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

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.

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
Fig. 1.3: Modes of welding with laser: (a) conduction and (b) keyhole welding
Fig. 1.3: Modes of welding with laser: (a) conduction and (b) keyhole welding

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.

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.

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. 1.6: External and internal weld defects that can occur in laser welding of (a) a butt joint and (b) a lap joint.

8. 참고 문헌:

  1. Lancaster, J. F., 1984, The physics of welding, Physics in Technology, 15:73-79.
  2. Kou, S., 2003, Fusion welding processes, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.3-36.
  3. Steen, W.M., Mazumder, J., 2010, Laser welding: laser material processing, 4th Ed., Springer-Verlag London Limited, UK, pp. 199-250.
  4. Merchant, V., Laser beam welding, In: Ahmed, N., editor, New developments in advanced welding, 1st Ed., Woodhead Publishing Limited, Cambridge, UK, pp. 83-84.
  5. Kugler, T.R., 2001, Fusion front penetration: Conduction Welding, In: Ready, J.F., editor, LIA handbook of laser materials processing, 1st Ed., Magnolia Publishing Inc., FL, USA, pp. 310-312.
  6. Matsunawa, A., 2002, Science of laser welding-mechanisms of keyhole and pool dynamics. In: ICALEO 2002 proceedings, Phoenix, LIA, Orlando, paper: 101.
  7. Lacroix, D., Jeandel, G., Boudot, C., 1996, Spectroscopic studies of laser-induced plume during welding with a Nd:YAG laser, In: Proceedings of SPIE, 2789, pp. 221–227.
  8. Dumord, E., Jouvard, J.M., Grevey, D., 1996, Keyhole modeling during CW Nd:YAG laser welding, In: Proceedings of SPIE, 2789, pp. 213–220.
  9. Berkmanns, J., Faerber, M., 2005, Facts about laser technology: laser welding, http://www.laserdeal.com/, access date: January 20, 2012.
  10. Coherent Inc., 2004, High speed welding of metals with diamond CO2 laser – stainless steels, Technical Note, http://www.coherent.de/, access date: November 15, 2011.
  11. LWS, 2006, A technical report on the LWS flexcell cladding system, http://www.laserweldingsolutions.com/, access date: April 01, 2009.
  12. Shannon, G., 2009, Source selection for laser welding, http://www.industrial-lasers.com/, access date: April 01, 2009.
  13. Faerber, M., Berkmanns, J., 1996, Gases for increased laser welding productivity, In: Proceedings of the ISATA Conference, pp. 791–798.
  14. Schuberth S, Schedin E, Fröhlich T, Ratte E., 2008, Next generation vehicle – engineering guidelines for stainless steel in automotive applications, In: Proceedings of the 6th stainless steel science and market conference, Helsinki, Finland.
  15. Kou, S., 2003, Weld metal solidification, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.199-207.
  16. Han, W., 2004, Computational and experimental investigations of laser drilling and welding for microelectronic packaging, Ph.D. Dissertation, Worcester Polytechnic Institute, Worcester, MA, USA, pp. 85-87.
  17. Buchfink, G., 2007, A world of possibilities – joining, In: Kammϋller, N.L., editor, The laser as a tool, 1st Ed., Vogel Buchverlag, Wϋrzburg, Germany, pp. 166-167.
  18. ISO13919-1:1996, Welding – Electrons and laser beam welded joints – guidance on quality levels for imperfections – Part I: Steel, pp. 4-13.
  19. Zhang, Y.M., Kovacevic, R., Li, L., 1996, Characterization and real time measurement of geometrical appearance of the weld pool. International Journal of Machine Tools and Manufacture, 36(7):799–816.
  20. Bull, C.E., Stacey, K.A., Calcraft, R., 1993, Online weld monitoring using ultrasonic. Journal of Non-destructive Test, 35(2):57–64.
  21. Tarng, Y.S., Yang, W.H., 1998, Optimization of the weld bead geometry in gas Tungsten Arc welding by the Taguchi Method. Journal of Advanced Manufacturing Technology, 14:549–54.
  22. Benyounis, K.Y., Olabi, A.G., Hasmi, M.S.J., 2008, Multi-response optimization of CO2 laser welding process of austenitic stainless steel, Optics & Laser Technology, 40:76–87.
  23. Antony, J., 2003, Introduction to industrial experimentation, In: Design of Experiments for Engineers and Scientists, Elsevier Publishing Solutions, USA, pp. 1-4.
  24. Sudnik, W., Radaj, D., Erofeev, W., 1996, Computerized simulation of laser beam welding, modeling and verification, Journal of Physics D: Applied Physics, 29:2811-2817.
  25. Arata, Y., Miyamoto, I., 1972, Heat processing by CO2 laser, Journal of Japan Welding Society, 41:81.
  26. Swift-Hook, D.T., Gick, A.E.F., 1973, Penetration welding with lasers, Welding Journal Research Supplement, 52:492s–9s.
  27. Steen, W.M., Dowden, J., Davis, M., Kapadia, P., 1988, A point and line source model of laser keyhole welding, Journal of Physics D, 21:1255–60.
  28. Dowden, J., Davis, M., Kapadia, P., 1983, Some aspects of the fluid-dynamics of laser-welding. Journal of Fluid Mechanics, 126:123–46.
  29. Ducharme, R., Kapadia, P., Dowden, J., 1993, A mathematical model of the defocusing of laser light above a workpiece in laser material processing. In: Farson, D., Steen, W., Miyamoto, I., editors, Proceedings of ICALEO’92, LIA, Orlando: Laser Institution of America, 75:187–97.
  30. Kaplan, A., 1994, A model of deep penetration laser welding based on calculation of the keyhole profile, Journal of Physics D: Applied Physics, 27(9):1805–1814.
  31. Klemens, P.G., 1976, Heat balance and flow conditions for electron beam and laser welding, Journal of Applied Physics, 47(5):2165–2174.
  32. Chande, T., Mazumder, J., 1984, Estimating effects of processing conditions and variable properties upon pool shape, cooling rates, and absorption coefficient in laser welding, Journal of Applied Physics, 56:1981–6.
  33. Borland, J.C., 1960, Generalized theory of super-solidus cracking in welds (and castings), British Welding Journal, 7: 508–512.
  34. Hemsworth, B., Boniszewski, T., Eaton, N.F., 1969, Classification and definition of high temperature welding cracks in alloys, Metal Construction and British Welding Journal, 2:5–16.
  35. Hoffmann, P., Geiger, M., 1995, Recent developments in laser system technology for welding applications, Annals of the CIRP, 44(1):151-156.
  36. Weichiat, C., Paul, A., Pal, M., 2009, CO2 laser welding of galvanized steel sheets using vent holes, Materials and Design, 30:245–251.
  37. Lippold, J.C., Kotecki, D.J., 2005, Welding metallurgy and weldability of stainless steel, 1st ed., John Willey & Sons, NJ, USA, pp. 63-70.
  38. Brooks, J.A., Garrison, W.M., 1999, Weld microstructure development and properties of precipitation-strengthened martensitic stainless steels, Welding Journal, 78(8): 280s -291s.
  39. Tzeng, Y.F., 2000, Parametric analysis of the pulsed Nd:YAG laser seam-welding process, Journal of Materials Processing Technology, 102: 40-47.
  40. Hector Jr., L.G., Chen, Y.-L., Agarwal, S., Briant. C.L., 2004, Texture characterization of autogenous Nd: YAG laser welds in AA5182-O and AA6111-T4 aluminum alloys, Metall. and Mater. Trans A, 35A:3032-3038.
  41. Al-kazzaz, H., Medraj, M., Cao, X., Jahazi, M., Xiao, M., 2005, Effects of welding speed on Nd:YAG laser weldability of ZE41A-T5 magnesium sand castings, Proceeding of 44th annual conference of metallurgists of CIM, Light Metals:137-149.
  42. Huang, R. S., Kang, L., Ma, X., 2008, Microstructure and phase composition of a low-power YAG laser-MAG welded stainless steel joint, Journal of Materials Engineering and Performance, 17:928–935.
  43. Liu, Q.S., Mahdavian, S.M., Aswin, D., Ding, S., 2009, Experimental study of temperature and clamping force during Nd:YAG laser butt welding, Optics & Laser Technology, 41(6):794-799.
  44. Berzins, M., Childs, T.H.C., Ryder, G.R., 1996, The selective laser sintering of polycarbonate, Annals of the CIRP, 45(1):187–190.
  45. Childs, T.H.C., Berzins, M., Ryder, G.R., Tontowi, A.E., 1999, Selective laser sintering of an amorphous polymer: simulations and experiments. Proc. IMechE, Part B: J. Engineering Manufacture, 213:333-349.
  46. Jin, X., Li, L., 2004, An experimental study on the keyhole shapes in laser deep penetration welding, Optics and Lasers in Engineering, 41: 779–790.
  47. Sudnik, W., Radaj, D., Breitschwerdt, S., Erofeew, W., 2000, Numerical simulation of weld pool geometry in laser beam welding, J. Phys. D: Appl. Phys. 33: 662–671.
  48. Antony, J., 2003, Systematic Methodology for design of experiment: Design of Experiment for Engineers and Scientists, 1st Ed., Butterworth-Heinemann Publication, MA, USA, pp. 38-39.
  49. Lippold, J.C., Kotecki, D.J., 2005, Welding metallurgy and weldability of stainless steel, 1st ed. John Willey & Sons, NJ, USA, pp. 63–70.
  50. Kurt, B., Orhan, N., Somunkiran, I., Kaya, M., 2009, The effect of austenitic interface layer on microstructure of AISI 420 martensitic stainless steel joined by keyhole PTA welding process, Materials and Design, 30:661–664.
  51. Ping, D.H., Ohnuma, M., Hirakawa, Y., Kadoya, Y., Hono, K., 2005, Microstructural evolution in 13Cr–8Ni–2.5Mo–2Al martensitic precipitation-hardened stainless steel, Materials Science and Engineering A, 394:285–295.
  52. Berretta, J.R., de Rossi, W., Neves, M.D.M., de Almeida, I.A., Junior, N.D.V., 2007, Pulsed Nd:YAG laser welding of AISI 304 to AISI 420 stainless steels, Optics and Lasers in Engineering, 45:960–966.
  53. Srinivasan, P.B., 2008, Effect of laser beam mode on the microstructural evolution in AISI 410 martensitic stainless steel welds, Lasers in Engineering, 18:351–359.
  54. Rajasekhar, A., Reddy, G.M., Mohandas, T., Murti, V.S.R., 2009, Influence of austenitizing temperature on microstructure and mechanical properties of AISI 431 martensitic stainless steel electron beam welds, Materials and Design, 30:1612–1624.
  55. Sharifitabar, M., Halvaee, A., 2010, Resistance upset butt welding of austenitic to martensitic stainless steels, Materials and Design, 31(6):3044–3050.
  56. Gualco, A., Svoboda, H.G., Surian, E.S., de Vedia, L. A., 2010, Effect of welding procedure on wear behaviour of a modified martensitic tool steel hardfacing deposit, Materials and Design, 31:4165–4173.
  57. Khan MMA, Romoli L, Fiaschi M, Dini G, Sarri F., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Material Processing Technology, 210:1340–53.
  58. Kou, S., 2002, Welding metallurgy, 2nd ed. John Willey & Sons Inc., NJ, USA, pp. 143- 169.
  59. Nakagawa H, Matsuda F, Uehara T, Katayama S, Arata Y. A., 1979, New explanation for role of delta ferrite improving weld solidification crack susceptibility in austenitic stainless steel, Trans Jpn Weld Res Inst. 8:105–12.
  60. Weichiat, C., Paul, A., Pal, M., 2009, CO2 laser welding of galvanized steel sheets using vent holes, Materials and Design, 30:245–251.
  61. Huang, Q., Hagstroem, J., Skoog, H., Kullberg, G., 1991, Effect of laser parameter variation on sheet metal welding, Int. J. Join. Mater., 3:79–88.
  62. Benyounis, K.Y., Olabi., A.G., 2008, Optimization of different welding processes using statistical and numerical approaches – A reference guide, Advances in Engineering Software, 39:483–496.
  63. Montgomery, D.C., 2004, Design and Analysis of Experiments, 6th ed. John Wiley and Sons, Inc., New York.
  64. Yang, Y.K., Chuang, M.T. Lin, S.S., 2009, Optimization of dry machining parameters for high-purity graphite in end milling process via design of experiments methods, Journal of Materials Processing Technology, 209:4395– 4400.
  65. Douglass, D.M., Wu, C.Y., 2003, Laser welding of polyolefin elastomers to thermoplastic polyolefin, In: Proceedings of the 22nd international Congress on applications of lasers & electro-optics, Jacksonville, Florida, USA, 95:118–23.
  66. Koganti, R., Karas, C., Joaquin, A., Henderson, D., Zaluzec, M., Caliskan, A., 2003, Metal inert gas (MIG) welding process optimization for joining aluminum sheet material using OTC/DAIHEN equipment, In: Proceedings of IMECE’03, November 15–21, Washington [DC]: ASME International Mechanical Engineering Congress, pp. 409–425.
  67. Balasubramanian, V., Guha, B., 2004, Fatigue life prediction of load carrying cruciform joints of pressure vessel steel by statistical tools. J Mater Des, 25:615–623.
  68. Cicala, E., Duffet, G., Andrzjewski, H., Grevey, D., 2005, Optimization of T-joint properties in Al-Mg-Si alloy laser welding, 24th International Congress on Applications of Lasers and Electro-Optics, ICALEO: 543-548.
  69. Kim, C., Choi, W., Kim, J., Rhee, S., 2008, Relationship between the weldability and the Process parameters for laser-TIG Hybrid welding of galvanized steel sheets, Materials Transactions, 49:179-186.
  70. Datta, S., Bandyaopadhyay, A., Pal, P.K., 2008, Modeling and optimization of features of bead geometry including percentage dilution in submerged arc welding using mixture of fresh flux and fused slag, Int. J. Adv. Manuf. Technol., 36:1080–1090.
  71. Benyounis, K.Y., Olabi, A.G., Hashmi, M.S.J., 2008, Multi-response optimization of CO2 laser-welding process of austenitic stainless steel, Optics & Laser Technology, 40:76–87.
  72. Sarsılmaz, F., Çaydaş, U., 2009, Statistical analysis on mechanical properties of friction-stir-welded AA 1050/AA 5083 couples, Int. J. Adv. Manuf. Technol., 43:248–255.
  73. Khan M.M.A., Romoli L., Fiaschi M., Sarri F., Dini G., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Materials Processing Technology, 210(10):1340-1353.
  74. Design-Expert software, v7, user’s guide, technical manual, Stat-Ease Inc., Minneapolis, MN; 2005.
  75. Zulkali, M.M.D., Ahmad, A.L., Norulakmal, N.H., 2006, Oryza sativa L. husk as heavy metal adsorbent: optimization with lead as model solution, Bioresour. Technol., 97:21–25.
  76. Sun, Z., 1996, Feasibility of producing ferritic/austenitic dissimilar metal joints by high energy density laser beam process, International Journal of Pressure Vessels and Piping, 68:153-160.
  77. Katayama, S., 2004, Laser welding of aluminium alloys and dissimilar metals, Weld International, 18(8):618–25.
  78. Kaiser, E., Schafer, P., 2005, Pulse sharpening optimizes the quality of seam and spot welds. In: Lasers in manufacturing, proceeding of the third international WLT conference on lasers in manufacturing, pp. 695–698.
  79. Li, Z., Fontana, G., 1998, Autogenous laser welding of stainless steel to free-cutting steel for the manufacture of hydraulic valves, Journal of Materials Processing Technology, 74:174–182.
  80. Mai, T.A., Spowage, A.C., 2004, Characterisation of dissimilar joints in laser welding of steel–kovar, copper–steel and copper–aluminium, Materials Science and Engineering: A, 374:224–233.
  81. Liu, X.B., Yu, G., Pang, M., Fan, J.W., Wang, H.H., Zheng, C.Y., 2007, Dissimilar autogenous full penetration welding of superalloy K418 and 42CrMo steel by a high power CW Nd:YAG laser, Applied Surface Science, 253:7281–7289.
  82. Berretta, J.R., de Rossi, W., Neves, M.D.M., de Almeida, I.A., Junior, N.D.V., 2007, Pulsed Nd:YAG laser welding of AISI 304 to AISI 420 stainless steels, Optics and Lasers in Engineering, 45:960–966.
  83. Mousavi, S.A.A.A., Sufizadeh, A.R., 2009, Metallurgical investigations of pulsed Nd:YAG laser welding of AISI 321 and AISI 630 stainless steels, Materials and Design, 30:3150–3157.
  84. Pekkarinen, J., Kujanpää, V., 2010, The effects of laser welding parameters on the microstructure of ferritic and duplex stainless steels welds, Physics Procedia, 5:517–523.
  85. Allabhakshi, S., Madhusudhan Reddy, G., Ramarao, V.V., Phani Babu, C., Ramachandran, C.S., 2002, Studies on weld overlaying of austenitic stainless steel (AISI 304) with ferritic stainless steel (AISI 430). In: Proceedings of the national welding conference, Indian Institute of Welding, Chennai, India, Paper 8.
  86. Pan, C., Zhang, E., 1996, Morphologies of the transition region in dissimilar austenitic–ferritic welds, Material Characterization, 36(1):5–10.
  87. Wang, S. C., Wang, C., Tu, Y. K., Hwang, C. J., Chi, S., Wang, W. H., Cheng, W. H., 1996, Effect of Au coating on joint strength in laser welding for invar-invar packages, Electronic Components and Technology Conference, IEEE, pp. 942-945.
  88. Cui, C., Hu, J., Gao, K., Pang, S., Yang, Y., Wang, H., Guo, Z., 2008, Effects of process parameters on weld metal keyhole characteristics with COR2R laser butt welding, Lasers in Engineering, 18:319–327.
  89. Khan, M.M.A., Romoli, L., Fiaschi, M., Dini, G., Sarri, F., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration. Journal of Material Processing Technology, 210:1340–53.
  90. Steem WM, Mazumder J, 2010, laser material processing, Springer-Verlag London limited, London.
  91. Weichiat C, Paul A, Pal M., 2009, CO2 laser welding of galvanized steel sheets using vent holes, Materials and Design, 30:245–51.
  92. Mackwood AP, Crafer RC, 2005, Thermal modeling of laser welding and related processes: a literature review, Opt Laser Technol, 37:99–115
  93. Kaiser E, Schafer P, 2005, Pulse shaping optimizes the quality of seam and spot welds. In: Lasers in manufacturing, proceeding of the third international WLT—conference on lasers in manufacturing. pp. 695–670
  94. Sun Z, Kuo M, 1998, Bridging the joint gap with wire feed laser welding, J Mater Process Technol, 87:213–222
  95. Liu X-B, Yu G,Guo J, Gu Y-J, Pang M, Zheng C-Y, Wang H-H, 2008, Research on laser welding of cast Ni-based superalloy K418 turbo disk and alloy steel 42CrMo shaft, J Alloy Comp, 453(1–2):371–378.
  96. Huang Q, Hagstroem J, Skoog H, Kullberg G, 1991, Effect of CO2 laser parameter variations on sheet metal welding, International Journal for the Joining of Materials, 3(3):79–88
  97. Juang SC, Tarng YS, 2002, Process parameter selection for optimizing the weld pool geometry in the tungsten inert gas welding of stainless steel, J Mater Process Technol, 122:33–37
  98. Marya M, Edwards G, Marya S, Olson DL, 2001, Fundamentals in the fusion welding of magnesium and its alloys. In: Proceedings of the seventh JWS international symposium. pp. 597–602.
  99. Haferkamp H, Niemeyer M, Dilthey U, Trager G, 2000, Laser and electron beam welding of magnesium materials, Weld Cutt 52(8):178–80.
  100. Haferkamp H, Bach Fr-W, Burmester I, Kreutzburg K, Niemeyer M, 1996, Nd:YAG laser beam welding of magnesium constructions. In: Proceedings of the third international magnesium conference. pp. 89–98.
  101. Benyounis KY, Olabi AG, Hashmi MSJ, 2005, Effect of laser welding parameters on the heat input and weld-bead profile, J Mater Process Technol, 164-165:978–985.
  102. Manonmani K, Murugan N, Buvanasekaran G, 2007, Effects of process parameters on the bead geometry of laser beam butt welded stainless steel sheets, J Adv Manuf Technol, 32(11-12):1125-1133.
  103. Elangovan K, Balasubramanian V, 2008, Developing an empirical relationship to predict tensile strength of friction stir welded AA2219 aluminium alloy joints, J Mater Eng Perform, 17:820–830.
  104. Benyounis KY, Olabi AG, Hashmi MSJ, 2008, Multi-response optimization of CO2 laser-welding process of austenitic stainless steel, Opt Laser Technol 40:76-87.
  105. Moradi M, Ghoreishi M, 2010, Influences of laser welding parameters on the geometric profile of NI-base superalloy Rene 80 weld-bead, Int J Adv Manuf Technol, doi: 10.1007/s00170-010-3036-1.
  106. Padmanaban G, Balasubramanian V, 2010, Optimization of laser beam welding process parameters to attain maximum tensile strength in AZ31B magnesium alloy, Opt Laser Technol, 42:1253–1260
  107. Rajakumar S, Muralidharan C, Balasubramanian V, 2010, Optimization of the friction-stir-welding process and the tool parameters to attain a maximum tensile strength of AA7075-T6 aluminium alloy, J Eng Manuf, 224:1175–1191.
  108. Ruggiero A, Tricarico L, Olabi AG, Benyounis KY, 2011, Weld-bead profile and costs optimization of the CO2 dissimilar laser welding process of low carbon steel and austenitic steel AISI316, Opt Laser Technol, 43:82–90.
  109. Myers RH, Montgomery DC, 2002, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York.
  110. Robinson TJ, Wulff SS, 2006, Response surface approaches to robust parameter design. In: Khuri AI (ed) Response surface methodology and related topics, World Scientific, Singapore, pp. 123-157.
  111. Gunaraj V, Murugan N, 1999, Application of response surface methodologies for predicting weld base quality in submerged arc welding of pipes, J Mater Process Technol, 88:266–275.
  112. Design-ExpertSoftware,V7, 2005, User’s guide: Technical Manual, Minneapolis, MN: Stat-Ease Inc.
  113. Zulkali MMD, Ahmad AL, Norulakmal NH, 2006, Oryza sativa L. husk as heavy metal adsorbent: optimization with lead as model solution, Bioresource Technology, 97:21–25.
  114. Cui C, Hu J, Gao K, Pang S, Yang Y, Wang H, Guo Z, 2008, Effects of process parameters on weld metal keyhole characteristics with CO2 laser butt welding, Lasers in Engineering, 18:319–327.
  115. Mackwood A.P., Crafer R.C., 2005, Thermal modelling of laser welding and related processes: a literature review, Optics & Laser Technology, 37:99– 115.
  116. Chang W. S., Na S.J., 2002, A study on the prediction of the laser weld shape with varying heat source equations and the thermal distortion of a small structure in micro-joining, Journal of Material Processing Technology, 120:208 – 214.
  117. Goldak J. A., Chakravarti M. B., 1984, A new finite element model for welding heat source, Metallurgical and Materials Transactions B, 15B:299–305.
  118. Su W., Haiyan Z., Yu W., Xiaohong Z., 2004, A new heat source model in numerical simulation of high energy beam welding, Transaction China Welding Institute, 25:91–94.
  119. Kazemi K., Goldak J. A., 2009, Numerical simulation of laser full penetration welding, Computational Materials Science, 44:841–849
  120. Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2012, Some studies on weld bead geometries for laser spot welding process using finite element analysis, Materials and Design, 34:412–426
  121. Balasubramanian K.R., Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2008, Numerical and experimental investigation of laser beam welding of AISI 304 stainless steel sheet, Advances in Production Engineering and Management, 3(2):93–105
  122. Sabbaghzadeh J., Azizi M., Torkamany M.J., 2008, Numerical and experimental investigation of seam welding with a pulsed laser. Journal of Optics and Laser Technology, 40:289–296
  123. Kruth J.P., Froyen L., Rombouts M., Van Vaerenbergh J., Mercells P., 2003, New Ferro Powder for Selective Laser Sintering of Dense Parts, CIRP Annals – Manufacturing Technology, 52/1: 139–142.
  124. Romoli L., Tantussi G., Dini G., 2007, Layered Laser Vaporization of PMMA Manufacturing 3D Mould Cavities, CIRP Annals -Manufacturing Technology, 56/1: 209-212.
  125. Vollertsen F., Walther R., 2008, Energy balance in laser-based free form heading, CIRP Annals – Manufacturing Technology 57/1: 291–294.
  126. Mills K.C., Su Y., Li Z., Brooks R.F., 2004, Equations for the Calculation of the Thermo-physical Properties of Stainless Steel, ISIJ International, Vol. 44, No. 10, pp. 1661–1668.
  127. Khan M.M.A., Romoli L., Fiaschi M., Sarri F., Dini G., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Materials Processing Technology, Volume 210, Issue 10, pp. 1340-1353.

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
  • 이메일 : flow3d@stikorea.co.kr

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.

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Figure 1.37: Scour amplification factor for spill-through abutments and clear-water conditions (Ettema et al. 2010)

교각 세굴 깊이 예측 정확도의 핵심: CFD로 밝혀낸 토질 매개변수의 영향

이 기술 요약은 Iqbal Singh Budwal이 2021년 워털루 대학교(University of Waterloo)에 제출한 석사 학위 논문 “Influence of Soil Parameters on Local Pier Scour Depth”를 기반으로 하며, STI C&D에서 기술 전문가를 위해 분석 및 요약했습니다.

키워드

  • Primary Keyword: 교각 세굴 깊이
  • Secondary Keywords: 토질 매개변수, CFD 시뮬레이션, 교량 안전, SSIIM, 수치 모델링, 세굴 예측

Executive Summary

  • 도전 과제: 현재 사용되는 교각 세굴 예측 방법들은 중요한 토질 매개변수를 간과하여 부정확한 설계와 잠재적인 교량 붕괴로 이어질 수 있습니다.
  • 연구 방법: CFD 소프트웨어(SSIIM)를 사용한 포괄적인 수치 연구를 통해 토양의 입자 크기, 안식각, 점착력이 교각 세굴 깊이에 미치는 영향을 체계적으로 분석했습니다.
  • 핵심 발견: 토양의 안식각과 점착력은 세굴 깊이에 극적인 영향을 미치는 것으로 나타났으며, 이들 변수의 변화는 세굴 깊이를 각각 100% 및 90% 이상 변화시켰습니다.
  • 핵심 결론: 안전하고 비용 효율적인 교량 설계를 위해서는 상세한 토질 매개변수를 세굴 분석에 반드시 포함해야 하며, CFD 시뮬레이션은 이를 위한 가장 효과적인 도구입니다.
Figure 1.3: Flow and scour at single pier (Akib et al. 2014)
Figure 1.3: Flow and scour at single pier (Akib et al. 2014)

도전 과제: 이 연구가 CFD 전문가에게 중요한 이유

교량 세굴(Scour)은 교량 붕괴의 가장 주된 원인으로 지목됩니다. 흐르는 물이 교각 주변의 하상 퇴적물을 침식시키면서 기초의 지지력을 약화시키기 때문입니다. 따라서 교각의 최대 세굴 깊이를 정확하게 예측하는 것은 교량의 안전성과 경제성을 확보하는 데 매우 중요합니다.

하지만 현재까지 널리 사용되는 세굴 깊이 예측 방법들은 대부분 실험실 데이터에 기반한 경험식에 의존하고 있습니다. 이러한 경험식들은 다음과 같은 근본적인 한계를 가집니다.

  1. 스케일링 효과: 실험실의 축소 모델에서 얻은 결과는 실제 크기의 교각에 적용될 때 오차를 유발합니다.
  2. 제한된 변수: 대부분의 공식은 유속, 수심, 교각 폭과 같은 유체 및 구조적 요인에만 초점을 맞춥니다.
  3. 토질 매개변수 무시: 토양의 입자 크기(D50) 외에, 침식 저항성에 결정적인 영향을 미치는 안식각(angle of repose)이나 점착력(cohesion)과 같은 중요한 토질 매개변수들이 대부분 무시됩니다.

이러한 한계로 인해 기존의 예측은 실제보다 과도하게 보수적이어서 불필요한 건설 비용을 증가시키거나, 반대로 세굴 깊이를 과소평가하여 교량의 안전을 심각하게 위협할 수 있습니다. 본 연구는 이러한 지식의 격차를 해소하고, 특히 중요한 토질 매개변수가 세굴 깊이에 미치는 영향을 정량적으로 분석하여 보다 신뢰성 높은 예측 방법론의 필요성을 제시합니다.

연구 접근법: 방법론 분석

본 연구는 실제 현장 계측의 어려움과 실험실 연구의 스케일링 한계를 극복하기 위해 수치 시뮬레이션, 특히 CFD(전산 유체 역학) 접근법을 채택했습니다. 연구에 사용된 주요 도구는 퇴적물 이동 해석 기능이 내장된 오픈 소스 CFD 소프트웨어인 SSIIM(Sediment Simulation in Intakes with Multiblock option)입니다.

연구는 다음 두 단계로 진행되었습니다.

  1. 수치 모델 검증: 먼저, 기존에 발표된 신뢰성 있는 실험 연구(고정상 및 이동상 조건)의 결과와 SSIIM 시뮬레이션 결과를 비교하여 모델의 정확도를 검증했습니다. 이를 통해 유동장, 전단 응력, 최대 세굴 깊이 예측에 대한 모델의 신뢰성을 확보했습니다.
  2. 매개변수 연구: 검증된 모델을 사용하여 대규모 매개변수 연구를 수행했습니다. 총 128개의 시뮬레이션 케이스를 통해 다음과 같은 주요 변수들의 영향을 체계적으로 분석했습니다.
    • 구조적 요인: 4가지 다른 직경의 원형 교각 (0.1m, 0.25m, 0.5m, 0.8m)
    • 유동 요인: 2가지 다른 유속 강도 (I=0.5, 0.75)
    • 토질 요인: 16가지 다른 토질 조건 (상이한 입자 크기, 안정 경사각, 점착력)

이 체계적인 접근법을 통해 각 토질 매개변수가 다른 구조 및 유동 조건 하에서 세굴 깊이에 미치는 영향을 독립적으로 정량화할 수 있었습니다.

핵심 발견: 주요 결과 및 데이터

매개변수 연구를 통해 기존 경험식들이 간과해왔던 토질 매개변수들이 교각 세굴 깊이에 얼마나 지대한 영향을 미치는지 명확히 밝혀졌습니다.

결과 1: 안정 경사각(안식각)의 극적인 영향

토양 입자가 무너지지 않고 쌓일 수 있는 최대 각도인 안정 경사각(안식각)은 세굴 구멍의 형태와 깊이를 결정하는 핵심 요소였습니다. 기준값인 30°와 비교했을 때, 안정 경사각의 변화는 세굴 깊이에 엄청난 변화를 가져왔습니다.

논문의 표 3.7에 따르면, 안정 경사각이 30°에서 40°로 증가했을 때 세굴 깊이는 평균 145.1%까지 증가했으며, 20°로 감소했을 때는 평균 41.9% 감소했습니다. 이는 안식각이 큰 토양일수록 더 깊고 가파른 세굴이 발생할 수 있음을 의미하며, 이 매개변수를 무시하는 것은 예측에 심각한 오차를 유발할 수 있음을 보여줍니다.

Figure 1.37: Scour amplification factor for spill-through abutments and clear-water conditions (Ettema et al. 2010)
Figure 1.37: Scour amplification factor for spill-through abutments and clear-water conditions (Ettema et al. 2010)

결과 2: 미소한 점착력의 막대한 세굴 억제 효과

모래에 점토나 실트 같은 미세 입자가 섞여 발생하는 점착력 또한 세굴 깊이를 결정하는 중요한 변수임이 확인되었습니다. 시뮬레이션 결과, 아주 작은 양의 점착력만으로도 토양의 침식 저항성이 크게 증가했습니다.

논문의 표 3.8에 따르면, 불과 0.5 Pa의 점착력이 추가되었을 때 세굴 깊이가 평균 90.9% 감소하는 것으로 나타났습니다. 이는 점착력을 고려하지 않는 현재의 설계 방식이 실제보다 훨씬 과도한 세굴 깊이를 예측하여 막대한 비용 낭비를 초래할 수 있음을 시사합니다.

R&D 및 운영을 위한 실질적 시사점

본 연구 결과는 교량 설계, 시공 및 유지관리와 관련된 다양한 분야의 전문가들에게 중요한 시사점을 제공합니다.

  • 공정/토목 엔지니어: 현장별 토질 데이터(특히 안식각, 점착력) 없이 표준 경험식에만 의존하는 것은 매우 위험합니다. CFD 시뮬레이션은 이러한 현장 고유의 특성을 설계에 반영하여 신뢰도를 높일 수 있는 강력한 도구를 제공합니다.
  • 품질 관리/지반 공학팀: 본 연구는 상세한 지반 조사의 중요성을 강조합니다. 안식각과 점착력 측정은 단순한 절차가 아니라, 정확한 세굴 위험 평가를 위한 핵심 입력 데이터입니다.
  • 설계 엔지니어: 연구 결과는 교량 기초 설계에 직접적인 영향을 미칩니다. 이러한 토질 매개변수를 고려하면 과소 설계(붕괴 위험)와 과대 설계(불필요한 비용)를 모두 피하고, 안전하면서도 경제적인 설계를 달성할 수 있습니다.

논문 상세 정보

Influence of Soil Parameters on Local Pier Scour Depth

1. 개요:

  • 제목: Influence of Soil Parameters on Local Pier Scour Depth (국부 교각 세굴 깊이에 대한 토질 매개변수의 영향)
  • 저자: Iqbal Singh Budwal
  • 발행 연도: 2021
  • 발행 학술지/학회: A thesis presented to the University of Waterloo (워털루 대학교 제출 석사 학위 논문)
  • 키워드: Bridge scour, pier scour, soil parameters, numerical simulation, SSIIM, cohesion, angle of repose

2. 초록:

교량 세굴은 교량 기초 주변의 퇴적층이 해류, 파랑, 난류로 인해 발생하는 유체력에 의해 침식되는 현상이다. 교각, 말뚝, 교대와 같은 기초 구성 요소 주변의 세굴은 구조적 불안정성과 붕괴 가능성을 초래할 수 있다. 세굴은 교량 붕괴의 주요 원인으로 기록되어 왔으며, 따라서 안전하고 비용 효율적인 교량 설계를 위해서는 세굴의 예측, 모니터링 및 완화가 가장 중요하다. 현재 교각 세굴 추정 방법은 계산에서 토질 매개변수에 대한 정보를 적절히 사용하지 않는다. 그러나 토질 매개변수는 다른 요인들 중에서도 세굴 과정에서 중요한 역할을 한다. 토질 매개변수 입력을 무시하면 교각 세굴 깊이를 상당히 과소평가하게 되고, 과도하게 비싼 교량 기초 설계로 이어진다. 더 정확한 세굴 예측 방법을 개발하기 위해서는 입도 분포, 광물 구성, 점착력, 안식각, 공극비와 같은 토질 매개변수의 영향을 체계적으로 조사하고 이를 세굴 예측 방정식에 통합하기 위한 매개변수 연구가 필요하다. 대부분의 발표된 세굴 연구는 축소된 실험실 실험을 활용했지만, 수치 시뮬레이션을 사용한 세굴 연구도 일부 제한적으로 이루어졌다. 수치 연구는 비용이 적게 들고 체계적인 매개변수 연구를 통해 다양한 시나리오를 조사할 기회를 제공한다.

본 논문에서는 기존 교량 세굴 이론 및 세굴 추정 방법에 대한 포괄적인 검토를 수행한다. 이어서 SSIIM 소프트웨어를 사용하여 교각 세굴의 수치 시뮬레이션을 수행한다. SSIIM을 사용하여 퇴적물 매개변수가 교각 세굴에 미치는 영향을 정량화하고 가장 적절한 세굴 예측 방법에 대한 권장 사항을 제공하기 위해 매개변수 연구를 수행한다. 본 논문에서 수행된 검토는 제어 메커니즘 및 교량에서 발생하는 세굴 유형을 포함한 기존 세굴 문헌을 다룬다. 관련 토양, 유체 및 구조적 요인과 세굴에 미치는 영향을 조사한다. 세굴에 가장 영향력 있는 토양 매개변수는 입자 크기, 안식각, 점착력으로 밝혀졌다. 그러나 현재 경험적 방법에서 고려되는 유일한 토양 매개변수는 입자 크기 또는 입도이다. 또한 평형 세굴 깊이와 세굴 속도를 추정하는 데 사용되는 일반적인 경험적 방정식에 대해 자세히 논의한다. 검토는 실험실 규모 연구, 수치 모델링, 그리고 인공 신경망과 같은 소프트 컴퓨팅 기술을 다룬다. 세굴 모니터링 기술과 세굴 완화를 위한 대책에 대한 간략한 논의도 이루어진다.

3. 서론:

교량에서의 세굴 과정과 영향을 이해하는 것은 안전하고 효율적인 엔지니어링 설계에 필수적이다. 세굴은 유체력으로 인해 해양 구조물 주변의 퇴적층 물질이 침식되거나 제거되는 것으로 정의된다. 시간이 지남에 따라 세굴 과정은 교량의 측면 저항력을 약화시키며, 교량 붕괴의 약 60%를 차지하는 원인이었다. Wardhana와 Hadiprio(2003)는 1989년에서 2000년 사이 미국에서 발생한 500건의 교량 붕괴 원인을 조사하여 주된 원인을 파악했다. 홍수와 세굴이 가장 큰 기여 요인으로, 교량 붕괴의 48.31%를 차지했다. 심각한 세굴은 유효 기초 깊이를 감소시키고 기초 푸팅을 노출시킨다. 본 장에서는 교량 기초에서의 세굴 속도와 평형 깊이를 예측하는 데 사용되는 이론과 방법을 논의한다. 토양, 유체, 구조물 간의 상호작용이 세굴 현상을 유발하고 제어한다. 이 세 가지 요소에서 비롯된 요인들의 영향과 상호작용을 연구하는 것은 교량 세굴을 이해하는 데 매우 중요하다. 실험실 테스트, 수치 시뮬레이션, 다양한 데이터 기반 알고리즘이 세굴 발생 방식과 추정 최적 관행을 조사하는 데 사용되어 왔다.

4. 연구 요약:

연구 주제의 배경:

교각 세굴은 교량 안전을 위협하는 가장 큰 요인 중 하나이다. 기존의 세굴 깊이 예측 공식들은 주로 유체역학적 변수와 구조물의 기하학적 형태에만 집중하며, 세굴 저항성의 핵심인 토질의 공학적 특성을 제대로 반영하지 못하는 한계가 있다. 이로 인해 예측의 정확도가 떨어져 과소 또는 과대 설계의 문제가 발생한다.

이전 연구 현황:

과거 연구들은 대부분 실험실 수조 실험을 통해 경험식을 개발하는 데 중점을 두었다. 일부 연구에서 토질의 입자 크기(D50)나 입도 분포를 고려했지만, 안식각이나 점착력과 같은 중요한 매개변수들은 거의 다루어지지 않았다. 최근 수치 모델링(CFD) 기술이 발전하면서 세굴 현상을 모사하려는 시도가 있었으나, 유체와 퇴적물 간의 복잡한 상호작용을 정확히 모델링하는 데에는 여전히 어려움이 있다.

연구 목적:

본 연구의 목적은 다음과 같다. 1. 수치 시뮬레이션을 통해 기존에 간과되었던 주요 토질 매개변수(안식각, 점착력)가 교각 세굴 깊이에 미치는 영향을 정량적으로 분석한다. 2. 시뮬레이션 결과를 바탕으로 현재 널리 사용되는 12개의 경험적 세굴 예측 공식의 성능을 평가한다. 3. 가장 정확하고 안전한 예측 방법을 제시하고, 향후 수치 모델링의 개선 방향을 논의한다.

핵심 연구:

본 연구는 CFD 소프트웨어 SSIIM을 사용하여 총 128가지 조건에 대한 교각 세굴 시뮬레이션을 수행했다. 4가지 다른 교각 직경과 2가지 유속 조건 하에서, 3가지 핵심 토질 매개변수인 입자 크기(D50), 안정 경사각, 점착력을 체계적으로 변화시키며 최대 세굴 깊이를 계산했다. 이 결과를 통해 각 매개변수의 민감도를 분석하고, 기존 경험식들의 예측 오차(SSE, UE)를 정량적으로 평가했다.

5. 연구 방법론

연구 설계:

본 연구는 수치 시뮬레이션을 기반으로 한 매개변수 연구로 설계되었다. 먼저 SSIIM 소프트웨어의 신뢰성을 확보하기 위해, 기존에 발표된 3가지 실험 연구(Roulund et al. 2005, Melville 1975, Ahmed and Rajaratnam 1998)의 결과를 수치적으로 재현하고 비교하는 검증 단계를 거쳤다. 검증 후, 교각 직경, 유속, 토질 매개변수를 조합한 총 128개의 가상 시나리오를 설정하여 매개변수 연구를 수행했다.

데이터 수집 및 분석 방법:

  • 데이터 생성: SSIIM 2.0 소프트웨어를 사용하여 각 시나리오에 대한 3차원 CFD 및 퇴적물 이동 시뮬레이션을 수행했다. 시간에 따른 세굴 깊이 변화를 기록하고, 최종 평형 세굴 깊이를 도출했다.
  • 데이터 분석: 시뮬레이션으로 얻은 최대 세굴 깊이 데이터를 12개의 주요 경험식으로 계산한 예측값과 비교했다. 분석 지표로는 총 제곱 오차 합(SSE)과 과소예측 오차(UE)를 사용하여 각 공식의 정확성과 안전성을 평가했다. 또한, 안정 경사각과 점착력 변화에 따른 세굴 깊이의 변화율을 계산하여 그 영향을 정량화했다.

연구 주제 및 범위:

  • 연구 주제: 원형 단일 교각 주변에서 발생하는 국부 세굴(Local Pier Scour)
  • 연구 범위:
    • 유동 조건: 유사 이동이 없는 청수 세굴(Clear-water scour) 조건
    • 토질: 균일한 입경의 깨끗한 모래(Clean sands)
    • 주요 변수: 교각 직경(4종), 유속 강도(2종), 토질 입자 크기(10종), 안정 경사각(5종), 점착력(5종)

6. 주요 결과:

주요 결과:

  • 안정 경사각의 영향: 안정 경사각은 세굴 깊이에 지대한 영향을 미쳤다. 기준 각도 30° 대비 40°에서는 세굴 깊이가 최대 +145.1% 증가했고, 20°에서는 최대 -41.9% 감소했다.
  • 점착력의 영향: 소량의 점착력(0.5 Pa)만으로도 세굴 깊이가 평균 90.9% 감소하여, 점착력이 세굴을 억제하는 데 매우 효과적임을 확인했다.
  • 경험식 성능 평가: 12개 경험식 중 TAMU(Texas A&M University) 방법이 과소예측 없이 SSIIM 결과와 가장 근접한 예측을 제공하여 최상의 성능을 보였다. 반면, 일부 널리 사용되는 공식들은 특정 조건에서 세굴 깊이를 심각하게 과소예측할 위험이 있었다.
  • 수치 모델링의 한계 및 가능성: SSIIM은 최대 세굴 깊이를 성공적으로 예측했지만, 미세 입자의 초기 침식률 모사나 안식각 효과를 통합적으로 모델링하는 데에는 한계를 보였다. 이는 향후 더 정교한 퇴적물 수치 모델 개발의 필요성을 시사한다.
Figure 3.19: Model 3b scour depth versus D50 with empirical equations
Figure 3.19: Model 3b scour depth versus D50 with empirical equations

Figure List:

  • Figure 1.1: Scoured bridge foundation (MTO 1997)
  • Figure 1.2: Flow and scouring at a contraction (MTO 1997)
  • Figure 1.3: Flow and scour at single pier (Akib et al. 2014)
  • Figure 1.4: Flow and local scour at abutment (Richardson and Davis 2001)
  • Figure 1.5: Live-bed and clear-water scour over time (Richardson and Davis 2001)
  • Figure 1.6: Live-bed and clear-water scour comparison on time (Melville 1999)
  • Figure 1.7: Forces acting on a bed sediment particle (Van Rijn 1993)
  • Figure 1.8: Difference between scour in sands and clays (Wang et al. 2017)
  • Figure 1.9: Critical shear stress as a function of mean grain size (Briaud et al. 2011)
  • Figure 1.10: Critical velocity as a function of mean grain size (Briaud et al. 2011)
  • Figure 1.11: Erosion rates versus flow velocity for soils (Briaud et al. 2011)
  • Figure 1.12: Erosion rates versus applied shear stress for soils (Briaud et al. 2011)
  • Figure 1.13: Erosion function plot from EFA (Briaud et al. 2001a)
  • Figure 1.14: EFA detail (Briaud et al. 2001a)
  • Figure 1.15: Open channel flow profile (Van Rijn 1993)
  • Figure 1.16: Channel velocity profile (Van Rijn 1993)
  • Figure 1.17: Wave and current coupled scour at a monopile (Qi and Gao 2014)
  • Figure 1.18: Compound pier shapes (Whitehouse 2004)
  • Figure 1.19: Single pile, pile group, and complex foundation example (Wang et al. 2017)
  • Figure 1.20: States of scour at complex piers due to elevations (Ataie-Ashtiani et al. 2010)
  • Figure 1.21: Flow around scoured abutment (Barbhuiya and Dey 2004)
  • Figure 1.22: Abutment scour in a compound channel (Richardson and Davis 2001)
  • Figure 1.23: Abutment shapes (Richardson and Davis 2001)
  • Figure 1.24: Competent velocity method design chart for critical velocity (MTO 1997)
  • Figure 1.25: RTAC guide to bridge hydraulics (1973) method (MTO 1997)
  • Figure 1.26: CSU (1977) method pier shape and angle of attack factors (MTO 1997)
  • Figure 1.27: Flow alignment correction factor (Melville and Sutherland 1988)
  • Figure 1.28: HEC-18, HEC-20, and HEC-23 manual summary chart (Richardson and Davis 2001)
  • Figure 1.29: Sediment fall velocity versus grain size (Richardson and Davis 2001)
  • Figure 1.30: Florida DOT pier scour curve (Richardson and Davis 2001)
  • Figure 1.31: FHWA pier debris dimensions (Richardson and Davis 2001)
  • Figure 1.32: Rock quarrying scour around bridge pier (Richardson and Davis 2001)
  • Figure 1.33: Pier scour in rock as a function Pc and GSN (Richardson and Davis 2001)
  • Figure 1.34: Abutment orientation angle (Richardson and Davis 2001)
  • Figure 1.35: Scour amplification factor for spill-through abutments and live-bed conditions (Ettema et al. 2010)
  • Figure 1.36: Scour amplification factor for wingwall abutments and live-bed conditions (Ettema et al. 2010)
  • Figure 1.37: Scour amplification factor for spill-through abutments and clear-water conditions (Ettema et al. 2010)
  • Figure 1.38: Scour amplification factor for wingwall abutments and clear-water conditions (Ettema et al. 2010)
  • Figure 1.39: Normalized scour depth versus flow intensity (Sheppard and Miller 2006)
  • Figure 1.40: Angle of attack correction factor (Breusers 1977)
  • Figure 1.41: Abutment alignment angle factor (Melville 1992)
  • Figure 1.42: Pier and abutment classifications (Melville 1997)
  • Figure 1.43: Influence of flow intensity on equilibrium time scale (Melville and Chiew 1999)
  • Figure 1.44: Example test results of scour depth versus time (Briaud et al. 1999)
  • Figure 1.45: Projected width of rectangular pier (Briaud et al. 2004)
  • Figure 1.46: Scour hole shape at rectangular piers (Briaud et al. 2004)
  • Figure 1.47: Contraction scour details (Briaud et al. 2005)
  • Figure 1.48: Location of maximum contraction scour (Briaud et al. 2005)
  • Figure 1.49: Abutment parameter details (Briaud 2015a)
  • Figure 1.50: Pier scour equation relationship comparison (Richardson and Davis 2001)
  • Figure 1.51: Underprediction error of dimensional scour depth versus total error for laboratory data (Sheppard et al. 2014)
  • Figure 1.52: Underprediction error of dimensionless scour depth versus total error for laboratory data (Sheppard et al. 2014)
  • Figure 1.53: Underprediction error of field dimensional scour depth versus total error for laboratory data (Sheppard et al. 2014)
  • Figure 1.54: Underprediction error of field dimensionless scour depth versus total error for laboratory data (Sheppard et al. 2014)
  • Figure 1.55: Comparisons of equations with laboratory scour measurements: (a) 65-1R; (b) 65-2; (c) HEC-18 4th;(d) Melville and Sutherland (1988); (e) Melville (1997) (Qi et al., 2016)
  • Figure 1.56: Comparisons of equations with field scour measurements: (a) 65-1R; (b) 65-2; (c) HEC-18 4th; (d) HEC-18 5th; (e) Melville and Sutherland (1988); (f) Melville (1997) (Qi et al., 2016)
  • Figure 1.57: Numerical model boundaries of flow around a pile (Roulund et al. 2005)
  • Figure 1.58: Numerical model of scour hole around a bridge pier (Afzal et al. 2015)
  • Figure 1.59: Particle modeling approaches at different time and length scales (Zhu et al. 2007)
  • Figure 1.60: Three-layer artificial neural network structure (Lee et al. 2007)
  • Figure 1.61: Circular and hooked collars for piers (Chen et al. 2018)
  • Figure 2.1: Case 1 model mesh and boundary conditions
  • Figure 2.2: Shields diagram example (Vanoni 1975)
  • Figure 2.3: Case 1 Velocity profiles flow development
  • Figure 2.4: Case 1 velocity profiles pier influence
  • Figure 2.5: Case 1 rigid bed horizontal velocities
  • Figure 2.6: Case 1 rigid bed vertical velocities
  • Figure 2.7: Case 1 bed shear stress amplification (a) Roulund et al. (2005) (b) Hjorth (1975)
  • Figure 2.8: Case 1 bed shear stress amplification around pier in SSIIM
  • Figure 2.9: Case 1 bed shear stress amplification comparison (a) Roulund et al. (2005) (b) Hjorth (1975)
  • Figure 2.10: Case 2 upstream horizontal velocity profiles
  • Figure 2.11: Case 2 experimental bed shear stress contour (Melville 1975) (flow towards left)
  • Figure 2.12: Case 2 bed shear stress contour comparison with Melville (1975) (Salaheldin et al. 2004)
  • Figure 2.13: Case 2 bed shear stress in SSIIM (flow towards right)
  • Figure 2.14: Case 2 bed shear stress in SSIIM compared with Melville (1975) (flow towards left)
  • Figure 2.15: Case 3 upstream horizontal velocity profiles
  • Figure 2.16: Case 3 Upstream vertical velocity profiles
  • Figure 2.17: Case 2 soil gradation (Melville 1975)
  • Figure 2.18: Case 2 experiment scour hole (upstream face view) (Melville 1975)
  • Figure 2.19: Case 2 SSIIM scour holes for Test A (left) and Test b (right) (flow towards right)
  • Figure 2.20: Case 2 experimental scour hole depth contours (units: cm) (Melville 1975)
  • Figure 2.21: Case 2 SSIIM scour hole depth contours (units: m) (Test A left and Test B right)
  • Figure 2.22: Case 2 scour depth over time
  • Figure 2.23: Case 2 scour hole cross section (view from upstream)
  • Figure 2.24: Case 2 scour hole longitudinal section (flows toward left)
  • Figure 2.25: Case 2 coarse grid SSIIM scour hole depth contours (units: m)
  • Figure 2.26: Case 2 20-layer grid SSIIM scour hole depth contours (units: m)
  • Figure 2.27: Case 2 Brooks (1963) uphill parameter test
  • Figure 2.28: Case 2 Brooks (1963) downhill parameter test
  • Figure 2.29: Case 3 SSIIM scour hole (flows to right)
  • Figure 2.30: Case 3 SSIIM Scour Hole Contour (Units: m)
  • Figure 2.31: Case 3 Scour Depth over Time
  • Figure 2.32: Case 3 scour hole longitudinal section (flows toward left)
  • Figure 2.33: Case 4 SSIIM scour hole (flows to right)
  • Figure 2.34: Case 4 SSIIM scour hole contour (units: m)
  • Figure 2.35: Case 4 scour depth over time
  • Figure 2.36: Case 4 scour hole longitudinal section (flows toward left)
  • Figure 3.1: Inlet and outlet erosion in model 1b (flow towards right)
  • Figure 3.2: Model 1a scour depth versus time
  • Figure 3.3: Model 1b scour depth versus time
  • Figure 3.4: Model 2a scour depth versus time
  • Figure 3.5: Model 2b scour depth versus time
  • Figure 3.6: Model 3a scour depth versus time
  • Figure 3.7: Model 3b scour depth versus time
  • Figure 3.8: Model 4a scour depth versus time
  • Figure 3.9: Model 4b scour depth versus time
  • Figure 3.10: Scour depth versus time for D50 = 1 mm
  • Figure 3.11: Scour depth versus time for D50 = 0.05 mm
  • Figure 3.12: Scour depth versus stable slope angle for all models
  • Figure 3.13: Scour depth versus D50 for all models
  • Figure 3.14: Model 1a scour depth versus D50 with empirical equations
  • Figure 3.15: Model 1b scour depth versus D50 with empirical equations
  • Figure 3.16: Model 2a scour depth versus D50 with empirical equations
  • Figure 3.17: Model 2b scour depth versus D50 with empirical equations
  • Figure 3.18: Model 3a scour depth versus D50 with empirical equations
  • Figure 3.19: Model 3b scour depth versus D50 with empirical equations
  • Figure 3.20: Model 4a scour depth versus D50 with empirical equations
  • Figure 3.21: Model 4b scour depth versus D50 with empirical equations
  • Figure 3.22: Scour depth versus stable slope angle for all models
  • Figure 3.23: SSE and UE for empirical pier scour equations
  • Figure 3.24: Live bed scour in model 1b

7. 결론:

본 논문은 교량 기초에서 발생하는 수축 및 국부 세굴에 대한 검토를 다루었다. 세굴 이론과 예측 방법은 영향 요인과 함께 상세히 논의되었다. 연구 범위는 교각에서의 국부 세굴 깊이 예측을 다루는 데 초점을 맞췄다. 교량 세굴 예측을 위한 기존 방법의 주요 격차는 입자 크기 이외의 토질 매개변수를 고려하지 않는다는 점이었다. Sheppard/Melville(2011) 및 HEC-18 방정식과 같은 방법은 좋은 성능을 보였지만, 토질 매개변수를 통합함으로써 크게 개선될 수 있다. 발표된 문헌을 검토한 결과, 세굴에 가장 중요한 토질 매개변수는 입자 크기, 입도, 점착력, 안식각임이 밝혀졌다. 이러한 토질 매개변수들은 운동 시작, 침식 거동, 그리고 교각에서의 최대 세굴 깊이를 제어하는 세굴 구멍의 모양을 제어하는 것으로 밝혀졌다. 더욱이, 대부분의 방법은 제한된 실험 시나리오에서 파생되었으며, 이로 인해 더 큰 구조물로 현장 세굴을 예측할 때 스케일링 효과가 부정확성을 유발한다. 따라서 현재의 설계 방법은 세굴을 과도하게 예측하여 비싼 건설 비용을 초래하는 경향이 있다. 또한, 토질 매개변수 입력의 부족은 세굴 깊이의 과소예측으로 이어져 세굴이 교량 붕괴의 가장 흔한 원인이 되었다. 더 나은 세굴 예측 방법을 개발하기 위해서는 토질 매개변수가 세굴 깊이에 미치는 영향에 대한 추가 연구가 필요했다.

8. 참고 문헌:

  1. Lancaster, J. F., 1984, The physics of welding, Physics in Technology, 15:73-79.
  2. Kou, S., 2003, Fusion welding processes, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.3-36.
  3. Steen, W.M., Mazumder, J., 2010, Laser welding: laser material processing, 4th Ed., Springer-Verlag London Limited, UK, pp. 199-250.
  4. Merchant, V., Laser beam welding, In: Ahmed, N., editor, New developments in advanced welding, 1st Ed., Woodhead Publishing Limited, Cambridge, UK, pp. 83-84.
  5. Kugler, T.R., 2001, Fusion front penetration: Conduction Welding, In: Ready, J.F., editor, LIA handbook of laser materials processing, 1st Ed., Magnolia Publishing Inc., FL, USA, pp. 310-312.
  6. Matsunawa, A., 2002, Science of laser welding-mechanisms of keyhole and pool dynamics. In: ICALEO 2002 proceedings, Phoenix, LIA, Orlando, paper: 101.
  7. Lacroix, D., Jeandel, G., Boudot, C., 1996, Spectroscopic studies of laser-induced plume during welding with a Nd:YAG laser, In: Proceedings of SPIE, 2789, pp. 221–227.
  8. Dumord, E., Jouvard, J.M., Grevey, D., 1996, Keyhole modeling during CW Nd:YAG laser welding, In: Proceedings of SPIE, 2789, pp. 213–220.
  9. Berkmanns, J., Faerber, M., 2005, Facts about laser technology: laser welding, http://www.laserdeal.com/, access date: January 20, 2012.
  10. Coherent Inc., 2004, High speed welding of metals with diamond CO2 laser – stainless steels, Technical Note, http://www.coherent.de/, access date: November 15, 2011.
  11. LWS, 2006, A technical report on the LWS flexcell cladding system, http://www.laserweldingsolutions.com/, access date: April 01, 2009.
  12. Shannon, G., 2009, Source selection for laser welding, http://www.industrial-lasers.com/, access date: April 01, 2009.
  13. Faerber, M., Berkmanns, J., 1996, Gases for increased laser welding productivity, In: Proceedings of the ISATA Conference, pp. 791–798.
  14. Schuberth S, Schedin E, Fröhlich T, Ratte E., 2008, Next generation vehicle – engineering guidelines for stainless steel in automotive applications, In: Proceedings of the 6th stainless steel science and market conference, Helsinki, Finland.
  15. Kou, S., 2003, Weld metal solidification, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.199-207.
  16. Han, W., 2004, Computational and experimental investigations of laser drilling and welding for microelectronic packaging, Ph.D. Dissertation, Worcester Polytechnic Institute, Worcester, MA, USA, pp. 85-87.
  17. Buchfink, G., 2007, A world of possibilities – joining, In: Kammϋller, N.L., editor, The laser as a tool, 1st Ed., Vogel Buchverlag, Wϋrzburg, Germany, pp. 166-167.
  18. ISO13919-1:1996, Welding – Electrons and laser beam welded joints – guidance on quality levels for imperfections – Part I: Steel, pp. 4-13.
  19. Zhang, Y.M., Kovacevic, R., Li, L., 1996, Characterization and real time measurement of geometrical appearance of the weld pool. International Journal of Machine Tools and Manufacture, 36(7):799–816.
  20. Bull, C.E., Stacey, K.A., Calcraft, R., 1993, Online weld monitoring using ultrasonic. Journal of Non-destructive Test, 35(2):57–64.
  21. Tarng, Y.S., Yang, W.H., 1998, Optimization of the weld bead geometry in gas Tungsten Arc welding by the Taguchi Method. Journal of Advanced Manufacturing Technology, 14:549–54.
  22. Benyounis, K.Y.,Olabi, A.G.,Hasmi, M.S.J., 2008, Multi-response optimization of CO2 laser welding process of austenitic stainless steel, Optics & Laser Technology, 40:76–87.
  23. Antony, J., 2003, Introduction to industrial experimentation, In: Design of Experiments for Engineers and Scientists, Elsevier Publishing Solutions, USA, pp. 1-4.
  24. Sudnik, W., Radaj, D., Erofeev, W., 1996, Computerized simulation of laser beam welding, modeling and verification, Journal of Physics D: Applied Physics, 29:2811-2817.
  25. Arata, Y., Miyamoto, I., 1972, Heat processing by CO2 laser, Journal of Japan Welding Society, 41:81.
  26. Swift-Hook, D.T., Gick, A.E.F., 1973, Penetration welding with lasers, Welding Journal Research Supplement, 52:492s–9s.
  27. Steen, W.M., Dowden, J., Davis, M., Kapadia, P., 1988, A point and line source model of laser keyhole welding, Journal of Physics D, 21:1255–60.
  28. Dowden, J., Davis, M., Kapadia, P., 1983, Some aspects of the fluid-dynamics of laser-welding. Journal of Fluid Mechanics, 126:123–46.
  29. Ducharme, R., Kapadia, P., Dowden, J., 1993, A mathematical model of the defocusing of laser light above a workpiece in laser material processing. In: Farson, D., Steen, W., Miyamoto, I., editors, Proceedings of ICALEO’92, LIA, Orlando: Laser Institution of America, 75:187–97.
  30. Kaplan, A., 1994, A model of deep penetration laser welding based on calculation of the keyhole profile, Journal of Physics D: Applied Physics, 27(9):1805–1814.
  31. Klemens, P.G., 1976, Heat balance and flow conditions for electron beam and laser welding, Journal of Applied Physics, 47(5):2165–2174.
  32. Chande, T., Mazumder, J., 1984, Estimating effects of processing conditions and variable properties upon pool shape, cooling rates, and absorption coefficient in laser welding, Journal of Applied Physics, 56:1981–6.
  33. Borland, J.C., 1960, Generalized theory of super-solidus cracking in welds (and castings), British Welding Journal, 7: 508–512.
  34. Hemsworth, B., Boniszewski, T., Eaton, N.F., 1969, Classification and definition of high temperature welding cracks in alloys, Metal Construction and British Welding Journal, 2:5–16.
  35. Hoffmann, P., Geiger, M., 1995, Recent developments in laser system technology for welding applications, Annals of the CIRP, 44(1):151-156.
  36. Weichiat, C., Paul, A., Pal, M., 2009, CO2 laser welding of galvanized steel sheets using vent holes, Materials and Design, 30:245–251.
  37. Lippold, J.C., Kotecki, D.J., 2005, Welding metallurgy and weldability of stainless steel, 1st ed., John Willey & Sons, NJ, USA, pp. 63-70.
  38. Brooks, J.A., Garrison, W.M., 1999, Weld microstructure development and properties of precipitation-strengthened martensitic stainless steels, Welding Journal, 78(8): 280s -291s
  39. Tzeng, Y.F., 2000, Parametric analysis of the pulsed Nd:YAG laser seam-welding process, Journal of Materials Processing Technology, 102: 40-47.
  40. Hector Jr., L.G., Chen, Y.-L., Agarwal, S., Briant. C.L., 2004, Texture characterization of autogenous Nd: YAG laser welds in AA5182-O and AA6111-T4 aluminum alloys, Metall. and Mater. Trans A, 35A:3032-3038.
  41. Al-kazzaz, H., Medraj, M., Cao, X., Jahazi, M., Xiao, M., 2005, Effects of welding speed on Nd:YAG laser weldability of ZE41A-T5 magnesium sand castings, Proceeding of 44th annual conference of metallurgists of CIM, Light Metals:137-149.
  42. Huang, R. S., Kang, L., Ma, X., 2008, Microstructure and phase composition of a low-power YAG laser-MAG welded stainless steel joint, Journal of Materials Engineering and Performance, 17:928–935.
  43. Liu, Q.S., Mahdavian, S.M., Aswin, D., Ding, S., 2009, Experimental study of temperature and clamping force during Nd:YAG laser butt welding, Optics & Laser Technology,41(6):794-799
  44. Berzins, M., Childs, T.H.C., Ryder, G.R., 1996, The selective laser sintering of polycarbonate, Annals of the CIRP, 45(1):187–190.
  45. Childs, T.H.C., Berzins, M., Ryder, G.R., Tontowi, A.E., 1999, Selective laser sintering of an amorphous polymer: simulations and experiments. Proc. IMechE, Part B: J. Engineering Manufacture, 213:333-349.
  46. Jin, X., Li, L., 2004, An experimental study on the keyhole shapes in laser deep penetration welding, Optics and Lasers in Engineering, 41: 779–790.
  47. Sudnik, W., Radaj, D., Breitschwerdt, S., Erofeew, W., 2000, Numerical simulation of weld pool geometry in laser beam welding, J. Phys. D: Appl. Phys. 33: 662–671.
  48. Antony, J., 2003, Systematic Methodology for design of experiment: Design of Experiment for Engineers and Scientists, 1st Ed., Butterworth-Heinemann Publication, MA, USA, pp. 38-39.
  49. Kurt, B., Orhan, N., Somunkiran, I., Kaya, M., 2009, The effect of austenitic interface layer on microstructure of AISI 420 martensitic stainless steel joined by keyhole PTA welding process, Materials and Design, 30:661–664.
  50. Ping, D.H., Ohnuma, M., Hirakawa, Y., Kadoya, Y., Hono, K., 2005, Microstructural evolution in 13Cr–8Ni–2.5Mo–2Al martensitic precipitation-hardened stainless steel, Materials Science and Engineering A, 394:285–295
  51. Berretta, J.R., de Rossi, W., Neves, M.D.M., de Almeida, I.A., Junior, N.D.V., 2007, Pulsed Nd:YAG laser welding of AISI 304 to AISI 420 stainless steels, Optics and Lasers in Engineering, 45:960–966.
  52. Srinivasan, P.B., 2008, Effect of laser beam mode on the microstructural evolution in AISI 410 martensitic stainless steel welds, Lasers in Engineering, 18:351–359.
  53. Rajasekhar, A., Reddy, G.M., Mohandas, T., Murti, V.S.R., 2009, Influence of austenitizing temperature on microstructure and mechanical properties of AISI 431 martensitic stainless steel electron beam welds, Materials and Design, 30:1612–1624.
  54. Sharifitabar, M., Halvaee, A., 2010, Resistance upset butt welding of austenitic to martensitic stainless steels, Materials and Design, 31(6):3044–3050.
  55. Gualco, A., Svoboda, H.G., Surian, E.S., de Vedia, L. A., 2010, Effect of welding procedure on wear behaviour of a modified martensitic tool steel hardfacing deposit, Materials and Design, 31:4165–4173
  56. Khan MMA, Romoli L, Fiaschi M, Dini G, Sarri F., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Material Processing Technology,210:1340–53
  57. Kou, S., 2002, Welding metallurgy, 2nd ed. John Willey & Sons Inc., NJ, USA, pp. 143- 169.
  58. Nakagawa H, Matsuda F, Uehara T, Katayama S, Arata Y. A., 1979, New explanation for role of delta ferrite improving weld solidification crack susceptibility in austenitic stainless steel, Trans Jpn Weld Res Inst. 8:105–12.
  59. Huang, Q., Hagstroem, J., Skoog, H., Kullberg, G., 1991, Effect of laser parameter variation on sheet metal welding, Int. J. Join. Mater., 3:79–88.
  60. Benyounis, K.Y., Olabi., A.G., 2008, Optimization of different welding processes using statistical and numerical approaches – A reference guide, Advances in Engineering Software, 39:483–496.
  61. Montgomery, D.C., 2004, Design and Analysis of Experiments, 6th ed. John Wiley and Sons, Inc., New York.
  62. Yang, Y.K., Chuang, M.T. Lin, S.S., 2009, Optimization of dry machining parameters for high-purity graphite in end milling process via design of experiments methods, Journal of Materials Processing Technology, 209:4395– 4400.
  63. Douglass, D.M., Wu, C.Y., 2003, Laser welding of polyolefin elastomers to thermoplastic polyolefin, In: Proceedings of the 22nd international Congress on applications of lasers & electro-optics, Jacksonville, Florida, USA, 95:118–23.
  64. Koganti, R., Karas, C., Joaquin, A., Henderson, D., Zaluzec, M., Caliskan, A., 2003, Metal inert gas (MIG) welding process optimization for joining aluminum sheet material using OTC/DAIHEN equipment, In: Proceedings of IMECE’03, November 15–21, Washington [DC]: ASME International Mechanical Engineering Congress, pp. 409–425.
  65. Balasubramanian, V., Guha, B., 2004, Fatigue life prediction of load carrying cruciform joints of pressure vessel steel by statistical tools. J Mater Des, 25:615–623.
  66. Cicala, E., Duffet, G., Andrzjewski, H., Grevey, D., 2005, Optimization of T-joint properties in Al-Mg-Si alloy laser welding, 24th International Congress on Applications of Lasers and Electro-Optics, ICALEO: 543-548.
  67. Kim, C., Choi, W., Kim, J., Rhee, S., 2008, Relationship between the weldability and the Process parameters for laser-TIG Hybrid welding of galvanized steel sheets, Materials Transactions, 49:179-186.
  68. Datta, S., Bandyaopadhyay, A., Pal, P.K., 2008, Modeling and optimization of features of bead geometry including percentage dilution in submerged arc welding using mixture of fresh flux and fused slag, Int. J. Adv. Manuf. Technol., 36:1080–1090.
  69. Sarsılmaz, F., Çaydaş, U., 2009, Statistical analysis on mechanical properties of friction-stir-welded AA 1050/AA 5083 couples, Int. J. Adv. Manuf. Technol., 43:248–255.
  70. Khan M.M.A., Romoli L., Fiaschi M., Sarri F., Dini G., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Materials Processing Technology, 210(10):1340-1353.
  71. Design-Expert software, v7, user’s guide, technical manual, Stat-Ease Inc., Minneapolis, MN; 2005.
  72. Zulkali, M.M.D., Ahmad, A.L., Norulakmal, N.H., 2006, Oryza sativa L. husk as heavy metal adsorbent: optimization with lead as model solution, Bioresour. Technol., 97:21–25.
  73. Sun, Z., 1996, Feasibility of producing ferritic/austenitic dissimilar metal joints by high energy density laser beam process, International Journal of Pressure Vessels and Piping, 68:153-160.
  74. Katayama, S., 2004, Laser welding of aluminium alloys and dissimilar metals, Weld International, 18(8):618–25.
  75. Kaiser, E., Schafer, P., 2005, Pulse sharpening optimizes the quality of seam and spot welds. In: Lasers in manufacturing, proceeding of the third international WLT conference on lasers in manufacturing, pp. 695–698.
  76. Li, Z., Fontana, G., 1998, Autogenous laser welding of stainless steel to free-cutting steel for the manufacture of hydraulic valves, Journal of Materials Processing Technology, 74:174–182.
  77. Mai, T.A., Spowage, A.C., 2004, Characterisation of dissimilar joints in laser welding of steel–kovar, copper–steel and copper–aluminium, Materials Science and Engineering: A, 374:224–233.
  78. Liu, X.B., Yu, G., Pang, M., Fan, J.W., Wang, H.H., Zheng, C.Y., 2007, Dissimilar autogenous full penetration welding of superalloy K418 and 42CrMo steel by a high power CW Nd:YAG laser, Applied Surface Science, 253:7281–7289.
  79. Mousavi, S.A.A.A., Sufizadeh, A.R., 2009, Metallurgical investigations of pulsed Nd:YAG laser welding of AISI 321 and AISI 630 stainless steels, Materials and Design, 30:3150–3157.
  80. Pekkarinen, J., Kujanpää, V., 2010, The effects of laser welding parameters on the microstructure of ferritic and duplex stainless steels welds, Physics Procedia, 5:517–523.
  81. Allabhakshi, S., Madhusudhan Reddy, G., Ramarao, V.V., Phani Babu, C., Ramachandran, C.S., 2002, Studies on weld overlaying of austenitic stainless steel (AISI 304) with ferritic stainless steel (AISI 430). In: Proceedings of the national welding conference, Indian Institute of Welding, Chennai, India, Paper 8.
  82. Pan, C., Zhang, E., 1996, Morphologies of the transition region in dissimilar austenitic–ferritic welds, Material Characterization, 36(1):5–10.
  83. Wang, S. C., Wang, C., Tu, Y. K., Hwang, C. J., Chi, S., Wang, W. H., Cheng, W. H., 1996, Effect of Au coating on joint strength in laser welding for invar-invar packages, Electronic Components and Technology Conference, IEEE, pp. 942-945.
  84. Cui, C., Hu, J., Gao, K., Pang, S., Yang, Y., Wang, H., Guo, Z., 2008, Effects of process parameters on weld metal keyhole characteristics with COR2R laser butt welding, Lasers in Engineering, 18:319–327.
  85. Steem WM, Mazumder J, 2010, laser material processing, Springer-Verlag London limited, London.
  86. Mackwood AP, Crafer RC, 2005, Thermal modeling of laser welding and related processes: a literature review, Opt Laser Technol, 37:99–115
  87. Sun Z, Kuo M, 1998, Bridging the joint gap with wire feed laser welding, J Mater Process Technol, 87:213–222
  88. Liu X-B, Yu G,Guo J, Gu Y-J, Pang M, Zheng C-Y, Wang H-H, 2008, Research on laser welding of cast Ni-based superalloy K418 turbo disk and alloy steel 42CrMo shaft, J Alloy Comp, 453(1–2):371–378.
  89. Juang SC, Tarng YS, 2002, Process parameter selection for optimizing the weld pool geometry in the tungsten inert gas welding of stainless steel, J Mater Process Technol, 122:33–37
  90. Marya M, Edwards G, Marya S, Olson DL, 2001, Fundamentals in the fusion welding of magnesium and its alloys. In: Proceedings of the seventh JWS international symposium. pp. 597–602.
  91. Haferkamp H, Niemeyer M, Dilthey U, Trager G, 2000, Laser and electron beam welding of magnesium materials, Weld Cutt 52(8):178–80.
  92. Haferkamp H, Bach Fr-W, Burmester I, Kreutzburg K, Niemeyer M, 1996, Nd:YAG laser beam welding of magnesium constructions. In: Proceedings of the third international magnesium conference. pp. 89–98.
  93. Benyounis KY, Olabi AG, Hashmi MSJ, 2005, Effect of laser welding parameters on the heat input and weld-bead profile, J Mater Process Technol, 164-165:978–985.
  94. Manonmani K, Murugan N, Buvanasekaran G, 2007, Effects of process parameters on the bead geometry of laser beam butt welded stainless steel sheets, J Adv Manuf Technol, 32(11-12):1125-1133.
  95. Elangovan K, Balasubramanian V, 2008, Developing an empirical relationship to predict tensile strength of friction stir welded AA2219 aluminium alloy joints, J Mater Eng Perform, 17:820–830.
  96. Moradi M, Ghoreishi M, 2010, Influences of laser welding parameters on the geometric profile of NI-base superalloy Rene 80 weld-bead, Int J Adv Manuf Technol, doi: 10.1007/s00170-010-3036-1.
  97. Padmanaban G, Balasubramanian V, 2010, Optimization of laser beam welding process parameters to attain maximum tensile strength in AZ31B magnesium alloy, Opt Laser Technol, 42:1253–1260
  98. Rajakumar S, Muralidharan C, Balasubramanian V, 2010, Optimization of the friction-stir-welding process and the tool parameters to attain a maximum tensile strength of AA7075-T6 aluminium alloy, J Eng Manuf, 224:1175–1191.
  99. Ruggiero A, Tricarico L, Olabi AG, Benyounis KY, 2011, Weld-bead profile and costs optimization of the CO2 dissimilar laser welding process of low carbon steel and austenitic steel AISI316, Opt Laser Technol, 43:82–90.
  100. Myers RH, Montgomery DC, 2002, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York.
  101. Robinson TJ, Wulff SS, 2006, Response surface approaches to robust parameter design. In: Khuri AI (ed) Response surface methodology and related topics, World Scientific, Singapore, pp. 123-157.
  102. Gunaraj V, Murugan N, 1999, Application of response surface methodologies for predicting weld base quality in submerged arc welding of pipes, J Mater Process Technol, 88:266–275.
  103. Chang W. S., Na S.J., 2002, A study on the prediction of the laser weld shape with varying heat source equations and the thermal distortion of a small structure in micro-joining, Journal of Material Processing Technology, 120:208 – 214.
  104. Goldak J. A., Chakravarti M. B., 1984, A new finite element model for welding heat source, Metallurgical and Materials Transactions B, 15B:299–305.
  105. Su W., Haiyan Z., Yu W., Xiaohong Z., 2004, A new heat source model in numerical simulation of high energy beam welding, Transaction China Welding Institute, 25:91–94.
  106. Kazemi K., Goldak J. A., 2009, Numerical simulation of laser full penetration welding, Computational Materials Science, 44:841–849
  107. Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2012, Some studies on weld bead geometries for laser spot welding process using finite element analysis, Materials and Design, 34:412–426
  108. Balasubramanian K.R., Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2008, Numerical and experimental investigation of laser beam welding of AISI 304 stainless steel sheet, Advances in Production Engineering and Management, 3(2):93–105
  109. Sabbaghzadeh J., Azizi M., Torkamany M.J., 2008, Numerical and experimental investigation of seam welding with a pulsed laser. Journal of Optics and Laser Technology, 40:289–296
  110. Kruth J.P., Froyen L., Rombouts M., Van Vaerenbergh J., Mercells P., 2003, New Ferro Powder for Selective Laser Sintering of Dense Parts, CIRP Annals – Manufacturing Technology, 52/1: 139–142.
  111. Romoli L., Tantussi G., Dini G., 2007, Layered Laser Vaporization of PMMA Manufacturing 3D Mould Cavities, CIRP Annals -Manufacturing Technology, 56/1: 209-212.
  112. Vollertsen F., Walther R., 2008, Energy balance in laser-based free form heading, CIRP Annals – Manufacturing Technology 57/1: 291–294.
  113. Mills K.C., Su Y., Li Z., Brooks R.F., 2004, Equations for the Calculation of the Thermo-physical Properties of Stainless Steel, ISIJ International, Vol. 44, No. 10, pp. 1661–1668.
  114. Ahmad, N., Bihs, H., Myrhaug, D., Kamath, A., & Arntsen, Ø. (2018). Three-dimensional numerical modelling of wave-induced scour around piles in a side-by-side arrangement. Coastal Engineering (Amsterdam), 138, 132–151. https://doi.org/10.1016/j.coastaleng.2018.04.016
  115. Ahmed, F., & Rajaratnam, N. (1998). Flow around Bridge Piers. Journal of Hydraulic Engineering (New York, N.Y.), 124(3), 288–300. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:3(288)
  116. Akib, S., Jahangirzadeh, A., & Basser, H. (2014). Local scour around complex pier groups and combined piles at semi-integral bridge. Vodohospodársky Časopis, 62(2), 108–116. https://doi.org/10.2478/johh-2014-0015
  117. Alemi, M., & Maia, R. (2018). Numerical Simulation of the Flow and Local Scour Process Around Single and Complex Bridge Piers. International Journal of Civil Engineering, 16(5), 475–487. https://doi.org/10.1007/s40999-016-0137-8
  118. Amini Baghbadorani, D., Beheshti, A., & Ataie-Ashtiani, B. (2017). Scour hole depth prediction around pile groups: review, comparison of existing methods, and proposition of a new approach. Natural Hazards (Dordrecht), 88(2), 977–1001. https://doi.org/10.1007/s11069-017-2900-9
  119. Amini, A., Melville, B., Ali, T., & Ghazali, A. (2012). Clear-Water Local Scour around Pile Groups in Shallow-Water Flow. Journal of Hydraulic Engineering (New York, N.Y.), 138(2), 177–185. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000488
  120. Annandale, G. (1995). Erodibility. Journal of Hydraulic Research. 33. 471-494.
  121. Annandale, G., Smith, S., Nairns, R., & Jones, J. (1996). Scour power. Civil Engineering (New York, N.Y. 1983), 66(7), 58–60.
  122. Annandale, G. (2000). Prediction of scour at bridge pier foundations founded on rock and other earth materials. Transportation Research Record, 2(1696), 67–70.
  123. Ataie-Ashtiani, B., & Beheshti, A. (2006). Experimental Investigation of Clear-Water Local Scour at Pile Groups. Journal of Hydraulic Engineering (New York, N.Y.), 132(10), 1100–1104. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:10(1100)
  124. Ataie-Ashtiani, B., Baratian-Ghorghi, Z., & Beheshti, A. (2010). Experimental Investigation of Clear-Water Local Scour of Compound Piers. Journal of Hydraulic Engineering (New York, N.Y.), 136(6), 343–351. https://doi.org/10.1061/(ASCE)0733-9429(2010)136:6(343)
  125. Babu, M., Sundar, V., & Rao, S. (2003). Measurement of scour in cohesive soils around a vertical pile – simplified instrumentation and regression analysis. IEEE Journal of Oceanic Engineering, 28(1), 106–116. https://doi.org/10.1109/JOE.2002.808198
  126. Barbhuiya, A., & Dey, S. (2004). Local scour at abutments: A review. Sadhana (Bangalore), 29(5), 449–476. https://doi.org/10.1007/BF02703255
  127. Bieniawski, Z. T. (1989). Engineering rock mass classifications: a complete manual for engineers and geologists in mining, civil, and petroleum engineering. John Wiley & Sons.
  128. Bierawski, L., & Maeno, S. (2006). DEM-FEM Model of Highly Saturated Soil Motion Due to Seepage Force. Journal of Waterway, Port, Coastal, and Ocean Engineering, 132(5), 401–409. https://doi.org/10.1061/(ASCE)0733-950X(2006)132:5(401)
  129. Bonnefille, R. (1963). Essais de synthese des lois du début d’entrainement des sédiments sous l’action d’un courant en regime continu. Bull. du Centre de Rech. et d’ess. de Chatou. 5. 17-22.
  130. Brandimarte, L., Montanari, A., Briaud, J., & D’Odorico, P. (2006). Stochastic Flow Analysis for Predicting River Scour of Cohesive Soils. Journal of Hydraulic Engineering (New York, N.Y.), 132(5), 493–500. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:5(493)
  131. Breusers H N C 1963 Discussion of ’Sediment transportation mechanics: erosion of sediment’ by Task Force on Preparation of Sedimentation Manual.J. Hydraul. Div, Am. Soc. Civ. Eng. 89: 277–281
  132. Breusers, H., Nicollet, G., & Shen, H. (1977). Local Scour Around Cylindrical Piers. Journal of Hydraulic Research, 15(3), 211–252. https://doi.org/10.1080/00221687709499645
  133. Briaud, J., Ting, F., Chen, H., Gudavalli, R., Perugu, S., & Wei, G. (1999). SRICOS: Prediction of Scour Rate in Cohesive Soils at Bridge Piers. Journal of Geotechnical and Geoenvironmental Engineering, 125(4), 237–246. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:4(237)
  134. Briaud, J., Ting, F., Chen, H., Cao, Y., Han, S., & Kwak, K. (2001a). Erosion Function Apparatus for Scour Rate Predictions. Journal of Geotechnical and Geoenvironmental Engineering, 127(2), 105–113. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:2(105)
  135. Briaud, J., Chen, H., Kwak, K., Han, S., & Ting, F. (2001b). Multiflood and Multilayer Method for Scour Rate Prediction at Bridge Piers. Journal of Geotechnical and Geoenvironmental Engineering, 127(2), 114–125. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:2(114)
  136. Briaud, J., Chen, H., Li, Y., & Nurtjahyo, P. (2004). SRICOS-EFA Method for Complex Piers in Fine-Grained Soils. Journal of Geotechnical and Geoenvironmental Engineering, 130(11), 1180–1191. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:11(1180)
  137. Briaud, J., Chen, H., Li, Y., Nurtjahyo, P., & Wang, J. (2005). SRICOS-EFA Method for Contraction Scour in Fine-Grained Soils. Journal of Geotechnical and Geoenvironmental Engineering, 131(10), 1283–1294. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:10(1283)
  138. Briaud, J., Brandimarte, L., Wang, J., & D’Odorico, P. (2007). Probability of scour depth exceedance owing to hydrologic uncertainty. Georisk, 1(2), 77–88. https://doi.org/10.1080/17499510701398844
  139. Briaud J.-L., Chen H.-C., Chang K.-A., Oh S.J., Chen S., Wang J., Li Y., Kwak K., Nartjaho P., Gudaralli R., Wei W., Pergu S., Cao Y.W., Ting F (2011). Summary Report: The SRICOS–EFA Method. Texas A&M University
  140. Briaud, J., & Govindasamy, A. (2014). Application of the Observation Method for Scour to Two Texas Bridges. In Geo-Congress 2014 (pp. 2640–2654). https://doi.org/10.1061/9780784413272.255
  141. Briaud, J., Gardoni, P., & Yao, C. (2014). Statistical, Risk, and Reliability Analyses of Bridge Scour. Journal of Geotechnical and Geoenvironmental Engineering, 140(2), 4013011–. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000989
  142. Briaud, J. (2015a). Scour Depth at Bridges: Method Including Soil Properties. I: Maximum Scour Depth Prediction. Journal of Geotechnical and Geoenvironmental Engineering, 141(2), 4014104–. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001222
  143. Briaud, J. (2015b). Scour Depth at Bridges: Method Including Soil Properties. II: Time Rate of Scour Prediction. Journal of Geotechnical and Geoenvironmental Engineering, 141(2), 4014105–. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001223
  144. Brooks, H. N. (1963), discussion of “Boundary Shear Stresses in Curved Trapezoidal Channels”, by A. T. Ippen and P. A. Drinker, ASCE Journal of Hydraulic Engineering, Vol. 89, No. HY3
  145. Chen, G., Schafer, B., Lin, Z., Huang, Y., Suaznabar, O., Shen, J., & Kerenyi, K. (2015). Maximum scour depth based on magnetic field change in smart rocks for foundation stability evaluation of bridges. Structural Health Monitoring, 14(1), 86–99. https://doi.org/10.1177/1475921714554141
  146. Chen, Q., Yang, Z., & Wu, H. (2019). Evolution of Turbulent Horseshoe Vortex System in Front of a Vertical Circular Cylinder in Open Channel. Water (Basel), 11(10), 2079–. https://doi.org/10.3390/w11102079
  147. Chen, S., Tfwala, S., Wu, T., Chan, H., & Chou, H. (2018). A hooked-collar for bridge piers protection: Flow fields and scour. Water (Basel), 10(9), 1251–. https://doi.org/10.3390/w10091251
  148. Cheng, Nian-Sheng. (2015). Representative Grain Size and Equivalent Roughness Height of a Sediment Bed. Journal of Hydrologic Engineering. 142. 10.1061/(ASCE)HY.1943-7900.0001069.
  149. Chiew, Y., & Melville, B. (1987). Local scour around bridge piers. Journal of Hydraulic Research, 25(1), 15–26. https://doi.org/10.1080/00221688709499285
  150. Coleman, S., Lauchlan, C., & Melville, B. (2003). Clear-water scour development at bridge abutments. Journal of Hydraulic Research, 41(5), 521–531. https://doi.org/10.1080/00221680309499997
  151. Coleman, S. (2005). Clearwater Local Scour at Complex Piers. Journal of Hydraulic Engineering (New York, N.Y.), 131(4), 330–334. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:4(330)
  152. Dargahi, B. (1987). ‘‘Flow field and local scouring around a pier.’’ Bulletin No. TRITA-VBI-137, Hydraulic Laboratory, Royal Institute of Technology, Stockholm, Sweden.
  153. Dargahi, B. (1989). The turbulent flow field around a circular cylinder. Experiments in Fluids, 8(1-2), 1–12. https://doi.org/10.1007/BF00203058
  154. Dargahi, B. (1990). Controlling Mechanism of Local Scouring. Journal of Hydraulic Engineering (New York, N.Y.), 116(10), 1197–1214. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:10(1197)
  155. Debnath, K., Nikora, V., Aberle, J., Westrich, B., & Muste, M. (2007). Erosion of Cohesive Sediments: Resuspension, Bed Load, and Erosion Patterns from Field Experiments. Journal of Hydraulic Engineering (New York, N.Y.), 133(5), 508–520. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:5(508)
  156. Debnath, K., & Chaudhuri, S. (2010a). Bridge Pier Scour in Clay-Sand Mixed Sediments at Near-Threshold Velocity for Sand. Journal of Hydraulic Engineering (New York, N.Y.), 136(9), 597–609. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000221
  157. Debnath, K., & Chaudhuri, S. (2010b). Laboratory experiments on local scour around cylinder for clay and clay–sand mixed beds. Engineering Geology, 111(1), 51–61. https://doi.org/10.1016/j.enggeo.2009.12.003
  158. Debnath, K., Chaudhuri, S., & Manik, M. (2014). Local scour around abutment in clay/sand-mixed cohesive sediment bed. ISH Journal of Hydraulic Engineering, 20(1), 46–64. https://doi.org/10.1080/09715010.2013.835103
  159. Deng, L., & Cai, C. (2010). Bridge Scour: Prediction, Modeling, Monitoring, and Countermeasures—Review. Practice Periodical on Structural Design and Construction, 15(2), 125–134. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000041
  160. Dey, S. (1999). Time-variation of scour in the vicinity of circular piers. Proceedings of the Institution of Civil Engineers. Water, Maritime and Energy, 136(2), 67–75. https://doi.org/10.1680/iwtme.1999.31422
  161. Dey, S. (2003) “Threshold of sediment motion on combined transverse and longitudinal sloping beds”, Journal of Hydraulic Research, Vol. 41, No. 4, pp. 405-415.
  162. Ehteram, M., & Mahdavi Meymand, A. (2015). Numerical modeling of scour depth at side piers of the bridge. Journal of Computational and Applied Mathematics, 280, 68–79. https://doi.org/10.1016/j.cam.2014.11.039
  163. Escauriaza, C., & Sotiropoulos, F. (2011). Initial stages of erosion and bed form development in a turbulent flow around a cylindrical pier. Journal of Geophysical Research: Earth Surface, 116(F3). https://doi.org/10.1029/2010JF001749
  164. Ettema, R., Constantinescu, G., & Melville, B. (2017). Flow-Field Complexity and Design Estimation of Pier-Scour Depth: Sixty Years since Laursen and Toch. Journal of Hydraulic Engineering (New York, N.Y.), 143(9), 3117006–. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001330
  165. Froehlich, D.C. (1988) Analysis of On-Site Measurements of Scour at Piers. In: Abt, S.R. and Gessler, J., Eds., Hydraulic Engineering—Proceedings of the 1988 National Conference on Hydraulic Engineering, American Society of Civil Engineers, New York, 534-539.
  166. Froehlich, D. C. (1989). Local scour at bridge abutments. In Proceedings of the 1989 national conference on hydraulic engineering (pp. 13-18).
  167. Ge, L., & Sotiropoulos, F. (2005a). 3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. I: Numerical Model. Journal of Hydraulic Engineering (New York, N.Y.), 131(9), 800–808. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:9(800)
  168. Ge, L., Lee, S., Sotiropoulos, F., & Sturm, T. (2005b). 3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics. Journal of Hydraulic Engineering (New York, N.Y.), 131(9), 809–820. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:9(809)
  169. Govindasamy, A., Briaud, J., Kim, D., Olivera, F., Gardoni, P., & Delphia, J. (2013). Observation Method for Estimating Future Scour Depth at Existing Bridges. Journal of Geotechnical and Geoenvironmental Engineering, 139(7), 1165–1175. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000838
  170. Guan, D., Chiew, Y., Wei, M., & Hsieh, S. (2019). Characterization of horseshoe vortex in a developing scour hole at a cylindrical bridge pier. International Journal of Sediment Research, 34(2), 118–124. https://doi.org/10.1016/j.ijsrc.2018.07.001
  171. Hamzah M. Beakawi Al-Hashemi, Omar S. Baghabra Al-Amoudi, A review on the angle of repose of granular materials, Powder Technology, Volume 330, 2018, Pages 397-417, ISSN 0032-5910, https://doi.org/10.1016/j.powtec.2018.02.003.
  172. Huang, W., Yang, Q., & Xiao, H. (2009). CFD modeling of scale effects on turbulence flow and scour around bridge piers with Ansys-Fluent. Computers & Fluids, 38(5), 1050–1058. https://doi.org/10.1016/j.compfluid.2008.01.029
  173. Ismail, A., Jeng, D., Zhang, L., & Zhang, J. (2013). Predictions of bridge scour: Application of a feed-forward neural network with an adaptive activation function. Engineering Applications of Artificial Intelligence, 26(5-6), 1540–1549. https://doi.org/10.1016/j.engappai.2012.12.011
  174. Jahangirzadeh, A., Basser, H., Akib, S., Karami, H., Naji, S., & Shamshirband, S. (2014). Experimental and numerical investigation of the effect of different shapes of collars on the reduction of scour around a single bridge pier. PloS One, 9(6), e98592–e98592. https://doi.org/10.1371/journal.pone.0098592
  175. Jain, S. C. (1981). Maximum clear-water scour around circular piers. Journal of the Hydraulics Division, 107(5), 611-626.
  176. Jain, S. C., and Fischer, E. E. (1979). “Scour around bridge piers at high Froude numbers.” FHWA-RD- 79-104, Federal Highway Administration, U.S. Dept. of Transportation, Washington, DC.
  177. Jiang, H., Cheng, L., & An, H. (2017). On numerical aspects of simulating flow past a circular cylinder. International Journal for Numerical Methods in Fluids, 85(2), 113–132. https://doi.org/10.1002/fld.4376
  178. Jones, J. S., & Sheppard, D. M. (2000). Local scour at complex pier geometries. In Building Partnerships (pp. 1-9).
  179. Karami, H., Basser, H., Ardeshir, A., & Hosseini, S. (2014). Verification of numerical study of scour around spur dikes using experimental data. Water and Environment Journal: WEJ, 28(1), 124–134. https://doi.org/10.1111/wej.12019
  180. Kaya, A. (2010). Artificial neural network study of observed pattern of scour depth around bridge piers. Computers and Geotechnics, 37(3), 413–418. https://doi.org/10.1016/j.compgeo.2009.10.003
  181. Keaton, J. (2013). Estimating erodible rock durability and geotechnical parameters for scour analysis. Environmental & Engineering Geoscience, 19(4), 319–343. https://doi.org/10.2113/gseegeosci.19.4.319
  182. Keaton, J. R. (2011). Modified Slake Durability Test Applicability for Soil. In International Symposium on Erosion and Landscape Evolution (ISELE), 18-21 September 2011, Anchorage, Alaska (p. 7). American Society of Agricultural and Biological Engineers.
  183. Khalid, M., Muzzammil, M., & Alam, J. (2019). A reliability-based assessment of live bed scour at bridge piers. ISH Journal of Hydraulic Engineering, 1–8. https://doi.org/10.1080/09715010.2019.1584543
  184. Khan, M., Azamathulla, H., Tufail, M., & Ab Ghani, A. (2012). Bridge pier scour prediction by gene expression programming. Proceedings of the Institution of Civil Engineers. Water Management, 165(9), 481–493. https://doi.org/10.1680/wama.11.00008
  185. Kocaman, S., Seckin, G., & Erduran, K. (2010). 3D model for prediction of flow profiles around bridges. Journal of Hydraulic Research, 48(4), 521–525. https://doi.org/10.1080/00221686.2010.507340
  186. Kumar, A., Kothyari, U., & Ranga Raju, K. (2012). Flow structure and scour around circular compound bridge piers – A review. Journal of Hydro-Environment Research, 6(4), 251–265. https://doi.org/10.1016/j.jher.2012.05.006
  187. Lagasse PF, Clopper PE, Zevenbergen LW et al (2007) National cooperative highway research program (NCHRP Report 593): countermeasures to protect bridge piers from scour. Transportation research Board, Washington DC
  188. Larras, J. (1963). Profondeurs Maximales d’Erosion des Fonds Mobiles Autour des Piles en Rivere. Ann. Ponts Chaussees, 133, 411-424.
  189. Laursen, E. M., & Toch, A. (1956). Scour around bridge piers and abutments (Vol. 4). Ames, IA: Iowa Highway Research Board.
  190. Laursen, E. M., 1960, Scour at Bridge Crossings, ASCE Hyd. Div. Jour., V 89, No. Hyd 3, May.
  191. Laursen, E M. (1963) An analysis of relief bridge scour. [Journal Article]. ASCE Journal of Hydraulic Division, 89(HY3), 93-109.
  192. LEE, T., JENG, D., ZHANG, G., & HONG, J. (2007). Neural network modeling for estimation of scour depth around bridge piers. Journal of Hydrodynamics. Series B, 19(3), 378–386. https://doi.org/10.1016/S1001-6058(07)60073-0
  193. Liang, F., Wang, C., Huang, M., & Wang, Y. (2017). Experimental observations and evaluations of formulae for local scour at pile groups in steady currents. Marine Georesources & Geotechnology, 35(2), 245–255. https://doi.org/10.1080/1064119X.2016.1147510
  194. Liang, F., Wang, C., & Yu, X. (2019). Widths, types, and configurations: Influences on scour behaviors of bridge foundations in non-cohesive soils. Marine Georesources & Geotechnology, 37(5), 578–588. https://doi.org/10.1080/1064119X.2018.1460644
  195. Link, O., Mignot, E., Roux, S., Camenen, B., Escauriaza, C., Chauchat, J., Brevis, W., & Manfreda, S. (2019). Scour at bridge foundations in supercritical flows: An analysis of knowledge gaps. Water (Basel), 11(8), 1656–. https://doi.org/10.3390/w11081656
  196. Lu, J., Hong, J., Su, C., Wang, C., & Lai, J. (2008). Field Measurements and Simulation of Bridge Scour Depth Variations during Floods. Journal of Hydraulic Engineering (New York, N.Y.), 134(6), 810–821. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:6(810)
  197. Manes, C., & Brocchini, M. (2015). Local scour around structures and the phenomenology of turbulence. Journal of Fluid Mechanics, 779, 309–324. https://doi.org/10.1017/jfm.2015.389
  198. Melville, B. W. (1975). ‘‘Local scour at bridge sites.’’ Rep. No. 117, Dept. of Civil Engineering, School of Engrg., Univ. of Auckland, Auckland, New Zealand.
  199. Melville, B., & Raudkivi, A. (1977). FLOW CHARACTERISTICS IN LOCAL SCOUR AT BRIDGE PIERS. Journal of Hydraulic Research, 15(4), 373–380. https://doi.org/10.1080/00221687709499641
  200. Melville, B. (1984). Live-bed Scour at Bridge Piers. Journal of Hydraulic Engineering (New York, N.Y.), 110(9), 1234–1247. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:9(1234)
  201. Melville, B., & Sutherland, A. (1988). Design Method for Local Scour at Bridge Piers. Journal of Hydraulic Engineering (New York, N.Y.), 114(10), 1210–1226. https://doi.org/10.1061/(ASCE)0733-9429(1988)114:10(1210)
  202. Melville, B. (1992). Local Scour at Bridge Abutments. Journal of Hydraulic Engineering (New York, N.Y.), 118(4), 615–631. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:4(615)
  203. Melville, B., & Raudkivi, A. (1996). Effects of Foundation Geometry on Bridge Pier Scour. Journal of Hydraulic Engineering (New York, N.Y.), 122(4), 203–209. https://doi.org/10.1061/(ASCE)0733-9429(1996)122:4(203)
  204. Melville, B. (1997). Pier and Abutment Scour: Integrated Approach. Journal of Hydraulic Engineering (New York, N.Y.), 123(2), 125–136. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(125)
  205. Melville, B., & Chiew, Y. (1999). Time Scale for Local Scour at Bridge Piers. Journal of Hydraulic Engineering (New York, N.Y.), 125(1), 59–65. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:1(59)
  206. Melville, B. W., and Coleman, S. E. (2000). Bridge scour, Water Resources, Colo.
  207. Ministry of Transportation of Ontario (MTO). 1997. Drainage Management Manual, Ministry of Transportation Ontario. Drainage and Hydrology Section, Transportation Engineering Branch, Quality and Standards Division.
  208. Mohamed, T., Noor, M., Ghazali, A., & Huat, B. (2005). Validation of Some Bridge Pier Scour Formulae Using Field and Laboratory Data. American Journal of Environmental Sciences, 1(2), 119–125. https://doi.org/10.3844/ajessp.2005.119.125
  209. Mohamed, Y., Abdel-Aal, G., Nasr-Allah, T., & Shawky, A. (2013). Experimental and theoretical investigations of scour at bridge abutment. Journal of King Saud University. Engineering Sciences, 28(1), 32–40. https://doi.org/10.1016/j.jksues.2013.09.005
  210. Nagel, T., Chauchat, J., Bonamy, C., Liu, X., Cheng, Z., & Hsu, T. (2020). Three-dimensional scour simulations with a two-phase flow model. Advances in Water Resources, 138, 103544–. https://doi.org/10.1016/j.advwatres.2020.103544
  211. Najafzadeh, M., Barani, G., & Hessami Kermani, M. (2013a). GMDH based back propagation algorithm to predict abutment scour in cohesive soils. Ocean Engineering, 59, 100–106. https://doi.org/10.1016/j.oceaneng.2012.12.006
  212. Najafzadeh, M., Barani, G., & Azamathulla, H. (2013b). GMDH to predict scour depth around a pier in cohesive soils. Applied Ocean Research, 40, 35–41. https://doi.org/10.1016/j.apor.2012.12.004
  213. Namaee, M., & Sui, J. (2019). Local scour around two side-by-side cylindrical bridge piers under ice-covered conditions. International Journal of Sediment Research, 34(4), 355–367. https://doi.org/10.1016/j.ijsrc.2018.11.007
  214. Nasr-Allah, T., Moussa, Y., Abdel-Aal, G., & Awad, A. (2016). Experimental and numerical simulation of scour at bridge abutment provided with different arrangements of collars. Alexandria Engineering Journal, 55(2), 1455–1463. https://doi.org/10.1016/j.aej.2016.01.021
  215. National Cooperative Highway Research Program, 2010b, “Estimation of Scour Depth at Bridge Abutments,” NCHRP Project 24-20, Draft Final Report, Transportation Research Board, National Academy of Science, Washington, D.C. (Ettema, R., T. Nakato, and M. Muste).
  216. Neill, C. R. 1964. Local scour around bridge piers. Council of Alberta, Highway and River Eng. Div., Alberta, Canada.
  217. Neill, C. R. (ed) (1973). RTAC Guide to Bridge Hydraulics, University of Toronto Press.
  218. Nielsen, A., Liu, X., Sumer, B., & Fredsøe, J. (2013). Flow and bed shear stresses in scour protections around a pile in a current. Coastal Engineering (Amsterdam), 72, 20–38. https://doi.org/10.1016/j.coastaleng.2012.09.001
  219. Olabarrieta, M., Medina, R., & Castanedo, S. (2010). Effects of wave–current interaction on the current profile. Coastal Engineering (Amsterdam), 57(7), 643–655. https://doi.org/10.1016/j.coastaleng.2010.02.003
  220. Olsen, Nils Reidar B. (2018). SSIIM User’s Manual. Department Of Civil and Environmental Engineering the Norwegian University of Science and Technology
  221. Olsen, Nils Reidar B. (1999). Class Notes: Computational; Fluid Dynamics in Hydraulic and Sedimentation Engineering. Department Of Civil and Environmental Engineering the Norwegian University of Science and Technology
  222. Pal, M., Singh, N., & Tiwari, N. (2011). Support vector regression based modeling of pier scour using field data. Engineering Applications of Artificial Intelligence, 24(5), 911–916. https://doi.org/10.1016/j.engappai.2010.11.002
  223. Pandey, M., Ahmad, Z., & Sharma, P. (2018). Scour around impermeable spur dikes: a review. ISH Journal of Hydraulic Engineering, 24(1), 25–44. https://doi.org/10.1080/09715010.2017.1342571
  224. Park, C., Park, H., & Cho, Y. (2017). Evaluation of the applicability of pier local scour formulae using laboratory and field data. Marine Georesources & Geotechnology, 35(1), 1–7. https://doi.org/10.1080/1064119X.2014.954658
  225. Patankar, S. V. (1980) “Numerical Heat Transfer and Fluid Flow”, McGraw-Hill Book Company New York
  226. Qi, W., & Gao, F. (2014). Physical modeling of local scour development around a large-diameter monopile in combined waves and current. Coastal Engineering (Amsterdam), 83, 72–81. https://doi.org/10.1016/j.coastaleng.2013.10.007
  227. Qi, M., Li, J., & Chen, Q. (2016). Comparison of existing equations for local scour at bridge piers: parameter influence and validation. Natural Hazards (Dordrecht), 82(3), 2089–2105. https://doi.org/10.1007/s11069-016-2287-z
  228. Rambabu, M., Rao, S., & Sundar, V. (2003). Current-induced scour around a vertical pile in cohesive soil. Ocean Engineering, 30(7), 893–920. https://doi.org/10.1016/S0029-8018(02)00063-X
  229. Raudkivi, A., & Ettema, R. (1985). Scour at Cylindrical Bridge Piers in Armored Beds. Journal of Hydraulic Engineering (New York, N.Y.), 111(4), 713–731. https://doi.org/10.1061/(ASCE)0733-9429(1985)111:4(713)
  230. Rhie, C.-M and Chow, W.L. (1983) “Numerical study of the turbulent flow past and airfoil with trailing edge separation”, AIAA Journal, Vol. 21, No. 11.
  231. Richardson, E., & Lagasse, P. (1996). Stream Stability and Scour at Highway Bridges. Water International, 21(3), 108–118. https://doi.org/10.1080/02508069608686502
  232. Richardson EV, Davis SR (2001) Evaluating scour at bridges. Hydraulic engineering circular no. 18 (HEC-18), Report no. FHWA: NHI 01-001, Federal Highway Administration, Washington, DC
  233. Richardson, J., & Panchang, V. (1998). Three-Dimensional Simulation of Scour-Inducing Flow at Bridge Piers. Journal of Hydraulic Engineering (New York, N.Y.), 124(5), 530–540. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:5(530)
  234. Roulund, A., Sumer, B., Fredsøe, J., & Michelsen, J. (2005). Numerical and experimental investigation of flow and scour around a circular pile. Journal of Fluid Mechanics, 534, 351–401. https://doi.org/10.1017/S0022112005004507
  235. Salaheldin, T., Imran, J., & Chaudhry, M. (2004). Numerical Modeling of Three-Dimensional Flow Field Around Circular Piers. Journal of Hydraulic Engineering (New York, N.Y.), 130(2), 91–100. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:2(91)
  236. Salim, M. and J.S. Jones, 1995, “Effects of Exposed Pile Foundations on Local Pier Scour,” Proceedings ASCE Water Resources Engineering Conference, San Antonio, TX.
  237. Salim, M. and J.S. Jones, 1996, “Scour Around Exposed Pile Foundations,” Proceedings ASCE North American and Water and Environment Congress, ’96, Anaheim, CA (also issued as FHWA Memo).
  238. Salim, M. and J.S. Jones, 1999, Scour Around Exposed Pile Foundations,” ASCE Compendium, Stream Stability and Scour at Highway Bridges, Richardson and Lagasse (eds.), Reston, VA.
  239. Schlichting, H. (1979) “Boundary layer theory”, McGraw-Hill.
  240. Sheppard, D., & Miller, W. (2006). Live-Bed Local Pier Scour Experiments. Journal of Hydraulic Engineering (New York, N.Y.), 132(7), 635–642. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:7(635)
  241. Sheppard, D., Demir, H., & Melville, B. (2011). Scour at wide piers and long skewed piers. Transportation Research Board.
  242. Sheppard, D., Melville, B., & Demir, H. (2014). Evaluation of Existing Equations for Local Scour at Bridge Piers. Journal of Hydraulic Engineering (New York, N.Y.), 140(1), 14–23. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000800
  243. Sheppard, D., Odeh, M., & Glasser, T. (2004). Large Scale Clear-Water Local Pier Scour Experiments. Journal of Hydraulic Engineering (New York, N.Y.), 130(10), 957–963. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:10(957)
  244. Shields, A. (1936). Application of similarity principles and turbulence research to bed-load movement (translated version). Mitteilungen der Preußischen Versuchsanstalt für Wasserbau.
  245. Smith, W.L., 1999, “Local Structure-Induced Sediment Scour at Pile Groups,” M.S. Thesis, University of Florida, Gainesville, FL.
  246. Sonia Devi, Y., & Barbhuiya, A. (2017). Bridge pier scour in cohesive soil: a review. Sadhana (Bangalore), 42(10), 1803–1819. https://doi.org/10.1007/s12046-017-0698-5
  247. Sturm, T., Ettema, R., & Melville, B. (2011). Evaluation of bridge-scour research abutment and contraction scour processes and prediction. National Cooperative Highway Research Program, Transportation Research Board of the National Academies.
  248. Sumer, B., Fredsøe, J., & Christiansen, N. (1992a). Scour Around Vertical Pile in Waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 118(1), 15–31. https://doi.org/10.1061/(ASCE)0733-950X(1992)118:1(15)
  249. Sumer, B. M., Christiansen, N., and Fredsoe, J. (1992b). “Time scale of scour around a vertical pile.” Proc., 2nd Int. Offshore and Polar Engrg. Conf., International Society of Offshore and Polar Engineers, San Francisco, Calif., Vol. III, 308-315.
  250. Sumer, B., Christiansen, N., & Fredsøe, J. (1993). Influence of Cross Section on Wave Scour around Piles. Journal of Waterway, Port, Coastal, and Ocean Engineering, 119(5), 477–495. https://doi.org/10.1061/(ASCE)0733-950X(1993)119:5(477)
  251. Sumer, B., & Fredsøe, J. (1998). Wave Scour around Group of Vertical Piles. Journal of Waterway, Port, Coastal, and Ocean Engineering, 124(5), 248–256. https://doi.org/10.1061/(ASCE)0733-950X(1998)124:5(248)
  252. Sumer, B., & Fredsøe, J. (2001). Wave Scour around a Large Vertical Circular Cylinder. Journal of Waterway, Port, Coastal, and Ocean Engineering, 127(3), 125–134. https://doi.org/10.1061/(ASCE)0733-950X(2001)127:3(125)
  253. Sumer, B., Whitehouse, R., & Tørum, A. (2001). Scour around coastal structures: a summary of recent research. Coastal Engineering, 44(2), 153–190. https://doi.org/10.1016/S0378-3839(01)00024-2
  254. Sumer, B., Hatipoglu, F., & Fredsøe, J. (2007). Wave Scour around a Pile in Sand, Medium Dense, and Dense Silt. Journal of Waterway, Port, Coastal, and Ocean Engineering, 133(1), 14–27. https://doi.org/10.1061/(ASCE)0733-950X(2007)133:1(14)
  255. Toth, E., & Brandimarte, L. (2011). Prediction of local scour depth at bridge piers under clear-water and live-bed conditions: Comparison of literature formulae and Artificial Neural networks. Journal of Hydroinformatics, 13(4), 812–824. https://doi.org/10.2166/hydro.2011.065
  256. Van Rijn, L. C. (1993). Principles of sediment transport in rivers, estuaries and coastal seas.
  257. Vanoni, V.A., ed., 1975, Sedimentation Engineering: American Society of Civil Engineers, Manuals and Reports on Engineering Practice, No. 54, 745 p.
  258. Wang, C., Yu, X., & Liang, F. (2017). A review of bridge scour: mechanism, estimation, monitoring and countermeasures. Natural Hazards (Dordrecht), 87(3), 1881–1906. https://doi.org/10.1007/s11069-017-2842-2
  259. Wardhana, K., & Hadipriono, F. (2003). Analysis of Recent Bridge Failures in the United States. Journal of Performance of Constructed Facilities, 17(3), 144–150. https://doi.org/10.1061/(ASCE)0887-3828(2003)17:3(144)
  260. White, C. M. (1940). The Equilibrium of Grains on the Bed of a Stream. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 174(958), 322–338. https://doi.org/10.1098/rspa.1940.0023
  261. Whitehouse, R. (2004). Marine scour at large foundations. In: Second international conference on scour and erosion (ICSE-2), Singapore
  262. Wu, Peng. Hirshfield, Faye. Sui, Jue-yi. (2015). Local scour around bridge abutments under ice covered condition-an experimental study. International Journal of Sediment Research, 30(1), 39–47. https://doi.org/10.1016/S1001-6279(15)60004-X
  263. Wu, P., Balachandar, R., & Sui, J. (2016). Local Scour around Bridge Piers under Ice-Covered Conditions. Journal of Hydraulic Engineering (New York, N.Y.), 142(1), 4015038–. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001063
  264. Wu, W., Rodi, W., & Wenka, T. (2000). 3D Numerical Modeling of Flow and Sediment Transport in Open Channels. Journal of Hydraulic Engineering (New York, N.Y.), 126(1), 4–15. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:1(4)
  265. Xiong, W., Cai, C., Kong, B., & Kong, X. (2016). CFD Simulations and Analyses for Bridge-Scour Development Using a Dynamic-Mesh Updating Technique. Journal of Computing in Civil Engineering, 30(1), 4014121–. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000458
  266. Yalin, M. S. (1971). Theory of hydraulic models. Macmillan International Higher Education.
  267. Yankielun, N., & Zabilansky, L. (1999). Laboratory Investigation of Time-Domain Reflectometry System for Monitoring Bridge Scour. Journal of Hydraulic Engineering (New York, N.Y.), 125(12), 1279–1284. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:12(1279)
  268. Zaid, M., Yazdanfar, Z., Chowdhury, H., & Alam, F. (2019). Numerical modeling of flow around a pier mounted in a flat and fixed bed. Energy Procedia, 160, 51–59. https://doi.org/10.1016/j.egypro.2019.02.118
  269. Zanke, U., Hsu, T., Roland, A., Link, O., & Diab, R. (2011). Equilibrium scour depths around piles in noncohesive sediments under currents and waves. Coastal Engineering (Amsterdam), 58(10), 986–991. https://doi.org/10.1016/j.coastaleng.2011.05.011
  270. Zhao, M., Zhu, X., Cheng, L., & Teng, B. (2012). Experimental study of local scour around subsea caissons in steady currents. Coastal Engineering (Amsterdam), 60(1), 30–40. https://doi.org/10.1016/j.coastaleng.2011.08.004
  271. Zheng, S., Zheng, S., Xu, Y., Xu, Y., Cheng, H., Cheng, H., Wang, B., Wang, B., Lu, X., & Lu, X. (2018). Assessment of bridge scour in the lower, middle, and upper Yangtze River estuary with riverbed sonar profiling techniques. Environmental Monitoring and Assessment, 190(1), 1–13. https://doi.org/10.1007/s10661-017-6393-5
  272. Zhu, H., Zhou, Z., Yang, R., & Yu, A. (2007). Discrete particle simulation of particulate systems: Theoretical developments. Chemical Engineering Science, 62(13), 3378–3396. https://doi.org/10.1016/j.ces.2006.12.089
  273. Zhu, H.P. Zhou, Z.Y. Hou, Q.F. Yu A.B. (2011). Linking discrete particle simulation to continuum process modelling for granular matter： Theory and application. Particuology, 9(4), 342–357. https://doi.org/10.1016/j.partic.2011.01.002
  274. Zhu, Zw., Liu, Zq.. (2012). CFD prediction of local scour hole around bridge piers. Journal of Central South University, 19(1), 273–281. https://doi.org/10.1007/s11771-012-1001-x

전문가 Q&A: 자주 묻는 질문

Q1: 이 연구에서 SSIIM 소프트웨어를 선택한 이유는 무엇입니까?

A1: SSIIM은 오픈 소스 CFD 소프트웨어이면서도 퇴적물 이동 해석을 위한 기능이 내장되어 있어 세굴 시뮬레이션에 이상적인 도구였습니다. 특히 입자 크기, 안식각, 점착력 등 다양한 토질 매개변수를 모델에 직접 입력하고 그 영향을 분석할 수 있는 유연성을 제공했기 때문에 본 연구의 목적에 가장 적합했습니다.

Q2: 연구 결과, 미세 모래(0.05mm)의 초기 침식률이 시뮬레이션에서 예상보다 낮게 나타났습니다. 이는 수치 모델에 대해 무엇을 시사합니까?

A2: 이는 SSIIM 모델이 침식률을 계산할 때 사용하는 ‘활성 퇴적층(active sediment layer)’ 두께가 D50(중앙 입경)을 기본값으로 사용하기 때문일 가능성이 높습니다. 미세 입자로 구성된 토양은 입자 단위가 아닌 덩어리(chunk) 단위로 침식될 수 있는데, 현재 모델이 이러한 물리적 현상을 완벽하게 포착하지 못함을 시사합니다. 따라서 시간에 따른 세굴 변화와 미세 토양의 침식 메커니즘을 더 정확히 모사하기 위한 수치 모델의 개선이 필요합니다.

Q3: 연구가 청수 세굴(clear-water scour) 조건에 국한된 이유는 무엇입니까?

A3: 청수 세굴은 유사(sediment)의 유입이 없어 침식만 발생하므로, 명확한 최대 평형 세굴 깊이에 도달합니다. 이는 수치 시뮬레이션에서 결과를 분석하고 비교하기에 더 용이한 조건입니다. 반면, 유사 이동이 활발한 유수 세굴(live-bed scour)은 침식과 퇴적이 반복되는 복잡한 주기적 거동을 보여, 특정 시점의 최대 깊이를 정의하기 어렵기 때문에 초기 연구 범위에서는 제외되었습니다.

Q4: 경사면의 임계 전단 응력 감소를 모델링하기 위해 Brooks(1963) 공식을 사용했지만, 그 매개변수가 실제 측정된 안식각과 직접적으로 일치하지 않았습니다. 이것의 의미는 무엇입니까?

A4: 이는 경사면 효과에 대한 현재의 경험적 모델이 가진 한계를 보여줍니다. 최적의 수치 매개변수는 물리적 특성을 직접 입력해서가 아니라, 실험 결과와 일치하도록 맞추는 과정을 통해 찾아졌습니다. 이는 향후 안식각과 같은 물리적 특성을 직접 입력하여 토사의 붕괴(sand slide)와 임계 전단 응력 감소를 통합적으로 계산할 수 있는 더 견고한 퇴적물 모델이 필요함을 의미합니다.

Q5: 테스트한 12개의 경험식 중 어떤 것이 가장 성능이 좋았으며, 그 이유는 무엇입니까?

A5: TAMU(Texas A&M University) 방법이 가장 우수한 성능을 보였습니다. 이 방법은 안전에 치명적인 과소예측 사례가 없으면서도 SSIIM 시뮬레이션 결과와 가장 근접한 예측값을 제공했습니다. 이는 TAMU 방법이 다른 오래된 공식들보다 더 많은 토질 및 유동 매개변수를 고려하여 현실을 더 잘 반영하기 때문인 것으로 분석됩니다.

결론: 더 높은 품질과 생산성을 향한 길

본 연구는 토양의 안식각과 점착력 같은 매개변수가 교각 세굴 깊이를 결정하는 데 있어 부차적인 요소가 아닌 핵심적인 역할을 한다는 것을 수치적으로 증명했습니다. 이러한 요인들을 무시한 기존의 예측 방식은 부정확하고 잠재적으로 위험한 설계를 초래할 수 있습니다. CFD 시뮬레이션은 이러한 실제 현장의 복잡성을 설계에 통합하여 안전성과 경제성을 동시에 확보할 수 있는 필수적인 도구입니다.

(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

저작권 정보

  • 이 콘텐츠는 Iqbal Singh Budwal의 논문 “Influence of Soil Parameters on Local Pier Scour Depth”를 기반으로 한 요약 및 분석 자료입니다.
  • 출처: https://uwspace.uwaterloo.ca/handle/10012/17156

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

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Fig. B8 Multislice STEM simulations for the structural models obtained from DFT calculations. Top: atomistic structural model. Bottom: Multislice STEM simulations. (a) T-type pure Mg Σ7 GB, and A-type units with (b) three and (c) six Ga columns.

원자 단위 특성 분석을 통한 결함 상평형도 구축: 차세대 소재 설계의 새로운 패러다임

이 기술 요약은 Xuyang Zhou 외 저자가 2023년 Springer Nature (arXiv)에 발표한 논문 “Constructing phase diagrams for defects by correlated atomic-scale characterization”을 기반으로 하며, STI C&D 기술 전문가를 위해 분석 및 요약되었습니다.

Keywords

  • Primary Keyword: 결함 상평형도 (Defect Phase Diagram)
  • Secondary Keywords: 입계 컴플렉션 (Grain boundary complexion), 원자 단위 특성 분석 (atomic-scale characterization), 소재 설계 (materials design), 상변태 (phase transformation), 밀도범함수이론 (density functional theory)

Executive Summary

  • The Challenge: 기존의 소재 상평형도는 재료의 특성을 지배하는 결정 결함의 화학적 상태를 설명하지 못하여, 결함을 이용한 체계적인 소재 설계에 한계가 있었습니다.
  • The Method: 연구팀은 국소적 합금화(local alloying)를 통해 개별 결함의 상변태를 유도하고, 원자 분해능 주사 투과 전자 현미경(STEM)으로 구조적, 화학적 변화를 순차적으로 이미징하는 새로운 접근법을 사용했습니다.
  • The Key Breakthrough: 단일 마그네슘(Mg) 입계(grain boundary)에 갈륨(Ga)을 첨가하여 원자 단위의 상변태를 유도 및 관찰했으며, 이를 바탕으로 실험 기반의 ‘결함 상평형도’를 성공적으로 구축했습니다.
  • The Bottom Line: 이 방법론은 결함의 화학적 복잡성과 상변태를 정밀하게 제어하여 원하는 물성을 구현하는, 새로운 소재 설계 패러다임의 기틀을 마련했습니다.

The Challenge: Why This Research Matters for CFD Professionals

소재 개발은 인류 문명 발전의 근간이 되어 왔습니다. 특히 다상(multi-phase) 재료와 상변태에 대한 이해는 다양한 산업 분야에서 맞춤형 애플리케이션을 가능하게 했습니다. 온도, 압력, 화학 조성에 따른 상(phase)의 변화를 체계적으로 정리한 상평형도(phase diagram)는 소재 설계를 위한 핵심 도구입니다.

하지만 기존의 상평형도는 재료의 기계적, 기능적 특성을 좌우하는 전위(dislocation), 입계(grain boundary)와 같은 결정 결함을 고려하지 않습니다. 이러한 결함 주변의 국소적인 화학 조성은 벌크(bulk) 상태와 크게 다를 수 있으며, 이는 재료 전체의 성능에 지대한 영향을 미칩니다. 최근에는 이러한 결함 주변의 화학적 복잡성을 피하기보다 적극적으로 활용하려는 패러다임의 전환이 이루어지고 있지만, 이를 체계적으로 안내할 열역학적 지침, 즉 ‘결함 상평형도’가 부재한 상황이었습니다. 본 연구는 바로 이 문제를 해결하기 위해 시작되었습니다.

The Approach: Unpacking the Methodology

연구팀은 결함 상변태를 원자 단위에서 연구하기 위해, 다양한 원자 구조를 가질 수 있는 육방정계 조밀 격자(HCP) 구조의 마그네슘(Mg) 내 대칭 입계(Σ7 GB)를 모델 시스템으로 선택했습니다. 연구 방법론은 다음과 같은 단계로 진행되었습니다.

  1. 초기 구조 분석: 먼저, 원자 분해능 주사 투과 전자 현미경(STEM)을 사용하여 순수 Mg 시편에 존재하는 Σ7 입계의 초기 원자 구조(T-type 단위)를 정밀하게 관찰했습니다.
  2. 국소적 합금화: 집속 이온 빔(FIB) 장비를 이용하여 동일한 입계 영역에 갈륨(Ga+) 이온을 국소적으로 주입했습니다. Ga의 농도를 점진적으로 증가시키며 입계의 화학적 환경을 정밀하게 제어했습니다.
  3. 상변태 추적: Ga 이온 주입 후, 다시 동일한 입계를 STEM으로 관찰하여 Ga 농도 증가에 따라 입계의 구조 단위가 T-type에서 A-type으로 변하는 상변태 과정을 직접적으로 이미징했습니다.
  4. 열역학적 모델링: 실험에서 관찰된 다양한 입계상(순수 Mg, Ga 원자 1, 3, 6개 포함 구조)의 열역학적 안정성을 평가하기 위해 밀도범함수이론(DFT) 계산을 수행했습니다.
  5. 결함 상평형도 구축: DFT 계산 결과를 바탕으로, 각 입계상의 형성 에너지를 Ga의 화학 포텐셜 함수로 도식화하여 세계 최초의 실험 기반 ‘결함 상평형도’를 완성했습니다.
Fig. B1 (a) Orientation and GB maps reconstructed from the 4D-STEM data set. The thin film sample shows sharp (0001) texture (red color). Grains with a confidence index of less than 0.1 are shown in black. (b) Bright-field STEM image for the highlighted region in (a). White arrows in both figures point to the Σ7 GB for the high-resolution STEM study.
Fig. B1 (a) Orientation and GB maps reconstructed from the 4D-STEM data set. The thin film sample shows sharp (0001) texture (red color). Grains with a confidence index of less than 0.1 are shown in black. (b) Bright-field STEM image for the highlighted region in (a). White arrows in both figures point to the Σ7 GB for the high-resolution STEM study.

The Breakthrough: Key Findings & Data

본 연구는 결함 수준에서 상변태를 제어하고 이를 열역학적으로 설명하는 중요한 두 가지 발견을 제시합니다.

Finding 1: Ga 합금화에 의한 입계 구조의 제어 가능한 상변태 유도

순수 Mg의 Σ7 입계는 ‘T-type’이라는 특정 구조 단위로 구성되어 있음이 확인되었습니다(그림 1a). 여기에 국소적으로 Ga를 합금화하자 입계 구조에 뚜렷한 변화가 관찰되었습니다. 0.5 at.%의 Ga를 첨가했을 때, 기존의 T-type과 새로운 ‘A-type’ 구조 단위가 혼재하는 상태가 나타났습니다(그림 1b). Ga 농도를 1.2 at.%까지 높이자, 입계는 완전히 A-type 구조 단위로 변형되었습니다(그림 1c). 이는 합금 원소의 농도를 조절하여 결함의 원자 구조, 즉 ‘결함상’을 의도적으로 제어할 수 있음을 실험적으로 증명한 첫 사례입니다.

Finding 2: 실험 기반 결함 상평형도의 성공적인 구축

연구팀은 실험적 관찰과 DFT 계산을 결합하여 Mg Σ7 입계에 대한 결함 상평형도를 구축했습니다(그림 3). 이 상평형도는 Ga의 화학 포텐셜(µGa, x축)에 따라 어떤 입계 구조(0-Ga T-type, 1-Ga A-type, 3-Ga 및 6-Ga 정렬 A-type)가 가장 안정적인지(형성 에너지, y축)를 명확하게 보여줍니다. 특히, 장시간 확산 후 벌크 내 Ga 농도가 0.7%로 측정된 시편에서, 상평형도는 ‘3-Ga’ 정렬상이 가장 안정적일 것이라고 예측했으며, 이는 실제 실험 관찰 결과와 정확히 일치했습니다. 이는 결함 상평형도가 실제 재료의 결함 상태를 예측하는 신뢰성 있는 도구가 될 수 있음을 입증합니다.

Practical Implications for R&D and Operations

  • For Process Engineers: 본 연구는 국소적 합금화나 열처리를 통한 확산 제어 등 특정 공정 변수를 조절하여 입계와 같은 결함의 구조를 엔지니어링할 수 있음을 시사합니다. 이는 재료의 기계적 강도나 수송 특성을 미세 조정하는 새로운 공정 개발로 이어질 수 있습니다.
  • For Quality Control Teams: 결함 상평형도(그림 3)는 벌크 조성에 따라 어떤 결함 구조가 존재할 수 있는지 예측하는 데 사용될 수 있습니다. 이는 재료의 취성이나 예기치 않은 물성 변화의 근본 원인을 파악하고, 새로운 품질 검사 기준을 수립하는 데 정보를 제공할 수 있습니다.
  • For Design Engineers: 이 연구 결과는 ‘결함 엔지니어링’이라는 새로운 소재 설계 가능성을 엽니다. 단순히 벌크 합금을 설계하는 것을 넘어, 특정 결함 구조를 표적으로 하여 향상된 강도, 연성 또는 기능성을 갖는 맞춤형 입계 특성을 가진 합금을 체계적으로 설계할 수 있는 열역학적 프레임워크를 제공합니다.

Paper Details

Constructing phase diagrams for defects by correlated atomic-scale characterization

1. Overview:

  • Title: Constructing phase diagrams for defects by correlated atomic-scale characterization
  • Author: Xuyang Zhou, Prince Mathews, Benjamin Berkels, Saba Ahmad, Amel Shamseldeen Ali Alhassan, Philipp Keuter, Jochen M. Schneider, Dierk Raabe, Jörg Neugebauer, Gerhard Dehm, Tilmann Hickel, Christina Scheu and Siyuan Zhang
  • Year of publication: 2023
  • Journal/academic society of publication: Springer Nature (arXiv:2303.09465v2)
  • Keywords: Grain boundary complexion, defect phase diagram, transmission electron microscopy, density functional theory, automatic pattern recognition

2. Abstract:

Phase transformations and crystallographic defects are two essential tools to drive innovations in materials. Bulk materials design via tuning chemical compositions has been systematized using phase diagrams. We show here that the same thermodynamic concept can be applied to understand the chemistry at defects. We present a combined experimental and modelling approach to scope and build phase diagrams for defects. The discovery was enabled by triggering phase transformations of individual defects through local alloying, and sequentially imaging the structural and chemical changes using atomic-resolution scanning transmission electron microscopy. By observing atomic-scale phase transformations of a Mg grain boundary through Ga alloying, we exemplified the method to construct a grain boundary phase diagram using ab initio simulations and thermodynamic principles. The methodology enables a systematic development of defect phase diagrams to propel a new paradigm for materials design utilizing chemical complexity and phase transformations at defects.

3. Introduction:

재료 개발은 인류 문명 발전의 핵심 동력이었습니다. 특히 상평형도는 온도, 압력, 화학 조성과 같은 변수가 재료의 상과 특성에 미치는 영향을 이해하는 데 결정적인 도구 역할을 해왔습니다. 그러나 기존의 상평형도는 재료의 많은 특성을 제어하는 전위나 입계와 같은 결정 결함을 설명하지 못합니다. 이러한 결함은 국소적인 구조적 왜곡뿐만 아니라, 주변 벌크상과 크게 다른 화학 조성을 가질 수 있습니다. 최근 재료 설계의 패러다임은 결함 주변의 화학적 복잡성을 피하는 대신 적극적으로 활용하는 방향으로 전환되고 있습니다. 이러한 결함에서의 국소적 화학 상태는 “저차원상”, “컴플렉션”, 또는 “결함상” 등으로 불리며, 벌크상과 구별됩니다. 본 연구는 이러한 결함상을 체계적으로 탐색하고 설계하기 위한 열역학적 지침, 즉 ‘결함 상평형도’를 실험적으로 구축하는 방법론을 제시하고자 합니다.

4. Summary of the study:

Background of the research topic:

벌크 재료의 설계는 화학 조성을 조절하여 원하는 상을 얻는 방식으로, 상평형도를 통해 체계화되었습니다. 그러나 재료의 기계적, 기능적 특성은 종종 입계와 같은 결정 결함에 의해 지배됩니다.

Fig. B2 Burgers circuit analysis for the (a) T-type and (b) A-type structural units. The black arrows show pairs of 1 3 ⟨2110⟩ vectors that are closed by the Burgers vectors ⃗b = 1 3 [2110] (red arrows). The nomenclature for the atomic columns is shown on top of them.
Fig. B2 Burgers circuit analysis for the (a) T-type and (b) A-type structural units. The black arrows show pairs of 1/3 ⟨2110⟩ vectors that are closed by the Burgers vectors ⃗b = 1/3 [2110] (red arrows). The nomenclature for the atomic columns is shown on top of them.

Status of previous research:

결함 주변에 용질 원자가 편석되는 현상은 잘 알려져 있으며, 이를 통해 재료 특성을 제어하려는 시도가 있었습니다. 예를 들어, 입계 편석을 통해 액상 입계상을 형성하여 금속의 취성을 유발하는 경우도 보고되었습니다. 그러나 이러한 결함상의 형성과 변태를 체계적으로 탐색하고 예측할 수 있는 열역학적 지침, 즉 ‘결함 상평형도’를 실험적으로 구축하는 방법론은 부족했습니다.

Purpose of the study:

본 연구의 목적은 동일한 결함을 대상으로 화학 포텐셜을 조절하며 나타나는 상변태를 직접 관찰하고, 이를 바탕으로 결함에 대한 열역학적 상평형도를 구축하는 새로운 통합 방법론을 제시하는 것입니다.

Core study:

연구팀은 Mg의 Σ7 입계에 Ga를 국소적으로 합금화하여 입계의 상변태를 유도했습니다. 원자 분해능 STEM 이미징을 통해 T-type에서 A-type으로의 구조적 변태와 Ga 원자의 다양한 정렬 상태를 확인했습니다. 이 실험 결과를 밀도범함수이론(DFT) 계산과 결합하여, Ga의 화학 포텐셜에 따른 각 결함상의 안정성을 평가하고, 이를 통해 해당 입계에 대한 ‘결함 상평형도’를 성공적으로 구축했습니다.

5. Research Methodology

Research Design:

본 연구는 실험적 관찰과 이론적 계산을 결합한 상관적(correlated) 접근법을 채택했습니다. 단일 입계를 대상으로 국소 합금화를 통해 화학적 환경을 변화시키고, 그에 따른 구조 변화를 원자 단위에서 직접 추적했습니다.

Data Collection and Analysis Methods:

  • 시편 제작: 나노결정 Mg 박막을 스퍼터 증착 방식으로 제작했습니다.
  • 국소 합금화 및 TEM 시편 준비: 집속 이온 빔(FIB)을 사용하여 Ga+ 이온을 특정 입계 영역에 주입하고, 동시에 TEM 관찰용 시편을 제작했습니다.
  • 전자 현미경 분석: 고분해능 STEM 이미징(HAADF-STEM)을 통해 원자 배열을 직접 관찰했으며, 에너지 분산형 X선 분광법(EDS)으로 화학 조성을 분석했습니다.
  • 계산 방법: 밀도범함수이론(DFT) 계산을 통해 실험에서 관찰된 다양한 입계 구조의 형성 에너지를 계산하여 열역학적 안정성을 평가했습니다.
  • 자동 패턴 인식: 개발된 알고리즘을 사용하여 STEM 이미지에서 T-type 및 A-type 구조 단위를 자동으로 식별하고 분류했습니다.

Research Topics and Scope:

연구는 HCP Mg의 [0001] 경사축을 따라 형성된 Σ7 대칭 경사 입계를 대상으로 합니다. 합금 원소로는 Ga을 사용하여 입계의 구조적, 화학적 상변태를 유도하고, 이에 대한 결함 상평형도를 구축하는 데 초점을 맞췄습니다.

6. Key Results:

Key Results:

  • 국소적 Ga 합금화는 Mg Σ7 입계의 구조 단위를 T-type에서 A-type으로 변형시키는 상변태를 유도했습니다.
  • Ga 농도가 증가함에 따라, A-type 구조 단위 내에서 Ga 원자들이 특정 위치에 규칙적으로 배열되는 화학적 정렬 현상이 관찰되었습니다. (6-Ga 및 3-Ga 정렬상)
  • 실험적 관찰과 DFT 계산을 결합하여, Ga의 화학 포텐셜에 따른 각 결함상의 안정성을 나타내는 결함 상평형도를 성공적으로 구축했습니다.
  • 구축된 결함 상평형도는 실험에서 관찰된 화학적 조건(예: 벌크 Ga 농도 0.7%)에서 가장 안정한 결함상(3-Ga 정렬상)을 정확하게 예측했습니다.
Fig. B8 Multislice STEM simulations for the structural models obtained from DFT calculations. Top: atomistic structural model. Bottom: Multislice STEM simulations. (a) T-type pure Mg Σ7 GB, and A-type units with (b) three and (c) six Ga columns.
Fig. B8 Multislice STEM simulations for the structural models obtained from DFT calculations.
Top: atomistic structural model. Bottom: Multislice STEM simulations. (a) T-type pure Mg Σ7 GB, and A-type units with (b) three and (c) six Ga columns.

Figure List:

  • Fig. 1 Experimental observation of a GB phase transformation in Mg by local alloying of Ga.
  • Fig. 2 Transformation of chemically-ordered GB phases.
  • Fig. 3 Construction of a defect phase diagram from observed phase transformations.
  • Fig. B1 (a) Orientation and GB maps reconstructed from the 4D-STEM data set.
  • Fig. B2 Burgers circuit analysis for the (a) T-type and (b) A-type structural units.
  • Fig. B3 The Ga composition inside the Mg sample as a function of the implantation time and the evaluated implantation rate.
  • Fig. B4 HAADF-STEM images without overlaid grids, corresponding to the ones presented in Fig. 1.
  • Fig. B5 Snapshots of DFT structural relaxation starting with a T-type unit with Ga atoms on the (a) b2 and (b) e2 sites, ending to an A-type unit with Ga atoms on the (a) a1 and (b) b2 sites.
  • Fig. B6 Automatic pattern recognition to classify experimental images into T-type and A-type structural units.
  • Fig. B7 HAADF-STEM images of the same Σ7 GB (a) 1 day and (b) 620 days after Ga+ beam thinning.
  • Fig. B8 Multislice STEM simulations for the structural models obtained from DFT calculations.

7. Conclusion:

본 연구는 원자 단위의 STEM 특성 분석, 자동 패턴 인식, DFT 모델링을 결합하여 결함 상평형도를 구축하는 효과적인 방법을 시연했습니다. 국소 합금화와 시간 경과에 따른 확산을 통해 다양한 화학 포텐셜 영역을 실험적으로 탐색했으며, 이를 통해 Mg Σ7 입계가 Ga 첨가에 따라 T-type에서 A-type으로 상변태하고, 다양한 화학적 정렬상을 형성하는 것을 관찰했습니다. 이 방법론은 방대한 수의 잠재적 결함 구조 중에서 실험적으로 유의미한 구조를 식별하여 이론적 계산의 범위를 좁혀주고, 계산 결과와 실제 열역학적 평형 상태를 연결해 줍니다. 개발된 방법론은 다양한 입계 및 결함 연구에 보편적으로 적용될 수 있으며, 과학 및 공학 분야에서 결함 상평형도의 활용을 촉진할 것입니다.

8. References:

  1. Tasan, C.C., Diehl, M., Yan, D., Bechtold, M., Roters, F., Schemmann, L., Zheng, C., Peranio, N., Ponge, D., Koyama, M., Tsuzaki, K., Raabe, D.: An Overview of Dual-Phase Steels: Advances in Microstructure-Oriented Processing and Micromechanically Guided Design. Annual Review of Materials Research 45, 391–431 (2015). https://doi.org/10. 1146/annurev-matsci-070214-021103
  2. Sharma, A., Tyagi, V.V., Chen, C.R., Buddhi, D.: Review on thermal energy storage with phase change materials and applications. Renewable and Sustainable Energy Reviews 13(2), 318–345 (2009). https://doi.org/ 10.1016/j.rser.2007.10.005
  3. Raabe, D., Sander, B., Friák, M., Ma, D., Neugebauer, J.: Theory-guided bottom-up design of β-titanium alloys as biomaterials based on first principles calculations: Theory and experiments. Acta Materialia 55(13), 4475–4487 (2007). https://doi.org/10.1016/j.actamat.2007.04.024
  4. Gibbs, J.W.: The collected works of j. willard gibbs. Technical report, Yale Univ. Press, (1948)
  5. Buban, J., Matsunaga, K., Chen, J., Shibata, N., Ching, W., Yamamoto, T., Ikuhara, Y.: Grain boundary strengthening in alumina by rare earth impurities. Science 311(5758), 212–215 (2006)
  6. Lu, L., Sui, M., Lu, K.: Superplastic extensibility of nanocrystalline copper at room temperature. Science 287(5457), 1463–1466 (2000)
  7. Legros, M., Dehm, G., Arzt, E., Balk, T.J.: Observation of giant diffusivity along dislocation cores. Science 319(5870), 1646–1649 (2008)
  8. Lu, L., Shen, Y., Chen, X., Qian, L., Lu, K.: Ultrahigh strength and high electrical conductivity in copper. Science 304(5669), 422–426 (2004)
  9. Cottrell, A.H., Bilby, B.A.: Dislocation theory of yielding and strain age-ing of iron. Proceedings of the Physical Society. Section A 62(1), 49–62 (1949). https://doi.org/10.1088/0370-1298/62/1/308
  10. Kuzmina, M., Herbig, M., Ponge, D., Sandlöbes, S., Raabe, D.: Lin-ear complexions: Confined chemical and structural states at dislocations. Science 349(6252), 1080–1083 (2015). https://doi.org/10.1126/science. aab2633
  11. Zhou, X., Mianroodi, J.R., Kwiatkowski da Silva, A., Koenig, T., Thomp-son, G.B., Shanthraj, P., Ponge, D., Gault, B., Svendsen, B., Raabe, D.: The hidden structure dependence of the chemical life of dislocations. Science Advances 7(16), 0563 (2021)
  12. Yu, Y., Zhou, C., Zhang, X., Abdellaoui, L., Doberstein, C., Berkels, B., Ge, B., Qiao, G., Scheu, C., Wuttig, M., Cojocaru-Mirédin, O., Zhang, S.: Dynamic doping and Cottrell atmosphere optimize the thermoelectric per-formance of n-type PbTe over a broad temperature interval. Nano Energy 101(April) (2022). https://doi.org/10.1016/j.nanoen.2022.107576
  13. Suzuki, H.: Segregation of solute atoms to stacking faults. Journal of the Physical Society of Japan 17(2), 322–325 (1962). https://doi.org/10. 1143/JPSJ.17.322
  14. Palanisamy, D., Raabe, D., Gault, B.: On the compositional partitioning during phase transformation in a binary ferromagnetic mnal alloy. Acta Materialia 174, 227–236 (2019)
  15. Lejček, P., Hofmann, S.: Segregation enthalpies of phosphorus, carbon and silicon at {013} and {012} symmetrical tilt grain boundaries in an fe-3.5 at.% si alloy. Acta metallurgica et materialia 39(10), 2469–2476 (1991)
  16. Kirchheim, R.: Grain coarsening inhibited by solute segregation. Acta Materialia 50(2), 413–419 (2002)
  17. Wang, Z., Saito, M., McKenna, K.P., Gu, L., Tsukimoto, S., Shluger, A.L., Ikuhara, Y.: Atom-resolved imaging of ordered defect superstructures at individual grain boundaries. Nature 479(7373), 380–383 (2011)
  18. Chookajorn, T., Murdoch, H.A., Schuh, C.A.: Design of stable nanocrys-talline alloys. Science 337(6097), 951–954 (2012). https://doi.org/10. 1126/science.1224737
  19. Nie, J.F., Zhu, Y., Liu, J., Fang, X.-Y.: Periodic segregation of solute atoms in fully coherent twin boundaries. Science 340(6135), 957–960 (2013)
  20. Raabe, D., Herbig, M., Sandlöbes, S., Li, Y., Tytko, D., Kuzmina, M., Ponge, D., Choi, P.P.: Grain boundary segregation engineering in metallic alloys: A pathway to the design of interfaces. Current Opinion in Solid State and Materials Science 18(4), 253–261 (2014). https://doi.org/10. 1016/j.cossms.2014.06.002
  21. Yu, Z., Cantwell, P.R., Gao, Q., Yin, D., Zhang, Y., Zhou, N., Rohrer, G.S., Widom, M., Luo, J., Harmer, M.P.: Segregation-induced ordered superstructures at general grain boundaries in a nickel-bismuth alloy. Science 358(6359), 97–101 (2017)
  22. Lejček, P., Šob, M., Paidar, V.: Interfacial segregation and grain boundary embrittlement: An overview and critical assessment of experimental data and calculated results. Progress in Materials Science 87, 83–139 (2017)
  23. Zhou, X., Ahmadian, A., Gault, B., Ophus, C., Liebscher, C.H., Dehm, G., Raabe, D.: Atomic motifs govern the decoration of grain boundaries by interstitial solutes. Nature Communications 14(1), 3535 (2023)
  24. Hart, E.W.: Two-dimensional phase transformation in grain bound-aries. Scripta Metallurgica 2(3), 179–182 (1968). https://doi.org/10.1016/ 0036-9748(68)90222-6
  25. Frolov, T., Mishin, Y.: Phases, phase equilibria, and phase rules in low-dimensional systems. The Journal of chemical physics 143(4), 044706 (2015)
  26. Brink, T., Langenohl, L., Bishara, H., Dehm, G.: Universality of grain boundary phases in fcc metals: Case study on high-angle sym-metric tilt grain boundaries. Physical Review B – Condensed Matter and Materials Physics 054103 (2022) https://arxiv.org/abs/2211.14170. https://doi.org/10.1103/PhysRevB.107.054103
  27. Dillon, S.J., Tang, M., Carter, W.C., Harmer, M.P.: Complexion: A new concept for kinetic engineering in materials science. Acta Materi-alia 55(18), 6208–6218 (2007). https://doi.org/10.1016/j.actamat.2007. 07.029
  28. Harmer, M.P.: The phase behavior of interfaces. Science 332(6026), 182– 183 (2011)
  29. Luo, J., Cheng, H., Asl, K.M., Kiely, C.J., Harmer, M.P.: The role of a bilayer interfacial phase on liquid metal embrittlement. Science 333(6050), 1730–1733 (2011)
  30. Kaplan, W.D., Chatain, D., Wynblatt, P., Carter, W.C.: A review of wet-ting versus adsorption, complexions, and related phenomena: The rosetta stone of wetting. Journal of Materials Science 48(17), 5681–5717 (2013). https://doi.org/10.1007/s10853-013-7462-y
  31. Cantwell, P.R., Tang, M., Dillon, S.J., Luo, J., Rohrer, G.S., Harmer, M.P.: Grain boundary complexions. Acta Materialia 62(1), 1–48 (2014). https://doi.org/10.1016/j.actamat.2013.07.037
  32. Korte-Kerzel, S., Hickel, T., Huber, L., Raabe, D., Sandlöbes-Haut, S., Todorova, M., Neugebauer, J.: Defect phases–thermodynamics and impact on material properties. International Materials Reviews 67(1), 89–117 (2022). https://doi.org/10.1080/09506608.2021.1930734
  33. Bishara, H., Lee, S., Brink, T., Ghidelli, M., Dehm, G.: Understanding Grain Boundary Electrical Resistivity in Cu: The Effect of Boundary Structure. ACS Nano 15(10), 16607–16615 (2021). https://doi.org/10. 1021/acsnano.1c06367
  34. Bueno Villoro, R., Zavanelli, D., Jung, C., Mattlat, D.A., Hatami Nader-loo, R., Pérez, N., Nielsch, K., Snyder, G.J., Scheu, C., He, R., Zhang, S.: Grain Boundary Phases in NbFeSb Half-Heusler Alloys: A New Avenue to Tune Transport Properties of Thermoelectric Materials. Advanced Energy Materials (2023). https://doi.org/10.1002/aenm.202204321
  35. Bueno Villoro, R., Wood, M., Luo, T., Bishara, H., Abdellaoui, L., Zavanelli, D., Gault, B., Snyder, G.J., Scheu, C., Zhang, S.: Fe Segregation as a Tool to Enhance Electrical Conductivity of Grain Boundaries in Ti ( Co , Fe ) Sb Half Heusler Thermoelectrics. Acta Materialia 249(March), 118816 (2023). https://doi.org/10.1016/j.actamat.2023.118816
  36. Duerrschnabel, M., Yi, M., Uestuener, K., Liesegang, M., Katter, M., Kleebe, H.J., Xu, B., Gutfleisch, O., Molina-Luna, L.: Atomic structure and domain wall pinning in samarium-cobalt-based permanent mag-nets. Nature Communications 8(1), 1–7 (2017). https://doi.org/10.1038/ s41467-017-00059-9
  37. Hall, E.O.: The deformation and ageing of mild steel: III Discussion of results. Proceedings of the Physical Society. Section B 64(9), 747–753 (1951). https://doi.org/10.1088/0370-1301/64/9/303
  38. Wu, R., Freeman, A., Olson, G.B.: First principles determination of the effects of phosphorus and boron on iron grain boundary cohesion. Science 265(5170), 376–380 (1994)
  39. Khalajhedayati, A., Pan, Z., Rupert, T.J.: Manipulating the interfacial structure of nanomaterials to achieve a unique combination of strength and ductility. Nature communications 7(1), 10802 (2016)
  40. Krause, A.R., Cantwell, P.R., Marvel, C.J., Compson, C., Rickman, J.M., Harmer, M.P.: Review of grain boundary complexion engineering: Know your boundaries. Journal of the American Ceramic Society 102(2), 778– 800 (2018). https://doi.org/10.1111/jace.16045
  41. Cantwell, P.R., Frolov, T., Rupert, T.J., Krause, A.R., Marvel, C.J., Rohrer, G.S., Rickman, J.M., Harmer, M.P.: Grain Boundary Complex-ion Transitions. Annual Review of Materials Research 50, 465–492 (2020). https://doi.org/10.1146/annurev-matsci-081619-114055
  42. Dehm, G., Cairney, J.: Implication of grain-boundary structure and chem-istry on plasticity and failure. MRS Bulletin 47(8), 800–807 (2022). https://doi.org/10.1557/s43577-022-00378-3
  43. Cahn, J. W.: Transitions and phase equilibria among grain boundary structures. J. Phys. Colloques 43(C6), 6–1996213 (1982). https://doi.org/ 10.1051/jphyscol:1982619
  44. Rottman, C.: Phase transitions at internal interfaces. MRS Proceedings 238, 191 (1991). https://doi.org/10.1557/PROC-238-191
  45. Tang, M., Carter, W.C., Cannon, R.M.: Diffuse interface model for struc-tural transitions of grain boundaries. Phys. Rev. B 73, 024102 (2006). https://doi.org/10.1103/PhysRevB.73.024102
  46. Frolov, T., Mishin, Y.: Thermodynamics of coherent interfaces under mechanical stresses. I. Theory. Physical Review B – Condensed Matter and Materials Physics 85(22), 12–15 (2012) https://arxiv.org/abs/1304.0144. https://doi.org/10.1103/PhysRevB.85.224106
  47. Frolov, T., Mishin, Y.: Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries. Physical Review B – Condensed Matter and Materials Physics 85(22) (2012). https://doi.org/10.1103/PhysRevB.85.224107
  48. Frolov, T., Divinski, S.V., Asta, M., Mishin, Y.: Effect of interface phase transformations on diffusion and segregation in high-angle grain bound-aries. Physical Review Letters 110(25), 1–5 (2013) https://arxiv.org/abs/ 1304.0276. https://doi.org/10.1103/PhysRevLett.110.255502
  49. Meiners, T., Frolov, T., Rudd, R.E., Dehm, G., Liebscher, C.H.: Observations of grain-boundary phase transformations in an elemen-tal metal. Nature 579(7799), 375–378 (2020). https://doi.org/10.1038/ s41586-020-2082-6
  50. Frommeyer, L., Brink, T., Freitas, R., Frolov, T., Dehm, G., Lieb-scher, C.H.: Dual phase patterning during a congruent grain boundary phase transition in elemental copper. Nature Communications 13(1), 1–11 (2022) https://arxiv.org/abs/2109.15192. https://doi.org/10.1038/ s41467-022-30922-3
  51. Ference, T.G., Balluffi, R.W.: Observation of a reversible grain boundary faceting transition induced by changes of composition. Scripta Metallur-gica 22(12), 1929–1934 (1988). https://doi.org/10.1016/S0036-9748(88) 80240-0
  52. Peter, N.J., Duarte, M.J., Kirchlechner, C., Liebscher, C.H., Dehm, G.: Faceting diagram for Ag segregation induced nanofaceting at an asym-metric Cu tilt grain boundary. Acta Materialia 214, 116960 (2021). https://doi.org/10.1016/j.actamat.2021.116960
  53. Sigle, W., Richter, G., Rühle, M., Schmidt, S.: Insight into the atomic-scale mechanism of liquid metal embrittlement. Applied Physics Letters 89(12), 1–4 (2006). https://doi.org/10.1063/1.2356322
  54. Zhao, H., Chakraborty, P., Ponge, D., Hickel, T., Sun, B., Wu, C.-H., Gault, B., Raabe, D.: Hydrogen trapping and embrittlement in high-strength al alloys. Nature 602(7897), 437–441 (2022)
  55. Zhang, S., Xie, Z., Keuter, P., Ahmad, S., Abdellaoui, L., Zhou, X., Cautaerts, N., Breitbach, B., Aliramaji, S., Korte-Kerzel, S., Hans, M., Schneider, J.M., Scheu, C.: Atomistic Structures of 0001 Tilt Grain Boundaries in a Textured Mg Thin Film. Nanoscale (2022). https://doi. org/10.1039/D2NR05505H
  56. Wang, Y.C., Ye, H.Q.: On the tilt grain boundaries in hcp Ti with orientation. Philosophical Magazine A: Physics of Condensed Mat-ter, Structure, Defects and Mechanical Properties 75(1), 261–272 (1997). https://doi.org/10.1080/01418619708210294
  57. Ashby, M.F., Spaepen, F., Williams, S.: The structure of grain boundaries described as a packing of polyhedra. Acta Metallurgica 26(11), 1647–1663 (1978). https://doi.org/10.1016/0001-6160(78)90075-5
  58. Pond, R.C., Vitek, V., Smith, D.A.: Grain boundary structures in f.c.c. and b.c.c. metals and sites for segregated impurities. Acta Crystal-lographica Section A 35(4), 689–693 (1979). https://doi.org/10.1107/ S0567739479001571
  59. Sutton, A.P.: On the structural unit model of grain boundary structure. Philosophical Magazine Letters 59(2), 53–59 (1989). https://doi.org/10. 1080/09500838908214777
  60. Huber, L., Rottler, J., Militzer, M.: Atomistic simulations of the inter-action of alloying elements with grain boundaries in mg. Acta materialia 80, 194–204 (2014)
  61. Sato, Y., Yamamoto, T., Ikuhara, Y.: Atomic structures and electrical properties of ZnO grain boundaries. Journal of the American Ceramic Society 90(2), 337–357 (2007). https://doi.org/10.1111/j.1551-2916.2006. 01481.x
  62. Feng, Y., Wang, R., Liu, H., Jin, Z.: Thermodynamic reassessment of the magnesium-gallium system. Journal of Alloys and Compounds 486(1-2), 581–585 (2009). https://doi.org/10.1016/j.jallcom.2009.07.010
  63. Zhang, S., Scheu, C.: Evaluation of EELS spectrum imaging data by spec-tral components and factors from multivariate analysis. Microscopy 67, 133–141 (2018). https://doi.org/10.1093/jmicro/dfx091
  64. Kresse, G., Hafner, J.: Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993). https://doi.org/10.1103/PhysRevB.47. 558
  65. Kresse, G., Furthmüller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical review B 54(16), 11169 (1996)
  66. Kresse, G., Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Physical review b 59(3), 1758 (1999)
  67. Monkhorst, H.J., Pack, J.D.: Special points for brillouin-zone integrations. Physical review B 13(12), 5188 (1976)
  68. Methfessel, M., Paxton, A.T.: High-precision sampling for brillouin-zone integration in metals. Phys. Rev. B 40, 3616–3621 (1989). https://doi. org/10.1103/PhysRevB.40.3616
  69. Alhasan, A.S.A., Zhang, S., Berkels, B.: Direct motif extraction from high resolution crystalline STEM images. Ultramicroscopy 254, 113827 (2023) https://arxiv.org/abs/2303.07438 [eess.IV]. https://doi.org/10. 1016/j.ultramic.2023.113827
  70. Allen, L.J., D’Alfonso, A.J., Findlay, S.D.: Modelling the inelastic scat-tering of fast electrons. Ultramicroscopy 151, 11–22 (2015). https://doi. org/10.1016/j.ultramic.2014.10.011. Special Issue: 80th Birthday of Har-ald Rose; PICO 2015 – Third Conference on Frontiers of Aberration Corrected Electron Microscopy
  71. Lancaster, J. F., 1984, The physics of welding, Physics in Technology, 15:73-79.
  72. Kou, S., 2003, Fusion welding processes, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.3-36.
  73. Steen, W.M., Mazumder, J., 2010, Laser welding: laser material processing, 4th Ed., Springer-Verlag London Limited, UK, pp. 199-250.
  74. Merchant, V., Laser beam welding, In: Ahmed, N., editor, New developments in advanced welding, 1st Ed., Woodhead Publishing Limited, Cambridge, UK, pp. 83-84.
  75. Kugler, T.R., 2001, Fusion front penetration: Conduction Welding, In: Ready, J.F., editor, LIA handbook of laser materials processing, 1st Ed., Magnolia Publishing Inc., FL, USA, pp. 310-312.
  76. Matsunawa, A., 2002, Science of laser welding-mechanisms of keyhole and pool dynamics. In: ICALEO 2002 proceedings, Phoenix, LIA, Orlando, paper: 101.
  77. Lacroix, D., Jeandel, G., Boudot, C., 1996, Spectroscopic studies of laser-induced plume during welding with a Nd:YAG laser, In: Proceedings of SPIE, 2789, pp. 221–227.
  78. Dumord, E., Jouvard, J.M., Grevey, D., 1996, Keyhole modeling during CW Nd:YAG laser welding, In: Proceedings of SPIE, 2789, pp. 213–220.
  79. Berkmanns, J., Faerber, M., 2005, Facts about laser technology: laser welding, http://www.laserdeal.com/, access date: January 20, 2012.
  80. Coherent Inc., 2004, High speed welding of metals with diamond CO2 laser – stainless steels, Technical Note, http://www.coherent.de/, access date: November 15, 2011.
  81. LWS, 2006, A technical report on the LWS flexcell cladding system, http://www.laserweldingsolutions.com/, access date: April 01, 2009.
  82. Shannon, G., 2009, Source selection for laser welding, http://www.industrial-lasers.com/, access date: April 01, 2009.
  83. Faerber, M., Berkmanns, J., 1996, Gases for increased laser welding productivity, In: Proceedings of the ISATA Conference, pp. 791–798.
  84. Schuberth S, Schedin E, Fröhlich T, Ratte E., 2008, Next generation vehicle – engineering guidelines for stainless steel in automotive applications, In: Proceedings of the 6th stainless steel science and market conference, Helsinki, Finland.
  85. Kou, S., 2003, Weld metal solidification, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.199-207.
  86. Han, W., 2004, Computational and experimental investigations of laser drilling and welding for microelectronic packaging, Ph.D. Dissertation, Worcester Polytechnic Institute, Worcester, MA, USA, pp. 85-87.
  87. Buchfink, G., 2007, A world of possibilities – joining, In: Kammϋller, N.L., editor, The laser as a tool, 1st Ed., Vogel Buchverlag, Wϋrzburg, Germany, pp. 166-167.
  88. ISO13919-1:1996, Welding – Electrons and laser beam welded joints – guidance on quality levels for imperfections – Part I: Steel, pp. 4-13.
  89. Zhang, Y.M., Kovacevic, R., Li, L., 1996, Characterization and real time measurement of geometrical appearance of the weld pool. International Journal of Machine Tools and Manufacture, 36(7):799–816.
  90. Bull, C.E., Stacey, K.A., Calcraft, R., 1993, Online weld monitoring using ultrasonic. Journal of Non-destructive Test, 35(2):57–64.
  91. Tarng, Y.S., Yang, W.H., 1998, Optimization of the weld bead geometry in gas Tungsten Arc welding by the Taguchi Method. Journal of Advanced Manufacturing Technology, 14:549–54.
  92. Benyounis, K.Y.,Olabi, A.G.,Hasmi, M.S.J., 2008, Multi-response optimization of CO2 laser welding process of austenitic stainless steel, Optics & Laser Technology, 40:76–87.
  93. Antony, J., 2003, Introduction to industrial experimentation, In: Design of Experiments for Engineers and Scientists, Elsevier Publishing Solutions, USA, pp. 1-4.
  94. Sudnik, W., Radaj, D., Erofeev, W., 1996, Computerized simulation of laser beam welding, modeling and verification, Journal of Physics D: Applied Physics, 29:2811-2817.
  95. Arata, Y., Miyamoto, I., 1972, Heat processing by CO2 laser, Journal of Japan Welding Society, 41:81.
  96. Swift-Hook, D.T., Gick, A.E.F., 1973, Penetration welding with lasers, Welding Journal Research Supplement, 52:492s–9s.
  97. Steen, W.M., Dowden, J., Davis, M., Kapadia, P., 1988, A point and line source model of laser keyhole welding, Journal of Physics D, 21:1255–60.
  98. Dowden, J., Davis, M., Kapadia, P., 1983, Some aspects of the fluid-dynamics of laser-welding. Journal of Fluid Mechanics, 126:123–46.
  99. Ducharme, R., Kapadia, P., Dowden, J., 1993, A mathematical model of the defocusing of laser light above a workpiece in laser material processing. In: Farson, D., Steen, W., Miyamoto, I., editors, Proceedings of ICALEO’92, LIA, Orlando: Laser Institution of America, 75:187–97.
  100. Kaplan, A., 1994, A model of deep penetration laser welding based on calculation of the keyhole profile, Journal of Physics D: Applied Physics, 27(9):1805–1814.
  101. Klemens, P.G., 1976, Heat balance and flow conditions for electron beam and laser welding, Journal of Applied Physics, 47(5):2165–2174.
  102. Chande, T., Mazumder, J., 1984, Estimating effects of processing conditions and variable properties upon pool shape, cooling rates, and absorption coefficient in laser welding, Journal of Applied Physics, 56:1981–6.
  103. Borland, J.C., 1960, Generalized theory of super-solidus cracking in welds (and castings), British Welding Journal, 7: 508–512.
  104. Hemsworth, B., Boniszewski, T., Eaton, N.F., 1969, Classification and definition of high temperature welding cracks in alloys, Metal Construction and British Welding Journal, 2:5–16.
  105. Hoffmann, P., Geiger, M., 1995, Recent developments in laser system technology for welding applications, Annals of the CIRP, 44(1):151-156.
  106. Weichiat, C., Paul, A., Pal, M., 2009, CO2 laser welding of galvanized steel sheets using vent holes, Materials and Design, 30:245–251.
  107. Lippold, J.C., Kotecki, D.J., 2005, Welding metallurgy and weldability of stainless steel, 1st ed., John Willey & Sons, NJ, USA, pp. 63-70.
  108. Brooks, J.A., Garrison, W.M., 1999, Weld microstructure development and properties of precipitation-strengthened martensitic stainless steels, Welding Journal, 78(8): 280s -291s
  109. Tzeng, Y.F., 2000, Parametric analysis of the pulsed Nd:YAG laser seam-welding process, Journal of Materials Processing Technology, 102: 40-47.
  110. Hector Jr., L.G., Chen, Y.-L., Agarwal, S., Briant. C.L., 2004, Texture characterization of autogenous Nd: YAG laser welds in AA5182-O and AA6111-T4 aluminum alloys, Metall. and Mater. Trans A, 35A:3032-3038.
  111. Al-kazzaz, H., Medraj, M., Cao, X., Jahazi, M., Xiao, M., 2005, Effects of welding speed on Nd:YAG laser weldability of ZE41A-T5 magnesium sand castings, Proceeding of 44th annual conference of metallurgists of CIM, Light Metals:137-149.
  112. Huang, R. S., Kang, L., Ma, X., 2008, Microstructure and phase composition of a low-power YAG laser-MAG welded stainless steel joint, Journal of Materials Engineering and Performance, 17:928–935.
  113. Liu, Q.S., Mahdavian, S.M., Aswin, D., Ding, S., 2009, Experimental study of temperature and clamping force during Nd:YAG laser butt welding, Optics & Laser Technology,41(6):794-799
  114. Berzins, M., Childs, T.H.C., Ryder, G.R., 1996, The selective laser sintering of polycarbonate, Annals of the CIRP, 45(1):187–190.
  115. Childs, T.H.C., Berzins, M., Ryder, G.R., Tontowi, A.E., 1999, Selective laser sintering of an amorphous polymer: simulations and experiments. Proc. IMechE, Part B: J. Engineering Manufacture, 213:333-349.
  116. Jin, X., Li, L., 2004, An experimental study on the keyhole shapes in laser deep penetration welding, Optics and Lasers in Engineering, 41: 779–790.
  117. Sudnik, W., Radaj, D., Breitschwerdt, S., Erofeew, W., 2000, Numerical simulation of weld pool geometry in laser beam welding, J. Phys. D: Appl. Phys. 33: 662–671.
  118. Antony, J., 2003, Systematic Methodology for design of experiment: Design of Experiment for Engineers and Scientists, 1st Ed., Butterworth-Heinemann Publication, MA, USA, pp. 38-39.
  119. Lippold, J.C., Kotecki, D.J., 2005, Welding metallurgy and weldability of stainless steel, 1st ed. John Willey & Sons, NJ, USA, pp. 63–70.
  120. Kurt, B., Orhan, N., Somunkiran, I., Kaya, M., 2009, The effect of austenitic interface layer on microstructure of AISI 420 martensitic stainless steel joined by keyhole PTA welding process, Materials and Design, 30:661–664.
  121. Ping, D.H., Ohnuma, M., Hirakawa, Y., Kadoya, Y., Hono, K., 2005, Microstructural evolution in 13Cr–8Ni–2.5Mo–2Al martensitic precipitation-hardened stainless steel, Materials Science and Engineering A, 394:285–295
  122. Berretta, J.R., de Rossi, W., Neves, M.D.M., de Almeida, I.A., Junior, N.D.V., 2007, Pulsed Nd:YAG laser welding of AISI 304 to AISI 420 stainless steels, Optics and Lasers in Engineering, 45:960–966.
  123. Srinivasan, P.B., 2008, Effect of laser beam mode on the microstructural evolution in AISI 410 martensitic stainless steel welds, Lasers in Engineering, 18:351–359.
  124. Rajasekhar, A., Reddy, G.M., Mohandas, T., Murti, V.S.R., 2009, Influence of austenitizing temperature on microstructure and mechanical properties of AISI 431 martensitic stainless steel electron beam welds, Materials and Design, 30:1612–1624.
  125. Sharifitabar, M., Halvaee, A., 2010, Resistance upset butt welding of austenitic to martensitic stainless steels, Materials and Design, 31(6):3044–3050.
  126. Gualco, A., Svoboda, H.G., Surian, E.S., de Vedia, L. A., 2010, Effect of welding procedure on wear behaviour of a modified martensitic tool steel hardfacing deposit, Materials and Design, 31:4165–4173
  127. Khan MMA, Romoli L, Fiaschi M, Dini G, Sarri F., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Material Processing Technology,210:1340–53
  128. Kou, S., 2002, Welding metallurgy, 2nd ed. John Willey & Sons Inc., NJ, USA, pp. 143- 169.
  129. Nakagawa H, Matsuda F, Uehara T, Katayama S, Arata Y. A., 1979, New explanation for role of delta ferrite improving weld solidification crack susceptibility in austenitic stainless steel, Trans Jpn Weld Res Inst. 8:105–12.
  130. Huang, Q., Hagstroem, J., Skoog, H., Kullberg, G., 1991, Effect of laser parameter variation on sheet metal welding, Int. J. Join. Mater., 3:79–88.
  131. Benyounis, K.Y., Olabi., A.G., 2008, Optimization of different welding processes using statistical and numerical approaches – A reference guide, Advances in Engineering Software, 39:483–496.
  132. Montgomery, D.C., 2004, Design and Analysis of Experiments, 6th ed. John Wiley and Sons, Inc., New York.
  133. Yang, Y.K., Chuang, M.T. Lin, S.S., 2009, Optimization of dry machining parameters for high-purity graphite in end milling process via design of experiments methods, Journal of Materials Processing Technology, 209:4395– 4400
  134. Douglass, D.M., Wu, C.Y., 2003, Laser welding of polyolefin elastomers to thermoplastic polyolefin, In: Proceedings of the 22nd international Congress on applications of lasers & electro-optics, Jacksonville, Florida, USA, 95:118–23.
  135. Koganti, R., Karas, C., Joaquin, A., Henderson, D., Zaluzec, M., Caliskan, A., 2003, Metal inert gas (MIG) welding process optimization for joining aluminum sheet material using OTC/DAIHEN equipment, In: Proceedings of IMECE’03, November 15–21, Washington [DC]: ASME International Mechanical Engineering Congress, pp. 409–425.
  136. Balasubramanian, V., Guha, B., 2004, Fatigue life prediction of load carrying cruciform joints of pressure vessel steel by statistical tools. J Mater Des, 25:615–623.
  137. Cicala, E., Duffet, G., Andrzjewski, H., Grevey, D., 2005, Optimization of T-joint properties in Al-Mg-Si alloy laser welding, 24th International Congress on Applications of Lasers and Electro-Optics, ICALEO: 543-548.
  138. Kim, C., Choi, W., Kim, J., Rhee, S., 2008, Relationship between the weldability and the Process parameters for laser-TIG Hybrid welding of galvanized steel sheets, Materials Transactions, 49:179-186.
  139. Datta, S., Bandyaopadhyay, A., Pal, P.K., 2008, Modeling and optimization of features of bead geometry including percentage dilution in submerged arc welding using mixture of fresh flux and fused slag, Int. J. Adv. Manuf. Technol., 36:1080–1090.
  140. Benyounis, K.Y., Olabi, A.G., Hashmi, M.S.J., 2008, Multi-response optimization of CO2 laser-welding process of austenitic stainless steel, Optics & Laser Technology, 40:76–87
  141. Sarsılmaz, F., Çaydaş, U., 2009, Statistical analysis on mechanical properties of friction-stir-welded AA 1050/AA 5083 couples, Int. J. Adv. Manuf. Technol., 43:248–255.
  142. Khan M.M.A., Romoli L., Fiaschi M., Sarri F., Dini G., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Materials Processing Technology, 210(10):1340-1353.
  143. Design-Expert software, v7, user’s guide, technical manual, Stat-Ease Inc., Minneapolis, MN; 2005.
  144. Zulkali, M.M.D., Ahmad, A.L., Norulakmal, N.H., 2006, Oryza sativa L. husk as heavy metal adsorbent: optimization with lead as model solution, Bioresour. Technol., 97:21–25.
  145. Sun, Z., 1996, Feasibility of producing ferritic/austenitic dissimilar metal joints by high energy density laser beam process, International Journal of Pressure Vessels and Piping, 68:153-160.
  146. Katayama, S., 2004, Laser welding of aluminium alloys and dissimilar metals, Weld International, 18(8):618–25.
  147. Kaiser, E., Schafer, P., 2005, Pulse sharpening optimizes the quality of seam and spot welds. In: Lasers in manufacturing, proceeding of the third international WLT conference on lasers in manufacturing, pp. 695–698.
  148. Li, Z., Fontana, G., 1998, Autogenous laser welding of stainless steel to free-cutting steel for the manufacture of hydraulic valves, Journal of Materials Processing Technology, 74:174–182.
  149. Mai, T.A., Spowage, A.C., 2004, Characterisation of dissimilar joints in laser welding of steel–kovar, copper–steel and copper–aluminium, Materials Science and Engineering: A, 374:224–233.
  150. Liu, X.B., Yu, G., Pang, M., Fan, J.W., Wang, H.H., Zheng, C.Y., 2007, Dissimilar autogenous full penetration welding of superalloy K418 and 42CrMo steel by a high power CW Nd:YAG laser, Applied Surface Science, 253:7281–7289.
  151. Berretta, J.R., de Rossi, W., Neves, M.D.M., de Almeida, I.A., Junior, N.D.V., 2007, Pulsed Nd:YAG laser welding of AISI 304 to AISI 420 stainless steels, Optics and Lasers in Engineering, 45:960–966.
  152. Mousavi, S.A.A.A., Sufizadeh, A.R., 2009, Metallurgical investigations of pulsed Nd:YAG laser welding of AISI 321 and AISI 630 stainless steels, Materials and Design, 30:3150–3157.
  153. Pekkarinen, J., Kujanpää, V., 2010, The effects of laser welding parameters on the microstructure of ferritic and duplex stainless steels welds, Physics Procedia, 5:517–523.
  154. Allabhakshi, S., Madhusudhan Reddy, G., Ramarao, V.V., Phani Babu, C., Ramachandran, C.S., 2002, Studies on weld overlaying of austenitic stainless steel (AISI 304) with ferritic stainless steel (AISI 430). In: Proceedings of the national welding conference, Indian Institute of Welding, Chennai, India, Paper 8.
  155. Pan, C., Zhang, E., 1996, Morphologies of the transition region in dissimilar austenitic–ferritic welds, Material Characterization, 36(1):5–10.
  156. Wang, S. C., Wang, C., Tu, Y. K., Hwang, C. J., Chi, S., Wang, W. H., Cheng, W. H., 1996, Effect of Au coating on joint strength in laser welding for invar-invar packages, Electronic Components and Technology Conference, IEEE, pp. 942-945.
  157. Cui, C., Hu, J., Gao, K., Pang, S., Yang, Y., Wang, H., Guo, Z., 2008, Effects of process parameters on weld metal keyhole characteristics with COR2R laser butt welding, Lasers in Engineering, 18:319–327.
  158. Khan, M.M.A., Romoli, L., Fiaschi, M., Dini, G., Sarri, F., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration. Journal of Material Processing Technology, 210:1340–53.
  159. Steem WM, Mazumder J, 2010, laser material processing, Springer-Verlag London limited, London.
  160. Weichiat C, Paul A, Pal M., 2009, CO2 laser welding of galvanized steel sheets using vent holes, Materials and Design, 30:245–51.
  161. Mackwood AP, Crafer RC, 2005, Thermal modeling of laser welding and related processes: a literature review, Opt Laser Technol, 37:99–115
  162. Kaiser E, Schafer P, 2005, Pulse shaping optimizes the quality of seam and spot welds. In: Lasers in manufacturing, proceeding of the third international WLT—conference on lasers in manufacturing. pp. 695–670
  163. Sun Z, Kuo M, 1998, Bridging the joint gap with wire feed laser welding, J Mater Process Technol, 87:213–222
  164. Liu X-B, Yu G,Guo J, Gu Y-J, Pang M, Zheng C-Y, Wang H-H, 2008, Research on laser welding of cast Ni-based superalloy K418 turbo disk and alloy steel 42CrMo shaft, J Alloy Comp, 453(1–2):371–378.
  165. Huang Q, Hagstroem J, Skoog H, Kullberg G, 1991, Effect of CO2 laser parameter variations on sheet metal welding, International Journal for the Joining of Materials, 3(3):79–88
  166. Juang SC, Tarng YS, 2002, Process parameter selection for optimizing the weld pool geometry in the tungsten inert gas welding of stainless steel, J Mater Process Technol, 122:33–37
  167. Marya M, Edwards G, Marya S, Olson DL, 2001, Fundamentals in the fusion welding of magnesium and its alloys. In: Proceedings of the seventh JWS international symposium. pp. 597–602.
  168. Haferkamp H, Niemeyer M, Dilthey U, Trager G, 2000, Laser and electron beam welding of magnesium materials, Weld Cutt 52(8):178–80.
  169. Haferkamp H, Bach Fr-W, Burmester I, Kreutzburg K, Niemeyer M, 1996, Nd:YAG laser beam welding of magnesium constructions. In: Proceedings of the third international magnesium conference. pp. 89–98.
  170. Benyounis KY, Olabi AG, Hashmi MSJ, 2005, Effect of laser welding parameters on the heat input and weld-bead profile, J Mater Process Technol, 164-165:978–985.
  171. Manonmani K, Murugan N, Buvanasekaran G, 2007, Effects of process parameters on the bead geometry of laser beam butt welded stainless steel sheets, J Adv Manuf Technol, 32(11-12):1125-1133.
  172. Elangovan K, Balasubramanian V, 2008, Developing an empirical relationship to predict tensile strength of friction stir welded AA2219 aluminium alloy joints, J Mater Eng Perform, 17:820–830.
  173. Benyounis KY, Olabi AG, Hashmi MSJ, 2008, Multi-response optimization of CO2 laser-welding process of austenitic stainless steel, Opt Laser Technol 40:76-87.
  174. Moradi M, Ghoreishi M, 2010, Influences of laser welding parameters on the geometric profile of NI-base superalloy Rene 80 weld-bead, Int J Adv Manuf Technol, doi: 10.1007/s00170-010-3036-1.
  175. Padmanaban G, Balasubramanian V, 2010, Optimization of laser beam welding process parameters to attain maximum tensile strength in AZ31B magnesium alloy, Opt Laser Technol, 42:1253–1260
  176. Rajakumar S, Muralidharan C, Balasubramanian V, 2010, Optimization of the friction-stir-welding process and the tool parameters to attain a maximum tensile strength of AA7075-T6 aluminium alloy, J Eng Manuf, 224:1175–1191.
  177. Ruggiero A, Tricarico L, Olabi AG, Benyounis KY, 2011, Weld-bead profile and costs optimization of the CO2 dissimilar laser welding process of low carbon steel and austenitic steel AISI316, Opt Laser Technol, 43:82–90.
  178. Myers RH, Montgomery DC, 2002, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York.
  179. Robinson TJ, Wulff SS, 2006, Response surface approaches to robust parameter design. In: Khuri AI (ed) Response surface methodology and related topics, World Scientific, Singapore, pp. 123-157.
  180. Gunaraj V, Murugan N, 1999, Application of response surface methodologies for predicting weld base quality in submerged arc welding of pipes, J Mater Process Technol, 88:266–275.
  181. Design-ExpertSoftware,V7, 2005, User’s guide: Technical Manual, Minneapolis, MN: Stat-Ease Inc.
  182. Zulkali MMD, Ahmad AL, Norulakmal NH, 2006, Oryza sativa L. husk as heavy metal adsorbent: optimization with lead as model solution, Bioresource Technology, 97:21–25.
  183. Cui C, Hu J, Gao K, Pang S, Yang Y, Wang H, Guo Z, 2008, Effects of process parameters on weld metal keyhole characteristics with CO2 laser butt welding, Lasers in Engineering, 18:319–327.
  184. Mackwood A.P., Crafer R.C., 2005, Thermal modelling of laser welding and related processes: a literature review, Optics & Laser Technology, 37:99– 115.
  185. Chang W. S., Na S.J., 2002, A study on the prediction of the laser weld shape with varying heat source equations and the thermal distortion of a small structure in micro-joining, Journal of Material Processing Technology, 120:208 – 214.
  186. Goldak J. A., Chakravarti M. B., 1984, A new finite element model for welding heat source, Metallurgical and Materials Transactions B, 15B:299–305.
  187. Su W., Haiyan Z., Yu W., Xiaohong Z., 2004, A new heat source model in numerical simulation of high energy beam welding, Transaction China Welding Institute, 25:91–94.
  188. Kazemi K., Goldak J. A., 2009, Numerical simulation of laser full penetration welding, Computational Materials Science, 44:841–849
  189. Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2012, Some studies on weld bead geometries for laser spot welding process using finite element analysis, Materials and Design, 34:412–426
  190. Balasubramanian K.R., Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2008, Numerical and experimental investigation of laser beam welding of AISI 304 stainless steel sheet, Advances in Production Engineering and Management, 3(2):93–105
  191. Sabbaghzadeh J., Azizi M., Torkamany M.J., 2008, Numerical and experimental investigation of seam welding with a pulsed laser. Journal of Optics and Laser Technology, 40:289–296
  192. Kruth J.P., Froyen L., Rombouts M., Van Vaerenbergh J., Mercells P., 2003, New Ferro Powder for Selective Laser Sintering of Dense Parts, CIRP Annals – Manufacturing Technology, 52/1: 139–142.
  193. Romoli L., Tantussi G., Dini G., 2007, Layered Laser Vaporization of PMMA Manufacturing 3D Mould Cavities, CIRP Annals -Manufacturing Technology, 56/1: 209-212.
  194. Vollertsen F., Walther R., 2008, Energy balance in laser-based free form heading, CIRP Annals – Manufacturing Technology 57/1: 291–294.
  195. Mills K.C., Su Y., Li Z., Brooks R.F., 2004, Equations for the Calculation of the Thermo-physical Properties of Stainless Steel, ISIJ International, Vol. 44, No. 10, pp. 1661–1668.
  196. Khan M.M.A., Romoli L., Fiaschi M., Sarri F., Dini G., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Materials Processing Technology, Volume 210, Issue 10, pp. 1340-1353.

Expert Q&A: Your Top Questions Answered

Q1: 이 연구에서 특별히 Mg의 Σ7 입계를 선택한 이유는 무엇인가요?

A1: Mg의 Σ7 입계는 다양한 원자 구조를 가질 수 있어 상변태를 관찰하기에 이상적인 모델 시스템이기 때문입니다. 특히, 이 입계는 순수 Mg 상태의 안정한 구조(T-type)와 합금 원소 첨가 시 나타날 수 있는 다른 구조(A-type)가 이미 알려져 있어, 명확한 구조적 변화를 연구하고 추적하는 데 매우 적합했습니다.

Q2: 결함 상평형도(그림 3)의 화학 포텐셜(µGa)은 실험 조건과 어떻게 연결되나요?

A2: 화학 포텐셜은 열역학적 변수로서, 두 가지 방식으로 실험 조건과 연결됩니다. 첫째, Ga 이온 주입 직후와 같이 Ga이 과잉인 상태는 Ga-rich 조건(µGa = 0 eV)에 해당하며, 이는 상평형도의 가장 오른쪽 끝을 나타냅니다. 둘째, 충분한 확산이 일어난 후에는 입계의 Ga이 벌크 고용체 내의 Ga과 국소적 평형을 이룹니다. 이 경우, 측정된 벌크 내 Ga 농도로부터 화학 포텐셜을 계산할 수 있으며, 이는 그림 3의 상단 축에 해당 농도 값으로 표시되어 있습니다.

Q3: 논문에서 언급된 ‘자동 패턴 인식’ 알고리즘의 역할은 무엇이며 왜 필요했나요?

A3: 이 알고리즘은 STEM 이미지에서 관찰된 수많은 입계 구조 단위들을 객관적으로 ‘T-type’ 또는 ‘A-type’으로 분류하는 데 사용되었습니다. 입계를 따라 일어나는 상변태 과정을 수동으로 분석하는 것은 시간이 많이 걸리고 주관이 개입될 수 있습니다. 자동 패턴 인식은 DFT로 계산된 원자 구조를 템플릿으로 사용하여 실험 이미지 내 구조 단위들을 신속하고 일관성 있게 식별함으로써, 상변태 과정을 정량적으로 추적하는 것을 가능하게 했습니다.

Q4: ‘T-type’에서 ‘A-type’ 단위로의 변태가 갖는 물리적 의미는 무엇인가요?

A4: 이는 2차원 결함 평면에서 일어나는 진정한 의미의 상변태입니다. 그림 1d와 1e에서 볼 수 있듯이, 두 단위는 사면체(tetrahedron)와 캡이 씌워진 삼각기둥(capped trigonal prism)이라는 서로 다른 원자 배열과 형태를 가집니다. 순수 Mg에서는 T-type이 안정하지만, Ga가 첨가되면 A-type이 더 안정해집니다. 이러한 원자 구조의 변화는 입계의 이동성, 강도, 또는 불순물 분리 능력과 같은 국소적 특성을 변화시킬 수 있습니다.

Q5: 연구에서 두 가지 다른 Ga 정렬상(6-Ga 및 3-Ga)이 관찰되었는데, 둘 사이의 전이는 어떻게 일어났나요?

A5: 전이는 전체 시스템의 열역학적 상태 변화에 의해 구동되었습니다. 6-Ga 상(그림 2a)은 Ga 이온 주입 직후의 Ga 과잉 상태에서 관찰되었습니다. 반면, 620일간의 장기 보관 후에는 확산을 통해 과잉 Ga이 Mg5Ga2 석출물을 형성하고 벌크 내 Ga 농도가 0.7%로 감소하며 시스템이 보다 안정적인 평형 상태에 도달했습니다. 이처럼 낮아진 화학 포텐셜 조건에서는 3-Ga 상(그림 2b)이 입계에서 더 안정한 구조가 되었으며, 이는 결함 상평형도(그림 3)의 예측과 정확히 일치하는 결과입니다.

Conclusion: Paving the Way for Higher Quality and Productivity

기존 소재 설계의 한계를 극복하기 위해, 본 연구는 결함의 화학적 상태를 체계적으로 이해하고 제어할 수 있는 강력한 방법론을 제시했습니다. 국소 합금화, 원자 단위 이미징, 그리고 이론 계산을 결합하여 구축한 결함 상평형도는 특정 화학적 조건에서 어떤 결함 구조가 안정적인지를 예측하는 최초의 실험적 가이드입니다. 이는 결함을 피해야 할 대상이 아닌, 재료의 성능을 극대화하기 위해 적극적으로 설계해야 할 대상으로 바라보는 새로운 패러다임을 열어줍니다.

“At STI C&D, we are committed to applying the latest industry research to help our customers achieve higher productivity and quality. If the challenges discussed in this paper align with your operational goals, contact our engineering team to explore how these principles can be implemented in your components.”

(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 “Constructing phase diagrams for defects by correlated atomic-scale characterization” by “Xuyang Zhou, et al.”.
  • Source: https://arxiv.org/abs/2303.09465v2

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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.

8. 참고 문헌:

  1. Lancaster, J. F., 1984, The physics of welding, Physics in Technology, 15:73-79.
  2. Kou, S., 2003, Fusion welding processes, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.3-36.
  3. Steen, W.M., Mazumder, J., 2010, Laser welding: laser material processing, 4th Ed., Springer-Verlag London Limited, UK, pp. 199-250.
  4. Merchant, V., Laser beam welding, In: Ahmed, N., editor, New developments in advanced welding, 1st Ed., Woodhead Publishing Limited, Cambridge, UK, pp. 83-84.
  5. Kugler, T.R., 2001, Fusion front penetration: Conduction Welding, In: Ready, J.F., editor, LIA handbook of laser materials processing, 1st Ed., Magnolia Publishing Inc., FL, USA, pp. 310-312.
  6. Matsunawa, A., 2002, Science of laser welding-mechanisms of keyhole and pool dynamics. In: ICALEO 2002 proceedings, Phoenix, LIA, Orlando, paper: 101.
  7. Lacroix, D., Jeandel, G., Boudot, C., 1996, Spectroscopic studies of laser-induced plume during welding with a Nd:YAG laser, In: Proceedings of SPIE, 2789, pp. 221–227.
  8. Dumord, E., Jouvard, J.M., Grevey, D., 1996, Keyhole modeling during CW Nd:YAG laser welding, In: Proceedings of SPIE, 2789, pp. 213–220.
  9. Berkmanns, J., Faerber, M., 2005, Facts about laser technology: laser welding, http://www.laserdeal.com/, access date: January 20, 2012.
  10. Coherent Inc., 2004, High speed welding of metals with diamond CO2 laser – stainless steels, Technical Note, http://www.coherent.de/, access date: November 15, 2011.
  11. LWS, 2006, A technical report on the LWS flexcell cladding system, http://www.laserweldingsolutions.com/, access date: April 01, 2009.
  12. Shannon, G., 2009, Source selection for laser welding, http://www.industrial-lasers.com/, access date: April 01, 2009.
  13. Faerber, M., Berkmanns, J., 1996, Gases for increased laser welding productivity, In: Proceedings of the ISATA Conference, pp. 791–798.
  14. Schuberth S, Schedin E, Fröhlich T, Ratte E., 2008, Next generation vehicle – engineering guidelines for stainless steel in automotive applications, In: Proceedings of the 6th stainless steel science and market conference, Helsinki, Finland.
  15. Kou, S., 2003, Weld metal solidification, In: Welding Technology, 2nd Ed., John Willey & Sons Inc., NJ, USA, pp.199-207.
  16. Han, W., 2004, Computational and experimental investigations of laser drilling and welding for microelectronic packaging, Ph.D. Dissertation, Worcester Polytechnic Institute, Worcester, MA, USA, pp. 85-87.
  17. Buchfink, G., 2007, A world of possibilities – joining, In: Kammϋller, N.L., editor, The laser as a tool, 1st Ed., Vogel Buchverlag, Wϋrzburg, Germany, pp. 166-167.
  18. ISO13919-1:1996, Welding – Electrons and laser beam welded joints – guidance on quality levels for imperfections – Part I: Steel, pp. 4-13.
  19. Zhang, Y.M., Kovacevic, R., Li, L., 1996, Characterization and real time measurement of geometrical appearance of the weld pool. International Journal of Machine Tools and Manufacture, 36(7):799–816.
  20. Bull, C.E., Stacey, K.A., Calcraft, R., 1993, Online weld monitoring using ultrasonic. Journal of Non-destructive Test, 35(2):57–64.
  21. Tarng, Y.S., Yang, W.H., 1998, Optimization of the weld bead geometry in gas Tungsten Arc welding by the Taguchi Method. Journal of Advanced Manufacturing Technology, 14:549–54.
  22. Benyounis, K.Y.,Olabi, A.G.,Hasmi, M.S.J., 2008, Multi-response optimization of CO2 laser welding process of austenitic stainless steel, Optics & Laser Technology, 40:76–87.
  23. Antony, J., 2003, Introduction to industrial experimentation, In: Design of Experiments for Engineers and Scientists, Elsevier Publishing Solutions, USA, pp. 1-4.
  24. Sudnik, W., Radaj, D., Erofeev, W., 1996, Computerized simulation of laser beam welding, modeling and verification, Journal of Physics D: Applied Physics, 29:2811-2817.
  25. Arata, Y., Miyamoto, I., 1972, Heat processing by CO2 laser, Journal of Japan Welding Society, 41:81.
  26. Swift-Hook, D.T., Gick, A.E.F., 1973, Penetration welding with lasers, Welding Journal Research Supplement, 52:492s–9s.
  27. Steen, W.M., Dowden, J., Davis, M., Kapadia, P., 1988, A point and line source model of laser keyhole welding, Journal of Physics D, 21:1255–60.
  28. Dowden, J., Davis, M., Kapadia, P., 1983, Some aspects of the fluid-dynamics of laser-welding. Journal of Fluid Mechanics, 126:123–46.
  29. Ducharme, R., Kapadia, P., Dowden, J., 1993, A mathematical model of the defocusing of laser light above a workpiece in laser material processing. In: Farson, D., Steen, W., Miyamoto, I., editors, Proceedings of ICALEO’92, LIA, Orlando: Laser Institution of America, 75:187–97.
  30. Kaplan, A., 1994, A model of deep penetration laser welding based on calculation of the keyhole profile, Journal of Physics D: Applied Physics, 27(9):1805–1814.
  31. Klemens, P.G., 1976, Heat balance and flow conditions for electron beam and laser welding, Journal of Applied Physics, 47(5):2165–2174.
  32. Chande, T., Mazumder, J., 1984, Estimating effects of processing conditions and variable properties upon pool shape, cooling rates, and absorption coefficient in laser welding, Journal of Applied Physics, 56:1981–6.
  33. Borland, J.C., 1960, Generalized theory of super-solidus cracking in welds (and castings), British Welding Journal, 7: 508–512.
  34. Hemsworth, B., Boniszewski, T., Eaton, N.F., 1969, Classification and definition of high temperature welding cracks in alloys, Metal Construction and British Welding Journal, 2:5–16.
  35. Hoffmann, P., Geiger, M., 1995, Recent developments in laser system technology for welding applications, Annals of the CIRP, 44(1):151-156.
  36. Weichiat, C., Paul, A., Pal, M., 2009, CO2 laser welding of galvanized steel sheets using vent holes, Materials and Design, 30:245–251.
  37. Lippold, J.C., Kotecki, D.J., 2005, Welding metallurgy and weldability of stainless steel, 1st ed., John Willey & Sons, NJ, USA, pp. 63-70.
  38. Brooks, J.A., Garrison, W.M., 1999, Weld microstructure development and properties of precipitation-strengthened martensitic stainless steels, Welding Journal, 78(8): 280s -291s
  39. Tzeng, Y.F., 2000, Parametric analysis of the pulsed Nd:YAG laser seam-welding process, Journal of Materials Processing Technology, 102: 40-47.
  40. Hector Jr., L.G., Chen, Y.-L., Agarwal, S., Briant. C.L., 2004, Texture characterization of autogenous Nd: YAG laser welds in AA5182-O and AA6111-T4 aluminum alloys, Metall. and Mater. Trans A, 35A:3032-3038.
  41. Al-kazzaz, H., Medraj, M., Cao, X., Jahazi, M., Xiao, M., 2005, Effects of welding speed on Nd:YAG laser weldability of ZE41A-T5 magnesium sand castings, Proceeding of 44th annual conference of metallurgists of CIM, Light Metals:137-149.
  42. Huang, R. S., Kang, L., Ma, X., 2008, Microstructure and phase composition of a low-power YAG laser-MAG welded stainless steel joint, Journal of Materials Engineering and Performance, 17:928–935.
  43. Liu, Q.S., Mahdavian, S.M., Aswin, D., Ding, S., 2009, Experimental study of temperature and clamping force during Nd:YAG laser butt welding, Optics & Laser Technology,41(6):794-799
  44. Berzins, M., Childs, T.H.C., Ryder, G.R., 1996, The selective laser sintering of polycarbonate, Annals of the CIRP, 45(1):187–190.
  45. Childs, T.H.C., Berzins, M., Ryder, G.R., Tontowi, A.E., 1999, Selective laser sintering of an amorphous polymer: simulations and experiments. Proc. IMechE, Part B: J. Engineering Manufacture, 213:333-349.
  46. Jin, X., Li, L., 2004, An experimental study on the keyhole shapes in laser deep penetration welding, Optics and Lasers in Engineering, 41: 779–790.
  47. Sudnik, W., Radaj, D., Breitschwerdt, S., Erofeew, W., 2000, Numerical simulation of weld pool geometry in laser beam welding, J. Phys. D: Appl. Phys. 33: 662–671.
  48. Antony, J., 2003, Systematic Methodology for design of experiment: Design of Experiment for Engineers and Scientists, 1st Ed., Butterworth-Heinemann Publication, MA, USA, pp. 38-39.
  49. Kurt, B., Orhan, N., Somunkiran, I., Kaya, M., 2009, The effect of austenitic interface layer on microstructure of AISI 420 martensitic stainless steel joined by keyhole PTA welding process, Materials and Design, 30:661–664.
  50. Ping, D.H., Ohnuma, M., Hirakawa, Y., Kadoya, Y., Hono, K., 2005, Microstructural evolution in 13Cr–8Ni–2.5Mo–2Al martensitic precipitation-hardened stainless steel, Materials Science and Engineering A, 394:285–295
  51. Berretta, J.R., de Rossi, W., Neves, M.D.M., de Almeida, I.A., Junior, N.D.V., 2007, Pulsed Nd:YAG laser welding of AISI 304 to AISI 420 stainless steels, Optics and Lasers in Engineering, 45:960–966.
  52. Srinivasan, P.B., 2008, Effect of laser beam mode on the microstructural evolution in AISI 410 martensitic stainless steel welds, Lasers in Engineering, 18:351–359.
  53. Rajasekhar, A., Reddy, G.M., Mohandas, T., Murti, V.S.R., 2009, Influence of austenitizing temperature on microstructure and mechanical properties of AISI 431 martensitic stainless steel electron beam welds, Materials and Design, 30:1612–1624.
  54. Sharifitabar, M., Halvaee, A., 2010, Resistance upset butt welding of austenitic (AISI304) to martensitic (AISI420) stainless steels, Materials and Design, 31(6):3044–3050.
  55. Gualco, A., Svoboda, H.G., Surian, E.S., de Vedia, L. A., 2010, Effect of welding procedure on wear behaviour of a modified martensitic tool steel hardfacing deposit, Materials and Design, 31:4165–4173
  56. Khan MMA, Romoli L, Fiaschi M, Dini G, Sarri F., 2010, Experimental investigation on laser beam welding of martensitic stainless steels in a constrained overlap joint configuration, Journal of Material Processing Technology,210:1340–53
  57. Kou, S., 2002, Welding metallurgy, 2nd ed. John Willey & Sons Inc., NJ, USA, pp. 143- 169.
  58. Nakagawa H, Matsuda F, Uehara T, Katayama S, Arata Y. A., 1979, New explanation for role of delta ferrite improving weld solidification crack susceptibility in austenitic stainless steel, Trans Jpn Weld Res Inst. 8:105–12.
  59. Huang, Q., Hagstroem, J., Skoog, H., Kullberg, G., 1991, Effect of laser parameter variation on sheet metal welding, Int. J. Join. Mater., 3:79–88.
  60. Benyounis, K.Y., Olabi., A.G., 2008, Optimization of different welding processes using statistical and numerical approaches – A reference guide, Advances in Engineering Software, 39:483–496.
  61. Montgomery, D.C., 2004, Design and Analysis of Experiments, 6th ed. John Wiley and Sons, Inc., New York.
  62. Yang, Y.K., Chuang, M.T. Lin, S.S., 2009, Optimization of dry machining parameters for high-purity graphite in end milling process via design of experiments methods, Journal of Materials Processing Technology, 209:4395– 4400
  63. Douglass, D.M., Wu, C.Y., 2003, Laser welding of polyolefin elastomers to thermoplastic polyolefin, In: Proceedings of the 22nd international Congress on applications of lasers & electro-optics, Jacksonville, Florida, USA, 95:118–23.
  64. Koganti, R., Karas, C., Joaquin, A., Henderson, D., Zaluzec, M., Caliskan, A., 2003, Metal inert gas (MIG) welding process optimization for joining aluminum sheet material using OTC/DAIHEN equipment, In: Proceedings of IMECE’03, November 15–21, Washington [DC]: ASME International Mechanical Engineering Congress, pp. 409–425.
  65. Balasubramanian, V., Guha, B., 2004, Fatigue life prediction of load carrying cruciform joints of pressure vessel steel by statistical tools. J Mater Des, 25:615–623.
  66. Cicala, E., Duffet, G., Andrzjewski, H., Grevey, D., 2005, Optimization of T-joint properties in Al-Mg–Si alloy laser welding, 24th International Congress on Applications of Lasers and Electro-Optics, ICALEO: 543-548.
  67. Kim, C., Choi, W., Kim, J., Rhee, S., 2008, Relationship between the weldability and the Process parameters for laser-TIG Hybrid welding of galvanized steel sheets, Materials Transactions, 49:179-186.
  68. Datta, S., Bandyaopadhyay, A., Pal, P.K., 2008, Modeling and optimization of features of bead geometry including percentage dilution in submerged arc welding using mixture of fresh flux and fused slag, Int. J. Adv. Manuf. Technol., 36:1080–1090.
  69. Sarsılmaz, F., Çaydaş, U., 2009, Statistical analysis on mechanical properties of friction-stir-welded AA 1050/AA 5083 couples, Int. J. Adv. Manuf. Technol., 43:248–255.
  70. Design-Expert software, v7, user’s guide, technical manual, Stat-Ease Inc., Minneapolis, MN; 2005.
  71. Zulkali, M.M.D., Ahmad, A.L., Norulakmal, N.H., 2006, Oryza sativa L. husk as heavy metal adsorbent: optimization with lead as model solution, Bioresour. Technol., 97:21–25.
  72. Sun, Z., 1996, Feasibility of producing ferritic/austenitic dissimilar metal joints by high energy density laser beam process, International Journal of Pressure Vessels and Piping, 68:153-160.
  73. Katayama, S., 2004, Laser welding of aluminium alloys and dissimilar metals, Weld International, 18(8):618–25.
  74. Li, Z., Fontana, G., 1998, Autogenous laser welding of stainless steel to free-cutting steel for the manufacture of hydraulic valves, Journal of Materials Processing Technology, 74:174–182.
  75. Mai, T.A., Spowage, A.C., 2004, Characterisation of dissimilar joints in laser welding of steel–kovar, copper–steel and copper–aluminium, Materials Science and Engineering: A, 374:224–233.
  76. Liu, X.B., Yu, G., Pang, M., Fan, J.W., Wang, H.H., Zheng, C.Y., 2007, Dissimilar autogenous full penetration welding of superalloy K418 and 42CrMo steel by a high power CW Nd:YAG laser, Applied Surface Science, 253:7281–7289.
  77. Mousavi, S.A.A.A., Sufizadeh, A.R., 2009, Metallurgical investigations of pulsed Nd:YAG laser welding of AISI 321 and AISI 630 stainless steels, Materials and Design, 30:3150–3157.
  78. Pekkarinen, J., Kujanpää, V., 2010, The effects of laser welding parameters on the microstructure of ferritic and duplex stainless steels welds, Physics Procedia, 5:517–523.
  79. Allabhakshi, S., Madhusudhan Reddy, G., Ramarao, V.V., Phani Babu, C., Ramachandran, C.S., 2002, Studies on weld overlaying of austenitic stainless steel (AISI 304) with ferritic stainless steel (AISI 430). In: Proceedings of the national welding conference, Indian Institute of Welding, Chennai, India, Paper 8.
  80. Pan, C., Zhang, E., 1996, Morphologies of the transition region in dissimilar austenitic–ferritic welds, Material Characterization, 36(1):5–10.
  81. Wang, S. C., Wang, C., Tu, Y. K., Hwang, C. J., Chi, S., Wang, W. H., Cheng, W. H., 1996, Effect of Au coating on joint strength in laser welding for invar-invar packages, Electronic Components and Technology Conference, IEEE, pp. 942-945.
  82. Cui, C., Hu, J., Gao, K., Pang, S., Yang, Y., Wang, H., Guo, Z., 2008, Effects of process parameters on weld metal keyhole characteristics with COR2R laser butt welding, Lasers in Engineering, 18:319–327.
  83. Steem WM, Mazumder J, 2010, laser material processing, Springer-Verlag London limited, London.
  84. Mackwood AP, Crafer RC, 2005, Thermal modeling of laser welding and related processes: a literature review, Opt Laser Technol, 37:99–115
  85. Sun Z, Kuo M, 1998, Bridging the joint gap with wire feed laser welding, J Mater Process Technol, 87:213–222
  86. Juang SC, Tarng YS, 2002, Process parameter selection for optimizing the weld pool geometry in the tungsten inert gas welding of stainless steel, J Mater Process Technol, 122:33–37
  87. Marya M, Edwards G, Marya S, Olson DL, 2001, Fundamentals in the fusion welding of magnesium and its alloys. In: Proceedings of the seventh JWS international symposium. pp. 597–602.
  88. Haferkamp H, Niemeyer M, Dilthey U, Trager G, 2000, Laser and electron beam welding of magnesium materials, Weld Cutt 52(8):178–80.
  89. Haferkamp H, Bach Fr-W, Burmester I, Kreutzburg K, Niemeyer M, 1996, Nd:YAG laser beam welding of magnesium constructions. In: Proceedings of the third international magnesium conference. pp. 89–98.
  90. Benyounis KY, Olabi AG, Hashmi MSJ, 2005, Effect of laser welding parameters on the heat input and weld-bead profile, J Mater Process Technol, 164-165:978–985.
  91. Manonmani K, Murugan N, Buvanasekaran G, 2007, Effects of process parameters on the bead geometry of laser beam butt welded stainless steel sheets, J Adv Manuf Technol, 32(11-12):1125-1133.
  92. Elangovan K, Balasubramanian V, 2008, Developing an empirical relationship to predict tensile strength of friction stir welded AA2219 aluminium alloy joints, J Mater Eng Perform, 17:820–830.
  93. Moradi M, Ghoreishi M, 2010, Influences of laser welding parameters on the geometric profile of NI-base superalloy Rene 80 weld-bead, Int J Adv Manuf Technol, doi: 10.1007/s00170-010-3036-1.
  94. Padmanaban G, Balasubramanian V, 2010, Optimization of laser beam welding process parameters to attain maximum tensile strength in AZ31B magnesium alloy, Opt Laser Technol, 42:1253–1260
  95. Rajakumar S, Muralidharan C, Balasubramanian V, 2010, Optimization of the friction-stir-welding process and the tool parameters to attain a maximum tensile strength of AA7075-T6 aluminium alloy, J Eng Manuf, 224:1175–1191.
  96. Ruggiero A, Tricarico L, Olabi AG, Benyounis KY, 2011, Weld-bead profile and costs optimization of the CO2 dissimilar laser welding process of low carbon steel and austenitic steel AISI316, Opt Laser Technol, 43:82–90.
  97. Myers RH, Montgomery DC, 2002, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York.
  98. Robinson TJ, Wulff SS, 2006, Response surface approaches to robust parameter design. In: Khuri AI (ed) Response surface methodology and related topics, World Scientific, Singapore, pp. 123-157.
  99. Gunaraj V, Murugan N, 1999, Application of response surface methodologies for predicting weld base quality in submerged arc welding of pipes, J Mater Process Technol, 88:266–275.
  100. Chang W. S., Na S.J., 2002, A study on the prediction of the laser weld shape with varying heat source equations and the thermal distortion of a small structure in micro-joining, Journal of Material Processing Technology, 120:208 – 214.
  101. Goldak J. A., Chakravarti M. B., 1984, A new finite element model for welding heat source, Metallurgical and Materials Transactions B, 15B:299–305.
  102. Su W., Haiyan Z., Yu W., Xiaohong Z., 2004, A new heat source model in numerical simulation of high energy beam welding, Transaction China Welding Institute, 25:91–94.
  103. Kazemi K., Goldak J. A., 2009, Numerical simulation of laser full penetration welding, Computational Materials Science, 44:841–849
  104. Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2012, Some studies on weld bead geometries for laser spot welding process using finite element analysis, Materials and Design, 34:412–426
  105. Balasubramanian K.R., Siva Shanmugam N., Buvanashekaran G., Sankaranarayanasamy K., 2008, Numerical and experimental investigation of laser beam welding of AISI 304 stainless steel sheet, Advances in Production Engineering and Management, 3(2):93–105
  106. Sabbaghzadeh J., Azizi M., Torkamany M.J., 2008, Numerical and experimental investigation of seam welding with a pulsed laser. Journal of Optics and Laser Technology, 40:289–296
  107. Kruth J.P., Froyen L., Rombouts M., Van Vaerenbergh J., Mercells P., 2003, New Ferro Powder for Selective Laser Sintering of Dense Parts, CIRP Annals – Manufacturing Technology, 52/1: 139–142.
  108. Romoli L., Tantussi G., Dini G., 2007, Layered Laser Vaporization of PMMA Manufacturing 3D Mould Cavities, CIRP Annals -Manufacturing Technology, 56/1: 209-212.
  109. Vollertsen F., Walther R., 2008, Energy balance in laser-based free form heading, CIRP Annals – Manufacturing Technology 57/1: 291–294.
  110. Mills K.C., Su Y., Li Z., Brooks R.F., 2004, Equations for the Calculation of the Thermo-physical Properties of Stainless Steel, ISIJ International, Vol. 44, No. 10, pp. 1661–1668.

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
  • 이메일 : flow3d@stikorea.co.kr

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/

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Welding

A multi-physics CFD study to investigate the impact of laser beam shaping on metal mixing and molten pool dynamics during laser welding of copper to steel for battery terminal-to-casing connections

배터리 단자-케이싱 접합을 위한 구리와 강철 간 레이저 용접 시 레이저 빔 형상이 금속 혼합 및 용융풀 역학에 미치는 영향을 조사하는 다중 물리 CFD 연구

Giovanni Chianese, Qamar Hayat, Sharhid Jabar, Pasquale Franciosa, Darek Ceglarek, Stanislao Patalano

Abstract

This study aims to investigate the impact of laser beam shaping on metal mixing and molten pool dynamics during laser beam welding of Cu-to-steel for battery terminal-to-casing connections. Four beam shapes were tested during LBW of 300 µm Cu to 300 µm nickel-plated steel. Both experiments and simulations were used to study the underlying physics. A CFD model was firstly calibrated against experiments and then deployed to explore the effect of the increasing ring-to-core diameter, as well as a tandem laser spot configuration. The study showed that metal mixing is influenced by the keyhole dynamics and collapse events, but also there is an intricate interplay between keyhole geometry, fluid dynamics via Marangoni forces and buoyancy forces. Notably, the buoyance forces due to the different densities of steel and Cu, along with the recoil pressure contribute to the upward flow of steel towards Cu, and hence impact meaningfully the material mixing. The study pointed-out that the selection of a custom ring-to-core diameter and ring-to-core power is a decision with a trade-off between the need of stabilising the keyhole dynamics and the need to reduce the mixing. Findings indicated that 350 µm ring and 90 µm core with 30% of ring power (weld configuration C3) resulted in more stable dynamics of the keyhole, with significant reduction of collapse events, and ultimately controlled migration of steel towards Cu. Additionally, the pre-heating approach with the tandem beam only led to local fusion of Cu and no significant improvement in keyhole stability was observed.

1. Introduction

The push towards net-zero mobility is globally influencing industrial strategies in the automotive sector as reported by IEA (2022). Manufacturers are introducing new vehicles by replacing internal combustion engines with hybrid or fully electric powertrains. The battery pack is a critical component for un-interrupted supply of electricity to e-drives and other electrical systems in electric vehicles (EV). A battery pack typically consists of several battery modules that are electrically connected in series and parallel based on the desired power and capacity requirements (Zwicker et al., 2020). Battery modules hold the battery cells that store the electrical charge and supply it on-demand to the electrical systems. Electrical connections play a critical role in the entire process of battery pack manufacturing since joints with different electrical resistance may result in uneven current loads that can affect the overall performances of the battery system (Kumar et al., 2021). Joining of dissimilar materials is the most deemed since it complements the properties of the individual materials and allows to develop functionally efficient connections. Joints in EV battery pack involve low-thickness materials (typically 0.3–1 mm) and the welding process is normally performed in lap or fillet configuration. Depending upon design and functional requirements as well as manufacturing costs, research has shown that the following combinations of materials are the most regarded: aluminium (Al) to copper (Cu), steel to Al, Al to steel, Cu to steel (Das et al., 2018).
Connections between Cu and steel have gained much attention in EV applications for joining cells in battery modules. For example, in the cylindrical format, the negative terminals are made of Cu and are generally connected to the steel casing of the cell (Sadeghian and Iqbal, 2022). Several joining processes have been studied for Cu-to-steel welding and they include wire bonding, micro-spot welding, ultrasonic welding, micro-TIG welding, electron beam welding and Laser Beam Welding (LBW) (Zwicker et al., 2020). LBW is an attractive option and has recently gained popularity due to advances in versatile methods for laser beam delivery and associated sensors technology for quality control and process monitoring that make LBW comparatively affordable (Kogel-Hollacher, 2020). Brand et al. (2015) demonstrated that LBW is a suitable process for joining battery terminals since it allows the lowest electrical resistance and the highest joint strength, when compared to micro-spot welding and ultrasonic welding; also, it is potentially applicable to any cell configuration and dissimilar metal combinations.
Despite the benefits of LBW, opening and maintaining a stable molten pool on the Cu-side is challenging when using LBW with infrared sources. The absorptivity of Cu at ambient temperature is approximate 5% and increases with rising temperature, and it suddenly jumps up when the melting temperature is reached. A problem with this is that when fusion of the material does happen, a surplus of energy flows through it, which can vaporise the material and create spatters, as well as pores inside the joint. These defects can reduce the electrical conductivity of the joint. At first sight, the solution to the low coupling efficiency of Cu is to switch from infrared sources to visible sources. The absorption increases drastically up to 60% when using visible sources. Green (515 nm) or blue (450 nm) lasers have been investigated by Kogel-Hollacher et al. (2022) and proved that lower power needed for same penetration achievable with infrared lasers and less thermal damage to enamel and insulators. Hummel et al. (2020) experimentally evaluated and proved the beneficial effects of blue laser during laser micro-welding of Cu, and achieved high welding speed with low input power. Nonetheless, compared to infrared lasers, the higher cost, lower plug efficiency and lower beam quality of visible lasers, push practitioners towards the use of multi-kW infrared sources at very high brightness for Cu welding.
In addition to the challenge posed by the laser beam coupling to the Cu, the welding of Cu to steel presents a series of problems. First, they are quite different in terms of physical properties such as density, melting points and thermal expansion and make defect-free welding difficult. Second, although Cu-Fe alloys are completely miscible in the stable liquid state and do not form brittle intermetallic compounds, the system shows a wide metastable miscibility gap at an undercooling level. The liquid phase separation occurs as the liquid cools in the miscibility gap resulting in the supersaturation of one or both liquids. Jeong et al. (2020) has shown that increasing the content of Fe tends to improve the mechanical properties of alloys but reduce electrical conductivity and ductility. Chen et al. (2013) proved that the toughness and fatigue strength of the joint decreases with the increase in the amount of molten Cu into the steel. Thus, melting of Cu was suggested to be kept at a minimum. Third, excessive penetration of Cu in grain boundaries of steel may result in cracks in the heat affected zone and fusion zone, and ultimately reducing structural performance of the joint. Therefore, to reduce these issues, controlling the mixing of Cu and steel in the molten pool is quite important for producing sound joints.
Laser beam shaping is gaining popularity since it holds the promise to control cooling rates and thermal gradients in and around the molten pool. This theoretically leads to a tailored material response to the heat input both spatially and temporally. A tailored power density profile (Fig. 1 shows typical power density profiles obtained via adjustable ring-mode laser) is generated via adequate insertion of optical components (specially coated lenses of silica substrate) in the optical chain of the welding head; or by electro-optical switching multiple laser beams generated in the laser source itself and enabled by beam combiners with optical phased array. Research has confirmed a positive effect of the laser beam shaping on the control of the weld profile and keyhole stabilization with suppression of spatters and significant reduction of porosity in the weldments. Caprio et al. (2023) investigated the use of beam shaping and beam oscillation to weld 0.2 mm Ni-plated steel sheets in lap joint configuration, which are materials commonly involved in cell to busbar connections. Sokolov et al. (2021) employed the ARM laser coupled with Optical Coherent Tomography (OCT) in Al-to-Cu thin sheets and observed that the use of combined core and ring-shaped laser beams reduced the fluctuations of the keyhole, improved the stability, and ultimately the accuracy of OCT measurements. Rinne et al. (2022) studied the effect of different power distributions between the inner core and outer ring-shaped laser beams on spatter ejection and penetration depth during welding of Cu sheets. Wagner et al. (2022) investigated and proved the influence of dynamic beam shaping on the geometry of the keyhole during welding of Cu by varying the patterns of the intensity distribution in longitudinal and transversal direction. Prieto et al. (2020) implemented dynamic laser beam shaping with infinite pattern and assessed quality of weld seam in 0.8 mm Al thin-sheet and observed that tailored beam with shape frequency over 10 kHz enables welding speed up to 18 m/min with stable keyhole.

Fig. 1. Example of laser beam shapes obtained via an adjustable ring-mode laser.

Despite the benefits, laser beam shaping introduces new set of parameters and finding the optimal combination of number of beams, shape of beams (multiple spots, C-spot, ring-core spots, pyramid, infinity, spiral shapes, etc. (Prieto et al., 2020)) can be expensive and time consuming since it may require dedicated equipment, expertise and experimental setups. In this context, multi-physics computational fluid dynamics (CFD) enable simulations of the process to reproduce mechanisms which are difficult to observe with in-situ investigations. With the raise of computational power and multi-core computing on high performance clusters, advanced simulations of LBW processes are now a close reality. Huang et al. (2020) developed a CFD model in FLOW-3D WELD® to study the metal mixing during linear laser welding of 200 µm Al to 500 µm Cu with different levels of laser power and velocity of the laser spot. They analysed the contribution of recoil pressure and Marangoni effect on the overall mixing process. Chianese et al. (2022) developed a multi-physics model using FLOW-3D and FLOW-3D WELD® to investigate the effect of part-to-part gap in LBW of Cu-to-steel thin sheets with beam wobbling. They showed that the presence of part-to-part gap and mixing mechanism between parent metals are linked, and the occurrence of part-to-part gap influences the temperature and velocity fields in the molten pool resulting in different mixing mechanisms. However, they did not implement any strategies for weld improvement. Drobniak et al. (2020) and Buttazzoni et al. (2021) implemented CFD multi-physics simulations of 1 mm-thick stainless steel plates with adaptive mesh refinement to predict the shape of the weld seam in presence of part-to-part gap, and they predicted the effect on the process of secondary laser beams with different shapes to optimize the weld quality. Recently, Huang et al. (2023) combined experimental approach and CFD simulations in FLOW-3D WELD® to reveal the effect of oscillation frequency and amplitude on fluid-flow and metal mixing during laser welding of 200 µm Al to 500 µm Cu with circular beam wobbling implemented. Additionally, they implemented a Scheil solidification model to predict the phase distributions in the welds based on the predicted thermo-solute conditions.
While significant research has been already developed using linear laser welding or laser welding with wobbling for joining of dissimilar materials, a clear understanding of metal mixing and dynamics of the keyhole during Cu-to-steel welding with beam shaping are not clearly reported. Research into application of beam shaping for Cu-to-steel welding entails a promising prospect for further development and investigation. Furthermore, the use of advanced CFD models is a viable approach to complement experimental investigations and explore weld configurations with different beam shaping profiles that would be difficult to achieve only with experimental work. Therefore, this paper aims to study the impact of laser beam shaping on metal mixing and dynamics of the keyhole during LBW of Cu-to-steel for battery terminal-to-casing connections. Four beam shapes were tested during LBW of 300 µm Cu to 300 µm nickel-plated steel. Both experiments and CFD simulations were used to study the underlying physics. A CFD model was firstly calibrated against experiments and then deployed to explore the effect of the increasing ring-to-core diameter, as well as a tandem laser spot configuration.

2. Experimental design and model description

2.1. Experimental design

Materials used in this work are Copper SE-Cu58 2.0070 and Nickel-plated steel (commercial name: Hilumin TATA STEEL). Experiments consisted of 25 mm long welds in lap joints configuration with 300 µm Cu on top of 300 µm nickel-plated steel.
Dimensions of the specimens were 65 mm × 30 mm. The laser source used was the Lumentum CORELIGHT, having 55 µm core diameter and 220 µm ring diameter, and BPP 1.4 mm·mrad and 11 mm·mrad for core and ring, respectively. The laser fiber was coupled to the Scout-200 (Laser and Control K-lab, South Korea) scanner to deliver the laser power to the specimens via 2D F-theta scanner with telecentric lenses. Fig. 2 shows the welding setup and specifications of the equipment are in Table 1. Caustic parameters were measured using PRIMES GmbH measurement system.

Fig. 2. (a) Welding setup with aluminium fixture; (b) schematical representation of the welding setup; (c) definition of weld features: top weld width, Wtop; width at the interface, Wi; weld penetration depth, Dpen.
Table 1. Specifications of the welding equipment.

Each weld seam was cut and prepared to obtain two cross sections for each experiment – cross sections were positioned at 10 mm and 15 mm away from the weld start. Three replicates were performed for each weld configuration. Sectioned samples were mounted in Bakelite resins and standard metallography procedure was performed for grinding and polishing to reveal weld profile under Nikon Eclipse LV150N optical microscope. To evaluate and characterize metal mixing with parent metals, elemental mapping of cross-sections was performed with an FEI Versa 3D dual beam scanning electron microscope using Energy Dispersive X-ray Spectroscopy (EDS mapping).
Welding experiments were performed in continuous power mode without power modulation. The laser beam was focussed perpendicularly on the upper surface of the Cu sheet, and the motion of the laser was linear (no wobbling). Although the use of shielding gas tends to avoid oxidation in the process and reduce hydrogen entrapment, when using scanners to deliver the laser beam, the gas nozzle cannot be positioned in proximity of the beam. Therefore, in this work, all experiments were conducted with no shielding gas. Part-to-part gap was manually checked and set to a nominal zero.
To study the impact of laser beam shaping on metal mixing and molten pool dynamics, 5 weld configurations (C1 to C5) were designed as shown in Table 2, with 4 beam shapes presented in Fig. 3. LBS#1 is single gaussian spot of 90 µm; LBS#2 super-imposes an inner core of 90 µm with an outer ring-shaped profile of 350 µm, with the ring accounting 30% of the total power. LBS#1 and LBS#2 were experimentally tested and enabled by the static beam shaping system of the Lumentum CORELIGHT source. LBS#3 follows the hollow sinh-Gaussian beam profile as defined in Liu et al. (2019), with 90 µm core and 500 µm ring, with 72% of the total power assigned to the ring. LBS#4 is a tandem beam with primary (90 µm) and secondary beam (150 µm) at a centre-to-centre distance of 300 µm, and 50% split of the power between primary and secondary beams – LBS#4 was introduced with the aim to increase the absorption rate by the pre-heating action of the secondary beam. LBS#3 and LBS#4 were only simulated since the laser beam shaping of the Lumentum CORELIGHT was only capable to work with fixed core-to-ring diameter ratio. Therefore, only a simulation-based approach (with the model pre-validated and calibrated in C1, C2 and C3) was deemed appropriate in this case to explore the effect of the increasing ring-to-core diameter and tandem laser spot configuration on material mixing.

Table 2. Process parameters used for the four selected laser beam shapes in Fig. 3.
Fig. 3. Normalized power density distribution for LBS#1, LBS#2, LBS#3 and LBS#4.

The power and speed of C1, C3, C4 and C5 were selected with an iterative process to ensure weld penetration depth, Dpen, ranging 400 – 500 µm. The choice of this penetration depth is based on the requirement that the temperature at the lower end of the steel sheet remains below 550 K. This precautionary measure aims to prevent any potential damage to the battery cell. Additionally, to minimise the effect of the weld depth on the metal mixing, a uniform depth of penetration was adopted across the different beam shapes for comparative analysis. Welding speeds were kept between 250 mm/s and 375 mm/s which is in line with the experimental work in (Perez Zapico et al., 2021). C2 is a variant of C1 and corresponds to a fully penetrated weld. Although fully penetrated welds must be avoided during LBW of battery terminals due to the risk of fire ignition, this work presents this variant for two reasons: first, to generate an additional weld configuration to validate the simulation; second, to discuss how the metal mixing behaves when transitioning from partial penetration to full penetration.

2.2. Model description

A multi-physics model was developed using the commercial CFD code FLOW-3D® (solver version: 12.0.2.01) and its module FLOW-3D® WELD (release: 7, update: 1). In order to develop a numerical model representing the essential physics during LBW of Cu-to-steel, the following assumptions were considered: (i) the liquid flow is considered Newtonian and incompressible; (ii) volumetric thermal expansion of the liquid metal due to temperature-dependent mass density is accounted; (iii) the air and vaporized metal are modelled as “void” type, with ambient temperature and pressure assigned to model the heat exchange with the metal as a natural convective flux (irradiance is neglected); (iv) the heat sinking effect of the clamping mask is neglected due to the clearance between the weld seam and the mask itself as already presented in (Chianese et al., 2022); (v) the effect of plasma plume on laser absorption is not directly modelled but is accounted in the calibration process as also proposed in previous studies by Lin et al. (2017) and Hao et al. (2021); furthermore, the laser absorption is assumed temperature dependent for Cu, constant for steel, and independent of the incidence angle. This assumption is in-line with the work presented by Huang et al. (2020), where they used the build-in ray-tracing function in FLOW-3D® WELD to predict the laser absorption in the keyhole.

2.2.1. Governing equations, boundary conditions and material properties

To reduce the computational cost of the simulations, the computational domain was divided in two zones (Fig. 4): (1) a process zone which was interested by phase change, and, (2) a thermal diffusion zone that models heat transmission in the sheets. A finer mesh size was used for cells in the process zone, and a mesh size 5 times greater than in the process zone was used for cells in the thermal diffusion zone.

Fig. 4. Top view (a) and side view (b) of a schematic representation of the computational domain and modelling approach with nested meshes (process zone and thermal diffusion zone).

Dimensions of the process zone are 2 mm × 0.8 mm× 0.775 mm. The length (2 mm) of the process zone was chosen to enable the simulation of approx. 1.8 mm weld length, which was experimentally evaluated to be sufficient for reaching the steady-state regime. The width (0.8 mm) of the process zone was selected to ensure that the molten pool was contained in it; the height of the computational domain was chosen equal to 0.8 mm so that, beside the stacked thickness of the processed sheets (0.6 mm), 0.2 mm of air (void type) are included in the computational domain. Extension of the thermal diffusion zone is calculated according to the Eq. (1), where k is the thermal conductivity, cp the specific heat at constant pressure, ρ the mass density, tend the simulation time, T the temperature, and Tamb= 20 °C the ambient temperature. The simulation time, tend, is function of the welding speed and the weld length (1.5 mm).

Four different values of the mesh size in the process zone were considered during sensitivity analysis, namely 40 µm, 20 µm, 15 µm, and 10 µm, that resulted in mesh independent solution for mesh size equal to or below 15 µm, which therefore is the selected size. This led to total number of cells approximatively equal to 528 thousand. The geometry of the thin sheets has been modelled in the computational domain, so that in-plane dimensions were parallel to X and Y axis, as shown in the top and side view in Fig. 4(a) and (b). Welding direction was parallel to X axis.
The following physics have been accounted to model the welding process: continuity, fluid flow via Navier-Stokes equations, energy conservation, evaporation, keyhole formation and evolution, solidification, species conservation and tracking, surface tension with Marangoni and Laplace forces and multiple reflections.
Phase change – Eq. (2) governs the evaporation phenomena which are modelled as mass transfer between the liquid phase and the void type and are proportional to the difference between the saturation pressure Psat and the partial pressure Pvap. In this equation, α is the accommodation coefficient, R is the gas constant, and T is the temperature. The saturation pressure is calculated as a function of the temperature according to the Clapeyron equation (Eq. (3)), in which the couple (Pv, Tv) represents a point on the saturation curve; γ, cv, and ΔHv are the specific heats ratio, the specific heat at constant volume, the latent heat of vaporization, respectively.

Recoil pressure – during laser welding process, intense localised heating of substrate material causes vaporization which results in recoil pressure. This pressure is proportional to the saturated vapor pressure. The relationship between the recoil pressure, Precoil, and the saturated vapor pressure, Psat, depends on the material properties and laser-to-material interaction. Eq. (4) is derived from Eq. (3) with the introduction of two coefficients, Ar and B, that will be calibrated using experimental data.

Tracking of the keyhole – surface of the keyhole is tracked by the volume of fluid (VOF) method (Daligault et al., 2022), which enables the calculation of the interface between the liquid metal and the void type, according to Eq. (5).

The interface between the cell is tracked using a scalar value f that indicates the fraction of fluid in it. A value of f=0 indicates that the cell has only void, conversely, f=1 corresponds to the case of a cell full of liquid, whereas the case of 0<f<1 indicates that the cell has both the liquid and the void type, and therefore the interface between the two falls in it. Similarly, metals involved in the welding process with fluid flow and mixing are tracked in each cell by means of a scalar value f2, which indicates the fraction of second material within the cells. Values of the generic material property ̅φ̅ in each cell is evaluated as weighted sum of the properties φ1 and φ2 of parent metals based on their mixing, as in Eq. (6).

Multiple reflections – Multiple reflections are implemented using a discrete grid cell system through the ray tracing technique. The laser beam is divided into a finite number of rays, which move in the laser beam irradiation direction. When the ray encounters the surface of the material, it is reflected according to vector Eq. (7), in which R→ is the direction of the reflected vector, I→ the direction of the incoming ray, and nˆ the normal direction of the material surface.

Laplace pressure and Marangoni effect – Recoil pressure contributes to the formation of the keyhole and mainly contributes to the velocity field in the fluid; however, surface tension-related phenomena such as Laplace pressure LP and the Marangoni force SM have great influence on the overall welding process. Laplace pressure and the Marangoni force are modelled according to (8), (9) which, σ is the surface tension, RI and RII are the principal curvature radii, and operator ∇t indicates the gradient along the tangent direction at the interface. Eq. (9) explicitly indicates the dependence of the Marangoni effect on the gradient of the surface tension, which in assumed temperature-dependent of the surface tension.

2.2.2. Boundary conditions and material properties

As shown in Fig. (4), the following boundary condition were assigned: wall in the X and Y direction (with constant ambient temperature); assigned pressure and temperature at the boundaries of the computational domain in the Z directions, with natural convective heat flux between the metallic sheets and the air. The heat source was directly imported from the power profiles defined in Fig. 3. Material properties were imported from the JMATPRO® material database. Fig. 5 shows the temperature-dependent plots.

Fig. 5. Temperature-dependent material properties defined in the model.

3. Results and discussion

3.1. Model validation

The model has been applied to simulate all the cases listed in Table 2. Model validation was conducted for the weld configurations C1, C2 and C3 by comparing the weld profile in cross sections and Fe concentration line profiles against the experimental results as shown in Fig. 6. Experimental and simulation results show that welding is done through keyhole mode. The generation of a keyhole is significantly influenced by recoil pressure. In the simulation, the recoil pressure is adjusted through the calibration of coefficients Ar and B, as indicated in Eq. 4. During the model calibration process, a value of Ar was determined to be 55,715 Pa, and the parameter B was set to 4, resulting in comparative results with those obtained in experiments. Five different mesh sizes were tested: 20 µm, 15 µm, 10 µm and 5 µm. The choice of the mesh size was driven by the need to have a minimum of 4 cells to discretise the smallest laser spot (i.e., LSB#1 has the smallest beam diameter of 90 µm among the tested beam shapes in Fig. 3). Mesh-independent solution was achieved with mesh size of 15 µm and this led to approximate a million cells in the whole computational domain.

Fig. 6. Comparison of the experimental and modelling results of the molten pool geometry and elemental maps for weld configurations C1 (a), C2 (b) and C3 (c).

The correlation was conducted looking at two cross-Section (10 mm 15 mm away from the weld start and end) – this was motivated by the need to take into account the experimental errors during the calibration and validation process.

Fig. 6 shows cross sections and elemental maps for experiments C1, C2, and C3, and corresponding simulations. Two representative cross-sections from the same weld seam are shown in each sub-figure to demonstrate the capability of the model to reproduce the geometric shape and the mixing phaenomena at different longitudinal positions along the weld seam. The fusion zones are marked in each cross section and show good correlation with predictions from simulations, as the cases with partial penetration are successfully predicted in for C1 and C3, along with full penetration in C2.

Elemental maps that were measured with EDS, and species concentration that were predicted with simulations, are reported for comparison to show capability of the model to reproduce the mixing mechanism. For each case, plots of the concentration of Fe along with line-scans are reported to quantitatively demonstrate the capability of the model to simulated diffusion of the molten metal from the bottom sheet to the upper one. They show that diffusion of Fe in Cu is well predicted in C1 and C3, as well as presence of Fe-rich clusters in the Cu near the interface between parent materials is reproduced in C2.

Good correlation between measurements and predictions of the weld geometry and metal mixing demonstrates capability of the model to simulate welding scenarios with different laser beam shapes, and weld penetration depth spanning from partial penetration to full penetration. This allows to confidently deploy the simulation model in conjunction with experiments to study the impact of laser beam shaping on metal mixing and molten pool dynamics.

3.2. Keyhole dynamics and impact on metal mixing

As keyhole instabilities have a significant impact on weld quality (Lu et al., 2015), this section highlights the impact of the laser beam shapes on the keyhole dynamics, which ultimately contributes to metal mixing. The discussion is presented by linking the laser power profile to the velocity field within the molten pool and ultimately to the metal mixing between the parent metals and the occurrence of collapse events of the keyhole.

Fig. 7 shows consecutive time frames in each weld configuration and reflects keyhole dynamic mechanisms. The keyhole’s shape and size vary, exhibiting irregularities, asymmetry and fluctuations. These shapes are directly correlated to the laser beam shape profile. The following observations are made:

  • Collapse events terminate in formation of pores and metal mixing. This is visible in the experimental results presented in Fig. 6(a) and (b), where relatively large pores are observed in the experimental cross-section. With a narrow beam profile (weld configuration C1, C2, C3 and C5) and high energy density, once fusion of the Cu does happen, a surplus of energy flows through the keyhole, increasing the temperature at the keyhole bottom. This generates a recoil pressure that pushes the fluid upwards. At the top surface and rear side of the keyhole, the opposing movements of the fluid, both clockwise and counter-clockwise, and driven by the Marangoni force, have an important consequence: they restrict the size of the molten pool. This restriction creates a high viscosity mushy layer that forms a barrier that limits the expansion of the molten pool. As result, closure or narrowing the top neck of the keyhole restricts the ejection of vapours out of keyhole which leads to increase in pressure within keyhole and creates a high-pressure lob. This ultimately results in pores formed to the toe of the keyhole as seen in Fig. 7(a) and (b). Although a collapse event is observed in C3 as shown Fig. 7(c), it does not necessarily create porosity in the solid front as sufficient room is available for gas vapours to escape from the bottom of the keyhole. The introduction of a pre-heat heating beam in weld configuration C5 does not produce any significant change to the keyhole dynamics as observed in Fig. 7(d). In partial penetration, narrow and deep keyhole is more unstable as slight fluctuations in fluid pressure, velocity and temperature on the rear wall of keyhole can create a collapse event. Additionally, the collapse of the keyhole in partial penetration creates a narrower fluid channel, resulting in localized increase of fluid velocity, which, in turn, affects metal mixing.
  • Weld configuration C4 leads to wider opening of the keyhole with greater stability as shown in Fig. 7(e). With the super-imposition of the core beam with the wider ring-shaped beam, the core beam penetrates the steel sheet, while the larger ring keeps the keyhole open at the Cu surface. This weld configuration drastically reduces the collapse events and the development of bubbles. It can be observed that the lower depth-to-width aspect ratio of the melt pool correlates to fewer number of collapse events.
  • Metal mixing is not only influenced by keyhole dynamics and collapse events, but there is an intricate interplay between keyhole geometry, fluid dynamics and buoyancy forces that are dependent upon density which varies with temperature in molten pool, and from top to bottom due to differences in density between Cu and steel. To test the influence of buoyancy forces, a simulation test was performed where the density of Cu and steel were artificially set to be equal. Fig. 8 shows the simulation results and confirm that buoyancy forces have an impact on the metal mixing especially at the interface between the two metals and in the Cu side of the weld. For example, the line-scan B-B in Fig. 8 shows an increase on average of the Fe vol% in the Cu side by 10%, when comparing results with same densities.
Fig. 8. Impact of buoyancy forces on the metal mixing for weld configuration C3. Sections taken at Y= 0.
Fig. 7. Consecutive time steps of the molten pool dynamics for configuration C1 (a), C2 (b), C3 (c) C5 (d) and C4 (e). The plot shows the fluid velocity (both direction and magnitude) visualized by black arrows. Cross sections taken at Y= 0.

The introduction of a ring beam (weld configuration C4 with LBS#3) in the laser welding process alters the shape of the keyhole compared to a single beam scenario (weld configuration C1 with LBS#1). In the single beam case, the keyhole walls develops predominantly in Z direction (schematically illustrated in Fig. 9(a)). The inclusion of a ring beam results in the critical change of the keyhole wall’s curvature, with a pronounced arc-like shape at the rear (Fig. 9(b)). The change of keyhole wall’s curvature plays a critical role and is explained by the complex equilibrium between the fluid pressure, the recoil pressure and the gravity load. A collapse event is associated with the non-equilibrium of the forces in the X direction. To explain this, it is first worth noting that with an idealised static molten pool (no fluid velocity) the fluid pressure would be higher at the bottom and would be governed by the hydrostatic law – with this, the pressure variation occurs linearly downwards and would be a function of the molten pool depth. Under this ideal condition, the keyhole would exhibit a stable equilibrium regime driven by the balanced effect of recoil pressure and fluid flow. With the actual molten pool, the equilibrium state is, however, perturbated by the non-linear variation of the fluid pressure due to the fast upwards motion generated by the recoil pressure itself. A near-equilibrium state is eventually achieved with the change of keyhole wall’s curvature with the resultant of the forces acting predominantly in the Z direction. The shallow angle of the keyhole wall observed at LBS#3 (θ3 < θ1) effectively decomposes the combined forces exerted by the fluid towards the Z direction, hence moving to the near-equilibrium state, with the fluid pushed downwards in Z rather than sidewise in X. It can be observed that the ring-to-core diameter and the ring-to-core power are essential to control the keyhole wall’s curvature and ultimately influence of the stability of the keyhole.

Fig. 9. Schematic representation of forces and pressures acting on the melt pool in case of welding with single laser beam (LBS#1) and ring-core configuration (LBS#3). Arrows represent forces/pressures, and the thickness is proportional of the intensity of the forces/pressures. Arrows are only shown to the rear-side of the keyhole since the physics involved there are more relevant for the dynamics of the keyhole.

3.3. Impact of beam shaping on metal mixing

Cu and steel are generally immiscible as studied by other researchers, such as Shi et al. (2013). This separation means the material solidifies as two separate phases from the liquid state. At this immiscible region a Cu-rich (α phase) and iron-rich (β phase) form FCC and BCC crystal structures, respectively. For the compositional data shown in Fig. 6, the highest amount of mixing for each of the three examples is 60%, 80% and 50% of Fe in the weld pool. When studying the Cu-Fe binary phase diagram, as performed by Chen et al. (2007), these compositions fall within the miscibility gap range. For which no IMCs are expected to form, but instead separate (α and β) phases. However, it is still clear that the formation of these separate phases still creates a mismatch in mechanical properties of the welded joint, both at the interface and enriched regions, which can lead to crack initiation, as reported by Rinne et al. (2020). For this reason, analysing the metal-mixing in dissimilar metals is an important step toward understanding and prevention of cracking mechanisms that can affect the performance of the weld.
Influence of the beam shapes on the metal mixing, can be investigated by analysing velocity fields and fluid flow which are predicted with the validated model. Fig. 10(a) and (b) show that in the weld configuration C1 and C2 (corresponding to LBS#1 – single beam with circular spot and gaussian distribution) the increase in laser power leads to more steel mixing with Cu due to greater recoil pressure and to a larger melt pool with more liquid metal involved. When comparing the parameters in Fig. 11, the increased melting of the bottom steel sheet leads to a greater region of keyhole necking with collapse; this can be due to the increased laser absorption, for which steel has a greater absorptivity than the more reflective Cu (Rinne et al., 2020). The lower density of steel creates an upward buoyancy force which allows the migration of more steel into the Cu-rich region. Fig. 11(c) and (d) show weld configurations C3 and C4 respectively, with combined secondary ring-shaped and primary laser beam (LBS#2 and LBS#3, respectively). They can be compared based on similar levels of weld penetration but different width at the interface between parent metals and at the top of the weld seam. Spread of the laser power over a wider surface due to the use of a ring results in a wider weld pool compared to simulations C1 and C2, which is consistent with results found by Jabar et al. (2023). However, one difference between these two cases is that, due to different power density distributions, to achieve adequate weld penetration depth, different laser power is provided leading to different thermal fields and time that the metal stays liquid. Line-scans of the temperature profiles in the melt pool can be observed in Fig. 12, with higher peak temperature in C4, compared to simulations C1 and C2, and C5; whereas a smaller secondary ring-shaped laser beam in simulation C3 results in intermediate behaviour.

Fig. 10. Plots of metal mixing in the longitudinal and a cross sections predicted with simulations C1 (a), C2 (b), C3 (c), C4 (d) and C5 (e).
Fig. 11. (a) Temperature, (b) velocity, (c) Fe concentration and (d) actual melt pool for all the tested weld configurations C1 to C5. Cross sections taken at Y= 0.
Fig. 12. Temperature profiles for weld configurations C1 (a), C2 (b), C3 (c), C4 (d) and C5 (e). Measurements were taken at X = 1.3 mm (just behind the keyhole wall) and Z = −300 µm (interface between Cu and steel).

The higher peak temperature in C4 eventually leads to a significant thermal gradient that promotes significant upward buoyancy forces and ultimately more migration of steel towards the Cu matrix. Similarity of simulation C5 with C1 can be explained considering that the secondary laser beam pre-heats the metal without widening the keyhole. Additionally, the higher peak temperature and larger size of the melt pool in C4 lead to longer time in which the steel stays in the liquid phase with more time available to migrate toward the Cu matrix due to recoil pressure and buoyancy forces and to diffuse. For these reasons, if use of larger spot helps with keyhole stabilisation, higher laser power required to establish sound connection enhances mixing between parent metal. Therefore, selection of custom ring-to-core diameter and ring-to-core power is a decision with a trade-off between the need of stabilising the keyhole dynamics and the need to reduce the mixing.
Velocity fields in Fig. 11 show also that the use of the ring-shaped secondary beam (C4), results in lower recoil pressure due to less localised laser power and vaporization. For this reason, the fluid flow and velocity of the liquid movements in considerably lower, as shown by contour plots, where regions of the molten pool in red are those in which the flow of the liquid metal is faster. The metal mixing in the molten pool of C3 weld is more homogeneous than in C1 and C2, due to the localised heat input of the ring laser beam. Rinne et al. (2020) found the addition of the ring laser produced a more homogeneous distribution of Cu and steel in the solidified structure. The lower density of the steel can also be used to explain the more even distribution of steel throughout the weld pool of C3. This is also confirmed by the EDS line-scans in Fig. 6(c) that show a significant drop of Fe into the Cu matrix compared to C1 (Fig. 6(a)).
The result of metal mixing has a significant effect on the crack formation in the weld pool and heat-affected zone (HAZ). Two main types of cracking are often referred to as “hot cracking” (Rinne et al., 2020) or “liquation cracking” (Li et al., 2019). During any fusion welding process of Cu to steel the miscibility gap can be identified in the binary phase diagram of Cu-Fe (Chen et al., 2013). When both Cu and steel are melted, there is separation of the liquids during cooling, once the mixture enters the miscibility gap seen on the phase diagram the primary separation of the α and β phases occurs. The secondary separation occurs in the miscibility gap because of a lack of diffusion and a supersaturation of the α and/or β phases. The solidified weld microstructure is found inhomogeneous, consisting of the α and β phases. The difference in the thermal expansion properties of both Cu and steel can create locations of stress concentrations where cracks are often initiated, ad observed by Chen et al. (2013) and Sadeghian and Iqbal (2022). Li et al. (2019) proposed a three-stage mechanism for the formation of liquation cracks in Cu to steel laser welds. The first stage was the penetration of Cu liquid into the grain boundaries of the steel, secondly, the Cu liquid surrounds the Cu phase creating a “film” of liquid in the grain boundary. This drastically reduces the cohesive forces between the grain boundaries due to the presence of the α phase. Cracking can then be initiated in a similar manner to that detailed earlier.

4. Conclusions

A combination of multi-physics CFD modelling results and experiments have been presented to study the impact of laser beam shaping on metal mixing and molten pool dynamics during LBW of Cu-to-steel for battery terminal-to-casing connections. The multi-physics model has been validated with ex-situ EDS element mapping and weld profile’s features. The model has provided useful insights about temperature and velocity fields, mixing mechanisms and dynamics of the keyhole, all of which are difficult to access via experiments due to technological difficulties. The major findings of the work are summarized below:

  • Metal mixing is largely influenced by the fluid dynamics via the Marangoni, buoyancy forces and recoil pressure. With a greater laser power, recoil pressure is increased, and this leads to more weld penetration and melting of steel. Additionally, spread of the laser power results in higher width of the fusion zone. Subsequently, the buoyance forces due to the different densities of steel and Cu contribute to the upward flow of steel towards Cu, and hence impact meaningfully to the mixing. This can be clearly observed in weld configurations C1 and C2.
  • Due to the collapse events of the keyhole wall, porosity formation was found in welds C1, C2 and C5. Furthermore, the collapse events create a narrow fluid channel, which results in localised surges in fluid velocity, therefore, promoting metal mixing. All in all, simulations revealed that increasing depth-to-width aspect ratio is correlated to higher frequency of collapse events in the keyhole. Therefore, stabilisation of the melt pool can be achieved with tailored laser beam shapes.
  • The study has pointed-out that the use of larger ring beam (configuration C4) helps with keyhole stabilisation, but at the same time leads to more laser power and higher temperature that contribute to the enhancement of mixing between parent metals. This poses a trade-off in the definition of a tailored ring-to-core diameter and the ring-to-core power. Analysis of the results showed that ring-to-core diameter (350–90 µm) and 30% of ring power (weld configuration C3) resulted in more stable dynamics of the keyhole, with significant reduction of collapse events, and ultimately controlled migration of steel towards Cu. Furthermore, compared to C4 (2500 W total power), the lower thermal gradient in C3 (1530 W total power) eventually leads to a reduction in the upward buoyancy forces.
  • The pre-heating approach with the tandem beam (C5) only led to local fusion of Cu and no significant improvement in keyhole stability was observed.
  • The combination of experiments and numerical modelling provides a powerful approach to understand complex fluid flow and metal mixing processes during laser keyhole welding. This helps to study mixing behaviour along with weld pool dynamics for selection of laser welding strategies with beam shaping in case of dissimilar material welding, especially in presence of miscibility gap at higher temperature as in case of Cu and steel.

References

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

Get rights and content Under a Creative Commons license open access

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 108 K 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 × 103 J 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 × 106 K s-1, G was in the range of 3.6 × 105–1.9 × 107 K 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 < Vcs. DL 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 × 107 K 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 ΔT0, DL, k, 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 × 106 K 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

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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.

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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.

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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) M 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) R 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.

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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.

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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.

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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.

REFERENCES

  1. S. L. Sing and W. Y. Yeong , “ Laser powder bed fusion for metal additive manufacturing: Perspectives on recent developments,” Virtual Phys. Prototyping. 15, 359–370 (2020).https://doi.org/10.1080/17452759.2020.1779999
    Google ScholarCrossref
  2. A. M. Khorasani , I. G. Jithin , J. K. Veetil , and A. H. Ghasemi , “ A review of technological improvements in laser-based powder bed fusion of metal printers,” Int. J. Adv. Manuf. Technol. 108, 191–209 (2020).https://doi.org/10.1007/s00170-020-05361-3
    Google ScholarCrossref
  3. Y. Qin , A. Brockett , Y. Ma , A. Razali , J. Zhao , C. Harrison , W. Pan , X. Dai , and D. Loziak , “ Micro-manufacturing: Research, technology outcomes and development issues,” Int. J. Adv. Manuf. Technol. 47, 821–837 (2010).https://doi.org/10.1007/s00170-009-2411-2
    Google ScholarCrossref
  4. B. Nagarajan , Z. Hu , X. Song , W. Zhai , and J. Wei , “ Development of micro selective laser melting: The state of the art and future perspectives,” Engineering. 5, 702–720 (2019).https://doi.org/10.1016/j.eng.2019.07.002
    Google ScholarCrossref
  5. Y. Wei , G. Chen , W. Li , Y. Zhou , Z. Nie , J. Xu , and W. Zhou , “ Micro selective laser melting of SS316L: Single tracks, defects, microstructures and thermal/mechanical properties,” Opt. Laser Technol. 145, 107469 (2022).https://doi.org/10.1016/j.optlastec.2021.107469
    Google ScholarCrossref
  6. Y. Wei , G. Chen , W. Li , M. Li , Y. Zhou , Z. Nie , and J. Xu , “ Process optimization of micro selective laser melting and comparison of different laser diameter for forming different powder,” Opt. Laser Technol. 150, 107953 (2022).https://doi.org/10.1016/j.optlastec.2022.107953
    Google ScholarCrossref
  7. H. Zhiheng , B. Nagarajan , X. Song , R. Huang , W. Zhai , and J. Wei , “ Formation of SS316L single tracks in micro selective laser melting: Surface, geometry, and defects,” Adv. Mater. Sci. Eng. 2019, 9451406.https://doi.org/10.1155/2019/9451406
    Crossref
  8. B. Nagarajan , Z. Hu , S. Gao , X. Song , R. Huang , M. Seita , and J. Wei , “ Effect of in-situ laser remelting on the microstructure of SS316L fabricated by micro selective laser melting,” in Advanced Surface Enhancement, edited by Sho Itoh and Shashwat Shukla , Lecture Notes in Mechanical Engineering ( Springer Singapore, Singapore, 2020), pp. 330–336.
    Google ScholarCrossref
  9. H. Zhiheng , B. Nagarajan , X. Song , R. Huang , W. Zhai , and J. Wei , “ Tailoring surface roughness of micro selective laser melted SS316L by in-situ laser remelting,” in Advanced Surface Enhancement, edited by Sho Itoh and Shashwat Shukla , Lecture Notes in Mechanical Engineering ( Springer Singapore, Singapore, 2020), pp. 337–343.
    Google Scholar
  10. J. Fu , Z. Hu , X. Song , W. Zhai , Y. Long , H. Li , and M. Fu , “ Micro selective laser melting of NiTi shape memory alloy: Defects, microstructures and thermal/mechanical properties,” Opt. Laser Technol. 131, 106374 (2020).https://doi.org/10.1016/j.optlastec.2020.106374
    Google ScholarCrossref
  11. E. Abele and M. Kniepkamp , “ Analysis and optimisation of vertical surface roughness in micro selective laser melting,” Surf. Topogr.: Metrol. Prop. 3, 034007 (2015).https://doi.org/10.1088/2051-672X/3/3/034007
    Google ScholarCrossref
  12. S. Qu , J. Ding , J. Fu , M. Fu , B. Zhang , and X. Song , “ High-precision laser powder bed fusion processing of pure copper,” Addit. Manuf. 48, 102417 (2021).https://doi.org/10.1016/j.addma.2021.102417
    Google ScholarCrossref
  13. Y. Wei , G. Chen , M. Li , W. Li , Y. Zhou , J. Xu , and Z. wei , “ High-precision laser powder bed fusion of 18Ni300 maraging steel and its SiC reinforcement composite materials,” J. Manuf. Process. 84, 750–763 (2022).https://doi.org/10.1016/j.jmapro.2022.10.049
    Google ScholarCrossref
  14. B. Liu , R. Wildman , T. Christopher , I. Ashcroft , and H. Richard , “ Investigation the effect of particle size distribution on processing parameters optimisation in selective laser melting process,” in 2011 International Solid Freeform Fabrication Symposium ( University of Texas at Austin, 2011).
    Google Scholar
  15. T. D. McLouth , G. E. Bean , D. B. Witkin , S. D. Sitzman , P. M. Adams , D. N. Patel , W. Park , J.-M. Yang , and R. J. Zaldivar , “ The effect of laser focus shift on microstructural variation of Inconel 718 produced by selective laser melting,” Mater. Des. 149, 205–213 (2018).https://doi.org/10.1016/j.matdes.2018.04.019
    Google ScholarCrossref
  16. Y. Qian , Y. Wentao , and L. Feng , “ Mesoscopic simulations of powder bed fusion: Research progresses and conditions,” Electromachining Mould 06, 46–52 (2017).https://doi.org/10.3969/j.issn.1009-279X.2017.06.012
    Google Scholar
  17. J. Fu , S. Qu , J. Ding , X. Song , and M. W. Fu , “ Comparison of the microstructure, mechanical properties and distortion of stainless Steel 316L fabricated by micro and conventional laser powder bed fusion,” Addit. Manuf. 44, 102067 (2021).https://doi.org/10.1016/j.addma.2021.102067
    Google ScholarCrossref
  18. N. T. Aboulkhair , I. Maskery , C. Tuck , I. Ashcroft , and N. M. Everitt , “ The microstructure and mechanical properties of selectively laser Melted AlSi10Mg: The effect of a conventional T6-like heat treatment,” Mater. Sci. Eng. A 667, 139–146 (2016).https://doi.org/10.1016/j.msea.2016.04.092
    Google ScholarCrossref
  19. S. Y. Chen , J. C. Huang , C. T. Pan , C. H. Lin , T. L. Yang , Y. S. Huang , C. H. Ou , L. Y. Chen , D. Y. Lin , H. K. Lin , T. H. Li , J. S. C. Jang , and C. C. Yang , “ Microstructure and mechanical properties of open-cell porous Ti-6Al-4V fabricated by selective laser melting,” J. Alloys Compd. 713, 248–254 (2017).https://doi.org/10.1016/j.jallcom.2017.04.190
    Google ScholarCrossref
  20. Y. Bai , Y. Yang , D. Wang , and M. Zhang , “ Influence mechanism of parameters process and mechanical properties evolution mechanism of Maraging steel 300 by selective laser melting,” Mater. Sci. Eng. A 703, 116–123 (2017).https://doi.org/10.1016/j.msea.2017.06.033
    Google ScholarCrossref
  21. Y. Bai , Y. Yang , Z. Xiao , M. Zhang , and D. Wang , “ Process optimization and mechanical property evolution of AlSiMg0.75 by selective laser melting,” Mater. Des. 140, 257–266 (2018).https://doi.org/10.1016/j.matdes.2017.11.045
    Google ScholarCrossref
  22. Y. Liu , M. Zhang , W. Shi , Y. Ma , and J. Yang , “ Study on performance optimization of 316L stainless steel parts by high-efficiency selective laser melting,” Opt. Laser Technol. 138, 106872 (2021).https://doi.org/10.1016/j.optlastec.2020.106872
    Google ScholarCrossref
  23. D. Gu , Y.-C. Hagedorn , W. Meiners , G. Meng , R. J. S. Batista , K. Wissenbach , and R. Poprawe , “ Densification behavior, microstructure evolution, and wear performance of selective laser melting processed commercially pure titanium,” Acta Mater. 60, 3849–3860 (2012).https://doi.org/10.1016/j.actamat.2012.04.006
    Google ScholarCrossref
  24. N. Read , W. Wang , K. Essa , and M. M. Attallah , “ Selective laser melting of AlSi10Mg alloy: Process optimisation and mechanical properties development,” Mater. Des. 65, 417–424 (2015).https://doi.org/10.1016/j.matdes.2014.09.044
    Google ScholarCrossref
  25. I. A. Roberts , C. J. Wang , R. Esterlein , M. Stanford , and D. J. Mynors , “ A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing,” Int. J. Mach. Tools Manuf. 49(12–13), 916–923 (2009).https://doi.org/10.1016/j.ijmachtools.2009.07.004
    Google ScholarCrossref
  26. K. Dai and L. Shaw , “ Finite element analysis of the effect of volume shrinkage during laser densification,” Acta Mater. 53(18), 4743–4754 (2005).https://doi.org/10.1016/j.actamat.2005.06.014
    Google ScholarCrossref
  27. K. Carolin , E. Attar , and P. Heinl , “ Mesoscopic simulation of selective beam melting processes,” J. Mater. Process. Technol. 211(6), 978–987 (2011).https://doi.org/10.1016/j.jmatprotec.2010.12.016
    Google ScholarCrossref
  28. F.-J. Gürtler , M. Karg , K.-H. Leitz , and M. Schmidt , “ Simulation of laser beam melting of steel powders using the three-dimensional volume of fluid method,” Phys. Procedia 41, 881–886 (2013).https://doi.org/10.1016/j.phpro.2013.03.162
    Google ScholarCrossref
  29. P. Meakin and R. Jullien , “ Restructuring effects in the rain model for random deposition,” J. Phys. France 48(10), 1651–1662 (1987).https://doi.org/10.1051/jphys:0198700480100165100
    Google ScholarCrossref
  30. J-m Wang , G-h Liu , Y-l Fang , and W-k Li , “ Marangoni effect in nonequilibrium multiphase system of material processing,” Rev. Chem. Eng. 32(5), 551–585 (2016).https://doi.org/10.1515/revce-2015-0067
    Google ScholarCrossref
  31. W. Ye , S. Zhang , L. L. Mendez , M. Farias , J. Li , B. Xu , P. Li , and Y. Zhang , “ Numerical simulation of the melting and alloying processes of elemental titanium and boron powders using selective laser alloying,” J. Manuf. Process. 64, 1235–1247 (2021).https://doi.org/10.1016/j.jmapro.2021.02.044
    Google ScholarCrossref
  32. U. S. Bertoli , A. J. Wolfer , M. J. Matthews , J.-P. R. Delplanque , and J. M. Schoenung , “ On the limitations of volumetric energy density as a design parameter for selective laser melting,” Mater. Des. 113, 331–340 (2017).https://doi.org/10.1016/j.matdes.2016.10.037
    Google ScholarCrossref
  33. W. E. King , H. D. Barth , V. M. Castillo , G. F. Gallegos , J. W. Gibbs , D. E. Hahn , C. Kamath , and A. M. Rubenchik , “ Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing,” J. Mater. Process. Technol. 214(12), 2915–2925 (2014).https://doi.org/10.1016/j.jmatprotec.2014.06.005
    Google ScholarCrossref
  34. L. Cao , “ Numerical simulation of the impact of laying powder on selective laser melting single-pass formation,” Int. J. Heat Mass Transfer 141, 1036–1048 (2019).https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.053
    Google ScholarCrossref
  35. L. Huang , X. Hua , D. Wu , and F. Li , “ Numerical study of keyhole instability and porosity formation mechanism in laser welding of aluminum alloy and steel,” J. Mater. Process. Technol. 252, 421–431 (2018).https://doi.org/10.1016/j.jmatprotec.2017.10.011
    Google ScholarCrossref
  36. K. Q. Le , C. Tang , and C. H. Wong , “ On the study of keyhole-mode melting in selective laser melting process,” Int. J. Therm. Sci. 145, 105992 (2019).https://doi.org/10.1016/j.ijthermalsci.2019.105992
    Google ScholarCrossref
  37. J.-H. Cho and S.-J. Na , “ Theoretical analysis of keyhole dynamics in polarized laser drilling,” J. Phys. D: Appl. Phys. 40(24), 7638 (2007).https://doi.org/10.1088/0022-3727/40/24/007
    Google ScholarCrossref
  38. W. Ye , “ Mechanism analysis of selective laser melting and metallurgy process based on base element powder of titanium and boron,” Ph.D. dissertation ( Nanchang University, 2021).
    Google Scholar
  39. R. Ammer , M. Markl , U. Ljungblad , C. Körner , and U. Rüde , “ Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method,” Comput. Math. Appl. 67(2), 318–330 (2014).https://doi.org/10.1016/j.camwa.2013.10.001
    Google ScholarCrossref
  40. H. Chen , Q. Wei , S. Wen , Z. Li , and Y. Shi , “ Flow behavior of powder particles in layering process of selective laser melting: Numerical modeling and experimental verification based on discrete element method,” Int. J. Mach. Tools Manuf. 123, 146–159 (2017).https://doi.org/10.1016/j.ijmachtools.2017.08.004
    Google ScholarCrossref
  41. F. Verhaeghe , T. Craeghs , J. Heulens , and L. Pandelaers , “ A pragmatic model for selective laser melting with evaporation,” Acta Mater. 57(20), 6006–6012 (2009).https://doi.org/10.1016/j.actamat.2009.08.027
    Google ScholarCrossref
  42. C. H. Fu and Y. B. Guo , “ Three-dimensional temperature gradient mechanism in selective laser melting of Ti-6Al-4V,” J. Manuf. Sci. Eng. 136(6), 061004 (2014).https://doi.org/10.1115/1.4028539
    Google ScholarCrossref
  43. Y. Xiang , Z. Shuzhe , L. Junfeng , W. Zhengying , Y. Lixiang , and J. Lihao , “ Numerical simulation and experimental verification for selective laser single track melting forming of Ti6Al4V,” J. Zhejiang Univ. (Eng. Sci.) 53(11), 2102–2109 + 2117 (2019).https://doi.org/10.3785/j.issn.1008-973X.2019.11.007
    Google Scholar
  44. Q. He , H. Xia , J. Liu , X. Ao , and S. Lin , “ Modeling and numerical studies of selective laser melting: Multiphase flow, solidification and heat transfer,” Mater. Des. 196, 109115 (2020).https://doi.org/10.1016/j.matdes.2020.109115
    Google ScholarCrossref
  45. L. Cao , “ Mesoscopic-scale numerical simulation including the influence of process parameters on SLM single-layer multi-pass formation,” Metall. Mater. Trans. A 51, 4130–4145 (2020).https://doi.org/10.1007/s11661-020-05831-z
    Google ScholarCrossref
  46. L. Cao , “ Mesoscopic-scale numerical investigation including the influence of process parameters on LPBF multi-layer multi-path formation,” Comput. Model. Eng. Sci. 126(1), 5–23 (2021).https://doi.org/10.32604/cmes.2021.014693
    Google ScholarCrossref
  47. H. Yin and S. D. Felicelli , “ Dendrite growth simulation during solidification in the LENS process,” Acta Mater. 58(4), 1455–1465 (2010).https://doi.org/10.1016/j.actamat.2009.10.053
    Google ScholarCrossref
  48. P. Nie , O. A. Ojo , and Z. Li , “ Numerical modeling of microstructure evolution during laser additive manufacturing of a nickel-based superalloy,” Acta Mater. 77, 85–95 (2014).https://doi.org/10.1016/j.actamat.2014.05.039
    Google ScholarCrossref
  49. Z. Liu and H. Qi , “ Effects of substrate crystallographic orientations on crystal growth and microstructure formation in laser powder deposition of nickel-based superalloy,” Acta Mater. 87, 248–258 (2015).https://doi.org/10.1016/j.actamat.2014.12.046
    Google ScholarCrossref
  50. L. Wei , L. Xin , W. Meng , and H. Weidong , “ Cellular automaton simulation of the molten pool of laser solid forming process,” Acta Phys. Sin. 64(01), 018103–018363 (2015).https://doi.org/10.7498/aps.64.018103
    Google ScholarCrossref
  51. R. Acharya , J. A. Sharon , and A. Staroselsky , “ Prediction of microstructure in laser powder bed fusion process,” Acta Mater. 124, 360–371 (2017).https://doi.org/10.1016/j.actamat.2016.11.018
    Google ScholarCrossref
  52. M. R. Rolchigo and R. LeSar , “ Modeling of binary alloy solidification under conditions representative of additive manufacturing,” Comput. Mater. Sci. 150, 535–545 (2018).https://doi.org/10.1016/j.commatsci.2018.04.004
    Google ScholarCrossref
  53. S. Geng , P. Jiang , L. Guo , X. Gao , and G. Mi , “ Multi-scale simulation of grain/sub-grain structure evolution during solidification in laser welding of aluminum alloys,” Int. J. Heat Mass Transfer 149, 119252 (2020).https://doi.org/10.1016/j.ijheatmasstransfer.2019.119252
    Google ScholarCrossref
  54. W. L. Wang , W. Q. Liu , X. Yang , R. R. Xu , and Q. Y. Dai , “ Multi-scale simulation of columnar-to-equiaxed transition during laser selective melting of rare earth magnesium alloy,” J. Mater. Sci. Technol. 119, 11–24 (2022).https://doi.org/10.1016/j.jmst.2021.12.029
    Google ScholarCrossref
  55. Q. Xia , J. Yang , and Y. Li , “ On the conservative phase-field method with the N-component incompressible flows,” Phys. Fluids 35, 012120 (2023).https://doi.org/10.1063/5.0135490
    Google ScholarCrossref
  56. Q. Xia , G. Sun , J. Kim , and Y. Li , “ Multi-scale modeling and simulation of additive manufacturing based on fused deposition technique,” Phys. Fluids 35, 034116 (2023).https://doi.org/10.1063/5.0141316
    Google ScholarCrossref
  57. A. Hussein , L. Hao , C. Yan , and R. Everson , “ Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting,” Mater. Des. 52, 638–647 (2013).https://doi.org/10.1016/j.matdes.2013.05.070
    Google ScholarCrossref
  58. J. Ding , P. Colegrove , J. Mehnen , S. Ganguly , P. M. Sequeira Almeida , F. Wang , and S. Williams , “ Thermo-mechanical analysis of wire and arc additive layer manufacturing process on large multi-layer parts,” Comput. Mater. Sci. 50(12), 3315–3322 (2011).https://doi.org/10.1016/j.commatsci.2011.06.023
    Google ScholarCrossref
  59. Y. Du , X. You , F. Qiao , L. Guo , and Z. Liu , “ A model for predicting the temperature field during selective laser melting,” Results Phys. 12, 52–60 (2019).https://doi.org/10.1016/j.rinp.2018.11.031
    Google ScholarCrossref
  60. X. Luo , M. Liu , L. Zhenhua , H. Li , and J. Shen , “ Effect of different heat-source models on calculated temperature field of selective laser melted 18Ni300,” Chin. J. Lasers 48(14), 1402005–1402062 (2021).https://doi.org/10.3788/CJL202148.1402005
    Google ScholarCrossref
  61. J. F. Li , L. Li , and F. H. Stott , “ Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52(14), 4385–4398 (2004).https://doi.org/10.1016/j.actamat.2004.06.005
    Google ScholarCrossref
  62. P. Aggarangsi and J. L. Beuth , “ Localized preheating approaches for reducing residual stress in additive manufacturing,” paper presented at the 2006 International Solid Freeform Fabrication Symposium, The University of Texas in Austin on August 14–16, 2006.
  63. K. Dai and L. Shaw , “ Thermal and mechanical finite element modeling of laser forming from metal and ceramic powders,” Acta Mater. 52(1), 69–80 (2004).https://doi.org/10.1016/j.actamat.2003.08.028
    Google ScholarCrossref
  64. A. H. Nickel , D. M. Barnett , and F. B. Prinz , “ Thermal stresses and deposition patterns in layered manufacturing,” Mater. Sci. Eng. A 317(1–2), 59–64 (2001).https://doi.org/10.1016/S0921-5093(01)01179-0
    Google ScholarCrossref
  65. M. F. Zaeh and G. Branner , “ Investigations on residual stresses and deformations in selective laser melting,” Prod. Eng. 4(1), 35–45 (2010).https://doi.org/10.1007/s11740-009-0192-y
    Google ScholarCrossref
  66. P. Bian , J. Shi , Y. Liu , and Y. Xie , “ Influence of laser power and scanning strategy on residual stress distribution in additively manufactured 316L steel,” Opt. Laser Technol. 132, 106477 (2020).https://doi.org/10.1016/j.optlastec.2020.106477
    Google ScholarCrossref
  67. B. M. Marques , C. M. Andrade , D. M. Neto , M. C. Oliveira , J. L. Alves , and L. F. Menezes , “ Numerical analysis of residual stresses in parts produced by selective laser melting process,” Procedia Manuf. 47, 1170–1177 (2020).https://doi.org/10.1016/j.promfg.2020.04.167
    Google ScholarCrossref
  68. W. Mu , “ Numerical simulation of SLM forming process and research and prediction of forming properties,” MA thesis ( Anhui Jianzhu University, 2022).
    Google Scholar
  69. Y. Zhang , “ Multi-scale multi-physics modeling of laser powder bed fusion process of metallic materials with experiment validation,” Ph.D. dissertation ( Purdue University, 2018).
    Google Scholar
  70. Y. Qian , “ Mesoscopic simulation studies of key processing issues for powder bed fusion technology,” Ph.D. dissertation ( Tsinghua University, 2019).
    Google Scholar
  71. N. V. Brilliantov , S. Frank , J.-M. Hertzsch , and T. Pöschel , “ Model for collisions in granular gases,” Phys. Rev. E 53(5), 5382–5392 (1996).https://doi.org/10.1103/PhysRevE.53.5382
    Google ScholarCrossref
  72. Z. Xiao , “ Research on microscale selective laser melting process of high strength pure copper specimens,” MA thesis ( Hunan University, 2022).
    Google Scholar
  73. Z. Li , K. Mukai , M. Zeze , and K. C. Mills , “ Determination of the surface tension of liquid stainless steel,” J. Mater. Sci. 40(9–10), 2191–2195 (2005).https://doi.org/10.1007/s10853-005-1931-x
    Google ScholarCrossref
  74. R. Scardovelli and S. Zaleski , “ Analytical relations connecting linear interfaces and volume fractions in rectangular grids,” J. Comput. Phys. 164(1), 228–237 (2000).https://doi.org/10.1006/jcph.2000.6567
    Google ScholarCrossref
  75. D.-W. Cho , W.-I. Cho , and S.-J. Na , “ Modeling and simulation of arc: Laser and hybrid welding process,” J. Manuf. Process. 16(1), 26–55 (2014).https://doi.org/10.1016/j.jmapro.2013.06.012
    Google ScholarCrossref
    76.Flow3D. Version 11.1.0: User Manual ( FlowScience, Santa Fe, NM, USA, 2015).
  76. Y. Tian , L. Yang , D. Zhao , Y. Huang , and J. Pan , “ Numerical analysis of powder bed generation and single track forming for selective laser melting of ss316l stainless steel,” J. Manuf. Process. 58, 964–974 (2020).https://doi.org/10.1016/j.jmapro.2020.09.002
    Google ScholarCrossref
  77. C. Tang , K. Q. Le , and C. H. Wong , “ Physics of humping formation in laser powder bed fusion,” Int. J. Heat Mass Transfer 149, 119172 (2020).https://doi.org/10.1016/j.ijheatmasstransfer.2019.119172
    Google ScholarCrossref
  78. L. Cao , “ Mesoscopic-scale simulation of pore evolution during laser powder bed fusion process,” Comput. Mater. Sci. 179, 109686 (2020).https://doi.org/10.1016/j.commatsci.2020.109686
    Google ScholarCrossref
  79. R. Li , J. Liu , Y. Shi , W. Li , and W. Jiang , “ Balling behavior of stainless steel and nickel powder during selective laser melting process,” Int. J. Adv. Manuf. Technol. 59(9–12), 1025–1035 (2012).https://doi.org/10.1007/s00170-011-3566-1
    Google ScholarCrossref
  80. S. A. Khairallah and A. Anderson , “ Mesoscopic simulation model of selective laser melting of stainless steel powder,” J. Mater. Process. Technol. 214(11), 2627–2636 (2014).https://doi.org/10.1016/j.jmatprotec.2014.06.001
    Google ScholarCrossref
  81. J. Liu , D. Gu , H. Chen , D. Dai , and H. Zhang , “ Influence of substrate surface morphology on wetting behavior of tracks during selective laser melting of aluminum-based alloys,” J. Zhejiang Univ. Sci. A 19(2), 111–121 (2018).https://doi.org/10.1631/jzus.A1700599
    Google ScholarCrossref
  82. L. Li , J. Li , and T. Fan , “ Phase-field modeling of wetting and balling dynamics in powder bed fusion process,” Phys. Fluids 33, 042116 (2021).https://doi.org/10.1063/5.0046771
    Google ScholarCrossref
  83. X. Nie , Z. Hu , H. Zhu , Z. Hu , L. Ke , and X. Zeng , “ Analysis of processing parameters and characteristics of selective laser melted high strength Al-Cu-Mg alloys: from single tracks to cubic samples,” J. Mater. Process. Technol. 256, 69–77 (2018).https://doi.org/10.1016/j.jmatprotec.2018.01.030
    Google ScholarCrossref
원본 바로가기
Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low overlapping rate defects(Scheme NO.5).

Molten pool structure, temperature and velocity
flow in selective laser melting AlCu5MnCdVA alloy

용융 풀 구조, 선택적 온도 및 속도 흐름 레이저 용융 AlCu5MnCdVA 합금

Pan Lu1 , Zhang Cheng-Lin2,6,Wang Liang3, Liu Tong4 and Liu Jiang-lin5
1 Aviation and Materials College, Anhui Technical College of Mechanical and Electrical Engineering, Wuhu Anhui 241000, People’s
Republic of China 2 School of Engineering Science, University of Science and Technology of China, Hefei Anhui 230026, People’s Republic of China 3 Anhui Top Additive Manufacturing Technology Co., Ltd., Wuhu Anhui 241300, People’s Republic of China 4 Anhui Chungu 3D Printing Institute of Intelligent Equipment and Industrial Technology, Anhui 241300, People’s Republic of China 5 School of Mechanical and Transportation Engineering, Taiyuan University of Technology, Taiyuan Shanxi 030024, People’s Republic of
China 6 Author to whom any correspondence should be addressed.
E-mail: ahjdpanlu@126.com, jiao__zg@126.com, ahjdjxx001@126.com,tongliu1988@126.com and liujianglin@tyut.edu.cn

Keywords

SLM, molten pool, AlCu5MnCdVA alloy, heat flow, velocity flow, numerical simulation

Abstract

선택적 레이저 용융(SLM)은 열 전달, 용융, 상전이, 기화 및 물질 전달을 포함하는 복잡한 동적 비평형 프로세스인 금속 적층 제조(MAM)에서 가장 유망한 기술 중 하나가 되었습니다. 용융 풀의 특성(구조, 온도 흐름 및 속도 흐름)은 SLM의 최종 성형 품질에 결정적인 영향을 미칩니다. 이 연구에서는 선택적 레이저 용융 AlCu5MnCdVA 합금의 용융 풀 구조, 온도 흐름 및 속도장을 연구하기 위해 수치 시뮬레이션과 실험을 모두 사용했습니다.

그 결과 용융풀의 구조는 다양한 형태(깊은 오목 구조, 이중 오목 구조, 평면 구조, 돌출 구조 및 이상적인 평면 구조)를 나타냈으며, 용융 풀의 크기는 약 132 μm × 107 μm × 50 μm였습니다. : 용융풀은 초기에는 여러 구동력에 의해 깊이 15μm의 깊은 오목형상이었으나, 성형 후기에는 장력구배에 의해 높이 10μm의 돌출형상이 되었다. 용융 풀 내부의 금속 흐름은 주로 레이저 충격력, 금속 액체 중력, 표면 장력 및 반동 압력에 의해 구동되었습니다.

AlCu5MnCdVA 합금의 경우, 금속 액체 응고 속도가 매우 빠르며(3.5 × 10-4 S), 가열 속도 및 냉각 속도는 각각 6.5 × 107 K S-1 및 1.6 × 106 K S-1 에 도달했습니다. 시각적 표준으로 표면 거칠기를 선택하고, 낮은 레이저 에너지 AlCu5MnCdVA 합금 최적 공정 매개변수 창을 수치 시뮬레이션으로 얻었습니다: 레이저 출력 250W, 부화 공간 0.11mm, 층 두께 0.03mm, 레이저 스캔 속도 1.5m s-1 .

또한, 실험 프린팅과 수치 시뮬레이션과 비교할 때, 용융 풀의 폭은 각각 약 205um 및 약 210um이었고, 인접한 두 용융 트랙 사이의 중첩은 모두 약 65um이었다. 결과는 수치 시뮬레이션 결과가 실험 인쇄 결과와 기본적으로 일치함을 보여 수치 시뮬레이션 모델의 정확성을 입증했습니다.

Selective Laser Melting (SLM) has become one of the most promising technologies in Metal Additive Manufacturing (MAM), which is a complex dynamic non-equilibrium process involving heat transfer, melting, phase transition, vaporization and mass transfer. The characteristics of the molten pool (structure, temperature flow and velocity flow) have a decisive influence on the final forming quality of SLM. In this study, both numerical simulation and experiments were employed to study molten pool structure, temperature flow and velocity field in Selective Laser Melting AlCu5MnCdVA alloy. The results showed the structure of molten pool showed different forms(deep-concave structure, double-concave structure, plane structure, protruding structure and ideal planar structure), and the size of the molten pool was approximately 132 μm × 107 μm × 50 μm: in the early stage, molten pool was in a state of deep-concave shape with a depth of 15 μm due to multiple driving forces, while a protruding shape with a height of 10 μm duo to tension gradient in the later stages of forming. The metal flow inside the molten pool was mainly driven by laser impact force, metal liquid gravity, surface tension and recoil pressure. For AlCu5MnCdVA alloy, metal liquid solidification speed was extremely fast(3.5 × 10−4 S), the heating rate and cooling rate reached 6.5 × 107 K S−1 and 1.6 × 106 K S−1 , respectively. Choosing surface roughness as a visual standard, low-laser energy AlCu5MnCdVA alloy optimum process parameters window was obtained by numerical simulation: laser power 250 W, hatching space 0.11 mm, layer thickness 0.03 mm, laser scanning velocity 1.5 m s−1 . In addition, compared with experimental printing and numerical simulation, the width of the molten pool was about 205 um and about 210 um, respectively, and overlapping between two adjacent molten tracks was all about 65 um. The results showed that the numerical simulation results were basically consistent with the experimental print results, which proved the correctness of the numerical simulation model.

Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 2. AlCu5MnCdVA powder
Figure 2. AlCu5MnCdVA powder
Figure 3. Finite element model and calculation domains of SLM.
Figure 3. Finite element model and calculation domains of SLM.
Figure 4. SLM heat transfer process.
Figure 4. SLM heat transfer process.
Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low overlapping rate defects(Scheme NO.5).
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.

References

[1] Cuiyun H 2008 Phase diagram determination and thermodynamic study of Al–Cu–Mn, Al–Cu–Si, Al–Mg–Ni and Ni–Ti–Si systems Central South University
[2] Zhanfei Z 2017 Study on theta phase segregation and room temperature properties of high strength cast Al–Cu–Mn alloy Lanzhou University of Technology
[3] Nie X et al 2018 Analysis of processing parameters and characteristics of selective laser melted high strength Al–Cu–Mg alloys: from single tracks to cubic samplesJ. Mater. Process. Technol. 256 69–77
[4] Shenping Y et al 2017 Laser absorptance measurement of commonly used metal materials in laser additive manufacturing technology Aviation Manufacturing Technology 12 23–9
[5] Wenqing W 2007 Relationship between cooling rate and grain size of AlCu5MnCdVA alloy Harbin University of Technology
[6] Majeed M, Vural M, Raja S and Bilal Naim Shaikh M 2019 Finite element analysis of thermal behavior in maraging steel during SLM process Optik 208 113–24
[7] Khairallah S A, Anderson A T, Rubenchik A and King W E 2016 Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones Acta Mater. 108 36–45
[8] Bo C, Zhiyu X, Quanquan Z, Yuanbiao W, Liping W and Jin C 2020 Process optimization and microstructure and properties of SLM forming Cu6AlNiSnInCe imitation gold alloy Chin. J. Nonferr. Met. 30 372–82
[9] Li W 2012 Research on performance of metal parts formed by selective laser melting Huazhong University of Science and Technology
[10] Yu Q 2013 The influence of different laser heat sources on the surface shape of the molten pool in laser cladding Surf. Technol. 42 40–3

[11] Xianfeng J, Xiangchen M, Rongwei S, Xigen Y and Ming Y 2015 Research on the influence of material state change on temperature field
in SLM processing Applied Laser 35 155–9
[12] Körner C, Attar E and Heinl P 2011 Mesoscopic simulation of selective beam melting processesJ. Mater. Process. Technol. 211 978–87
[13] Yadroitsev I, Gusarov A, Yadroitsava I and Smurov I 2010 Single track formation in selective laser melting of metal powdersJ. Mater.
Process. Technol. 210 1624–31
[14] King W, Anderson A T, Ferencz R M, Hodge N E, Kamath C and Khairallah S A 2014 Overview of modelling and simulation of metal
powder bed fusion process at Lawrence Livermore National Laboratory Mater. Sci. Technol. 31 957–68
[15] Hussein A, Hao L, Yan C and Everson R 2013 Finite element simulation of the temperature and stress fields in single layers built
without-support in selective laser melting Materials & Design (1980–2015) 52 638–47
[16] Qiu C, Panwisawas C, Ward M, Basoalto H C, Brooks J W and Attallah M M 2015 On the role of melt flow into the surface structure and
porosity development during selective laser melting Acta Mater. 96 72–9
[17] Weihao Y, Hui C and Qingsong W 2020 Thermodynamic behavior of laser selective melting molten pool under the action of recoil
pressure Journal of Mechanical Engineering 56 213–9
[18] Weijuan Y 2019 Numerical simulation of melt pool temperature field and morphology evolution during laser selective melting process
Xi’an University of Technology
[19] Genwang W 2017 Research on the establishment of laser heat source model based on energy distribution and its simulation application
Harbin Institute of Technology
[20] FLOW-3D 2017 User Manual (USA: FLOW SCIENCE)
[21] Hirt C and Nichols B 1981 Volume of fluid (VOF) method for the dynamics of free boundariesJ. Comput. Phys. 39 201–25
[22] Hu Z, Zhang H, Zhu H, Xiao Z, Nie X and Zeng X 2019 Microstructure, mechanical properties and strengthening mechanisms of
AlCu5MnCdVA aluminum alloy fabricated by selective laser melting Materials Science and Engineering: A 759 154–66
[23] Ketai H, Liu Z and Lechang Y 2020 Simulation of temperature field, microstructure and mechanical properties of 316L stainless steel in
selected laser melting Progress in Laser and Optoelectronics 9 1–18
[24] Cao L 2020 Workpiece-scale numerical simulations of SLM molten pool dynamic behavior of 316L stainless steel Comput. Math. Appl.
4 22–34
[25] Dening Z, Yongping L, Tinglu H and Junyi S 2000 Numerical study of fluid flow and heat transfer in molten pool under the condition of
moving heat source J. Met. 4 387–90
[26] Chengyun C, Cui F and Wenlong Z 2018 The effect of Marangoni flow on the thermal behavior and melt flow behavior of laser cladding
Applied Laser 38 409–16
[27] Peiying B and Enhuai Y 2020 The effect of laser power on the morphology and residual stress of the molten pool of metal laser selective
melting Progress in Laser and Optoelectronics 7 1–12 http://kns.cnki.net/kcms/detail/31.1690.TN.20190717.0933.032.html
[28] Zhen L, Dongyun Z, Zhe F and Chengjie W 2017 Numerical simulation of the influence of overlap rate on the forming quality of
Inconel 718 alloy by selective laser melting processing Applied Laser 37 187–93
[29] Wei W, Qi L, Guang Y, Lanyun Q and Xiong X 2015 Numerical simulation of electromagnetic field, temperature field and flowfield of
laser melting pool under the action of electromagnetic stirring China Laser 42 48–55
[30] Hu Y, He X, Yu G and Zhao S 2016 Capillary convection in pulsed—butt welding of miscible dissimilar couple Proc. Inst. Mech. Eng.
Part C J. Mech. Eng. Sci. 231 2429–40
[31] Li R 2010 Research on the key basic problems of selective laser melting forming of metal powder Huazhong University of Science and
Technology
[32] Zijue T, Weiwei L, Zhaorui Y, Hao W and Hongchao Z 2019 Study on the shape evolution behavior of metal laser melting deposition
based on molten pool dynamic characteristicsJournal of Mechanical Engineering 55 39–47
[33] Pan L, Cheng-Lin Z, Hai-Yi L, Liang W and Tong L 2020 A new two-step selective laser remelting of 316L stainless steel: process,
density, surface roughness, mechanical properties, microstructure Mater. Res. Express 7 056503
[34] Pan L, Cheng-Lin Z, Hai-Yi L, Jiang H, Tong L and Liang W 2019 The influence and optimization of forming process parameters of
316L stainless steel prepared by laser melting on the density Forging Technology 44 103–9

원본보기
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.

References

[1] T. DebRoy et al., “Additive manufacturing of metallic components – Process, structure
and properties,” Prog. Mater. Sci., vol. 92, pp. 112–224, 2018, doi:
10.1016/j.pmatsci.2017.10.001.
[2] M. Markl and C. Körner, “Multiscale Modeling of Powder Bed–Based Additive
Manufacturing,” Annu. Rev. Mater. Res., vol. 46, no. 1, pp. 93–123, 2016, doi:
10.1146/annurev-matsci-070115-032158.
[3] A. Zinoviev, O. Zinovieva, V. Ploshikhin, V. Romanova, and R. Balokhonov, “Evolution
of grain structure during laser additive manufacturing. Simulation by a cellular automata
method,” Mater. Des., vol. 106, pp. 321–329, 2016, doi: 10.1016/j.matdes.2016.05.125.
[4] Y. Zhang and J. Zhang, “Modeling of solidification microstructure evolution in laser
powder bed fusion fabricated 316L stainless steel using combined computational fluid
dynamics and cellular automata,” Addit. Manuf., vol. 28, no. July 2018, pp. 750–765,
2019, doi: 10.1016/j.addma.2019.06.024.
[5] A. A. Martin et al., “Ultrafast dynamics of laser-metal interactions in additive
manufacturing alloys captured by in situ X-ray imaging,” Mater. Today Adv., vol. 1, p.
100002, 2019, doi: 10.1016/j.mtadv.2019.01.001.
[6] Y. C. Wu et al., “Numerical modeling of melt-pool behavior in selective laser melting
with random powder distribution and experimental validation,” J. Mater. Process.
Technol., vol. 254, no. July 2017, pp. 72–78, 2018, doi:
10.1016/j.jmatprotec.2017.11.032.
[7] W. Gao, S. Zhao, Y. Wang, Z. Zhang, F. Liu, and X. Lin, “Numerical simulation of
thermal field and Fe-based coating doped Ti,” Int. J. Heat Mass Transf., vol. 92, pp. 83–
90, 2016, doi: 10.1016/j.ijheatmasstransfer.2015.08.082.
[8] A. Charles, M. Bayat, A. Elkaseer, L. Thijs, J. H. Hattel, and S. Scholz, “Elucidation of
dross formation in laser powder bed fusion at down-facing surfaces: Phenomenonoriented multiphysics simulation and experimental validation,” Addit. Manuf., vol. 50,
2022, doi: 10.1016/j.addma.2021.102551.
[9] C. Meier, R. W. Penny, Y. Zou, J. S. Gibbs, and A. J. Hart, “Thermophysical phenomena
in metal additive manufacturing by selective laser melting: Fundamentals, modeling,
simulation and experimentation,” arXiv, 2017, doi:
10.1615/annualrevheattransfer.2018019042.
[10] W. King, A. T. Anderson, R. M. Ferencz, N. E. Hodge, C. Kamath, and S. A. Khairallah,
“Overview of modelling and simulation of metal powder bed fusion process at Lawrence
Livermore National Laboratory,” Mater. Sci. Technol. (United Kingdom), vol. 31, no. 8,
pp. 957–968, 2015, doi: 10.1179/1743284714Y.0000000728.

PDF 원문보기
Figure 3: 3D temperature contours and 2D melt pool cross-sections where the melt pool is stabilized at x=500 µm from the start of the laser initial location for cases where (a) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 12 µm, (b) absorptivity = 0.1, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (c) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (d) absorptivity = 0.45, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (e) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (f) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 18 µm.

MULTI-PHYSICS NUMERICAL MODELLING OF 316L AUSTENITIC STAINLESS STEEL IN LASER POWDER BED FUSION PROCESS AT MESO-SCALE

W.E. Alphonso1, M.Bayat1,*, M. Baier 2, S. Carmignato2, J.H. Hattel1
1Department of Mechanical Engineering, Technical University of Denmark (DTU), Lyngby, Denmark
2Department of Management and Engineering – University of Padova, Padova, Italy

ABSTRACT

L-PBF(Laser Powder Bed Fusion)는 레이저 열원을 사용하여 선택적으로 통합되는 분말 층으로 복잡한 3D 금속 부품을 만드는 금속 적층 제조(MAM) 기술입니다. 처리 영역은 수십 마이크로미터 정도이므로 L-PBF를 다중 규모 제조 공정으로 만듭니다.

기체 기공의 형성 및 성장 및 용융되지 않은 분말 영역의 생성은 다중물리 모델에 의해 예측할 수 있습니다. 또한 이러한 모델을 사용하여 용융 풀 모양 및 크기, 온도 분포, 용융 풀 유체 흐름 및 입자 크기 및 형태와 같은 미세 구조 특성을 계산할 수 있습니다.

이 작업에서는 용융, 응고, 유체 흐름, 표면 장력, 열 모세관, 증발 및 광선 추적을 통한 다중 반사를 포함하는 스테인리스 스틸 316-L에 대한 충실도 다중 물리학 중간 규모 수치 모델이 개발되었습니다. 완전한 실험 설계(DoE) 방법을 사용하는 통계 연구가 수행되었으며, 여기서 불확실한 재료 특성 및 공정 매개변수, 즉 흡수율, 반동 압력(기화) 및 레이저 빔 크기가 용융수지 모양 및 크기에 미치는 영향을 분석했습니다.

또한 용융 풀 역학에 대한 위에서 언급한 불확실한 입력 매개변수의 중요성을 강조하기 위해 흡수율이 가장 큰 영향을 미치고 레이저 빔 크기가 그 뒤를 잇는 주요 효과 플롯이 생성되었습니다. 용융 풀 크기에 대한 반동 압력의 중요성은 흡수율에 따라 달라지는 용융 풀 부피와 함께 증가합니다.

모델의 예측 정확도는 유사한 공정 매개변수로 생성된 단일 트랙 실험과 시뮬레이션의 용융 풀 모양 및 크기를 비교하여 검증됩니다.

더욱이, 열 렌즈 효과는 레이저 빔 크기를 증가시켜 수치 모델에서 고려되었으며 나중에 결과적인 용융 풀 프로파일은 모델의 견고성을 보여주기 위한 실험과 비교되었습니다.

Laser Powder Bed Fusion (L-PBF) is a Metal Additive Manufacturing (MAM) technology where a complex 3D metal part is built from powder layers, which are selectively consolidated using a laser heat source. The processing zone is in the order of a few tenths of micrometer, making L-PBF a multi-scale manufacturing process. The formation and growth of gas pores and the creation of un-melted powder zones can be predicted by multiphysics models. Also, with these models, the melt pool shape and size, temperature distribution, melt pool fluid flow and its microstructural features like grain size and morphology can be calculated. In this work, a high fidelity multi-physics meso-scale numerical model is developed for stainless steel 316-L which includes melting, solidification, fluid flow, surface tension, thermo-capillarity, evaporation and multiple reflection with ray-tracing. A statistical study using a full Design of Experiments (DoE) method was conducted, wherein the impact of uncertain material properties and process parameters namely absorptivity, recoil pressure (vaporization) and laser beam size on the melt pool shape and size was analysed. Furthermore, to emphasize on the significance of the above mentioned uncertain input parameters on the melt pool dynamics, a main effects plot was created which showed that absorptivity had the highest impact followed by laser beam size. The significance of recoil pressure on the melt pool size increases with melt pool volume which is dependent on absorptivity. The prediction accuracy of the model is validated by comparing the melt pool shape and size from the simulation with single track experiments that were produced with similar process parameters. Moreover, the effect of thermal lensing was considered in the numerical model by increasing the laser beam size and later on the resultant melt pool profile was compared with experiments to show the robustness of the model.

Figure 1: a) Computational domain for single track L-PBF which includes a 200 μm thick substrate and 45 μm powder layer thickness b) 3D temperature contour plot after scanning a single track with melt pool contours at two locations along the scanning direction where the green region indicates the melted regions.
Figure 1: a) Computational domain for single track L-PBF which includes a 200 μm thick substrate and 45 μm powder layer thickness b) 3D temperature contour plot after scanning a single track with melt pool contours at two locations along the scanning direction where the green region indicates the melted regions.
Figure 2: Main effects plot of uncertain parameters: absorptivity, recoil pressure coefficient and laser beam radius on the melt pool dimensions (width and depth)
Figure 2: Main effects plot of uncertain parameters: absorptivity, recoil pressure coefficient and laser beam radius on the melt pool dimensions (width and depth)
Figure 3: 3D temperature contours and 2D melt pool cross-sections where the melt pool is stabilized at x=500 µm from the start of the laser initial location for cases where (a) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 12 µm, (b) absorptivity = 0.1, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (c) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (d) absorptivity = 0.45, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (e) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (f) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 18 µm.
Figure 3: 3D temperature contours and 2D melt pool cross-sections where the melt pool is stabilized at x=500 µm from the start of the laser initial location for cases where (a) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 12 µm, (b) absorptivity = 0.1, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (c) absorptivity = 0.1, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (d) absorptivity = 0.45, Recoil pressure coefficient B = 1 and laser beam radius = 18 µm, (e) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 12 µm, (f) absorptivity = 0.45, Recoil pressure coefficient B = 20 and laser beam radius = 18 µm.
Figure 4: Validation of Numerical model with Recoil pressure coefficient B= 20, absorptivity = 0.45 and a) laser beam radius = 15 µm b) laser beam radius = 20 µm
Figure 4: Validation of Numerical model with Recoil pressure coefficient B= 20, absorptivity = 0.45 and a) laser beam radius = 15 µm b) laser beam radius = 20 µm

CONCLUSION

In this work, a high-fidelity multi-physics numerical model was developed for L-PBF using the FVM method in Flow-3D. The impact of uncertainty in the input parameters including absorptivity, recoil pressure and laser beam size on the melt pool is addressed using a DoE method. The DoE analysis shows that absorptivity has the highest impact on the melt pool. The recoil pressure and laser beam size only become significant once absorptivity is 0.45. Furthermore, the numerical model is validated by comparing the predicted melt pool shape and size with experiments conducted with similar process parameters wherein a high prediction accuracy is achieved by the model. In addition, the impact of thermal lensing on the melt pool dimensions by increasing the laser beam spot size is considered in the validated numerical model and the resultant melt pool is compared with experiments.

REFERENCES

[1] T. Bonhoff, M. Schniedenharn, J. Stollenwerk, P. Loosen, Experimental and theoretical analysis of thermooptical effects in protective window for selective laser melting, Proc. Int. Conf. Lasers Manuf. LiM. (2017)
26–29. https://www.wlt.de/lim/Proceedings2017/Data/PDF/Contribution31_final.pdf.
[2] L.R. Goossens, Y. Kinds, J.P. Kruth, B. van Hooreweder, On the influence of thermal lensing during selective
laser melting, Solid Free. Fabr. 2018 Proc. 29th Annu. Int. Solid Free. Fabr. Symp. – An Addit. Manuf. Conf.
SFF 2018. (2020) 2267–2274.
[3] J. Shinjo, C. Panwisawas, Digital materials design by thermal-fluid science for multi-metal additive
manufacturing, Acta Mater. 210 (2021) 116825. https://doi.org/10.1016/j.actamat.2021.116825.
[4] Z. Zhang, Y. Huang, A. Rani Kasinathan, S. Imani Shahabad, U. Ali, Y. Mahmoodkhani, E. Toyserkani, 3-
Dimensional heat transfer modeling for laser powder-bed fusion additive manufacturing with volumetric heat
sources based on varied thermal conductivity and absorptivity, Opt. Laser Technol. 109 (2019) 297–312.
https://doi.org/10.1016/j.optlastec.2018.08.012.
[5] M. Bayat, A. Thanki, S. Mohanty, A. Witvrouw, S. Yang, J. Thorborg, N.S. Tiedje, J.H. Hattel, Keyholeinduced porosities in Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V: High-fidelity modelling and
experimental validation, Addit. Manuf. 30 (2019) 100835. https://doi.org/10.1016/j.addma.2019.100835.
[6] M. Bayat, S. Mohanty, J.H. Hattel, Multiphysics modelling of lack-of-fusion voids formation and evolution
in IN718 made by multi-track/multi-layer L-PBF, Int. J. Heat Mass Transf. 139 (2019) 95–114.
https://doi.org/10.1016/j.ijheatmasstransfer.2019.05.003.
[7] J. Metelkova, Y. Kinds, K. Kempen, C. de Formanoir, A. Witvrouw, B. Van Hooreweder, On the influence
of laser defocusing in Selective Laser Melting of 316L, Addit. Manuf. 23 (2018) 161–169.
https://doi.org/10.1016/j.addma.2018.08.006.

PDF 전체 원문 보기
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling

Laser Powder Bed에서 Laser Drilling에 의한 Keyhole 형성 Ti6Al4V 생체 의학 합금의 융합: 메조스코픽 전산유체역학 시뮬레이션 대 경험적 검증을 사용한 수학적 모델링

Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation

Asif Ur Rehman 1,2,3,*
,† , Muhammad Arif Mahmood 4,*
,† , Fatih Pitir 1
, Metin Uymaz Salamci 2,3
,
Andrei C. Popescu 4 and Ion N. Mihailescu 4

Abstract

LPBF(Laser Powder Bed fusion) 공정에서 작동 조건은 열 분포를 기반으로 레이저 유도 키홀 영역을 결정하는 데 필수적입니다. 얕은 구멍과 깊은 구멍으로 분류되는 이러한 영역은 LPBF 프로세스에서 확률과 결함 형성 강도를 제어합니다.

LPBF 프로세스의 핵심 구멍을 연구하고 제어하기 위해 수학적 및 CFD(전산 유체 역학) 모델이 제공됩니다. CFD의 경우 이산 요소 모델링 기법을 사용한 유체 체적 방법이 사용되었으며, 분말 베드 보이드 및 표면에 의한 레이저 빔 흡수를 포함하여 수학적 모델이 개발되었습니다.

동적 용융 풀 거동을 자세히 살펴봅니다. 실험적, CFD 시뮬레이션 및 분석적 컴퓨팅 결과 간에 정량적 비교가 수행되어 좋은 일치를 얻습니다.

LPBF에서 레이저 조사 영역 주변의 온도는 높은 내열성과 분말 입자 사이의 공기로 인해 분말층 주변에 비해 급격히 상승하여 레이저 횡방향 열파의 이동이 느려집니다. LPBF에서 키홀은 에너지 밀도에 의해 제어되는 얕고 깊은 키홀 모드로 분류될 수 있습니다. 에너지 밀도를 높이면 얕은 키홀 구멍 모드가 깊은 키홀 구멍 모드로 바뀝니다.

깊은 키홀 구멍의 에너지 밀도는 다중 반사와 키홀 구멍 내의 2차 반사 빔의 집중으로 인해 더 높아져 재료가 빠르게 기화됩니다.

깊은 키홀 구멍 모드에서는 온도 분포가 높기 때문에 액체 재료가 기화 온도에 가까우므로 얕은 키홀 구멍보다 구멍이 형성될 확률이 훨씬 높습니다. 온도가 급격히 상승하면 재료 밀도가 급격히 떨어지므로 비열과 융해 잠열로 인해 유체 부피가 증가합니다.

그 대가로 표면 장력을 낮추고 용융 풀 균일성에 영향을 미칩니다.

In the laser powder bed fusion (LPBF) process, the operating conditions are essential in determining laser-induced keyhole regimes based on the thermal distribution. These regimes, classified into shallow and deep keyholes, control the probability and defects formation intensity in the LPBF process. To study and control the keyhole in the LPBF process, mathematical and computational fluid dynamics (CFD) models are presented. For CFD, the volume of fluid method with the discrete element modeling technique was used, while a mathematical model was developed by including the laser beam absorption by the powder bed voids and surface. The dynamic melt pool behavior is explored in detail. Quantitative comparisons are made among experimental, CFD simulation and analytical computing results leading to a good correspondence. In LPBF, the temperature around the laser irradiation zone rises rapidly compared to the surroundings in the powder layer due to the high thermal resistance and the air between the powder particles, resulting in a slow travel of laser transverse heat waves. In LPBF, the keyhole can be classified into shallow and deep keyhole mode, controlled by the energy density. Increasing the energy density, the shallow keyhole mode transforms into the deep keyhole mode. The energy density in a deep keyhole is higher due to the multiple reflections and concentrations of secondary reflected beams within the keyhole, causing the material to vaporize quickly. Due to an elevated temperature distribution in deep keyhole mode, the probability of pores forming is much higher than in a shallow keyhole as the liquid material is close to the vaporization temperature. When the temperature increases rapidly, the material density drops quickly, thus, raising the fluid volume due to the specific heat and fusion latent heat. In return, this lowers the surface tension and affects the melt pool uniformity.

Keywords: laser powder bed fusion; computational fluid dynamics; analytical modelling; shallow
and deep keyhole modes; experimental correlation

Figure 1. Powder bed schematic with voids.
Figure 1. Powder bed schematic with voids.
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 2. (a) Scanning electron microscopy images of Ti6Al4V powder particles and (b) simulated powder bed using discrete element modelling
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 3. Temperature field contour formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 4. Detailed view of shallow depth melt mode with temperature field at 0.695 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 5. Melt flow stream traces formation at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 6. Density evolution of the melt pool at various time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms.
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 7. Un-melted and melted regions at different time intervals (a) 0.695 ms, (b) 0.795 ms, (c) 0.995 ms and (d) 1.3 ms
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 8. Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (a) 170 W to (b) 200 W
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 9. Stream traces and laser beam multiple reflections in deep keyhole melt flow mode
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 10. A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width
Figure 11. A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width

References

  1. Kok, Y.; Tan, X.P.; Wang, P.; Nai, M.L.S.; Loh, N.H.; Liu, E.; Tor, S.B. Anisotropy and heterogeneity of microstructure and
    mechanical properties in metal additive manufacturing: A critical review. Mater. Des. 2018, 139, 565–586. [CrossRef]
  2. Ansari, P.; Salamci, M.U. On the selective laser melting based additive manufacturing of AlSi10Mg: The process parameter
    investigation through multiphysics simulation and experimental validation. J. Alloys Compd. 2022, 890, 161873. [CrossRef]
  3. Guo, N.; Leu, M.C. Additive manufacturing: Technology, applications and research needs. Front. Mech. Eng. 2013, 8, 215–243.
    [CrossRef]
  4. Mohsin Raza, M.; Lo, Y.L. Experimental investigation into microstructure, mechanical properties, and cracking mechanism of
    IN713LC processed by laser powder bed fusion. Mater. Sci. Eng. A 2021, 819, 141527. [CrossRef]
  5. Dezfoli, A.R.A.; Lo, Y.L.; Raza, M.M. Prediction of Epitaxial Grain Growth in Single-Track Laser Melting of IN718 Using Integrated
    Finite Element and Cellular Automaton Approach. Materials 2021, 14, 5202. [CrossRef]
  6. Tiwari, S.K.; Pande, S.; Agrawal, S.; Bobade, S.M. Selection of selective laser sintering materials for different applications. Rapid
    Prototyp. J. 2015, 21, 630–648. [CrossRef]
  7. Liu, F.H. Synthesis of bioceramic scaffolds for bone tissue engineering by rapid prototyping technique. J. Sol-Gel Sci. Technol.
    2012, 64, 704–710. [CrossRef]
  8. Ur Rehman, A.; Sglavo, V.M. 3D printing of geopolymer-based concrete for building applications. Rapid Prototyp. J. 2020, 26,
    1783–1788. [CrossRef]
  9. Ur Rehman, A.; Sglavo, V.M. 3D printing of Portland cement-containing bodies. Rapid Prototyp. J. 2021. ahead of print. [CrossRef]
  10. Popovich, A.; Sufiiarov, V. Metal Powder Additive Manufacturing. In New Trends in 3D Printing; InTech: Rijeka, Croatia, 2016.
  11. Jia, T.; Zhang, Y.; Chen, J.K.; He, Y.L. Dynamic simulation of granular packing of fine cohesive particles with different size
    distributions. Powder Technol. 2012, 218, 76–85. [CrossRef]
  12. Ansari, P.; Ur Rehman, A.; Pitir, F.; Veziroglu, S.; Mishra, Y.K.; Aktas, O.C.; Salamci, M.U. Selective Laser Melting of 316L
    Austenitic Stainless Steel: Detailed Process Understanding Using Multiphysics Simulation and Experimentation. Metals 2021,
    11, 1076. [CrossRef]
  13. Ur Rehman, A.; Tingting, L.; Liao, W. 4D Printing; Printing Ceramics from Metals with Selective Oxidation. Patent No.
    W0/2019/052128, 21 March 2019.
  14. Ullah, A.; Wu, H.; Ur Rehman, A.; Zhu, Y.; Liu, T.; Zhang, K. Influence of laser parameters and Ti content on the surface
    morphology of L-PBF fabricated Titania. Rapid Prototyp. J. 2021, 27, 71–80. [CrossRef]
  15. Ur Rehman, A. Additive Manufacturing of Ceramic Materials and Combinations with New Laser Strategies. Master’s Thesis,
    Nanjing University of Science and Technology, Nanjing, China, 2017.
  16. Wong, K.V.; Hernandez, A. A Review of Additive Manufacturing. ISRN Mech. Eng. 2012, 2012, 1–10. [CrossRef]
  17. Körner, C. Additive manufacturing of metallic components by selective electron beam melting—A review. Int. Mater. Rev. 2016,
    61, 361–377. [CrossRef]
  18. Fayazfar, H.; Salarian, M.; Rogalsky, A.; Sarker, D.; Russo, P.; Paserin, V.; Toyserkani, E. A critical review of powder-based additive
    manufacturing of ferrous alloys: Process parameters, microstructure and mechanical properties. Mater. Des. 2018, 144, 98–128.
    [CrossRef]
  19. Everton, S.K.; Hirsch, M.; Stavroulakis, P.I.; Leach, R.K.; Clare, A.T. Review of in-situ process monitoring and in-situ metrology
    for metal additive manufacturing. Mater. Des. 2016, 95, 431–445. [CrossRef]
  20. Sing, S.L.; An, J.; Yeong, W.Y.; Wiria, F.E. Laser and electron-beam powder-bed additive manufacturing of metallic implants: A
    review on processes, materials and designs. J. Orthop. Res. 2016, 34, 369–385. [CrossRef] [PubMed]
  21. Olakanmi, E.O.; Cochrane, R.F.; Dalgarno, K.W. A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy
    powders: Processing, microstructure, and properties. Prog. Mater. Sci. 2015, 74, 401–477. [CrossRef]
  22. Mahmood, M.A.; Popescu, A.C.; Hapenciuc, C.L.; Ristoscu, C.; Visan, A.I.; Oane, M.; Mihailescu, I.N. Estimation of clad geometry
    and corresponding residual stress distribution in laser melting deposition: Analytical modeling and experimental correlations.
    Int. J. Adv. Manuf. Technol. 2020, 111, 77–91. [CrossRef]
  23. Mahmood, M.A.; Popescu, A.C.; Oane, M.; Ristoscu, C.; Chioibasu, D.; Mihai, S.; Mihailescu, I.N. Three-jet powder flow
    and laser–powder interaction in laser melting deposition: Modelling versus experimental correlations. Metals 2020, 10, 1113.
    [CrossRef]
  24. King, W.; Anderson, A.T.; Ferencz, R.M.; Hodge, N.E.; Kamath, C.; Khairallah, S.A. Overview of modelling and simulation of
    metal powder bed fusion process at Lawrence Livermore National Laboratory. Mater. Sci. Technol. 2015, 31, 957–968. [CrossRef]
  1. Gong, H.; Rafi, K.; Gu, H.; Starr, T.; Stucker, B. Analysis of defect generation in Ti-6Al-4V parts made using powder bed fusion
    additive manufacturing processes. Addit. Manuf. 2014, 1, 87–98. [CrossRef]
  2. Frazier, W.E. Metal additive manufacturing: A review. J. Mater. Eng. Perform. 2014, 23, 1917–1928. [CrossRef]
  3. Panwisawas, C.; Qiu, C.L.; Sovani, Y.; Brooks, J.W.; Attallah, M.M.; Basoalto, H.C. On the role of thermal fluid dynamics into the
    evolution of porosity during selective laser melting. Scr. Mater. 2015, 105, 14–17. [CrossRef]
  4. Yan, W.; Ge, W.; Qian, Y.; Lin, S.; Zhou, B.; Liu, W.K.; Lin, F.; Wagner, G.J. Multi-physics modeling of single/multiple-track defect
    mechanisms in electron beam selective melting. Acta Mater. 2017, 134, 324–333. [CrossRef]
  5. Qian, Y.; Yan, W.; Lin, F. Parametric study and surface morphology analysis of electron beam selective melting. Rapid Prototyp. J.
    2018, 24, 1586–1598. [CrossRef]
  6. Panwisawas, C.; Perumal, B.; Ward, R.M.; Turner, N.; Turner, R.P.; Brooks, J.W.; Basoalto, H.C. Keyhole formation and thermal
    fluid flow-induced porosity during laser fusion welding in titanium alloys: Experimental and modelling. Acta Mater. 2017, 126,
    251–263. [CrossRef]
  7. King, W.E.; Barth, H.D.; Castillo, V.M.; Gallegos, G.F.; Gibbs, J.W.; Hahn, D.E.; Kamath, C.; Rubenchik, A.M. Observation of
    keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J. Mater. Process. Technol. 2014, 214, 2915–2925.
    [CrossRef]
  8. Panwisawas, C.; Sovani, Y.; Turner, R.P.; Brooks, J.W.; Basoalto, H.C.; Choquet, I. Modelling of thermal fluid dynamics for fusion
    welding. J. Mater. Process. Technol. 2018, 252, 176–182. [CrossRef]
  9. Martin, A.A.; Calta, N.P.; Hammons, J.A.; Khairallah, S.A.; Nielsen, M.H.; Shuttlesworth, R.M.; Sinclair, N.; Matthews, M.J.;
    Jeffries, J.R.; Willey, T.M.; et al. Ultrafast dynamics of laser-metal interactions in additive manufacturing alloys captured by in situ
    X-ray imaging. Mater. Today Adv. 2019, 1, 100002. [CrossRef]
  10. Cunningham, R.; Zhao, C.; Parab, N.; Kantzos, C.; Pauza, J.; Fezzaa, K.; Sun, T.; Rollett, A.D. Keyhole threshold and morphology
    in laser melting revealed by ultrahigh-speed x-ray imaging. Science 2019, 363, 849–852. [CrossRef] [PubMed]
  11. Tang, C.; Tan, J.L.; Wong, C.H. A numerical investigation on the physical mechanisms of single track defects in selective laser
    melting. Int. J. Heat Mass Transf. 2018, 126, 957–968. [CrossRef]
  12. Mirkoohi, E.; Ning, J.; Bocchini, P.; Fergani, O.; Chiang, K.-N.; Liang, S. Thermal Modeling of Temperature Distribution in Metal
    Additive Manufacturing Considering Effects of Build Layers, Latent Heat, and Temperature-Sensitivity of Material Properties. J.
    Manuf. Mater. Process. 2018, 2, 63. [CrossRef]
  13. Oane, M.; Sporea, D. Temperature profiles modeling in IR optical components during high power laser irradiation. Infrared Phys.
    Technol. 2001, 42, 31–40. [CrossRef]
  14. Cleary, P.W.; Sawley, M.L. DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper
    discharge. Appl. Math. Model. 2002, 26, 89–111. [CrossRef]
  15. Parteli, E.J.R.; Pöschel, T. Particle-based simulation of powder application in additive manufacturing. Powder Technol. 2016, 288,
    96–102. [CrossRef]
  16. Cao, L. Numerical simulation of the impact of laying powder on selective laser melting single-pass formation. Int. J. Heat Mass
    Transf. 2019, 141, 1036–1048. [CrossRef]
  17. Tian, Y.; Yang, L.; Zhao, D.; Huang, Y.; Pan, J. Numerical analysis of powder bed generation and single track forming for selective
    laser melting of SS316L stainless steel. J. Manuf. Process. 2020, 58, 964–974. [CrossRef]
  18. Lee, Y.S.; Zhang, W. Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base superalloy fabricated by
    laser powder bed fusion. Addit. Manuf. 2016, 12, 178–188. [CrossRef]
  19. Tang, M.; Pistorius, P.C.; Beuth, J.L. Prediction of lack-of-fusion porosity for powder bed fusion. Addit. Manuf. 2017, 14, 39–48.
    [CrossRef]
  20. Promoppatum, P.; Yao, S.C.; Pistorius, P.C.; Rollett, A.D. A Comprehensive Comparison of the Analytical and Numerical
    Prediction of the Thermal History and Solidification Microstructure of Inconel 718 Products Made by Laser Powder-Bed Fusion.
    Engineering 2017, 3, 685–694. [CrossRef]
  21. Rosenthal, D. Mathematical Theory of Heat Distribution During Welding and Cutting. Weld. J. 1941, 20, 220–234.
  22. Chen, Q.; Zhao, Y.Y.; Strayer, S.; Zhao, Y.Y.; Aoyagi, K.; Koizumi, Y.; Chiba, A.; Xiong, W.; To, A.C. Elucidating the Effect
    of Preheating Temperature on Melt Pool Morphology Variation in Inconel 718 Laser Powder Bed Fusion via Simulation and
    Experiment. Available online: https://www.sciencedirect.com/science/article/pii/S2214860420310149#bb8 (accessed on 30
    April 2021).
  23. Ur Rehman, A.; Pitir, F.; Salamci, M.U. Laser Powder Bed Fusion (LPBF) of In718 and the Impact of Pre-Heating at 500 and
    1000 ◦C: Operando Study. Materials 2021, 14, 6683. [CrossRef] [PubMed]
  24. Ur Rehman, A.; Pitir, F.; Salamci, M.U. Full-Field Mapping and Flow Quantification of Melt Pool Dynamics in Laser Powder Bed
    Fusion of SS316L. Materials 2021, 14, 6264. [CrossRef] [PubMed]
  25. Gong, H.; Gu, H.; Zeng, K.; Dilip, J.J.S.; Pal, D.; Stucker, B.; Christiansen, D.; Beuth, J.; Lewandowski, J.J. Melt Pool Characterization
    for Selective Laser Melting of Ti-6Al-4V Pre-alloyed Powder. In Proceedings of the International Solid Freeform Fabrication
    Symposium, Austin, TX, USA, 10–12 August 2014; 2014; pp. 256–267.
  26. Song, B.; Dong, S.; Liao, H.; Coddet, C. Process parameter selection for selective laser melting of Ti6Al4V based on temperature
    distribution simulation and experimental sintering. Int. J. Adv. Manuf. Technol. 2012, 61, 967–974. [CrossRef]
  27. Guo, Q.; Zhao, C.; Qu, M.; Xiong, L.; Hojjatzadeh, S.M.H.; Escano, L.I.; Parab, N.D.; Fezzaa, K.; Sun, T.; Chen, L. In-situ full-field
  28. mapping of melt flow dynamics in laser metal additive manufacturing. Addit. Manuf. 2020, 31, 100939. [CrossRef]
  29. Messler, J.R.W. Principles of Welding: Processes, Physics, Chemistry, and Metallurgy; John Wiley & Sons: New York, NY, USA, 2008;
  30. ISBN 9783527617494.
  31. Khairallah, S.A.; Anderson, A.T.; Rubenchik, A.M.; King, W.E. Laser powder-bed fusion additive manufacturing: Physics of
  32. complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater. 2016, 108, 36–45. [CrossRef]
  33. Ur Rehman, A.; Mahmood, M.A.; Pitir, F.; Salamci, M.U.; Popescu, A.C.; Mihailescu, I.N. Mesoscopic Computational Fluid
  34. Dynamics Modelling for the Laser-Melting Deposition of AISI 304 Stainless Steel Single Tracks with Experimental Correlation: A
  35. Novel Study. Metals 2021, 11, 1569. [CrossRef]
  36. Paul, A.; Debroy, T. Free surface flow and heat transfer in conduction mode laser welding. Metall. Trans. B 1988, 19, 851–858.
  37. [CrossRef]
  38. Aucott, L.; Dong, H.; Mirihanage, W.; Atwood, R.; Kidess, A.; Gao, S.; Wen, S.; Marsden, J.; Feng, S.; Tong, M.; et al. Revealing
  39. internal flow behaviour in arc welding and additive manufacturing of metals. Nat. Commun. 2018, 9, 5414. [CrossRef]
  40. Abderrazak, K.; Bannour, S.; Mhiri, H.; Lepalec, G.; Autric, M. Numerical and experimental study of molten pool formation
  41. during continuous laser welding of AZ91 magnesium alloy. Comput. Mater. Sci. 2009, 44, 858–866. [CrossRef]
  42. Bayat, M.; Thanki, A.; Mohanty, S.; Witvrouw, A.; Yang, S.; Thorborg, J.; Tiedje, N.S.; Hattel, J.H. Keyhole-induced porosities in
  43. Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V: High-fidelity modelling and experimental validation. Addit. Manuf. 2019,
  44. 30, 100835. [CrossRef]
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nanomaterials-11-03284-v2다운로드

Additive Manufacturing & Welding Bibliography

Additive Manufacturing & Welding Bibliography

다음은 적층 제조 및 용접 참고 문헌의 기술 문서 모음입니다. 이 모든 논문에는 FLOW-3D AM 결과가 나와 있습니다. FLOW-3D AM을 사용하여 적층 제조, 레이저 용접 및 기타 용접 기술에서 발견되는 프로세스를 성공적으로 시뮬레이션하는 방법에 대해 자세히 알아보십시오.

2024년 11월 20일 update

121-24 Lovejoy Mutswatiwa, Lauren Katch, Nathan John Kizer, Judith Anne Todd, Tao Sun, Samuel James Clark, Kamel Fezzaa, Jordan Lum, David Matthew Stobbe, Griffin Jones, Kenneth Charles Meinert Jr., Andrea Paola Argüelles, Christopher Micheal Kube, High-speed synchrotron X-ray imaging of melt pool dynamics during ultrasonic melt processing of Al6061, Communications Materials, 5; 143, 2024. doi.org/10.1038/s43246-024-00584-3

120-24 Mysore Nagaraja Kishore, Dong Qian, Masakazu Soshi, Wei Li, Conforming mesh modeling of multi-physics effect on residual stress in multi-layer powder bed fusion process, Journal of Manufacturing Processes, 124; pp. 793-804, 2024. doi.org/10.1016/j.jmapro.2024.06.033

113-24 Yusufu Ekubaru, Takuya Nakabayashi, Tomoharu Fujiwara, Behrang Poorganji, Processing windows of Ni625 alloy fabricated using direct energy deposition, Advanced Engineering Materials, 2024. doi.org/10.1002/adem.202400962

111-24 Ruijie Liu, Melt pool dynamic modelling for the titanium-based metal additive manufacturing process, Thesis, The University of Auckland, 2024.

104-24 Ju Wang, Meng Li, Huarong Zhang, Zhe Liu, Xiaodan Li, Dengzhi Yao, Yuhang Wu, Qiong Wu, Xizhong An, Shujun Li, Jian Wang, Xing Zhang , Cumulative effects of powder beds and melted areas on pore defects in electron beam powder bed fusion of tungsten, Powder Technology, 443; 119971, 2024. doi.org/10.1016/j.powtec.2024.119971

100-24 Xuesong Gao, Aryan Aryan, Wei Zhang, Numerical analysis of rotating scans’ effect on surface roughness in laser-powder bed fusion, Journal of Materials Research and Technology, 30; pp. 8671-8682, 2024. doi.org/10.1016/j.jmrt.2024.05.214

95-24 Yongbiao Wang, Yue Zhang, Junjie Jiang, Yang Zhang, Hongyang Cui, Xintian Liu, Yujuan Wu, Cross-scale simulation of macro/microstructure evolution during selective laser melting of Mg–Gd–Y alloy, Metallurgical and Materials Transactions B , 2024. doi.org/10.1007/s11663-024-03104-3

94-24 Yang Chu, Haichuan Shi, Peilei Zhang, Zhishui Yu, Hua Yan, Qinghua Lu, Shijie Song, Kaichang Yu, Simulation-assisted parameter optimization and tribological behavior of graphene reinforced IN718 matrix composite prepared by SLM, Intermetallics, 170; 108307, 2024. doi.org/10.1016/j.intermet.2024.108307

92-24 Ying Wei, Song Han, Shiwei Yu, Ziwei Chen, Ziang Li, Hailong Wang, Wenbo Cheng, Mingzhe An , Parameter impact on 3D concrete printing from single to multi-layer stacking, Automation in Construction, 164; 105449, 2024. doi.org/10.1016/j.autcon.2024.105449

90-24 Chuanbin Du, Yuewei Ai, Yiyuan Wang, Chenglong Ye, The effect mechanism of laser beam defocusing on the surface quality of IN718 alloy prepared by laser powder bed fusion, Powder Technology, 443; 119841, 2024. doi.org/10.1016/j.powtec.2024.119841

88-24 Arash Samaei, Joseph P. Leonor, Zhengtao Gan, Zhongsheng Sang, Xiaoyu Xie, Brian J. Simonds, Wing Kam Liu, Gregory J. Wagner, Benchmark study of melt pool and keyhole dynamics, laser absorptance, and porosity in additive manufacturing of Ti-6Al-4V, Progress in Additive Manufacturing, 2024. doi.org/10.1007/s40964-024-00637-6

83-24 Ao Fu, Zhonghao Xie, Jian Wang, Yuankui Cao, Bingfeng Wang, Jia Li, Qihong Fang, Xiaofeng Li, Bin Liu, Yong Liu, Controlling of cellular substructure and its effect on mechanical properties of FeCoCrNiMo0.2 high entropy alloy fabricated by selective laser melting, Materials Science and Engineering: A, 901; 146547, 2024. doi.org/10.1016/j.msea.2024.146547

82-24 Fatemeh Bodaghi, Mojtaba Movahedi, Suck-Joo Na, Lin-Jie Zhang, Amir Hossein Kokabi, Effect of welding current and speed on solidification cracking susceptibility in gas tungsten arc fillet welding of dissimilar aluminum alloys: Coupling a weld simulation and a cracking criterion, Journal of Materials Research and Technology, 30: pp. 4777-4785, 2024. doi.org/10.1016/j.jmrt.2024.04.195

81-24 Myeonghwan Choi, Dae-Won Cho, Kwang-Hyeon Lee, Seonghoon Yoo, Sangyong Nam, Namhyun Kang, Severe Mn vaporization for partial-penetrated laser keyhole welds of high-manganese cryogenic steel, International Journal of Heat and Mass Transfer, 227; 125567, 2024. doi.org/10.1016/j.ijheatmasstransfer.2024.125567

78-24 An Wang, Qianglong Wei, Zijue Tang, J.P. Oliviera, Chu Lun Alex Leung, Pengyuan Ren, Xiaolin Zhang, Yi Wu, Haowei Wang, Hongze Wang, Effects of hatch spacing on pore segregation and mechanical properties during blue laser directed energy deposition of AlSi10Mg, Additive Manufacturing, 85; 104147, 2024. doi.org/10.1016/j.addma.2024.104147

77-24 Jeongho Yang, Seonghun Ji, Du-Rim Eo, Jongcheon Yoon, Parviz Kahhal, Hyub Lee, Sang Hu Park, Effect of abnormal powder feeding on mechanical properties of fabricated part in directed energy deposition, International Journal of Precision Engineering and Manufacturing – Green Technology, 2024. doi.org/10.1007/s40684-024-00620-0

72-24 Minglei Qu, Jiandong Yuan, Ali Nabaa, Junye Huang, Chihpin Andrew Chuang, Lianyi Chen, Melting and solidification dynamics during laser melting of reaction-based metal matrix composites uncovered by in-situ synchrotron X-ray diffraction, Acta Materialia, 271; 119875, 2024. doi.org/10.1016/j.actamat.2024.119875

71-24 Chenze Li, Manish Jain, Qian Liu, Zhuohan Cao, Michael Ferry, Jamie J. Kruzic, Bernd Gludovatz, Xiaopeng Li, Multi-scale microstructure manipulation of an additively manufactured CoCrNi medium entropy alloy for superior mechanical properties and tunable mechanical anisotropy, Additive Manufacturing, 84; 104104, 2024. doi.org/10.1016/j.addma.2024.104104

68-24 Jialu Wang, Shuaicheng Zhu, Miaojin Jiang, Yunwei Gui, Huadong Fu, Jianxin Xie, Solidification track morphology, residual stress behavior, and microstructure evolution mechanism of FGH96-R nickel-based superalloys during laser powder bed fusion process, Journal of Materials Engineering and Performance, 2024. doi.org/10.1007/s11665-024-09326-5

66-24 Erik Holmen Olofsson, Ashley Dan, Michael Roland, Ninna Halberg Jokil, Rohit Ramachandran, Jesper Henri Hattel, Numerical modeling of fill-level and residence time in starve-fed single-screw extrusion: a dimensionality reduction study from a 3D CFD model to a 2D convection-diffusion model, The International Journal of Advanced Manufacturing Technology, 132; pp. 1111-1125, 2024. doi.org/10.1007/s00170-024-13378-1

64-24 Feipeng An, Linjie Zhang, Wei Ma, Suck Joo Na, Influences of the powder size and process parameters on the quasi-stability of molten pool shape in powder bed fusion-laser beam of molybdenum, Journal of Materials Engineering and Performance, 2024. doi.org/10.1007/s11665-024-09328-3

63-24 Haodong Chen, Xin Lin, Yajing Sun, Shuhao Wang, Kunpeng Zhu, Binbin Dan, Revealing formation mechanism of end of process depression in laser powder bed fusion by multi-physics meso-scale simulation, Virtual and Physical Prototyping, 19.1; e2326599, 2024. doi.org/10.1080/17452759.2024.2326599

57-24 Masayuki Okugawa, Kenji Saito, Haruki Yoshima, Katsuhiko Sawaizumi, Sukeharu Nomoto, Makoto Watanabe, Takayoshi Nakano, Yuichiro Koizumi, Solute segregation in a rapidly solidified Hastelloy-X Ni-based superalloy during laser powder bed fusion investigated by phase-field and computational thermal-fluid dynamics simulations, Additive Manufacturing, 84; 104079, 2024. doi.org/10.1016/j.addma.2024.104079

51-24 Jeongho Yang, Dongseok Kang, Si Mo Yeon, Yong Son, Sang Hu Park, Interval island laser-scanning strategy of Ti–6Al–4V part additively manufactured for anisotropic stress reduction, International Journal of Precision Engineering and Manufacturing, 25; pp. 1087-1099, 2024. doi.org/10.1007/s12541-024-00967-z

50-24 James Lamb, Ruben Ochoa, Adriana Eres-Castellanos, Jonah Klemm-Toole, McLean P. Echlin, Tao Sun, Kamel Fezzaa, Amy Clarke, Tresa M. Pollack, Quantification of melt pool dynamics and microstructure during simulated additive manufacturing, Scripta Materialia, 245; 116036, 2024. doi.org/10.1016/j.scriptamat.2024.116036

41-24 Xiong Zhang, Chunjin Wang, Benny C.F. Cheung, Gaoyang Mi, Chunming Wang, Ultrafast laser ablation of tungsten carbide: Quantification of threshold range and interpretation of feature transition, Journal of the American Ceramic Society, 107.6; pp. 3724-3734, 2024. doi.org/10.1111/jace.19718

38-24 Hao-Ping Yeh, Mohamad Bayat, Amirhossein Arzani, Jesper H. Hattel, Accelerated process parameter selection of polymer-based selective laser sintering via hybrid physics-informed neural network and finite element surrogate modelling, Applied Mathematical Modelling, 130; pp. 693-712, 2024. doi.org/10.1016/j.apm.2024.03.030

34-24 Khalid El Abbaoui, Issam Al Korachi, Mostapha El Jai, Berin Šeta, Md. Tusher Mollah, 3D concrete printing using computational fluid dynamics: Modeling of material extrusion with slip boundaries, Journal of Manufacturing Processes, 118; pp. 448-459, 2024. doi.org/10.1016/j.jmapro.2024.03.042

33-24 Hao Lu, Lida Zhu, Pengsheng Xue, Boling Yan, Yanpeng Hao, Zhichao Yang, Jinsheng Ning, Chuanliang Shi, Hao Wang, Ultrasonic machining response and improvement mechanism for differentiated bio-CoCrMo alloys manufactured by directed energy deposition, Journal of Materials Science & Technology, 193; pp. 226-243, 2024. doi.org/10.1016/j.jmst.2023.12.037

32-24 Yinghang Liu, Zhe Song, Yi Guo, Gaoming Zhu, Yunhao Fan, Huamiao Wang, Wentao Yan, Xiaoqin Zeng, Leyun Wang, Simultaneously enhancing strength and ductility of LPBF Ti alloy via trace Y2O3 nanoparticle addition, Journal of Materials Science & Technology, 191; pp. 146-156, 2024. doi.org/10.1016/j.jmst.2024.01.011

27-24 Zehui Liu, Yiyang Hu, Mingyang Zhang, Wei Zhang, Jun Wang, Wenbo Lei, Chunming Wang, Surface morphology evolution mechanisms of pulse laser polishing mold steel, International Journal of Mechanical Sciences, 269; 109039, 2024. doi.org/10.1016/j.ijmecsci.2024.109039

25-24 Muhammad Arif Mahmood, Kashif Ishfaq, Marwan Khraisheh, Inconel-718 processing windows by directed energy deposition: a framework combining computational fluid dynamics and machine learning models with experimental validation, The International Journal of Advanced Manufacturing Technology, 130; pp. 3997-4011, 2024. doi.org/10.1007/s00170-024-12980-7

24-24   Jinsheng Ning, Lida Zhu, Shuhao Wang, Zhichao Yang, Peihua Xu, Pengsheng Xue, Hao Lu, Miao Yu, Yunhang Zhao, Jiachen Li, Susmita Bose, Amit Bandyopadhyay, Printability disparities in heterogeneous material combinations via laser directed energy deposition: a comparative study, International Journal of Extreme Manufacturing, 6; 025001, 2024. doi.org/10.1088/2631-7990/ad172f

18-24   Delong Jia, Dong Zhou, Peng Yi, Chuanwei Zhang, Junru Li, Yankuo Guo, Shengyue Zhang, Yanhui Li, Splat deposition stress formation mechanism of droplets impacting onto texture, International Journal of Mechanical Sciences, 266; 109002, 2024. doi.org/10.1016/j.ijmecsci.2024.109002

11-24   Dae Gune Jung, Ji Young Park, Choong Mo Ryu, Jong Jin Hwang, Seung Jae Moon, Numerical study of laser welding of 270 μm thick silicon-steel sheets for electrical motors, Metals, 14.1; 24, 2024. doi.org/10.3390/met14010024

8-24   Zhifu Yao, Longke Bao, Mujin Yang, Yuechao Chen, Minglin He, Jiang Yi, Xintong Yang, Tao Yang, Yilu Zhao, Cuiping Wang, Zheng Zhong, Shuai Wang, Xingjun Liu, Thermally stabe strong <101> texture in additively manufactured cobalt-based superalloys, Scripta Materialia, 242; 115942, 2024. doi.org/10.1016/j.scriptamat.2023.115942

5-24   Xi Shu, Chunyu Wang, Guoqing Chen, Chunju Wang, Lining Sun, Pre-melted electron beam freeform fabrication additive manufacturing: modeling and numerical simulation, Welding in the World, 68; pp. 163-176, 2024. doi.org/10.1007/s40194-023-01647-8

4-24   Lin Gao, Andrew C. Chuang, Peter Kenesei, Zhongshu Ren, Lilly Balderson, Tao Sun, An operando synchrotron study on the effect of wire melting state on solidification microstructures of Inconel 718 in wire-laser directed energy deposition, International Journal of Machine Tools and Manufacture, 194; 104089, 2024. doi.org/10.1016/j.ijmachtools.2023.104089

3-24 Kunjie Dai, Xing He, Decheng Kong, Chaofang Dong, Multi-physical field simulation to yield defect-free IN718 alloy fabricated by laser powder bed fusion, Materials Letters, 355; 135437, 2024. doi.org/10.1016/j.matlet.2023.135437

2-24 You Wang, Yinkai Xie, Huaixue Li, Caiyou Zeng, Ming Xu, Hongqiang Zhang, In-situ monitoring plume, spattering behavior and revealing their relationship with melt flow in laser powder bed fusion of nickel-based superalloy, Journal of Materials Science & Technology, 177; pp. 44-58, 2024. doi.org/10.1016/j.jmst.2023.07.068

1-24 Yukai Chen, Hongtu Xu, Yu Lu, Yin Wang, Shuangyuzhou Wang, Ke Huang, Qi Zhang, Prediction of microstructure for Inconel 718 laser welding process using multi-scale model, Proceedings of the 14th International Conference on the Technology of Plasticity – Current Trends in the Technology of Plasticity, pp. 713-722, 2024. doi.org/10.1007/978-3-031-41341-4_75

211-23 Giovanni Chianese, Qamar Hayat, Sharhid Jabar, Pasquale Franciosa, Darek Ceglarek, Stanislao Patalano, A multi-physics CFD study to investigate the impact of laser beam shaping on metal mixing and molten pool dynamics during laser welding of copper to steel for battery terminal-to-casing connections, Journal of Materials Processing Technology, 322; 118202, 2023. doi.org/10.1016/j.jmatprotec.2023.118202

207-23 Dong Liu, Jiaqi Pei, Hua Hou, Xiaofeng Niu, Yuhong Zhao, Optimizing solidification dendrites and process parameters for laser powder bed fusion additive manufacturing of GH3536 superalloy by finite volume and phase-field method, Journal of Materials Research and Technology, 27; pp. 3323-3338, 2023. doi.org/10.1016/j.jmrt.2023.10.188

206-23 Houshang Yin, Jingfan Yang, Ralf D. Fischer, Zilong Zhang, Bart Prorok, Lang Yuan, Xiaoyuan Lou, Pulsed laser additive manufacturing for 316L stainless steel: a new approach to control subgrain cellular structure, JOM, 75; pp. 5027-5036, 2023. doi.org/10.1007/s11837-023-06177-8

205-23 Francis Ogoke, William Lee, Ning-Yu Kao, Alexander Myers, Jack Beuth, Jonathan Malen, Amir Barati Farimani, Convolutional neural networks for melt depth prediction and visualization in laser powder bed fusion, The International Journal of Advanced Manufacturing Technology, 129; pp. 3047-3062, 2023. doi.org/10.1007/s00170-023-12384-z

202-23 Habib Hamed Zargari, Kazuhiro Ito, Abhay Sharma, Effect of workpiece vibration frequency on heat distribution and material flow in the molten pool in tandem-pulsed gas metal arc welding, The International Journal of Advanced Manufacturing Technology, 129; pp. 2507-2522, 2023. doi.org/10.1007/s00170-023-12424-8

199-23 Yukai Chen, Yin Wang, Hao Li, Yu Lu, Bin Han, Qi Zhang, Effects of process parameters on the microstructure of Inconel 718 during powder bed fusion based on cellular automata approach, Virtual and Physical Prototyping, 18.1; e2251032, 2023. doi.org/10.1080/17452759.2023.2251032

197-23 Qiong Wu, Chuang Qiao, Yuhang Wu, Zhe Liu, Xiaodan Li, Ju Wang, Xizhong An, Aijun Huang, Chao Voon Samuel Lim, Numerical investigation on the reuse of recycled powders in powder bed fusion additive manufacturing, Additive Manufacturing, 77; 103821, 2023. doi.org/10.1016/j.addma.2023.103821

196-23 Daicong Zhang, Chunhui Jing, Wei Guo, Yuan Xiao, Jun Luo, Lehua Qi, Microchannels formed using metal microdroplets, Micromachines, 14.10; 1922, 2023. doi.org/10.3390/mi14101922

195-23 Trong-Nhan Le, Santosh Rauniyar, V.H. Nismath, Kevin Chou, An investigation into the effects of contouring process parameters on the up-skin surface characteristics in laser powder-bed fusion process, Manufacturing Letters, 35; Supplement, pp. 707-716, 2023. doi.org/10.1016/j.mfglet.2023.08.085

194-23 Kyubok Lee, Teresa J. Rinker, Masoud M. Pour, Wayne Cai, Wenkang Huang, Wenda Tan, Jennifer Bracey, Jingjing Li, A study on cracks and IMCs in laser welding of Al and Cu, Manufacturing Letters, 35; Supplement, pp. 221-231, 2023. doi.org/10.1016/j.mfglet.2023.08.026

192-23 Kunjie Dai, Xing He, Wei Zhang, Decheng Kong, Rong Guo, Minlei Hu, Ketai He, Chaofang Dong, Tailoring the microstructure and mechanical properties for Hastelloy X alloy by laser powder bed fusion via scanning strategy, Materials & Design, 235; 112386, 2023. doi.org/10.1016/j.matdes.2023.112386

191-23 Jun Du, Daqing Wang, Jimiao He, Yongheng Zhang, Zhike Peng, Influence of droplet size and ejection frequency on molten pool dynamics and deposition morphology in TIG-aided droplet deposition manufacturing, International Communications in Heat and Mass Transfer, 148; 107075, 2023. doi.org/10.1016/j.icheatmasstransfer.2023.107075

188-23 Jin-Hyeong Park, Du-Song Kim, Dae-Won Cho, Jaewoong Kim, Changmin Pyo, Influence of thermal flow and predicting phase transformation on various welding positions, Heat and Mass Transfer, 2023. doi.org/10.1007/s00231-023-03429-w

184-23 Lin Gao, Jishnu Bhattacharyya, Wenhao Lin, Zhongshu Ren, Andrew C. Chuang, Pavel D. Shevchenko, Viktor Nikitin, Ji Ma, Sean R. Agnew, Tao Sun, Tailoring material microstructure and property in wire-laser directed energy deposition through a wiggle deposition strategy, Additive Manufacturing, 77; 103801, 2023. doi.org/10.1016/j.addma.2023.103801

182-23 Liping Guo, Hanjie Liu, Hongze Wang, Qianglong Wei, Jiahui Zhang, Yingyan Chen, Chu Lun Alex Leung, Qing Lian, Yi Wu, Yu Zou, Haowei Wang, A high-fidelity comprehensive framework for the additive manufacturing printability assessment, Journal of Manufacturing Processes, 105; pp. 219-231, 2023. doi.org/10.1016/j.jmapro.2023.09.041

172-23 Liping Guo, Hanjie Liu, Hongze Wang, Qianglong Wei, Yakai Xiao, Zijue Tang, Yi Wu, Haowei Wang, Identifying the keyhole stability and pore formation mechanisms in laser powder bed fusion additive manufacturing, Journal of Materials Processing Technology, 321; 118153, 2023. doi.org/10.1016/j.jmatprotec.2023.118153

171-23 Yuhang Wu, Qiong Wu, Meng Li, Ju Wang, Dengzhi Yao, Hao Luo, Xizhong An, Haitao Fu, Hao Zhang, Xiaohong Yang, Qingchuan Zou, Shujun Li, Haibin Ji, Xing Zhang, Numerical investigation on effects of operating conditions and final dimension predictions in laser powder bed fusion of molybdenum, Additive Manufacturing, 76; 103783, 2023. doi.org/10.1016/j.addma.2023.103783

158-23 K. El Abbaoui, I. Al Korachi, M.T. Mollah, J. Spangenberg, Numerical modelling of planned corner deposition in 3D concrete printing, Archives of Materials Science and Engineering, 121.2; pp. 71-79, 2023. doi.org/10.5604/01.3001.0053.8488

156-23 Liping Guo, Hanjie Liu, Hongze Wang, Valentino A.M. Cristino, C.T. Kwok, Qianglong Wei, Zijue Tang, Yi Wu, Haowei Wang, Deepening the scientific understanding of different phenomenology in laser powder bed fusion by an integrated framework, International Journal of Heat and Mass Transfer, 216; 124596, 2023. doi.org/10.1016/j.ijheatmasstransfer.2023.124596

154-23 Zhiyong Li, Xiuli He, Shaoxia Li, Xinfeng Kan, Yanjun Yin, Gang Yu, Sulfur-induced transitions of thermal behavior and flow dynamics in laser powder bed fusion of 316L powders, Thermal Science and Engineering Progress, 45; 102072, 2023. doi.org/10.1016/j.tsep.2023.102072

149-23 Shardul Kamat, Wayne Cai, Teresa J. Rinker, Jennifer Bracey, Liang Xi, Wenda Tan, A novel integrated process-performance model for laser welding of multi-layer battery foils and tabs, Journal of Materials Processing Technology, 320; 118121, 2023. doi.org/10.1016/j.jmatprotec.2023.118121

148-23 Reza Ghomashchi, Shahrooz Nafisi, Solidification of Al12Si melt pool in laser powder bed fusion, Journal of Materials En gineering and Performance, 2023. doi.org/10.1007/s11665-023-08502-3

133-23 Hesam Moghadasi, Md Tusher Mollah, Deepak Marla, Hamid Saffari, Jon Spangenberg, Computational fluid dynamics modeling of top-down digital light processing additive manufacturing, Polymers, 15.11; 2459, 2023. doi.org/10.3390/polym15112459

131-23 Luca Santoro, Raffaella Sesana, Rosario Molica Nardo, Francesca Curà, In line defect detection in steel welding process by means of thermography, Experimental Mechanics in Engineering and Biomechanics – Proceedings ICEM20, 19981, 2023.

128-23 Md Tusher Mollah, Raphaël Comminal, Wilson Ricardo Leal da Silva, Berin Šeta, Jon Spangenberg, Computational fluid dynamics modelling and experimental analysis of reinforcement bar integration in 3D concrete printing, Cement and Concrete Research, 173; 107263, 2023. doi.org/10.1016/j.cemconres.2023.107263

123-23 Arash Samaei, Zhongsheng Sang, Jennifer A. Glerum, Jon-Erik Mogonye, Gregory J. Wagner, Multiphysics modeling of mixing and material transport in additive manufacturing with multicomponent powder beds, Additive Manufacturing, 67; 103481, 2023. doi.org/10.1016/j.addma.2023.103481

122-23 Chu Han, Ping Jiang, Shaoning Geng, Lingyu Guo, Kun Liu, Inhomogeneous microstructure distribution and its formation mechanism in deep penetration laser welding of medium-thick aluminum-lithium alloy plates, Optics & Laser Technology, 167; 109783, 2023. doi.org/10.1016/j.optlastec.2023.109783

111-23 Alexander J. Myers, Guadalupe Quirarte, Francis Ogoke, Brandon M. Lane, Syed Zia Uddin, Amir Barati Farimani, Jack L. Beuth, Jonathan A. Malen, High-resolution melt pool thermal imaging for metals additive manufacturing using the two-color method with a color camera, Additive Manufacturing, 73; 103663, 2023. doi.org/10.1016/j.addma.2023.103663

107-23 M. Mohsin Raza, Yu-Lung Lo, Hua-Bin Lee, Chang Yu-Tsung, Computational modeling of laser welding for aluminum–copper joints using a circular strategy, Journal of Materials Research and Technology, 25; pp. 3350-3364, 2023. doi.org/10.1016/j.jmrt.2023.06.122

106-23 H.Z. Lu, L.H. Liu, X. Luo, H.W. Ma, W.S. Cai, R. Lupoi, S. Yin, C. Yang, Formation mechanism of heterogeneous microstructures and shape memory effect in NiTi shape memory alloy fabricated via laser powder bed fusion, Materials & Design, 232; 112107, 2023. doi.org/10.1016/j.matdes.2023.112107

105-23 Harun Kahya, Hakan Gurun, Gokhan Kucukturk, Experimental and analytical investigation of the re-melting effect in the manufacturing of 316L by direct energy deposition (DED) method, Metals, 13.6; 1144, 2023. doi.org/10.3390/met13061144

100-23 Dongju Chen, Gang Li, Peng Wang, Zhiqiang Zeng, Yuhang Tang, Numerical simulation of melt pool size and flow evolution for laser powder bed fusion of powder grade Ti6Al4V, Finite Elements in Analysis and Design, 223; 103971, 2023. doi.org/10.1016/j.finel.2023.103971

97-23 Mahyar Khorasani, Martin Leary, David Downing, Jason Rogers, Amirhossein Ghasemi, Ian Gibson, Simon Brudler, Bernard Rolfe, Milan Brandt, Stuart Bateman, Numerical and experimental investigations on manufacturability of Al–Si–10Mg thin wall structures made by LB-PBF, Thin-Walled Structures, 188; 110814, 2023. doi.org/10.1016/j.tws.2023.110814

95-23 M.S. Serdeczny, Laser welding of dissimilar materials – simulation driven optimization of process parameters, IOP Conference Series: Materials Science and Engineering, 1281; 012018, 2023. doi.org/10.1088/1757-899X/1281/1/012018

90-23 Lin Liu, Tubin Liu, Xi Dong, Min Huang, Fusheng Cao, Mingli Qin, Numerical simulation of thermal dynamic behavior and morphology evolution of the molten pool of selective laser melting BN/316L stainless steel composite, Journal of Materials Engineering and Performance, 2023. doi.org/10.1007/s11665-023-08210-y

89-23 M. P. Serdeczny, A. Jackman, High fidelity modelling of bead geometry in directed energy deposition – simulation driven optimization, Journal of Physics: Conference Series, NOLAMP19, 2023.

88-23 Lu Wang, Shuhao Wang, Yanming Zhang, Wentao Yan, Multi-phase flow simulation of powder streaming in laser-based directed energy deposition, International Journal of Heat and Mass Transfer, 212; 124240, 2023. doi.org/10.1016/j.ijheatmasstransfer.2023.124240

80-23 Mahyar Khorasani, AmirHossein Ghasemi, Martin Leary, David Downing, Ian Gibson, Elmira G. Sharabian, Jithin Kozuthala Veetil, Milan Brandt, Stuart Batement, Bernard Rolfe, Benchmark models for conduction and keyhole modes in laser-based powder bed fusion of Inconel 718, Optics & Laser Technology, 164; 109509, 2023. doi.org/10.1016/j.optlastec.2023.109509

78-23   Md. Tusher Mollah, Raphaël Comminal, Marcin P. Serdeczny, Berin Šeta, Jon Spangenberg, Computational analysis of yield stress buildup and stability of deposited layers in material extrusion additive manufacturing, Additive Manufacturing, 71; 103605, 2023. doi.org/10.1016/j.addma.2023.103605

76-23   Asif Ur Rehman, Kashif Azher, Abid Ullah, Celal Sami Tüfekci, Metin Uymaz Salamci, Binder jetting of SS316L: a computational approach for droplet-powder interaction, Rapid Prototyping Journal, 2023. doi.org/10.1108/RPJ-08-2022-0264

75-23   Dengzhi Yao, Ju Wang, Hao Luo, Yuhang Wu, Xizhong An, Thermal behavior and control during multi-track laser powder bed fusion of 316 L stainless steel, Additive Manufacturing, 70; 103562, 2023. doi.org/10.1016/j.addma.2023.103562

61-23   Yaqing Hou, Hang Su, Hao Zhang, Fafa Li, Xuandong Wang, Yazhou He, Dupeng He, An integrated simulation model towards laser powder bed fusion in-situ alloying technology, Materials & Design, 228; 111795, 2023. doi.org/10.1016/j.matdes.2023.111795

56-23   Maohong Yang, Guiyi Wu, Xiangwei Li, Shuyan Zhang, Honghong Wang, Jiankang Huang, Influence of heat source model on the behavior of laser cladding pool, Journal of Laser Applications, 35.2; 2023. doi.org/10.2351/7.0000963

45-23   Daniel Martinez, Philip King, Santosh Reddy Sama, Jay Sim, Hakan Toykoc, Guha Manogharan, Effect of freezing range on reducing casting defects through 3D sand-printed mold designs, The International Journal of Advanced Manufacturing Technology, 2023. doi.org/10.1007/s00170-023-11112-x

39-23   Peter S. Cook, David J. Ritchie, Determining the laser absorptivity of Ti-6Al-4V during laser powder bed fusion by calibrated melt pool simulation, Optics & Laser Technology, 162; 109247. 2023. doi.org/10.1016/j.optlastec.2023.109247

36-23   Yixuan Chen, Weihao Wang, Yao Ou, Yingna Wu, Zirong Zhai, Rui Yang, Impact of laser power and scanning velocity on microstructure and mechanical properties of Inconel 738LC alloys fabricated by laser powder bed fusion, TMS 2023 152nd Annual Meeting & Exhibition Supplemental Proceedings, pp. 138-149, 2023. doi.org/10.1007/978-3-031-22524-6_15

34-23   Chao Kang, Ikki Ikeda, Motoki Sakaguchi, Recoil and solidification of a paraffin droplet impacted on a metal substrate: Numerical study and experimental verification, Journal of Fluids and Structures, 118; 103839, 2023. doi.org/10.1016/j.jfluidstructs.2023.103839

30-23   Fei Wang, Tiechui Yuan, Ruidi Li, Shiqi Lin, Zhonghao Xie, Lanbo Li, Valentino Cristino, Rong Xu, Bing liu, Comparative study on microstructures and mechanical properties of ultra ductility single-phase Nb40Ti40Ta20 refractory medium entropy alloy by selective laser melting and vacuum arc melting, Journal of Alloys and Compounds, 942; 169065, 2023. doi.org/10.1016/j.jallcom.2023.169065

29-23   Haejin Lee, Yeonghwan Song, Seungkyun Yim, Kenta Aoyagi, Akihiko Chiba, Byoungsoo Lee, Influence of linear energy on side surface roughness in powder bed fusion electron beam melting process: Coupled experimental and simulation study, Powder Technology, 418; 118292, 2023.

27-23   Yinan Chen, Bo Li, Double-phase refractory medium entropy alloy NbMoTi via selective laser melting (SLM) additive manufacturing, Journal of Physics: Conference Series, 2419; 012074, 2023. doi.org/10.1088/1742-6596/2419/1/012074

23-23   Yunwei Gui, Kenta Aoyagi, Akihiko Chiba, Development of macro-defect-free PBF-EB-processed Ti–6Al–4V alloys with superior plasticity using PREP-synthesized powder and machine learning-assisted process optimization, Materials Science and Engineering: A, 864; 144595, 2023. doi.org/10.1016/j.msea.2023.144595

21-23   Tatsuhiko Sakai, Yasuhiro Okamoto, Nozomi Taura, Riku Saito, Akira Okada, Effect of scanning speed on molten metal behaviour under angled irradiation with a continuous-wave laser, Journal of Materials Processing Technology, 313; 117866, 2023. doi.org/10.1016/j.jmatprotec.2023.117866

19-23   Gianna M. Valentino, Arunima Banerjee, Alexander lark, Christopher M. Barr, Seth H. Myers, Ian D. McCue, Influence of laser processing parameters on the density-ductility tradeoff in additively manufactured pure tantalum, Additive Manufacturing Letters, 4; 100117, 2023. doi.org/10.1016/j.addlet.2022.100117

15-23   Runbo Jiang, Zhongshu Ren, Joseph Aroh, Amir Mostafaei, Benjamin Gould, Tao Sun, Anthony D. Rollett, Quantifying equiaxed vs epitaxial solidification in laser melting of CMSX-4 single crystal superalloy, Metallurgical and Materials Transactions A, 54; pp. 808-822, 2023. doi.org/10.1007/s11661-022-06929-2

14-23   Nguyen Thi Tien, Yu-Lung Lo, M. Mohsin Raza, Cheng-Yen Chen, Chi-Pin Chiu, Optimization of processing parameters for pulsed laser welding of dissimilar metal interconnects, Optics & Laser Technology, 159; 109022, 2023. doi.org/10.1016/j.optlastec.2022.109022

9-23 Hou Yi Chia, Wentao Yan, High-fidelity modeling of metal additive manufacturing, Additive Manufacturing Technology: Design, Optimization, and Modeling, Ed. Kun Zhou, 2023.

8-23 Akash Aggarwal, Yung C. Shin, Arvind Kumar, Investigation of the transient coupling between the dynamic laser beam absorptance and the melt pool – vapor depression morphology in laser powder bed fusion process, International Journal of Heat and Mass Transfer, 201.2; 123663, 2023. doi.org/10.1016/j.ijheatmasstransfer.2022.123663

199-22 Md. Tusher Mollah, Raphaël Comminal, Marcin P. Serdeczny, David B. Pedersen, Jon Spangenberg, Numerical predictions of bottom layer stability in material extrusion additive manufacturing, JOM, 74; pp. 1096-1101, 2022. doi.org/10.1007/s11837-021-05035-9

198-22 Md. Tusher Mollah, Amirpasha Moetazedian, Andy Gleadall, Jiongyi Yan, Wayne Edgar Alphonso, Raphael Comminal, Berin Seta, Tony Lock, Jon Spangenberg, Investigation on corner precision at different corner angles in material extrusion additive manufacturing: An experimental and computational fluid dynamics analysis, Proceedings of the 33rd Annual Solid Freeform Fabrication Symposium, 2022.

197-22 Md. Tusher Mollah, Marcin P. Serdeczny, Raphaël Comminal, Berin Šeta, Marco Brander, David B. Pedersen, Jon Spangenberg, A numerical investigation of the inter-layer bond and surface roughness during the yield stress buildup in wet-on-wet material extrusion additive manufacturing, ASPE and euspen Summer Topical Meeting, 77, 2022.

182-22   Chan Kyu Kim, Dae-Won Cho, Seok Kim, Sang Woo Song, Kang Myung Seo, Young Tae Cho, High-throughput metal 3D printing pen enabled by a continuous molten droplet transfer, Advanced Science, 2205085, 2022. doi.org/10.1002/advs.202205085

180-22 Xu Kaikai, Gong Yadong, Zhang Qiang, Numerical simulation of dynamic analysis of molten pool in the process of direct energy deposition, The International Journal of Advanced Manufacturing Technology, 2022. doi.org/10.1007/s00170-022-10271-7

179-22 Yasuhiro Okamoto, Nozomi Taura, Akira Okada, Study on laser drilling process of solid metal on its liquid, International Journal of Electrical Machining, 27; 2022. doi.org/10.2526/ijem.27.35

175-22 Lu Min, Xhi Xiaojie, Lu Peipei, Wu Meiping, Forming quality and wettability of surface texture on CuSn10 fabricated by laser powder bed fusion, AIP Advances, 12.12; 125114, 2022. doi.org/10.1063/5.0122076

174-22 Thinus Van Rhijn, Willie Du Preez, Maina Maringa, Dean Kouprianoff, An investigation into the optimization of the selective laser melting process parameters for Ti6Al4V through numerical modelling, JOM, 2022. doi.org/10.1007/s11837-022-05608-2

171-22 Jonathan Yoshioka, Mohsen Eshraghi, Temporal evolution of temperature gradient and solidification rate in laser powder bed fusion additive manufacturing, Heat and Mass Transfer, 2022. doi.org/10.1007/s00231-022-03318-8

170-22 Subin Shrestha and Kevin Chou, Residual heat effect on the melt pool geometry during the laser powder bed fusion process, Journal of Manufacturing and Materials Processing, 6.6; 153, 2022. doi.org/10.3390/jmmp6060153

169-22 Aryan Aryan, Obinna Chukwubuzo, Desmond Bourgeois, Wei Zhang, Hardness prediction by incorporating heat transfer and molten pool fluid flow in a mult-pass, multi-layer weld for onsite repair of Grade 91 steel, U.S. Department of Energy Office of Scientific and Technical Information, DOE-OSU-0032067, 2022. doi.org/10.2172/1898594

158-22 Dafan Du, Lu Wang, Anping Dong, Wentao Yan, Guoliang Zhu, Baode Sun, Promoting the densification and grain refinement with assistance of static magnetic field in laser powder bed fusion, International Journal of Machine Tools and Manufacture, 183; 103965, 2022. doi.org/10.1016/j.ijmachtools.2022.103965

157-22 Han Chu, Jiang Ping, Geng Shaoning, Liu Kun, Nucleation mechanism in oscillating laser welds of 2024 aluminium alloy: A combined experimental and numerical study, Optics & Laser Technology, 158.A; 108812, 2022. doi.org/10.1016/j.optlastec.2022.108812

153-22 Zixiang Li, Yinan Cui, Baohua Chang, Guan Liu, Ze Pu, Haoyu Zhang, Zhiyue Liang, Changmeng Liu, Li Wang, Dong Du, Manipulating molten pool in in-situ additive manufacturing of Ti-22Al-25 Nb through alternating dual-electron beams, Additive Manufacturing, 60.A; 103230, 2022. doi.org/10.1016/j.addma.2022.103230

149-22   Qian Chen, Yao Fu, Albert C. To, Multiphysics modeling of particle spattering and induced defect formation mechanism in Inconel 718 laser powder bed fusion, The International Journal of Advanced Manufacturing Technology, 123; pp. 783-791, 2022. doi.org/10.1007/s00170-022-10201-7

146-22   Zixuan Wan, Hui-ping Wang, Jingjing Li, Baixuan Yang, Joshua Solomon, Blair Carlson, Effect of welding mode on remote laser stitch welding of zinc-coated steel with different sheet thickness combinations, Journal of Manufacturing Science and Engineering, MANU-21-1598, 2022. doi.org/10.1115/1.4055792

143-22   Du-Rim Eo, Seong-Gyu Chung, JeongHo Yang, Won Tae Cho, Sun-Hong Park, Jung-Wook Cho, Surface modification of high-Mn steel via laser-DED: Microstructural characterization and hot crack susceptibility of clad layer, Materials & Design, 223; 111188, 2022. doi.org/10.1016/j.matdes.2022.111188

142-22   Zichuan Fu, Xiangman Zhou, Bin Luo, Qihua Tian, Numerical simulation study of the effect of weld current on WAAM welding pool dynamic and weld bead morphology, International Conference on Mechanical Design and Simulation, Proceedings, 12261; 122614G, 2022. doi.org/10.1117/12.2639074

132-22   Yiyu Huang, Zhonghao Xie, Wenshu Li, Haoyu Chen, Bin Liu, Bingfeng Wang, Dynamic mechanical properties of the selective laser melting NiCrFeCoMo0.2 high entropy alloy and the microstructure of molten pool, Journal of Alloys and Compounds, 927; 167011, 2022. doi.org/10.1016/j.jallcom.2022.167011

126-22   Jingqi Zhang, Yingang Liu, Gang Sha, Shenbao Jin, Ziyong Hou, Mohamad Bayat, Nan Yang, Qiyang Tan, Yu Yin, Shiyang Liu, Jesper Henri Hattel, Matthew Dargusch, Xiaoxu Huang, Ming-Xing Zhang, Designing against phase and property heterogeneities in additively manufactured titanium alloys, Nature Communications, 13; 4660, 2022. doi.org/10.1038/s41467-022-32446-2

119-22   Xu Kaikai, Gong Yadong, Zhao Qiang, Numerical simulation on molten pool flow of Inconel718 alloy based on VOF during additive manufacturing, Materials Today Communications, 33; 104147, 2022. doi.org/10.1016/j.mtcomm.2022.104147

118-22   AmirPouya Hemmasian, Francis Ogoke, Parand Akbari, Jonathan Malen, Jack Beuth, Amir Barati Farimani, Surrogate modeling of melt pool thermal field using deep learning, SSRN, 2022. doi.org/10.2139/ssrn.4190835

117-22   Chiara Ransenigo, Marialaura Tocci, Filippo Palo, Paola Ginestra, Elisabetta Ceretti, Marcello Gelfi, Annalisa Pola, Evolution of melt pool and porosity during laser powder bed fusion of Ti6Al4V alloy: Numerical modelling and experimental validation, Lasers in Manufacturing and Materials Processing, 2022. doi.org/10.1007/s40516-022-00185-3

112-22   Chris Jasien, Alec Saville, Chandler Gus Becker, Jonah Klemm-Toole, Kamel Fezzaa, Tao Sun, Tresa Pollock, Amy J. Clarke, In situ x-ray radiography and computational modeling to predict grain morphology in β-titanium during simulated additive manufacturing, Metals, 12.7; 1217, 2022. doi.org/10.3390/met12071217

110-22   Haotian Zhou, Haijun Su, Yinuo Guo, Peixin Yang, Yuan Liu, Zhonglin Shen, Di Zhao, Haifang Liu, Taiwen Huang, Min Guo, Jun Zhang, Lin Liu, Hengzhi Fu, Formation and evolution mechanisms of pores in Inconel 718 during selective laser melting: Meso-scale modeling and experimental investigations, Journal of Manufacturing Processes, 81; pp. 202-213, 2022. doi.org/10.1016/j.jmapro.2022.06.072

109-22   Yufan Zhao, Huakang Bian, Hao Wang, Aoyagi Kenta, Yamanaka Kenta, Akihiko Chiba, Non-equilibrium solidification behavior associated with powder characteristics during electron beam additive manufacturing, Materials & Design, 221; 110915, 2022. doi.org/10.1016/j.matdes.2022.110915

107-22   Dan Lönn, David Spångberg, Study of process parameters in laser beam welding of copper hairpins, Thesis, University of Skövde, 2022.

106-22   Liping Guo, Hongze Wang, Qianglong Wei, Hanjie Liu, An Wang, Yi Wu, Haowei Wang, A comprehensive model to quantify the effects of additional nano-particles on the printability in laser powder bed fusion of aluminum alloy and composite, Additive Manufacturing, 58; 103011, 2022. doi.org/10.1016/j.addma.2022.103011

104-22   Hongjiang Pan, Thomas Dahmen, Mohamad Bayat, Kang Lin, Xiaodan Zhang, Independent effects of laser power and scanning speed on IN718’s precipitation and mechanical properties produced by LBPF plus heat treatment, Materials Science and Engineering: A, 849; 143530, 2022. doi.org/10.1016/j.msea.2022.143530

101-22   Yufan Zhao, Kenta Aoyagi, Kenta Yamanaka, Akihiko Chiba, A survey on basic influencing factors of solidified grain morphology during electron beam melting, Materials & Design, 221; 110927, 2022. doi.org/10.1016/j.matdes.2022.110927

98-22   Jon Spangenberg, Wilson Ricardo Leal da Silva, Md. Tusher Mollah, Raphaël Comminal, Thomas Juul Andersen, Henrik Stang, Integrating reinforcement with 3D concrete printing: Experiments and numerical modelling, Third RILEM International Conference on Concrete and Digital Fabrication, Eds. Ana Blanco, Peter Kinnell, Richard Buswell, Sergio Cavalaro, pp. 379-384, 2022.

93-22   Minglei Qu, Qilin Guo, Luis I. Escano, Samuel J. Clark Kamel Fezzaa, Lianyi Chen, Mitigating keyhole pore formation by nanoparticles during laser powder bed fusion additive manufacturing, Additive Manufacturing Letters, 100068, 2022. doi.org/10.1016/j.addlet.2022.100068

86-22   Patiparn Ninpetch, Prasert Chalermkarnnon, Pruet Kowitwarangkul, Multiphysics simulation of thermal-fluid behavior in laser powder bed fusion of H13 steel: Influence of layer thickness and energy input, Metals and Materials International, 2022. doi.org/10.1007/s12540-022-01239-z

85-22   Merve Biyikli, Taner Karagoz, Metin Calli, Talha Muslim, A. Alper Ozalp, Ali Bayram, Single track geometry prediction of laser metal deposited 316L-Si via multi-physics modelling and regression analysis with experimental validation, Metals and Materials International, 2022. doi.org/10.1007/s12540-022-01243-3

76-22   Zhichao Yang, Shuhao Wang, Lida Zhu, Jinsheng Ning, Bo Xin, Yichao Dun, Wentao Yan, Manipulating molten pool dynamics during metal 3D printing by ultrasound, Applied Physics Reviews, 9; 021416, 2022. doi.org/10.1063/5.0082461

73-22   Yu Sun, Liqun Li, Yu Hao, Sanbao Lin, Xinhua Tang, Fenggui Lu, Numerical modeling on formation of periodic chain-like pores in high power laser welding of thick steel plate, Journal of Materials Processing Technology, 306; 117638, 2022. doi.org/10.1016/j.jmatprotec.2022.117638

67-22   Yu Hao, Hiu-Ping Wang, Yu Sun, Liqun Li, Yihan Wu, Fenggui Lu, The evaporation behavior of zince and its effect on spattering in laser overlap welding of galvanized steels, Journal of Materials Processing Technology, 306; 117625, 2022. doi.org/10.1016/j.jmatprotec.2022.117625

65-22   Yanhua Zhao, Chuanbin Du, Peifu Wang, Wei Meng, Changming Li, The mechanism of in-situ laser polishing and its effect on the surface quality of nickel-based alloy fabricated by selective laser melting, Metals, 12.5; 778, 2022. doi.org/10.3390/met12050778

58-22   W.E. Alphonso, M. Bayat, M. Baier, S. Carmignato, J.H. Hattel, Multi-physics numerical modelling of 316L Austenitic stainless steel in laser powder bed fusion process at meso-scale, 17th UK Heat Transfer Conference (UKHTC2021), Manchester, UK, April 4-6, 2022.

57-22   Brandon Hayes, Travis Hainsworth, Robert MacCurdy, Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting, Additive Manufacturing, in press, 102785, 2022. doi.org/10.1016/j.addma.2022.102785

55-22   Xiang Wang, Lin-Jie Zhang, Jie Ning, Suck-joo Na, Fluid thermodynamic simulation of Ti-6Al-4V alloy in laser wire deposition, 3D Printing and Additive Manufacturing, 2022. doi.org/10.1089/3dp.2021.0159

54-22   Junhao Zhao, Binbin Wang, Tong Liu, Liangshu Luo, Yanan Wang, Xiaonan Zheng, Liang Wang, Yanqing Su, Jingjie Guo, Hengzhi Fu, Dayong Chen, Study of in situ formed quasicrystals in Al-Mn based alloys fabricated by SLM, Journal of Alloys and Compounds, 909; 164847, 2022. doi.org/10.1016/j.jallcom.2022.164847

48-22   Yueming Sun, Jianxing Ma, Fei Peng, Konstantin G. Kornev, Making droplets from highly viscous liquids by pushing a wire through a tube, Physics of Fluids, 34; 032119, 2022. doi.org/10.1063/5.0082003

46-22   H.Z. Lu, T. Chen, H. Liu, H. Wang, X. Luo, C.H. Song, Constructing function domains in NiTi shape memory alloys by additive manufacturing, Virtual and Physical Prototyping, 17.3; 2022. doi.org/10.1080/17452759.2022.2053821

42-22   Islam Hassan, P. Ravi Selvaganapathy, Microfluidic printheads for highly switchable multimaterial 3D printing of soft materials, Advanced Materials Technologies, 2101709, 2022. doi.org/10.1002/admt.202101709

41-22   Nan Yang, Youping Gong, Honghao Chen, Wenxin Li, Chuanping Zhou, Rougang Zhou, Huifeng Shao, Personalized artificial tibia bone structure design and processing based on laser powder bed fusion, Machines, 10.3; 205, 2022. doi.org/10.3390/machines10030205

31-22   Bo Shen, Raghav Gnanasambandam, Rongxuan Wang, Zhenyu (James) Kong, Multi-Task Gaussian process upper confidence bound for hyperparameter tuning and its application for simulation studies of additive manufacturing, IISE Transactions, 2022. doi.org/10.1080/24725854.2022.2039813

27-22   Lida Zhu, Shuhao Wang, Hao Lu, Dongxing Qi, Dan Wang, Zhichao Yang, Investigation on synergism between additive and subtractive manufacturing for curved thin-walled structure, Virtual and Physical Prototyping, 17.2; 2022. doi.org/10.1080/17452759.2022.2029009

24-22   Hoon Sohn, Peipei Liu, Hansol Yoon, Kiyoon Yi, Liu Yang, Sangjun Kim, Real-time porosity reduction during metal directed energy deposition using a pulse laser, Journal of Materials Science & Technology, 116; pp. 214-223. doi.org/10.1016/j.jmst.2021.12.013

18-22   Yaohong Xiao, Zixuan Wan, Pengwei Liu, Zhuo Wang, Jingjing Li, Lei Chen, Quantitative simulations of grain nucleation and growth at additively manufactured bimetallic interfaces of SS316L and IN625, Journal of Materials Processing Technology, 302; 117506, 2022. doi.org/10.1016/j.jmatprotec.2022.117506

06-22   Amal Charles, Mohamad Bayat, Ahmed Elkaseer, Lore Thijs, Jesper Henri Hattel, Steffen Scholz, Elucidation of dross formation in laser powder bed fusion at down-facing surfaces: Phenomenon-oriented multiphysics simulation and experimental validation, Additive Manufacturing, 50; 102551, 2022. doi.org/10.1016/j.addma.2021.102551

05-22   Feilong Ji, Xunpeng Qin, Zeqi Hu, Xiaochen Xiong, Mao Ni, Mengwu Wu, Influence of ultrasonic vibration on molten pool behavior and deposition layer forming morphology for wire and arc additive manufacturing, International Communications in Heat and Mass Transfer, 130; 105789, 2022. doi.org/10.1016/j.icheatmasstransfer.2021.105789

150-21   Daniel Knüttel, Stefano Baraldo, Anna Valente, Konrad Wegener, Emanuele Carpanzano, Model based learning for efficient modelling of heat transfer dynamics, Procedia CIRP, 102; pp. 252-257, 2021. doi.org/10.1016/j.procir.2021.09.043

149-21   T. van Rhijn, W. du Preez, M. Maringa, D. Kouprianoff, Towards predicting process parameters for selective laser melting of titanium alloys through the modelling of melt pool characteristics, Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 40.1; 2021. 

148-21   Qian Chen, Multiscale process modeling of residual deformation and defect formation for laser powder bed fusion additive manufacturing, Thesis, University of Pittsburgh, Pittsburgh, PA USA, 2021. 

147-21   Pareekshith Allu, Developing process parameters through CFD simulations, Lasers in Manufacturing Conference, 2021.

143-21   Asif Ur Rehman, Muhammad Arif Mahmood, Fatih Pitir, Metin Uymaz Salamci, Andrei C. Popescu, Ion N. Mihailescu, Spatter formation and splashing induced defects in laser-based powder bed fusion of AlSi10Mg alloy: A novel hydrodynamics modelling with empirical testing, Metals, 11.12; 2023, 2021. doi.org/10.3390/met11122023

142-21   Islam Hassan, Ponnambalam Ravi Selvaganapathy, A microfluidic printhead with integrated hybrid mixing by sequential injection for multimaterial 3D printing, Additive Manufacturing, 102559, 2021. doi.org/10.1016/j.addma.2021.102559

137-21   Ting-Yu Cheng, Ying-Chih Liao, Enhancing drop mixing in powder bed by alternative particle arrangements with contradictory hydrophilicity, Journal of the Taiwan Institute of Chemical Engineers, 104160, 2021. doi.org/10.1016/j.jtice.2021.104160

134-21   Asif Ur Rehman, Muhammad Arif Mahmood, Fatih Pitir, Metin Uymaz Salamci, Andrei C. Popescu, Ion N. Mihailescu, Keyhole formation by laser drilling in laser powder bed fusion of Ti6Al4V biomedical alloy: Mesoscopic computational fluid dynamics simulation versus mathematical modelling using empirical validation, Nanomaterials, 11.2; 3284, 2021. doi.org/10.3390/nano11123284

128-21   Sang-Woo Han, Won-Ik Cho, Lin-Jie Zhang, Suck-Joo Na, Coupled simulation of thermal-metallurgical-mechanical behavior in laser keyhole welding of AH36 steel, Materials & Design, 212; 110275, 2021. doi.org/10.1016/j.matdes.2021.110275

127-21   Jiankang Huang, Zhuoxuan Li, Shurong Yu, Xiaoquan Yu, Ding Fan, Real-time observation and numerical simulation of the molten pool flow and mass transfer behavior during wire arc additive manufacturing, Welding in the World, 2021. doi.org/10.1007/s40194-021-01214-z

123-21   Boxue Song, Tianbiao Yu, Xingyu Jiang, Wenchao Xi, Xiaoli Lin, Zhelun Ma, ZhaoWang, Development of the molten pool and solidification characterization in single bead multilayer direct energy deposition, Additive Manufacturing, 102479, 2021. doi.org/10.1016/j.addma.2021.102479

112-21   Kathryn Small, Ian D. McCue, Katrina Johnston, Ian Donaldson, Mitra L. Taheri, Precision modification of microstructure and properties through laser engraving, JOM, 2021. doi.org/10.1007/s11837-021-04959-6

111-21   Yongki Lee, Jason Cheon, Byung-Kwon Min, Cheolhee Kim, Modelling of fume particle behaviour and coupling glass contamination during vacuum laser beam welding, Science and Technology of Welding and Joining, 2021. doi.org/10.1080/13621718.2021.1990658

110-21   Menglin Liu, Hao Yi, Huajun Cao, Rufeng Huang, Le Jia, Heat accumulation effect in metal droplet-based 3D printing: Evolution mechanism and elimination strategy, Additive Manufacturing, 48.A; 102413, 2021. doi.org/10.1016/j.addma.2021.102413

108-21   Nozomi Taura, Akiya Mitsunobu, Tatsuhiko Sakai, Yasuhiro Okamoto, Akira Okada, Formation and its mechanism of high-speed micro-grooving on metal surface by angled CW laser irradiation, Journal of Laser Micro/Nanoengineering, 16.2, 2021. doi.org/10.2961/jlmn.2021.02.2006

105-21   Jon Spangenberg, Wilson Ricardo Leal da Silva, Raphaël Comminal, Md. Tusher Mollah, Thomas Juul Andersen, Henrik Stang, Numerical simulation of multi-layer 3D concrete printing, RILEM Technical Letters, 6; pp. 119-123, 2021. doi.org/10.21809/rilemtechlett.2021.142

104-21   Lin Chen, Chunming Wang, Gaoyang Mi, Xiong Zhang, Effects of laser oscillating frequency on energy distribution, molten pool morphology and grain structure of AA6061/AA5182 aluminum alloys lap welding, Journal of Materials Research and Technology, 15; pp. 3133-3148, 2021. doi.org/10.1016/j.jmrt.2021.09.141

101-21   R.J.M. Wolfs, T.A.M. Salet, N. Roussel, Filament geometry control in extrusion-based additive manufacturing of concrete: The good, the bad and the ugly, Cement and Concrete Research, 150; 106615, 2021. doi.org/10.1016/j.cemconres.2021.106615

89-21   Wenlin Ye, Jin Bao, Jie Lei, Yichang Huang, Zhihao Li, Peisheng Li, Ying Zhang, Multiphysics modeling of thermal behavior of commercial pure titanium powder during selective laser melting, Metals and Materials International, 2021. doi.org/10.1007/s12540-021-01019-1

81-21   Lin Chen, Gaoyang Mi, Xiong Zhang, Chunming Wang, Effects of sinusoidal oscillating laser beam on weld formation, melt flow and grain structure during aluminum alloys lap welding, Journals of Materials Processing Technology, 298; 117314, 2021. doi.org/10.1016/j.jmatprotec.2021.117314

77-21   Yujie Cui, Yufan Zhao, Haruko Numata, Kenta Yamanaka, Huakang Bian, Kenta Aoyagi, Akihiko Chiba, Effects of process parameters and cooling gas on powder formation during the plasma rotating electrode process, Powder Technology, 393; pp. 301-311, 2021. doi.org/10.1016/j.powtec.2021.07.062

76-21   Md Tusher Mollah, Raphaël Comminal, Marcin P. Serdeczny, David B. Pedersen, Jon Spangenberg, Stability and deformations of deposited layers in material extrusion additive manufacturing, Additive Manufacturing, 46; 102193, 2021. doi.org/10.1016/j.addma.2021.102193

72-21   S. Sabooni, A. Chabok, S.C. Feng, H. Blaauw, T.C. Pijper, H.J. Yang, Y.T. Pei, Laser powder bed fusion of 17–4 PH stainless steel: A comparative study on the effect of heat treatment on the microstructure evolution and mechanical properties, Additive Manufacturing, 46; 102176, 2021. doi.org/10.1016/j.addma.2021.102176

71-21   Yu Hao, Nannan Chena, Hui-Ping Wang, Blair E. Carlson, Fenggui Lu, Effect of zinc vapor forces on spattering in partial penetration laser welding of zinc-coated steels, Journal of Materials Processing Technology, 298; 117282, 2021. doi.org/10.1016/j.jmatprotec.2021.117282

67-21   Lu Wang, Wentao Yan, Thermoelectric magnetohydrodynamic model for laser-based metal additive manufacturing, Physical Review Applied, 15.6; 064051, 2021. doi.org/10.1103/PhysRevApplied.15.064051

61-21   Ian D. McCue, Gianna M. Valentino, Douglas B. Trigg, Andrew M. Lennon, Chuck E. Hebert, Drew P. Seker, Salahudin M. Nimer, James P. Mastrandrea, Morgana M. Trexler, Steven M. Storck, Controlled shape-morphing metallic components for deployable structures, Materials & Design, 208; 109935, 2021. doi.org/10.1016/j.matdes.2021.109935

60-21   Mahyar Khorasani, AmirHossein Ghasemi, Martin Leary, William O’Neil, Ian Gibson, Laura Cordova, Bernard Rolfe, Numerical and analytical investigation on meltpool temperature of laser-based powder bed fusion of IN718, International Journal of Heat and Mass Transfer, 177; 121477, 2021. doi.org/10.1016/j.ijheatmasstransfer.2021.121477

57-21   Dae-Won Cho, Yeong-Do Park, Muralimohan Cheepu, Numerical simulation of slag movement from Marangoni flow for GMAW with computational fluid dynamics, International Communications in Heat and Mass Transfer, 125; 105243, 2021. doi.org/10.1016/j.icheatmasstransfer.2021.105243

55-21   Won-Sang Shin, Dae-Won Cho, Donghyuck Jung, Heeshin Kang, Jeng O Kim, Yoon-Jun Kim, Changkyoo Park, Investigation on laser welding of Al ribbon to Cu sheet: Weldability, microstructure and mechanical and electrical properties, Metals, 11.5; 831, 2021. doi.org/10.3390/met11050831

50-21   Mohamad Bayat, Venkata K. Nadimpalli, Francesco G. Biondani, Sina Jafarzadeh, Jesper Thorborg, Niels S. Tiedje, Giuliano Bissacco, David B. Pedersen, Jesper H. Hattel, On the role of the powder stream on the heat and fluid flow conditions during directed energy deposition of maraging steel—Multiphysics modeling and experimental validation, Additive Manufacturing, 43;102021, 2021. doi.org/10.1016/j.addma.2021.102021

47-21   Subin Shrestha, Kevin Chou, An investigation into melting modes in selective laser melting of Inconel 625 powder: single track geometry and porosity, The International Journal of Advanced Manufacturing Technology, 2021. doi.org/10.1007/s00170-021-07105-3

34-21   Haokun Sun, Xin Chu, Cheng Luo, Haoxiu Chen, Zhiying Liu, Yansong Zhang, Yu Zou, Selective laser melting for joining dissimilar materials: Investigations ofiInterfacial characteristics and in situ alloying, Metallurgical and Materials Transactions A, 52; pp. 1540-1550, 2021. doi.org/10.1007/s11661-021-06178-9

32-21   Shanshan Zhang, Subin Shrestha, Kevin Chou, On mesoscopic surface formation in metal laser powder-bed fusion process, Supplimental Proceedings, TMS 150th Annual Meeting & Exhibition (Virtual), pp. 149-161, 2021. doi.org/10.1007/978-3-030-65261-6_14

22-21   Patiparn Ninpetch, Pruet Kowitwarangkul, Sitthipong Mahathanabodee, Prasert Chalermkarnnon, Phadungsak Rattanadecho, Computational investigation of thermal behavior and molten metal flow with moving laser heat source for selective laser melting process, Case Studies in Thermal Engineering, 24; 100860, 2021. doi.org/10.1016/j.csite.2021.100860

19-21   M.B. Abrami, C. Ransenigo, M. Tocci, A. Pola, M. Obeidi, D. Brabazon, Numerical simulation of laser powder bed fusion processes, La Metallurgia Italiana, February; pp. 81-89, 2021.

16-21   Wenjun Ge, Jerry Y.H. Fuh, Suck Joo Na, Numerical modelling of keyhole formation in selective laser melting of Ti6Al4V, Journal of Manufacturing Processes, 62; pp. 646-654, 2021. doi.org/10.1016/j.jmapro.2021.01.005

11-21   Mohamad Bayat, Venkata K. Nadimpalli, David B. Pedersen, Jesper H. Hattel, A fundamental investigation of thermo-capillarity in laser powder bed fusion of metals and alloys, International Journal of Heat and Mass Transfer, 166; 120766, 2021. doi.org/10.1016/j.ijheatmasstransfer.2020.120766

10-21   Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Kenta Yamanaka, Akihiko Chiba, Thermal properties of powder beds in energy absorption and heat transfer during additive manufacturing with electron beam, Powder Technology, 381; pp. 44-54, 2021. doi.org/10.1016/j.powtec.2020.11.082

9-21   Subin Shrestha, Kevin Chou, A study of transient and steady-state regions from single-track deposition in laser powder bed fusion, Journal of Manufacturing Processes, 61; pp. 226-235, 2021. doi.org/10.1016/j.jmapro.2020.11.023

6-21   Qian Chen, Yunhao Zhao, Seth Strayer, Yufan Zhao, Kenta Aoyagi, Yuichiro Koizumi, Akihiko Chiba, Wei Xiong, Albert C. To, Elucidating the effect of preheating temperature on melt pool morphology variation in Inconel 718 laser powder bed fusion via simulation and experiment, Additive Manufacturing, 37; 101642, 2021. doi.org/10.1016/j.addma.2020.101642

04-21   Won-Ik Cho, Peer Woizeschke, Analysis of molten pool dynamics in laser welding with beam oscillation and filler wire feeding, International Journal of Heat and Mass Transfer, 164; 120623, 2021. doi.org/10.1016/j.ijheatmasstransfer.2020.120623

128-20   Mahmood Al Bashir, Rajeev Nair, Martina M. Sanchez, Anil Mahapatro, Improving fluid retention properties of 316L stainless steel using nanosecond pulsed laser surface texturing, Journal of Laser Applications, 32.4, 2020. doi.org/10.2351/7.0000199

127-20   Eric Riedel, Niklas Bergedieck, Stefan Scharf, CFD simulation based investigation of cavitation cynamics during high intensity ultrasonic treatment of A356, Metals, 10.11; 1529, 2020. doi.org/10.3390/met10111529

126-20   Benjamin Himmel, Material jetting of aluminium: Analysis of a novel additive manufacturing process, Thesis, Technical University of Munich, Munich, Germany, 2020. 

121-20   Yufan Zhao, Yujie Cui, Haruko Numata, Huakang Bian, Kimio Wako, Kenta Yamanaka, Kenta Aoyagi, Akihiko Chiba, Centrifugal granulation behavior in metallic powder fabrication by plasma rotating electrode process, Scientific Reports, 10; 18446, 2020. doi.org/10.1038/s41598-020-75503-w

116-20   Raphael Comminal, Wilson Ricardo Leal da Silva, Thomas Juul Andersen, Henrik Stang, Jon Spangenberg, Modelling of 3D concrete printing based on computational fluid dynamics, Cement and Concrete Research, 138; 106256, 2020. doi.org/10.1016/j.cemconres.2020.106256

112-20   Peng Liu, Lijin Huan, Yu Gan, Yuyu Lei, Effect of plate thickness on weld pool dynamics and keyhole-induced porosity formation in laser welding of Al alloy, The International Journal of Advanced Manufacturing Technology, 111; pp. 735-747, 2020. doi.org/10.1007/s00170-020-05818-5

108-20   Fan Chen, Wentao Yan, High-fidelity modelling of thermal stress for additive manufacturing by linking thermal-fluid and mechanical models, Materials & Design, 196; 109185, 2020. doi.org/10.1016/j.matdes.2020.109185

104-20   Yunfu Tian, Lijun Yang, Dejin Zhao, Yiming Huang, Jiajing Pan, Numerical analysis of powder bed generation and single track forming for selective laser melting of SS316L stainless steel, Journal of Manufacturing Processes, 58; pp. 964-974, 2020. doi.org/10.1016/j.jmapro.2020.09.002

100-20   Raphaël Comminal, Sina Jafarzadeh, Marcin Serdeczny, Jon Spangenberg, Estimations of interlayer contacts in extrusion additive manufacturing using a CFD model, International Conference on Additive Manufacturing in Products and Applications (AMPA), Zurich, Switzerland, September 1-3: Industrializing Additive Manufacturing, pp. 241-250, 2020. doi.org/10.1007/978-3-030-54334-1_17

97-20   Paree Allu, CFD simulation for metal Additive Manufacturing: Applications in laser- and sinter-based processes, Metal AM, 6.4; pp. 151-158, 2020.

95-20   Yufan Zhao, Kenta Aoyagi, Kenta Yamanaka, Akihiko Chiba, Role of operating and environmental conditions in determining molten pool dynamics during electron beam melting and selective laser melting, Additive Manufacturing, 36; 101559, 2020. doi.org/10.1016/j.addma.2020.101559

94-20   Yan Zeng, David Himmler, Peter Randelzhofer, Carolin Körner, Processing of in situ Al3Ti/Al composites by advanced high shear technology: influence of mixing speed, The International Journal of Advanced Manufacturing Technology, 110; pp. 1589-1599, 2020. doi.org/10.1007/s00170-020-05956-w

93-20   H. Hamed Zargari, K. Ito, M. Kumar, A. Sharma, Visualizing the vibration effect on the tandem-pulsed gas metal arc welding in the presence of surface tension active elements, International Journal of Heat and Mass Transfer, 161; 120310, 2020. doi.org/10.1016/j.ijheatmasstransfer.2020.120310

90-20   Guangxi Zhao, Jun Du, Zhengying Wei, Siyuan Xu, Ruwei Geng, Numerical analysis of aluminum alloy fused coating process, Journal of the Brazilian Society of Mechanical Science and Engineering, 42; 483, 2020. doi.org/10.1007/s40430-020-02569-y

85-20   Wenkang Huang, Hongliang Wang, Teresa Rinker, Wenda Tan, Investigation of metal mixing in laser keyhold welding of dissimilar metals, Materials & Design, 195; 109056, 2020. doi.org/10.1016/j.matdes.2020.109056

82-20   Pan Lu, Zhang Cheng-Lin, Wang Liang, Liu Tong, Liu Jiang-lin, Molten pool structure, temperature and velocity flow in selective laser melting AlCu5MnCdVA alloy, Materials Research Express, 7; 086516, 2020. doi.org/10.1088/2053-1591/abadcf

80-20   Yujie Cui, Yufan Zhao, Haruko Numata, Huakang Bian, Kimio Wako, Kento Yamanaka, Kenta Aoyagi, Chen Zhang, Akihiko Chiba, Effects of plasma rotating electrode process parameters on the particle size distribution and microstructure of Ti-6Al-4 V alloy powder, Powder Technology, 376; pp. 363-372, 2020. doi.org/10.1016/j.powtec.2020.08.027

78-20   F.Q. Liu, L. Wei, S.Q. Shi, H.L. Wei, On the varieties of build features during multi-layer laser directed energy deposition, Additive Manufacturing, 36; 101491, 2020. doi.org/10.1016/j.addma.2020.101491

75-20   Nannan Chen, Zixuan Wan, Hui-Ping Wang, Jingjing Li, Joshua Solomon, Blair E. Carlson, Effect of Al single bond Si coating on laser spot welding of press hardened steel and process improvement with annular stirring, Materials & Design, 195; 108986, 2020. doi.org/10.1016/j.matdes.2020.108986

72-20   Yujie Cui, Kenta Aoyagi, Yufan Zhao, Kenta Yamanaka, Yuichiro Hayasaka, Yuichiro Koizumi, Tadashi Fujieda, Akihiko Chiba, Manufacturing of a nanosized TiB strengthened Ti-based alloy via electron beam powder bed fusion, Additive Manufacturing, 36; 101472, 2020. doi.org/10.1016/j.addma.2020.101472

64-20   Dong-Rong Liu, Shuhao Wang, Wentao Yan, Grain structure evolution in transition-mode melting in direct energy deposition, Materials & Design, 194; 108919, 2020. doi.org/10.1016/j.matdes.2020.108919

61-20   Raphael Comminal, Wilson Ricardo Leal da Silva, Thomas Juul Andersen, Henrik Stang, Jon Spangenberg, Influence of processing parameters on the layer geometry in 3D concrete printing: Experiments and modelling, 2nd RILEM International Conference on Concrete and Digital Fabrication, RILEM Bookseries, 28; pp. 852-862, 2020. doi.org/10.1007/978-3-030-49916-7_83

60-20   Marcin P. Serdeczny, Raphaël Comminal, Md. Tusher Mollah, David B. Pedersen, Jon Spangenberg, Numerical modeling of the polymer flow through the hot-end in filament-based material extrusion additive manufacturing, Additive Manufacturing, 36; 101454, 2020. doi.org/10.1016/j.addma.2020.101454

58-20   H.L. Wei, T. Mukherjee, W. Zhang, J.S. Zuback, G.L. Knapp, A. De, T. DebRoy, Mechanistic models for additive manufacturing of metallic components, Progress in Materials Science, 116; 100703, 2020. doi.org/10.1016/j.pmatsci.2020.100703

55-20   Masoud Mohammadpour, Experimental study and numerical simulation of heat transfer and fluid flow in laser welded and brazed joints, Thesis, Southern Methodist University, Dallas, TX, US; Available in Mechanical Engineering Research Theses and Dissertations, 24, 2020.

48-20   Masoud Mohammadpour, Baixuan Yang, Hui-Ping Wang, John Forrest, Michael Poss, Blair Carlson, Radovan Kovacevica, Influence of laser beam inclination angle on galvanized steel laser braze quality, Optics and Laser Technology, 129; 106303, 2020. doi.org/10.1016/j.optlastec.2020.106303

34-20   Binqi Liu, Gang Fang, Liping Lei, Wei Liu, A new ray tracing heat source model for mesoscale CFD simulation of selective laser melting (SLM), Applied Mathematical Modeling, 79; pp. 506-520, 2020. doi.org/10.1016/j.apm.2019.10.049

27-20   Xuesong Gao, Guilherme Abreu Farira, Wei Zhang and Kevin Wheeler, Numerical analysis of non-spherical particle effect on molten pool dynamics in laser-powder bed fusion additive manufacturing, Computational Materials Science, 179, art. no. 109648, 2020. doi.org/10.1016/j.commatsci.2020.109648

26-20   Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Kenta Yamanaka and Akihiko Chiba, Isothermal γ → ε phase transformation behavior in a Co-Cr-Mo alloy depending on thermal history during electron beam powder-bed additive manufacturing, Journal of Materials Science & Technology, 50, pp. 162-170, 2020. doi.org/10.1016/j.jmst.2019.11.040

21-20   Won-Ik Cho and Peer Woizeschke, Analysis of molten pool behavior with buttonhole formation in laser keyhole welding of sheet metal, International Journal of Heat and Mass Transfer, 152, art. no. 119528, 2020. doi.org/10.1016/j.ijheatmasstransfer.2020.119528

06-20  Wei Xing, Di Ouyang, Zhen Chen and Lin Liu, Effect of energy density on defect evolution in 3D printed Zr-based metallic glasses by selective laser melting, Science China Physics, Mechanics & Astronomy, 63, art. no. 226111, 2020. doi.org/10.1007/s11433-019-1485-8

04-20   Santosh Reddy Sama, Tony Badamo, Paul Lynch and Guha Manogharan, Novel sprue designs in metal casting via 3D sand-printing, Additive Manufacturing, 25, pp. 563-578, 2019. doi.org/10.1016/j.addma.2018.12.009

02-20   Dongsheng Wu, Shinichi Tashiro, Ziang Wu, Kazufumi Nomura, Xueming Hua, and Manabu Tanaka, Analysis of heat transfer and material flow in hybrid KPAW-GMAW process based on the novel three dimensional CFD simulation, International Journal of Heat and Mass Transfer, 147, art. no. 118921, 2020. doi.org/10.1016/j.ijheatmasstransfer.2019.118921

01-20   Xiang Huang, Siying Lin, Zhenxiang Bu, Xiaolong Lin, Weijin Yi, Zhihong Lin, Peiqin Xie, and Lingyun Wang, Research on nozzle and needle combination for high frequency piezostack-driven dispenser, International Journal of Adhesion and Adhesives, 96, 2020. doi.org/10.1016/j.ijadhadh.2019.102453

88-19   Bo Cheng and Charles Tuffile, Numerical study of porosity formation with implementation of laser multiple reflection in selective laser melting, Proceedings Volume 1: Additive Manufacturing; Manufacturing Equipment and Systems; Bio and Sustainable Manufacturing, ASME 2019 14th International Manufacturing Science and Engineering Conference, Erie, Pennsylvania, USA, June 10-14, 2019. doi.org/10.1115/MSEC2019-2891

87-19   Shuhao Wang, Lida Zhu, Jerry Ying His Fuh, Haiquan Zhang, and Wentao Yan, Multi-physics modeling and Gaussian process regression analysis of cladding track geometry for direct energy deposition, Optics and Lasers in Engineering, 127:105950, 2019. doi.org/10.1016/j.optlaseng.2019.105950

78-19   Bo Cheng, Lukas Loeber, Hannes Willeck, Udo Hartel, and Charles Tuffile, Computational investigation of melt pool process dynamics and pore formation in laser powder bed fusion, Journal of Materials Engineering and Performance, 28:11, 6565-6578, 2019. doi.org/10.1007/s11665-019-04435-y

77-19   David Souders, Pareekshith Allu, Anurag Chandorkar, and Ruendy Castillo, Application of computational fluid dynamics in developing process parameters for additive manufacturing, Additive Manufacturing Journal, 9th International Conference on 3D Printing and Additive Manufacturing Technologies (AM 2019), Bangalore, India, September 7-9, 2019.

75-19   Raphaël Comminal, Marcin Piotr Serdeczny, Navid Ranjbar, Mehdi Mehrali, David Bue Pedersen, Henrik Stang, Jon Spangenberg, Modelling of material deposition in big area additive manufacturing and 3D concrete printing, Proceedings, Advancing Precision in Additive Manufacturing, Nantes, France, September 16-18, 2019.

73-19   Baohua Chang, Zhang Yuan, Hao Cheng, Haigang Li, Dong Du 1, and Jiguo Shan, A study on the influences of welding position on the keyhole and molten pool behavior in laser welding of a titanium alloy, Metals, 9:1082, 2019. doi.org/10.3390/met9101082

57-19     Shengjie Deng, Hui-Ping Wang, Fenggui Lu, Joshua Solomon, and Blair E. Carlson, Investigation of spatter occurrence in remote laser spiral welding of zinc-coated steels, International Journal of Heat and Mass Transfer, Vol. 140, pp. 269-280, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.06.009

53-19     Mohamad Bayat, Aditi Thanki, Sankhya Mohanty, Ann Witvrouw, Shoufeng Yang, Jesper Thorborg, Niels Skat Tieldje, and Jesper Henri Hattel, Keyhole-induced porosities in Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V: High-fidelity modelling and experimental validation, Additive Manufacturing, Vol. 30, 2019. doi.org/10.1016/j.addma.2019.100835

51-19     P. Ninpetch, P. Kowitwarangkul, S. Mahathanabodee, R. Tongsri, and P. Ratanadecho, Thermal and melting track simulations of laser powder bed fusion (L-PBF), International Conference on Materials Research and Innovation (ICMARI), Bangkok, Thailand, December 17-21, 2018. IOP Conference Series: Materials Science and Engineering, Vol. 526, 2019. doi.org/10.1088/1757-899X/526/1/012030

46-19     Hongze Wang and Yu Zou, Microscale interaction between laser and metal powder in powder-bed additive manufacturing: Conduction mode versus keyhole mode, International Journal of Heat and Mass Transfer, Vol. 142, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.118473

45-19     Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Kenta Yamanaka, and Akihiko Chiba, Manipulating local heat accumulation towards controlled quality and microstructure of a Co-Cr-Mo alloy in powder bed fusion with electron beam, Materials Letters, Vol. 254, pp. 269-272, 2019. doi.org/10.1016/j.matlet.2019.07.078

44-19     Guoxiang Xu, Lin Li, Houxiao Wang, Pengfei Li, Qinghu Guo, Qingxian Hu, and Baoshuai Du, Simulation and experimental studies of keyhole induced porosity in laser-MIG hybrid fillet welding of aluminum alloy in the horizontal position, Optics & Laser Technology, Vol. 119, 2019. doi.org/10.1016/j.optlastec.2019.105667

38-19     Subin Shrestha and Y. Kevin Chou, A numerical study on the keyhole formation during laser powder bed fusion process, Journal of Manufacturing Science and Engineering, Vol. 141, No. 10, 2019. doi.org/10.1115/1.4044100

34-19     Dae-Won Cho, Jin-Hyeong Park, and Hyeong-Soon Moon, A study on molten pool behavior in the one pulse one drop GMAW process using computational fluid dynamics, International Journal of Heat and Mass Transfer, Vol. 139, pp. 848-859, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.05.038

30-19     Mohamad Bayat, Sankhya Mohanty, and Jesper Henri Hattel, Multiphysics modelling of lack-of-fusion voids formation and evolution in IN718 made by multi-track/multi-layer L-PBF, International Journal of Heat and Mass Transfer, Vol. 139, pp. 95-114, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.05.003

29-19     Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Daixiu Wei, Kenta Yamanaka, and Akihiko Chiba, Comprehensive study on mechanisms for grain morphology evolution and texture development in powder bed fusion with electron beam of Co–Cr–Mo alloy, Materialia, Vol. 6, 2019. doi.org/10.1016/j.mtla.2019.100346

28-19     Pareekshith Allu, Computational fluid dynamics modeling in additive manufacturing processes, The Minerals, Metals & Materials Society (TMS) 148th Annual Meeting & Exhibition, San Antonio, Texas, USA, March 10-14, 2019.

24-19     Simulation Software: Use, Advantages & Limitations, The Additive Manufacturing and Welding Magazine, Vol. 2, No. 2, 2019

22-19     Hunchul Jeong, Kyungbae Park, Sungjin Baek, and Jungho Cho, Thermal efficiency decision of variable polarity aluminum arc welding through molten pool analysis, International Journal of Heat and Mass Transfer, Vol. 138, pp. 729-737, 2019. doi.org/10.1016/j.ijheatmasstransfer.2019.04.089

07-19   Guangxi Zhao, Jun Du, Zhengying Wei, Ruwei Geng and Siyuan Xu, Numerical analysis of arc driving forces and temperature distribution in pulsed TIG welding, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 41, No. 60, 2019. doi.org/10.1007/s40430-018-1563-0

04-19   Santosh Reddy Sama, Tony Badamo, Paul Lynch and Guha Manogharan, Novel sprue designs in metal casting via 3D sand-printing, Additive Manufacturing, Vol. 25, pp. 563-578, 2019. doi.org/10.1016/j.addma.2018.12.009

03-19   Dongsheng Wu, Anh Van Nguyen, Shinichi Tashiro, Xueming Hua and Manabu Tanaka, Elucidation of the weld pool convection and keyhole formation mechanism in the keyhold plasma arc welding, International Journal of Heat and Mass Transfer, Vol. 131, pp. 920-931, 2019. doi.org/10.1016/j.ijheatmasstransfer.2018.11.108

97-18   Wentao Yan, Ya Qian, Wenjun Ge, Stephen Lin, Wing Kam Liu, Feng Lin, Gregory J. Wagner, Meso-scale modeling of multiple-layer fabrication process in Selective Electron Beam Melting: Inter-layer/track voids formation, Materials & Design, 2018. doi.org/10.1016/j.matdes.2017.12.031

84-18   Bo Cheng, Xiaobai Li, Charles Tuffile, Alexander Ilin, Hannes Willeck and Udo Hartel, Multi-physics modeling of single track scanning in selective laser melting: Powder compaction effect, Proceedings of the 29th Annual International Solid Freeform Fabrication Symposium, pp. 1887-1902, 2018.

81-18 Yufan Zhao, Yuichiro Koizumi, Kenta Aoyagi, Daixiu Wei, Kenta Yamanaka and Akihiko Chiba, Molten pool behavior and effect of fluid flow on solidification conditions in selective electron beam melting (SEBM) of a biomedical Co-Cr-Mo alloy, Additive Manufacturing, Vol. 26, pp. 202-214, 2019. doi.org/10.1016/j.addma.2018.12.002

77-18   Jun Du and Zhengying Wei, Numerical investigation of thermocapillary-induced deposited shape in fused-coating additive manufacturing process of aluminum alloy, Journal of Physics Communications, Vol. 2, No. 11, 2018. doi.org/10.1088/2399-6528/aaedc7

76-18   Yu Xiang, Shuzhe Zhang, Zhengying We, Junfeng Li, Pei Wei, Zhen Chen, Lixiang Yang and Lihao Jiang, Forming and defect analysis for single track scanning in selective laser melting of Ti6Al4V, Applied Physics A, 124:685, 2018. doi.org/10.1007/s00339-018-2056-9

74-18   Paree Allu, CFD simulations for laser welding of Al Alloys, Proceedings, Die Casting Congress & Exposition, Indianapolis, IN, October 15-17, 2018.

72-18   Hunchul Jeong, Kyungbae Park, Sungjin Baek, Dong-Yoon Kim, Moon-Jin Kang and Jungho Cho, Three-dimensional numerical analysis of weld pool in GMAW with fillet joint, International Journal of Precision Engineering and Manufacturing, Vol. 19, No. 8, pp. 1171-1177, 2018. doi.org/10.1007/s12541-018-0138-4

60-18   R.W. Geng, J. Du, Z.Y. Wei and G.X. Zhao, An adaptive-domain-growth method for phase field simulation of dendrite growth in arc preheated fused-coating additive manufacturing, IOP Conference Series: Journal of Physics: Conference Series 1063, 012077, 2018. doi.org/10.1088/1742-6596/1063/1/012077

59-18   Guangxi Zhao, Jun Du, Zhengying Wei, Ruwei Geng and Siyuan Xu, Coupling analysis of molten pool during fused coating process with arc preheating, IOP Conference Series: Journal of Physics: Conference Series 1063, 012076, 2018. doi.org/10.1088/1742-6596/1063/1/012076 (Available at http://iopscience.iop.org/article/10.1088/1742-6596/1063/1/012076/pdf and in shared drive)

58-18   Siyuan Xu, Zhengying Wei, Jun Du, Guangxi Zhao and Wei Liu, Numerical simulation and analysis of metal fused coating forming, IOP Conference Series: Journal of Physics: Conference Series 1063, 012075, 2018. doi.org/10.1088/1742-6596/1063/1/012075

55-18   Jason Cheon, Jin-Young Yoon, Cheolhee Kim and Suck-Joo Na, A study on transient flow characteristic in friction stir welding with realtime interface tracking by direct surface calculation, Journal of Materials Processing Tech., vol. 255, pp. 621-634, 2018.

54-18   V. Sukhotskiy, P. Vishnoi, I. H. Karampelas, S. Vader, Z. Vader, and E. P. Furlani, Magnetohydrodynamic drop-on-demand liquid metal additive manufacturing: System overview and modeling, Proceedings of the 5th International Conference of Fluid Flow, Heat and Mass Transfer, Niagara Falls, Canada, June 7 – 9, 2018; Paper no. 155, 2018. doi.org/10.11159/ffhmt18.155

52-18   Michael Hilbinger, Claudia Stadelmann, Matthias List and Robert F. Singer, Temconex® – Kontinuierliche Pulverextrusion: Verbessertes Verständnis mit Hilfe der numerischen Simulation, Hochleistungsmetalle und Prozesse für den Leichtbau der Zukunft, Tagungsband 10. Ranshofener Leichtmetalltage, 13-14 Juni 2018, Linz, pp. 175-186, 2018.

38-18   Zhen Chen, Yu Xiang, Zhengying Wei, Pei Wei, Bingheng Lu, Lijuan Zhang and Jun Du, Thermal dynamic behavior during selective laser melting of K418 superalloy: numerical simulation and experimental verification, Applied Physics A, vol. 124, pp. 313, 2018. doi.org/10.1007/s00339-018-1737-8

19-18   Chenxiao Zhu, Jason Cheon, Xinhua Tang, Suck-Joo Na, and Haichao Cui, Molten pool behaviors and their influences on welding defects in narrow gap GMAW of 5083 Al-alloy, International Journal of Heat and Mass Transfer, vol. 126:A, pp.1206-1221, 2018. doi.org/10.1016/j.ijheatmasstransfer.2018.05.132

16-18   P. Schneider, V. Sukhotskiy, T. Siskar, L. Christie and I.H. Karampelas, Additive Manufacturing of Microfluidic Components via Wax Extrusion, Biotech, Biomaterials and Biomedical TechConnect Briefs, vol. 3, pp. 162 – 165, 2018.

09-18   The Furlani Research Group, Magnetohydrodynamic Liquid Metal 3D Printing, Department of Chemical and Biological Engineering, © University at Buffalo, May 2018.

08-18   Benjamin Himmel, Dominik Rumschöttel and Wolfram Volk, Thermal process simulation of droplet based metal printing with aluminium, Production Engineering, March 2018 © German Academic Society for Production Engineering (WGP) 2018.

07-18   Yu-Che Wu, Cheng-Hung San, Chih-Hsiang Chang, Huey-Jiuan Lin, Raed Marwan, Shuhei Baba and Weng-Sing Hwang, Numerical modeling of melt-pool behavior in selective laser melting with random powder distribution and experimental validation, Journal of Materials Processing Tech. 254 (2018) 72–78.

60-17   Pei Wei, Zhengying Wei, Zhen Chen, Yuyang He and Jun Du, Thermal behavior in single track during selective laser melting of AlSi10Mg powder, Applied Physics A: Materials Science & Processing, 123:604, 2017. doi.org/10.1007/z00339-017-1194-9

51-17   Koichi Ishizaka, Keijiro Saitoh, Eisaku Ito, Masanori Yuri, and Junichiro Masada, Key Technologies for 1700°C Class Ultra High Temperature Gas Turbine, Mitsubishi Heavy Industries Technical Review, vol. 54, no. 3, 2017.

49-17   Yu-Che Wu, Weng-Sing Hwang, Cheng-Hung San, Chih-Hsiang Chang and Huey-Jiuan Lin, Parametric study of surface morphology for selective laser melting on Ti6Al4V powder bed with numerical and experimental methods, International Journal of Material Forming, © Springer-Verlag France SAS, part of Springer Nature 2017. doi.org/10.1007/s12289-017-1391-2.

37-17   V. Sukhotskiy, I. H. Karampelas, G. Garg, A. Verma, M. Tong, S. Vader, Z. Vader, and E. P. Furlani, Magnetohydrodynamic Drop-on-Demand Liquid Metal 3D Printing, Solid Freeform Fabrication 2017: Proceedings of the 28th Annual International Solid Freeform Fabrication Symposium – An Additive Manufacturing Conference

15-17   I.H. Karampelas, S. Vader, Z. Vader, V. Sukhotskiy, A. Verma, G. Garg, M. Tong and E.P. Furlani, Drop-on-Demand 3D Metal Printing, Informatics, Electronics and Microsystems TechConnect Briefs 2017, Vol. 4

14-17   Jason Cheon and Suck-Joo Na, Prediction of welding residual stress with real-time phase transformation by CFD thermal analysis, International Journal of Mechanical Sciences 131–132 (2017) 37–51.

91-16   Y. S. Lee and D. F. Farson, Surface tension-powered build dimension control in laser additive manufacturing process, Int J Adv Manuf Technol (2016) 85:1035–1044, doi.org/10.1007/s00170-015-7974-5.

84-16   Runqi Lin, Hui-ping Wang, Fenggui Lu, Joshua Solomon, Blair E. Carlson, Numerical study of keyhole dynamics and keyhole-induced porosity formation in remote laser welding of Al alloys, International Journal of Heat and Mass Transfer 108 (2017) 244–256, Available online December 2016.

68-16   Dongsheng Wu, Xueming Hua, Dingjian Ye and Fang Li, Understanding of humping formation and suppression mechanisms using the numerical simulation, International Journal of Heat and Mass Transfer, Volume 104, January 2017, Pages 634–643, Published online 2016.

39-16   Chien-Hsun Wang, Ho-Lin Tsai, Yu-Che Wu and Weng-Sing Hwang, Investigation of molten metal droplet deposition and solidification for 3D printing techniques, IOP Publishing, J. Micromech. Microeng. 26 (2016) 095012 (14pp), doi: 10.1088/0960-1317/26/9/095012, July 8, 2016

29-16   Scott Vader, Zachary Vader, Ioannis H. Karampelas and Edward P. Furlani, Advances in Magnetohydrodynamic Liquid Metal Jet Printing, Nanotech 2016 Conference & Expo, May 22-25, Washington, DC.

26-16   Y.S. Lee and W. Zhang, Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base superalloy fabricated by laser powder bed fusion, S2214-8604(16)30087-2, doi.org/10.1016/j.addma.2016.05.003, ADDMA 86.

123-15   Koji Tsukimoto, Masashi Kitamura, Shuji Tanigawa, Sachio Shimohata, and Masahiko Mega, Laser welding repair for single crystal blades, Proceedings of International Gas Turbine Congress, pp. 1354-1358, 2015.

122-15   Y.S. Lee, W. Zhang, Mesoscopic simulation of heat transfer and fluid flow in laser powder bed additive manufacturing, Proceedings, 26th Solid Freeform Fabrication Symposium, Austin, Texas, 2015. 

116-15   Yousub Lee, Simulation of Laser Additive Manufacturing and its Applications, Ph.D. Thesis: Graduate Program in Welding Engineering, The Ohio State University, 2015, Copyright by Yousub Lee 2015

103-15   Ligang Wu, Jason Cheon, Degala Venkata Kiran, and Suck-Joo Na, CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models, Journal of Materials Processing Technology, Available online December 29, 2015

96-15   Jason Cheon, Degala Venkata Kiran, and Suck-Joo Na, Thermal metallurgical analysis of GMA welded AH36 steel using CFD – FEM framework, Materials & Design, Volume 91, February 5 2016, Pages 230-241, published online November 2015

86-15   Yousub Lee and Dave F. Farson, Simulation of transport phenomena and melt pool shape for multiple layer additive manufacturing, J. Laser Appl. 28, 012006 (2016). doi: 10.2351/1.4935711, published online 2015.

63-15   Scott Vader, Zachary Vader, Ioannis H. Karampelas and Edward P. Furlani, Magnetohydrodynamic Liquid Metal Jet Printing, TechConnect World Innovation Conference & Expo, Washington, D.C., June 14-17, 2015

46-15   Adwaith Gupta, 3D Printing Multi-Material, Single Printhead Simulation, Advanced Qualification of Additive Manufacturing Materials Workshop, July 20 – 21, 2015, Santa Fe, NM

25-15   Dae-Won Cho and Suck-Joo Na, Molten pool behaviors for second pass V-groove GMAW, International Journal of Heat and Mass Transfer 88 (2015) 945–956.

21-15   Jungho Cho, Dave F. Farson, Kendall J. Hollis and John O. Milewski, Numerical analysis of weld pool oscillation in laser welding, Journal of Mechanical Science and Technology 29 (4) (2015) 1715~1722, www.springerlink.com/content/1738-494x, doi.org/10.1007/s12206-015-0344-2.

82-14  Yousub Lee, Mark Nordin, Sudarsanam Suresh Babu, and Dave F. Farson, Effect of Fluid Convection on Dendrite Arm Spacing in Laser Deposition, Metallurgical and Materials Transactions B, August 2014, Volume 45, Issue 4, pp 1520-1529

59-14   Y.S. Lee, M. Nordin, S.S. Babu, and D.F. Farson, Influence of Fluid Convection on Weld Pool Formation in Laser Cladding, Welding Research/ August 2014, VOL. 93

18-14  L.J. Zhang, J.X. Zhang, A. Gumenyuk, M. Rethmeier, and S.J. Na, Numerical simulation of full penetration laser welding of thick steel plate with high power high brightness laser, Journal of Materials Processing Technology (2014), doi.org/10.1016/j.jmatprotec.2014.03.016.

36-13  Dae-Won Cho,Woo-Hyun Song, Min-Hyun Cho, and Suck-Joo Na, Analysis of Submerged Arc Welding Process by Three-Dimensional Computational Fluid Dynamics Simulations, Journal of Materials Processing Technology, 2013. doi.org/10.1016/j.jmatprotec.2013.06.017

12-13 D.W. Cho, S.J. Na, M.H. Cho, J.S. Lee, A study on V-groove GMAW for various welding positions, Journal of Materials Processing Technology, April 2013, doi.org/10.1016/j.jmatprotec.2013.02.015.

01-13  Dae-Won Cho & Suck-Joo Na & Min-Hyun Cho & Jong-Sub Lee, Simulations of weld pool dynamics in V-groove GTA and GMA welding, Weld World, doi.org/10.1007/s40194-012-0017-z, © International Institute of Welding 2013.

63-12  D.W. Cho, S.H. Lee, S.J. Na, Characterization of welding arc and weld pool formation in vacuum gas hollow tungsten arc welding, Journal of Materials Processing Technology, doi.org/10.1016/j.jmatprotec.2012.09.024, September 2012.

77-10  Lim, Y. C.; Yu, X.; Cho, J. H.; et al., Effect of magnetic stirring on grain structure refinement Part 1-Autogenous nickel alloy welds, Science and Technology of Welding and Joining, Volume: 15 Issue: 7, Pages: 583-589, doi.org/10.1179/136217110X12720264008277, October 2010

18-10 K Saida, H Ohnishi, K Nishimoto, Fluxless laser brazing of aluminium alloy to galvanized steel using a tandem beam–dissimilar laser brazing of aluminium alloy and steels, Welding International, 2010

58-09  Cho, Jung-Ho; Farson, Dave F.; Milewski, John O.; et al., Weld pool flows during initial stages of keyhole formation in laser welding, Journal of Physics D-Applied Physics, Volume: 42 Issue: 17 Article Number: 175502 ; doi.org/10.1088/0022-3727/42/17/175502, September 2009

57-09  Lim, Y. C.; Farson, D. F.; Cho, M. H.; et al., Stationary GMAW-P weld metal deposit spreading, Science and Technology of Welding and Joining, Volume: 14 Issue: 7 ;Pages: 626-635, doi.org/10.1179/136217109X441173, October 2009

1-09 J.-H. Cho and S.-J. Na, Three-Dimensional Analysis of Molten Pool in GMA-Laser Hybrid Welding, Welding Journal, February 2009, Vol. 88

52-07   Huey-Jiuan Lin and Wei-Kuo Chang, Design of a sheet forming apparatus for overflow fusion process by numerical simulation, Journal of Non-Crystalline Solids 353 (2007) 2817–2825.

50-07  Cho, Min Hyun; Farson, Dave F., Understanding bead hump formation in gas metal arc welding using a numerical simulation, Metallurgical and Mateials Transactions B-Process Metallurgy and Materials Processing Science, Volume: 38, Issue: 2, Pages: 305-319, doi.org/10.1007/s11663-007-9034-5, April 2007

49-07  Cho, M. H.; Farson, D. F., Simulation study of a hybrid process for the prevention of weld bead hump formation, Welding Journal Volume: 86, Issue: 9, Pages: 253S-262S, September 2007

48-07  Cho, M. H.; Farson, D. F.; Lim, Y. C.; et al., Hybrid laser/arc welding process for controlling bead profile, Science and Technology of Welding and Joining, Volume: 12 Issue: 8, Pages: 677-688, doi.org/10.1179/174329307X236878, November 2007

47-07   Min Hyun Cho, Dave F. Farson, Understanding Bead Hump Formation in Gas Metal Arc Welding Using a Numerical Simulation, Metallurgical and Materials Transactions B, Volume 38, Issue 2, pp 305-319, April 2007

36-06  Cho, M. H.; Lim, Y. C.; Farson, D. F., Simulation of weld pool dynamics in the stationary pulsed gas metal arc welding process and final weld shape, Welding Journal, Volume: 85 Issue: 12, Pages: 271S-283S, December 2006

Initiating Homogeneous Bubbles in Pure Liquid

Initiating Homogeneous Bubbles in Pure Liquid

  1. Barkhudarov and C.W. Hirt

Flow Science, Inc.

The combined Temperature-Dependent-Cavitation and Homogenous Bubble models work together as a way to simulate the formation and growth of vapor bubbles by locally heating a liquid. The Homogeneous Bubble model is only activated when a bubble has a size that encompasses at least one complete grid cell, i.e., can be resolved as a “bubble” or void region.

The Cavitation model contains a mechanism for the initiation of bubbles, which works in the follow way. At the end of each time cycle of a transient computation every grid cell containing liquid is tested to see if its pressure is less than the saturation pressure corresponding to the temperature in the cell. The saturation pressure is computed from the pressure-temperature saturation relation specified by the user (e.g., usually a Clapeyron relation). If the cell pressure is less than its saturation pressure it is assumed that boiling can begin. The essential assumption is that there exist sufficient impurities or nucleation sites for this to happen. A very simple model nucleation has been incorporated into FLOW-3D®.

Once a cell has been identified for possible boiling it is given a time delay before vaporization begins. For vaporization to occur it is necessary to have at least 1% void fraction in the cell. This small void can be thought of as the nucleation process. The time delay is input as variable CAVRT (denoted as Ccav in the following).

Thermal Bubble Jets

Thermal Bubble Jets

잉크젯은 높은 품질의 디지털 인쇄를 생산하기 위해 생성되는 몇 가지 방법이 있습니다. 하나의 효과적인 방법은 노즐에서 잉크를 밀어 확장 및 토출되는 잉크를 밀어 다시 노즐 안으로 잉크를 빨아 잉크의 증기 거품을 만드는 것입니다. 이 유체 동력학 공정은 유체와 증기 모두에 대해서 열전달, 상 변화, 압력 역학의 복잡한 혼합을 포함하게 됩니다.

Bubble Modeling Options

  • Adiabatic Vapor Bubbles—No heat exchange to surroundings
  • Vapor Bubbles with Heat Transfer—Heat is transferred to/from fluid and solids
  • Vapor Bubbles—Heat Transfer and Vaporization/Condensation

Alternative Drop Ejector Architecture from Eastman Kodak

Comparison between physical experiments (top row) and simulation (bottom row) – Early experimental device configuration. Image courtesy of Eastman Kodak.

전류가 상기 이젝터의 베이스에 heater를 통과 할 때 아래 그림 어떻게 증기 기포가 형성되는지를 나타냅니다. 잉크의 증발에 의한 버블 형성은 운동 이론 상 변화 모델의 적용을 받습니다. 거품을 확장하기 시작하고 증기 기포의 표면에 응축 냉각 직후의 원인이 차례로 핀치 오프 노즐에서 추력 잉크를 일으키고 붕괴합니다. 표면 장력과 점성 힘은 잉크젯 및 이산 방울로의 전환의 역학을 크게 적용 받습니다.

Thermal Bubble Videos