability to control and utilize fluid flow patterns at microscales has gained considerable interest across a myriad of scientific and engineering disciplines, leading to growing interest in scientific research of microfluidics. 

(1) Microfluidics, an interdisciplinary field that straddles physics, engineering, and biotechnology, is dedicated to the behavior, precise control, and manipulation of fluids geometrically constrained to a small, typically submillimeter, scale. 

(2) The engineering community has increasingly focused on microfluidics, exploring different driving forces to enhance working fluid transport, with the aim of accurately and efficiently describing, controlling, designing, and applying microfluidic flow principles and transport phenomena, particularly for miniaturized applications. 

(3) This attention has chiefly been fueled by the potential to revolutionize diagnostic and therapeutic techniques in the biomedical and pharmaceutical sectorsUnder various driving forces in microfluidic flows, intriguing transport phenomena have bolstered confidence in sustainable and efficient applications in fields such as pharmaceutical, biochemical, and environmental science. The “lab-on-a-chip” (LOC) system harnesses microfluidic flow to enable fluid processing and the execution of laboratory tasks on a chip-sized scale. LOC systems have played a vital role in the miniaturization of laboratory operations such as mixing, chemical reaction, separation, flow control, and detection on small devices, where a wide variety of fluids is adapted. Biological fluid flow like blood and other viscoelastic fluids are notably studied among the many working fluids commonly utilized by LOC systems, owing to the optimization in small fluid sample volumed, rapid response times, precise control, and easy manipulation of flow patterns offered by the system under various driving forces. 

(4)The driving forces in blood flow can be categorized as passive or active transport mechanisms and, in some cases, both. Under various transport mechanisms, the unique design of microchannels enables different functionalities in driving, mixing, separating, and diagnosing blood and drug delivery in the blood. 

(5) Understanding and manipulating these driving forces are crucial for optimizing the performance of a LOC system. Such knowledge presents the opportunity to achieve higher efficiency and reliability in addressing cellular level challenges in medical diagnostics, forensic studies, cancer detection, and other fundamental research areas, for applications of point-of-care (POC) devices. 

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

Different transport mechanisms exhibit unique properties at submillimeter length scales in microfluidic devices, leading to significant transport phenomena that differ from those of macroscale flows. An in-depth understanding of these unique transport phenomena under microfluidic systems is often required in fluidic mechanics to fully harness the potential functionality of a LOC system to obtain systematically designed and precisely controlled transport of microfluids under their respective driving force. Fluid mechanics is considered a vital component in chemical engineering, enabling the analysis of fluid behaviors in various unit designs, ranging from large-scale reactors to separation units. Transport phenomena in fluid mechanics provide a conceptual framework for analytically and descriptively explaining why and how experimental results and physiological phenomena occur. The Navier–Stokes (N–S) equation, along with other governing equations, is often adapted to accurately describe fluid dynamics by accounting for pressure, surface properties, velocity, and temperature variations over space and time. In addition, limiting factors and nonidealities for these governing equations should be considered to impose corrections for empirical consistency before physical models are assembled for more accurate controls and efficiency. Microfluidic flow systems often deviate from ideal conditions, requiring adjustments to the standard governing equations. These deviations could arise from factors such as viscous effects, surface interactions, and non-Newtonian fluid properties from different microfluid types and geometrical layouts of microchannels. Addressing these nonidealities supports the refining of theoretical models and prediction accuracy for microfluidic flow behaviors.

The analytical calculation of coupled nonlinear governing equations, which describes the material and energy balances of systems under ideal conditions, often requires considerable computational efforts. However, advancements in computation capabilities, cost reduction, and improved accuracy have made numerical simulations using different numerical and modeling methods a powerful tool for effectively solving these complex coupled equations and modeling various transport phenomena. Computational fluid dynamics (CFD) is a numerical technique used to investigate the spatial and temporal distribution of various flow parameters. It serves as a critical approach to provide insights and reasoning for decision-making regarding the optimal designs involving fluid dynamics, even prior to complex physical model prototyping and experimental procedures. The integration of experimental data, theoretical analysis, and reliable numerical simulations from CFD enables systematic variation of analytical parameters through quantitative analysis, where adjustment to delivery of blood flow and other working fluids in LOC systems can be achieved.

Numerical methods such as the Finite-Difference Method (FDM), Finite-Element-Method (FEM), and Finite-Volume Method (FVM) are heavily employed in CFD and offer diverse approaches to achieve discretization of Eulerian flow equations through filling a mesh of the flow domain. A more in-depth review of numerical methods in CFD and its application for blood flow simulation is provided in Section 2.2.2.

1.3. Scope of the Review

In this Review, we explore and characterize the blood flow phenomena within the LOC systems, utilizing both physiological and engineering modeling approaches. Similar approaches will be taken to discuss capillary-driven flow and electric-osmotic flow (EOF) under electrokinetic phenomena as a passive and active transport scheme, respectively, for blood transport in LOC systems. Such an analysis aims to bridge the gap between physical (experimental) and engineering (analytical) perspectives in studying and manipulating blood flow delivery by different driving forces in LOC systems. Moreover, the Review hopes to benefit the interests of not only blood flow control in LOC devices but also the transport of viscoelastic fluids, which are less studied in the literature compared to that of Newtonian fluids, in LOC systems.

Section 2 examines the complex interplay between viscoelastic properties of blood and blood flow patterns under shear flow in LOC systems, while engineering numerical modeling approaches for blood flow are presented for assistance. Sections 3 and 4 look into the theoretical principles, numerical governing equations, and modeling methodologies for capillary driven flow and EOF in LOC systems as well as their impact on blood flow dynamics through the quantification of key parameters of the two driving forces. Section 5 concludes the characterized blood flow transport processes in LOC systems under these two forces. Additionally, prospective areas of research in improving the functionality of LOC devices employing blood and other viscoelastic fluids and potentially justifying mechanisms underlying microfluidic flow patterns outside of LOC systems are presented. Finally, the challenges encountered in the numerical studies of blood flow under LOC systems are acknowledged, paving the way for further research.

2. Blood Flow Phenomena

ARTICLE SECTIONS

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2.1. Physiological Blood Flow Behavior

Blood, an essential physiological fluid in the human body, serves the vital role of transporting oxygen and nutrients throughout the body. Additionally, blood is responsible for suspending various blood cells including erythrocytes (red blood cells or RBCs), leukocytes (white blood cells), and thrombocytes (blood platelets) in a plasma medium.Among the cells mentioned above, red blood cells (RBCs) comprise approximately 40–45% of the volume of healthy blood. 

(7) An RBC possesses an inherent elastic property with a biconcave shape of an average diameter of 8 μm and a thickness of 2 μm. This biconcave shape maximizes the surface-to-volume ratio, allowing RBCs to endure significant distortion while maintaining their functionality. 

(8,9) Additionally, the biconcave shape optimizes gas exchange, facilitating efficient uptake of oxygen due to the increased surface area. The inherent elasticity of RBCs allows them to undergo substantial distortion from their original biconcave shape and exhibits high flexibility, particularly in narrow channels.RBC deformability enables the cell to deform from a biconcave shape to a parachute-like configuration, despite minor differences in RBC shape dynamics under shear flow between initial cell locations. As shown in Figure 1(a), RBCs initiating with different resting shapes and orientations displaying display a similar deformation pattern 

(10) in terms of its shape. Shear flow induces an inward bending of the cell at the rear position of the rim to the final bending position, 

(11) resulting in an alignment toward the same position of the flow direction.

Figure 1. Images of varying deformation of RBCs and different dynamic blood flow behaviors. (a) The deforming shape behavior of RBCs at four different initiating positions under the same experimental conditions of a flow from left to right, (10) (b) RBC aggregation, (13) (c) CFL region. (18) Reproduced with permission from ref (10). Copyright 2011 Elsevier. Reproduced with permission from ref (13). Copyright 2022 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/. Reproduced with permission from ref (18). Copyright 2019 Elsevier.

The flexible property of RBCs enables them to navigate through narrow capillaries and traverse a complex network of blood vessels. The deformability of RBCs depends on various factors, including the channel geometry, RBC concentration, and the elastic properties of the RBC membrane. 

(12) Both flexibility and deformability are vital in the process of oxygen exchange among blood and tissues throughout the body, allowing cells to flow in vessels even smaller than the original cell size prior to deforming.As RBCs serve as major components in blood, their collective dynamics also hugely affect blood rheology. RBCs exhibit an aggregation phenomenon due to cell to cell interactions, such as adhesion forces, among populated cells, inducing unique blood flow patterns and rheological behaviors in microfluidic systems. For blood flow in large vessels between a diameter of 1 and 3 cm, where shear rates are not high, a constant viscosity and Newtonian behavior for blood can be assumed. However, under low shear rate conditions (0.1 s

–1) in smaller vessels such as the arteries and venules, which are within a diameter of 0.2 mm to 1 cm, blood exhibits non-Newtonian properties, such as shear-thinning viscosity and viscoelasticity due to RBC aggregation and deformability. The nonlinear viscoelastic property of blood gives rise to a complex relationship between viscosity and shear rate, primarily influenced by the highly elastic behavior of RBCs. A wide range of research on the transient behavior of the RBC shape and aggregation characteristics under varied flow circumstances has been conducted, aiming to obtain a better understanding of the interaction between blood flow shear forces from confined flows.

For a better understanding of the unique blood flow structures and rheological behaviors in microfluidic systems, some blood flow patterns are introduced in the following section.

2.1.1. RBC Aggregation

RBC aggregation is a vital phenomenon to be considered when designing LOC devices due to its impact on the viscosity of the bulk flow. Under conditions of low shear rate, such as in stagnant or low flow rate regions, RBCs tend to aggregate, forming structures known as rouleaux, resembling stacks of coins as shown in Figure 1(b). 

(13) The aggregation of RBCs increases the viscosity at the aggregated region, 

(14) hence slowing down the overall blood flow. However, when exposed to high shear rates, RBC aggregates disaggregate. As shear rates continue to increase, RBCs tend to deform, elongating and aligning themselves with the direction of the flow. 

(15) Such a dynamic shift in behavior from the cells in response to the shear rate forms the basis of the viscoelastic properties observed in whole blood. In essence, the viscosity of the blood varies according to the shear rate conditions, which are related to the velocity gradient of the system. It is significant to take the intricate relationship between shear rate conditions and the change of blood viscosity due to RBC aggregation into account since various flow driving conditions may induce varied effects on the degree of aggregation.

2.1.2. Fåhræus-Lindqvist Effect

The Fåhræus–Lindqvist (FL) effect describes the gradual decrease in the apparent viscosity of blood as the channel diameter decreases. 

(16) This effect is attributed to the migration of RBCs toward the central region in the microchannel, where the flow rate is higher, due to the presence of higher pressure and asymmetric distribution of shear forces. This migration of RBCs, typically observed at blood vessels less than 0.3 mm, toward the higher flow rate region contributes to the change in blood viscosity, which becomes dependent on the channel size. Simultaneously, the increase of the RBC concentration in the central region of the microchannel results in the formation of a less viscous region close to the microchannel wall. This region called the Cell-Free Layer (CFL), is primarily composed of plasma. 

(17) The combination of the FL effect and the following CFL formation provides a unique phenomenon that is often utilized in passive and active plasma separation mechanisms, involving branched and constriction channels for various applications in plasma separation using microfluidic systems.

2.1.3. Cell-Free Layer Formation

In microfluidic blood flow, RBCs form aggregates at the microchannel core and result in a region that is mostly devoid of RBCs near the microchannel walls, as shown in Figure 1(c). 

(18) The region is known as the cell-free layer (CFL). The CFL region is often known to possess a lower viscosity compared to other regions within the blood flow due to the lower viscosity value of plasma when compared to that of the aggregated RBCs. Therefore, a thicker CFL region composed of plasma correlates to a reduced apparent whole blood viscosity. 

(19) A thicker CFL region is often established following the RBC aggregation at the microchannel core under conditions of decreasing the tube diameter. Apart from the dependence on the RBC concentration in the microchannel core, the CFL thickness is also affected by the volume concentration of RBCs, or hematocrit, in whole blood, as well as the deformability of RBCs. Given the influence CFL thickness has on blood flow rheological parameters such as blood flow rate, which is strongly dependent on whole blood viscosity, investigating CFL thickness under shear flow is crucial for LOC systems accounting for blood flow.

2.1.4. Plasma Skimming in Bifurcation Networks

The uneven arrangement of RBCs in bifurcating microchannels, commonly termed skimming bifurcation, arises from the axial migration of RBCs within flowing streams. This uneven distribution contributes to variations in viscosity across differing sizes of bifurcating channels but offers a stabilizing effect. Notably, higher flow rates in microchannels are associated with increased hematocrit levels, resulting in higher viscosity compared with those with lower flow rates. Parametric investigations on bifurcation angle, 

(20) thickness of the CFL, 

(21) and RBC dynamics, including aggregation and deformation, 

(22) may alter the varying viscosity of blood and its flow behavior within microchannels.

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

Under different shear rate conditions in blood flow, the elastic characteristics and dynamic changes of the RBC induce a complex velocity and stress relationship, resulting in the incompatibility of blood flow characterization through standard presumptions of constant viscosity used for Newtonian fluid flow. Blood flow is categorized as a viscoelastic non-Newtonian fluid flow where constitutive equations governing this type of flow take into consideration the nonlinear viscometric properties of blood. To mathematically characterize the evolving blood viscosity and the relationship between the elasticity of RBC and the shear blood flow, respectively, across space and time of the system, a stress tensor (τ) defined by constitutive models is often coupled in the Navier–Stokes equation to account for the collective impact of the constant dynamic viscosity (η) and the elasticity from RBCs on blood flow.The dynamic viscosity of blood is heavily dependent on the shear stress applied to the cell and various parameters from the blood such as hematocrit value, plasma viscosity, mechanical properties of the RBC membrane, and red blood cell aggregation rate. The apparent blood viscosity is considered convenient for the characterization of the relationship between the evolving blood viscosity and shear rate, which can be defined by Casson’s law, as shown in eq 1.

𝜇=𝜏0𝛾˙+2𝜂𝜏0𝛾˙⎯⎯⎯⎯⎯⎯⎯√+𝜂�=�0�˙+2��0�˙+�

(1)where τ

0 is the yield stress–stress required to initiate blood flow motion, η is the Casson rheological constant, and γ̇ is the shear rate. The value of Casson’s law parameters under blood with normal hematocrit level can be defined as τ

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

(23) With the known property of blood and Casson’s law parameters, an approximation can be made to the dynamic viscosity under various flow condition domains. The Power Law model is often employed to characterize the dynamic viscosity in relation to the shear rate, since precise solutions exist for specific geometries and flow circumstances, acting as a fundamental standard for definition. The Carreau and Carreau–Yasuda models can be advantageous over the Power Law model due to their ability to evaluate the dynamic viscosity at low to zero shear rate conditions. However, none of the above-mentioned models consider the memory or other elastic behavior of blood and its RBCs. Some other commonly used mathematical models and their constants for the non-Newtonian viscosity property characterization of blood are listed in Table 1 below. 

(24−26)Table 1. Comparison of Various Non-Newtonian Models for Blood Viscosity 

(24−26)

ModelNon-Newtonian ViscosityParameters
Power Law(2)n = 0.61, k = 0.42
Carreau(3)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 3.1736 s, m = 2.406, a = 0.254
Walburn–Schneck(4)C1 = 0.000797 Pa·s, C2 = 0.0608 Pa·s, C3 = 0.00499, C4 = 14.585 g–1, TPMA = 25 g/L
Carreau–Yasuda(5)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 1.902 s, n = 0.22, a = 1.25
Quemada(6)μp = 0.0012 Pa·s, k = 2.07, k0 = 4.33, γ̇c = 1.88 s–1

The blood rheology is commonly known to be influenced by two key physiological factors, namely, the hematocrit value (H

t) and the fibrinogen concentration (c

f), with an average value of 42% and 0.252 gd·L

–1, respectively. Particularly in low shear conditions, the presence of varying fibrinogen concentrations affects the tendency for aggregation and rouleaux formation, while the occurrence of aggregation is contingent upon specific levels of hematocrit. 

(27) The study from Apostolidis et al. 

(28) modifies the Casson model through emphasizing its reliance on hematocrit and fibrinogen concentration parameter values, owing to the extensive knowledge of the two physiological blood parameters.The viscoelastic response of blood is heavily dependent on the elasticity of the RBC, which is defined by the relationship between the deformation and stress relaxation from RBCs under a specific location of shear flow as a function of the velocity field. The stress tensor is usually characterized by constitutive equations such as the Upper-Convected Maxwell Model 

(29) and the Oldroyd-B model 

(30) to track the molecule effects under shear from different driving forces. The prominent non-Newtonian features, such as shear thinning and yield stress, have played a vital role in the characterization of blood rheology, particularly with respect to the evaluation of yield stress under low shear conditions. The nature of stress measurement in blood, typically on the order of 1 mPa, is challenging due to its low magnitude. The occurrence of the CFL complicates the measurement further due to the significant decrease in apparent viscosity near the wall over time and a consequential disparity in viscosity compared to the bulk region.In addition to shear thinning viscosity and yield stress, the formation of aggregation (rouleaux) from RBCs under low shear rates also contributes to the viscoelasticity under transient flow 

(31) and thixotropy 

(32) of whole blood. Given the difficulty in evaluating viscoelastic behavior of blood under low strain magnitudes and limitations in generalized Newtonian models, the utilization of viscoelastic models is advocated to encompass elasticity and delineate non-shear components within the stress tensor. Extending from the Oldroyd-B model, Anand et al. 

(33) developed a viscoelastic model framework for adapting elasticity within blood samples and predicting non-shear stress components. However, to also address the thixotropic effects, the model developed by Horner et al. 

(34) serves as a more comprehensive approach than the viscoelastic model from Anand et al. Thixotropy 

(32) typically occurs from the structural change of the rouleaux, where low shear rate conditions induce rouleaux formation. Correspondingly, elasticity increases, while elasticity is more representative of the isolated RBCs, under high shear rate conditions. The model of Horner et al. 

(34) considers the contribution of rouleaux to shear stress, taking into account factors such as the characteristic time for Brownian aggregation, shear-induced aggregation, and shear-induced breakage. Subsequent advancements in the model from Horner et al. often revolve around refining the three aforementioned key terms for a more substantial characterization of rouleaux dynamics. Notably, this has led to the recently developed mHAWB model 

(35) and other model iterations to enhance the accuracy of elastic and viscoelastic contributions to blood rheology, including the recently improved model suggested by Armstrong et al. 

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

Numerical simulation has become increasingly more significant in analyzing the geometry, boundary layers of flow, and nonlinearity of hyperbolic viscoelastic flow constitutive equations. CFD is a powerful and efficient tool utilizing numerical methods to solve the governing hydrodynamic equations, such as the Navier–Stokes (N–S) equation, continuity equation, and energy conservation equation, for qualitative evaluation of fluid motion dynamics under different parameters. CFD overcomes the challenge of analytically solving nonlinear forms of differential equations by employing numerical methods such as the Finite-Difference Method (FDM), Finite-Element Method (FEM), and Finite-Volume Method (FVM) to discretize and solve the partial differential equations (PDEs), allowing for qualitative reproduction of transport phenomena and experimental observations. Different numerical methods are chosen to cope with various transport systems for optimization of the accuracy of the result and control of error during the discretization process.FDM is a straightforward approach to discretizing PDEs, replacing the continuum representation of equations with a set of finite-difference equations, which is typically applied to structured grids for efficient implementation in CFD programs. 

(37) However, FDM is often limited to simple geometries such as rectangular or block-shaped geometries and struggles with curved boundaries. In contrast, FEM divides the fluid domain into small finite grids or elements, approximating PDEs through a local description of physics. 

(38) All elements contribute to a large, sparse matrix solver. However, FEM may not always provide accurate results for systems involving significant deformation and aggregation of particles like RBCs due to large distortion of grids. 

(39) FVM evaluates PDEs following the conservation laws and discretizes the selected flow domain into small but finite size control volumes, with each grid at the center of a finite volume. 

(40) The divergence theorem allows the conversion of volume integrals of PDEs with divergence terms into surface integrals of surface fluxes across cell boundaries. Due to its conservation property, FVM offers efficient outcomes when dealing with PDEs that embody mass, momentum, and energy conservation principles. Furthermore, widely accessible software packages like the OpenFOAM toolbox 

(41) include a viscoelastic solver, making it an attractive option for viscoelastic fluid flow modeling. 

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

The complexity in the blood flow simulation arises from deformability and aggregation that RBCs exhibit during their interaction with neighboring cells under different shear rate conditions induced by blood flow. Numerical models coupled with simulation programs have been applied as a groundbreaking method to predict such unique rheological behavior exhibited by RBCs and whole blood. The conventional approach of a single-phase flow simulation is often applied to blood flow simulations within large vessels possessing a moderate shear rate. However, such a method assumes the properties of plasma, RBCs and other cellular components to be evenly distributed as average density and viscosity in blood, resulting in the inability to simulate the mechanical dynamics, such as RBC aggregation under high-shear flow field, inherent in RBCs. To accurately describe the asymmetric distribution of RBC and blood flow, multiphase flow simulation, where numerical simulations of blood flows are often modeled as two immiscible phases, RBCs and blood plasma, is proposed. A common assumption is that RBCs exhibit non-Newtonian behavior while the plasma is treated as a continuous Newtonian phase.Numerous multiphase numerical models have been proposed to simulate the influence of RBCs on blood flow dynamics by different assumptions. In large-scale simulations (above the millimeter range), continuum-based methods are wildly used due to their lower computational demands. 

(43) Eulerian multiphase flow simulations offer the solution of a set of conservation equations for each separate phase and couple the phases through common pressure and interphase exchange coefficients. Xu et al. 

(44) utilized the combined finite-discrete element method (FDEM) to replicate the dynamic behavior and distortion of RBCs subjected to fluidic forces, utilizing the Johnson–Kendall–Roberts model 

(45) to define the adhesive forces of cell-to-cell interactions. The iterative direct-forcing immersed boundary method (IBM) is commonly employed in simulations of the fluid–cell interface of blood. This method effectively captures the intricacies of the thin and flexible RBC membranes within various external flow fields. 

(46) The study by Xu et al. 

(44) also adopts this approach to bridge the fluid dynamics and RBC deformation through IBM. Yoon and You utilized the Maxwell model to define the viscosity of the RBC membrane. 

(47) It was discovered that the Maxwell model could represent the stress relaxation and unloading processes of the cell. Furthermore, the reduced flexibility of an RBC under particular situations such as infection is specified, which was unattainable by the Kelvin–Voigt model 

(48) when compared to the Maxwell model in the literature. The Yeoh hyperplastic material model was also adapted to predict the nonlinear elasticity property of RBCs with FEM employed to discretize the RBC membrane using shell-type elements. Gracka et al. 

(49) developed a numerical CFD model with a finite-volume parallel solver for multiphase blood flow simulation, where an updated Maxwell viscoelasticity model and a Discrete Phase Model are adopted. In the study, the adapted IBM, based on unstructured grids, simulates the flow behavior and shape change of the RBCs through fluid-structure coupling. It was found that the hybrid Euler–Lagrange (E–L) approach 

(50) for the development of the multiphase model offered better results in the simulated CFL region in the microchannels.To study the dynamics of individual behaviors of RBCs and the consequent non-Newtonian blood flow, cell-shape-resolved computational models are often adapted. The use of the boundary integral method has become prevalent in minimizing computational expenses, particularly in the exclusive determination of fluid velocity on the surfaces of RBCs, incorporating the option of employing IBM or particle-based techniques. The cell-shaped-resolved method has enabled an examination of cell to cell interactions within complex ambient or pulsatile flow conditions 

(51) surrounding RBC membranes. Recently, Rydquist et al. 

(52) have looked to integrate statistical information from macroscale simulations to obtain a comprehensive overview of RBC behavior within the immediate proximity of the flow through introduction of respective models characterizing membrane shape definition, tension, bending stresses of RBC membranes.At a macroscopic scale, continuum models have conventionally been adapted for assessing blood flow dynamics through the application of elasticity theory and fluid dynamics. However, particle-based methods are known for their simplicity and adaptability in modeling complex multiscale fluid structures. Meshless methods, such as the boundary element method (BEM), smoothed particle hydrodynamics (SPH), and dissipative particle dynamics (DPD), are often used in particle-based characterization of RBCs and the surrounding fluid. By representing the fluid as discrete particles, meshless methods provide insights into the status and movement of the multiphase fluid. These methods allow for the investigation of cellular structures and microscopic interactions that affect blood rheology. Non-confronting mesh methods like IBM can also be used to couple a fluid solver such as FEM, FVM, or the Lattice Boltzmann Method (LBM) through membrane representation of RBCs. In comparison to conventional CFD methods, LBM has been viewed as a favorable numerical approach for solving the N–S equations and the simulation of multiphase flows. LBM exhibits the notable advantage of being amenable to high-performance parallel computing environments due to its inherently local dynamics. In contrast to DPD and SPH where RBC membranes are modeled as physically interconnected particles, LBM employs the IBM to account for the deformation dynamics of RBCs 

(53,54) under shear flows in complex channel geometries. 

(54,55) However, it is essential to acknowledge that the utilization of LBM in simulating RBC flows often entails a significant computational overhead, being a primary challenge in this context. Krüger et al. 

(56) proposed utilizing LBM as a fluid solver, IBM to couple the fluid and FEM to compute the response of membranes to deformation under immersed fluids. This approach decouples the fluid and membranes but necessitates significant computational effort due to the requirements of both meshes and particles.Despite the accuracy of current blood flow models, simulating complex conditions remains challenging because of the high computational load and cost. Balachandran Nair et al. 

(57) suggested a reduced order model of RBC under the framework of DEM, where the RBC is represented by overlapping constituent rigid spheres. The Morse potential force is adapted to account for the RBC aggregation exhibited by cell to cell interactions among RBCs at different distances. Based upon the IBM, the reduced-order RBC model is adapted to simulate blood flow transport for validation under both single and multiple RBCs with a resolved CFD-DEM solver. 

(58) In the resolved CFD-DEM model, particle sizes are larger than the grid size for a more accurate computation of the surrounding flow field. A continuous forcing approach is taken to describe the momentum source of the governing equation prior to discretization, which is different from a Direct Forcing Method (DFM). 

(59) As no body-conforming moving mesh is required, the continuous forcing approach offers lower complexity and reduced cost when compared to the DFM. Piquet et al. 

(60) highlighted the high complexity of the DFM due to its reliance on calculating an additional immersed boundary flux for the velocity field to ensure its divergence-free condition.The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries 

(61,62) and capillaries, 

(63) where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.In general, three numerical methods are broadly used: mesh-based, particle-based, and hybrid mesh–particle techniques, based on the spatial scale and the fundamental numerical approach, mesh-based methods tend to neglect the effects of individual particles, assuming a continuum and being efficient in terms of time and cost. However, the particle-based approach highlights more of the microscopic and mesoscopic level, where the influence of individual RBCs is considered. A review from Freund et al. 

(64) addressed the three numerical methodologies and their respective modeling approaches of RBC dynamics. Given the complex mechanics and the diverse levels of study concerning numerical simulations of blood and cellular flow, a broad spectrum of numerical methods for blood has been subjected to extensive review. 

(64−70) Ye at al. 

(65) offered an extensive review of the application of the DPD, SPH, and LBM for numerical simulations of RBC, while Rathnayaka et al. 

(67) conducted a review of the particle-based numerical modeling for liquid marbles through drawing parallels to the transport of RBCs in microchannels. A comparative analysis between conventional CFD methods and particle-based approaches for cellular and blood flow dynamic simulation can be found under the review by Arabghahestani et al. 

(66) Literature by Li et al. 

(68) and Beris et al. 

(69) offer an overview of both continuum-based models at micro/macroscales and multiscale particle-based models encompassing various length and temporal dimensions. Furthermore, these reviews deliberate upon the potential of coupling continuum-particle methods for blood plasma and RBC modeling. Arciero et al. 

(70) investigated various modeling approaches encompassing cellular interactions, such as cell to cell or plasma interactions and the individual cellular phases. A concise overview of the reviews is provided in Table 2 for reference.

Table 2. List of Reviews for Numerical Approaches Employed in Blood Flow Simulation

ReferenceNumerical methods
Li et al. (2013) (68)Continuum-based modeling (BIM), particle-based modeling (LBM, LB-FE, SPH, DPD)
Freund (2014) (64)RBC dynamic modeling (continuum-based modeling, complementary discrete microstructure modeling), blood flow dynamic modeling (FDM, IBM, LBM, particle-mesh methods, coupled boundary integral and mesh-based methods, DPD)
Ye et al. (2016) (65)DPD, SPH, LBM, coupled IBM-Smoothed DPD
Arciero et al. (2017) (70)LBM, IBM, DPD, conventional CFD Methods (FDM, FVM, FEM)
Arabghahestani et al. (2019) (66)Particle-based methods (LBM, DPD, direct simulation Monte Carlo, molecular dynamics), SPH, conventional CFD methods (FDM, FVM, FEM)
Beris et al. (2021) (69)DPD, smoothed DPD, IBM, LBM, BIM
Rathnayaka (2022) (67)SPH, CG, LBM

3. Capillary Driven Blood Flow in LOC Systems

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3.1. Capillary Driven Flow Phenomena

Capillary driven (CD) flow is a pivotal mechanism in passive microfluidic flow systems 

(9) such as the blood circulation system and LOC systems. 

(71) CD flow is essentially the movement of a liquid to flow against drag forces, where the capillary effect exerts a force on the liquid at the borders, causing a liquid–air meniscus to flow despite gravity or other drag forces. A capillary pressure drops across the liquid–air interface with surface tension in the capillary radius and contact angle. The capillary effect depends heavily on the interaction between the different properties of surface materials. Different values of contact angles can be manipulated and obtained under varying levels of surface wettability treatments to manipulate the surface properties, resulting in different CD blood delivery rates for medical diagnostic device microchannels. CD flow techniques are appealing for many LOC devices, because they require no external energy. However, due to the passive property of liquid propulsion by capillary forces and the long-term instability of surface treatments on channel walls, the adaptability of CD flow in geometrically complex LOC devices may be limited.

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

The study of transport phenomena regarding either blood flow driven by capillary forces or externally applied forces under microfluid systems all demands a comprehensive recognition of the significant differences in flow dynamics between microscale and macroscale. The fundamental assumptions and principles behind fluid transport at the microscale are discussed in this section. Such a comprehension will lay the groundwork for the following analysis of the theoretical basis of capillary forces and their role in blood transport in LOC systems.

At the macroscale, fluid dynamics are often strongly influenced by gravity due to considerable fluid mass. However, the high surface to volume ratio at the microscale shifts the balance toward surface forces (e.g., surface tension and viscous forces), much larger than the inertial force. This difference gives rise to transport phenomena unique to microscale fluid transport, such as the prevalence of laminar flow due to a very low Reynolds number (generally lower than 1). Moreover, the fluid in a microfluidic system is often assumed to be incompressible due to the small flow velocity, indicating constant fluid density in both space and time.Microfluidic flow behaviors are governed by the fundamental principles of mass and momentum conservation, which are encapsulated in the continuity equation and the Navier–Stokes (N–S) equation. The continuity equation describes the conservation of mass, while the N–S equation captures the spatial and temporal variations in velocity, pressure, and other physical parameters. Under the assumption of the negligible influence of gravity in microfluidic systems, the continuity equation and the Eulerian representation of the incompressible N–S equation can be expressed as follows:

∇·𝐮⇀=0∇·�⇀=0

(7)

−∇𝑝+𝜇∇2𝐮⇀+∇·𝝉⇀−𝐅⇀=0−∇�+�∇2�⇀+∇·�⇀−�⇀=0

(8)Here, p is the pressure, u is the fluid viscosity, 

𝝉⇀�⇀ represents the stress tensor, and F is the body force exerted by external forces if present.

3.2.2. Theoretical Basis and Modeling of Capillary Force in LOC Systems

The capillary force is often the major driving force to manipulate and transport blood without an externally applied force in LOC systems. Forces induced by the capillary effect impact the free surface of fluids and are represented not directly in the Navier–Stokes equations but through the pressure boundary conditions of the pressure term p. For hydrophilic surfaces, the liquid generally induces a contact angle between 0° and 30°, encouraging the spread and attraction of fluid under a positive cos θ condition. For this condition, the pressure drop becomes positive and generates a spontaneous flow forward. A hydrophobic solid surface repels the fluid, inducing minimal contact. Generally, hydrophobic solids exhibit a contact angle larger than 90°, inducing a negative value of cos θ. Such a value will result in a negative pressure drop and a flow in the opposite direction. The induced contact angle is often utilized to measure the wall exposure of various surface treatments on channel walls where different wettability gradients and surface tension effects for CD flows are established. Contact angles between different interfaces are obtainable through standard values or experimental methods for reference. 

(72)For the characterization of the induced force by the capillary effect, the Young–Laplace (Y–L) equation 

(73) is widely employed. In the equation, the capillary is considered a pressure boundary condition between the two interphases. Through the Y–L equation, the capillary pressure force can be determined, and subsequently, the continuity and momentum balance equations can be solved to obtain the blood filling rate. Kim et al. 

(74) studied the effects of concentration and exposure time of a nonionic surfactant, Silwet L-77, on the performance of a polydimethylsiloxane (PDMS) microchannel in terms of plasma and blood self-separation. The study characterized the capillary pressure force by incorporating the Y–L equation and further evaluated the effects of the changing contact angle due to different levels of applied channel wall surface treatments. The expression of the Y–L equation utilized by Kim et al. 

(74) is as follows:

𝑃=−𝜎(cos𝜃b+cos𝜃tℎ+cos𝜃l+cos𝜃r𝑤)�=−�(cos⁡�b+cos⁡�tℎ+cos⁡�l+cos⁡�r�)

(9)where σ is the surface tension of the liquid and θ

bθ

tθ

l, and θ

r are the contact angle values between the liquid and the bottom, top, left, and right walls, respectively. A numerical simulation through Coventor software is performed to evaluate the dynamic changes in the filling rate within the microchannel. The simulation results for the blood filling rate in the microchannel are expressed at a specific time stamp, shown in Figure 2. The results portray an increasing instantaneous filling rate of blood in the microchannel following the decrease in contact angle induced by a higher concentration of the nonionic surfactant treated to the microchannel wall.

Figure 2. Numerical simulation of filling rate of capillary driven blood flow under various contact angle conditions at a specific timestamp. (74) Reproduced with permission from ref (74). Copyright 2010 Elsevier.

When in contact with hydrophilic or hydrophobic surfaces, blood forms a meniscus with a contact angle due to surface tension. The Lucas–Washburn (L–W) equation 

(75) is one of the pioneering theoretical definitions for the position of the meniscus over time. In addition, the L–W equation provides the possibility for research to obtain the velocity of the blood formed meniscus through the derivation of the meniscus position. The L–W equation 

(75) can be shown below:

𝐿(𝑡)=𝑅𝜎cos(𝜃)𝑡2𝜇⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�(�)=��⁡cos(�)�2�

(10)Here L(t) represents the distance of the liquid driven by the capillary forces. However, the generalized L–W equation solely assumes the constant physical properties from a Newtonian fluid rather than considering the non-Newtonian fluid behavior of blood. Cito et al. 

(76) constructed an enhanced version of the L–W equation incorporating the power law to consider the RBC aggregation and the FL effect. The non-Newtonian fluid apparent viscosity under the Power Law model is defined as

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

(11)where γ̇ is the strain rate tensor defined as 

𝛾˙=12𝛾˙𝑖𝑗𝛾˙𝑗𝑖⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�˙=12�˙���˙��. The stress tensor term τ is computed as τ = μγ̇

ij. The updated L–W equation by Cito 

(76) is expressed as

𝐿(𝑡)=𝑅[(𝑛+13𝑛+1)(𝜎cos(𝜃)𝑅𝑘)1/𝑛𝑡]𝑛/𝑛+1�(�)=�[(�+13�+1)(�⁡cos(�)��)1/��]�/�+1

(12)where k is the flow consistency index and n is the power law index, respectively. The power law index, from the Power Law model, characterizes the extent of the non-Newtonian behavior of blood. Both the consistency and power law index rely on blood properties such as hematocrit, the appearance of the FL effect, the formation of RBC aggregates, etc. The updated L–W equation computes the location and velocity of blood flow caused by capillary forces at specified time points within the LOC devices, taking into account the effects of blood flow characteristics such as RBC aggregation and the FL effect on dynamic blood viscosity.Apart from the blood flow behaviors triggered by inherent blood properties, unique flow conditions driven by capillary forces that are portrayed under different microchannel geometries also hold crucial implications for CD blood delivery. Berthier et al. 

(77) studied the spontaneous Concus–Finn condition, the condition to initiate the spontaneous capillary flow within a V-groove microchannel, as shown in Figure 3(a) both experimentally and numerically. Through experimental studies, the spontaneous Concus–Finn filament development of capillary driven blood flow is observed, as shown in Figure 3(b), while the dynamic development of blood flow is numerically simulated through CFD simulation.

Figure 3. (a) Sketch of the cross-section of Berthier’s V-groove microchannel, (b) experimental view of blood in the V-groove microchannel, (78) (c) illustration of the dynamic change of the extension of filament from FLOW 3D under capillary flow at three increasing time intervals. (78) Reproduced with permission from ref (78). Copyright 2014 Elsevier.

Berthier et al. 

(77) characterized the contact angle needed for the initiation of the capillary driving force at a zero-inlet pressure, through the half-angle (α) of the V-groove geometry layout, and its relation to the Concus–Finn filament as shown below:

𝜃<𝜋2−𝛼sin𝛼1+2(ℎ2/𝑤)sin𝛼<cos𝜃{�<�2−�sin⁡�1+2(ℎ2/�)⁡sin⁡�<cos⁡�

(13)Three possible regimes were concluded based on the contact angle value for the initiation of flow and development of Concus–Finn filament:

𝜃>𝜃1𝜃1>𝜃>𝜃0𝜃0no SCFSCF without a Concus−Finn filamentSCF without a Concus−Finn filament{�>�1no SCF�1>�>�0SCF without a Concus−Finn filament�0SCF without a Concus−Finn filament

(14)Under Newton’s Law, the force balance with low Reynolds and Capillary numbers results in the neglect of inertial terms. The force balance between the capillary forces and the viscous force induced by the channel wall is proposed to derive the analytical fluid velocity. This relation between the two forces offers insights into the average flow velocity and the penetration distance function dependent on time. The apparent blood viscosity is defined by Berthier et al. 

(78) through Casson’s law, 

(23) given in eq 1. The research used the FLOW-3D program from Flow Science Inc. software, which solves transient, free-surface problems using the FDM in multiple dimensions. The Volume of Fluid (VOF) method 

(79) is utilized to locate and track the dynamic extension of filament throughout the advancing interface within the channel ahead of the main flow at three progressing time stamps, as depicted in Figure 3(c).

4. Electro-osmotic Flow (EOF) in LOC Systems

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The utilization of external forces, such as electric fields, has significantly broadened the possibility of manipulating microfluidic flow in LOC systems. 

(80) Externally applied electric field forces induce a fluid flow from the movement of ions in fluid terms as the “electro-osmotic flow” (EOF).Unique transport phenomena, such as enhanced flow velocity and flow instability, induced by non-Newtonian fluids, particularly viscoelastic fluids, under EOF, have sparked considerable interest in microfluidic devices with simple or complicated geometries within channels. 

(81) However, compared to the study of Newtonian fluids and even other electro-osmotic viscoelastic fluid flows, the literature focusing on the theoretical and numerical modeling of electro-osmotic blood flow is limited due to the complexity of blood properties. Consequently, to obtain a more comprehensive understanding of the complex blood flow behavior under EOF, theoretical and numerical studies of the transport phenomena in the EOF section will be based on the studies of different viscoelastic fluids under EOF rather than that of blood specifically. Despite this limitation, we believe these studies offer valuable insights that can help understand the complex behavior of blood flow under EOF.

4.1. EOF Phenomena

Electro-osmotic flow occurs at the interface between the microchannel wall and bulk phase solution. When in contact with the bulk phase, solution ions are absorbed or dissociated at the solid–liquid interface, resulting in the formation of a charge layer, as shown in Figure 4. This charged channel surface wall interacts with both negative and positive ions in the bulk sample, causing repulsion and attraction forces to create a thin layer of immobilized counterions, known as the Stern layer. The induced electric potential from the wall gradually decreases with an increase in the distance from the wall. The Stern layer potential, commonly termed the zeta potential, controls the intensity of the electrostatic interactions between mobile counterions and, consequently, the drag force from the applied electric field. Next to the Stern layer is the diffuse mobile layer, mainly composed of a mobile counterion. These two layers constitute the “electrical double layer” (EDL), the thickness of which is directly proportional to the ionic strength (concentration) of the bulk fluid. The relationship between the two parameters is characterized by a Debye length (λ

D), expressed as

𝜆𝐷=𝜖𝑘B𝑇2(𝑍𝑒)2𝑐0⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√��=��B�2(��)2�0

(15)where ϵ is the permittivity of the electrolyte solution, k

B is the Boltzmann constant, T is the electron temperature, Z is the integer valence number, e is the elementary charge, and c

0 is the ionic density.

Figure 4. Schematic diagram of an electro-osmotic flow in a microchannel with negative surface charge. (82) Reproduced with permission from ref (82). Copyright 2012 Woodhead Publishing.

When an electric field is applied perpendicular to the EDL, viscous drag is generated due to the movement of excess ions in the EDL. Electro-osmotic forces can be attributed to the externally applied electric potential (ϕ) and the zeta potential, the system wall induced potential by charged walls (ψ). As illustrated in Figure 4, the majority of ions in the bulk phase have a uniform velocity profile, except for a shear rate condition confined within an extremely thin Stern layer. Therefore, EOF displays a unique characteristic of a “near flat” or plug flow velocity profile, different from the parabolic flow typically induced by pressure-driven microfluidic flow (Hagen–Poiseuille flow). The plug-shaped velocity profile of the EOF possesses a high shear rate above the Stern layer.Overall, the EOF velocity magnitude is typically proportional to the Debye Length (λ

D), zeta potential, and magnitude of the externally applied electric field, while a more viscous liquid reduces the EOF velocity.

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

The EOF of an incompressible viscoelastic fluid is commonly governed by the continuity and incompressible N–S equations, as shown in eqs 7 and 8, where the stress tensor and the electrostatic force term are coupled. The electro-osmotic body force term F, representing the body force exerted by the externally applied electric force, is defined as 

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

𝐸⇀�⇀ are the net electric charge density and the applied external electric field, respectively.Numerous models are established to theoretically study the externally applied electric potential and the system wall induced potential by charged walls. The following Laplace equation, expressed as eq 16, is generally adapted and solved to calculate the externally applied potential (ϕ).

∇2𝜙=0∇2�=0

(16)Ion diffusion under applied electric fields, together with mass transport resulting from convection and diffusion, transports ionic solutions in bulk flow under electrokinetic processes. The Nernst–Planck equation can describe these transport methods, including convection, diffusion, and electro-diffusion. Therefore, the Nernst–Planck equation is used to determine the distribution of the ions within the electrolyte. The electric potential induced by the charged channel walls follows the Poisson–Nernst–Plank (PNP) equation, which can be written as eq 17.

∇·[𝐷𝑖∇𝑛𝑖−𝑢⇀𝑛𝑖+𝑛𝑖𝐷𝑖𝑧𝑖𝑒𝑘𝑏𝑇∇(𝜙+𝜓)]=0∇·[��∇��−�⇀��+����������∇(�+�)]=0

(17)where D

in

i, and z

i are the diffusion coefficient, ionic concentration, and ionic valence of the ionic species I, respectively. However, due to the high nonlinearity and numerical stiffness introduced by different lengths and time scales from the PNP equations, the Poisson–Boltzmann (PB) model is often considered the major simplified method of the PNP equation to characterize the potential distribution of the EDL region in microchannels. In the PB model, it is assumed that the ionic species in the fluid follow the Boltzmann distribution. This model is typically valid for steady-state problems where charge transport can be considered negligible, the EDLs do not overlap with each other, and the intrinsic potentials are low. It provides a simplified representation of the potential distribution in the EDL region. The PB equation governing the EDL electric potential distribution is described as

∇2𝜓=(2𝑒𝑧𝑛0𝜀𝜀0)sinh(𝑧𝑒𝜓𝑘b𝑇)∇2�=(2���0��0)⁡sinh(����b�)

(18)where n

0 is the ion bulk concentration, z is the ionic valence, and ε

0 is the electric permittivity in the vacuum. Under low electric potential conditions, an even further simplified model to illustrate the EOF phenomena is the Debye–Hückel (DH) model. The DH model is derived by obtaining a charge density term by expanding the exponential term of the Boltzmann equation in a Taylor series.

4.2.2. EOF Modeling for Viscoelastic Fluids

Many studies through numerical modeling were performed to obtain a deeper understanding of the effect exhibited by externally applied electric fields on viscoelastic flow in microchannels under various geometrical designs. Bello et al. 

(83) found that methylcellulose solution, a non-Newtonian polymer solution, resulted in stronger electro-osmotic mobility in experiments when compared to the predictions by the Helmholtz–Smoluchowski equation, which is commonly used to define the velocity of EOF of a Newtonian fluid. Being one of the pioneers to identify the discrepancies between the EOF of Newtonian and non-Newtonian fluids, Bello et al. attributed such discrepancies to the presence of a very high shear rate in the EDL, resulting in a change in the orientation of the polymer molecules. Park and Lee 

(84) utilized the FVM to solve the PB equation for the characterization of the electric field induced force. In the study, the concept of fractional calculus for the Oldroyd-B model was adapted to illustrate the elastic and memory effects of viscoelastic fluids in a straight microchannel They observed that fluid elasticity and increased ratio of viscoelastic fluid contribution to overall fluid viscosity had a significant impact on the volumetric flow rate and sensitivity of velocity to electric field strength compared to Newtonian fluids. Afonso et al. 

(85) derived an analytical expression for EOF of viscoelastic fluid between parallel plates using the DH model to account for a zeta potential condition below 25 mV. The study established the understanding of the electro-osmotic viscoelastic fluid flow under low zeta potential conditions. Apart from the electrokinetic forces, pressure forces can also be coupled with EOF to generate a unique fluid flow behavior within the microchannel. Sousa et al. 

(86) analytically studied the flow of a standard viscoelastic solution by combining the pressure gradient force with an externally applied electric force. It was found that, at a near wall skimming layer and the outer layer away from the wall, macromolecules migrating away from surface walls in viscoelastic fluids are observed. In the study, the Phan-Thien Tanner (PTT) constitutive model is utilized to characterize the viscoelastic properties of the solution. The approach is found to be valid when the EDL is much thinner than the skimming layer under an enhanced flow rate. Zhao and Yang 

(87) solved the PB equation and Carreau model for the characterization of the EOF mechanism and non-Newtonian fluid respectively through the FEM. The numerical results depict that, different from the EOF of Newtonian fluids, non-Newtonian fluids led to an increase of electro-osmotic mobility for shear thinning fluids but the opposite for shear thickening fluids.Like other fluid transport driving forces, EOF within unique geometrical layouts also portrays unique transport phenomena. Pimenta and Alves 

(88) utilized the FVM to perform numerical simulations of the EOF of viscoelastic fluids considering the PB equation and the Oldroyd-B model, in a cross-slot and flow-focusing microdevices. It was found that electroelastic instabilities are formed due to the development of large stresses inside the EDL with streamlined curvature at geometry corners. Bezerra et al. 

(89) used the FDM to numerically analyze the vortex formation and flow instability from an electro-osmotic non-Newtonian fluid flow in a microchannel with a nozzle geometry and parallel wall geometry setting. The PNP equation is utilized to characterize the charge motion in the EOF and the PTT model for non-Newtonian flow characterization. A constriction geometry is commonly utilized in blood flow adapted in LOC systems due to the change in blood flow behavior under narrow dimensions in a microchannel. Ji et al. 

(90) recently studied the EOF of viscoelastic fluid in a constriction microchannel connected by two relatively big reservoirs on both ends (as seen in Figure 5) filled with the polyacrylamide polymer solution, a viscoelastic fluid, and an incompressible monovalent binary electrolyte solution KCl.

Figure 5. Schematic diagram of a negatively charged constriction microchannel connected to two reservoirs at both ends. An electro-osmotic flow is induced in the system by the induced potential difference between the anode and cathode. (90) Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

In studying the EOF of viscoelastic fluids, the Oldroyd-B model is often utilized to characterize the polymeric stress tensor and the deformation rate of the fluid. The Oldroyd-B model is expressed as follows:

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

p, λ, c, and I represent the polymer dynamic viscosity, polymer relaxation time, symmetric conformation tensor of the polymer molecules, and the identity matrix, respectively.A log-conformation tensor approach is taken to prevent convergence difficulty induced by the viscoelastic properties. The conformation tensor (c) in the polymeric stress tensor term is redefined by a new tensor (Θ) based on the natural logarithm of the c. The new tensor is defined as

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

(20)in which Λ is the diagonal matrix and R is the orthogonal matrix.Under the new conformation tensor, the induced EOF of a viscoelastic fluid is governed by the continuity and N–S equations adapting the Oldroyd-B model, which is expressed as

∂𝚯∂𝑡+𝐮·∇𝚯=𝛀Θ−ΘΩ+2𝐁+1𝜆(eΘ−𝐈)∂�∂�+�·∇�=�Θ−ΘΩ+2�+1�(eΘ−�)

(21)where Ω and B represent the anti-symmetric matrix and the symmetric traceless matrix of the decomposition of the velocity gradient tensor ∇u, respectively. The conformation tensor can be recovered by c = exp(Θ). The PB model and Laplace equation are utilized to characterize the charged channel wall induced potential and the externally applied potential.The governing equations are numerically solved through the FVM by RheoTool, 

(42) an open-source viscoelastic EOF solver on the OpenFOAM platform. A SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm was applied to solve the velocity-pressure coupling. The pressure field and velocity field were computed by the PCG (Preconditioned Conjugate Gradient) solver and the PBiCG (Preconditioned Biconjugate Gradient) solver, respectively.Ranging magnitudes of an applied electric field or fluid concentration induce both different streamlines and velocity magnitudes at various locations and times of the microchannel. In the study performed by Ji et al., 

(90) notable fluctuation of streamlines and vortex formation is formed at the upper stream entrance of the constriction as shown in Figure 6(a) and (b), respectively, due to the increase of electrokinetic effect, which is seen as a result of the increase in polymeric stress (τ

xx). 

(90) The contraction geometry enhances the EOF velocity within the constriction channel under high E

app condition (600 V/cm). Such phenomena can be attributed to the dependence of electro-osmotic viscoelastic fluid flow on the system wall surface and bulk fluid properties. 

(91)

Figure 6. Schematic diagram of vortex formation and streamlines of EOF depicting flow instability at (a) 1.71 s and (b) 1.75 s. Spatial distribution of the elastic normal stress at (c) high Eapp condition. Streamline of an electro-osmotic flow under Eapp of 600 V/cm (90) for (d) non-Newtonian and (e) Newtonian fluid through a constriction geometry. Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

As elastic normal stress exceeds the local shear stress, flow instability and vortex formation occur. The induced elastic stress under EOF not only enhances the instability of the flow but often generates an irregular secondary flow leading to strong disturbance. 

(92) It is also vital to consider the effect of the constriction layout of microchannels on the alteration of the field strength within the system. The contraction geometry enhances a larger electric field strength compared with other locations of the channel outside the constriction region, resulting in a higher velocity gradient and stronger extension on the polymer within the viscoelastic solution. Following the high shear flow condition, a higher magnitude of stretch for polymer molecules in viscoelastic fluids exhibits larger elastic stresses and enhancement of vortex formation at the region. 

(93)As shown in Figure 6(c), significant elastic normal stress occurs at the inlet of the constriction microchannel. Such occurrence of a polymeric flow can be attributed to the dominating elongational flow, giving rise to high deformation of the polymers within the viscoelastic fluid flow, resulting in higher elastic stress from the polymers. Such phenomena at the entrance result in the difference in velocity streamline as circled in Figure 6(d) compared to that of the Newtonian fluid at the constriction entrance in Figure 6(e). 

(90) The difference between the Newtonian and polymer solution at the exit, as circled in Figure 6(d) and (e), can be attributed to the extrudate swell effect of polymers 

(94) within the viscoelastic fluid flow. The extrudate swell effect illustrates that, as polymers emerge from the constriction exit, they tend to contract in the flow direction and grow in the normal direction, resulting in an extrudate diameter greater than the channel size. The deformation of polymers within the polymeric flow at both the entrance and exit of the contraction channel facilitates the change in shear stress conditions of the flow, leading to the alteration in streamlines of flows for each region.

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

Rather than relying on the micromixing controlled by molecular diffusion under low Reynolds number conditions, active mixers actively leverage convective instability and vortex formation induced by electro-osmotic flows from alternating current (AC) or direct current (DC) electric fields. Such adaptation is recognized as significant breakthroughs for promotion of fluid mixing in chemical and biological applications such as drug delivery, medical diagnostics, chemical synthesis, and so on. 

(95)Many researchers proposed novel designs of electro-osmosis micromixers coupled with numerical simulations in conjunction with experimental findings to increase their understanding of the role of flow instability and vortex formation in the mixing process under electrokinetic phenomena. Matsubara and Narumi 

(96) numerically modeled the mixing process in a microchannel with four electrodes on each side of the microchannel wall, which generated a disruption through unstable electro-osmotic vortices. It was found that particle mixing was sensitive to both the convection effect induced by the main and secondary vortex within the micromixer and the change in oscillation frequency caused by the supplied AC voltage when the Reynolds number was varied. Qaderi et al. 

(97) adapted the PNP equation to numerically study the effect of the geometry and zeta potential configuration of the microchannel on the mixing process with a combined electro-osmotic pressure driven flow. It was reported that the application of heterogeneous zeta potential configuration enhances the mixing efficiency by around 23% while the height of the hurdles increases the mixing efficiency at most 48.1%. Cho et al. 

(98) utilized the PB model and Laplace equation to numerically simulate the electro-osmotic non-Newtonian fluid mixing process within a wavy and block layout of microchannel walls. The Power Law model is adapted to describe the fluid rheological characteristic. It was found that shear-thinning fluids possess a higher volumetric flow rate, which could result in poorer mixing efficiency compared to that of Newtonian fluids. Numerous studies have revealed that flow instability and vortex generation, in particular secondary vortices produced by barriers or greater magnitudes of heterogeneous zeta potential distribution, enhance mixing by increasing bulk flow velocity and reducing flow distance.To better understand the mechanism of disturbance formed in the system due to externally applied forces, known as electrokinetic instability, literature often utilize the Rayleigh (Ra) number, 

(1) as described below:

𝑅𝑎𝑣=𝑢ev𝑢eo=(𝛾−1𝛾+1)2𝑊𝛿2𝐸el2𝐻2𝜁𝛿Ra�=�ev�eo=(�−1�+1)2��2�el2�2��

(22)where γ is the conductivity ratio of the two streams and can be written as 

𝛾=𝜎el,H𝜎el,L�=�el,H�el,L. The Ra number characterizes the ratio between electroviscous and electro-osmotic flow. A high Ra

v value often results in good mixing. It is evident that fluid properties such as the conductivity (σ) of the two streams play a key role in the formation of disturbances to enhance mixing in microsystems. At the same time, electrokinetic parameters like the zeta potential (ζ) in the Ra number is critical in the characterization of electro-osmotic velocity and a slip boundary condition at the microchannel wall.To understand the mixing result along the channel, the concentration field can be defined and simulated under the assumption of steady state conditions and constant diffusion coefficient for each of the working fluid within the system through the convection–diffusion equation as below:

∂𝑐𝒊∂𝑡+∇⇀(𝑐𝑖𝑢⇀−𝐷𝑖∇⇀𝑐𝒊)=0∂��∂�+∇⇀(���⇀−��∇⇀��)=0

(23)where c

i is the species concentration of species i and D

i is the diffusion coefficient of the corresponding species.The standard deviation of concentration (σ

sd) can be adapted to evaluate the mixing quality of the system. 

(97) The standard deviation for concentration at a specific portion of the channel may be calculated using the equation below:

𝜎sd=∫10(𝐶∗(𝑦∗)−𝐶m)2d𝑦∗∫10d𝑦∗⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯�sd=∫01(�*(�*)−�m)2d�*∫01d�*

(24)where C*(y*) and C

m are the non-dimensional concentration profile and the mean concentration at the portion, respectively. C* is the non-dimensional concentration and can be calculated as 

𝐶∗=𝐶𝐶ref�*=��ref, where C

ref is the reference concentration defined as the bulk solution concentration. The mean concentration profile can be calculated as 

𝐶m=∫10(𝐶∗(𝑦∗)d𝑦∗∫10d𝑦∗�m=∫01(�*(�*)d�*∫01d�*. With the standard deviation of concentration, the mixing efficiency 

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

sd,0 is the standard derivation of the case of no mixing. The value of the mixing efficiency is typically utilized in conjunction with the simulated flow field and concentration field to explore the effect of geometrical and electrokinetic parameters on the optimization of the mixing results.

5. Summary

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5.1. Conclusion

Viscoelastic fluids such as blood flow in LOC systems are an essential topic to proceed with diagnostic analysis and research through microdevices in the biomedical and pharmaceutical industries. The complex blood flow behavior is tightly controlled by the viscoelastic characteristics of blood such as the dynamic viscosity and the elastic property of RBCs under various shear rate conditions. Furthermore, the flow behaviors under varied driving forces promote an array of microfluidic transport phenomena that are critical to the management of blood flow and other adapted viscoelastic fluids in LOC systems. This review addressed the blood flow phenomena, the complicated interplay between shear rate and blood flow behaviors, and their numerical modeling under LOC systems through the lens of the viscoelasticity characteristic. Furthermore, a theoretical understanding of capillary forces and externally applied electric forces leads to an in-depth investigation of the relationship between blood flow patterns and the key parameters of the two driving forces, the latter of which is introduced through the lens of viscoelastic fluids, coupling numerical modeling to improve the knowledge of blood flow manipulation in LOC systems. The flow disturbances triggered by the EOF of viscoelastic fluids and their impact on blood flow patterns have been deeply investigated due to their important role and applications in LOC devices. Continuous advancements of various numerical modeling methods with experimental findings through more efficient and less computationally heavy methods have served as an encouraging sign of establishing more accurate illustrations of the mechanisms for multiphase blood and other viscoelastic fluid flow transport phenomena driven by various forces. Such progress is fundamental for the manipulation of unique transport phenomena, such as the generated disturbances, to optimize functionalities offered by microdevices in LOC systems.

The following section will provide further insights into the employment of studied blood transport phenomena to improve the functionality of micro devices adapting LOC technology. A discussion of the novel roles that external driving forces play in microfluidic flow behaviors is also provided. Limitations in the computational modeling of blood flow and electrokinetic phenomena in LOC systems will also be emphasized, which may provide valuable insights for future research endeavors. These discussions aim to provide guidance and opportunities for new paths in the ongoing development of LOC devices that adapt blood flow.

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

Despite substantial research, mixing results through flow instability and vortex formation phenomena induced by electro-osmotic mixing still deviate from the effective mixing results offered by chaotic mixing results such as those seen in turbulent flows. However, recent discoveries of a mixing phenomenon that is generally observed under turbulent flows are found within electro-osmosis micromixers under low Reynolds number conditions. Zhao 

(99) experimentally discovered a rapid mixing process in an AC applied micromixer, where the power spectrum of concentration under an applied voltage of 20 V

p-p induces a −5/3 slope within a frequency range. This value of the slope is considered as the O–C spectrum in macroflows, which is often visible under relatively high Re conditions, such as the Taylor microscale Reynolds number Re > 500 in turbulent flows. 

(100) However, the Re value in the studied system is less than 1 at the specific location and applied voltage. A secondary flow is also suggested to occur close to microchannel walls, being attributed to the increase of convective instability within the system.Despite the experimental phenomenon proposed by Zhao et al., 

(99) the range of effects induced by vital parameters of an EOF mixing system on the enhanced mixing results and mechanisms of disturbance generated by the turbulent-like flow instability is not further characterized. Such a gap in knowledge may hinder the adaptability and commercialization of the discovery of micromixers. One of the parameters for further evaluation is the conductivity gradient of the fluid flow. A relatively strong conductivity gradient (5000:1) was adopted in the system due to the conductive properties of the two fluids. The high conductivity gradients may contribute to the relatively large Rayleigh number and differences in EDL layer thickness, resulting in an unusual disturbance in laminar flow conditions and enhanced mixing results. However, high conductivity gradients are not always achievable by the working fluids due to diverse fluid properties. The reliance on turbulent-like phenomena and rapid mixing results in a large conductivity gradient should be established to prevent the limited application of fluids for the mixing system. In addition, the proposed system utilizes distinct zeta potential distributions at the top and bottom walls due to their difference in material choices, which may be attributed to the flow instability phenomena. Further studies should be made on varying zeta potential magnitude and distribution to evaluate their effect on the slip boundary conditions of the flow and the large shear rate condition close to the channel wall of EOF. Such a study can potentially offer an optimized condition in zeta potential magnitude through material choices and geometrical layout of the zeta potential for better mixing results and manipulation of mixing fluid dynamics. The two vital parameters mentioned above can be varied with the aid of numerical simulation to understand the effect of parameters on the interaction between electro-osmotic forces and electroviscous forces. At the same time, the relationship of developed streamlines of the simulated velocity and concentration field, following their relationship with the mixing results, under the impact of these key parameters can foster more insight into the range of impact that the two parameters have on the proposed phenomena and the microfluidic dynamic principles of disturbances.

In addition, many of the current investigations of electrokinetic mixers commonly emphasize the fluid dynamics of mixing for Newtonian fluids, while the utilization of biofluids, primarily viscoelastic fluids such as blood, and their distinctive response under shear forces in these novel mixing processes of LOC systems are significantly less studied. To develop more compatible microdevice designs and efficient mixing outcomes for the biomedical industry, it is necessary to fill the knowledge gaps in the literature on electro-osmotic mixing for biofluids, where properties of elasticity, dynamic viscosity, and intricate relationship with shear flow from the fluid are further considered.

5.2.2. Electro-osmosis Separation in LOC Systems

Particle separation in LOC devices, particularly in biological research and diagnostics, is another area where disturbances may play a significant role in optimization. 

(101) Plasma analysis in LOC systems under precise control of blood flow phenomena and blood/plasma separation procedures can detect vital information about infectious diseases from particular antibodies and foreign nucleic acids for medical treatments, diagnostics, and research, 

(102) offering more efficient results and simple operating procedures compared to that of the traditional centrifugation method for blood and plasma separation. However, the adaptability of LOC devices for blood and plasma separation is often hindered by microchannel clogging, where flow velocity and plasma yield from LOC devices is reduced due to occasional RBC migration and aggregation at the filtration entrance of microdevices. 

(103)It is important to note that the EOF induces flow instability close to microchannel walls, which may provide further solutions to clogging for the separation process of the LOC systems. Mohammadi et al. 

(104) offered an anti-clogging effect of RBCs at the blood and plasma separating device filtration entry, adjacent to the surface wall, through RBC disaggregation under high shear rate conditions generated by a forward and reverse EOF direction.

Further theoretical and numerical research can be conducted to characterize the effect of high shear rate conditions near microchannel walls toward the detachment of binding blood cells on surfaces and the reversibility of aggregation. Through numerical modeling with varying electrokinetic parameters to induce different degrees of disturbances or shear conditions at channel walls, it may be possible to optimize and better understand the process of disrupting the forces that bind cells to surface walls and aggregated cells at filtration pores. RBCs that migrate close to microchannel walls are often attracted by the adhesion force between the RBC and the solid surface originating from the van der Waals forces. Following RBC migration and attachment by adhesive forces adjacent to the microchannel walls as shown in Figure 7, the increase in viscosity at the region causes a lower shear condition and encourages RBC aggregation (cell–cell interaction), which clogs filtering pores or microchannels and reduces flow velocity at filtration region. Both the impact that shear forces and disturbances may induce on cell binding forces with surface walls and other cells leading to aggregation may suggest further characterization. Kinetic parameters such as activation energy and the rate-determining step for cell binding composition attachment and detachment should be considered for modeling the dynamics of RBCs and blood flows under external forces in LOC separation devices.

Figure 7. Schematic representations of clogging at a microchannel pore following the sequence of RBC migration, cell attachment to channel walls, and aggregation. (105) Reproduced with permission from ref (105). Copyright 2018 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

5.2.3. Relationship between External Forces and Microfluidic Systems

In blood flow, a thicker CFL suggests a lower blood viscosity, suggesting a complex relationship between shear stress and shear rate, affecting the blood viscosity and blood flow. Despite some experimental and numerical studies on electro-osmotic non-Newtonian fluid flow, limited literature has performed an in-depth investigation of the role that applied electric forces and other external forces could play in the process of CFL formation. Additional studies on how shear rates from external forces affect CFL formation and microfluidic flow dynamics can shed light on the mechanism of the contribution induced by external driving forces to the development of a separate phase of layer, similar to CFL, close to the microchannel walls and distinct from the surrounding fluid within the system, then influencing microfluidic flow dynamics.One of the mechanisms of phenomena to be explored is the formation of the Exclusion Zone (EZ) region following a “Self-Induced Flow” (SIF) phenomenon discovered by Li and Pollack, 

(106) as shown in Figure 8(a) and (b), respectively. A spontaneous sustained axial flow is observed when hydrophilic materials are immersed in water, resulting in the buildup of a negative layer of charges, defined as the EZ, after water molecules absorb infrared radiation (IR) energy and break down into H and OH

+.

Figure 8. Schematic representations of (a) the Exclusion Zone region and (b) the Self Induced Flow through visualization of microsphere movement within a microchannel. (106) Reproduced with permission from ref (106). Copyright 2020 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

Despite the finding of such a phenomenon, the specific mechanism and role of IR energy have yet to be defined for the process of EZ development. To further develop an understanding of the role of IR energy in such phenomena, a feasible study may be seen through the lens of the relationships between external forces and microfluidic flow. In the phenomena, the increase of SIF velocity under a rise of IR radiation resonant characteristics is shown in the participation of the external electric field near the microchannel walls under electro-osmotic viscoelastic fluid flow systems. The buildup of negative charges at the hydrophilic surfaces in EZ is analogous to the mechanism of electrical double layer formation. Indeed, research has initiated the exploration of the core mechanisms for EZ formation through the lens of the electrokinetic phenomena. 

(107) Such a similarity of the role of IR energy and the transport phenomena of SIF with electrokinetic phenomena paves the way for the definition of the unknown SIF phenomena and EZ formation. Furthermore, Li and Pollack 

(106) suggest whether CFL formation might contribute to a SIF of blood using solely IR radiation, a commonly available source of energy in nature, as an external driving force. The proposition may be proven feasible with the presence of the CFL region next to the negatively charged hydrophilic endothelial glycocalyx layer, coating the luminal side of blood vessels. 

(108) Further research can dive into the resonating characteristics between the formation of the CFL region next to the hydrophilic endothelial glycocalyx layer and that of the EZ formation close to hydrophilic microchannel walls. Indeed, an increase in IR energy is known to rapidly accelerate EZ formation and SIF velocity, depicting similarity to the increase in the magnitude of electric field forces and greater shear rates at microchannel walls affecting CFL formation and EOF velocity. Such correlation depicts a future direction in whether SIF blood flow can be observed and characterized theoretically further through the lens of the relationship between blood flow and shear forces exhibited by external energy.

The intricate link between the CFL and external forces, more specifically the externally applied electric field, can receive further attention to provide a more complete framework for the mechanisms between IR radiation and EZ formation. Such characterization may also contribute to a greater comprehension of the role IR can play in CFL formation next to the endothelial glycocalyx layer as well as its role as a driving force to propel blood flow, similar to the SIF, but without the commonly assumed pressure force from heart contraction as a source of driving force.

5.3. Challenges

Although there have been significant improvements in blood flow modeling under LOC systems over the past decade, there are still notable constraints that may require special attention for numerical simulation applications to benefit the adaptability of the designs and functionalities of LOC devices. Several points that require special attention are mentioned below:

1.The majority of CFD models operate under the relationship between the viscoelasticity of blood and the shear rate conditions of flow. The relative effect exhibited by the presence of highly populated RBCs in whole blood and their forces amongst the cells themselves under complex flows often remains unclearly defined. Furthermore, the full range of cell populations in whole blood requires a much more computational load for numerical modeling. Therefore, a vital goal for future research is to evaluate a reduced modeling method where the impact of cell–cell interaction on the viscoelastic property of blood is considered.
2.Current computational methods on hemodynamics rely on continuum models based upon non-Newtonian rheology at the macroscale rather than at molecular and cellular levels. Careful considerations should be made for the development of a constructive framework for the physical and temporal scales of micro/nanoscale systems to evaluate the intricate relationship between fluid driving forces, dynamic viscosity, and elasticity.
3.Viscoelastic fluids under the impact of externally applied electric forces often deviate from the assumptions of no-slip boundary conditions due to the unique flow conditions induced by externally applied forces. Furthermore, the mechanism of vortex formation and viscoelastic flow instability at laminar flow conditions should be better defined through the lens of the microfluidic flow phenomenon to optimize the prediction of viscoelastic flow across different geometrical layouts. Mathematical models and numerical methods are needed to better predict such disturbance caused by external forces and the viscoelasticity of fluids at such a small scale.
4.Under practical situations, zeta potential distribution at channel walls frequently deviates from the common assumption of a constant distribution because of manufacturing faults or inherent surface charges prior to the introduction of electrokinetic influence. These discrepancies frequently lead to inconsistent surface potential distribution, such as excess positive ions at relatively more negatively charged walls. Accordingly, unpredicted vortex formation and flow instability may occur. Therefore, careful consideration should be given to these discrepancies and how they could trigger the transport process and unexpected results of a microdevice.

Author Information

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  • Corresponding Authors
    • Zhe Chen – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: zaccooky@sjtu.edu.cn
    • Bo Ouyang – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: bouy93@sjtu.edu.cn
    • Zheng-Hong Luo – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-9011-6020; Email: luozh@sjtu.edu.cn
  • Authors
    • Bin-Jie Lai – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0009-0002-8133-5381
    • Li-Tao Zhu – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-6514-8864
  • NotesThe authors declare no competing financial interest.

Acknowledgments

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This work was supported by the National Natural Science Foundation of China (No. 22238005) and the Postdoctoral Research Foundation of China (No. GZC20231576).

Vocabulary

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Microfluidicsthe field of technological and scientific study that investigates fluid flow in channels with dimensions between 1 and 1000 μm
Lab-on-a-Chip Technologythe field of research and technological development aimed at integrating the micro/nanofluidic characteristics to conduct laboratory processes on handheld devices
Computational Fluid Dynamics (CFD)the method utilizing computational abilities to predict physical fluid flow behaviors mathematically through solving the governing equations of corresponding fluid flows
Shear Ratethe rate of change in velocity where one layer of fluid moves past the adjacent layer
Viscoelasticitythe property holding both elasticity and viscosity characteristics relying on the magnitude of applied shear stress and time-dependent strain
Electro-osmosisthe flow of fluid under an applied electric field when charged solid surface is in contact with the bulk fluid
Vortexthe rotating motion of a fluid revolving an axis line

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Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

Predicting solid-state phase transformations during metal additive manufacturing: A case study on electron-beam powder bed fusion of Inconel-738

금속 적층 제조 중 고체 상 변형 예측: Inconel-738의 전자빔 분말층 융합에 대한 사례 연구

Nana Kwabena Adomako a, Nima Haghdadi a, James F.L. Dingle bc, Ernst Kozeschnik d, Xiaozhou Liao bc, Simon P. Ringer bc, Sophie Primig a

Abstract

Metal additive manufacturing (AM) has now become the perhaps most desirable technique for producing complex shaped engineering parts. However, to truly take advantage of its capabilities, advanced control of AM microstructures and properties is required, and this is often enabled via modeling. The current work presents a computational modeling approach to studying the solid-state phase transformation kinetics and the microstructural evolution during AM. Our approach combines thermal and thermo-kinetic modelling. A semi-analytical heat transfer model is employed to simulate the thermal history throughout AM builds. Thermal profiles of individual layers are then used as input for the MatCalc thermo-kinetic software. The microstructural evolution (e.g., fractions, morphology, and composition of individual phases) for any region of interest throughout the build is predicted by MatCalc. The simulation is applied to an IN738 part produced by electron beam powder bed fusion to provide insights into how γ′ precipitates evolve during thermal cycling. Our simulations show qualitative agreement with our experimental results in predicting the size distribution of γ′ along the build height, its multimodal size character, as well as the volume fraction of MC carbides. Our findings indicate that our method is suitable for a range of AM processes and alloys, to predict and engineer their microstructures and properties.

Graphical Abstract

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Keywords

Additive manufacturing, Simulation, Thermal cycles, γ′ phase, IN738

1. Introduction

Additive manufacturing (AM) is an advanced manufacturing method that enables engineering parts with intricate shapes to be fabricated with high efficiency and minimal materials waste. AM involves building up 3D components layer-by-layer from feedstocks such as powder [1]. Various alloys, including steel, Ti, Al, and Ni-based superalloys, have been produced using different AM techniques. These techniques include directed energy deposition (DED), electron- and laser powder bed fusion (E-PBF and L-PBF), and have found applications in a variety of industries such as aerospace and power generation [2][3][4]. Despite the growing interest, certain challenges limit broader applications of AM fabricated components in these industries and others. One of such limitations is obtaining a suitable and reproducible microstructure that offers the desired mechanical properties consistently. In fact, the AM as-built microstructure is highly complex and considerably distinctive from its conventionally processed counterparts owing to the complicated thermal cycles arising from the deposition of several layers upon each other [5][6].

Several studies have reported that the solid-state phases and solidification microstructure of AM processed alloys such as CMSX-4, CoCr [7][8], Ti-6Al-4V [9][10][11]IN738 [6]304L stainless steel [12], and IN718 [13][14] exhibit considerable variations along the build direction. For instance, references [9][10] have reported that there is a variation in the distribution of α and β phases along the build direction in Ti-alloys. Similarly, the microstructure of an L-PBF fabricated martensitic steel exhibits variations in the fraction of martensite [15]. Furthermore, some of the present authors and others [6][16][17][18][19][20] have recently reviewed and reported that there is a difference in the morphology and fraction of nanoscale precipitates as a function of build height in Ni-based superalloys. These non-uniformities in the as-built microstructure result in an undesired heterogeneity in mechanical and other important properties such as corrosion and oxidation [19][21][22][23]. To obtain the desired microstructure and properties, additional processing treatments are utilized, but this incurs extra costs and may lead to precipitation of detrimental phases and grain coarsening. Therefore, a through-process understanding of the microstructure evolution under repeated heating and cooling is now needed to further advance 3D printed microstructure and property control.

It is now commonly understood that the microstructure evolution during printing is complex, and most AM studies concentrate on the microstructure and mechanical properties of the final build only. Post-printing studies of microstructure characteristics at room temperature miss crucial information on how they evolve. In-situ measurements and modelling approaches are required to better understand the complex microstructural evolution under repeated heating and cooling. Most in-situ measurements in AM focus on monitoring the microstructural changes, such as phase transformations and melt pool dynamics during fabrication using X-ray scattering and high-speed X-ray imaging [24][25][26][27]. For example, Zhao et al. [25] measured the rate of solidification and described the α/β phase transformation during L-PBF of Ti-6Al-4V in-situ. Also, Wahlmann et al. [21] recently used an L-PBF machine coupled with X-ray scattering to investigate the changes in CMSX-4 phase during successive melting processes. Although these techniques provide significant understanding of the basic principles of AM, they are not widely accessible. This is due to the great cost of the instrument, competitive application process, and complexities in terms of the experimental set-up, data collection, and analysis [26][28].

Computational modeling techniques are promising and more widely accessible tools that enable advanced understanding, prediction, and engineering of microstructures and properties during AM. So far, the majority of computational studies have concentrated on physics based process models for metal AM, with the goal of predicting the temperature profile, heat transfer, powder dynamics, and defect formation (e.g., porosity) [29][30]. In recent times, there have been efforts in modeling of the AM microstructure evolution using approaches such as phase-field [31], Monte Carlo (MC) [32], and cellular automata (CA) [33], coupled with finite element simulations for temperature profiles. However, these techniques are often restricted to simulating the evolution of solidification microstructures (e.g., grain and dendrite structure) and defects (e.g., porosity). For example, Zinovieva et al. [33] predicted the grain structure of L-PBF Ti-6Al-4V using finite difference and cellular automata methods. However, studies on the computational modelling of the solid-state phase transformations, which largely determine the resulting properties, remain limited. This can be attributed to the multi-component and multi-phase nature of most engineering alloys in AM, along with the complex transformation kinetics during thermal cycling. This kind of research involves predictions of the thermal cycle in AM builds, and connecting it to essential thermodynamic and kinetic data as inputs for the model. Based on the information provided, the thermokinetic model predicts the history of solid-state phase microstructure evolution during deposition as output. For example, a multi-phase, multi-component mean-field model has been developed to simulate the intermetallic precipitation kinetics in IN718 [34] and IN625 [35] during AM. Also, Basoalto et al. [36] employed a computational framework to examine the contrasting distributions of process-induced microvoids and precipitates in two Ni-based superalloys, namely IN718 and CM247LC. Furthermore, McNamara et al. [37] established a computational model based on the Johnson-Mehl-Avrami model for non-isothermal conditions to predict solid-state phase transformation kinetics in L-PBF IN718 and DED Ti-6Al-4V. These models successfully predicted the size and volume fraction of individual phases and captured the repeated nucleation and dissolution of precipitates that occur during AM.

In the current study, we propose a modeling approach with appreciably short computational time to investigate the detailed microstructural evolution during metal AM. This may include obtaining more detailed information on the morphologies of phases, such as size distribution, phase fraction, dissolution and nucleation kinetics, as well as chemistry during thermal cycling and final cooling to room temperature. We utilize the combination of the MatCalc thermo-kinetic simulator and a semi-analytical heat conduction model. MatCalc is a software suite for simulation of phase transformations, microstructure evolution and certain mechanical properties in engineering alloys. It has successfully been employed to simulate solid-state phase transformations in Ni-based superalloys [38][39], steels [40], and Al alloys [41] during complex thermo-mechanical processes. MatCalc uses the classical nucleation theory as well as the so-called Svoboda-Fischer-Fratzl-Kozeschnik (SFFK) growth model as the basis for simulating precipitation kinetics [42]. Although MatCalc was originally developed for conventional thermo-mechanical processes, we will show that it is also applicable for AM if the detailed time-temperature profile of the AM build is known. The semi-analytical heat transfer code developed by Stump and Plotkowski [43] is used to simulate these profile throughout the AM build.

1.1. Application to IN738

Inconel-738 (IN738) is a precipitation hardening Ni-based superalloy mainly employed in high-temperature components, e.g. in gas turbines and aero-engines owing to its exceptional mechanical properties at temperatures up to 980 °C, coupled with high resistance to oxidation and corrosion [44]. Its superior high-temperature strength (∼1090 MPa tensile strength) is provided by the L12 ordered Ni3(Al,Ti) γ′ phase that precipitates in a face-centered cubic (FCC) γ matrix [45][46]. Despite offering great properties, IN738, like most superalloys with high γ′ fractions, is challenging to process owing to its propensity to hot cracking [47][48]. Further, machining of such alloys is challenging because of their high strength and work-hardening rates. It is therefore difficult to fabricate complex INC738 parts using traditional manufacturing techniques like casting, welding, and forging.

The emergence of AM has now made it possible to fabricate such parts from IN738 and other superalloys. Some of the current authors’ recent research successfully applied E-PBF to fabricate defect-free IN738 containing γ′ throughout the build [16][17]. The precipitated γ′ were heterogeneously distributed. In particular, Haghdadi et al. [16] studied the origin of the multimodal size distribution of γ′, while Lim et al. [17] investigated the gradient in γ′ character with build height and its correlation to mechanical properties. Based on these results, the present study aims to extend the understanding of the complex and site-specific microstructural evolution in E-PBF IN738 by using a computational modelling approach. New experimental evidence (e.g., micrographs not published previously) is presented here to support the computational results.

2. Materials and Methods

2.1. Materials preparation

IN738 Ni-based superalloy (59.61Ni-8.48Co-7.00Al-17.47Cr-3.96Ti-1.01Mo-0.81W-0.56Ta-0.49Nb-0.47C-0.09Zr-0.05B, at%) gas-atomized powder was used as feedstock. The powders, with average size of 60 ± 7 µm, were manufactured by Praxair and distributed by Astro Alloys Inc. An Arcam Q10 machine by GE Additive with an acceleration voltage of 60 kV was used to fabricate a 15 × 15 × 25 mm3 block (XYZ, Z: build direction) on a 316 stainless steel substrate. The block was 3D-printed using a ‘random’ spot melt pattern. The random spot melt pattern involves randomly selecting points in any given layer, with an equal chance of each point being melted. Each spot melt experienced a dwell time of 0.3 ms, and the layer thickness was 50 µm. Some of the current authors have previously characterized the microstructure of the very same and similar builds in more detail [16][17]. A preheat temperature of ∼1000 °C was set and kept during printing to reduce temperature gradients and, in turn, thermal stresses [49][50][51]. Following printing, the build was separated from the substrate through electrical discharge machining. It should be noted that this sample was simultaneously printed with the one used in [17] during the same build process and on the same build plate, under identical conditions.

2.2. Microstructural characterization

The printed sample was longitudinally cut in the direction of the build using a Struers Accutom-50, ground, and then polished to 0.25 µm suspension via standard techniques. The polished x-z surface was electropolished and etched using Struers A2 solution (perchloric acid in ethanol). Specimens for image analysis were polished using a 0.06 µm colloidal silica. Microstructure analyses were carried out across the height of the build using optical microscopy (OM) and scanning electron microscopy (SEM) with focus on the microstructure evolution (γ′ precipitates) in individual layers. The position of each layer being analyzed was determined by multiplying the layer number by the layer thickness (50 µm). It should be noted that the position of the first layer starts where the thermal profile is tracked (in this case, 2 mm from the bottom). SEM images were acquired using a JEOL 7001 field emission microscope. The brightness and contrast settings, acceleration voltage of 15 kV, working distance of 10 mm, and other SEM imaging parameters were all held constant for analysis of the entire build. The ImageJ software was used for automated image analysis to determine the phase fraction and size of γ′ precipitates and carbides. A 2-pixel radius Gaussian blur, following a greyscale thresholding and watershed segmentation was used [52]. Primary γ′ sizes (>50 nm), were measured using equivalent spherical diameters. The phase fractions were considered equal to the measured area fraction. Secondary γ′ particles (<50 nm) were not considered here. The γ′ size in the following refers to the diameter of a precipitate.

2.3. Hardness testing

A Struers DuraScan tester was utilized for Vickers hardness mapping on a polished x-z surface, from top to bottom under a maximum load of 100 mN and 10 s dwell time. 30 micro-indentations were performed per row. According to the ASTM standard [53], the indentations were sufficiently distant (∼500 µm) to assure that strain-hardened areas did not interfere with one another.

2.4. Computational simulation of E-PBF IN738 build

2.4.1. Thermal profile modeling

The thermal history was generated using the semi-analytical heat transfer code (also known as the 3DThesis code) developed by Stump and Plotkowski [43]. This code is an open-source C++ program which provides a way to quickly simulate the conductive heat transfer found in welding and AM. The key use case for the code is the simulation of larger domains than is practicable with Computational Fluid Dynamics/Finite Element Analysis programs like FLOW-3D AM. Although simulating conductive heat transfer will not be an appropriate simplification for some investigations (for example the modelling of keyholding or pore formation), the 3DThesis code does provide fast estimates of temperature, thermal gradient, and solidification rate which can be useful for elucidating microstructure formation across entire layers of an AM build. The mathematics involved in the code is as follows:

In transient thermal conduction during welding and AM, with uniform and constant thermophysical properties and without considering fluid convection and latent heat effects, energy conservation can be expressed as:(1)��∂�∂�=�∇2�+�̇where � is density, � specific heat, � temperature, � time, � thermal conductivity, and �̇ a volumetric heat source. By assuming a semi-infinite domain, Eq. 1 can be analytically solved. The solution for temperature at a given time (t) using a volumetric Gaussian heat source is presented as:(2)��,�,�,�−�0=33�����32∫0�1������exp−3�′�′2��+�′�′2��+�′�′2����′(3)and��=12��−�′+��2for�=�,�,�(4)and�′�′=�−���′Where � is the vector �,�,� and �� is the location of the heat source.

The numerical integration scheme used is an adaptive Gaussian quadrature method based on the following nondimensionalization:(5)�=��xy2�,�′=��xy2�′,�=��xy,�=��xy,�=��xy,�=���xy

A more detailed explanation of the mathematics can be found in reference [43].

The main source of the thermal cycling present within a powder-bed fusion process is the fusion of subsequent layers. Therefore, regions near the top of a build are expected to undergo fewer thermal cycles than those closer to the bottom. For this purpose, data from the single scan’s thermal influence on multiple layers was spliced to represent the thermal cycles experienced at a single location caused by multiple subsequent layers being fused.

The cross-sectional area simulated by this model was kept constant at 1 × 1 mm2, and the depth was dependent on the build location modelled with MatCalc. For a build location 2 mm from the bottom, the maximum number of layers to simulate is 460. Fig. 1a shows a stitched overview OM image of the entire build indicating the region where this thermal cycle is simulated and tracked. To increase similarity with the conditions of the physical build, each thermal history was constructed from the results of two simulations generated with different versions of a random scan path. The parameters used for these thermal simulations can be found in Table 1. It should be noted that the main purpose of the thermal profile modelling was to demonstrate how the conditions at different locations of the build change relative to each other. Accurately predicting the absolute temperature during the build would require validation via a temperature sensor measurement during the build process which is beyond the scope of the study. Nonetheless, to establish the viability of the heat source as a suitable approximation for this study, an additional sensitivity analysis was conducted. This analysis focused on the influence of energy input on γ′ precipitation behavior, the central aim of this paper. This was achieved by employing varying beam absorption energies (0.76, 0.82 – the values utilized in the simulation, and 0.9). The direct impact of beam absorption efficiency on energy input into the material was investigated. Specifically, the initial 20 layers of the build were simulated and subsequently compared to experimental data derived from SEM. While phase fractions were found to be consistent across all conditions, disparities emerged in the mean size of γ′ precipitates. An absorption efficiency of 0.76 yielded a mean size of approximately 70 nm. Conversely, absorption efficiencies of 0.82 and 0.9 exhibited remarkably similar mean sizes of around 130 nm, aligning closely with the outcomes of the experiments.

Fig. 1

Table 1. A list of parameters used in thermal simulation of E-PBF.

ParameterValue
Spatial resolution5 µm
Time step0.5 s
Beam diameter200 µm
Beam penetration depth1 µm
Beam power1200 W
Beam absorption efficiency0.82
Thermal conductivity25.37 W/(m⋅K)
Chamber temperature1000 °C
Specific heat711.756 J/(kg⋅K)
Density8110 kg/m3

2.4.2. Thermo-kinetic simulation

The numerical analyses of the evolution of precipitates was performed using MatCalc version 6.04 (rel 0.011). The thermodynamic (‘mc_ni.tdb’, version 2.034) and diffusion (‘mc_ni.ddb’, version 2.007) databases were used. MatCalc’s basic principles are elaborated as follows:

The nucleation kinetics of precipitates are computed using a computational technique based on a classical nucleation theory [54] that has been modified for systems with multiple components [42][55]. Accordingly, the transient nucleation rate (�), which expresses the rate at which nuclei are formed per unit volume and time, is calculated as:(6)�=�0��*∙�xp−�*�∙�∙exp−��where �0 denotes the number of active nucleation sites, �* the rate of atomic attachment, � the Boltzmann constant, � the temperature, �* the critical energy for nucleus formation, τ the incubation time, and t the time. � (Zeldovich factor) takes into consideration that thermal excitation destabilizes the nucleus as opposed to its inactive state [54]. Z is defined as follows:(7)�=−12�kT∂2∆�∂�2�*12where ∆� is the overall change in free energy due to the formation of a nucleus and n is the nucleus’ number of atoms. ∆�’s derivative is evaluated at n* (critical nucleus size). �* accounts for the long-range diffusion of atoms required for nucleation, provided that the matrix’ and precipitates’ composition differ. Svoboda et al. [42] developed an appropriate multi-component equation for �*, which is given by:(8)�*=4��*2�4�∑�=1��ki−�0�2�0��0�−1where �* denotes the critical radius for nucleation, � represents atomic distance, and � is the molar volume. �ki and �0� represent the concentration of elements in the precipitate and matrix, respectively. The parameter �0� denotes the rate of diffusion of the ith element within the matrix. The expression for the incubation time � is expressed as [54]:(9)�=12�*�2

and �*, which represents the critical energy for nucleation:(10)�*=16�3�3∆�vol2where � is the interfacial energy, and ∆Gvol the change in the volume free energy. The critical nucleus’ composition is similar to the γ′ phase’s equilibrium composition at the same temperature. � is computed based on the precipitate and matrix compositions, using a generalized nearest neighbor broken bond model, with the assumption of interfaces being planar, sharp, and coherent [56][57][58].

In Eq. 7, it is worth noting that �* represents the fundamental variable in the nucleation theory. It contains �3/∆�vol2 and is in the exponent of the nucleation rate. Therefore, even small variations in γ and/or ∆�vol can result in notable changes in �, especially if �* is in the order of �∙�. This is demonstrated in [38] for UDIMET 720 Li during continuous cooling, where these quantities change steadily during precipitation due to their dependence on matrix’ and precipitate’s temperature and composition. In the current work, these changes will be even more significant as the system is exposed to multiple cycles of rapid cooling and heating.

Once nucleated, the growth of a precipitate is assessed using the radius and composition evolution equations developed by Svoboda et al. [42] with a mean-field method that employs the thermodynamic extremal principle. The expression for the total Gibbs free energy of a thermodynamic system G, which consists of n components and m precipitates, is given as follows:(11)�=∑���0��0�+∑�=1�4���33��+∑�=1��ki�ki+∑�=1�4���2��.

The chemical potential of component � in the matrix is denoted as �0�(�=1,…,�), while the chemical potential of component � in the precipitate is represented by �ki(�=1,…,�,�=1,…,�). These chemical potentials are defined as functions of the concentrations �ki(�=1,…,�,�=1,…,�). The interface energy density is denoted as �, and �� incorporates the effects of elastic energy and plastic work resulting from the volume change of each precipitate.

Eq. (12) establishes that the total free energy of the system in its current state relies on the independent state variables: the sizes (radii) of the precipitates �� and the concentrations of each component �ki. The remaining variables can be determined by applying the law of mass conservation to each component �. This can be represented by the equation:(12)��=�0�+∑�=1�4���33�ki,

Furthermore, the global mass conservation can be expressed by equation:(13)�=∑�=1���When a thermodynamic system transitions to a more stable state, the energy difference between the initial and final stages is dissipated. This model considers three distinct forms of dissipation effects [42]. These include dissipations caused by the movement of interfaces, diffusion within the precipitate and diffusion within the matrix.

Consequently, �̇� (growth rate) and �̇ki (chemical composition’s rate of change) of the precipitate with index � are derived from the linear system of equation system:(14)�ij��=��where �� symbolizes the rates �̇� and �̇ki [42]. Index i contains variables for precipitate radius, chemical composition, and stoichiometric boundary conditions suggested by the precipitate’s crystal structure. Eq. (10) is computed separately for every precipitate �. For a more detailed description of the formulae for the coefficients �ij and �� employed in this work please refer to [59].

The MatCalc software was used to perform the numerical time integration of �̇� and �̇ki of precipitates based on the classical numerical method by Kampmann and Wagner [60]. Detailed information on this method can be found in [61]. Using this computational method, calculations for E-PBF thermal cycles (cyclic heating and cooling) were computed and compared to experimental data. The simulation took approximately 2–4 hrs to complete on a standard laptop.

3. Results

3.1. Microstructure

Fig. 1 displays a stitched overview image and selected SEM micrographs of various γ′ morphologies and carbides after observations of the X-Z surface of the build from the top to 2 mm above the bottom. Fig. 2 depicts a graph that charts the average size and phase fraction of the primary γ′, as it changes with distance from the top to the bottom of the build. The SEM micrographs show widespread primary γ′ precipitation throughout the entire build, with the size increasing in the top to bottom direction. Particularly, at the topmost height, representing the 460th layer (Z = 22.95 mm), as seen in Fig. 1b, the average size of γ′ is 110 ± 4 nm, exhibiting spherical shapes. This is representative of the microstructure after it solidifies and cools to room temperature, without experiencing additional thermal cycles. The γ′ size slightly increases to 147 ± 6 nm below this layer and remains constant until 0.4 mm (∼453rd layer) from the top. At this position, the microstructure still closely resembles that of the 460th layer. After the 453rd layer, the γ′ size grows rapidly to ∼503 ± 19 nm until reaching the 437th layer (1.2 mm from top). The γ′ particles here have a cuboidal shape, and a small fraction is coarser than 600 nm. γ′ continue to grow steadily from this position to the bottom (23 mm from the top). A small fraction of γ′ is > 800 nm.

Fig. 2

Besides primary γ′, secondary γ′ with sizes ranging from 5 to 50 nm were also found. These secondary γ′ precipitates, as seen in Fig. 1f, were present only in the bottom and middle regions. A detailed analysis of the multimodal size distribution of γ′ can be found in [16]. There is no significant variation in the phase fraction of the γ′ along the build. The phase fraction is ∼ 52%, as displayed in Fig. 2. It is worth mentioning that the total phase fraction of γ′ was estimated based on the primary γ′ phase fraction because of the small size of secondary γ′. Spherical MC carbides with sizes ranging from 50 to 400 nm and a phase fraction of 0.8% were also observed throughout the build. The carbides are the light grey precipitates in Fig. 1g. The light grey shade of carbides in the SEM images is due to their composition and crystal structure [52]. These carbides are not visible in Fig. 1b-e because they were dissolved during electro-etching carried out after electropolishing. In Fig. 1g, however, the sample was examined directly after electropolishing, without electro-etching.

Table 2 shows the nominal and measured composition of γ′ precipitates throughout the build by atom probe microscopy as determined in our previous study [17]. No build height-dependent composition difference was observed in either of the γ′ precipitate populations. However, there was a slight disparity between the composition of primary and secondary γ′. Among the main γ′ forming elements, the primary γ′ has a high Ti concentration while secondary γ′ has a high Al concentration. A detailed description of the atom distribution maps and the proxigrams of the constituent elements of γ′ throughout the build can be found in [17].

Table 2. Bulk IN738 composition determined using inductively coupled plasma atomic emission spectroscopy (ICP-AES). Compositions of γ, primary γ′, and secondary γ′ at various locations in the build measured by APT. This information is reproduced from data in Ref. [17] with permission.

at%NiCrCoAlMoWTiNbCBZrTaOthers
Bulk59.1217.478.487.001.010.813.960.490.470.050.090.560.46
γ matrix
Top50.4832.9111.591.941.390.820.440.80.030.030.020.24
Mid50.3732.6111.931.791.540.890.440.10.030.020.020.010.23
Bot48.1034.5712.082.141.430.880.480.080.040.030.010.12
Primary γ′
Top72.172.513.4412.710.250.397.780.560.030.020.050.08
Mid71.602.573.2813.550.420.687.040.730.010.030.040.04
Bot72.342.473.8612.500.260.447.460.500.050.020.020.030.04
Secondary γ′
Mid70.424.203.2314.190.631.035.340.790.030.040.040.05
Bot69.914.063.6814.320.811.045.220.650.050.100.020.11

3.2. Hardness

Fig. 3a shows the Vickers hardness mapping performed along the entire X-Z surface, while Fig. 3b shows the plot of average hardness at different build heights. This hardness distribution is consistent with the γ′ precipitate size gradient across the build direction in Fig. 1Fig. 2. The maximum hardness of ∼530 HV1 is found at ∼0.5 mm away from the top surface (Z = 22.5), where γ′ particles exhibit the smallest observed size in Fig. 2b. Further down the build (∼ 2 mm from the top), the hardness drops to the 440–490 HV1 range. This represents the region where γ′ begins to coarsen. The hardness drops further to 380–430 HV1 at the bottom of the build.

Fig. 3

3.3. Modeling of the microstructural evolution during E-PBF

3.3.1. Thermal profile modeling

Fig. 4 shows the simulated thermal profile of the E-PBF build at a location of 23 mm from the top of the build, using a semi-analytical heat conduction model. This profile consists of the time taken to deposit 460 layers until final cooling, as shown in Fig. 4a. Fig. 4b-d show the magnified regions of Fig. 4a and reveal the first 20 layers from the top, a single layer (first layer from the top), and the time taken for the build to cool after the last layer deposition, respectively.

Fig. 4

The peak temperatures experienced by previous layers decrease progressively as the number of layers increases but never fall below the build preheat temperature (1000 °C). Our simulated thermal cycle may not completely capture the complexity of the actual thermal cycle utilized in the E-PBF build. For instance, the top layer (Fig. 4c), also representing the first deposit’s thermal profile without additional cycles (from powder heating, melting, to solidification), recorded the highest peak temperature of 1390 °C. Although this temperature is above the melting range of the alloy (1230–1360 °C) [62], we believe a much higher temperature was produced by the electron beam to melt the powder. Nevertheless, the solidification temperature and dynamics are outside the scope of this study as our focus is on the solid-state phase transformations during deposition. It takes ∼25 s for each layer to be deposited and cooled to the build temperature. The interlayer dwell time is 125 s. The time taken for the build to cool to room temperature (RT) after final layer deposition is ∼4.7 hrs (17,000 s).

3.3.2. MatCalc simulation

During the MatCalc simulation, the matrix phase is defined as γ. γ′, and MC carbide are included as possible precipitates. The domain of these precipitates is set to be the matrix (γ), and nucleation is assumed to be homogenous. In homogeneous nucleation, all atoms of the unit volume are assumed to be potential nucleation sitesTable 3 shows the computational parameters used in the simulation. All other parameters were set at default values as recommended in the version 6.04.0011 of MatCalc. The values for the interfacial energies are automatically calculated according to the generalized nearest neighbor broken bond model and is one of the most outstanding features in MatCalc [56][57][58]. It should be noted that the elastic misfit strain was not included in the calculation. The output of MatCalc includes phase fraction, size, nucleation rate, and composition of the precipitates. The phase fraction in MatCalc is the volume fraction. Although the experimental phase fraction is the measured area fraction, it is relatively similar to the volume fraction. This is because of the generally larger precipitate size and similar morphology at the various locations along the build [63]. A reliable phase fraction comparison between experiment and simulation can therefore be made.

Table 3. Computational parameters used in the simulation.

Precipitation domainγ
Nucleation site γ′Bulk (homogenous)
Nucleation site MC carbideBulk (Homogenous)
Precipitates class size250
Regular solution critical temperature γ′2500 K[64]
Calculated interfacial energyγ′ = 0.080–0.140 J/m2 and MC carbide = 0.410–0.430 J/m2
3.3.2.1. Precipitate phase fraction

Fig. 5a shows the simulated phase fraction of γ′ and MC carbide during thermal cycling. Fig. 5b is a magnified view of 5a showing the simulated phase fraction at the center points of the top 70 layers, whereas Fig. 5c corresponds to the first two layers from the top. As mentioned earlier, the top layer (460th layer) represents the microstructure after solidification. The microstructure of the layers below is determined by the number of thermal cycles, which increases with distance to the top. For example, layers 459, 458, 457, up to layer 1 (region of interest) experience 1, 2, 3 and 459 thermal cycles, respectively. In the top layer in Fig. 5c, the volume fraction of γ′ and carbides increases with temperature. For γ′, it decreases to zero when the temperature is above the solvus temperature after a few seconds. Carbides, however, remain constant in their volume fraction reaching equilibrium (phase fraction ∼ 0.9%) in a short time. The topmost layer can be compared to the first deposit, and the peak in temperature symbolizes the stage where the electron beam heats the powder until melting. This means γ′ and carbide precipitation might have started in the powder particles during heating from the build temperature and electron beam until the onset of melting, where γ′ dissolves, but carbides remain stable [28].

Fig. 5

During cooling after deposition, γ′ reprecipitates at a temperature of 1085 °C, which is below its solvus temperature. As cooling progresses, the phase fraction increases steadily to ∼27% and remains constant at 1000 °C (elevated build temperature). The calculated equilibrium fraction of phases by MatCalc is used to show the complex precipitation characteristics in this alloy. Fig. 6 shows that MC carbides form during solidification at 1320 °C, followed by γ′, which precipitate when the solidified layer cools to 1140 °C. This indicates that all deposited layers might contain a negligible amount of these precipitates before subsequent layer deposition, while being at the 1000 °C build temperature or during cooling to RT. The phase diagram also shows that the equilibrium fraction of the γ′ increases as temperature decreases. For instance, at 1000, 900, and 800 °C, the phase fractions are ∼30%, 38%, and 42%, respectively.

Fig. 6

Deposition of subsequent layers causes previous layers to undergo phase transformations as they are exposed to several thermal cycles with different peak temperatures. In Fig. 5c, as the subsequent layer is being deposited, γ′ in the previous layer (459th layer) begins to dissolve as the temperature crosses the solvus temperature. This is witnessed by the reduction of the γ′ phase fraction. This graph also shows how this phase dissolves during heating. However, the phase fraction of MC carbide remains stable at high temperatures and no dissolution is seen during thermal cycling. Upon cooling, the γ′ that was dissolved during heating reprecipitates with a surge in the phase fraction until 1000 °C, after which it remains constant. This microstructure is similar to the solidification microstructure (layer 460), with a similar γ′ phase fraction (∼27%).

The complete dissolution and reprecipitation of γ′ continue for several cycles until the 50th layer from the top (layer 411), where the phase fraction does not reach zero during heating to the peak temperature (see Fig. 5d). This indicates the ‘partial’ dissolution of γ′, which continues progressively with additional layers. It should be noted that the peak temperatures for layers that underwent complete dissolution were much higher (1170–1300 °C) than the γ′ solvus.

The dissolution and reprecipitation of γ′ during thermal cycling are further confirmed in Fig. 7, which summarizes the nucleation rate, phase fraction, and concentration of major elements that form γ′ in the matrix. Fig. 7b magnifies a single layer (3rd layer from top) within the full dissolution region in Fig. 7a to help identify the nucleation and growth mechanisms. From Fig. 7b, γ′ nucleation begins during cooling whereby the nucleation rate increases to reach a maximum value of approximately 1 × 1020 m−3s−1. This fast kinetics implies that some rearrangement of atoms is required for γ′ precipitates to form in the matrix [65][66]. The matrix at this stage is in a non-equilibrium condition. Its composition is similar to the nominal composition and remains unchanged. The phase fraction remains insignificant at this stage although nucleation has started. The nucleation rate starts declining upon reaching the peak value. Simultaneously, diffusion-controlled growth of existing nuclei occurs, depleting the matrix of γ′ forming elements (Al and Ti). Thus, from (7)(11), ∆�vol continuously decreases until nucleation ceases. The growth of nuclei is witnessed by the increase in phase fraction until a constant level is reached at 27% upon cooling to and holding at build temperature. This nucleation event is repeated several times.

Fig. 7

At the onset of partial dissolution, the nucleation rate jumps to 1 × 1021 m−3s−1, and then reduces sharply at the middle stage of partial dissolution. The nucleation rate reaches 0 at a later stage. Supplementary Fig. S1 shows a magnified view of the nucleation rate, phase fraction, and thermal profile, underpinning this trend. The jump in nucleation rate at the onset is followed by a progressive reduction in the solute content of the matrix. The peak temperatures (∼1130–1160 °C) are lower than those in complete dissolution regions but still above or close to the γ′ solvus. The maximum phase fraction (∼27%) is similar to that of the complete dissolution regions. At the middle stage, the reduction in nucleation rate is accompanied by a sharp drop in the matrix composition. The γ′ fraction drops to ∼24%, where the peak temperatures of the layers are just below or at γ′ solvus. The phase fraction then increases progressively through the later stage of partial dissolution to ∼30% towards the end of thermal cycling. The matrix solute content continues to drop although no nucleation event is seen. The peak temperatures are then far below the γ′ solvus. It should be noted that the matrix concentration after complete dissolution remains constant. Upon cooling to RT after final layer deposition, the nucleation rate increases again, indicating new nucleation events. The phase fraction reaches ∼40%, with a further depletion of the matrix in major γ′ forming elements.

3.3.2.2. γ′ size distribution

Fig. 8 shows histograms of the γ′ precipitate size distributions (PSD) along the build height during deposition. These PSDs are predicted at the end of each layer of interest just before final cooling to room temperature, to separate the role of thermal cycles from final cooling on the evolution of γ′. The PSD for the top layer (layer 460) is shown in Fig. 8a (last solidified region with solidification microstructure). The γ′ size ranges from 120 to 230 nm and is similar to the 44 layers below (2.2 mm from the top).

Fig. 8

Further down the build, γ′ begins to coarsen after layer 417 (44th layer from top). Fig. 8c shows the PSD after the 44th layer, where the γ′ size exhibits two peaks at ∼120–230 and ∼300 nm, with most of the population being in the former range. This is the onset of partial dissolution where simultaneously with the reprecipitation and growth of fresh γ′, the undissolved γ′ grows rapidly through diffusive transport of atoms to the precipitates. This is shown in Fig. 8c, where the precipitate class sizes between 250 and 350 represent the growth of undissolved γ′. Although this continues in the 416th layer, the phase fractions plot indicates that the onset of partial dissolution begins after the 411th layer. This implies that partial dissolution started early, but the fraction of undissolved γ′ was too low to impact the phase fraction. The reprecipitated γ′ are mostly in the 100–220 nm class range and similar to those observed during full dissolution.

As the number of layers increases, coarsening intensifies with continued growth of more undissolved γ′, and reprecipitation and growth of partially dissolved ones. Fig. 8d, e, and f show this sequence. Further down the build, coarsening progresses rapidly, as shown in Figs. 8d, 8e, and 8f. The γ′ size ranges from 120 to 1100 nm, with the peaks at 160, 180, and 220 nm in Figs. 8d, 8e, and 8f, respectively. Coarsening continues until nucleation ends during dissolution, where only the already formed γ′ precipitates continue to grow during further thermal cycling. The γ′ size at this point is much larger, as observed in layers 361 and 261, and continues to increase steadily towards the bottom (layer 1). Two populations in the ranges of ∼380–700 and ∼750–1100 nm, respectively, can be seen. The steady growth of γ′ towards the bottom is confirmed by the gradual decrease in the concentration of solute elements in the matrix (Fig. 7a). It should be noted that for each layer, the γ′ class with the largest size originates from continuous growth of the earliest set of the undissolved precipitates.

Fig. 9Fig. 10 and supplementary Figs. S2 and S3 show the γ′ size evolution during heating and cooling of a single layer in the full dissolution region, and early, middle stages, and later stages of partial dissolution, respectively. In all, the size of γ′ reduces during layer heating. Depending on the peak temperature of the layer which varies with build height, γ′ are either fully or partially dissolved as mentioned earlier. Upon cooling, the dissolved γ′ reprecipitate.

Fig. 9
Fig. 10

In Fig. 9, those layers that underwent complete dissolution (top layers) were held above γ′ solvus temperature for longer. In Fig. 10, layers at the early stage of partial dissolution spend less time in the γ′ solvus temperature region during heating, leading to incomplete dissolution. In such conditions, smaller precipitates are fully dissolved while larger ones shrink [67]. Layers in the middle stages of partial dissolution have peak temperatures just below or at γ′ solvus, not sufficient to achieve significant γ′ dissolution. As seen in supplementary Fig. S2, only a few smaller γ′ are dissolved back into the matrix during heating, i.e., growth of precipitates is more significant than dissolution. This explains the sharp decrease in concentration of Al and Ti in the matrix in this layer.

The previous sections indicate various phenomena such as an increase in phase fraction, further depletion of matrix composition, and new nucleation bursts during cooling. Analysis of the PSD after the final cooling of the build to room temperature allows a direct comparison to post-printing microstructural characterization. Fig. 11 shows the γ′ size distribution of layer 1 (460th layer from the top) after final cooling to room temperature. Precipitation of secondary γ′ is observed, leading to the multimodal size distribution of secondary and primary γ′. The secondary γ′ size falls within the 10–80 nm range. As expected, a further growth of the existing primary γ′ is also observed during cooling.

Fig. 11
3.3.2.3. γ′ chemistry after deposition

Fig. 12 shows the concentration of the major elements that form γ′ (Al, Ti, and Ni) in the primary and secondary γ′ at the bottom of the build, as calculated by MatCalc. The secondary γ′ has a higher Al content (13.5–14.5 at% Al), compared to 13 at% Al in the primary γ′. Additionally, within the secondary γ′, the smallest particles (∼10 nm) have higher Al contents than larger ones (∼70 nm). In contrast, for the primary γ′, there is no significant variation in the Al content as a function of their size. The Ni concentration in secondary γ′ (71.1–72 at%) is also higher in comparison to the primary γ′ (70 at%). The smallest secondary γ′ (∼10 nm) have higher Ni contents than larger ones (∼70 nm), whereas there is no substantial change in the Ni content of primary γ′, based on their size. As expected, Ti shows an opposite size-dependent variation. It ranges from ∼ 7.7–8.7 at% Ti in secondary γ′ to ∼9.2 at% in primary γ′. Similarly, within the secondary γ′, the smallest (∼10 nm) have lower Al contents than the larger ones (∼70 nm). No significant variation is observed for Ti content in primary γ′.

Fig. 12

4. Discussion

A combined modelling method is utilized to study the microstructural evolution during E-PBF of IN738. The presented results are discussed by examining the precipitation and dissolution mechanism of γ′ during thermal cycling. This is followed by a discussion on the phase fraction and size evolution of γ′ during thermal cycling and after final cooling. A brief discussion on carbide morphology is also made. Finally, a comparison is made between the simulation and experimental results to assess their agreement.

4.1. γ′ morphology as a function of build height

4.1.1. Nucleation of γ′

The fast precipitation kinetics of the γ′ phase enables formation of γ′ upon quenching from higher temperatures (above solvus) during thermal cycling [66]. In Fig. 7b, for a single layer in the full dissolution region, during cooling, the initial increase in nucleation rate signifies the first formation of nuclei. The slight increase in nucleation rate during partial dissolution, despite a decrease in the concentration of γ′ forming elements, may be explained by the nucleation kinetics. During partial dissolution and as the precipitates shrink, it is assumed that the regions at the vicinity of partially dissolved precipitates are enriched in γ′ forming elements [68][69]. This differs from the full dissolution region, in which case the chemical composition is evenly distributed in the matrix. Several authors have attributed the solute supersaturation of the matrix around primary γ′ to partial dissolution during isothermal ageing [69][70][71][72]. The enhanced supersaturation in the regions close to the precipitates results in a much higher driving force for nucleation, leading to a higher nucleation rate upon cooling. This phenomenon can be closely related to the several nucleation bursts upon continuous cooling of Ni-based superalloys, where second nucleation bursts exhibit higher nucleation rates [38][68][73][74].

At middle stages of partial dissolution, the reduction in the nucleation rate indicates that the existing composition and low supersaturation did not trigger nucleation as the matrix was closer to the equilibrium state. The end of a nucleation burst means that the supersaturation of Al and Ti has reached a low level, incapable of providing sufficient driving force during cooling to or holding at 1000 °C for further nucleation [73]. Earlier studies on Ni-based superalloys have reported the same phenomenon during ageing or continuous cooling from the solvus temperature to RT [38][73][74].

4.1.2. Dissolution of γ′ during thermal cycling

γ′ dissolution kinetics during heating are fast when compared to nucleation due to exponential increase in phase transformation and diffusion activities with temperature [65]. As shown in Fig. 9Fig. 10, and supplementary Figs. S2 and S3, the reduction in γ′ phase fraction and size during heating indicates γ′ dissolution. This is also revealed in Fig. 5 where phase fraction decreases upon heating. The extent of γ′ dissolution mostly depends on the temperature, time spent above γ′ solvus, and precipitate size [75][76][77]. Smaller γ′ precipitates are first to be dissolved [67][77][78]. This is mainly because more solute elements need to be transported away from large γ′ precipitates than from smaller ones [79]. Also, a high temperature above γ′ solvus temperature leads to a faster dissolution rate [80]. The equilibrium solvus temperature of γ′ in IN738 in our MatCalc simulation (Fig. 6) and as reported by Ojo et al. [47] is 1140 °C and 1130–1180 °C, respectively. This means the peak temperature experienced by previous layers decreases progressively from γ′ supersolvus to subsolvus, near-solvus, and far from solvus as the number of subsequent layers increases. Based on the above, it can be inferred that the degree of dissolution of γ′ contributes to the gradient in precipitate distribution.

Although the peak temperatures during later stages of partial dissolution are much lower than the equilibrium γ′ solvus, γ′ dissolution still occurs but at a significantly lower rate (supplementary Fig. S3). Wahlmann et al. [28] also reported a similar case where they observed the rapid dissolution of γ′ in CMSX-4 during fast heating and cooling cycles at temperatures below the γ′ solvus. They attributed this to the γ′ phase transformation process taking place in conditions far from the equilibrium. While the same reasoning may be valid for our study, we further believe that the greater surface area to volume ratio of the small γ′ precipitates contributed to this. This ratio means a larger area is available for solute atoms to diffuse into the matrix even at temperatures much below the solvus [81].

4.2. γ′ phase fraction and size evolution

4.2.1. During thermal cycling

In the first layer, the steep increase in γ′ phase fraction during heating (Fig. 5), which also represents γ′ precipitation in the powder before melting, has qualitatively been validated in [28]. The maximum phase fraction of 27% during the first few layers of thermal cycling indicates that IN738 theoretically could reach the equilibrium state (∼30%), but the short interlayer time at the build temperature counteracts this. The drop in phase fraction at middle stages of partial dissolution is due to the low number of γ′ nucleation sites [73]. It has been reported that a reduction of γ′ nucleation sites leads to a delay in obtaining the final volume fraction as more time is required for γ′ precipitates to grow and reach equilibrium [82]. This explains why even upon holding for 150 s before subsequent layer deposition, the phase fraction does not increase to those values that were observed in the previous full γ′ dissolution regions. Towards the end of deposition, the increase in phase fraction to the equilibrium value of 30% is as a result of the longer holding at build temperature or close to it [83].

During thermal cycling, γ′ particles begin to grow immediately after they first precipitate upon cooling. This is reflected in the rapid increase in phase fraction and size during cooling in Fig. 5 and supplementary Fig. S2, respectively. The rapid growth is due to the fast diffusion of solute elements at high temperatures [84]. The similar size of γ′ for the first 44 layers from the top can be attributed to the fact that all layers underwent complete dissolution and hence, experienced the same nucleation event and growth during deposition. This corresponds with the findings by Balikci et al. [85], who reported that the degree of γ′ precipitation in IN738LC does not change when a solution heat treatment is conducted above a certain critical temperature.

The increase in coarsening rate (Fig. 8) during thermal cycling can first be ascribed to the high peak temperature of the layers [86]. The coarsening rate of γ′ is known to increase rapidly with temperature due to the exponential growth of diffusion activity. Also, the simultaneous dissolution with coarsening could be another reason for the high coarsening rate, as γ′ coarsening is a diffusion-driven process where large particles grow by consuming smaller ones [78][84][86][87]. The steady growth of γ′ towards the bottom of the build is due to the much lower layer peak temperature, which is almost close to the build temperature, and reduced dissolution activity, as is seen in the much lower solute concentration in γ′ compared to those in the full and partial dissolution regions.

4.2.2. During cooling

The much higher phase fraction of ∼40% upon cooling signifies the tendency of γ′ to reach equilibrium at lower temperatures (Fig. 4). This is due to the precipitation of secondary γ′ and a further increase in the size of existing primary γ′, which leads to a multimodal size distribution of γ′ after cooling [38][73][88][89][90]. The reason for secondary γ′ formation during cooling is as follows: As cooling progresses, it becomes increasingly challenging to redistribute solute elements in the matrix owing to their lower mobility [38][73]. A higher supersaturation level in regions away from or free of the existing γ′ precipitates is achieved, making them suitable sites for additional nucleation bursts. More cooling leads to the growth of these secondary γ′ precipitates, but as the temperature and in turn, the solute diffusivity is low, growth remains slow.

4.3. Carbides

MC carbides in IN738 are known to have a significant impact on the high-temperature strength. They can also act as effective hardening particles and improve the creep resistance [91]. Precipitation of MC carbides in IN738 and several other superalloys is known to occur during solidification or thermal treatments (e.g., hot isostatic pressing) [92]. In our case, this means that the MC carbides within the E-PBF build formed because of the thermal exposure from the E-PBF thermal cycle in addition to initial solidification. Our simulation confirms this as MC carbides appear during layer heating (Fig. 5). The constant and stable phase fraction of MC carbides during thermal cycling can be attributed to their high melting point (∼1360 °C) and the short holding time at peak temperatures [75][93][94]. The solvus temperature for most MC carbides exceeds most of the peak temperatures observed in our simulation, and carbide dissolution kinetics at temperatures above the solvus are known to be comparably slow [95]. The stable phase fraction and random distribution of MC carbides signifies the slight influence on the gradient in hardness.

4.4. Comparison of simulations and experiments

4.4.1. Precipitate phase fraction and morphology as a function of build height

A qualitative agreement is observed for the phase fraction of carbides, i.e. ∼0.8% in the experiment and ∼0.9% in the simulation. The phase fraction of γ′ differs, with the experiment reporting a value of ∼51% and the simulation, 40%. Despite this, the size distribution of primary γ′ along the build shows remarkable consistency between experimental and computational analyses. It is worth noting that the primary γ′ morphology in the experimental analysis is observed in the as-fabricated state, whereas the simulation (Fig. 8) captures it during deposition process. The primary γ′ size in the experiment is expected to experience additional growth during the cooling phase. Regardless, both show similar trends in primary γ′ size increments from the top to the bottom of the build. The larger primary γ’ size in the simulation versus the experiment can be attributed to the fact that experimental and simulation results are based on 2D and 3D data, respectively. The absence of stereological considerations [96] in our analysis could have led to an underestimation of the precipitate sizes from SEM measurements. The early starts of coarsening (8th layer) in the experiment compared to the simulation (45th layer) can be attributed to a higher actual γ′ solvus temperature than considered in our simulation [47]. The solvus temperature of γ′ in a Ni-based superalloy is mainly determined by the detailed composition. A high amount of Cr and Co are known to reduce the solvus temperature, whereas Ta and Mo will increase it [97][98][99]. The elemental composition from our experimental work was used for the simulation except for Ta. It should be noted that Ta is not included in the thermodynamic database in MatCalc used, and this may have reduced the solvus temperature. This could also explain the relatively higher γ′ phase fraction in the experiment than in simulation, as a higher γ′ solvus temperature will cause more γ′ to precipitate and grow early during cooling [99][100].

Another possible cause of this deviation can be attributed to the extent of γ′ dissolution, which is mainly determined by the peak temperature. It can be speculated that individual peak temperatures at different layers in the simulation may have been over-predicted. However, one needs to consider that the true thermal profile is likely more complicated in the actual E-PBF process [101]. For example, the current model assumes that the thermophysical properties of the material are temperature-independent, which is not realistic. Many materials, including IN738, exhibit temperature-dependent properties such as thermal conductivityspecific heat capacity, and density [102]. This means that heat transfer simulations may underestimate or overestimate the temperature gradients and cooling rates within the powder bed and the solidified part. Additionally, the model does not account for the reduced thermal diffusivity through unmelted powder, where gas separating the powder acts as insulation, impeding the heat flow [1]. In E-PBF, the unmelted powder regions with trapped gas have lower thermal diffusivity compared to the fully melted regions, leading to localized temperature variations, and altered solidification behavior. These limitations can impact the predictions, particularly in relation to the carbide dissolution, as the peak temperatures may be underestimated.

While acknowledging these limitations, it is worth emphasizing that achieving a detailed and accurate representation of each layer’s heat source would impose tough computational challenges. Given the substantial layer count in E-PBF, our decision to employ a semi-analytical approximation strikes a balance between computational feasibility and the capture of essential trends in thermal profiles across diverse build layers. In future work, a dual-calibration strategy is proposed to further reduce simulation-experiment disparities. By refining temperature-independent thermophysical property approximations and absorptivity in the heat source model, and by optimizing interfacial energy descriptions in the kinetic model, the predictive precision could be enhanced. Further refining the simulation controls, such as adjusting the precipitate class size may enhance quantitative comparisons between modeling outcomes and experimental data in future work.

4.4.2. Multimodal size distribution of γ′ and concentration

Another interesting feature that sees qualitative agreement between the simulation and the experiment is the multimodal size distribution of γ′. The formation of secondary γ′ particles in the experiment and most E-PBF Ni-based superalloys is suggested to occur at low temperatures, during final cooling to RT [16][73][90]. However, so far, this conclusion has been based on findings from various continuous cooling experiments, as the study of the evolution during AM would require an in-situ approach. Our simulation unambiguously confirms this in an AM context by providing evidence for secondary γ′ precipitation during slow cooling to RT. Additionally, it is possible to speculate that the chemical segregation occurring during solidification, due to the preferential partitioning of certain elements between the solid and liquid phases, can contribute to the multimodal size distribution during deposition [51]. This is because chemical segregation can result in variations in the local composition of superalloys, which subsequently affects the nucleation and growth of γ′. Regions with higher concentrations of alloying elements will encourage the formation of larger γ′ particles, while regions with lower concentrations may favor the nucleation of smaller precipitates. However, it is important to acknowledge that the elevated temperature during the E-PBF process will largely homogenize these compositional differences [103][104].

A good correlation is also shown in the composition of major γ′ forming elements (Al and Ti) in primary and secondary γ′. Both experiment and simulation show an increasing trend for Al content and a decreasing trend for Ti content from primary to secondary γ′. The slight composition differences between primary and secondary γ′ particles are due to the different diffusivity of γ′ stabilizers at different thermal conditions [105][106]. As the formation of multimodal γ′ particles with different sizes occurs over a broad temperature range, the phase chemistry of γ′ will be highly size dependent. The changes in the chemistry of various γ′ (primary, secondary, and tertiary) have received significant attention since they have a direct influence on the performance [68][105][107][108][109]. Chen et al. [108][109], reported a high Al content in the smallest γ′ precipitates compared to the largest, while Ti showed an opposite trend during continuous cooling in a RR1000 Ni-based superalloy. This was attributed to the temperature and cooling rate at which the γ′ precipitates were formed. The smallest precipitates formed last, at the lowest temperature and cooling rate. A comparable observation is evident in the present investigation, where the secondary γ′ forms at a low temperature and cooling rate in comparison to the primary. The temperature dependence of γ′ chemical composition is further evidenced in supplementary Fig. S4, which shows the equilibrium chemical composition of γ′ as a function of temperature.

5. Conclusions

A correlative modelling approach capable of predicting solid-state phase transformations kinetics in metal AM was developed. This approach involves computational simulations with a semi-analytical heat transfer model and the MatCalc thermo-kinetic software. The method was used to predict the phase transformation kinetics and detailed morphology and chemistry of γ′ and MC during E-PBF of IN738 Ni-based superalloy. The main conclusions are:

  • 1.The computational simulations are in qualitative agreement with the experimental observations. This is particularly true for the γ′ size distribution along the build height, the multimodal size distribution of particles, and the phase fraction of MC carbides.
  • 2.The deviations between simulation and experiment in terms of γ′ phase fraction and location in the build are most likely attributed to a higher γ′ solvus temperature during the experiment than in the simulation, which is argued to be related to the absence of Ta in the MatCalc database.
  • 3.The dissolution and precipitation of γ′ occur fast and under non-equilibrium conditions. The level of γ′ dissolution determines the gradient in γ′ size distribution along the build. After thermal cycling, the final cooling to room temperature has further significant impacts on the final γ′ size, morphology, and distribution.
  • 4.A negligible amount of γ′ forms in the first deposited layer before subsequent layer deposition, and a small amount of γ′ may also form in the powder induced by the 1000 °C elevated build temperature before melting.

Our findings confirm the suitability of MatCalc to predict the microstructural evolution at various positions throughout a build in a Ni-based superalloy during E-PBF. It also showcases the suitability of a tool which was originally developed for traditional thermo-mechanical processing of alloys to the new additive manufacturing context. Our simulation capabilities are likely extendable to other alloy systems that undergo solid-state phase transformations implemented in MatCalc (various steels, Ni-based superalloys, and Al-alloys amongst others) as well as other AM processes such as L-DED and L-PBF which have different thermal cycle characteristics. New tools to predict the microstructural evolution and properties during metal AM are important as they provide new insights into the complexities of AM. This will enable control and design of AM microstructures towards advanced materials properties and performances.

CRediT authorship contribution statement

Primig Sophie: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Adomako Nana Kwabena: Writing – original draft, Writing – review & editing, Visualization, Software, Investigation, Formal analysis, Conceptualization. Haghdadi Nima: Writing – review & editing, Supervision, Project administration, Methodology, Conceptualization. Dingle James F.L.: Methodology, Conceptualization, Software, Writing – review & editing, Visualization. Kozeschnik Ernst: Writing – review & editing, Software, Methodology. Liao Xiaozhou: Writing – review & editing, Project administration, Funding acquisition. Ringer Simon P: Writing – review & editing, Project administration, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was sponsored by the Department of Industry, Innovation, and Science under the auspices of the AUSMURI program – which is a part of the Commonwealth’s Next Generation Technologies Fund. The authors acknowledge the facilities and the scientific and technical assistance at the Electron Microscope Unit (EMU) within the Mark Wainwright Analytical Centre (MWAC) at UNSW Sydney and Microscopy Australia. Nana Adomako is supported by a UNSW Scientia PhD scholarship. Michael Haines’ (UNSW Sydney) contribution to the revised version of the original manuscript is thankfully acknowledged.

Appendix A. Supplementary material

Download : Download Word document (462KB)

Supplementary material.

Data Availability

Data will be made available on request.

References

Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

Yupeng Ren abc, Huiguang Zhou cd, Houjie Wang ab, Xiao Wu ab, Guohui Xu cd, Qingsheng Meng cd

Abstract

해저 퇴적물 흐름은 퇴적물을 심해로 운반하는 주요 수단 중 하나이며, 종종 장거리를 이동하고 수십 또는 수백 킬로미터에 걸쳐 상당한 양의 퇴적물을 운반합니다. 그것의 강력한 파괴력은 종종 이동 과정에서 잠수함 유틸리티에 심각한 손상을 초래합니다.

퇴적물 흐름의 퇴적물 농도는 주변 해수와의 밀도차를 결정하며, 이 밀도 차이는 퇴적물 흐름의 흐름 능력을 결정하여 이송된 퇴적물의 최종 퇴적 위치에 영향을 미칩니다. 본 논문에서는 다양한 미사 및 점토 중량비(미사/점토 비율이라고 함)를 갖는 다양한 퇴적물 농도의 퇴적물 흐름을 수로 테스트를 통해 연구합니다.

우리의 테스트 결과는 특정 퇴적물 구성에 대해 퇴적물 흐름이 가장 빠르게 이동하는 임계 퇴적물 농도가 있음을 나타냅니다. 4가지 미사/점토 비율 각각에 대한 임계 퇴적물 농도와 이에 상응하는 최대 속도가 구해집니다. 결과는 점토 함량이 임계 퇴적물 농도와 선형적으로 음의 상관 관계가 있음을 나타냅니다.

퇴적물 농도가 증가함에 따라 퇴적물의 흐름 거동은 흐름 상태에서 붕괴된 상태로 변환되고 흐름 거동이 변화하는 두 탁한 현탁액의 유체 특성은 모두 Bingham 유체입니다.

또한 본 논문에서는 퇴적물 흐름 내 입자 배열을 분석하여 위에서 언급한 결과에 대한 미시적 설명도 제공합니다.

Submarine sediment flows is one of the main means for transporting sediment to the deep sea, often traveling long-distance and transporting significant volumes of sediment for tens or even hundreds of kilometers. Its strong destructive force often causes serious damage to submarine utilities on its course of movement. The sediment concentration of the sediment flow determines its density difference with the ambient seawater, and this density difference determines the flow ability of the sediment flow, and thus affects the final deposition locations of the transported sediment. In this paper, sediment flows of different sediment concentration with various silt and clay weight ratios (referred to as silt/clay ratio) are studied using flume tests. Our test results indicate that there is a critical sediment concentration at which sediment flows travel the fastest for a specific sediment composition. The critical sediment concentrations and their corresponding maximum velocities for each of the four silt/clay ratios are obtained. The results further indicate that the clay content is linearly negatively correlated with the critical sediment concentration. As the sediment concentration increases, the flow behaviors of sediment flows transform from the flow state to the collapsed state, and the fluid properties of the two turbid suspensions with changing flow behaviors are both Bingham fluids. Additionally, this paper also provides a microscopic explanation of the above-mentioned results by analyzing the arrangement of particles within the sediment flow.

Introduction

Submarine sediment flows are important carriers for sea floor sediment movement and may carry and transport significant volumes of sediment for tens or even hundreds of kilometers (Prior et al., 1987; Pirmez and Imran, 2003; Zhang et al., 2018). Earthquakes, storms, and floods may all trigger submarine sediment flow events (Hsu et al., 2008; Piper and Normark, 2009; Pope et al., 2017b; Gavey et al., 2017). Sediment flows have strong forces during the movement, which will cause great harm to submarine structures such as cables and pipelines (Pope et al., 2017a). It was first confirmed that the cable breaking event caused by the sediment flow occurred in 1929. The sediment flow triggered by the Grand Banks earthquake damaged 12 cables. According to the time sequence of the cable breaking, the maximum velocity of the sediment flow is as high as 28 m/s (Heezen and Ewing, 1952; Kuenen, 1952; Heezen et al., 1954). Subsequent research shows that the lowest turbidity velocity that can break the cable also needs to reach 19 m/s (Piper et al., 1988). Since then, there have been many damage events of submarine cables and oil and gas pipelines caused by sediment flows in the world (Hsu et al., 2008; Carter et al., 2012; Cattaneo et al., 2012; Carter et al., 2014). During its movement, the sediment flow will gradually deposit a large amount of sediment carried by it along the way, that is, the deposition process of the sediment flow. On the one hand, this process brings a large amount of terrestrial nutrients and other materials to the ocean, while on the other hand, it causes damage and burial to benthic organisms, thus forming the largest sedimentary accumulation on Earth – submarine fans, which are highly likely to become good reservoirs for oil and gas resources (Daly, 1936; Yuan et al., 2010; Wu et al., 2022). The study on sediment flows (such as, the study of flow velocity and the forces acting on seabed structures) can provide important references for the safe design of seabed structures, the protection of submarine ecosystems, and exploration of turbidity sediments related oil and gas deposits. Therefore, it is of great significance to study the movement of sediment flows.

The sediment flow, as a highly sediment-concentrated fluid flowing on the sea floor, has a dense bottom layer and a dilute turbulent cloud. Observations at the Monterey Canyon indicated that the sediment flow can maintain its movement over long distances if its bottom has a relatively high sediment concentration. This dense bottom layer can be very destructive along its movement path to any facilities on the sea floor (Paull et al., 2018; Heerema et al., 2020; Wang et al., 2020). The sediment flow mentioned in this research paper is the general term of sediment density flow.

The sediment flow, which occurs on the seafloor, has the potential to cause erosion along its path. In this process, the suspended sediment is replenished, allowing the sediment flow to maintain its continuous flow capacity (Zhao et al., 2018). The dynamic force of sediment flow movement stem from its own gravity and density difference with surrounding water. In cases that the gravity drive of the slope is absent (on a flat sea floor), the flow velocity and distance of sediment flows are essentially determined by the sediment composition and concentration of the sediment flows as previous studies have demonstrated. Ilstad et al. (2004) conducted underwater flow tests in a sloped tank and employed high speed video camera to perform particle tracking. The results indicated that the premixed sand-rich and clay-rich slurries demonstrated different flow velocity and flow behavior. Using mixed kaolinite(d50 = 6 μm) and silica flour(d50 = 9 μm) in three compositions with total volumetric concentration ranged 22% or 28%, Felix and Peakall (2006) carried out underwater flow tests in a 5° slope Perspex channel and found that the flow ability of sediment flows is different depending on sediment compositions and concentrations. Sumner et al. (2009) used annular flume experiments to investigate the depositional dynamics and deposits of waning sediment-laden flows, finding that decelerating fast flows with fixed sand content and variable mud content resulted in four different deposit types. Chowdhury and Testik (2011) used lock-exchange tank, and experimented the kaolin clay sediment flows in the concentration range of 25–350 g/L, and predicted the fluid mud sediment flows propagation characteristics, but this study focused on giving sediment flows propagate phase transition time parameters, and is limited to clay. Lv et al. (2017) found through experiments that the rheological properties and flow behavior of kaolin clay (d50 = 3.7 μm) sediment flows were correlated to clay concentrations. In the field monitoring conducted by Liu et al. (2023) at the Manila Trench in the South China Sea in 2021, significant differences in the velocity, movement distance, and flow morphology of turbidity currents were observed. These differences may be attributed to variations in the particle composition of the turbidity currents.

On low and gentle slopes, although sediment flow with sand as the main sediment composition moves faster, it is difficult to propagate over long distances because sand has greater settling velocity and subaqueous angle of repose. Whereas the sediment flows with silt and clay as main composition may maintain relatively stable currents. Although its movement speed is slow, it has the ability to propagate over long distances because of the low settling rate of the fine particles (Ilstad et al., 2004; Liu et al., 2023). In a field observation at the Gaoping submarine canyon, the sediments collected from the sediment flows exhibited grain size gradation and the sediment was mostly composed of silt and clay (Liu et al., 2012). At the largest deltas in the world, for instance, the Mississippi River Delta, the sediments are mainly composed of silt and clay, which generally distributed along the coast in a wide range and provided the sediment sources for further distribution. The sediment flows originated and transported sediment from the coast to the deep sea are therefore share the same sediment compositions as delta sediments. To study the sediment flows composed of silt and clay is of great importance.

The sediment concentration of the sediment flows determines the density difference between the sediment flows and the ambient water and plays a key role in its flow ability. For the sediment flow with sediment composed of silt and clay, low sediment concentration means low density and therefore leads to low flow ability; however, although high sediment concentration results in high density, since there is cohesion between fine particles, it changes fluid properties and leads to low flow ability as well. Therefore, there should be a critical sediment concentration with mixed composition of silt and clay, at which the sediment flow maintains its strongest flow capacity and have the highest movement speed. In other words, the two characteristics of particle diameter and concentration of the sediment flow determine its own motion ability, which, if occurs, may become the most destructive force to submarine structures.

The objectives of this work was to study how the sediment composition (measured in relative weight of silt and clay, and referred as silt/clay ratio) and sediment concentration affect flow ability and behavior of the sediment flows, and to quantify the critical sediment concentration at which the sediment flows reached the greatest flow velocity under the experiment setting. We used straight flume without slope and conducted a series of flume tests with varying sediment compositions (silt-rich or clay-rich) and concentrations (96 to 1212 g/L). Each sediment flow sample was tested and analyzed for rheological properties using a rheometer, in order to characterize the relationship between flow behavior and rheological properties. Combined with the particle diameter, density and viscosity characteristics of the sediment flows measured in the experiment, a numerical modeling study is conducted, which are mutually validated with the experimental results.

The sediment concentration determines the arrangements of the sediment particles in the turbid suspension, and the arrangement impacts the fluid properties of the turbid suspension. The microscopic mode of particle arrangement in the turbid suspension can be constructed to further analyze the relationship between the fluid properties of turbid suspension and the flow behaviors of the sediment flow, and then characterize the critical sediment concentration at which the sediment flow runs the fastest. A simplified microscopic model of particle arrangement in turbid suspension was constructed to analyze the microscopic arrangement characteristics of sediment particles in turbid suspension with the fastest velocity.

Section snippets

Equipment and materials

The sediment flows flow experiments were performed in a Perspex channel with smooth transparent walls. The layout and dimensions of the experimental set-up were shown in Fig. 1. The bottom of the channel was flat and straight, and a gate was arranged to separate the two tanks. In order to study the flow capacity of turbidity currents from the perspective of their own composition (particle size distribution and concentration), we used a straight channel instead of an inclined one, to avoid any

Relationship between sediment flow flow velocity and sediment concentration

After the sediment flow is generated, its movement in the first half (50 cm) of the channel is relatively stable, and there is obvious shock diffusion in the second half. The reason is that the excitation wave (similar to the surge) will be formed during the sediment flow movement, and its speed is much faster than the speed of the sediment flow head. When the excitation wave reaches the tail of the channel, it will be reflected, thus affecting the subsequent flow of the sediment flow.

Sediment flows motion simulation based on FLOW-3D

As a relatively mature 3D fluid simulation software, FLOW-3D can accurately predict the free surface flow, and has been used to simulate the movement process of sediment flows for many times (Heimsund, 2007). The model adopted in this paper is RNG turbulence model, which can better deal with the flow with high strain rate and is suitable for the simulation of sediment flows with variable shape during movement. The governing equations of the numerical model involved include continuity equation,

Conclusions

In this study, we conducted a series of sediment flow flume tests with mixed silt and clay sediment samples in four silt/clay ratios on a flat slope. Rheological measurements were carried out on turbid suspension samples and microstructure analysis of the sediment particle arrangements was conducted, we concluded that:

  • (1)The flow velocity of the sediment flow is controlled by the sediment concentration and its own particle diameter composition, the flow velocity increased with the increase of the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant no. 42206055]; the National Natural Science Foundation of China [Grant no. 41976049]; and the National Natural Science Foundation of China [Grant no. 42272327].

References (39)

There are more references available in the full text version of this article.

Figure 2-15: Système expérimental du plan incliné

새로운 콘크리트의 유체 흐름 모델링

Sous la direction de :
Marc Jolin, directeur de recherche
Benoit Bissonnette, codirecteur de recherche

Modélisation de l’écoulement du béton frais

Abstract

현재의 기후 비상 사태와 기후 변화에 관한 다양한 과학적 보고서를 고려할 때 인간이 만든 오염을 대폭 줄이는 것은 필수적이며 심지어 중요합니다. 최신 IPCC(기후변화에 관한 정부 간 패널) 보고서(2022)는 2030년까지 배출량을 절반으로 줄여야 함을 나타내며, 지구 보존을 위해 즉각적인 조치를 취해야 한다고 강력히 강조합니다.

이러한 의미에서 콘크리트 생산 산업은 전체 인간 이산화탄소 배출량의 4~8%를 담당하고 있으므로 환경에 미치는 영향을 줄이기 위한 진화가 시급히 필요합니다.

본 연구의 주요 목적은 이미 사용 가능한 기술적 품질 관리 도구를 사용하여 생산을 최적화하고 혼합 시간을 단축하며 콘크리트 폐기물을 줄이기 위한 신뢰할 수 있고 활용 가능한 수치 모델을 개발함으로써 이러한 산업 전환에 참여하는 것입니다.

실제로, 혼합 트럭 내부의 신선한 콘크리트의 거동과 흐름 프로파일을 더 잘 이해할 수 있는 수치 시뮬레이션을 개발하면 혼합 시간과 비용을 더욱 최적화할 수 있으므로 매우 유망합니다. 이러한 복잡한 수치 도구를 활용할 수 있으려면 수치 시뮬레이션을 검증, 특성화 및 보정하기 위해 기본 신 콘크리트 흐름 모델의 구현이 필수적입니다.

이 논문에서는 세 가지 단순 유동 모델의 개발이 논의되고 얻은 결과는 신선한 콘크리트 유동의 수치적 거동을 검증하는 데 사용됩니다. 이러한 각 모델은 강점과 약점을 갖고 있으며, 신선한 콘크리트의 유변학과 유동 거동을 훨씬 더 잘 이해할 수 있는 수치 작업 환경을 만드는 데 기여합니다.

따라서 이 연구 프로젝트는 새로운 콘크리트 생산의 완전한 모델링을 위한 진정한 관문입니다.

In view of the current climate emergency and the various scientific reports on climate change, it is essential and even vital to drastically reduce man-made pollution. The latest IPCC (Intergovernmental Panel on Climate Change) report (2022) indicates that emissions must be halved by 2030 and strongly emphasizes the need to act immediately to preserve the planet. In this sense, the concrete production industry is responsible for 4-8% of total human carbon dioxide emissions and therefore urgently needs to evolve to reduce its environmental impact. The main objective of this study is to participate in this industrial transition by developing a reliable and exploitable numerical model to optimize the production, reduce mixing time and also reduce concrete waste by using technological quality control tools already available. Indeed, developing a numerical simulation allowing to better understand the behavior and flow profiles of fresh concrete inside a mixing-truck is extremely promising as it allows for further optimization of mixing times and costs. In order to be able to exploit such a complex numerical tool, the implementation of elementary fresh concrete flow models is essential to validate, characterize and calibrate the numerical simulations. In this thesis, the development of three simple flow models is discussed and the results obtained are used to validate the numerical behavior of fresh concrete flow. Each of these models has strengths and weaknesses and contributes to the creation of a numerical working environment that provides a much better understanding of the rheology and flow behavior of fresh concrete. This research project is therefore a real gateway to a full modelling of fresh concrete production.


Key words

fresh concrete, rheology, numerical simulation, mixer-truck, rheological probe.

Figure 2-15: Système expérimental du plan incliné
Figure 2-15: Système expérimental du plan incliné
Figure 2-19: Essai d'affaissement au cône d'Abrams
Figure 2-19: Essai d’affaissement au cône d’Abrams

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Figure 1. US bath modified as an EC reactor

물에서 초음파를 이용한 전기화학적 스트론튬 제거에 대한 단시간 수치 시뮬레이션

전기화학 반응기에 대한 3D 수치 시뮬레이션 및 측정을 사용하여 동시 초음파 처리 유무에 관계없이 물에서 스트론튬 제거 효율을 분석했습니다. 초음파는 작동 주파수가 25kHz인 4개의 초음파 변환기를 사용하여 생성되었습니다. 반응기는 2개의 블록으로 배열된 8개의 알루미늄 전극을 사용했습니다.

LICHT K.1*, LONČAR G.1, POSAVČIĆ H.1, HALKIJEVIĆ I.1
1 Department of Hydroscience and Engineering, Faculty of Civil Engineering, University of Zagreb, Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia
*corresponding author:
e-mail:katarina.licht@grad.unizg.hr

물 속의 스트론튬 이온은 3.2∙10-19C의 전하와 1.2∙10-8m의 직경을 특징으로 하는 입자로 모델링됩니다. 수치 모델은 기본 유체 역학 모듈, 정전기 모듈 및 일반 이동 객체 모듈을 사용하여 Flow-3D 소프트웨어에서 생성되었습니다.

수치 시뮬레이션을 통해 연구된 원자로 변형의 성능은 시뮬레이션 기간이 끝날 때 전극에 영구적으로 유지되는 모델 스트론튬 입자 수와 물 속의 초기 입자 수의 비율로 정의됩니다. 실험실 반응기의 경우 스트론튬 제거 효과는 실험 종료 시와 시작 시 물 내 균일한 스트론튬 농도의 비율로 정의됩니다.

결과는 초음파를 사용하면 수처리 180초 후에 스트론튬 제거 효과가 10.3%에서 11.2%로 증가한다는 것을 보여줍니다. 수치 시뮬레이션 결과는 동일한 기하학적 특성을 갖는 원자로에 대한 측정 결과와 일치합니다.

3D numerical simulations and measurements on an electrochemical reactor were used to analyze the efficiency of strontium removal from water, with and without simultaneous ultrasound treatment. Ultrasound was generated using 4 ultrasonic transducers with an operating frequency of 25 kHz. The reactor used 8 aluminum electrodes arranged in two blocks. Strontium ions in water are modeled as particles characterized by a charge of 3.2∙10-19 C and a diameter of 1.2∙10-8 m. The numerical model was created in Flow-3D software using the basic hydrodynamic module, electrostatic module, and general moving objects module. The performance of the studied reactor variants by numerical simulations is defined by the ratio of the number of model strontium particles permanently retained on the electrodes at the end of the simulation period to the initial number of particles in the water. For the laboratory reactor, the effect of strontium removal is defined by the ratio of the homogeneous strontium concentration in the water at the end and at the beginning of the experiments. The results show that the use of ultrasound increases the effect of strontium removal from 10.3% to 11.2% after 180 seconds of water treatment. The results of numerical simulations agree with the results of measurements on a reactor with the same geometrical characteristics.

Keywords

numerical model, electrochemical reactor, strontium

Figure 1. US bath modified as an EC reactor
Figure 1. US bath modified as an EC reactor
Figure 2. Schematic view of the experimental set-up
Figure 2. Schematic view of the experimental set-up

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Intrusion of fine sediments into river bed and its effect on river environment – a research review

미세한 퇴적물이 강바닥에 침투하고 하천 환경에 미치는 영향 – 연구 검토

Intrusion of fine sediments into river bed and its effect on river environment – a research review

Nilav Karna,K.S. Hari Prasad, Sanjay Giri & A.S. Lodhi

Abstract

Fine sediments enter into the river through various sources such as channel bed, bank, and catchment. It has been regarded as a type of pollution in river. Fine sediments present in a river have a significant effect on river health. Benthic micro-organism, plants, and large fishes, all are part of food chain of river biota. Any detrimental effect on any of these components of food chain misbalances the entire riverine ecosystem. Numerous studies have been carried out on the various environmental aspects of rivers considering the presence of fine sediment in river flow. The present paper critically reviews many of these aspects to understand the various environmental impacts of suspended sediment on river health, flora and fauna.

Keywords: 

  1. Introduction
    The existence of fine sediment in a river system is a natural phenomenon. But in many cases it is exacerbated by the manmade activities. The natural cause of fines being in flow generally keeps the whole system in equilibrium except during some calamites whereas anthropogenic activities leading to fines entering into the flow puts several adverse impacts on the entire river system and its ecology. Presence of fines in flow is considered as a type of pollution in water. In United States,
    the fine sediment in water along with other non point source pollution is considered as a major obstacle in providing quality water for fishes and recreation activities (Diplas and Parker 1985).
    Sediments in a river are broadly of two types, organic and inorganic, and they both move in two ways either along the bed of the channel called bed load or in suspension called suspended load and their movements depend upon fluid flow and sediment characteristics. Further many investigators have divided the materials in suspension into two different types.
    One which originates from channel bed and bank is called bed material suspended load and another that migrates from feeding catchment area is called wash load. A general perception is that wash loads are very fine materials like clay, silt but it may not always be true (Woo et al. 1986). In general, suspended materials are of size less than 2 mm. The impact of sand on the various aspects of river is comparatively less than that of silt and clay. The latter are chemically active and good carrier of many contaminants and nutrients such as dioxins, phosphorous, heavy and trace metals, polychlorinated biphenyl (PCBs), radionuclide, etc. (Foster and Charlesworth 1996; Horowitz et al. 1995; Owens et al. 2001; Salomons and Förstner 1984; Stone and Droppo 1994; Thoms 1987). Foy and Bailey-Watt (1998) reported that out of 129 lakes in England and Wales, 69% have phosphorous contamination. Ten percent lakes, rivers, and bays of United States have sediment contaminants with chemicals as reported by USEPA. Several field and experimental studies have been conducted
    considering, sand, silt, and clay as suspended material. Hence, the subject reported herein is based on considering the fine sediment size smaller than 2 mm.
    Fine sediments have the ability to alter the hydraulics of the flow. Presence of fines in flow can change the magnitude of turbulence, it can change the friction resistance to flow. Fines can change the mobility and permeability of the bed material. In some extreme cases, fines in flow may even change the morphology of the river (Doeg and Koehn 1994; Nuttall 1972; Wright and Berrie 1987). Fines in the flow adversely affect the producer by increasing the turbidity, hindering the
    photosynthesis process by limiting the light penetration. This is ultimately reflected in the entire food ecosystem of river (Davis-Colley et al. 1992; Van Niewenhuyre and Laparrieve 1986). In addition, abrasion due to flowing sediment kills the aquatic flora (Edwards 1969; Brookes 1986). Intrusion of fines into the pores of river bed reduces space for several invertebrates, affects the spawning process (Petts 1984; Richards and Bacon 1994; Schalchli 1992). There are several other direct
    or indirect, short-term or long-term impacts of fines in river.
    The present paper reports the physical/environmental significance of fines in river. The hydraulic significance of presence of fines in the river has been reviewed in another paper (Effect of fine sediments on river hydraulics – a research review – http://dx.doi.org/10.1080/09715010.2014.982001).

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Figure 11. Sketch of scour mechanism around USAF under random waves.

Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves

by Ruigeng Hu 1,Hongjun Liu 2,Hao Leng 1,Peng Yu 3 andXiuhai Wang 1,2,*

1College of Environmental Science and Engineering, Ocean University of China, Qingdao 266000, China

2Key Lab of Marine Environment and Ecology (Ocean University of China), Ministry of Education, Qingdao 266000, China

3Qingdao Geo-Engineering Survering Institute, Qingdao 266100, China

*Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 20219(8), 886; https://doi.org/10.3390/jmse9080886

Received: 6 July 2021 / Revised: 8 August 2021 / Accepted: 13 August 2021 / Published: 17 August 2021

(This article belongs to the Section Ocean Engineering)

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Abstract

A series of numerical simulation were conducted to study the local scour around umbrella suction anchor foundation (USAF) under random waves. In this study, the validation was carried out firstly to verify the accuracy of the present model. Furthermore, the scour evolution and scour mechanism were analyzed respectively. In addition, two revised models were proposed to predict the equilibrium scour depth Seq around USAF. At last, a parametric study was carried out to study the effects of the Froude number Fr and Euler number Eu for the Seq. The results indicate that the present numerical model is accurate and reasonable for depicting the scour morphology under random waves. The revised Raaijmakers’s model shows good agreement with the simulating results of the present study when KCs,p < 8. The predicting results of the revised stochastic model are the most favorable for n = 10 when KCrms,a < 4. The higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.

Keywords: 

scournumerical investigationrandom wavesequilibrium scour depthKC number

1. Introduction

The rapid expansion of cities tends to cause social and economic problems, such as environmental pollution and traffic jam. As a kind of clean energy, offshore wind power has developed rapidly in recent years. The foundation of offshore wind turbine (OWT) supports the upper tower, and suffers the cyclic loading induced by waves, tides and winds, which exerts a vital influence on the OWT system. The types of OWT foundation include the fixed and floating foundation, and the fixed foundation was used usually for nearshore wind turbine. After the construction of fixed foundation, the hydrodynamic field changes in the vicinity of the foundation, leading to the horseshoe vortex formation and streamline compression at the upside and sides of foundation respectively [1,2,3,4]. As a result, the neighboring soil would be carried away by the shear stress induced by vortex, and the scour hole would emerge in the vicinity of foundation. The scour holes increase the cantilever length, and weaken the lateral bearing capacity of foundation [5,6,7,8,9]. Moreover, the natural frequency of OWT system increases with the increase of cantilever length, causing the resonance occurs when the system natural frequency equals the wave or wind frequency [10,11,12]. Given that, an innovative foundation called umbrella suction anchor foundation (USAF) has been designed for nearshore wind power. The previous studies indicated the USAF was characterized by the favorable lateral bearing capacity with the low cost [6,13,14]. The close-up of USAF is shown in Figure 1, and it includes six parts: 1-interal buckets, 2-external skirt, 3-anchor ring, 4-anchor branch, 5-supporting rod, 6-telescopic hook. The detailed description and application method of USAF can be found in reference [13].

Jmse 09 00886 g001 550

Figure 1. The close-up of umbrella suction anchor foundation (USAF).

Numerical and experimental investigations of scour around OWT foundation under steady currents and waves have been extensively studied by many researchers [1,2,15,16,17,18,19,20,21,22,23,24]. The seabed scour can be classified as two types according to Shields parameter θ, i.e., clear bed scour (θ < θcr) or live bed scour (θ > θcr). Due to the set of foundation, the adverse hydraulic pressure gradient exists at upstream foundation edges, resulting in the streamline separation between boundary layer flow and seabed. The separating boundary layer ascended at upstream anchor edges and developed into the horseshoe vortex. Then, the horseshoe vortex moved downstream gradually along the periphery of the anchor, and the vortex shed off continually at the lee-side of the anchor, i.e., wake vortex. The core of wake vortex is a negative pressure center, liking a vacuum cleaner. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortexes. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow when the turbulence energy could not support the survival of wake vortex. According to Tavouktsoglou et al. [25], the scale of pile wall boundary layer is proportional to 1/ln(Rd) (Rd is pile Reynolds), which means the turbulence intensity induced by the flow-structure interaction would decrease with Rd increases, but the effects of Rd can be neglected only if the flow around the foundation is fully turbulent [26]. According to previous studies [1,15,27,28,29,30,31,32], the scour development around pile foundation under waves was significantly influenced by Shields parameter θ and KC number simultaneously (calculated by Equation (1)). Sand ripples widely existed around pile under waves in the case of live bed scour, and the scour morphology is related with θ and KC. Compared with θKC has a greater influence on the scour morphology [21,27,28]. The influence mechanism of KC on the scour around the pile is reflected in two aspects: the horseshoe vortex at upstream and wake vortex shedding at downstream.

KC=UwmTD��=�wm��(1)

where, Uwm is the maximum velocity of the undisturbed wave-induced oscillatory flow at the sea bottom above the wave boundary layer, T is wave period, and D is pile diameter.

There are two prerequisites to satisfy the formation of horseshoe vortex at upstream pile edges: (1) the incoming flow boundary layer with sufficient thickness and (2) the magnitude of upstream adverse pressure gradient making the boundary layer separating [1,15,16,18,20]. The smaller KC results the lower adverse pressure gradient, and the boundary layer cannot separate, herein, there is almost no horseshoe vortex emerging at upside of pile. Sumer et al. [1,15] carried out several sets of wave flume experiments under regular and irregular waves respectively, and the experiment results show that there is no horseshoe vortex when KC is less than 6. While the scale and lifespan of horseshoe vortex increase evidently with the increase of KC when KC is larger than 6. Moreover, the wake vortex contributes to the scour at lee-side of pile. Similar with the case of horseshoe vortex, there is no wake vortex when KC is less than 6. The wake vortex is mainly responsible for scour around pile when KC is greater than 6 and less than O(100), while horseshoe vortex controls scour nearly when KC is greater than O(100).

Sumer et al. [1] found that the equilibrium scour depth was nil around pile when KC was less than 6 under regular waves for live bed scour, while the equilibrium scour depth increased with the increase of KC. Based on that, Sumer proposed an equilibrium scour depth predicting equation (Equation (2)). Carreiras et al. [33] revised Sumer’s equation with m = 0.06 for nonlinear waves. Different with the findings of Sumer et al. [1] and Carreiras et al. [33], Corvaro et al. [21] found the scour still occurred for KC ≈ 4, and proposed the revised equilibrium scour depth predicting equation (Equation (3)) for KC > 4.

Rudolph and Bos [2] conducted a series of wave flume experiments to investigate the scour depth around monopile under waves only, waves and currents combined respectively, indicting KC was one of key parameters in influencing equilibrium scour depth, and proposed the equilibrium scour depth predicting equation (Equation (4)) for low KC (1 < KC < 10). Through analyzing the extensive data from published literatures, Raaijmakers and Rudolph [34] developed the equilibrium scour depth predicting equation (Equation (5)) for low KC, which was suitable for waves only, waves and currents combined. Khalfin [35] carried out several sets of wave flume experiments to study scour development around monopile, and proposed the equilibrium scour depth predicting equation (Equation (6)) for low KC (0.1 < KC < 3.5). Different with above equations, the Khalfin’s equation considers the Shields parameter θ and KC number simultaneously in predicting equilibrium scour depth. The flow reversal occurred under through in one wave period, so sand particles would be carried away from lee-side of pile to upside, resulting in sand particles backfilled into the upstream scour hole [20,29]. Considering the backfilling effects, Zanke et al. [36] proposed the equilibrium scour depth predicting equation (Equation (7)) around pile by theoretical analysis, and the equation is suitable for the whole range of KC number under regular waves and currents combined.

S/D=1.3(1−exp([−m(KC−6)])�/�=1.3(1−exp(−�(��−6))(2)

where, m = 0.03 for linear waves.

S/D=1.3(1−exp([−0.02(KC−4)])�/�=1.3(1−exp(−0.02(��−4))(3)

S/D=1.3γKwaveKhw�/�=1.3��wave�ℎw(4)

where, γ is safety factor, depending on design process, typically γ = 1.5, Kwave is correction factor considering wave action, Khw is correction factor considering water depth.

S/D=1.5[tanh(hwD)]KwaveKhw�/�=1.5tanh(ℎw�)�wave�ℎw(5)

where, hw is water depth.

S/D=0.0753(θθcr−−−√−0.5)0.69KC0.68�/�=0.0753(��cr−0.5)0.69��0.68(6)

where, θ is shields parameter, θcr is critical shields parameter.

S/D=2.5(1−0.5u/uc)xrelxrel=xeff/(1+xeff)xeff=0.03(1−0.35ucr/u)(KC−6)⎫⎭⎬⎪⎪�/�=2.5(1−0.5�/��)��������=����/(1+����)����=0.03(1−0.35�cr/�)(��−6)(7)

where, u is near-bed orbital velocity amplitude, uc is critical velocity corresponding the onset of sediment motion.

S/D=1.3{1−exp[−0.03(KC2lnn+36)1/2−6]}�/�=1.31−exp−0.03(��2ln�+36)1/2−6(8)

where, n is the 1/n’th highest wave for random waves

For predicting equilibrium scour depth under irregular waves, i.e., random waves, Sumer and Fredsøe [16] found it’s suitable to take Equation (2) to predict equilibrium scour depth around pile under random waves with the root-mean-square (RMS) value of near-bed orbital velocity amplitude Um and peak wave period TP to calculate KC. Khalfin [35] recommended the RMS wave height Hrms and peak wave period TP were used to calculate KC for Equation (6). References [37,38,39,40] developed a series of stochastic theoretical models to predict equilibrium scour depth around pile under random waves, nonlinear random waves plus currents respectively. The stochastic approach thought the 1/n’th highest wave were responsible for scour in vicinity of pile under random waves, and the KC was calculated in Equation (8) with Um and mean zero-crossing wave period Tz. The results calculated by Equation (8) agree well with experimental values of Sumer and Fredsøe [16] if the 1/10′th highest wave was used. To author’s knowledge, the stochastic approach proposed by Myrhaug and Rue [37] is the only theoretical model to predict equilibrium scour depth around pile under random waves for the whole range of KC number in published documents. Other methods of predicting scour depth under random waves are mainly originated from the equation for regular waves-only, waves and currents combined, which are limited to the large KC number, such as KC > 6 for Equation (2) and KC > 4 for Equation (3) respectively. However, situations with relatively low KC number (KC < 4) often occur in reality, for example, monopile or suction anchor for OWT foundations in ocean environment. Moreover, local scour around OWT foundations under random waves has not yet been investigated fully. Therefore, further study are still needed in the aspect of scour around OWT foundations with low KC number under random waves. Given that, this study presents the scour sediment model around umbrella suction anchor foundation (USAF) under random waves. In this study, a comparison of equilibrium scour depth around USAF between this present numerical models and the previous theoretical models and experimental results was presented firstly. Then, this study gave a comprehensive analysis for the scour mechanisms around USAF. After that, two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] respectively to predict the equilibrium scour depth. Finally, a parametric study was conducted to study the effects of the Froude number (Fr) and Euler number (Eu) to equilibrium scour depth respectively.

2. Numerical Method

2.1. Governing Equations of Flow

The following equations adopted in present model are already available in Flow 3D software. The authors used these theoretical equations to simulate scour in random waves without modification. The incompressible viscous fluid motion satisfies the Reynolds-averaged Navier-Stokes (RANS) equation, so the present numerical model solves RANS equations:

∂u∂t+1VF(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρf∂p∂x+Gx+fx∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(9)

∂v∂t+1VF(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρf∂p∂y+Gy+fy∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(10)

∂w∂t+1VF(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρf∂p∂z+Gz+fz∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(11)

where, VF is the volume fraction; uv, and w are the velocity components in xyz direction respectively with Cartesian coordinates; Ai is the area fraction; ρf is the fluid density, fi is the viscous fluid acceleration, Gi is the fluid body acceleration (i = xyz).

2.2. Turbulent Model

The turbulence closure is available by the turbulent model, such as one-equation, the one-equation k-ε model, the standard k-ε model, RNG k-ε turbulent model and large eddy simulation (LES) model. The LES model requires very fine mesh grid, so the computational time is large, which hinders the LES model application in engineering. The RNG k-ε model can reduce computational time greatly with high accuracy in the near-wall region. Furthermore, the RNG k-ε model computes the maximum turbulent mixing length dynamically in simulating sediment scour model. Therefore, the RNG k-ε model was adopted to study the scour around anchor under random waves [41,42].

∂kT∂T+1VF(uAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z)=PT+GT+DiffkT−εkT∂��∂�+1��(���∂��∂�+���∂��∂�+���∂��∂�)=��+��+������−���(12)

∂εT∂T+1VF(uAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z)=CDIS1εTkT(PT+CDIS3GT)+Diffε−CDIS2ε2TkT∂��∂�+1��(���∂��∂�+���∂��∂�+���∂��∂�)=����1����(��+����3��)+�����−����2��2��(13)

where, kT is specific kinetic energy involved with turbulent velocity, GT is the turbulent energy generated by buoyancy; εT is the turbulent energy dissipating rate, PT is the turbulent energy, Diffε and DiffkT are diffusion terms associated with VFAiCDIS1CDIS2 and CDIS3 are dimensionless parameters, and CDIS1CDIS3 have default values of 1.42, 0.2 respectively. CDIS2 can be obtained from PT and kT.

2.3. Sediment Scour Model

The sand particles may suffer four processes under waves, i.e., entrainment, bed load transport, suspended load transport, and deposition, so the sediment scour model should depict the above processes efficiently. In present numerical simulation, the sediment scour model includes the following aspects:

2.3.1. Entrainment and Deposition

The combination of entrainment and deposition determines the net scour rate of seabed in present sediment scour model. The entrainment lift velocity of sand particles was calculated as [43]:

ulift,i=αinsd0.3∗(θ−θcr)1.5∥g∥di(ρi−ρf)ρf−−−−−−−−−−−−√�lift,i=�����*0.3(�−�cr)1.5���(��−�f)�f(14)

where, αi is the entrainment parameter, ns is the outward point perpendicular to the seabed, d* is the dimensionless diameter of sand particles, which was calculated by Equation (15), θcr is the critical Shields parameter, g is the gravity acceleration, di is the diameter of sand particles, ρi is the density of seabed species.

d∗=di(∥g∥ρf(ρi−ρf)μ2f)1/3�*=��(��f(��−�f)�f2)1/3(15)

where μf is the fluid dynamic viscosity.

In Equation (14), the entrainment parameter αi confirms the rate at which sediment erodes when the given shear stress is larger than the critical shear stress, and the recommended value 0.018 was adopted according to the experimental data of Mastbergen and Von den Berg [43]. ns is the outward pointing normal to the seabed interface, and ns = (0,0,1) according to the Cartesian coordinates used in present numerical model.

The shields parameter was obtained from the following equation:

θ=U2f,m(ρi/ρf−1)gd50�=�f,m2(��/�f−1)��50(16)

where, Uf,m is the maximum value of the near-bed friction velocity; d50 is the median diameter of sand particles. The detailed calculation procedure of θ was available in Soulsby [44].

The critical shields parameter θcr was obtained from the Equation (17) [44]

θcr=0.31+1.2d∗+0.055[1−exp(−0.02d∗)]�cr=0.31+1.2�*+0.0551−exp(−0.02�*)(17)

The sand particles begin to deposit on seabed when the turbulence energy weaken and cann’t support the particles suspending. The setting velocity of the particles was calculated from the following equation [44]:

usettling,i=νfdi[(10.362+1.049d3∗)0.5−10.36]�settling,�=�f��(10.362+1.049�*3)0.5−10.36(18)

where νf is the fluid kinematic viscosity.

2.3.2. Bed Load Transport

This is called bed load transport when the sand particles roll or bounce over the seabed and always have contact with seabed. The bed load transport velocity was computed by [45]:

ubedload,i=qb,iδicb,ifb�bedload,�=�b,����b,��b(19)

where, qb,i is the bed load transport rate, which was obtained from Equation (20), δi is the bed load thickness, which was calculated by Equation (21), cb,i is the volume fraction of sand i in the multiple species, fb is the critical packing fraction of the seabed.

qb,i=8[∥g∥(ρi−ρfρf)d3i]1/2�b,�=8�(��−�f�f)��31/2(20)

δi=0.3d0.7∗(θθcr−1)0.5di��=0.3�*0.7(��cr−1)0.5��(21)

2.3.3. Suspended Load Transport

Through the following transport equation, the suspended sediment concentration could be acquired.

∂Cs,i∂t+∇(us,iCs,i)=∇∇(DfCs,i)∂�s,�∂�+∇(�s,��s,�)=∇∇(�f�s,�)(22)

where, Cs,i is the suspended sand particles mass concentration of sand i in the multiple species, us,i is the sand particles velocity of sand iDf is the diffusivity.

The velocity of sand i in the multiple species could be obtained from the following equation:

us,i=u¯¯+usettling,ics,i�s,�=�¯+�settling,��s,�(23)

where, u¯�¯ is the velocity of mixed fluid-particles, which can be calculated by the RANS equation with turbulence model, cs,i is the suspended sand particles volume concentration, which was computed from Equation (24).

cs,i=Cs,iρi�s,�=�s,���(24)

3. Model Setup

The seabed-USAF-wave three-dimensional scour numerical model was built using Flow-3D software. As shown in Figure 2, the model includes sandy seabed, USAF model, sea water, two baffles and porous media. The dimensions of USAF are shown in Table 1. The sandy bed (210 m in length, 30 m in width and 11 m in height) is made up of uniform fine sand with median diameter d50 = 0.041 cm. The USAF model includes upper steel tube with the length of 20 m, which was installed in the middle of seabed. The location of USAF is positioned at 140 m from the upstream inflow boundary and 70 m from the downstream outflow boundary. Two baffles were installed at two ends of seabed. In order to eliminate the wave reflection basically, the porous media was set at the outflow side on the seabed.

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Figure 2. (a) The sketch of seabed-USAF-wave three-dimensional model; (b) boundary condation:Wv-wave boundary, S-symmetric boundary, O-outflow boundary; (c) USAF model.

Table 1. Numerical simulating cases.

Table

3.1. Mesh Geometric Dimensions

In the simulation of the scour under the random waves, the model includes the umbrella suction anchor foundation, seabed and fluid. As shown in Figure 3, the model mesh includes global mesh grid and nested mesh grid, and the total number of grids is 1,812,000. The basic procedure for building mesh grid consists of two steps. Step 1: Divide the global mesh using regular hexahedron with size of 0.6 × 0.6. The global mesh area is cubic box, embracing the seabed and whole fluid volume, and the dimensions are 210 m in length, 30 m in width and 32 m in height. The details of determining the grid size can see the following mesh sensitivity section. Step 2: Set nested fine mesh grid in vicinity of the USAF with size of 0.3 × 0.3 so as to shorten the computation cost and improve the calculation accuracy. The encryption range is −15 m to 15 m in x direction, −15 m to 15 m in y direction and 0 m to 32 m in z direction, respectively. In order to accurately capture the free-surface dynamics, such as the fluid-air interface, the volume of fluid (VOF) method was adopted for tracking the free water surface. One specific algorithm called FAVORTM (Fractional Area/Volume Obstacle Representation) was used to define the fractional face areas and fractional volumes of the cells which are open to fluid flow.

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Figure 3. The sketch of mesh grid.

3.2. Boundary Conditions

As shown in Figure 2, the initial fluid length is 210 m as long as seabed. A wave boundary was specified at the upstream offshore end. The details of determining the random wave spectrum can see the following wave parameters section. The outflow boundary was set at the downstream onshore end. The symmetry boundary was used at the top and two sides of the model. The symmetric boundaries were the better strategy to improve the computation efficiency and save the calculation cost [46]. At the seabed bottom, the wall boundary was adopted, which means the u = v = w= 0. Besides, the upper steel tube of USAF was set as no-slip condition.

3.3. Wave Parameters

The random waves with JONSWAP wave spectrum were used for all simulations as realistic representation of offshore conditions. The unidirectional JONSWAP frequency spectrum was described as [47]:

S(ω)=αg2ω5exp[−54(ωpω)4]γexp[−(ω−ωp)22σ2ω2p]�(�)=��2�5exp−54(�p�)4�exp−(�−�p)22�2�p2(25)

where, α is wave energy scale parameter, which is calculated by Equation (26), ω is frequency, ωp is wave spectrum peak frequency, which can be obtained from Equation (27). γ is wave spectrum peak enhancement factor, in this study γ = 3.3. σ is spectral width factor, σ equals 0.07 for ω ≤ ωp and 0.09 for ω > ωp respectively.

α=0.0076(gXU2)−0.22�=0.0076(���2)−0.22(26)

ωp=22(gU)(gXU2)−0.33�p=22(��)(���2)−0.33(27)

where, X is fetch length, U is average wind velocity at 10 m height from mean sea level.

In present numerical model, the input key parameters include X and U for wave boundary with JONSWAP wave spectrum. The objective wave height and period are available by different combinations of X and U. In this study, we designed 9 cases with different wave heights, periods and water depths for simulating scour around USAF under random waves (see Table 2). For random waves, the wave steepness ε and Ursell number Ur were acquired form Equations (28) and (29) respectively

ε=2πgHsT2a�=2���s�a2(28)

Ur=Hsk2h3w�r=�s�2ℎw3(29)

where, Hs is significant wave height, Ta is average wave period, k is wave number, hw is water depth. The Shield parameter θ satisfies θ > θcr for all simulations in current study, indicating the live bed scour prevails.

Table 2. Numerical simulating cases.

Table

3.4. Mesh Sensitivity

In this section, a mesh sensitivity analysis was conducted to investigate the influence of mesh grid size to results and make sure the calculation is mesh size independent and converged. Three mesh grid size were chosen: Mesh 1—global mesh grid size of 0.75 × 0.75, nested fine mesh grid size of 0.4 × 0.4, and total number of grids 1,724,000, Mesh 2—global mesh grid size of 0.6 × 0.6, nested fine mesh grid size of 0.3 × 0.3, and total number of grids 1,812,000, Mesh 3—global mesh grid size of 0.4 × 0.4, nested fine mesh grid size of 0.2 × 0.2, and total number of grids 1,932,000. The near-bed shear velocity U* is an important factor for influencing scour process [1,15], so U* at the position of (4,0,11.12) was evaluated under three mesh sizes. As the Figure 4 shown, the maximum error of shear velocity ∆U*1,2 is about 39.8% between the mesh 1 and mesh 2, and 4.8% between the mesh 2 and mesh 3. According to the mesh sensitivity criterion adopted by Pang et al. [48], it’s reasonable to think the results are mesh size independent and converged with mesh 2. Additionally, the present model was built according to prototype size, and the mesh size used in present model is larger than the mesh size adopted by Higueira et al. [49] and Corvaro et al. [50]. If we choose the smallest cell size, it will take too much time. For example, the simulation with Mesh3 required about 260 h by using a computer with Intel Xeon Scalable Gold 4214 CPU @24 Cores, 2.2 GHz and 64.00 GB RAM. Therefore, in this case, considering calculation accuracy and computation efficiency, the mesh 2 was chosen for all the simulation in this study.

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Figure 4. Comparison of near-bed shear velocity U* with different mesh grid size.

The nested mesh block was adopted for seabed in vicinity of the USAF, which was overlapped with the global mesh block. When two mesh blocks overlap each other, the governing equations are by default solved on the mesh block with smaller average cell size (i.e., higher grid resolution). It is should be noted that the Flow 3D software used the moving mesh captures the scour evolution and automatically adjusts the time step size to be as large as possible without exceeding any of the stability limits, affecting accuracy, or unduly increasing the effort required to enforce the continuity condition [51].

3.5. Model Validation

In order to verify the reliability of the present model, the results of present study were compared with the experimental data of Khosronejad et al. [52]. The experiment was conducted in an open channel with a slender vertical pile under unidirectional currents. The comparison of scour development between the present results and the experimental results is shown in Figure 5. The Figure 5 reveals that the present results agree well with the experimental data of Khosronejad et al. [52]. In the first stage, the scour depth increases rapidly. After that, the scour depth achieves a maximum value gradually. The equilibrium scour depth calculated by the present model is basically corresponding with the experimental results of Khosronejad et al. [52], although scour depth in the present model is slightly larger than the experimental results at initial stage.

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Figure 5. Comparison of time evolution of scour between the present study and Khosronejad et al. [52], Petersen et al. [17].

Secondly, another comparison was further conducted between the results of present study and the experimental data of Petersen et al. [17]. The experiment was carried out in a flume with a circular vertical pile in combined waves and current. Figure 4 shows a comparison of time evolution of scour depth between the simulating and the experimental results. As Figure 5 indicates, the scour depth in this study has good overall agreement with the experimental results proposed in Petersen et al. [17]. The equilibrium scour depth calculated by the present model is 0.399 m, which equals to the experimental value basically. Overall, the above verifications prove the present model is accurate and capable in dealing with sediment scour under waves.

In addition, in order to calibrate and validate the present model for hydrodynamic parameters, the comparison of water surface elevation was carried out with laboratory experiments conducted by Stahlmann [53] for wave gauge No. 3. The Figure 6 depicts the surface wave profiles between experiments and numerical model results. The comparison indicates that there is a good agreement between the model results and experimental values, especially the locations of wave crest and trough. Comparison of the surface elevation instructs the present model has an acceptable relative error, and the model is a calibrated in terms of the hydrodynamic parameters.

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Figure 6. Comparison of surface elevation between the present study and Stahlmann [53].

Finally, another comparison was conducted for equilibrium scour depth or maximum scour depth under random waves with the experimental data of Sumer and Fredsøe [16] and Schendel et al. [22]. The Figure 7 shows the comparison between the numerical results and experimental data of Run01, Run05, Run21 and Run22 in Sumer and Fredsøe [16] and test A05 and A09 in Schendel et al. [22]. As shown in Figure 7, the equilibrium scour depth or maximum scour depth distributed within the ±30 error lines basically, meaning the reliability and accuracy of present model for predicting equilibrium scour depth around foundation in random waves. However, compared with the experimental values, the present model overestimated the equilibrium scour depth generally. Given that, a calibration for scour depth was carried out by multiplying the mean reduced coefficient 0.85 in following section.

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Figure 7. Comparison of equilibrium (or maximum) scour depth between the present study and Sumer and Fredsøe [16], Schendel et al. [22].

Through the various examination for hydrodynamic and morphology parameters, it can be concluded that the present model is a validated and calibrated model for scour under random waves. Thus, the present numerical model would be utilized for scour simulation around foundation under random waves.

4. Numerical Results and Discussions

4.1. Scour Evolution

Figure 8 displays the scour evolution for case 1–9. As shown in Figure 8a, the scour depth increased rapidly at the initial stage, and then slowed down at the transition stage, which attributes to the backfilling occurred in scour holes under live bed scour condition, resulting in the net scour decreasing. Finally, the scour reached the equilibrium state when the amount of sediment backfilling equaled to that of scouring in the scour holes, i.e., the net scour transport rate was nil. Sumer and Fredsøe [16] proposed the following formula for the scour development under waves

St=Seq(1−exp(−t/Tc))�t=�eq(1−exp(−�/�c))(30)

where Tc is time scale of scour process.

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Figure 8. Time evolution of scour for case 1–9: (a) Case 1–5; (b) Case 6–9.

The computing time is 3600 s and the scour development curves in Figure 8 kept fluctuating, meaning it’s still not in equilibrium scour stage in these cases. According to Sumer and Fredsøe [16], the equilibrium scour depth can be acquired by fitting the data with Equation (30). From Figure 8, it can be seen that the scour evolution obtained from Equation (30) is consistent with the present study basically at initial stage, but the scour depth predicted by Equation (30) developed slightly faster than the simulating results and the Equation (30) overestimated the scour depth to some extent. Overall, the whole tendency of the results calculated by Equation (30) agrees well with the simulating results of the present study, which means the Equation (30) is applicable to depict the scour evolution around USAF under random waves.

4.2. Scour Mechanism under Random Waves

The scour morphology and scour evolution around USAF are similar under random waves in case 1~9. Taking case 7 as an example, the scour morphology is shown in Figure 9.

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Figure 9. Scour morphology under different times for case 7.

From Figure 9, at the initial stage (t < 1200 s), the scour occurred at upstream foundation edges between neighboring anchor branches. The maximum scour depth appeared at the lee-side of the USAF. Correspondingly, the sediments deposited at the periphery of the USAF, and the location of the maximum accretion depth was positioned at an angle of about 45° symmetrically with respect to the wave propagating direction in the lee-side of the USAF. After that, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.

According to previous studies [1,15,16,19,30,31], the horseshoe vortex, streamline compression and wake vortex shedding were responsible for scour around foundation. The Figure 10 displays the distribution of flow velocity in vicinity of foundation, which reflects the evolving processes of horseshoe vertex.

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Figure 10. Velocity profile around USAF: (a) Flow runup and down stream at upstream anchor edges; (b) Horseshoe vortex at upstream anchor edges; (c) Flow reversal during wave through stage at lee side.

As shown in Figure 10, the inflow tripped to the upstream edges of the USAF and it was blocked by the upper tube of USAF. Then, the downflow formed the horizontal axis clockwise vortex and rolled on the seabed bypassing the tube, that is, the horseshoe vortex (Figure 11). The Figure 12 displays the turbulence intensity around the tube on the seabed. From Figure 12, it can be seen that the turbulence intensity was high-intensity with respect to the region of horseshoe vortex. This phenomenon occurred because of drastic water flow momentum exchanging in the horseshoe vortex. As a result, it created the prominent shear stress on the seabed, causing the local scour at the upstream edges of USAF. Besides, the horseshoe vortex moved downstream gradually along the periphery of the tube and the wake vortex shed off continually at the lee-side of the USAF, i.e., wake vortex.

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Figure 11. Sketch of scour mechanism around USAF under random waves.

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Figure 12. Turbulence intensity: (a) Turbulence intensity of horseshoe vortex; (b) Turbulence intensity of wake vortex; (c) Turbulence intensity of accretion area.

The core of wake vortex is a negative pressure center, liking a vacuum cleaner [11,42]. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortex. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow at the downside of USAF. As is shown in Figure 12, the turbulence intensity was low where the downflow occurred at lee-side, which means the turbulence energy may not be able to support the survival of wake vortex, leading to accretion happening. As mentioned in previous section, the formation of horseshoe vortex was dependent with adverse pressure gradient at upside of foundation. As shown in Figure 13, the evaluated range of pressure distribution is −15 m to 15 m in x direction. The t = 450 s and t = 1800 s indicate that the wave crest and trough arrived at the upside and lee-side of the foundation respectively, and the t = 350 s was neither the wave crest nor trough. The adverse gradient pressure reached the maximum value at t = 450 s corresponding to the wave crest phase. In this case, it’s helpful for the wave boundary separating fully from seabed, which leads to the formation of horseshoe vortex with high turbulence intensity. Therefore, the horseshoe vortex is responsible for the local scour between neighboring anchor branches at upside of USAF. What’s more, due to the combination of the horseshoe vortex and streamline compression, the maximum scour depth occurred at the upside of the USAF with an angle of about 45° corresponding to the wave propagating direction. This is consistent with the findings of Pang et al. [48] and Sumer et al. [1,15] in case of regular waves. At the wave trough phase (t = 1800 s), the pressure gradient became positive at upstream USAF edges, which hindered the separating of wave boundary from seabed. In the meantime, the flow reversal occurred (Figure 10) and the adverse gradient pressure appeared at downstream USAF edges, but the magnitude of adverse gradient pressure at lee-side was lower than the upstream gradient pressure under wave crest. In this way, the intensity of horseshoe vortex behind the USAF under wave trough was low, which explains the difference of scour depth at upstream and downstream, i.e., the scour asymmetry. In other words, the scour asymmetry at upside and downside of USAF was attributed to wave asymmetry for random waves, and the phenomenon became more evident for nonlinear waves [21]. Briefly speaking, the vortex system at wave crest phase was mainly related to the scour process around USAF under random waves.

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Figure 13. Pressure distribution around USAF.

4.3. Equilibrium Scour Depth

The KC number is a key parameter for horseshoe vortex emerging and evolving under waves. According to Equation (1), when pile diameter D is fixed, the KC depends on the maximum near-bed velocity Uwm and wave period T. For random waves, the Uwm can be denoted by the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms or the significant value of near-bed velocity amplitude Uwm,s. The Uwm,rms and Uwm,s for all simulating cases of the present study are listed in Table 3 and Table 4. The T can be denoted by the mean up zero-crossing wave period Ta, peak wave period Tp, significant wave period Ts, the maximum wave period Tm, 1/10′th highest wave period Tn = 1/10 and 1/5′th highest wave period Tn = 1/5 for random waves, so the different combinations of Uwm and T will acquire different KC. The Table 3 and Table 4 list 12 types of KC, for example, the KCrms,s was calculated by Uwm,rms and Ts. Sumer and Fredsøe [16] conducted a series of wave flume experiments to investigate the scour depth around monopile under random waves, and found the equilibrium scour depth predicting equation (Equation (2)) for regular waves was applicable for random waves with KCrms,p. It should be noted that the Equation (2) is only suitable for KC > 6 under regular waves or KCrms,p > 6 under random waves.

Table 3. Uwm,rms and KC for case 1~9.

Table

Table 4. Uwm,s and KC for case 1~9.

Table

Raaijmakers and Rudolph [34] proposed the equilibrium scour depth predicting model (Equation (5)) around pile under waves, which is suitable for low KC. The format of Equation (5) is similar with the formula proposed by Breusers [54], which can predict the equilibrium scour depth around pile at different scour stages. In order to verify the applicability of Raaijmakers’s model for predicting the equilibrium scour depth around USAF under random waves, a validation of the equilibrium scour depth Seq between the present study and Raaijmakers’s equation was conducted. The position where the scour depth Seq was evaluated is the location of the maximum scour depth, and it was depicted in Figure 14. The Figure 15 displays the comparison of Seq with different KC between the present study and Raaijmakers’s model.

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Figure 14. Sketch of the position where the Seq was evaluated.

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Figure 15. Comparison of the equilibrium scour depth between the present model and the model of Raaijmakers and Rudolph [34]: (aKCrms,sKCrms,a; (bKCrms,pKCrms,m; (cKCrms,n = 1/10KCrms,n = 1/5; (dKCs,sKCs,a; (eKCs,pKCs,m; (fKCs,n = 1/10KCs,n = 1/5.

As shown in Figure 15, there is an error in predicting Seq between the present study and Raaijmakers’s model, and Raaijmakers’s model underestimates the results generally. Although the error exists, the varying trend of Seq with KC obtained from Raaijmakers’s model is consistent with the present study basically. What’s more, the error is minimum and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves by using KCs,p. Based on this, a further revision was made to eliminate the error as much as possible, i.e., add the deviation value ∆S/D in the Raaijmakers’s model. The revised equilibrium scour depth predicting equation based on Raaijmakers’s model can be written as

S′eq/D=1.95[tanh(hD)](1−exp(−0.012KCs,p))+ΔS/D�eq′/�=1.95tanh(ℎ�)(1−exp(−0.012��s,p))+∆�/�(31)

As the Figure 16 shown, through trial-calculation, when ∆S/D = 0.05, the results calculated by Equation (31) show good agreement with the simulating results of the present study. The maximum error is about 18.2% and the engineering requirements have been met basically. In order to further verify the accuracy of the revised model for large KC (KCs,p > 4) under random waves, a validation between the revised model and the previous experimental results [21]. The experiment was conducted in a flume (50 m in length, 1.0 m in width and 1.3 m in height) with a slender vertical pile (D = 0.1 m) under random waves. The seabed is composed of 0.13 m deep layer of sand with d50 = 0.6 mm and the water depth is 0.5 m for all tests. The significant wave height is 0.12~0.21 m and the KCs,p is 5.52~11.38. The comparison between the predicting results by Equation (31) and the experimental results of Corvaro et al. [21] is shown in Figure 17. From Figure 17, the experimental data evenly distributes around the predicted results and the prediction accuracy is favorable when KCs,p < 8. However, the gap between the predicting results and experimental data becomes large and the Equation (31) overestimates the equilibrium scour depth to some extent when KCs,p > 8.

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Figure 16. Comparison of Seq between the simulating results and the predicting values by Equation (31).

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Figure 17. Comparison of Seq/D between the Experimental results of Corvaro et al. [21] and the predicting values by Equation (31).

In ocean environment, the waves are composed of a train of sinusoidal waves with different frequencies and amplitudes. The energy of constituent waves with very large and very small frequencies is relatively low, and the energy of waves is mainly concentrated in a certain range of moderate frequencies. Myrhaug and Rue [37] thought the 1/n’th highest wave was responsible for scour and proposed the stochastic model to predict the equilibrium scour depth around pile under random waves for full range of KC. Noteworthy is that the KC was denoted by KCrms,a in the stochastic model. To verify the application of the stochastic model for predicting scour depth around USAF, a validation between the simulating results of present study and predicting results by the stochastic model with n = 2,3,5,10,20,500 was carried out respectively.

As shown in Figure 18, compared with the simulating results, the stochastic model underestimates the equilibrium scour depth around USAF generally. Although the error exists, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. What’s more, the gap between the predicting values by stochastic model and the simulating results decreases with the increase of n, but for large n, for example n = 500, the varying trend diverges between the predicting values and simulating results, meaning it’s not feasible only by increasing n in stochastic model to predict the equilibrium scour depth around USAF.

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Figure 18. Comparison of Seq between the simulating results and the predicting values by Equation (8).

The Figure 19 lists the deviation value ∆Seq/D′ between the predicting values and simulating results with different KCrms,a and n. Then, fitted the relationship between the ∆S′and n under different KCrms,a, and the fitting curve can be written by Equation (32). The revised stochastic model (Equation (33)) can be acquired by adding ∆Seq/D′ to Equation (8).

ΔSeq/D=0.052*exp(−n/6.566)+0.068∆�eq/�=0.052*exp(−�/6.566)+0.068(32)

S′eq¯/D=S′eq/D+0.052*exp(−n/6.566)+0.068�eq′¯/�=�eq′/�+0.052*exp(−�/6.566)+0.068(33)

Jmse 09 00886 g019 550

Figure 19. The fitting line between ∆S′and n.

The comparison between the predicting results by Equation (33) and the simulating results of present study is shown in Figure 20. According to the Figure 20, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. Compared with predicting results by the stochastic model, the results calculated by Equation (33) is favorable. Moreover, comparison with simulating results indicates that the predicting results are the most favorable for n = 10, which is consistent with the findings of Myrhaug and Rue [37] for equilibrium scour depth predicting around slender pile in case of random waves.

Jmse 09 00886 g020 550

Figure 20. Comparison of Seq between the simulating results and the predicting values by Equation (33).

In order to further verify the accuracy of the Equation (33) for large KC (KCrms,a > 4) under random waves, a validation was conducted between the Equation (33) and the previous experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. The details of experiments conducted by Corvaro et al. [21] were described in above section. Sumer and Fredsøe [16] investigated the local scour around pile under random waves. The experiments were conducted in a wave basin with a slender vertical pile (D = 0.032, 0.055 m). The seabed is composed of 0.14 m deep layer of sand with d50 = 0.2 mm and the water depth was maintained at 0.5 m. The JONSWAP wave spectrum was used and the KCrms,a was 5.29~16.95. The comparison between the predicting results by Equation (33) and the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] are shown in Figure 21. From Figure 21, contrary to the case of low KCrms,a (KCrms,a < 4), the error between the predicting values and experimental results increases with decreasing of n for KCrms,a > 4. Therefore, the predicting results are the most favorable for n = 2 when KCrms,a > 4.

Jmse 09 00886 g021 550

Figure 21. Comparison of Seq between the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] and the predicting values by Equation (33).

Noteworthy is that the present model was built according to prototype size, so the errors between the numerical results and experimental data of References [16,21] may be attribute to the scale effects. In laboratory experiments on scouring process, it is typically impossible to ensure a rigorous similarity of all physical parameters between the model and prototype structure, leading to the scale effects in the laboratory experiments. To avoid a cohesive behaviour, the bed material was not scaled geometrically according to model scale. As a consequence, the relatively large-scaled sediments sizes may result in the overestimation of bed load transport and underestimation of suspended load transport compared with field conditions. What’s more, the disproportional scaled sediment presumably lead to the difference of bed roughness between the model and prototype, and thus large influences for wave boundary layer on the seabed and scour process. Besides, according to Corvaro et al. [21] and Schendel et al. [55], the pile Reynolds numbers and Froude numbers both affect the scour depth for the condition of non fully developed turbulent flow in laboratory experiments.

4.4. Parametric Study

4.4.1. Influence of Froude Number

As described above, the set of foundation leads to the adverse pressure gradient appearing at upstream, leading to the wave boundary layer separating from seabed, then horseshoe vortex formatting and the horseshoe vortex are mainly responsible for scour around foundation (see Figure 22). The Froude number Fr is the key parameter to influence the scale and intensity of horseshoe vortex. The Fr under waves can be calculated by the following formula [42]

Fr=UwgD−−−√�r=�w��(34)

where Uw is the mean water particle velocity during 1/4 cycle of wave oscillation, obtained from the following formula. Noteworthy is that the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms is used for calculating Uwm.

Uw=1T/4∫0T/4Uwmsin(t/T)dt=2πUwm�w=1�/4∫0�/4�wmsin(�/�)��=2��wm(35)

Jmse 09 00886 g022 550

Figure 22. Sketch of flow field at upstream USAF edges.

Tavouktsoglou et al. [25] proposed the following formula between Fr and the vertical location of the stagnation y

yh∝Fer�ℎ∝�r�(36)

where e is constant.

The Figure 23 displays the relationship between Seq/D and Fr of the present study. In order to compare with the simulating results, the experimental data of Corvaro et al. [21] was also depicted in Figure 23. As shown in Figure 23, the equilibrium scour depth appears a logarithmic increase as Fr increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increase of Fr, which is benefit for the wave boundary layer separating from seabed, resulting in the high-intensity horseshoe vortex, hence, causing intensive scour around USAF. Based on the previous study of Tavouktsoglou et al. [25] for scour around pile under currents, the high Fr leads to the stagnation point is closer to the mean sea level for shallow water, causing the stronger downflow kinetic energy. As mentioned in previous section, the energy of downflow at upstream makes up the energy of the subsequent horseshoe vortex, so the stronger downflow kinetic energy results in the more intensive horseshoe vortex. Therefore, the higher Fr leads to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably. Qi and Gao [19] carried out a series of flume tests to investigate the scour around pile under regular waves, and proposed the fitting formula between Seq/D and Fr as following

lg(Seq/D)=Aexp(B/Fr)+Clg(�eq/�)=�exp(�/�r)+�(37)

where AB and C are constant.

Jmse 09 00886 g023 550

Figure 23. The fitting curve between Seq/D and Fr.

Jmse 09 00886 g024 550

Figure 24. Sketch of adverse pressure gradient at upstream USAF edges.

Took the Equation (37) to fit the simulating results with A = −0.002, B = 0.686 and C = −0.808, and the results are shown in Figure 23. From Figure 23, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Fr in present study is consistent with Equation (37) basically, meaning the Equation (37) is applicable to express the relationship of Seq/D with Fr around USAF under random waves.

4.4.2. Influence of Euler Number

The Euler number Eu is the influencing factor for the hydrodynamic field around foundation. The Eu under waves can be calculated by the following formula. The Eu can be represented by the Equation (38) for uniform cylinders [25]. The root-mean-square (RMS) value of near-bed velocity amplitude Um,rms is used for calculating Um.

Eu=U2mgD�u=�m2��(38)

where Um is depth-averaged flow velocity.

The Figure 25 displays the relationship between Seq/D and Eu of the present study. In order to compare with the simulating results, the experimental data of Sumer and Fredsøe [16] and Corvaro et al. [21] were also plotted in Figure 25. As shown in Figure 25, similar with the varying trend of Seq/D and Fr, the equilibrium scour depth appears a logarithmic increase as Eu increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increasing of Eu, which is benefit for the wave boundary layer separating from seabed, inducing the high-intensity horseshoe vortex, hence, causing intensive scour around USAF.

Jmse 09 00886 g025 550

Figure 25. The fitting curve between Seq/D and Eu.

Therefore, the variation of Fr and Eu reflect the magnitude of adverse pressure gradient pressure at upstream. Given that, the Equation (37) also was used to fit the simulating results with A = 8.875, B = 0.078 and C = −9.601, and the results are shown in Figure 25. From Figure 25, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Eu in present study is consistent with Equation (37) basically, meaning the Equation (37) is also applicable to express the relationship of Seq/D with Eu around USAF under random waves. Additionally, according to the above description of Fr, it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably.

5. Conclusions

A series of numerical models were established to investigate the local scour around umbrella suction anchor foundation (USAF) under random waves. The numerical model was validated for hydrodynamic and morphology parameters by comparing with the experimental data of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22]. Based on the simulating results, the scour evolution and scour mechanisms around USAF under random waves were analyzed respectively. Two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves. Finally, a parametric study was carried out with the present model to study the effects of the Froude number Fr and Euler number Eu to the equilibrium scour depth around USAF under random waves. The main conclusions can be described as follows.(1)

The packed sediment scour model and the RNG k−ε turbulence model were used to simulate the sand particles transport processes and the flow field around UASF respectively. The scour evolution obtained by the present model agrees well with the experimental results of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22], which indicates that the present model is accurate and reasonable for depicting the scour morphology around UASF under random waves.(2)

The vortex system at wave crest phase is mainly related to the scour process around USAF under random waves. The maximum scour depth appeared at the lee-side of the USAF at the initial stage (t < 1200 s). Subsequently, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.(3)

The error is negligible and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves when KC is calculated by KCs,p. Given that, a further revision model (Equation (31)) was proposed according to Raaijmakers’s model to predict the equilibrium scour depth around USAF under random waves and it shows good agreement with the simulating results of the present study when KCs,p < 8.(4)

Another further revision model (Equation (33)) was proposed according to the stochastic model established by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves, and the predicting results are the most favorable for n = 10 when KCrms,a < 4. However, contrary to the case of low KCrms,a, the predicting results are the most favorable for n = 2 when KCrms,a > 4 by the comparison with experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21].(5)

The same formula (Equation (37)) is applicable to express the relationship of Seq/D with Eu or Fr, and it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.

Author Contributions

Conceptualization, H.L. (Hongjun Liu); Data curation, R.H. and P.Y.; Formal analysis, X.W. and H.L. (Hao Leng); Funding acquisition, X.W.; Writing—original draft, R.H. and P.Y.; Writing—review & editing, X.W. and H.L. (Hao Leng); The final manuscript has been approved by all the authors. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Fundamental Research Funds for the Central Universities (grant number 202061027) and the National Natural Science Foundation of China (grant number 41572247).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Hu, R.; Liu, H.; Leng, H.; Yu, P.; Wang, X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. J. Mar. Sci. Eng. 20219, 886. https://doi.org/10.3390/jmse9080886

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Hu R, Liu H, Leng H, Yu P, Wang X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. Journal of Marine Science and Engineering. 2021; 9(8):886. https://doi.org/10.3390/jmse9080886Chicago/Turabian Style

Hu, Ruigeng, Hongjun Liu, Hao Leng, Peng Yu, and Xiuhai Wang. 2021. “Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves” Journal of Marine Science and Engineering 9, no. 8: 886. https://doi.org/10.3390/jmse9080886

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Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

레이저 보조 분말 기반 직접 에너지 증착에서 용융 풀 거동에 대한 감쇠 레이저 빔 강도 프로파일의 영향에 대한 열유체 모델링

Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

Mohammad Sattari, Amin Ebrahimi, Martin Luckabauer, Gert-willem R.B.E. Römer

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Professional

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Abstract

A numerical framework based on computational fluid dynamics (CFD), using the finite volume method (FVM) and volume of fluid (VOF) technique is presented to investigate the effect of the laser beam intensity profile on melt pool behavior in laser-assisted powder-based directed energy deposition (L-DED). L-DED is an additive manufacturing (AM) process that utilizes a laser beam to fuse metal powder particles. To assure high-fidelity modeling, it was found that it is crucial to accurately model the interaction between the powder stream and the laser beam in the gas region above the substrate. The proposed model considers various phenomena including laser energy attenuation and absorption, multiple reflections of the laser rays, powder particle stream, particle-fluid interaction, temperature-dependent properties, buoyancy effects, thermal expansion, solidification shrinkage and drag, and Marangoni flow. The latter is induced by temperature and element-dependent surface tension. The model is validated using experimental results and highlights the importance of considering laser energy attenuation. Furthermore, the study investigates how the laser beam intensity profile affects melt pool size and shape, influencing the solidification microstructure and mechanical properties of the deposited material. The proposed model has the potential to optimize the L-DED process for a variety of materials and provides insights into the capability of numerical modeling for additive manufacturing optimization.

Original languageEnglish
Title of host publicationFlow-3D World Users Conference
Publication statusPublished – 2023
EventFlow-3D World User Conference – Strasbourg, France
Duration: 5 Jun 2023 → 7 Jun 2023

Conference

ConferenceFlow-3D World User Conference
Country/TerritoryFrance
CityStrasbourg
Period5/06/23 → 7/06/23

What’s New – FLOW-3D 2023R2

FLOW-3D 소프트웨어 제품군의 모든 제품은 2023R1에서 IT 관련 개선 사항을 받았습니다. FLOW-3D 2023R1은 이제 Windows 11 및 RHEL 8을 지원합니다. 누락된 종속성을 보고하도록 Linux 설치 프로그램이 개선되었으며 더 이상 루트 수준 권한이 필요하지 않으므로 설치가 더 쉽고 안전해집니다. 또한 워크플로를 자동화한 사용자를 위해 입력 파일 변환기에 명령줄 인터페이스를 추가하여 스크립트 환경에서도 워크플로가 업데이트된 입력 파일로 작동하는지 확인할 수 있습니다.

확장된 PQ 2 분석

제조에 사용되는 유압 시스템은 PQ 2 곡선을 사용하여 모델링할 수 있습니다. 장치의 세부 사항을 건너뛰고 흐름에 미치는 영향을 포함하기 위해 질량-운동량 소스 또는 속도 경계 조건을 사용하여 유압 시스템을 근사화하는 것이 편리한 단순화인 경우가 많습니다. 기존 PQ 2 분석 모델을 확장하여 이러한 유형의 기하학적 단순화를 허용하면서도 여전히 현실적인 결과를 제공합니다. 이것은 시뮬레이션 시간과 모델 복잡성의 감소로 해석됩니다.

FLOW-3D 2022R2 의 새로운 기능

FLOW-3D 2022R2 제품군 의 출시와 함께 Flow Science는 워크스테이션과 FLOW-3D 의 HPC 버전 을 통합하여 단일 노드 CPU 구성에서 다중 구성에 이르기까지 모든 유형의 하드웨어 아키텍처를 활용할 수 있는 단일 솔버 엔진을 제공합니다. 노드 병렬 고성능 컴퓨팅 실행. 추가 개발에는 점탄성 흐름을 위한 새로운 로그 구조 텐서 방법, 지속적인 솔버 속도 성능 개선, 고급 냉각 채널 및 팬텀 구성 요소 제어, 향상된 연행 공기 기능이 포함됩니다.

통합 솔버

FLOW-3D 제품을 단일 통합 솔버로 마이그레이션하여  로컬 워크스테이션 또는 고성능 컴퓨팅 하드웨어 환경에서 원활하게 실행했습니다.

많은 사용자가 노트북이나 로컬 워크스테이션에서 모델을 실행하지만 고성능 컴퓨팅 클러스터에서 더 큰 모델을 실행합니다. 2022R2 릴리스에서는 통합 솔버를 통해 사용자가 HPC 솔루션에서 OpenMP/MPI 하이브리드 병렬화의 동일한 이점을 활용하여 워크스테이션 및 노트북에서 실행할 수 있습니다.

성능 확장의 예
점점 더 많은 수의 CPU 코어를 사용하는 성능 확장의 예
메쉬 분해의 예
OpenMP/MPI 하이브리드 병렬화를 위한 메시 분해의 예

솔버 성능 개선

멀티 소켓 워크스테이션

멀티 소켓 워크스테이션은 이제 매우 일반적이며 대규모 시뮬레이션을 실행할 수 있습니다. 새로운 통합 솔버를 통해 이러한 유형의 하드웨어를 사용하는 사용자는 일반적으로 HPC 클러스터 구성에서만 사용할 수 있었던 OpenMP/MPI 하이브리드 병렬화를 활용하여 모델을 실행할 수 있는 성능 이점을 볼 수 있습니다.

낮은 수준의 루틴으로 벡터화 및 메모리 액세스 개선

대부분의 테스트 사례에서 10%에서 20% 정도의 성능 향상이 관찰되었으며 일부 사례에서는 20%를 초과하는 런타임 이점이 있었습니다.

정제된 체적 대류 안정성 한계

시간 단계 안정성 한계는 모델 런타임의 주요 동인입니다. 2022R2에서는 새로운 시간 단계 안정성 한계인 3D 대류 안정성 한계를 숫자 위젯에서 사용할 수 있습니다. 실행 중이고 대류가 제한된(cx, cy 또는 cz 제한) 모델의 경우 새 옵션은 30% 정도의 일반적인 속도 향상을 보여주었습니다.

압력 솔버 프리 컨디셔너

경우에 따라 까다로운 흐름 구성의 경우 과도한 압력 솔버 반복으로 인해 실행 시간이 길어질 수 있습니다. 어려운 경우 2022R2에서는 모델이 너무 많이 반복될 때 FLOW-3D가 자동으로 새로운 프리 컨디셔너를 활성화하여 압력 수렴을 돕습니다. 테스트의 런타임이 1.9배에서 335배까지 빨라졌습니다!

점탄성 유체에 대한 로그 형태 텐서 방법

점탄성 유체에 대한 새로운 솔버 옵션을 사용자가 사용할 수 있으며 특히 높은 Weissenberg 수치에 효과적입니다.

점탄성 흐름을 위한 개선된 솔루션
로그 구조 텐서 솔루션을 사용하여 점탄성 흐름에 대한 높은 Weissenberg 수에서 개선된 솔루션의 예. Courtesy MF Tome, et al., J. Non-Newton. 체액. 기계 175-176 (2012) 44–54

활성 시뮬레이션 제어 확장

능동 시뮬레이션 제어 기능은 연속 주조 및 적층 제조 응용 프로그램과 주조 및 기타 여러 열 관리 응용 프로그램에 사용되는 냉각 채널에 일반적으로 사용되는 팬텀 개체를 포함하도록 확장되었습니다.

동적 열 제어의 예
융합 증착 모델링 애플리케이션을 위한 동적 열 제어의 예
가상 물체 속도 제어의 예
산업용 탱크 적용을 위한 동적 냉각 채널 제어의 예
동적 열 제어의 예
연속 주조 애플리케이션을 위한 팬텀 물체 속도 제어의 예

연행 공기 기능 개선

디퓨저 및 유사한 산업용 기포 흐름 응용 분야의 경우 이제 대량 공급원을 사용하여 물 기둥에 공기를 도입할 수 있습니다. 또한 혼입 공기 및 용존 산소의 난류 확산에 대한 기본값이 업데이트되었으며 매우 낮은 공기 농도에 대한 모델 정확도가 향상되었습니다.

디퓨저 모델의 예
디퓨저 모델의 예: 질량원을 사용하여 물기둥에 공기를 도입할 수 있습니다.
Figure 5 A schematic of the water model of reactor URO 200.

Physical and Numerical Modeling of the Impeller Construction Impact on the Aluminum Degassing Process

알루미늄 탈기 공정에 미치는 임펠러 구성의 물리적 및 수치적 모델링

Kamil Kuglin,1 Michał Szucki,2 Jacek Pieprzyca,3 Simon Genthe,2 Tomasz Merder,3 and Dorota Kalisz1,*

Mikael Ersson, Academic Editor

Author information Article notes Copyright and License information Disclaimer

Associated Data

Data Availability Statement

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Abstract

This paper presents the results of tests on the suitability of designed heads (impellers) for aluminum refining. The research was carried out on a physical model of the URO-200, followed by numerical simulations in the FLOW 3D program. Four design variants of impellers were used in the study. The degree of dispersion of the gas phase in the model liquid was used as a criterion for evaluating the performance of each solution using different process parameters, i.e., gas flow rate and impeller speed. Afterward, numerical simulations in Flow 3D software were conducted for the best solution. These simulations confirmed the results obtained with the water model and verified them.

Keywords: aluminum, impeller construction, degassing process, numerical modeling, physical modeling

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1. Introduction

Constantly increasing requirements concerning metallurgical purity in terms of hydrogen content and nonmetallic inclusions make casting manufacturers use effective refining techniques. The answer to this demand is the implementation of the aluminum refining technique making use of a rotor with an original design guaranteeing efficient refining [1,2,3,4]. The main task of the impeller (rotor) is to reduce the contamination of liquid metal (primary and recycled aluminum) with hydrogen and nonmetallic inclusions. An inert gas, mainly argon or a mixture of gases, is introduced through the rotor into the liquid metal to bring both hydrogen and nonmetallic inclusions to the metal surface through the flotation process. Appropriately and uniformly distributed gas bubbles in the liquid metal guarantee achieving the assumed level of contaminant removal economically. A very important factor in deciding about the obtained degassing effect is the optimal rotor design [5,6,7,8]. Thanks to the appropriate geometry of the rotor, gas bubbles introduced into the liquid metal are split into smaller ones, and the spinning movement of the rotor distributes them throughout the volume of the liquid metal bath. In this solution impurities in the liquid metal are removed both in the volume and from the upper surface of the metal. With a well-designed impeller, the costs of refining aluminum and its alloys can be lowered thanks to the reduced inert gas and energy consumption (optimal selection of rotor rotational speed). Shorter processing time and a high degree of dehydrogenation decrease the formation of dross on the metal surface (waste). A bigger produced dross leads to bigger process losses. Consequently, this means that the choice of rotor geometry has an indirect impact on the degree to which the generated waste is reduced [9,10].

Another equally important factor is the selection of process parameters such as gas flow rate and rotor speed [11,12]. A well-designed gas injection system for liquid metal meets two key requirements; it causes rapid mixing of the liquid metal to maintain a uniform temperature throughout the volume and during the entire process, to produce a chemically homogeneous metal composition. This solution ensures effective degassing of the metal bath. Therefore, the shape of the rotor, the arrangement of the nozzles, and their number are significant design parameters that guarantee the optimum course of the refining process. It is equally important to complete the mixing of the metal bath in a relatively short time, as this considerably shortens the refining process and, consequently, reduces the process costs. Another important criterion conditioning the implementation of the developed rotor is the generation of fine diffused gas bubbles which are distributed throughout the metal volume, and whose residence time will be sufficient for the bubbles to collide and adsorb the contaminants. The process of bubble formation by the spinning rotors differs from that in the nozzles or porous molders. In the case of a spinning rotor, the shear force generated by the rotor motion splits the bubbles into smaller ones. Here, the rotational speed, mixing force, surface tension, and fluid density have a key effect on the bubble size. The velocity of the bubbles, which depends mainly on their size and shape, determines their residence time in the reactor and is, therefore, very important for the refining process, especially since gas bubbles in liquid aluminum may remain steady only below a certain size [13,14,15].

The impeller designs presented in the article were developed to improve the efficiency of the process and reduce its costs. The impellers used so far have a complicated structure and are very pricey. The success of the conducted research will allow small companies to become independent of external supplies through the possibility of making simple and effective impellers on their own. The developed structures were tested on the water model. The results of this study can be considered as pilot.

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2. Materials and Methods

Rotors were realized with the SolidWorks computer design technique and a 3D printer. The developed designs were tested on a water model. Afterward, the solution with the most advantageous refining parameters was selected and subjected to calculations with the Flow3D package. As a result, an impeller was designed for aluminum refining. Its principal lies in an even distribution of gas bubbles in the entire volume of liquid metal, with the largest possible participation of the bubble surface, without disturbing the metal surface. This procedure guarantees the removal of gaseous, as well as metallic and nonmetallic, impurities.

2.1. Rotor Designs

The developed impeller constructions, shown in Figure 1Figure 2Figure 3 and Figure 4, were printed on a 3D printer using the PLA (polylactide) material. The impeller design models differ in their shape and the number of holes through which the inert gas flows. Figure 1Figure 2 and Figure 3 show the same impeller model but with a different number of gas outlets. The arrangement of four, eight, and 12 outlet holes was adopted in the developed design. A triangle-shaped structure equipped with three gas outlet holes is presented in Figure 4.

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Figure 1

A 3D model—impeller with four holes—variant B4.

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Figure 2

A 3D model—impeller with eight holes—variant B8.

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Figure 3

A 3D model—impeller with twelve holes—variant B12.

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Figure 4

A 3D model—‘red triangle’ impeller with three holes—variant RT3.

2.2. Physical Models

Investigations were carried out on a water model of the URO 200 reactor of the barbotage refining process (see Figure 5).

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Figure 5

A schematic of the water model of reactor URO 200.

The URO 200 reactor can be classified as a cyclic reactor. The main element of the device is a rotor, which ends the impeller. The whole system is attached to a shaft via which the refining gas is supplied. Then, the shaft with the rotor is immersed in the liquid metal in the melting pot or the furnace chamber. In URO 200 reactors, the refining process lasts 600 s (10 min), the gas flow rate that can be obtained ranges from 5 to 20 dm3·min−1, and the speed at which the rotor can move is 0 to 400 rpm. The permissible quantity of liquid metal for barbotage refining is 300 kg or 700 kg [8,16,17]. The URO 200 has several design solutions which improve operation and can be adapted to the existing equipment in the foundry. These solutions include the following [8,16]:

  • URO-200XR—used for small crucible furnaces, the capacity of which does not exceed 250 kg, with no control system and no control of the refining process.
  • URO-200SA—used to service several crucible furnaces of capacity from 250 kg to 700 kg, fully automated and equipped with a mechanical rotor lift.
  • URO-200KA—used for refining processes in crucible furnaces and allows refining in a ladle. The process is fully automated, with a hydraulic rotor lift.
  • URO-200KX—a combination of the XR and KA models, designed for the ladle refining process. Additionally, refining in heated crucibles is possible. The unit is equipped with a manual hydraulic rotor lift.
  • URO-200PA—designed to cooperate with induction or crucible furnaces or intermediate chambers, the capacity of which does not exceed one ton. This unit is an integral part of the furnace. The rotor lift is equipped with a screw drive.

Studies making use of a physical model can be associated with the observation of the flow and circulation of gas bubbles. They require meeting several criteria regarding the similarity of the process and the object characteristics. The similarity conditions mainly include geometric, mechanical, chemical, thermal, and kinetic parameters. During simulation of aluminum refining with inert gas, it is necessary to maintain the geometric similarity between the model and the real object, as well as the similarity related to the flow of liquid metal and gas (hydrodynamic similarity). These quantities are characterized by the Reynolds, Weber, and Froude numbers. The Froude number is the most important parameter characterizing the process, its magnitude is the same for the physical model and the real object. Water was used as the medium in the physical modeling. The factors influencing the choice of water are its availability, relatively low cost, and kinematic viscosity at room temperature, which is very close to that of liquid aluminum.

The physical model studies focused on the flow of inert gas in the form of gas bubbles with varying degrees of dispersion, particularly with respect to some flow patterns such as flow in columns and geysers, as well as disturbance of the metal surface. The most important refining parameters are gas flow rate and rotor speed. The barbotage refining studies for the developed impeller (variants B4, B8, B12, and RT3) designs were conducted for the following process parameters:

  • Rotor speed: 200, 300, 400, and 500 rpm,
  • Ideal gas flow: 10, 20, and 30 dm3·min−1,
  • Temperature: 293 K (20 °C).

These studies were aimed at determining the most favorable variants of impellers, which were then verified using the numerical modeling methods in the Flow-3D program.

2.3. Numerical Simulations with Flow-3D Program

Testing different rotor impellers using a physical model allows for observing the phenomena taking place while refining. This is a very important step when testing new design solutions without using expensive industrial trials. Another solution is modeling by means of commercial simulation programs such as ANSYS Fluent or Flow-3D [18,19]. Unlike studies on a physical model, in a computer program, the parameters of the refining process and the object itself, including the impeller design, can be easily modified. The simulations were performed with the Flow-3D program version 12.03.02. A three-dimensional system with the same dimensions as in the physical modeling was used in the calculations. The isothermal flow of liquid–gas bubbles was analyzed. As in the physical model, three speeds were adopted in the numerical tests: 200, 300, and 500 rpm. During the initial phase of the simulations, the velocity field around the rotor generated an appropriate direction of motion for the newly produced bubbles. When the required speed was reached, the generation of randomly distributed bubbles around the rotor was started at a rate of 2000 per second. Table 1 lists the most important simulation parameters.

Table 1

Values of parameters used in the calculations.

ParameterValueUnit
Maximum number of gas particles1,000,000
Rate of particle generation20001·s−1
Specific gas constant287.058J·kg−1·K−1
Atmospheric pressure1.013 × 105Pa
Water density1000kg·m−3
Water viscosity0.001kg·m−1·s−1
Boundary condition on the wallsNo-slip
Size of computational cell0.0034m

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In the case of the CFD analysis, the numerical solutions require great care when generating the computational mesh. Therefore, computational mesh tests were performed prior to the CFD calculations. The effect of mesh density was evaluated by taking into account the velocity of water in the tested object on the measurement line A (height of 0.065 m from the bottom) in a characteristic cross-section passing through the object axis (see Figure 6). The mesh contained 3,207,600, 6,311,981, 7,889,512, 11,569,230, and 14,115,049 cells.

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Figure 6

The velocity of the water depending on the size of the computational grid.

The quality of the generated computational meshes was checked using the criterion skewness angle QEAS [18]. This criterion is described by the following relationship:

QEAS=max{βmax−βeq180−βeq,βeq−βminβeq},

(1)

where βmaxβmin are the maximal and minimal angles (in degrees) between the edges of the cell, and βeq is the angle corresponding to an ideal cell, which for cubic cells is 90°.

Normalized in the interval [0;1], the value of QEAS should not exceed 0.75, which identifies the permissible skewness angle of the generated mesh. For the computed meshes, this value was equal to 0.55–0.65.

Moreover, when generating the computational grids in the studied facility, they were compacted in the areas of the highest gradients of the calculated values, where higher turbulence is to be expected (near the impeller). The obtained results of water velocity in the studied object at constant gas flow rate are shown in Figure 6.

The analysis of the obtained water velocity distributions (see Figure 6) along the line inside the object revealed that, with the density of the grid of nodal points, the velocity changed and its changes for the test cases of 7,889,512, 11,569,230, and 14,115,049 were insignificant. Therefore, it was assumed that a grid containing not less than 7,900,000 (7,889,512) cells would not affect the result of CFD calculations.

A single-block mesh of regular cells with a size of 0.0034 m was used in the numerical calculations. The total number of cells was approximately 7,900,000 (7,889,512). This grid resolution (see Figure 7) allowed the geometry of the system to be properly represented, maintaining acceptable computation time (about 3 days on a workstation with 2× CPU and 12 computing cores).

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Figure 7

Structured equidistant mesh used in numerical calculations: (a) mesh with smoothed, surface cells (the so-called FAVOR method) used in Flow-3D; (b) visualization of the applied mesh resolution.

The calculations were conducted with an explicit scheme. The timestep was selected by the program automatically and controlled by stability and convergence. From the moment of the initial velocity field generation (start of particle generation), it was 0.0001 s.

When modeling the degassing process, three fluids are present in the system: water, gas supplied through the rotor head (impeller), and the surrounding air. Modeling such a multiphase flow is a numerically very complex issue. The necessity to overcome the liquid backpressure by the gas flowing out from the impeller leads to the formation of numerical instabilities in the volume of fluid (VOF)-based approach used by Flow-3D software. Therefore, a mixed description of the analyzed flow was used here. In this case, water was treated as a continuous medium, while, in the case of gas bubbles, the discrete phase model (DPM) model was applied. The way in which the air surrounding the system was taken into account is later described in detail.

The following additional assumptions were made in the modeling:

  • —The liquid phase was considered as an incompressible Newtonian fluid.
  • —The effect of chemical reactions during the refining process was neglected.
  • —The composition of each phase (gas and liquid) was considered homogeneous; therefore, the viscosity and surface tension were set as constants.
  • —Only full turbulence existed in the liquid, and the effect of molecular viscosity was neglected.
  • —The gas bubbles were shaped as perfect spheres.
  • —The mutual interaction between gas bubbles (particles) was neglected.

2.3.1. Modeling of Liquid Flow 

The motion of the real fluid (continuous medium) is described by the Navier–Stokes Equation [20].

dudt=−1ρ∇p+ν∇2u+13ν∇(∇⋅ u)+F,

(2)

where du/dt is the time derivative, u is the velocity vector, t is the time, and F is the term accounting for external forces including gravity (unit components denoted by XYZ).

In the simulations, the fluid flow was assumed to be incompressible, in which case the following equation is applicable:

∂u∂t+(u⋅∇)u=−1ρ∇p+ν∇2u+F.

(3)

Due to the large range of liquid velocities during flows, the turbulence formation process was included in the modeling. For this purpose, the k–ε model turbulence kinetic energy k and turbulence dissipation ε were the target parameters, as expressed by the following equations [21]:

∂(ρk)∂t+∂(ρkvi)∂xi=∂∂xj[(μ+μtσk)⋅∂k∂xi]+Gk+Gb−ρε−Ym+Sk,

(4)

∂(ρε)∂t+∂(ρεui)∂xi=∂∂xj[(μ+μtσε)⋅∂k∂xi]+C1εεk(Gk+G3εGb)+C2ερε2k+Sε,

(5)

where ρ is the gas density, σκ and σε are the Prandtl turbulence numbers, k and ε are constants of 1.0 and 1.3, and Gk and Gb are the kinetic energy of turbulence generated by the average velocity and buoyancy, respectively.

As mentioned earlier, there are two gas phases in the considered problem. In addition to the gas bubbles, which are treated here as particles, there is also air, which surrounds the system. The boundary of phase separation is in this case the free surface of the water. The shape of the free surface can change as a result of the forming velocity field in the liquid. Therefore, it is necessary to use an appropriate approach to free surface tracking. The most commonly used concept in liquid–gas flow modeling is the volume of fluid (VOF) method [22,23], and Flow-3D uses a modified version of this method called TrueVOF. It introduces the concept of the volume fraction of the liquid phase fl. This parameter can be used for classifying the cells of a discrete grid into areas filled with liquid phase (fl = 1), gaseous phase, or empty cells (fl = 0) and those through which the phase separation boundary (fl ∈ (0, 1)) passes (free surface). To determine the local variations of the liquid phase fraction, it is necessary to solve the following continuity equation:

dfldt=0.

(6)

Then, the fluid parameters in the region of coexistence of the two phases (the so-called interface) depend on the volume fraction of each phase.

ρ=flρl+(1−fl)ρg,

(7)

ν=flνl+(1−fl)νg,

(8)

where indices l and g refer to the liquid and gaseous phases, respectively.

The parameter of fluid velocity in cells containing both phases is also determined in the same way.

u=flul+(1−fl)ug.

(9)

Since the processes taking place in the surrounding air can be omitted, to speed up the calculations, a single-phase, free-surface model was used. This means that no calculations were performed in the gas cells (they were treated as empty cells). The liquid could fill them freely, and the air surrounding the system was considered by the atmospheric pressure exerted on the free surface. This approach is often used in modeling foundry and metallurgical processes [24].

2.3.2. Modeling of Gas Bubble Flow 

As stated, a particle model was used to model bubble flow. Spherical particles (gas bubbles) of a given size were randomly generated in the area marked with green in Figure 7b. In the simulations, the gas bubbles were assumed to have diameters of 0.016 and 0.02 m corresponding to the gas flow rates of 10 and 30 dm3·min−1, respectively.

Experimental studies have shown that, as a result of turbulent fluid motion, some of the bubbles may burst, leading to the formation of smaller bubbles, although merging of bubbles into larger groupings may also occur. Therefore, to be able to observe the behavior of bubbles of different sizes (diameter), the calculations generated two additional particle types with diameters twice smaller and twice larger, respectively. The proportion of each species in the system was set to 33.33% (Table 2).

Table 2

Data assumed for calculations.

NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
A2000.01610D2000.0230
0.0080.01
0.0320.04
B3000.01610E3000.0230
0.0080.01
0.0320.04
C5000.01610F5000.0230
0.0080.01
0.0320.04

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The velocity of the particle results from the generated velocity field (calculated from Equation (3) in the liquid ul around it and its velocity resulting from the buoyancy force ub. The effect of particle radius r on the terminal velocity associated with buoyancy force can be determined according to Stokes’ law.

ub=29 (ρg−ρl)μlgr2,

(10)

where g is the acceleration (9.81).

The DPM model was used for modeling the two-phase (water–air) flow. In this model, the fluid (water) is treated as a continuous phase and described by the Navier–Stokes equation, while gas bubbles are particles flowing in the model fluid (discrete phase). The trajectories of each bubble in the DPM system are calculated at each timestep taking into account the mass forces acting on it. Table 3 characterizes the DPM model used in our own research [18].

Table 3

Characteristic of the DPM model.

MethodEquations
Euler–LagrangeBalance equation:
dugdt=FD(u−ug)+g(ϱg−ϱ)ϱg+F.
FD (u − up) denotes the drag forces per mass unit of a bubble, and the expression for the drag coefficient FD is of the form
FD=18μCDReϱ⋅gd2g24.
The relative Reynolds number has the form
Re≡ρdg|ug−u|μ.
On the other hand, the force resulting from the additional acceleration of the model fluid has the form
F=12dρdtρg(u−ug),
where ug is the gas bubble velocity, u is the liquid velocity, dg is the bubble diameter, and CD is the drag coefficient.

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3. Results and Discussion

3.1. Calculations of Power and Mixing Time by the Flowing Gas Bubbles

One of the most important parameters of refining with a rotor is the mixing power induced by the spinning rotor and the outflowing gas bubbles (via impeller). The mixing power of liquid metal in a ladle of height (h) by gas injection can be determined from the following relation [15]:

pgVm=ρ⋅g⋅uB,

(11)

where pg is the mixing power, Vm is the volume of liquid metal in the reactor, ρ is the density of liquid aluminum, and uB is the average speed of bubbles, given below.

uB=n⋅R⋅TAc⋅Pm⋅t,

(12)

where n is the number of gas moles, R is the gas constant (8.314), Ac is the cross-sectional area of the reactor vessel, T is the temperature of liquid aluminum in the reactor, and Pm is the pressure at the middle tank level. The pressure at the middle level of the tank is calculated by a function of the mean logarithmic difference.

Pm=(Pa+ρ⋅g⋅h)−Paln(Pa+ρ⋅g⋅h)Pa,

(13)

where Pa is the atmospheric pressure, and h is the the height of metal in the reactor.

Themelis and Goyal [25] developed a model for calculating mixing power delivered by gas injection.

pg=2Q⋅R⋅T⋅ln(1+m⋅ρ⋅g⋅hP),

(14)

where Q is the gas flow, and m is the mass of liquid metal.

Zhang [26] proposed a model taking into account the temperature difference between gas and alloy (metal).

pg=QRTgVm[ln(1+ρ⋅g⋅hPa)+(1−TTg)],

(15)

where Tg is the gas temperature at the entry point.

Data for calculating the mixing power resulting from inert gas injection into liquid aluminum are given below in Table 4. The design parameters were adopted for the model, the parameters of which are shown in Figure 5.

Table 4

Data for calculating mixing power introduced by an inert gas.

ParameterValueUnit
Height of metal column0.7m
Density of aluminum2375kg·m−3
Process duration20s
Gas temperature at the injection site940K
Cross-sectional area of ladle0.448m2
Mass of liquid aluminum546.25kg
Volume of ladle0.23M3
Temperature of liquid aluminum941.15K

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Table 5 presents the results of mixing power calculations according to the models of Themelis and Goyal and of Zhang for inert gas flows of 10, 20, and 30 dm3·min−1. The obtained calculation results significantly differed from each other. The difference was an order of magnitude, which indicates that the model is highly inaccurate without considering the temperature of the injected gas. Moreover, the calculations apply to the case when the mixing was performed only by the flowing gas bubbles, without using a rotor, which is a great simplification of the phenomenon.

Table 5

Mixing power calculated from mathematical models.

Mathematical ModelMixing Power (W·t−1)
for a Given Inert Gas Flow (dm3·min−1)
102030
Themelis and Goyal11.4923.3335.03
Zhang0.821.662.49

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The mixing time is defined as the time required to achieve 95% complete mixing of liquid metal in the ladle [27,28,29,30]. Table 6 groups together equations for the mixing time according to the models.

Table 6

Models for calculating mixing time.

AuthorsModelRemarks
Szekely [31]τ=800ε−0.4ε—W·t−1
Chiti and Paglianti [27]τ=CVQlV—volume of reactor, m3
Ql—flow intensity, m3·s−1
Iguchi and Nakamura [32]τ=1200⋅Q−0.4D1.97h−1.0υ0.47υ—kinematic viscosity, m2·s−1
D—diameter of ladle, m
h—height of metal column, m
Q—liquid flow intensity, m3·s−1

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Figure 8 and Figure 9 show the mixing time as a function of gas flow rate for various heights of the liquid column in the ladle and mixing power values.

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Figure 8

Mixing time as a function of gas flow rate for various heights of the metal column (Iguchi and Nakamura model).

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Figure 9

Mixing time as a function of mixing power (Szekly model).

3.2. Determining the Bubble Size

The mechanisms controlling bubble size and mass transfer in an alloy undergoing refining are complex. Strong mixing conditions in the reactor promote impurity mass transfer. In the case of a spinning rotor, the shear force generated by the rotor motion separates the bubbles into smaller bubbles. Rotational speed, mixing force, surface tension, and liquid density have a strong influence on the bubble size. To characterize the kinetic state of the refining process, parameters k and A were introduced. Parameters kA, and uB can be calculated using the below equations [33].

k=2D⋅uBdB⋅π−−−−−−√,

(16)

A=6Q⋅hdB⋅uB,

(17)

uB=1.02g⋅dB,−−−−−√

(18)

where D is the diffusion coefficient, and dB is the bubble diameter.

After substituting appropriate values, we get

dB=3.03×104(πD)−2/5g−1/5h4/5Q0.344N−1.48.

(19)

According to the last equation, the size of the gas bubble decreases with the increasing rotational speed (see Figure 10).

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Figure 10

Effect of rotational speed on the bubble diameter.

In a flow of given turbulence intensity, the diameter of the bubble does not exceed the maximum size dmax, which is inversely proportional to the rate of kinetic energy dissipation in a viscous flow ε. The size of the gas bubble diameter as a function of the mixing energy, also considering the Weber number and the mixing energy in the negative power, can be determined from the following equations [31,34]:

  • —Sevik and Park:

dBmax=We0.6kr⋅(σ⋅103ρ⋅10−3)0.6⋅(10⋅ε)−0.4⋅10−2.

(20)

  • —Evans:

dBmax=⎡⎣Wekr⋅σ⋅1032⋅(ρ⋅10−3)13⎤⎦35 ⋅(10⋅ε)−25⋅10−2.

(21)

The results of calculating the maximum diameter of the bubble dBmax determined from Equation (21) are given in Table 7.

Table 7

The results of calculating the maximum diameter of the bubble using Equation (21).

ModelMixing Energy
ĺ (m2·s−3)
Weber Number (Wekr)
0.591.01.2
Zhang and Taniguchi
dmax
0.10.01670.02300.026
0.50.00880.01210.013
1.00.00670.00910.010
1.50.00570.00780.009
Sevik and Park
dBmax
0.10.2650.360.41
0.50.1390.190.21
1.00.1060.140.16
1.50.0900.120.14
Evans
dBmax
0.10.2470.3400.38
0.50.1300.1780.20
1.00.0980.1350.15
1.50.0840.1150.13

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3.3. Physical Modeling

The first stage of experiments (using the URO-200 water model) included conducting experiments with impellers equipped with four, eight, and 12 gas outlets (variants B4, B8, B12). The tests were carried out for different process parameters. Selected results for these experiments are presented in Figure 11Figure 12Figure 13 and Figure 14.

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Figure 11

Impeller variant B4—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 12

Impeller variant B8—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 13

Gas bubble dispersion registered for different processing parameters (impeller variant B12).

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Figure 14

Gas bubble dispersion registered for different processing parameters (impeller variant RT3).

The analysis of the refining variants presented in Figure 11Figure 12Figure 13 and Figure 14 reveals that the proposed impellers design model is not useful for the aluminum refining process. The number of gas outlet orifices, rotational speed, and flow did not affect the refining efficiency. In all the variants shown in the figures, very poor dispersion of gas bubbles was observed in the object. The gas bubble flow had a columnar character, and so-called dead zones, i.e., areas where no inert gas bubbles are present, were visible in the analyzed object. Such dead zones were located in the bottom and side zones of the ladle, while the flow of bubbles occurred near the turning rotor. Another negative phenomenon observed was a significant agitation of the water surface due to excessive (rotational) rotor speed and gas flow (see Figure 13, cases 20; 400, 30; 300, 30; 400, and 30; 500).

Research results for a ‘red triangle’ impeller equipped with three gas supply orifices (variant RT3) are presented in Figure 14.

In this impeller design, a uniform degree of bubble dispersion in the entire volume of the modeling fluid was achieved for most cases presented (see Figure 14). In all tested variants, single bubbles were observed in the area of the water surface in the vessel. For variants 20; 200, 30; 200, and 20; 300 shown in Figure 14, the bubble dispersion results were the worst as the so-called dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further applications. Interestingly, areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model. This means that the presented model had the best performance in terms of dispersion of gas bubbles in the model liquid. Its design with sharp edges also differed from previously analyzed models, which is beneficial for gas bubble dispersion, but may interfere with its suitability in industrial conditions due to possible premature wear.

3.4. Qualitative Comparison of Research Results (CFD and Physical Model)

The analysis (physical modeling) revealed that the best mixing efficiency results were obtained with the RT3 impeller variant. Therefore, numerical calculations were carried out for the impeller model with three outlet orifices (variant RT3). The CFD results are presented in Figure 15 and Figure 16.

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Figure 15

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 1 s: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

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Figure 16

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 5.4 s.: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

CFD results are presented for all analyzed variants (impeller RT3) at two selected calculation timesteps of 1 and 5.40 s. They show the velocity field of the medium (water) and the dispersion of gas bubbles.

Figure 15 shows the initial refining phase after 1 s of the process. In this case, the gas bubble formation and flow were observed in an area close to contact with the rotor. Figure 16 shows the phase when the dispersion and flow of gas bubbles were advanced in the reactor area of the URO-200 model.

The quantitative evaluation of the obtained results of physical and numerical model tests was based on the comparison of the degree of gas dispersion in the model liquid. The degree of gas bubble dispersion in the volume of the model liquid and the areas of strong turbulent zones formation were evaluated during the analysis of the results of visualization and numerical simulations. These two effects sufficiently characterize the required course of the process from the physical point of view. The known scheme of the below description was adopted as a basic criterion for the evaluation of the degree of dispersion of gas bubbles in the model liquid.

  • Minimal dispersion—single bubbles ascending in the region of their formation along the ladle axis; lack of mixing in the whole bath volume.
  • Accurate dispersion—single and well-mixed bubbles ascending toward the bath mirror in the region of the ladle axis; no dispersion near the walls and in the lower part of the ladle.
  • Uniform dispersion—most desirable; very good mixing of fine bubbles with model liquid.
  • Excessive dispersion—bubbles join together to form chains; large turbulence zones; uneven flow of gas.

The numerical simulation results give a good agreement with the experiments performed with the physical model. For all studied variants (used process parameters), the single bubbles were observed in the area of water surface in the vessel. For variants presented in Figure 13 (200 rpm, gas flow 20 and dm3·min−1) and relevant examples in numerical simulation Figure 16, the worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further use. The areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model (physical model). This means that the presented impeller model had the best performance in terms of dispersion of gas bubbles in the model liquid. The worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and side walls of the vessel, which disqualifies these work parameters for further use.

Figure 17 presents exemplary results of model tests (CFD and physical model) with marked gas bubble dispersion zones. All variants of tests were analogously compared, and this comparison allowed validating the numerical model.

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Figure 17

Compilations of model research results (CFD and physical): A—single gas bubbles formed on the surface of the modeling liquid, B—excessive formation of gas chains and swirls, C—uniform distribution of gas bubbles in the entire volume of the tank, and D—dead zones without gas bubbles, no dispersion. (a) Variant B; (b) variant F.

It should be mentioned here that, in numerical simulations, it is necessary to make certain assumptions and simplifications. The calculations assumed three particle size classes (Table 2), which represent the different gas bubbles that form due to different gas flow rates. The maximum number of particles/bubbles (Table 1) generated was assumed in advance and related to the computational capabilities of the computer. Too many particles can also make it difficult to visualize and analyze the results. The size of the particles, of course, affects their behavior during simulation, while, in the figures provided in the article, the bubbles are represented by spheres (visualization of the results) of the same size. Please note that, due to the adopted Lagrangian–Eulerian approach, the simulation did not take into account phenomena such as bubble collapse or fusion. However, the obtained results allow a comprehensive analysis of the behavior of gas bubbles in the system under consideration.

The comparative analysis of the visualization (quantitative) results obtained with the water model and CFD simulations (see Figure 17) generated a sufficient agreement from the point of view of the trends. A precise quantitative evaluation is difficult to perform because of the lack of a refraction compensating system in the water model. Furthermore, in numerical simulations, it is not possible to determine the geometry of the forming gas bubbles and their interaction with each other as opposed to the visualization in the water model. The use of both research methods is complementary. Thus, a direct comparison of images obtained by the two methods requires appropriate interpretation. However, such an assessment gives the possibility to qualitatively determine the types of the present gas bubble dispersion, thus ultimately validating the CFD results with the water model.

A summary of the visualization results for impellers RT3, i.e., analysis of the occurring gas bubble dispersion types, is presented in Table 8.

Table 8

Summary of visualization results (impeller RT3)—different types of gas bubble dispersion.

No Exp.ABCDEF
Gas flow rate, dm3·min−11030
Impeller speed, rpm200300500200300500
Type of dispersionAccurateUniformUniform/excessiveMinimalExcessiveExcessive

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Tests carried out for impeller RT3 confirmed the high efficiency of gas bubble distribution in the volume of the tested object at a low inert gas flow rate of 10 dm3·min−1. The most optimal variant was variant B (300 rpm, 10 dm3·min−1). However, the other variants A and C (gas flow rate 10 dm3·min−1) seemed to be favorable for this type of impeller and are recommended for further testing. The above process parameters will be analyzed in detail in a quantitative analysis to be performed on the basis of the obtained efficiency curves of the degassing process (oxygen removal). This analysis will give an unambiguous answer as to which process parameters are the most optimal for this type of impeller; the results are planned for publication in the next article.

It should also be noted here that the high agreement between the results of numerical calculations and physical modelling prompts a conclusion that the proposed approach to the simulation of a degassing process which consists of a single-phase flow model with a free surface and a particle flow model is appropriate. The simulation results enable us to understand how the velocity field in the fluid is formed and to analyze the distribution of gas bubbles in the system. The simulations in Flow-3D software can, therefore, be useful for both the design of the impeller geometry and the selection of process parameters.

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4. Conclusions

The results of experiments carried out on the physical model of the device for the simulation of barbotage refining of aluminum revealed that the worst results in terms of distribution and dispersion of gas bubbles in the studied object were obtained for the black impellers variants B4, B8, and B12 (multi-orifice impellers—four, eight, and 12 outlet holes, respectively).

In this case, the control of flow, speed, and number of gas exit orifices did not improve the process efficiency, and the developed design did not meet the criteria for industrial tests. In the case of the ‘red triangle’ impeller (variant RT3), uniform gas bubble dispersion was achieved throughout the volume of the modeling fluid for most of the tested variants. The worst bubble dispersion results due to the occurrence of the so-called dead zones in the area near the bottom and sidewalls of the vessel were obtained for the flow variants of 20 dm3·min−1 and 200 rpm and 30 dm3·min−1 and 200 rpm. For the analyzed model, areas where swirls and gas bubble chains were formed were found only for the inert gas flow of 20 and 30 dm3·min−1 and 200 rpm. The model impeller (variant RT3) had the best performance compared to the previously presented impellers in terms of dispersion of gas bubbles in the model liquid. Moreover, its design differed from previously presented models because of its sharp edges. This can be advantageous for gas bubble dispersion, but may negatively affect its suitability in industrial conditions due to premature wearing.

The CFD simulation results confirmed the results obtained from the experiments performed on the physical model. The numerical simulation of the operation of the ‘red triangle’ impeller model (using Flow-3D software) gave good agreement with the experiments performed on the physical model. This means that the presented model impeller, as compared to other (analyzed) designs, had the best performance in terms of gas bubble dispersion in the model liquid.

In further work, the developed numerical model is planned to be used for CFD simulations of the gas bubble distribution process taking into account physicochemical parameters of liquid aluminum based on industrial tests. Consequently, the obtained results may be implemented in production practice.

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Funding Statement

This paper was created with the financial support grants from the AGH-UST, Faculty of Foundry Engineering, Poland (16.16.170.654 and 11/990/BK_22/0083) for the Faculty of Materials Engineering, Silesian University of Technology, Poland.

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Author Contributions

Conceptualization, K.K. and D.K.; methodology, J.P. and T.M.; validation, M.S. and S.G.; formal analysis, D.K. and T.M.; investigation, J.P., K.K. and S.G.; resources, M.S., J.P. and K.K.; writing—original draft preparation, D.K. and T.M.; writing—review and editing, D.K. and T.M.; visualization, J.P., K.K. and S.G.; supervision, D.K.; funding acquisition, D.K. and T.M. All authors have read and agreed to the published version of the manuscript.

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Institutional Review Board Statement

Not applicable.

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Informed Consent Statement

Not applicable.

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Data Availability Statement

Data are contained within the article.

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Conflicts of Interest

The authors declare no conflict of interest.

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Footnotes

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

범람으로 인한 비점착성 흙댐 붕괴에 대한 테일워터 깊이의 영향

ShaimaaAmanaMohamedAbdelrazek RezkbRabieaNasrc

Abstract

본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.

결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.

실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.

The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.

Keywords

Earth dam, Eroded volume, Flow 3D model, Non-cohesive soil, Overtopping failure, Tailwater depth

Notation

d50

Mean partical diameterWc

Optimum water contentZo

Dam height (cm)do

Tailwater depth (cm)Zeroded

Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t

Total time of failure (sec)t1

Time of crest width erosion (sec)Zcrest

The crest height (cm)Vtotal

Total volume of the dam (m3)Veroded

Cumulative eroded volume (m3)RMSE

The statistical variable root- mean- square errord

Degree of agreement indexyu.s.

The upstream water depth (cm)yd.s

The downstream water depth (cm)H

Water surface elevation over sharp crested weir (cm)Q

Outflow discharge (liter/sec)Qpeak

Peak discharge (liter/sec)

1. Introduction

Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1][2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.

Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4][5][6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.

Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.

Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.

Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.

Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.

Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.

Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.

In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are used in model assessment.

2. Material and methods

The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.

To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.

A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter d50,equals 0.38 mm and internal friction angle equals 32.6°.

2.1. Experimental procedures

To investigate the effect of the tailwater depth (do), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.

The optimum water content, Wc, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m3. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.

After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.

Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m3/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/sec for all experiments, while the downstream boundary is an outflow boundary condition.

Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.

2.2. Repeatability

To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, Zeroded / Zo, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.

3. Numerical model

The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (RNG, K-e, and k-w) and sediment scour equations (Van Rin, Meyer- peter and Muller, and Nielsen) that produce the best results. In this, the flow field is solved by the RNG turbulence model, and the van Rijn equation is used for the sediment scour model. A geometry file is imported before applying the mesh.

A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.

In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.

The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2

where N is the number of samples, Pi and Mi are the models and experimental values, P and M are the means of the model and experimental values. The best fit between the experimental and model results would have an RMSE = 0 and degree of agreement, d = 1.

4. Results of experimental work

The results of the total time of failure, t (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion t1, cumulative eroded volume Veroded, and peak discharge Qpeak for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.

Table 1. Results of experimental work.

Tailwater depth, do (cm)Total time of failure, t (sec)Time of crest width erosion, t1 (sec)cumulative eroded volume, Veroded (m3)Peak discharge, Qpeak (liter/sec)
5255220.2113.12
15165300.1612.19
20140340.1311.29
25110390.0510.84

5. Discussion

5.1. Side erosion

The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/sec) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.

Fig. 9 shows a sample of numerical model output. Fig. 10Fig. 11Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of RMSE and d for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an RMSE value equals 0.023, 0.0218, and 0.0167 and degree of agreement, d, equals 0.95, 0.968, and 0.988 for relative tailwater depths, do/(do)ref, = 3, 4 and 5, respectively. The low values of RMSE and high values of d show that the Flow 3D can effectively simulate the erosion process. From Fig. 10Fig. 11Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the d50 value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].

It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, do/(do)ref = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths, do/(do)ref = 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively.

The relation between the relative eroded crest height, Zeroded /Zo, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively. The time required for the erosion of the crest width, t1, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing, do /Zo. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth, do /(do)ref = 3, 4 and 5, respectively.

Crest height, Zcrest is calculated from the experimental results and the Flow 3D results for relative tailwater depths, do/(do)ref, = 3, 4, and 5. A relation between relative crest height, Zcrest/Zo with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.

5.2. Upstream and downstream water depths

It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.

5.3. Eroded volume

A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, Vtotal is 0.256 m3. The cumulative eroded volume, Veroded is 0.21, 0.16, 0.13, and 0.05 m3 for tailwater depths, do = 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume, Veroded and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.

5.4. The outflow discharge

The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, H, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 sec.

The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively.

The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.

6. Conclusions

The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:

The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Cited by (0)

My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.

Peer review under responsibility of Ain Shams University.

© 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

Nanoparticle-enabled increase of energy efficiency during laser metal additive manufacturing

레이저 금속 적층 제조 중 나노 입자로 에너지 효율 증가

Minglei Quo bQilin Guo a bLuis IzetEscano a bAli Nabaa a bKamel Fezzaa cLianyi Chen a b

레이저 금속 적층 제조(AM) 공정의 낮은 에너지 효율은 대규모 산업 생산에서 잠재적인 지속 가능성 문제입니다. 레이저 용융을 위한 에너지 효율의 명시적 조사는 용융 금속의 불투명한 특성으로 인해 매우 어려운 용융 풀 치수 및 증기 내림의 직접적인 특성화를 요구합니다. 

여기에서 우리는 현장 고속 고에너지 x-선 이미징에 의해 Al6061의 레이저 분말 베드 융합(LPBF) 동안 증기 강하 및 용융 풀 형성에 대한 TiC 나노 입자의 효과에 대한 직접적인 관찰 및 정량화를 보고합니다. 정량 결과를 바탕으로, 우리는 Al6061의 LPBF 동안 TiC 나노 입자가 있거나 없을 때 레이저 용융 에너지 효율(여기서 재료를 용융하는 데 필요한 에너지 대 레이저 빔에 의해 전달되는 에너지의 비율로 정의)을 계산했습니다. 

결과는 TiC 나노 입자를 Al6061에 추가하면 레이저 용융 에너지 효율이 크게 증가한다는 것을 보여줍니다(평균 114% 증가, 312에서 521% 증가). W 레이저 출력, 0.4m  /s 스캔 속도). 체계적인 특성 측정, 시뮬레이션 및 x-선 이미징 연구를 통해 우리는 처음으로 세 가지 메커니즘이 함께 작동하여 레이저 용융 에너지 효율을 향상시킨다는 것을 확인할 수 있었습니다.

(1) TiC 나노 입자를 추가하면 흡수율이 증가합니다. (2) TiC 나노입자를 추가하면 열전도율이 감소하고, (3) TiC 나노입자를 추가하면 더 낮은 레이저 출력에서 ​​증기 억제 및 다중 반사를 시작할 수 있습니다(즉, 키홀링에 대한 레이저 출력 임계값을 낮춤). 

여기서 보고한 Al6061의 LPBF 동안 레이저 용융 에너지 효율을 증가시키기 위해 TiC 나노입자를 사용하는 방법 및 메커니즘은 보다 에너지 효율적인 레이저 금속 AM을 위한 공급원료 재료의 개발을 안내할 수 있습니다.

The low energy efficiency of the laser metal additive manufacturing (AM) process is a potential sustainability concern for large-scale industrial production. Explicit investigation of the energy efficiency for laser melting requires the direct characterization of melt pool dimension and vapor depression, which is very difficult due to the opaque nature of the molten metal. Here we report the direct observation and quantification of effects of the TiC nanoparticles on the vapor depression and melt pool formation during laser powder bed fusion (LPBF) of Al6061 by in-situ high-speed high-energy x-ray imaging. Based on the quantification results, we calculated the laser melting energy efficiency (defined here as the ratio of the energy needed to melt the material to the energy delivered by the laser beam) with and without TiC nanoparticles during LPBF of Al6061. The results show that adding TiC nanoparticles into Al6061 leads to a significant increase of laser melting energy efficiency (114% increase on average, 521% increase under 312 W laser power, 0.4 m/s scan speed). Systematic property measurement, simulation, and x-ray imaging studies enable us, for the first time, to identify that three mechanisms work together to enhance the laser melting energy efficiency: (1) adding TiC nanoparticles increases the absorptivity; (2) adding TiC nanoparticles decreases the thermal conductivity, and (3) adding TiC nanoparticles enables the initiation of vapor depression and multiple reflection at lower laser power (i.e., lowers the laser power threshold for keyholing). The method and mechanisms of using TiC nanoparticles to increase the laser melting energy efficiency during LPBF of Al6061 we reported here may guide the development of feedstock materials for more energy efficient laser metal AM.

Nanoparticle-enabled increase of energy efficiency during laser metal additive manufacturing
Nanoparticle-enabled increase of energy efficiency during laser metal additive manufacturing

Keywords

Additive manufacturing

laser powder bed fusion

energy efficiency

keyhole

melt pool

x-ray imaging

metal matrix nanocomposites

Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.

AZ91 합금 주물 내 연행 결함에 대한 캐리어 가스의 영향

TianLiabJ.M.T.DaviesaXiangzhenZhuc
aUniversity of Birmingham, Birmingham B15 2TT, United Kingdom
bGrainger and Worrall Ltd, Bridgnorth WV15 5HP, United Kingdom
cBrunel Centre for Advanced Solidification Technology, Brunel University London, Kingston Ln, London, Uxbridge UB8 3PH, United Kingdom

Abstract

An entrainment defect (also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres (i.e., SF6/CO2, SF6/air). The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.

연행 결함(이중 산화막 결함 또는 이중막이라고도 함)은 경합금 용융물에 잠길 때 갇힌 가스를 포함하는 공극으로 작용하여 최종 주물의 품질과 재현성을 저하시킵니다. Al-합금 주물을 사용하여 수행된 이전 간행물에서는 이 갇힌 가스가 주변 용융물과의 반응에 의해 후속적으로 소모되어 공극 부피와 연행 결함의 부정적인 영향을 줄일 수 있다고 보고했습니다. Al-합금에 비해 마그네슘의 상대적으로 높은 반응성으로 인해 Mg-합금 내에 포집된 가스가 더 효율적으로 소모될 수 있습니다. 그러나 Mg 합금 내 연행 결함에 대한 연구는 상당히 제한적이었습니다. 현재 작업에서 AZ91 합금 주물은 다양한 캐리어 가스 분위기(즉, SF6/CO2, SF6/공기)에서 생산되었습니다. AZ91 합금에 포함된 연행 결함의 진화 과정은 미세 조직 검사 및 열역학 계산에 따라 제안되었습니다. 서로 다른 분위기에서 형성된 결함은 유사한 샌드위치 구조를 갖지만 산화막에는 서로 다른 화합물 조합이 포함되어 있습니다. 다른 동반 가스 소비율과 관련된 운반 가스의 사용은 AZ91 주물의 재현성에 영향을 미쳤습니다.

Keywords

Magnesium alloy, Casting, Oxide film, Bifilm, Entrainment defect, Reproducibility

1. Introduction

As the lightest structural metal available on Earth, magnesium became one of the most attractive light metals over the last few decades. The magnesium industry has consequently experienced a rapid development in the last 20 years [1,2], indicating a large growth in demand for Mg alloys all over the world. Nowadays, the use of Mg alloys can be found in the fields of automobiles, aerospace, electronics and etc.[3,4]. It has been predicted that the global consumption of Mg metals will further increase in the future, especially in the automotive industry, as the energy efficiency requirement of both traditional and electric vehicles further push manufactures lightweight their design [3,5,6].

The sustained growth in demand for Mg alloys motivated a wide interest in the improvement of the quality and mechanical properties of Mg-alloy castings. During a Mg-alloy casting process, surface turbulence of the melt can lead to the entrapment of a doubled-over surface film containing a small quantity of the surrounding atmosphere, thus forming an entrainment defect (also known as a double oxide film defect or bifilm) [7][8][9][10]. The random size, quantity, orientation, and placement of entrainment defects are widely accepted to be significant factors linked to the variation of casting properties [7]. In addition, Peng et al. [11] found that entrained oxides films in AZ91 alloy melt acted as filters to Al8Mn5 particles, trapping them as they settle. Mackie et al. [12] further suggested that entrained oxide films can act to trawl the intermetallic particles, causing them to cluster and form extremely large defects. The clustering of intermetallic compounds made the entrainment defects more detrimental for the casting properties.

Most of the previous studies regarding entrainment defects were carried out on Al-alloys [7,[13][14][15][16][17][18], and a few potential methods have been suggested for diminishing their negative effect on the quality of Al-alloy castings. Nyahumwa et al.,[16] shows that the void volume within entrainment defects could be reduced by a hot isostatic pressing (HIP) process. Campbell [7] suggested the entrained gas within the defects could be consumed due to reaction with the surrounding melt, which was further verified by Raiszedeh and Griffiths [19].The effect of the entrained gas consumption on the mechanical properties of Al-alloy castings has been investigated by [8,9], suggesting that the consumption of the entrained gas promoted the improvement of the casting reproducibility.

Compared with the investigation concerning the defects within Al-alloys, research into the entrainment defects within Mg-alloys has been significantly limited. The existence of entrainment defects has been demonstrated in Mg-alloy castings [20,21], but their behaviour, evolution, as well as entrained gas consumption are still not clear.

In a Mg-alloy casting process, the melt is usually protected by a cover gas to avoid magnesium ignition. The cavities of sand or investment moulds are accordingly required to be flushed with the cover gas prior to the melt pouring [22]. Therefore, the entrained gas within Mg-alloy castings should contain the cover gas used in the casting process, rather than air only, which may complicate the structure and evolution of the corresponding entrainment defects.

SF6 is a typical cover gas widely used for Mg-alloy casting processes [23][24][25]. Although this cover gas has been restricted to use in European Mg-alloy foundries, a commercial report has pointed out that this cover is still popular in global Mg-alloy industry, especially in the countries which dominated the global Mg-alloy production, such as China, Brazil, India, etc. [26]. In addition, a survey in academic publications also showed that this cover gas was widely used in recent Mg-alloy studies [27]. The protective mechanism of SF6 cover gas (i.e., the reaction between liquid Mg-alloy and SF6 cover gas) has been investigated by several previous researchers, but the formation process of the surface oxide film is still not clearly understood, and even some published results are conflicting with each other. In early 1970s, Fruehling [28] found that the surface film formed under SF6 was MgO mainly with traces of fluorides, and suggested that SF6 was absorbed in the Mg-alloy surface film. Couling [29] further noticed that the absorbed SF6 reacted with the Mg-alloy melt to form MgF2. In last 20 years, different structures of the Mg-alloy surface films have been reported, as detailed below.(1)

Single-layered film. Cashion [30,31] used X-ray Photoelectron Spectroscopy (XPS) and Auger Spectroscopy (AES) to identify the surface film as MgO and MgF2. He also found that composition of the film was constant throughout the thickness and the whole experimental holding time. The film observed by Cashion had a single-layered structure created from a holding time from 10 min to 100 min.(2)

Double-layered film. Aarstad et. al [32] reported a doubled-layered surface oxide film in 2003. They observed several well-distributed MgF2 particles attached to the preliminary MgO film and grew until they covered 25–50% of the total surface area. The inward diffusion of F through the outer MgO film was the driving force for the evolution process. This double-layered structure was also supported by Xiong’s group [25,33] and Shih et al. [34].(3)

Triple-layered film. The triple-layered film and its evolution process were reported in 2002 by Pettersen [35]. Pettersen found that the initial surface film was a MgO phase and then gradually evolved to the stable MgF2 phase by the inward diffusion of F. In the final stage, the film has a triple-layered structure with a thin O-rich interlayer between the thick top and bottom MgF2 layers.(4)

Oxide film consisted of discrete particles. Wang et al [36] stirred the Mg-alloy surface film into the melt under a SF6 cover gas, and then inspect the entrained surface film after the solidification. They found that the entrained surface films were not continues as the protective surface films reported by other researchers but composed of discrete particles. The young oxide film was composed of MgO nano-sized oxide particles, while the old oxide films consist of coarse particles (about 1  µm in average size) on one side that contained fluorides and nitrides.

The oxide films of a Mg-alloy melt surface or an entrained gas are both formed due to the reaction between liquid Mg-alloy and the cover gas, thus the above-mentioned research regarding the Mg-alloy surface film gives valuable insights into the evolution of entrainment defects. The protective mechanism of SF6 cover gas (i.e., formation of a Mg-alloy surface film) therefore indicated a potential complicated evolution process of the corresponding entrainment defects.

However, it should be noted that the formation of a surface film on a Mg-alloy melt is in a different situation to the consumption of an entrained gas that is submerged into the melt. For example, a sufficient amount of cover gas was supported during the surface film formation in the studies previously mentioned, which suppressed the depletion of the cover gas. In contrast, the amount of entrained gas within a Mg-alloy melt is finite, and the entrained gas may become fully depleted. Mirak [37] introduced 3.5%SF6/air bubbles into a pure Mg-alloy melt solidifying in a specially designed permanent mould. It was found that the gas bubbles were entirely consumed, and the corresponding oxide film was a mixture of MgO and MgF2. However, the nucleation sites (such as the MgF2 spots observed by Aarstad [32] and Xiong [25,33]) were not observed. Mirak also speculated that the MgF2 formed prior to MgO in the oxide film based on the composition analysis, which was opposite to the surface film formation process reported in previous literatures (i.e., MgO formed prior to MgF2). Mirak’s work indicated that the oxide-film formation of an entrained gas may be quite different from that of surface films, but he did not reveal the structure and evolution of the oxide films.

In addition, the use of carrier gas in the cover gases also influenced the reaction between the cover gas and the liquid Mg-alloy. SF6/air required a higher content of SF6 than did a SF6/CO2 carrier gas [38], to avoid the ignition of molten magnesium, revealing different gas-consumption rates. Liang et.al [39] suggested that carbon was formed in the surface film when CO2 was used as a carrier gas, which was different from the films formed in SF6/air. An investigation into Mg combustion [40] reported a detection of Mg2C3 in the Mg-alloy sample after burning in CO2, which not only supported Liang’s results, but also indicated a potential formation of Mg carbides in double oxide film defects.

The work reported here is an investigation into the behaviour and evolution of entrainment defects formed in AZ91 Mg-alloy castings, protected by different cover gases (i.e., SF6/air and SF6/CO2). These carrier gases have different protectability for liquid Mg alloy, which may be therefore associated with different consumption rates and evolution processes of the corresponding entrained gases. The effect of the entrained-gas consumption on the reproducibility of AZ91 castings was also studied.

2. Experiment

2.1. Melting and casting

Three kilograms AZ91 alloy was melted in a mild steel crucible at 700 ± 5 °C. The composition of the AZ91 alloy has been shown in Table 1. Prior to heating, all oxide scale on the ingot surface was removed by machining. The cover gases used were 0.5%SF6/air or 0.5%SF6/CO2 (vol.%) at a flow rate of 6 L/min for different castings. The melt was degassed by argon with a flow rate of 0.3 L/min for 15 min [41,42], and then poured into sand moulds. Prior to pouring, the sand mould cavity was flushed with the cover gas for 20 min [22]. The residual melt (around 1 kg) was solidified in the crucible.

Table 1. Composition (wt.%) of the AZ91 alloy used in this study.

AlZnMnSiFeNiMg
9.40.610.150.020.0050.0017Residual

Fig. 1(a) shows the dimensions of the casting with runners. A top-filling system was deliberately used to generate entrainment defects in the final castings. Green and Campbell [7,43] suggested that a top-filling system caused more entrainment events (i.e., bifilms) during a casting process, compared with a bottom-filling system. A melt flow simulation (Flow-3D software) of this mould, using Reilly’s model [44] regarding the entrainment events, also predicted that a large amount of bifilms would be contained in the final casting (denoted by the black particles in Fig. 1b).

Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.

Shrinkage defects also affect the mechanical properties and reproducibility of castings. Since this study focused on the effect of bifilms on the casting quality, the mould has been deliberately designed to avoid generating shrinkage defects. A solidification simulation using ProCAST software showed that no shrinkage defect would be contained in the final casting, as shown in Fig. 1c. The casting soundness has also been confirmed using a real time X-ray prior to the test bar machining.

The sand moulds were made from resin-bonded silica sand, containing 1wt. % PEPSET 5230 resin and 1wt. % PEPSET 5112 catalyst. The sand also contained 2 wt.% Na2SiF6 to act as an inhibitor [45]. The pouring temperature was 700 ± 5 °C. After the solidification, a section of the runner bars was sent to the Sci-Lab Analytical Ltd for a H-content analysis (LECO analysis), and all the H-content measurements were carried out on the 5th day after the casting process. Each of the castings was machined into 40 test bars for a tensile strength test, using a Zwick 1484 tensile test machine with a clip extensometer. The fracture surfaces of the broken test bars were examined using Scanning Electron Microscope (SEM, Philips JEOL7000) with an accelerating voltage of 5–15 kV. The fractured test bars, residual Mg-alloy solidified in the crucible, and the casting runners were then sectioned, polished and also inspected using the same SEM. The cross-section of the oxide film found on the test-bar fracture surface was exposed by the Focused Ion Beam milling technique (FIB), using a CFEI Quanta 3D FEG FIB-SEM. The oxide film required to be analysed was coated with a platinum layer. Then, a gallium ion beam, accelerated to 30 kV, milled the material substrate surrounding the platinum coated area to expose the cross section of the oxide film. EDS analysis of the oxide film’s cross section was carried out using the FIB equipment at accelerating voltage of 30 kV.

2.2. Oxidation cell

As previously mentioned, several past researchers investigated the protective film formed on a Mg-alloy melt surface [38,39,[46][47][48], [49], [50][51][52]. During these experiments, the amount of cover gas used was sufficient, thus suppressing the depletion of fluorides in the cover gas. The experiment described in this section used a sealed oxidation cell, which limited the supply of cover gas, to study the evolution of the oxide films of entrainment defects. The cover gas contained in the oxidation cell was regarded as large-size “entrained bubble”.

As shown in Fig. 2, the main body of the oxidation cell was a closed-end mild steel tube which had an inner length of 400 mm, and an inner diameter of 32 mm. A water-cooled copper tube was wrapped around the upper section of the cell. When the tube was heated, the cooling system created a temperature difference between the upper and lower sections, causing the interior gas to convect within the tube. The temperature was monitored by a type-K thermocouple located at the top of the crucible. Nie et al. [53] suggested that the SF6 cover gas would react with the steel wall of the holding furnace when they investigated the surface film of a Mg-alloy melt. To avoid this reaction, the interior surface of the steel oxidation cell (shown in Fig. 2) and the upper half section of the thermocouple were coated with boron nitride (the Mg-alloy was not in contact with boron nitride).

Fig. 2. Schematic of the oxidation cell used to study the evolution of the oxide films of the entrainment defects (unit mm).

During the experiment, a block of solid AZ91 alloy was placed in a magnesia crucible located at the bottom of the oxidation cell. The cell was heated to 100 °C in an electric resistance furnace under a gas flow rate of 1 L/min. The cell was held at this temperature for 20 min, to replace the original trapped atmosphere (i.e. air). Then, the oxidation cell was further heated to 700 °C, melting the AZ91 sample. The gas inlet and exit valves were then closed, creating a sealed environment for oxidation under a limited supply of cover gas. The oxidation cell was then held at 700 ± 10 °C for periods of time from 5 min to 30 min in 5-min intervals. At the end of each holding time, the cell was quenched in water. After cooling to room temperature, the oxidised sample was sectioned, polished, and subsequently examined by SEM.

3. Results

3.1. Structure and composition of the entrainment defects formed in SF6/air

The structure and composition of the entrainment defect formed in the AZ91 castings under a cover gas of 0.5%SF6/air was observed by SEM and EDS. The results indicate that there exist two types of entrainment defects which are sketched in Fig. 3: (1) Type A defect whose oxide film has a traditional single-layered structure and (2) Type B defect, whose oxide film has two layers. The details of these defects were introduced in the following. Here it should be noticed that, as the entrainment defects are also known as biofilms or double oxide film, the oxide films of Type B defect were referred to as “multi-layered oxide film” or “multi-layered structure” in the present work to avoid a confusing description such as “the double-layered oxide film of a double oxide film defect”.

Fig. 3. Schematic of the different types of entrainment defects found in AZ91 castings. (a) Type A defect with a single-layered oxide film and (b) Type B defect with two-layered oxide film.

Fig. 4(a-b) shows a Type A defect having a compact single-layered oxide film with about 0.4 µm thickness. Oxygen, fluorine, magnesium and aluminium were detected in this film (Fig. 4c). It is speculated that oxide film is the mixture of fluoride and oxide of magnesium and aluminium. The detection of fluorine revealed that an entrained cover gas was contained in the formation of this defect. That is to say that the pores shown in Fig. 4(a) were not shrinkage defects or hydrogen porosity, but entrainment defects. The detection of aluminium was different with Xiong and Wang’s previous study [47,48], which showed that no aluminium was contained in their surface film of an AZ91 melt protected by a SF6 cover gas. Sulphur could not be clearly recognized in the element map, but there was a S-peak in the corresponding ESD spectrum.

Fig. 4. (a) A Type A entrainment defect formed in SF6/air and having a single-layered oxide film, (b) the oxide film of this defect, (c) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area highlighted in (b).

Fig. 5(a-b) shows a Type B entrainment defect having a multi-layered oxide film. The compact outer layers of the oxide films were enriched with fluorine and oxygen (Fig. 5c), while their relatively porous inner layers were only enriched with oxygen (i.e., poor in fluorine) and partly grew together, thus forming a sandwich-like structure. Therefore, it is speculated that the outer layer is the mixture of fluoride and oxide, while the inner layer is mainly oxide. Sulphur could only be recognized in the EDX spectrum and could not be clearly identified in the element map, which might be due to the small S-content in the cover gas (i.e., 0.5% volume content of SF6 in the cover gas). In this oxide film, aluminium was contained in the outer layer of this oxide film but could not be clearly detected in the inner layer. Moreover, the distribution of Al seems to be uneven. It can be found that, in the right side of the defect, aluminium exists in the film but its concentration can not be identified to be higher than the matrix. However, there is a small area with much higher aluminium concentration in the left side of the defect. Such an uneven distribution of aluminium was also observed in other defects (shown in the following), and it is the result of the formation of some oxide particles in or under the film.

Fig. 5. (a) A Type B entrainment defect formed in SF6/air and having a multi-layered oxide film, (b) the oxide films of this defect have grown together, (c) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area shown in (b).

Figs. 4 and 5 show cross sectional observations of the entrainment defects formed in the AZ91 alloy sample cast under a cover gas of SF6/air. It is not sufficient to characterize the entrainment defects only by the figures observed from the two-dimensional section. To have a further understanding, the surface of the entrainment defects (i.e. the oxide film) was further studied by observing the fracture surface of the test bars.

Fig. 6(a) shows fracture surfaces of an AZ91 alloy tensile test bar produced in SF6/air. Symmetrical dark regions can be seen on both sides of the fracture surfaces. Fig. 6(b) shows boundaries between the dark and bright regions. The bright region consisted of jagged and broken features, while the surface of the dark region was relatively smooth and flat. In addition, the EDS results (Fig. 6c-d and Table 2) show that fluorine, oxygen, sulphur, and nitrogen were only detected in the dark regions, indicating that the dark regions were surface protective films entrained into the melt. Therefore, it could be suggested that the dark regions were an entrainment defect with consideration of their symmetrical nature. Similar defects on fracture surfaces of Al-alloy castings have been previously reported [7]Nitrides were only found in the oxide films on the test-bar fracture surfaces but never detected in the cross-sectional samples shown in Figs. 4 and 5. An underlying reason is that the nitrides contained in these samples may have hydrolysed during the sample polishing process [54].

Fig. 6. (a) A pair of the fracture surfaces of a AZ91 alloy tensile test bar produced under a cover gas of SF6/air. The dimension of the fracture surface is 5 mm × 6 mm, (b) a section of the boundary between the dark and bright regions shown in (a), (c-d) EDS spectrum of the (c) bright regions and (d) dark regions, (e) schematic of an entrainment defect contained in a test bar.

Table 2. EDS results (wt.%) corresponding to the regions shown in Fig. 6 (cover gas: SF6/air).

Empty CellCOMgFAlZnSN
Dark region in Fig. 6(b)3.481.3279.130.4713.630.570.080.73
Bright region in Fig. 6(b)3.5884.4811.250.68

In conjunction with the cross-sectional observation of the defects shown in Figs. 4 and 5, the structure of an entrainment defect contained in a tensile test bar was sketched as shown in Fig. 6(e). The defect contained an entrained gas enclosed by its oxide film, creating a void section inside the test bar. When the tensile force applied on the defect during the fracture process, the crack was initiated at the void section and propagated along the entrainment defect, since cracks would be propagated along the weakest path [55]. Therefore, when the test bar was finally fractured, the oxide films of entrainment defect appeared on both fracture surfaces of the test bar, as shown in Fig. 6(a).

3.2. Structure and composition of the entrainment defects formed in SF6/CO2

Similar to the entrainment defect formed in SF6/air, the defects formed under a cover gas of 0.5%SF6/CO2 also had two types of oxide films (i.e., single-layered and multi-layered types). Fig. 7(a) shows an example of the entrainment defects containing a multi-layered oxide film. A magnified observation to the defect (Fig. 7b) shows that the inner layers of the oxide films had grown together, presenting a sandwich-like structure, which was similar to the defects formed in an atmosphere of SF6/air (Fig. 5b). An EDS spectrum (Fig. 7c) revealed that the joint area (inner layer) of this sandwich-like structure mainly contained magnesium oxides. Peaks of fluorine, sulphur, and aluminium were recognized in this EDS spectrum, but their amount was relatively small. In contrast, the outer layers of the oxide films were compact and composed of a mixture of fluorides and oxides (Fig. 7d-e).

Fig. 7. (a) An example of entrainment defects formed in SF6/CO2 and having a multi-layered oxide film, (b) magnified observation of the defect, showing the inner layer of the oxide films has grown together, (c) EDS spectrum of the point denoted in (b), (d) outer layer of the oxide film, (e) SEM-EDS element maps (using Philips JEOL7000) corresponding to the area shown in (d).

Fig. 8(a) shows an entrainment defect on the fracture surfaces of an AZ91 alloy tensile test bar, which was produced in an atmosphere of 0.5%SF6/CO2. The corresponding EDS results (Table 3) showed that oxide film contained fluorides and oxides. Sulphur and nitrogen were not detected. Besides, a magnified observation (Fig. 8b) indicated spots on the oxide film surface. The diameter of the spots ranged from hundreds of nanometres to a few micron meters.

Fig. 8. (a) A pair of the fracture surfaces of a AZ91 alloy tensile test bar, produced in an atmosphere of SF6/CO2. The dimension of the fracture surface is 5 mm × 6 mm, (b) surface appearance of the oxide films on the fracture surfaces, showing spots on the film surface.

To further reveal the structure and composition of the oxide film clearly, the cross-section of the oxide film on a test-bar fracture surface was onsite exposed using the FIB technique (Fig. 9). As shown in Fig. 9a, a continuous oxide film was found between the platinum coating layer and the Mg-Al alloy substrate. Fig. 9 (b-c) shows a magnified observation to oxide films, indicating a multi-layered structure (denoted by the red box in Fig. 9c). The bottom layer was enriched with fluorine and oxygen and should be the mixture of fluoride and oxide, which was similar to the “outer layer” shown in Figs. 5 and 7, while the only-oxygen-enriched top layer was similar to the “inner layer” shown in Figs. 5 and 7.

Fig. 9. (a) A cross-sectional observation of the oxide film on the fracture surface of the AZ91 casting produced in SF6/CO2, exposed by FIB, (b) a magnified observation of area highlighted in (a), and (c) SEM-EDS elements map of the area shown in (b), obtained by CFEI Quanta 3D FEG FIB-SEM.

Except the continuous film, some individual particles were also observed in or below the continuous film, as shown in Fig. 9. An Al-enriched particle was detected in the left side of the oxide film shown in Fig. 9b and might be speculated to be spinel Mg2AlO4 because it also contains abundant magnesium and oxygen elements. The existing of such Mg2AlO4 particles is responsible for the high concentration of aluminium in small areas of the observed film and the uneven distribution of aluminium, as shown in Fig. 5(c). Here it should be emphasized that, although the other part of the bottom layer of the continuous oxide film contains less aluminium than this Al-enriched particle, the Fig. 9c indicated that the amount of aluminium in this bottom layer was still non-negligible, especially when comparing with the outer layer of the film. Below the right side of the oxide film shown in Fig. 9b, a particle was detected and speculated to be MgO because it is rich in Mg and O. According to Wang’s result [56], lots of discrete MgO particles can be formed on the surface of the Mg melt by the oxidation of Mg melt and Mg vapor. The MgO particles observed in our present work may be formed due to the same reasons. While, due to the differences in experimental conditions, less Mg melt can be vapored or react with O2, thus only a few of MgO particles formed in our work. An enrichment of carbon was also found in the film, revealing that CO2 was able to react with the melt, thus forming carbon or carbides. This carbon concentration was consistent with the relatively high carbon content of the oxide film shown in Table 3 (i.e., the dark region). In the area next to the oxide film.

Table 3. EDS results (wt.%) corresponding to the regions shown in Fig. 8 (cover gas: SF6/ CO2).

Empty CellCOMgFAlZnSN
Dark region in Fig. 8(a)7.253.6469.823.827.030.86
Bright region in Fig. 8(a)2.100.4482.8313.261.36

This cross-sectional observation of the oxide film on a test bar fracture surface (Fig. 9) further verified the schematic of the entrainment defect shown in Fig. 6(e). The entrainment defects formed in different atmospheres of SF6/CO2 and SF6/air had similar structures, but their compositions were different.

3.3. Evolution of the oxide films in the oxidation cell

The results in Section 3.1 and 3.2 have shown the structures and compositions of entrainment defects formed in AZ91 castings under cover gases of SF6/air and SF6/CO2. Different stages of the oxidation reaction may lead to the different structures and compositions of entrainment defects. Although Campbell has conjectured that an entrained gas may react with the surrounding melt, it is rarely reported that the reaction occurring between the Mg-alloy melt and entrapped cover gas. Previous researchers normally focus on the reaction between a Mg-alloy melt and the cover gas in an open environment [38,39,[46][47][48], [49], [50][51][52], which was different from the situation of a cover gas trapped into the melt. To further understand the formation of the entrainment defect in an AZ91 alloy, the evolution process of oxide films of the entrainment defect was further studied using an oxidation cell.

Fig. 10 (a and d) shows a surface film held for 5 min in the oxidation cell, protected by 0.5%SF6/air. There was only one single layer consisting of fluoride and oxide (MgF2 and MgO). In this surface film. Sulphur was detected in the EDS spectrum, but its amount was too small to be recognized in the element map. The structure and composition of this oxide film was similar to the single-layered films of entrainment defects shown in Fig. 4.

Fig. 10. Oxide films formed in the oxidation cell under a cover gas of 0.5%SF6/air and held at 700 °C for (a) 5 min; (b) 10 min; (c) 30 min, and (d-f) the SEM-EDS element maps (using Philips JEOL7000) corresponding to the oxide film shown in (a-c) respectively, (d) 5 min; (e) 10 min; (f) 30 min. The red points in (c and f) are the location references, denoting the boundary of the F-enriched layer in different element maps.

After a holding time of 10 min, a thin (O, S)-enriched top layer (around 700 nm) appeared upon the preliminary F-enriched film, forming a multi-layered structure, as shown in Fig. 10(b and e). The thickness of the (O, S)-enriched top layer increased with increased holding time. As shown in Fig. 10(c and f), the oxide film held for 30 min also had a multi-layered structure, but the thickness of its (O, S)-enriched top layer (around 2.5 µm) was higher than the that of the 10-min oxide film. The multi-layered oxide films shown in Fig. 10(b-c) presented a similar appearance to the films of the sandwich-like defect shown in Fig. 5.

The different structures of the oxide films shown in Fig. 10 indicated that fluorides in the cover gas would be preferentially consumed due to the reaction with the AZ91 alloy melt. After the depletion of fluorides, the residual cover gas reacted further with the liquid AZ91 alloy, forming the top (O, S)-enriched layer in the oxide film. Therefore, the different structures and compositions of entrainment defects shown in Figs. 4 and 5 may be due to an ongoing oxidation reaction between melt and entrapped cover gas.

This multi-layered structure has not been reported in previous publications concerning the protective surface film formed on a Mg-alloy melt [38,[46][47][48], [49], [50][51]. This may be due to the fact that previous researchers carried out their experiments with an un-limited amount of cover gas, creating a situation where the fluorides in the cover gas were not able to become depleted. Therefore, the oxide film of an entrainment defect had behaviour traits similar to the oxide films shown in Fig. 10, but different from the oxide films formed on the Mg-alloy melt surface reported in [38,[46][47][48], [49], [50][51].

Similar with the oxide films held in SF6/air, the oxide films formed in SF6/CO2 also had different structures with different holding times in the oxidation cell. Fig. 11(a) shows an oxide film, held on an AZ91 melt surface under a cover gas of 0.5%SF6/CO2 for 5 min. This film had a single-layered structure consisting of MgF2. The existence of MgO could not be confirmed in this film. After the holding time of 30 min, the film had a multi-layered structure; the inner layer was of a compact and uniform appearance and composed of MgF2, while the outer layer is the mixture of MgF2 and MgO. Sulphur was not detected in this film, which was different from the surface film formed in 0.5%SF6/air. Therefore, fluorides in the cover gas of 0.5%SF6/CO2 were also preferentially consumed at an early stage of the film growth process. Compared with the film formed in SF6/air, the MgO in film formed in SF6/CO2 appeared later and sulphide did not appear within 30 min. It may mean that the formation and evolution of film in SF6/air is faster than SF6/CO2. CO2 may have subsequently reacted with the melt to form MgO, while sulphur-containing compounds accumulated in the cover gas and reacted to form sulphide in very late stage (may after 30 min in oxidation cell).

Fig. 11. Oxide films formed in the oxidation cell under a cover gas of 0.5%SF6/CO2, and their SEM-EDS element maps (using Philips JEOL7000). They were held at 700 °C for (a) 5 min; (b) 30 min. The red points in (b) are the location references, denoting the boundary between the top and bottom layers in the oxide film.

4. Discussion

4.1. Evolution of entrainment defects formed in SF6/air

HSC software from Outokumpu HSC Chemistry for Windows (http://www.hsc-chemistry.net/) was used to carry out thermodynamic calculations needed to explore the reactions which might occur between the trapped gases and liquid AZ91 alloy. The solutions to the calculations suggest which products are most likely to form in the reaction process between a small amount of cover gas (i.e., the amount within a trapped bubble) and the AZ91-alloy melt.

In the trials, the pressure was set to 1 atm, and the temperature set to 700 °C. The amount of the cover gas was assumed to be 7 × 10−7 kg, with a volume of approximately 0.57 cm3 (3.14 × 10−8 kmol) for 0.5%SF6/air, and 0.35 cm3 (3.12 × 10−8 kmol) for 0.5%SF6/CO2. The amount of the AZ91 alloy melt in contact with the trapped gas was assumed to be sufficient to complete all reactions. The decomposition products of SF6 were SF5, SF4, SF3, SF2, F2, S(g), S2(g) and F(g) [57], [58][59][60].

Fig. 12 shows the equilibrium diagram of the thermodynamic calculation of the reaction between the AZ91 alloy and 0.5%SF6/air. In the diagram, the reactants and products with less than 10−15 kmol have not been shown, as this was 5 orders of magnitude less than the amount of SF6 present (≈ 1.57 × 10−10 kmol) and therefore would not affect the observed process in a practical way.

Fig. 12. An equilibrium diagram for the reaction between 7e-7 kg 0.5%SF6/air and a sufficient amount of AZ91 alloy. The X axis is the amount of AZ91 alloy melt having reacted with the entrained gas, and the vertical Y-axis is the amount of the reactants and products.

This reaction process could be divided into 3 stages.

Stage 1: The formation of fluorides. the AZ91 melt preferentially reacted with SF6 and its decomposition products, producing MgF2, AlF3, and ZnF2. However, the amount of ZnF2 may have been too small to be detected practically (1.25 × 10−12 kmol of ZnF2 compared with 3 × 10−10 kmol of MgF2), which may be the reason why Zn was not detected in any the oxide films shown in Sections 3.13.3. Meanwhile, sulphur accumulated in the residual gas as SO2.

Stage 2: The formation of oxides. After the liquid AZ91 alloy had depleted all the available fluorides in the entrapped gas, the amount of AlF3 and ZnF2 quickly reduced due to a reaction with Mg. O2(g) and SO2 reacted with the AZ91 melt, forming MgO, Al2O3, MgAl2O4, ZnO, ZnSO4 and MgSO4. However, the amount of ZnO and ZnSO4 would have been too small to be found practically by EDS (e.g. 9.5 × 10−12 kmol of ZnO,1.38 × 10−14 kmol of ZnSO4, in contrast to 4.68 × 10−10 kmol of MgF2, when the amount of AZ91 on the X-axis is 2.5 × 10−9 kmol). In the experimental cases, the concentration of F in the cover gas is very low, whole the concentration f O is much higher. Therefore, the stage 1 and 2, i.e, the formation of fluoride and oxide may happen simultaneously at the beginning of the reaction, resulting in the formation of a singer-layered mixture of fluoride and oxide, as shown in Figs. 4 and 10(a). While an inner layer consisted of oxides but fluorides could form after the complete depletion of F element in the cover gas.

Stages 1- 2 theoretically verified the formation process of the multi-layered structure shown in Fig. 10.

The amount of MgAl2O4 and Al2O3 in the oxide film was of a sufficient amount to be detected, which was consistent with the oxide films shown in Fig. 4. However, the existence of aluminium could not be recognized in the oxide films grown in the oxidation cell, as shown in Fig. 10. This absence of Al may be due to the following reactions between the surface film and AZ91 alloy melt:(1)

Al2O3 + 3Mg + = 3MgO + 2Al, △G(700 °C) = -119.82 kJ/mol(2)

Mg + MgAl2O4 = MgO + Al, △G(700 °C) =-106.34 kJ/molwhich could not be simulated by the HSC software since the thermodynamic calculation was carried out under an assumption that the reactants were in full contact with each other. However, in a practical process, the AZ91 melt and the cover gas would not be able to be in contact with each other completely, due to the existence of the protective surface film.

Stage 3: The formation of Sulphide and nitride. After a holding time of 30 min, the gas-phase fluorides and oxides in the oxidation cell had become depleted, allowing the melt reaction with the residual gas, forming an additional sulphur-enriched layer upon the initial F-enriched or (F, O)-enriched surface film, thus resulting in the observed multi-layered structure shown in Fig. 10 (b and c). Besides, nitrogen reacted with the AZ91 melt until all reactions were completed. The oxide film shown in Fig. 6 may correspond to this reaction stage due to its nitride content. However, the results shows that the nitrides were not detected in the polished samples shown in Figs. 4 and 5, but only found on the test bar fracture surfaces. The nitrides may have hydrolysed during the sample preparation process, as follows [54]:(3)

Mg3N2 + 6H2O =3Mg(OH)2 + 2NH3↑(4)

AlN+ 3H2O =Al(OH)3 + NH3

In addition, Schmidt et al. [61] found that Mg3N2 and AlN could react to form ternary nitrides (Mg3AlnNn+2, n= 1, 2, 3…). HSC software did not contain the database of ternary nitrides, and it could not be added into the calculation. The oxide films in this stage may also contain ternary nitrides.

4.2. Evolution of entrainment defects formed in SF6/CO2

Fig. 13 shows the results of the thermodynamic calculation between AZ91 alloy and 0.5%SF6/CO2. This reaction processes can also be divided into three stages.

Fig. 13. An equilibrium diagram for the reaction between 7e-7 kg 0.5%SF6/CO2 and a sufficient amount of AZ91 alloy. The X axis denotes the amount of Mg alloy melt having reacted with the entrained gas, and the vertical Y-axis denotes the amounts of the reactants and products.

Stage 1: The formation of fluorides. SF6 and its decomposition products were consumed by the AZ91 melt, forming MgF2, AlF3, and ZnF2. As in the reaction of AZ91 in 0.5%SF6/air, the amount of ZnF2 was too small to be detected practically (1.51 × 10−13 kmol of ZnF2 compared with 2.67 × 10−10 kmol of MgF2). Sulphur accumulated in the residual trapped gas as S2(g) and a portion of the S2(g) reacted with CO2, to form SO2 and CO. The products in this reaction stage were consistent with the film shown in Fig. 11(a), which had a single layer structure that contained fluorides only.

Stage 2: The formation of oxides. AlF3 and ZnF2 reacted with the Mg in the AZ91 melt, forming MgF2, Al and Zn. The SO2 began to be consumed, producing oxides in the surface film and S2(g) in the cover gas. Meanwhile, the CO2 directly reacted with the AZ91 melt, forming CO, MgO, ZnO, and Al2O3. The oxide films shown in Figs. 9 and 11(b) may correspond to this reaction stage due to their oxygen-enriched layer and multi-layered structure.

The CO in the cover gas could further react with the AZ91 melt, producing C. This carbon may further react with Mg to form Mg carbides, when the temperature reduced (during solidification period) [62]. This may be the reason for the high carbon content in the oxide film shown in Figs. 89. Liang et al. [39] also reported carbon-detection in an AZ91 alloy surface film protected by SO2/CO2. The produced Al2O3 may be further combined with MgO, forming MgAl2O4 [63]. As discussed in Section 4.1, the alumina and spinel can react with Mg, causing an absence of aluminium in the surface films, as shown in Fig. 11.

Stage 3: The formation of Sulphide. the AZ91 melt began to consume S2(g) in the residual entrapped gas, forming ZnS and MgS. These reactions did not occur until the last stage of the reaction process, which could be the reason why the S-content in the defect shown Fig. 7(c) was small.

In summary, thermodynamic calculations indicate that the AZ91 melt will react with the cover gas to form fluorides firstly, then oxides and sulphides in the last. The oxide film in the different reaction stages would have different structures and compositions.

4.3. Effect of the carrier gases on consumption of the entrained gas and the reproducibility of AZ91 castings

The evolution processes of entrainment defects, formed in SF6/air and SF6/CO2, have been suggested in Sections 4.1 and 4.2. The theoretical calculations were verified with respect to the corresponding oxide films found in practical samples. The atmosphere within an entrainment defect could be efficiently consumed due to the reaction with liquid Mg-alloy, in a scenario dissimilar to the Al-alloy system (i.e., nitrogen in an entrained air bubble would not efficiently react with Al-alloy melt [64,65], however, nitrogen would be more readily consumed in liquid Mg alloys, commonly referred to as “nitrogen burning” [66]).

The reaction between the entrained gas and the surrounding liquid Mg-alloy converted the entrained gas into solid compounds (e.g. MgO) within the oxide film, thus reducing the void volume of the entrainment defect and hence probably causing a collapse of the defect (e.g., if an entrained gas of air was depleted by the surrounding liquid Mg-alloy, under an assumption that the melt temperature is 700 °C and the depth of liquid Mg-alloy is 10 cm, the total volume of the final solid products would be 0.044% of the initial volume taken by the entrapped air).

The relationship between the void volume reduction of entrainment defects and the corresponding casting properties has been widely studied in Al-alloy castings. Nyahumwa and Campbell [16] reported that the Hot Isostatic Pressing (HIP) process caused the entrainment defects in Al-alloy castings to collapse and their oxide surfaces forced into contact. The fatigue lives of their castings were improved after HIP. Nyahumwa and Campbell [16] also suggested a potential bonding of the double oxide films that were in contact with each other, but there was no direct evidence to support this. This binding phenomenon was further investigated by Aryafar et.al.[8], who re-melted two Al-alloy bars with oxide skins in a steel tube and then carried out a tensile strength test on the solidified sample. They found that the oxide skins of the Al-alloy bars strongly bonded with each other and became even stronger with an extension of the melt holding time, indicating a potential “healing” phenomenon due to the consumption of the entrained gas within the double oxide film structure. In addition, Raidszadeh and Griffiths [9,19] successfully reduced the negative effect of entrainment defects on the reproducibility of Al-alloy castings, by extending the melt holding time before solidification, which allowed the entrained gas to have a longer time to react with the surrounding melt.

With consideration of the previous work mentioned, the consumption of the entrained gas in Mg-alloy castings may diminish the negative effect of entrainment defects in the following two ways.

(1) Bonding phenomenon of the double oxide films. The sandwich-like structure shown in Fig. 5 and 7 indicated a potential bonding of the double oxide film structure. However, more evidence is required to quantify the increase in strength due to the bonding of the oxide films.

(2) Void volume reduction of entrainment defects. The positive effect of void-volume reduction on the quality of castings has been widely demonstrated by the HIP process [67]. As the evolution processes discussed in Section 4.14.2, the oxide films of entrainment defects can grow together due to an ongoing reaction between the entrained gas and surrounding AZ91 alloy melt. The volume of the final solid products was significant small compared with the entrained gas (i.e., 0.044% as previously mentioned).

Therefore, the consumption rate of the entrained gas (i.e., the growth rate of oxide films) may be a critical parameter for improving the quality of AZ91 alloy castings. The oxide film growth rate in the oxidization cell was accordingly further investigated.

Fig. 14 shows a comparison of the surface film growth rates in different cover gases (i.e., 0.5%SF6/air and 0.5%SF6/CO2). 15 random points on each sample were selected for film thickness measurements. The 95% confidence interval (95%CI) was computed under an assumption that the variation of the film thickness followed a Gaussian distribution. It can be seen that all the surface films formed in 0.5%SF6/air grew faster than those formed in 0.5%SF6/CO2. The different growth rates suggested that the entrained-gas consumption rate of 0.5%SF6/air was higher than that of 0.5%SF6/CO2, which was more beneficial for the consumption of the entrained gas.

Fig. 14. A comparison of the AZ91 alloy oxide film growth rates in 0.5%SF6/air and 0.5%SF6/CO2

It should be noted that, in the oxidation cell, the contact area of liquid AZ91 alloy and cover gas (i.e. the size of the crucible) was relatively small with consideration of the large volume of melt and gas. Consequently, the holding time for the oxide film growth within the oxidation cell was comparatively long (i.e., 5–30 min). However, the entrainment defects contained in a real casting are comparatively very small (i.e., a few microns size as shown in Figs. 36, and [7]), and the entrained gas is fully enclosed by the surrounding melt, creating a relatively large contact area. Hence the reaction time for cover gas and the AZ91 alloy melt may be comparatively short. In addition, the solidification time of real Mg-alloy sand castings can be a few minutes (e.g. Guo [68] reported that a Mg-alloy sand casting with 60 mm diameter required 4 min to be solidified). Therefore, it can be expected that an entrained gas trapped during an Mg-alloy melt pouring process will be readily consumed by the surrounding melt, especially for sand castings and large-size castings, where solidification times are long.

Therefore, the different cover gases (0.5%SF6/air and 0.5%SF6/CO2) associated with different consumption rates of the entrained gases may affect the reproducibility of the final castings. To verify this assumption, the AZ91 castings produced in 0.5%SF6/air and 0.5%SF6/CO2 were machined into test bars for mechanical evaluation. A Weibull analysis was carried out using both linear least square (LLS) method and non-linear least square (non-LLS) method [69].

Fig. 15(a-b) shows a traditional 2-p linearized Weibull plot of the UTS and elongation of the AZ91 alloy castings, obtained by the LLS method. The estimator used is P= (i-0.5)/N, which was suggested to cause the lowest bias among all the popular estimators [69,70]. The casting produced in SF6/air has an UTS Weibull moduli of 16.9, and an elongation Weibull moduli of 5.0. In contrast, the UTS and elongation Weibull modulus of the casting produced in SF6/CO2 are 7.7 and 2.7 respectively, suggesting that the reproducibility of the casting protected by SF6/CO2 were much lower than that produced in SF6/air.

Fig. 15. The Weibull modulus of AZ91 castings produced in different atmospheres, estimated by (a-b) the linear least square method, (c-d) the non-linear least square method, where SSR is the sum of residual squares.

In addition, the author’s previous publication [69] demonstrated a shortcoming of the linearized Weibull plots, which may cause a higher bias and incorrect R2 interruption of the Weibull estimation. A Non-LLS Weibull estimation was therefore carried out, as shown in Fig. 15 (c-d). The UTS Weibull modulus of the SF6/air casting was 20.8, while the casting produced under SF6/CO2 had a lower UTS Weibull modulus of 11.4, showing a clear difference in their reproducibility. In addition, the SF6/air elongation (El%) dataset also had a Weibull modulus (shape = 5.8) higher than the elongation dataset of SF6/CO2 (shape = 3.1). Therefore, both the LLS and Non-LLS estimations suggested that the SF6/air casting has a higher reproducibility than the SF6/CO2 casting. It supports the method that the use of air instead of CO2 contributes to a quicker consumption of the entrained gas, which may reduce the void volume within the defects. Therefore, the use of 0.5%SF6/air instead of 0.5%SF6/CO2 (which increased the consumption rate of the entrained gas) improved the reproducibility of the AZ91 castings.

However, it should be noted that not all the Mg-alloy foundries followed the casting process used in present work. The Mg-alloy melt in present work was degassed, thus reducing the effect of hydrogen on the consumption of the entrained gas (i.e., hydrogen could diffuse into the entrained gas, potentially suppressing the depletion of the entrained gas [7,71,72]). In contrast, in Mg-alloy foundries, the Mg-alloy melt is not normally degassed, since it was widely believed that there is not a ‘gas problem’ when casting magnesium and hence no significant change in tensile properties [73]. Although studies have shown the negative effect of hydrogen on the mechanical properties of Mg-alloy castings [41,42,73], a degassing process is still not very popular in Mg-alloy foundries.

Moreover, in present work, the sand mould cavity was flushed with the SF6 cover gas prior to pouring [22]. However, not all the Mg-alloy foundries flushed the mould cavity in this way. For example, the Stone Foundry Ltd (UK) used sulphur powder instead of the cover-gas flushing. The entrained gas within their castings may be SO2/air, rather than the protective gas.

Therefore, although the results in present work have shown that using air instead of CO2 improved the reproducibility of the final casting, it still requires further investigations to confirm the effect of carrier gases with respect to different industrial Mg-alloy casting processes.

7. Conclusion

Entrainment defects formed in an AZ91 alloy were observed. Their oxide films had two types of structure: single-layered and multi-layered. The multi-layered oxide film can grow together forming a sandwich-like structure in the final casting.2.

Both the experimental results and the theoretical thermodynamic calculations demonstrated that fluorides in the trapped gas were depleted prior to the consumption of sulphur. A three-stage evolution process of the double oxide film defects has been suggested. The oxide films contained different combinations of compounds, depending on the evolution stage. The defects formed in SF6/air had a similar structure to those formed in SF6/CO2, but the compositions of their oxide films were different. The oxide-film formation and evolution process of the entrainment defects were different from that of the Mg-alloy surface films previous reported (i.e., MgO formed prior to MgF2).3.

The growth rate of the oxide film was demonstrated to be greater under SF6/air than SF6/CO2, contributing to a quicker consumption of the damaging entrapped gas. The reproducibility of an AZ91 alloy casting improved when using SF6/air instead of SF6/CO2.

Acknowledgements

The authors acknowledge funding from the EPSRC LiME grant EP/H026177/1, and the help from Dr W.D. Griffiths and Mr. Adrian Carden (University of Birmingham). The casting work was carried out in University of Birmingham.

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Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.

Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale

WenjunLiuaBoWangaYakunGuobaState Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinabFaculty of Engineering & Informatics, University of Bradford, BD7 1DP, UK

Highlights

경사진 습윤층에서 댐파괴유동과 FFavre 파를 수치적으로 조사하였다.
수직 대 수평 속도의 비율이 먼저 정량화됩니다.
유동 상태는 유상 경사가 큰 후기 단계에서 크게 변경됩니다.
Favre 파도는 수직 속도와 수직 가속도에 큰 영향을 미칩니다.
베드 전단응력의 변화는 베드 기울기와 꼬리물의 영향을 받습니다.

Abstract

The bed slope and the tailwater depth are two important ones among the factors that affect the propagation of the dam-break flood and Favre waves. Most previous studies have only focused on the macroscopic characteristics of the dam-break flows or Favre waves under the condition of horizontal bed, rather than the internal movement characteristics in sloped channel. The present study applies two numerical models, namely, large eddy simulation (LES) and shallow water equations (SWEs) models embedded in the CFD software package FLOW-3D to analyze the internal movement characteristics of the dam-break flows and Favre waves, such as water level, the velocity distribution, the fluid particles acceleration and the bed shear stress, under the different bed slopes and water depth ratios. The results under the conditions considered in this study show that there is a flow state transition in the flow evolution for the steep bed slope even in water depth ratio α = 0.1 (α is the ratio of the tailwater depth to the reservoir water depth). The flow state transition shows that the wavefront changes from a breaking state to undular. Such flow transition is not observed for the horizontal slope and mild bed slope. The existence of the Favre waves leads to a significant increase of the vertical velocity and the vertical acceleration. In this situation, the SWEs model has poor prediction. Analysis reveals that the variation of the maximum bed shear stress is affected by both the bed slope and tailwater depth. Under the same bed slope (e.g., S0 = 0.02), the maximum bed shear stress position develops downstream of the dam when α = 0.1, while it develops towards the end of the reservoir when α = 0.7. For the same water depth ratio (e.g., α = 0.7), the maximum bed shear stress position always locates within the reservoir at S0 = 0.02, while it appears in the downstream of the dam for S0 = 0 and 0.003 after the flow evolves for a while. The comparison between the numerical simulation and experimental measurements shows that the LES model can predict the internal movement characteristics with satisfactory accuracy. This study improves the understanding of the effect of both the bed slope and the tailwater depth on the internal movement characteristics of the dam-break flows and Favre waves, which also provides a valuable reference for determining the flood embankment height and designing the channel bed anti-scouring facility.

Fig. 1. Sketch of related variables involved in shallow water model.
Fig. 1. Sketch of related variables involved in shallow water model.
Fig. 2. Flume model in numerical simulation.
Fig. 2. Flume model in numerical simulation.
Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
Fig. 4. Sketch of experimental set-up for validating the velocity profile.
Fig. 4. Sketch of experimental set-up for validating the velocity profile.
Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
Fig. 7. Schematic diagram of regional division.
Fig. 7. Schematic diagram of regional division.
Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. (continued).
Fig. 12. (continued).
Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. (continued).
Fig. 15. (continued).

Keywords

Dam-break flow, Bed slope, Wet bed, Velocity profile, Bed shear stress, Large eddy simulation

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Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.

316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링

316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링

M. BAYAT1,* , AND J. H. HATTEL1

  • Corresponding author
    1 Technical University of Denmark (DTU), Building 425, Kgs. 2800 Lyngby, Denmark

ABSTRACT

Spatter and denudation are two very well-known phenomena occurring mainly during the laser powder bed fusion process and are defined as ejection and displacement of powder particles, respectively. The main driver of this phenomenon is the formation of a vapor plume jet that is caused by the vaporization of the melt pool which is subjected to the laser beam. In this work, a 3-dimensional transient turbulent computational fluid dynamics model coupled with a discrete element model is developed in the finite volume-based commercial software package Flow-3D AM to simulate the spatter phenomenon. The numerical results show that a localized low-pressure zone forms at the bottom side of the plume jet and this leads to a pseudo-Bernoulli effect that drags nearby powder particles into the area of influence of the vapor plume jet. As a result, the vapor plume acts like a momentum sink and therefore all nearby particles point are dragged towards this region. Furthermore, it is noted that due to the jet’s attenuation, powder particles start diverging from the central core region of the vapor plume as they move vertically upwards. It is moreover observed that only particles which are in the very central core region of the plume jet get sufficiently accelerated to depart the computational domain, while the rest of the dragged particles, especially those which undergo an early divergence from the jet axis, get stalled pretty fast as they come in contact with the resting fluid. In the last part of the work, two simulations with two different scanning speeds are carried out, where it is clearly observed that the angle between the departing powder particles and the vertical axis of the plume jet increases with increasing scanning speed.

스패터와 denudation은 주로 레이저 분말 베드 융합 과정에서 발생하는 매우 잘 알려진 두 가지 현상으로 각각 분말 입자의 배출 및 변위로 정의됩니다.

이 현상의 주요 동인은 레이저 빔을 받는 용융 풀의 기화로 인해 발생하는 증기 기둥 제트의 형성입니다. 이 작업에서 이산 요소 모델과 결합된 3차원 과도 난류 ​​전산 유체 역학 모델은 스패터 현상을 시뮬레이션하기 위해 유한 체적 기반 상용 소프트웨어 패키지 Flow-3D AM에서 개발되었습니다.

수치적 결과는 플룸 제트의 바닥면에 국부적인 저압 영역이 형성되고, 이는 근처의 분말 입자를 증기 플룸 제트의 영향 영역으로 끌어들이는 의사-베르누이 효과로 이어진다는 것을 보여줍니다.

결과적으로 증기 기둥은 운동량 흡수원처럼 작용하므로 근처의 모든 입자 지점이 이 영역으로 끌립니다. 또한 제트의 감쇠로 인해 분말 입자가 수직으로 위쪽으로 이동할 때 증기 기둥의 중심 코어 영역에서 발산하기 시작합니다.

더욱이 플룸 제트의 가장 중심 코어 영역에 있는 입자만 계산 영역을 벗어날 만큼 충분히 가속되는 반면, 드래그된 나머지 입자, 특히 제트 축에서 초기 발산을 겪는 입자는 정체되는 것으로 관찰됩니다. 그들은 휴식 유체와 접촉하기 때문에 꽤 빠릅니다.

작업의 마지막 부분에서 두 가지 다른 스캔 속도를 가진 두 가지 시뮬레이션이 수행되었으며, 여기서 출발하는 분말 입자와 연기 제트의 수직 축 사이의 각도가 스캔 속도가 증가함에 따라 증가하는 것이 명확하게 관찰되었습니다.

Fig 1. Two different views of the computational domain for the fluid domain. The vapor plume is simulated by a moving momentum source with a prescribed temperature of 3000 K.
Fig 1. Two different views of the computational domain for the fluid domain. The vapor plume is simulated by a moving momentum source with a prescribed temperature of 3000 K.
Fig 2. (a) and (b) are two snapshots taken at an x-y plane parallel to the powder layer plane before and 0.008 seconds after the start of the scanning process. (c) Shows a magnified view of (b) where detailed powder particles' movement along with their velocity magnitude and directions are shown.
Fig 2. (a) and (b) are two snapshots taken at an x-y plane parallel to the powder layer plane before and 0.008 seconds after the start of the scanning process. (c) Shows a magnified view of (b) where detailed powder particles’ movement along with their velocity magnitude and directions are shown.
Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.
Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.

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Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

플라즈마 회전 전극 공정 중 분말 형성에 대한 공정 매개변수 및 냉각 가스의 영향

Effects of process parameters and cooling gas on powder formation during the plasma rotating electrode process

Yujie Cuia Yufan Zhaoa1 Haruko Numatab Kenta Yamanakaa Huakang Biana Kenta Aoyagia AkihikoChibaa
aInstitute for Materials Research, Tohoku University, Sendai 980-8577, JapanbDepartment of Materials Processing, Graduate School of Engineering, Tohoku University, Sendai 980-8577, Japan

Highlights

•The limitation of increasing the rotational speed in decreasing powder size was clarified.

•Cooling and disturbance effects varied with the gas flowing rate.

•Inclined angle of the residual electrode end face affected powder formation.

•Additional cooling gas flowing could be applied to control powder size.

Abstract

The plasma rotating electrode process (PREP) is rapidly becoming an important powder fabrication method in additive manufacturing. However, the low production rate of fine PREP powder limits the development of PREP. Herein, we investigated different factors affecting powder formation during PREP by combining experimental methods and numerical simulations. The limitation of increasing the rotation electrode speed in decreasing powder size is attributed to the increased probability of adjacent droplets recombining and the decreased tendency of granulation. The effects of additional Ar/He gas flowing on the rotational electrode on powder formation is determined through the cooling effect, the disturbance effect, and the inclined effect of the residual electrode end face simultaneously. A smaller-sized powder was obtained in the He atmosphere owing to the larger inclined angle of the residual electrode end face compared to the Ar atmosphere. Our research highlights the route for the fabrication of smaller-sized powders using PREP.

플라즈마 회전 전극 공정(PREP)은 적층 제조 에서 중요한 분말 제조 방법으로 빠르게 자리잡고 있습니다. 그러나 미세한 PREP 분말의 낮은 생산율은 PREP의 개발을 제한합니다. 여기에서 우리는 실험 방법과 수치 시뮬레이션을 결합하여 PREP 동안 분말 형성에 영향을 미치는 다양한 요인을 조사했습니다. 분말 크기 감소에서 회전 전극 속도 증가의 한계는 인접한 액적 재결합 확률 증가 및 과립화 경향 감소에 기인합니다.. 회전 전극에 흐르는 추가 Ar/He 가스가 분말 형성에 미치는 영향은 냉각 효과, 외란 효과 및 잔류 전극 단면의 경사 효과를 통해 동시에 결정됩니다. He 분위기에서는 Ar 분위기에 비해 잔류 전극 단면의 경사각이 크기 때문에 더 작은 크기의 분말이 얻어졌다. 우리의 연구는 PREP를 사용하여 더 작은 크기의 분말을 제조하는 경로를 강조합니다.

Keywords

Plasma rotating electrode process

Ti-6Al-4 V alloy, Rotating speed, Numerical simulation, Gas flowing, Powder size

Introduction

With the development of additive manufacturing, there has been a significant increase in high-quality powder production demand [1,2]. The initial powder characteristics are closely related to the uniform powder spreading [3,4], packing density [5], and layer thickness observed during additive manufacturing [6], thus determining the mechanical properties of the additive manufactured parts [7,8]. Gas atomization (GA) [9–11], centrifugal atomization (CA) [12–15], and the plasma rotating electrode process (PREP) are three important powder fabrication methods.

Currently, GA is the dominant powder fabrication method used in additive manufacturing [16] for the fabrication of a wide range of alloys [11]. GA produces powders by impinging a liquid metal stream to droplets through a high-speed gas flow of nitrogen, argon, or helium. With relatively low energy consumption and a high fraction of fine powders, GA has become the most popular powder manufacturing technology for AM.

The entrapped gas pores are generally formed in the powder after solidification during GA, in which the molten metal is impacted by a high-speed atomization gas jet. In addition, satellites are formed in GA powder when fine particles adhere to partially molten particles.

The gas pores of GA powder result in porosity generation in the additive manufactured parts, which in turn deteriorates its mechanical properties because pores can become crack initiation sites [17]. In CA, a molten metal stream is poured directly onto an atomizer disc spinning at a high rotational speed. A thin film is formed on the surface of the disc, which breaks into small droplets due to the centrifugal force. Metal powder is obtained when these droplets solidify.

Compared with GA powder, CA powder exhibits higher sphericity, lower impurity content, fewer satellites, and narrower particle size distribution [12]. However, very high speed is required to obtain fine powder by CA. In PREP, the molten metal, melted using the plasma arc, is ejected from the rotating rod through centrifugal force. Compared with GA powder, PREP-produced powders also have higher sphericity and fewer pores and satellites [18].

For instance, PREP-fabricated Ti6Al-4 V alloy powder with a powder size below 150 μm exhibits lower porosity than gas-atomized powder [19], which decreases the porosity of additive manufactured parts. Furthermore, the process window during electron beam melting was broadened using PREP powder compared to GA powder in Inconel 718 alloy [20] owing to the higher sphericity of the PREP powder.

In summary, PREP powder exhibits many advantages and is highly recommended for powder-based additive manufacturing and direct energy deposition-type additive manufacturing. However, the low production rate of fine PREP powder limits the widespread application of PREP powder in additive manufacturing.

Although increasing the rotating speed is an effective method to decrease the powder size [21,22], the reduction in powder size becomes smaller with the increased rotating speed [23]. The occurrence of limiting effects has not been fully clarified yet.

Moreover, the powder size can be decreased by increasing the rotating electrode diameter [24]. However, these methods are quite demanding for the PREP equipment. For instance, it is costly to revise the PREP equipment to meet the demand of further increasing the rotating speed or electrode diameter.

Accordingly, more feasible methods should be developed to further decrease the PREP powder size. Another factor that influences powder formation is the melting rate [25]. It has been reported that increasing the melting rate decreases the powder size of Inconel 718 alloy [26].

In contrast, the powder size of SUS316 alloy was decreased by decreasing the plasma current within certain ranges. This was ascribed to the formation of larger-sized droplets from fluid strips with increased thickness and spatial density at higher plasma currents [27]. The powder size of NiTi alloy also decreases at lower melting rates [28]. Consequently, altering the melting rate, varied with the plasma current, is expected to regulate the PREP powder size.

Furthermore, gas flowing has a significant influence on powder formation [27,29–31]. On one hand, the disturbance effect of gas flowing promotes fluid granulation, which in turn contributes to the formation of smaller-sized powder [27]. On the other hand, the cooling effect of gas flowing facilitates the formation of large-sized powder due to increased viscosity and surface tension. However, there is a lack of systematic research on the effect of different gas flowing on powder formation during PREP.

Herein, the authors systematically studied the effects of rotating speed, electrode diameter, plasma current, and gas flowing on the formation of Ti-6Al-4 V alloy powder during PREP as additive manufactured Ti-6Al-4 V alloy exhibits great application potential [32]. Numerical simulations were conducted to explain why increasing the rotating speed is not effective in decreasing powder size when the rotation speed reaches a certain level. In addition, the different factors incited by the Ar/He gas flowing on powder formation were clarified.

Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.
Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

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Fig. 8. Pressure distribution during the infiltration of preform with the 50 ¯m particles and 20 % starches: (a) 25 % filled, (b) 57 % filled, and (c) 99 % filled.

Experimental study and numerical simulation of infiltration of AlSi12 alloys into Si porous preforms with micro-computed tomography inspection characteristics

마이크로 컴퓨터 단층 촬영 검사 특성을 가진 Si 다공성 프리폼에 AlSi12 합금의 침투에 대한 실험적 연구 및 수치 시뮬레이션

Ruizhe LIU1 and Haidong ZHAO1
1National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials, South China University of Technology,
Guangzhou 510640, China

Abstract

전분 함량(10, 20 및 30%)과 입자 크기(20, 50 및 90 m)가 다른 실리콘 입자 예비 성형체는 압축 성형 및 열처리를 통해 제작되었습니다. 프리폼의 기공 특성은 고해상도(³1 m) 3차원(3D) X선 마이크로 컴퓨터 단층 촬영(V-CT)으로 검사되었습니다. AlSi12 합금의 프리폼으로의 침투는 진공 보조 압력 침투 장치에서 800 °C 및 400 kPa의 조건에서 서로 다른 압력 적용 시간(3, 8 및 15초)으로 수행되었습니다. 고해상도(³500 nm) 수직 주사 백색광 간섭 프로파일로미터를 사용하여 복합 재료의 전면을 감지했습니다. Navier-Stokes 방정식을 기반으로 하는 ¯-CT 검사에서 실제 기공 형상을 고려하여 침투를 미시적으로 시뮬레이션했습니다. 그 결과 전분 함량과 입자크기가 증가할수록 복합재료의 표면적이 증가하는 것으로 나타났다. 전분 함량과 비교하여 입자 크기는 전면 표면적에 더 많은 영향을 미칩니다. 시뮬레이션에서 침투가 진행됨에 따라 액체 AlSi12의 압력이 감소했습니다. 복합재의 잔류 기공은 침투와 함께 증가했습니다. 실험 및 시뮬레이션 결과에 따르면 침투 방향을 따라 더 큰 압력 강하가 복합 재료의 더 많은 잔류 기공을 유도합니다.

Silicon particle preforms with different starch contents (10, 20 and 30%) and particle sizes (20, 50 and 90 ¯m) were fabricated by compression mold forming and heat treatment. The pore characteristics of preforms were inspected with a high-resolution (³1 ¯m) three-dimensional (3D) X-ray micro-computed tomography (¯-CT). The infiltration of AlSi12 alloys into the preforms were carried out under the condition of 800 °C and 400 kPa with different pressure-applied times (3, 8 and 15 s) in a vacuum-assisted pressure infiltration apparatus. A highresolution (³500 nm) vertical scanning white light interfering profilometer was used to detect the front surfaces of composites. The infiltration was simulated at micro-scale by considering the actual pore geometry from the ¯- CT inspection based on the Navier-Stokes equation. The results demonstrated that as the starch content and particle size increased, the front surface area of composite increased. Compared with the starch content, the particle size has more influence on the front surface area. In the simulation, as the infiltration progressed, the pressure of liquid AlSi12 decreased. The residual pores of composites increased with infiltration. According to the experiment and simulation results, a larger pressure drop along the infiltration direction leads to more residual pores of composites.

Fig. 1. Size distributions of Si particles.
Fig. 1. Size distributions of Si particles.
Fig. 2. Schematic of different locations of composites.
Fig. 2. Schematic of different locations of composites.
Fig. 3. Three-dimensional geometry with the reconstruction technology, enmeshment and infiltration parameters of Si preforms: (a) geometry, and (b) meshes and flow direction.
Fig. 3. Three-dimensional geometry with the reconstruction technology, enmeshment and infiltration parameters of Si preforms: (a) geometry, and (b) meshes and flow direction.
Fig. 4. Number-based frequencies of effective pore radius and throat radius: (a) effective pore radius of preforms with the 50 ¯m particles, (b) effective throat radius of preforms with the 50 ¯m particles, (c) effective pore radius of preforms with the 20 % starches, and (d) effective throat radius of preforms with the 20 % starches.
Fig. 4. Number-based frequencies of effective pore radius and throat radius: (a) effective pore radius of preforms with the 50 ¯m particles, (b) effective throat radius of preforms with the 50 ¯m particles, (c) effective pore radius of preforms with the 20 % starches, and (d) effective throat radius of preforms with the 20 % starches.
Fig. 5. 3D topological morphologies of front surfaces of composites: (a) 50 ¯m-10 %, (b) 50 ¯m-20 %, (c) 50 ¯m-30 %, (d) 20 ¯m-20 %, and (e) 90 ¯m-20 %.
Fig. 5. 3D topological morphologies of front surfaces of composites: (a) 50 ¯m-10 %, (b) 50 ¯m-20 %, (c) 50 ¯m-30 %, (d) 20 ¯m-20 %, and (e) 90 ¯m-20 %.
Fig. 6. Schematic of capillary tube.
Fig. 6. Schematic of capillary tube.
Fig. 8. Pressure distribution during the infiltration of preform with the 50 ¯m particles and 20 % starches: (a) 25 % filled, (b) 57 % filled, and (c) 99 % filled.
Fig. 8. Pressure distribution during the infiltration of preform with the 50 ¯m particles and 20 % starches: (a) 25 % filled, (b) 57 % filled, and (c) 99 % filled.
Fig. 9. Pressure distributions of liquid AlSi12 during the infiltration of preforms: (a) different fill fractions, (b) different starch contents, and (c) different particle sizes.
Fig. 9. Pressure distributions of liquid AlSi12 during the infiltration of preforms: (a) different fill fractions, (b) different starch contents, and (c) different particle sizes.
Fig. 10. Metallographs of composites: (a) different locations of composite with the 20 ¯m particles and 20 % starches, and (b) different locations of composite with the 90 ¯m particles and 20 % starches.
Fig. 10. Metallographs of composites: (a) different locations of composite with the 20 ¯m particles and 20 % starches, and (b) different locations of composite with the 90 ¯m particles and 20 % starches.
Fig. 11. Area fractions of residual pores of composites: (a) 50 ¯m (different starch contents), and (b) 20 % (different particle sizes).
Fig. 11. Area fractions of residual pores of composites: (a) 50 ¯m (different starch contents), and (b) 20 % (different particle sizes).

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Effect of roughness on separation zone dimensions.

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

조도 계수 및 역전 수준 변화가 개선된 90도 측면 분출구에서의 유동에 대한 실험적 및 수치적 연구

Maryam BagheriSeyed M. Ali ZomorodianMasih ZolghadrH. Md. AzamathullaC. Venkata Siva Rama Prasad

Abstract

측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.

Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.

HIGHLIGHTS

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  • Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance.
  • Installation of 7 types of roughening elements at the turnout entrance and 3 different bed level inverts were investigated.
  • Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow.
  • Combining both methods can reduce the separation zone dimensions by up to 63%.
Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

Keywords

discharge ratioflow separation zoneintakethree dimensional simulation

INTRODUCTION

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Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.

The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.

Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).

Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).

Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011)Nikbin & Borghei (2011)Seyedian et al. (2008).

Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.

Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE

Laboratory channel dimensions.

Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.

The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.

METHOD

Experimental setup

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The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.

Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE

Roughness plates.

The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).

The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).

Numerical simulation

ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:

formula

(1)where uv, and w represent the velocity components in the x, y, and z directions, respectively; AxAy, and Az are the surface flow fractions in the xy, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in xy and z dimensions respectively :

formula

(2)

formula

(3)

formula

(4)where GxGy, and Gz are the accelerations caused by gravity in the xy, and z directions, respectively; and fxfy, and fz are the accelerations caused by viscosity in the xy, and z directions, respectively.

The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.

Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.

The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1

Hydraulic conditions of the flow

Q(L/s)FrY1 (m)Q2/Q1
16 0.449 0.09 0.22 
18 0.335 0.09 0.61 
21 0.242 0.09 0.71 
23 0.180 0.09 1.04 

RESULTS AND DISCUSSION

Experimental results

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During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.

At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions.Figure 4VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions.

It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE

Comparison of separation zone for n=0.023 and n=0.032.

Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.

The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.

In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2

Decrease percentage of separation zone area in 5 cm drop

Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
0.08 10.56 11.06 25.27 33.03 35.57 36.5 
0.121 7.66 11.14 11.88 15.93 34.59 36.25 
0.353 1.38 2.63 8.17 14.39 31.20 31.29 
0.362 11.54 19.56 25.73 37.89 38.31 

Table 3

Decrease percentage of separation zone area in 10 cm drop

Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
0.047 4.30 8.75 23.47 31.22 34.96 35.13 
0.119 11.01 13.16 15.02 21.48 39.45 40.68 
0.348 3.89 5.71 9.82 16.09 29 30.96 
0.354 2.84 10.44 18.42 25.45 35.68 35.76 

Figure 6VIEW LARGEDOWNLOAD SLIDE

Effect of drop implementation on separation zone dimensions.

The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4

Reduction in percentage of combined effect of roughness and 10 cm drop

Qin=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
16 32.3 35.07 37.2 45.7 58.01 59.1 
18 44.5 34.15 36.18 48.13 54.2 56.18 
21 43.18 32.33 42.30 37.79 57.16 63.2 
23 40.56 34.5 34.09 46.25 50.12 57.2 

Figure 7VIEW LARGEDOWNLOAD SLIDE

Combined effect of roughness and drop on separation zone dimensions.

This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.

Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE

Velocity profiles for various roughness coefficients along turnout width.

A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions in numerical study.

Numerical results

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This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE

Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,

formula

where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.

Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE

Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE

Velocity vector for flow condition Q1/422 l/s, near surface.

The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE

Exprimental and numerical measured velocity.

CONCLUSION

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This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.

This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.

DATA AVAILABILITY STATEMENT

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All relevant data are included in the paper or its Supplementary Information.

REFERENCES

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Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition

Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition

Xiang WangLin-Jie ZhangJie Ning, and Suck-Joo Na
Published Online:8 Apr 2022https://doi.org/10.1089/3dp.2021.0159

Abstract

A 3D numerical model of heat transfer and fluid flow of molten pool in the process of laser wire deposition was presented by computational fluid dynamics technique. The simulation results of the deposition morphology were also compared with the experimental results under the condition of liquid bridge transfer mode. Moreover, they showed a good agreement. Considering the effect of recoil pressure, the morphology of the deposit metal obtained by the simulation was similar to the experiment result. Molten metal at the wire tip was peeled off and flowed into the molten pool, and then spread to both sides of the deposition layer under the recoil pressure. In addition, the results of simulation and high-speed charge-coupled device presented that a wedge transition zone, with a length of ∼6 mm, was formed behind the keyhole in the liquid bridge transfer process, where the height of deposited metal decreased gradually. After solidification, metal in the transition zone retained the original melt morphology, resulting in a decrease in the height of the tail of the deposition layer.

Keywords

LWD, CFD, liquid bridge transfer, fluid dynamics, wedge transition zone

Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition
Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition
Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition
Fluid Thermodynamic Simulation of Ti-6Al-4V Alloy in Laser Wire Deposition

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Figure 6. Circular section of the viscosity and shear-rate clouds.

Simulation and Visual Tester Verification of Solid Propellant Slurry Vacuum Plate Casting

Wu Yue,Li Zhuo,Lu RongFirst published: 26 February 2020 https://doi.org/10.1002/prep.201900411Citations: 3

Abstract

Using an improved Carreau constitutive model, a numerical simulation of the casting process of a type of solid propellant slurry vacuum plate casting was carried out using the Flow3D software. Through the flow process in the orifice flow channel and the combustion chamber, the flow velocity of the slurry passing through the plate flow channel was quantitatively analyzed, and the viscosity, shear rate, and leveling characteristics of the slurry in the combustion chamber were qualitatively analyzed and predicted. The pouring time, pouring quality, and flow state predicted by the numerical simulation were verified using a visual tester consisting of a vacuum plate casting system in which a pouring experiment was carried out. Studies have shown that HTPB three-component propellant slurry is a typical yielding pseudoplastic fluid. When the slurry flows through the flower plate and the airfoil, the fluid shear rate reaches its maximum value and the viscosity of the slurry decreases. The visual pouring platform was built and the experiment was controlled according to the numerically-calculated parameters, ensuring the same casting speed. The comparison between the predicted casting quality and the one obtained in the verification test resulted in an error less than 10 %. Moreover, the error between the simulated casting completion time and the process verification test result was also no more than 10 %. Last, the flow state of the slurry during the simulation was consistent with the one during the experimental test. The overall leveling of the slurry in the combustion chamber was adequate and no relatively large holes and flaws developed during the pouring process.

개선된 Carreau 구성 모델을 사용하여 FLOW-3D 소프트웨어를 사용하여 고체 추진제 슬러리 진공판 유형의 Casting Process에 대한 수치 시뮬레이션을 수행했습니다. 오리피스 유로와 연소실에서의 유동과정을 통해 판 유로를 통과하는 슬러리의 유속을 정량적으로 분석하고, 연소실에서 슬러리의 점도, 전단율, 레벨링 특성을 정성적으로 분석하하고, 예측하였습니다.

타설시간, 타설품질, 수치해석으로 예측된 ​​유동상태는 타설실험을 수행한 진공판주조시스템으로 구성된 비주얼 테스터를 이용하여 검증하였습니다.

연구에 따르면 HTPB 3성분 추진제 슬러리는 전형적인 생성 가소성 유체입니다. 슬러리가 플라워 플레이트와 에어포일을 통과할 때 유체 전단율이 최대값에 도달하고 슬러리의 점도가 감소합니다.

시각적 주입 플랫폼이 구축되었고 동일한 주조 속도를 보장하기 위해 수치적으로 계산된 매개변수에 따라 실험이 제어되었습니다. 예측된 casting 품질과 검증 테스트에서 얻은 품질을 비교한 결과 10 % 미만의 오류가 발생했습니다.

또한 모의 casting 완료시간과 공정검증시험 결과의 오차도 10 % 이하로 나타났습니다.

마지막으로 시뮬레이션 중 슬러리의 흐름 상태는 실험 테스트 시와 일치하였다. 연소실에서 슬러리의 전체 레벨링은 적절했으며 주입 과정에서 상대적으로 큰 구멍과 결함이 발생하지 않았습니다.

Figure 1. The equipment used in the vacuum flower-plate pouring process.
Figure 1. The equipment used in the vacuum flower-plate pouring process.
Figure 2. Calculation model.
Figure 2. Calculation model.
Figure 3. Grid block division unit.
Figure 3. Grid block division unit.
Figure 4. Circular section of the speed cloud.
Figure 4. Circular section of the speed cloud.
Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
Figure 6. Circular section of the viscosity and shear-rate clouds.
Figure 6. Circular section of the viscosity and shear-rate clouds.
Figure 7. Volume fraction cloud chart at different time.
Figure 7. Volume fraction cloud chart at different time.
Figure 8. Experimental program.
Figure 8. Experimental program.
Figure 9. Emulation experimental device.
Figure 9. Emulation experimental device.
Figure 10. Visualization of the flow state of the pulp inside the tester.
Figure 10. Visualization of the flow state of the pulp inside the tester.

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