Qian Chen, PhD

University of Pittsburgh, 2021

레이저 분말 베드 퓨전(L-PBF) 적층 제조(AM)는 우수한 기계적 특성으로 그물 모양에 가까운 복잡한 부품을 생산할 수 있습니다. 그러나 빌드 실패 및 다공성과 같은 결함으로 이어지는 원치 않는 잔류 응력 및 왜곡이 L-PBF의 광범위한 적용을 방해하고 있습니다.

L-PBF의 잠재력을 최대한 실현하기 위해 잔류 변형, 용융 풀 및 다공성 형성을 예측하는 다중 규모 모델링 방법론이 개발되었습니다. L-PBF의 잔류 변형 및 응력을 부품 규모에서 예측하기 위해 고유 변형 방법을 기반으로 하는 다중 규모 프로세스 모델링 프레임워크가 제안됩니다.

고유한 변형 벡터는 마이크로 스케일에서 충실도가 높은 상세한 다층 프로세스 시뮬레이션에서 추출됩니다. 균일하지만 이방성인 변형은 잔류 왜곡 및 응력을 예측하기 위해 준 정적 평형 유한 요소 분석(FEA)에서 레이어별로 L-PBF 부품에 적용됩니다.

부품 규모에서의 잔류 변형 및 응력 예측 외에도 분말 규모의 다중물리 모델링을 수행하여 공정 매개변수, 예열 온도 및 스패터링 입자에 의해 유도된 용융 풀 변동 및 결함 형성을 연구합니다. 이러한 요인과 관련된 용융 풀 역학 및 다공성 형성 메커니즘은 시뮬레이션 및 실험을 통해 밝혀졌습니다.

제안된 부품 규모 잔류 응력 및 왜곡 모델을 기반으로 경로 계획 방법은 큰 잔류 변형 및 건물 파손을 방지하기 위해 주어진 형상에 대한 레이저 스캐닝 경로를 조정하기 위해 개발되었습니다.

연속 및 아일랜드 스캐닝 전략을 위한 기울기 기반 경로 계획이 공식화되고 공식화된 컴플라이언스 및 스트레스 최소화 문제에 대한 전체 감도 분석이 수행됩니다. 이 제안된 경로 계획 방법의 타당성과 효율성은 AconityONE L-PBF 시스템을 사용하여 실험적으로 입증되었습니다.

또한 기계 학습을 활용한 데이터 기반 프레임워크를 개발하여 L-PBF에 대한 부품 규모의 열 이력을 예측합니다. 본 연구에서는 실시간 열 이력 예측을 위해 CNN(Convolutional Neural Network)과 RNN(Recurrent Neural Network)을 포함하는 순차적 기계 학습 모델을 제안합니다.

유한 요소 해석과 비교하여 100배의 예측 속도 향상이 달성되어 실제 제작 프로세스보다 빠른 예측이 가능하고 실시간 온도 프로파일을 사용할 수 있습니다.

Laser powder bed fusion (L-PBF) additive manufacturing (AM) is capable of producing complex parts near net shape with good mechanical properties. However, undesired residual stress and distortion that lead to build failure and defects such as porosity are preventing broader applications of L-PBF. To realize the full potential of L-PBF, a multiscale modeling methodology is developed to predict residual deformation, melt pool, and porosity formation. To predict the residual deformation and stress in L-PBF at part-scale, a multiscale process modeling framework based on inherent strain method is proposed.

Inherent strain vectors are extracted from detailed multi-layer process simulation with high fidelity at micro-scale. Uniform but anisotropic strains are then applied to L-PBF part in a layer-by-layer fashion in a quasi-static equilibrium finite element analysis (FEA) to predict residual distortion and stress. Besides residual distortion and stress prediction at part scale, multiphysics modeling at powder scale is performed to study the melt pool variation and defect formation induced by process parameters, preheating temperature and spattering particles. Melt pool dynamics and porosity formation mechanisms associated with these factors are revealed through simulation and experiments.

Based on the proposed part-scale residual stress and distortion model, path planning method is developed to tailor the laser scanning path for a given geometry to prevent large residual deformation and building failures. Gradient based path planning for continuous and island scanning strategy is formulated and full sensitivity analysis for the formulated compliance- and stress-minimization problem is performed.

The feasibility and effectiveness of this proposed path planning method is demonstrated experimentally using the AconityONE L-PBF system. In addition, a data-driven framework utilizing machine learning is developed to predict the thermal history at part-scale for L-PBF.

In this work, a sequential machine learning model including convolutional neural network (CNN) and recurrent neural network (RNN), long shortterm memory unit, is proposed for real-time thermal history prediction. A 100x prediction speed improvement is achieved compared to the finite element analysis which makes the prediction faster than real fabrication process and real-time temperature profile available.

## Bibliography

[1] I. Astm, ASTM52900-15 Standard Terminology for Additive Manufacturing—General

Principles—Terminology, ASTM International, West Conshohocken, PA 3(4) (2015) 5.

[2] W.E. King, A.T. Anderson, R.M. Ferencz, N.E. Hodge, C. Kamath, S.A. Khairallah, A.M.

Rubenchik, Laser powder bed fusion additive manufacturing of metals; physics, computational,

and materials challenges, Applied Physics Reviews 2(4) (2015) 041304.

[3] W. Yan, Y. Lu, K. Jones, Z. Yang, J. Fox, P. Witherell, G. Wagner, W.K. Liu, Data-driven

characterization of thermal models for powder-bed-fusion additive manufacturing, Additive

Manufacturing (2020) 101503.

[4] K. Dai, L. Shaw, Thermal and stress modeling of multi-material laser processing, Acta

Materialia 49(20) (2001) 4171-4181.

[5] K. Dai, L. Shaw, Distortion minimization of laser-processed components through control of

laser scanning patterns, Rapid Prototyping Journal 8(5) (2002) 270-276.

[6] S.S. Bo Cheng, Kevin Chou, Stress and deformation evaluations of scanning strategy effect in

selective laser melting, Additive Manufacturing (2017).

[7] C. Fu, Y. Guo, Three-dimensional temperature gradient mechanism in selective laser melting

of Ti-6Al-4V, Journal of Manufacturing Science and Engineering 136(6) (2014) 061004.

[8] P. Prabhakar, W.J. Sames, R. Dehoff, S.S. Babu, Computational modeling of residual stress

formation during the electron beam melting process for Inconel 718, Additive Manufacturing 7

(2015) 83-91.

[9] A. Hussein, L. Hao, C. Yan, R. Everson, Finite element simulation of the temperature and

stress fields in single layers built without-support in selective laser melting, Materials & Design

(1980-2015) 52 (2013) 638-647.

[10] P.Z. Qingcheng Yang, Lin Cheng, Zheng Min, Minking Chyu, Albert C. To, articleFinite

element modeling and validation of thermomechanicalbehavior of Ti-6Al-4V in directed energy

deposition additivemanufacturing, Additive Manufacturing (2016).

[11] E.R. Denlinger, J. Irwin, P. Michaleris, Thermomechanical Modeling of Additive

Manufacturing Large Parts, Journal of Manufacturing Science and Engineering 136(6) (2014)

061007.

[12] E.R. Denlinger, M. Gouge, J. Irwin, P. Michaleris, Thermomechanical model development

and in situ experimental validation of the Laser Powder-Bed Fusion process, Additive

Manufacturing 16 (2017) 73-80.

[13] V.J. Erik R Denlinger, G.V. Srinivasan, Tahany EI-Wardany, Pan Michaleris, Thermal

modeling of Inconel 718 processed with powder bed fusionand experimental validation using in

situ measurements, Additive Manufacturing 11 (2016) 7-15.

[14] N. Patil, D. Pal, H.K. Rafi, K. Zeng, A. Moreland, A. Hicks, D. Beeler, B. Stucker, A

Generalized Feed Forward Dynamic Adaptive Mesh Refinement and Derefinement Finite Element

Framework for Metal Laser Sintering—Part I: Formulation and Algorithm Development, Journal

of Manufacturing Science and Engineering 137(4) (2015) 041001.

[15] D. Pal, N. Patil, K.H. Kutty, K. Zeng, A. Moreland, A. Hicks, D. Beeler, B. Stucker, A

Generalized Feed-Forward Dynamic Adaptive Mesh Refinement and Derefinement FiniteElement Framework for Metal Laser Sintering—Part II: Nonlinear Thermal Simulations and

Validations, Journal of Manufacturing Science and Engineering 138(6) (2016) 061003.

[16] N. Keller, V. Ploshikhin, New method for fast predictions of residual stress and distortion of

AM parts, Solid Freeform Fabrication Symposium, Austin, Texas, 2014, pp. 1229-1237.

[17] S.A. Khairallah, A.T. Anderson, A. Rubenchik, W.E. King, Laser powder-bed fusion additive

manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and

denudation zones, Acta Materialia 108 (2016) 36-45.

[18] M.J. Matthews, G. Guss, S.A. Khairallah, A.M. Rubenchik, P.J. Depond, W.E. King,

Denudation of metal powder layers in laser powder bed fusion processes, Acta Materialia 114

(2016) 33-42.

[19] A.A. Martin, N.P. Calta, S.A. Khairallah, J. Wang, P.J. Depond, A.Y. Fong, V. Thampy, G.M.

Guss, A.M. Kiss, K.H. Stone, Dynamics of pore formation during laser powder bed fusion additive

manufacturing, Nature communications 10(1) (2019) 1987.

[20] R. Shi, S.A. Khairallah, T.T. Roehling, T.W. Heo, J.T. McKeown, M.J. Matthews,

Microstructural control in metal laser powder bed fusion additive manufacturing using laser beam

shaping strategy, Acta Materialia (2019).

[21] S.A. Khairallah, A.A. Martin, J.R. Lee, G. Guss, N.P. Calta, J.A. Hammons, M.H. Nielsen,

K. Chaput, E. Schwalbach, M.N. Shah, Controlling interdependent meso-nanosecond dynamics

and defect generation in metal 3D printing, Science 368(6491) (2020) 660-665.

[22] W. Yan, W. Ge, Y. Qian, S. Lin, B. Zhou, W.K. Liu, F. Lin, G.J. Wagner, Multi-physics

modeling of single/multiple-track defect mechanisms in electron beam selective melting, Acta

Materialia 134 (2017) 324-333.

[23] S. Shrestha, Y. Kevin Chou, A Numerical Study on the Keyhole Formation During Laser

Powder Bed Fusion Process, Journal of Manufacturing Science and Engineering 141(10) (2019).

[24] S. Shrestha, B. Cheng, K. Chou, An Investigation into Melt Pool Effective Thermal

Conductivity for Thermal Modeling of Powder-Bed Electron Beam Additive Manufacturing.

[25] D. Rosenthal, Mathematical theory of heat distribution during welding and cutting, Welding

journal 20 (1941) 220-234.

[26] P. Promoppatum, S.-C. Yao, P.C. Pistorius, A.D. Rollett, 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 3(5) (2017) 685-694.

[27] M. Tang, P.C. Pistorius, J.L. Beuth, Prediction of lack-of-fusion porosity for powder bed

fusion, Additive Manufacturing 14 (2017) 39-48.

[28] T. Moran, P. Li, D. Warner, N. Phan, Utility of superposition-based finite element approach

for part-scale thermal simulation in additive manufacturing, Additive Manufacturing 21 (2018)

215-219.

[29] Y. Yang, M. Knol, F. van Keulen, C. Ayas, A semi-analytical thermal modelling approach

for selective laser melting, Additive Manufacturing 21 (2018) 284-297.

[30] B. Cheng, S. Shrestha, K. Chou, Stress and deformation evaluations of scanning strategy

effect in selective laser melting, Additive Manufacturing 12 (2016) 240-251.

[31] L.H. Ahmed Hussein, Chunze Yan, Richard Everson, Finite element simulation of the

temperature and stress fields in single layers built without-support in selective laser melting,

Materials and Design 52 (2013) 638-647.

[32] H. Peng, D.B. Go, R. Billo, S. Gong, M.R. Shankar, B.A. Gatrell, J. Budzinski, P. Ostiguy,

R. Attardo, C. Tomonto, Part-scale model for fast prediction of thermal distortion in DMLS

additive manufacturing; Part 2: a quasi-static thermo-mechanical model, Austin, Texas (2016).

[33] M.F. Zaeh, G. Branner, Investigations on residual stresses and deformations in selective laser

melting, Production Engineering 4(1) (2010) 35-45.

[34] C. Li, C. Fu, Y. Guo, F. Fang, A multiscale modeling approach for fast prediction of part

distortion in selective laser melting, Journal of Materials Processing Technology 229 (2016) 703-

712.

[35] C. Li, Z. Liu, X. Fang, Y. Guo, On the Simulation Scalability of Predicting Residual Stress

and Distortion in Selective Laser Melting, Journal of Manufacturing Science and Engineering

140(4) (2018) 041013.

[36] S. Afazov, W.A. Denmark, B.L. Toralles, A. Holloway, A. Yaghi, Distortion Prediction and

Compensation in Selective Laser Melting, Additive Manufacturing 17 (2017) 15-22.

[37] Y. Lee, W. Zhang, Modeling of heat transfer, fluid flow and solidification microstructure of

nickel-base superalloy fabricated by laser powder bed fusion, Additive Manufacturing 12 (2016)

178-188.

[38] L. Scime, J. Beuth, A multi-scale convolutional neural network for autonomous anomaly

detection and classification in a laser powder bed fusion additive manufacturing process, Additive

Manufacturing 24 (2018) 273-286.

[39] L. Scime, J. Beuth, Using machine learning to identify in-situ melt pool signatures indicative

of flaw formation in a laser powder bed fusion additive manufacturing process, Additive

Manufacturing 25 (2019) 151-165.

[40] X. Xie, J. Bennett, S. Saha, Y. Lu, J. Cao, W.K. Liu, Z. Gan, Mechanistic data-driven

prediction of as-built mechanical properties in metal additive manufacturing, npj Computational

Materials 7(1) (2021) 1-12.

[41] C. Wang, X. Tan, S. Tor, C. Lim, Machine learning in additive manufacturing: State-of-theart and perspectives, Additive Manufacturing (2020) 101538.

[42] J. Li, R. Jin, Z.Y. Hang, Integration of physically-based and data-driven approaches for

thermal field prediction in additive manufacturing, Materials & Design 139 (2018) 473-485.

[43] M. Mozaffar, A. Paul, R. Al-Bahrani, S. Wolff, A. Choudhary, A. Agrawal, K. Ehmann, J.

Cao, Data-driven prediction of the high-dimensional thermal history in directed energy deposition

processes via recurrent neural networks, Manufacturing letters 18 (2018) 35-39.

[44] A. Paul, M. Mozaffar, Z. Yang, W.-k. Liao, A. Choudhary, J. Cao, A. Agrawal, A real-time

iterative machine learning approach for temperature profile prediction in additive manufacturing

processes, 2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA),

IEEE, 2019, pp. 541-550.

[45] S. Clijsters, T. Craeghs, J.-P. Kruth, A priori process parameter adjustment for SLM process

optimization, Innovative developments on virtual and physical prototyping, Taylor & Francis

Group., 2012, pp. 553-560.

[46] R. Mertens, S. Clijsters, K. Kempen, J.-P. Kruth, Optimization of scan strategies in selective

laser melting of aluminum parts with downfacing areas, Journal of Manufacturing Science and

Engineering 136(6) (2014) 061012.

[47] J.-P. Kruth, J. Deckers, E. Yasa, R. Wauthlé, Assessing and comparing influencing factors of

residual stresses in selective laser melting using a novel analysis method, Proceedings of the

institution of mechanical engineers, Part B: Journal of Engineering Manufacture 226(6) (2012)

980-991.

[48] Y. Lu, S. Wu, Y. Gan, T. Huang, C. Yang, L. Junjie, J. Lin, Study on the microstructure,

mechanical property and residual stress of SLM Inconel-718 alloy manufactured by differing

island scanning strategy, Optics & Laser Technology 75 (2015) 197-206.

[49] E. Foroozmehr, R. Kovacevic, Effect of path planning on the laser powder deposition process:

thermal and structural evaluation, The International Journal of Advanced Manufacturing

Technology 51(5-8) (2010) 659-669.

[50] L.H. Ahmed Hussein, Chunze Yan, Richard Everson, Finite element simulation of the

temperature and stress fields in single layers built without-support in selective laser melting,

Materials and Design (2013).

[51] J.-P. Kruth, M. Badrossamay, E. Yasa, J. Deckers, L. Thijs, J. Van Humbeeck, Part and

material properties in selective laser melting of metals, Proceedings of the 16th international

symposium on electromachining, 2010, pp. 1-12.

[52] L. Thijs, K. Kempen, J.-P. Kruth, J. Van Humbeeck, Fine-structured aluminium products with

controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder, Acta Materialia

61(5) (2013) 1809-1819.

[53] D. Ding, Z.S. Pan, D. Cuiuri, H. Li, A tool-path generation strategy for wire and arc additive

manufacturing, The international journal of advanced manufacturing technology 73(1-4) (2014)

173-183.

[54] B.E. Carroll, T.A. Palmer, A.M. Beese, Anisotropic tensile behavior of Ti–6Al–4V

components fabricated with directed energy deposition additive manufacturing, Acta Materialia

87 (2015) 309-320.

[55] D. Ding, Z. Pan, D. Cuiuri, H. Li, A practical path planning methodology for wire and arc

additive manufacturing of thin-walled structures, Robotics and Computer-Integrated

Manufacturing 34 (2015) 8-19.

[56] D. Ding, Z. Pan, D. Cuiuri, H. Li, S. van Duin, N. Larkin, Bead modelling and implementation

of adaptive MAT path in wire and arc additive manufacturing, Robotics and Computer-Integrated

Manufacturing 39 (2016) 32-42.

[57] R. Ponche, O. Kerbrat, P. Mognol, J.-Y. Hascoet, A novel methodology of design for Additive

Manufacturing applied to Additive Laser Manufacturing process, Robotics and ComputerIntegrated Manufacturing 30(4) (2014) 389-398.

[58] D.E. Smith, R. Hoglund, Continuous fiber angle topology optimization for polymer fused

fillament fabrication, Annu. Int. Solid Free. Fabr. Symp. Austin, TX, 2016.

[59] J. Liu, J. Liu, H. Yu, H. Yu, Concurrent deposition path planning and structural topology

optimization for additive manufacturing, Rapid Prototyping Journal 23(5) (2017) 930-942.

[60] Q. Xia, T. Shi, Optimization of composite structures with continuous spatial variation of fiber

angle through Shepard interpolation, Composite Structures 182 (2017) 273-282.

[61] C. Kiyono, E. Silva, J. Reddy, A novel fiber optimization method based on normal distribution

function with continuously varying fiber path, Composite Structures 160 (2017) 503-515.

[62] C.J. Brampton, K.C. Wu, H.A. Kim, New optimization method for steered fiber composites

using the level set method, Structural and Multidisciplinary Optimization 52(3) (2015) 493-505.

[63] J. Liu, A.C. To, Deposition path planning-integrated structural topology optimization for 3D

additive manufacturing subject to self-support constraint, Computer-Aided Design 91 (2017) 27-

45.

[64] H. Shen, J. Fu, Z. Chen, Y. Fan, Generation of offset surface for tool path in NC machining

through level set methods, The International Journal of Advanced Manufacturing Technology

46(9-12) (2010) 1043-1047.

[65] C. Zhuang, Z. Xiong, H. Ding, High speed machining tool path generation for pockets using

level sets, International Journal of Production Research 48(19) (2010) 5749-5766.

[66] K.C. Mills, Recommended values of thermophysical properties for selected commercial

alloys, Woodhead Publishing2002.

[67] S.S. Sih, J.W. Barlow, The prediction of the emissivity and thermal conductivity of powder

beds, Particulate Science and Technology 22(4) (2004) 427-440.

[68] L. Dong, A. Makradi, S. Ahzi, Y. Remond, Three-dimensional transient finite element

analysis of the selective laser sintering process, Journal of materials processing technology 209(2)

(2009) 700-706.

[69] J.J. Beaman, J.W. Barlow, D.L. Bourell, R.H. Crawford, H.L. Marcus, K.P. McAlea, Solid

freeform fabrication: a new direction in manufacturing, Kluwer Academic Publishers, Norwell,

MA 2061 (1997) 25-49.

[70] G. Bugeda Miguel Cervera, G. Lombera, Numerical prediction of temperature and density

distributions in selective laser sintering processes, Rapid Prototyping Journal 5(1) (1999) 21-26.

[71] T. Mukherjee, W. Zhang, T. DebRoy, An improved prediction of residual stresses and

distortion in additive manufacturing, Computational Materials Science 126 (2017) 360-372.

[72] A.J. Dunbar, E.R. Denlinger, M.F. Gouge, P. Michaleris, Experimental validation of finite

element modeling for laser powderbed fusion deformation, Additive Manufacturing 12 (2016)

108-120.

[73] J. Goldak, A. Chakravarti, M. Bibby, A new finite element model for welding heat sources,

Metallurgical and Materials Transactions B 15(2) (1984) 299-305.

[74] J. Liu, Q. Chen, Y. Zhao, W. Xiong, A. To, Quantitative Texture Prediction of Epitaxial

Columnar Grains in Alloy 718 Processed by Additive Manufacturing, Proceedings of the 9th

International Symposium on Superalloy 718 & Derivatives: Energy, Aerospace, and Industrial

Applications, Springer, 2018, pp. 749-755.

[75] J. Irwin, P. Michaleris, A line heat input model for additive manufacturing, Journal of

Manufacturing Science and Engineering 138(11) (2016) 111004.

[76] M. Gouge, J. Heigel, P. Michaleris, T. Palmer, Modeling forced convection in the thermal

simulation of laser cladding processes, International Journal of Advanced Manufacturing

Technology 79 (2015).

[77] J. Heigel, P. Michaleris, E. Reutzel, Thermo-mechanical model development and validation

of directed energy deposition additive manufacturing of Ti–6Al–4V, Additive manufacturing 5

(2015) 9-19.

[78] E.R. Denlinger, J.C. Heigel, P. Michaleris, Residual stress and distortion modeling of electron

beam direct manufacturing Ti-6Al-4V, Proceedings of the Institution of Mechanical Engineers,

Part B: Journal of Engineering Manufacture 229(10) (2015) 1803-1813.

[79] X. Liang, Q. Chen, L. Cheng, Q. Yang, A. To, A modified inherent strain method for fast

prediction of residual deformation in additive manufacturing of metal parts, 2017 Solid Freeform

Fabrication Symposium Proceedings, Austin, Texas, 2017.

[80] X. Liang, L. Cheng, Q. Chen, Q. Yang, A. To, A Modified Method for Estimating Inherent

Strains from Detailed Process Simulation for Fast Residual Distortion Prediction of Single-Walled

Structures Fabricated by Directed Energy Deposition, Additive Manufacturing 23 (2018) 471-486.

[81] L. Sochalski-Kolbus, E.A. Payzant, P.A. Cornwell, T.R. Watkins, S.S. Babu, R.R. Dehoff,

M. Lorenz, O. Ovchinnikova, C. Duty, Comparison of residual stresses in Inconel 718 simple parts

made by electron beam melting and direct laser metal sintering, Metallurgical and Materials

Transactions A 46(3) (2015) 1419-1432.

[82] P. Mercelis, J.-P. Kruth, Residual stresses in selective laser sintering and selective laser

melting, Rapid Prototyping Journal 12(5) (2006) 254-265.

[83] N. Hodge, R. Ferencz, J. Solberg, Implementation of a thermomechanical model for the

simulation of selective laser melting, Computational Mechanics 54(1) (2014) 33-51.

[84] A.S. Wu, D.W. Brown, M. Kumar, G.F. Gallegos, W.E. King, An experimental investigation

into additive manufacturing-induced residual stresses in 316L stainless steel, Metallurgical and

Materials Transactions A 45(13) (2014) 6260-6270.

[85] C. Li, J. liu, Y. Guo, Efficient predictive model of part distortion and residual stress in

selective laser melting, Solid Freeform Fabrication 2016, 2017.

[86] Y. Zhao, Y. Koizumi, K. Aoyagi, D. Wei, K. Yamanaka, A. 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 26 (2019) 202-214.

[87] J.-H. Cho, S.-J. Na, Implementation of real-time multiple reflection and Fresnel absorption of

laser beam in keyhole, Journal of Physics D: Applied Physics 39(24) (2006) 5372.

[88] Q. Guo, C. Zhao, M. Qu, L. Xiong, L.I. Escano, S.M.H. Hojjatzadeh, N.D. Parab, K. Fezzaa,

W. Everhart, T. Sun, In-situ characterization and quantification of melt pool variation under

constant input energy density in laser powder-bed fusion additive manufacturing process, Additive

Manufacturing (2019).

[89] E. Assuncao, S. Williams, D. Yapp, Interaction time and beam diameter effects on the

conduction mode limit, Optics and Lasers in Engineering 50(6) (2012) 823-828.

[90] R. Cunningham, C. Zhao, N. Parab, C. Kantzos, J. Pauza, K. Fezzaa, T. Sun, A.D. Rollett,

Keyhole threshold and morphology in laser melting revealed by ultrahigh-speed x-ray imaging,

Science 363(6429) (2019) 849-852.

[91] W. Tan, N.S. Bailey, Y.C. Shin, Investigation of keyhole plume and molten pool based on a

three-dimensional dynamic model with sharp interface formulation, Journal of Physics D: Applied

Physics 46(5) (2013) 055501.

[92] W. Tan, Y.C. Shin, Analysis of multi-phase interaction and its effects on keyhole dynamics

with a multi-physics numerical model, Journal of Physics D: Applied Physics 47(34) (2014)

345501.

[93] R. Fabbro, K. Chouf, Keyhole modeling during laser welding, Journal of applied Physics

87(9) (2000) 4075-4083.

[94] Q. Guo, C. Zhao, M. Qu, L. Xiong, S.M.H. Hojjatzadeh, L.I. Escano, N.D. Parab, K. Fezzaa,

T. Sun, L. Chen, In-situ full-field mapping of melt flow dynamics in laser metal additive

manufacturing, Additive Manufacturing 31 (2020) 100939.

[95] Y. Ueda, K. Fukuda, K. Nakacho, S. Endo, A new measuring method of residual stresses with

the aid of finite element method and reliability of estimated values, Journal of the Society of Naval

Architects of Japan 1975(138) (1975) 499-507.

[96] M.R. Hill, D.V. Nelson, The inherent strain method for residual stress determination and its

application to a long welded joint, ASME-PUBLICATIONS-PVP 318 (1995) 343-352.

[97] H. Murakawa, Y. Luo, Y. Ueda, Prediction of welding deformation and residual stress by

elastic FEM based on inherent strain, Journal of the society of Naval Architects of Japan 1996(180)

(1996) 739-751.

[98] M. Yuan, Y. Ueda, Prediction of residual stresses in welded T-and I-joints using inherent

strains, Journal of Engineering Materials and Technology, Transactions of the ASME 118(2)

(1996) 229-234.

[99] L. Zhang, P. Michaleris, P. Marugabandhu, Evaluation of applied plastic strain methods for

welding distortion prediction, Journal of Manufacturing Science and Engineering 129(6) (2007)

1000-1010.

[100] M. Bugatti, Q. Semeraro, Limitations of the Inherent Strain Method in Simulating Powder

Bed Fusion Processes, Additive Manufacturing 23 (2018) 329-346.

[101] L. Cheng, X. Liang, J. Bai, Q. Chen, J. Lemon, A. To, On Utilizing Topology Optimization

to Design Support Structure to Prevent Residual Stress Induced Build Failure in Laser Powder Bed

Metal Additive Manufacturing, Additive Manufacturing (2019).

[102] Q. Chen, X. Liang, D. Hayduke, J. Liu, L. Cheng, J. Oskin, R. Whitmore, A.C. To, An

inherent strain based multiscale modeling framework for simulating part-scale residual

deformation for direct metal laser sintering, Additive Manufacturing 28 (2019) 406-418.

[103] S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based

on Hamilton-Jacobi formulations, Journal of computational physics 79(1) (1988) 12-49.

[104] M.Y. Wang, X. Wang, D. Guo, A level set method for structural topology optimization,

Computer methods in applied mechanics and engineering 192(1) (2003) 227-246.

[105] G. Allaire, F. Jouve, A.-M. Toader, Structural optimization using sensitivity analysis and a

level-set method, Journal of computational physics 194(1) (2004) 363-393.

[106] Y. Wang, Z. Luo, Z. Kang, N. Zhang, A multi-material level set-based topology and shape

optimization method, Computer Methods in Applied Mechanics and Engineering 283 (2015)

1570-1586.

[107] P. Dunning, C. Brampton, H. Kim, Simultaneous optimisation of structural topology and

material grading using level set method, Materials Science and Technology 31(8) (2015) 884-894.

[108] P. Liu, Y. Luo, Z. Kang, Multi-material topology optimization considering interface

behavior via XFEM and level set method, Computer methods in applied mechanics and

engineering 308 (2016) 113-133.

[109] J. Liu, Q. Chen, Y. Zheng, R. Ahmad, J. Tang, Y. Ma, Level set-based heterogeneous object

modeling and optimization, Computer-Aided Design (2019).

[110] J. Liu, Q. Chen, X. Liang, A.C. To, Manufacturing cost constrained topology optimization

for additive manufacturing, Frontiers of Mechanical Engineering 14(2) (2019) 213-221.

[111] Z. Kang, Y. Wang, Integrated topology optimization with embedded movable holes based

on combined description by material density and level sets, Computer methods in applied

mechanics and engineering 255 (2013) 1-13.

[112] P.D. Dunning, H. Alicia Kim, A new hole insertion method for level set based structural

topology optimization, International Journal for Numerical Methods in Engineering 93(1) (2013)

118-134.

[113] J.A. Sethian, A fast marching level set method for monotonically advancing fronts,

Proceedings of the National Academy of Sciences 93(4) (1996) 1591-1595.

[114] J.A. Sethian, Level set methods and fast marching methods: evolving interfaces in

computational geometry, fluid mechanics, computer vision, and materials science, Cambridge

university press1999.

[115] C. Le, J. Norato, T. Bruns, C. Ha, D. Tortorelli, Stress-based topology optimization for

continua, Structural and Multidisciplinary Optimization 41(4) (2010) 605-620.

[116] A. Takezawa, G.H. Yoon, S.H. Jeong, M. Kobashi, M. Kitamura, Structural topology

optimization with strength and heat conduction constraints, Computer Methods in Applied

Mechanics and Engineering 276 (2014) 341-361.

[117] S. Hochreiter, J. Schmidhuber, Long short-term memory, Neural computation 9(8) (1997)

1735-1780.

[118] A. Krizhevsky, I. Sutskever, G.E. Hinton, Imagenet classification with deep convolutional

neural networks, Advances in neural information processing systems 25 (2012) 1097-1105.

[119] K. Simonyan, A. Zisserman, Very deep convolutional networks for large-scale image

recognition, arXiv preprint arXiv:1409.1556 (2014).

[120] K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition, Proceedings

of the IEEE conference on computer vision and pattern recognition, 2016, pp. 770-778.

[121] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A.

Khosla, M. Bernstein, Imagenet large scale visual recognition challenge, International journal of

computer vision 115(3) (2015) 211-252.

[122] S. Ren, K. He, R. Girshick, J. Sun, Faster r-cnn: Towards real-time object detection with

region proposal networks, Advances in neural information processing systems 28 (2015) 91-99.

[123] E.J. Schwalbach, S.P. Donegan, M.G. Chapman, K.J. Chaput, M.A. Groeber, A discrete

source model of powder bed fusion additive manufacturing thermal history, Additive

Manufacturing 25 (2019) 485-498.

[124] D.G. Duffy, Green’s functions with applications, Chapman and Hall/CRC2015.

[125] J. Martínez-Frutos, D. Herrero-Pérez, Efficient matrix-free GPU implementation of fixed

grid finite element analysis, Finite Elements in Analysis and Design 104 (2015) 61-71.

[126] F. Dugast, P. Apostolou, A. Fernandez, W. Dong, Q. Chen, S. Strayer, R. Wicker, A.C. To,

Part-scale thermal process modeling for laser powder bed fusion with matrix-free method and GPU

computing, Additive Manufacturing 37 (2021) 101732.

[127] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A.N. Gomez, Ł. Kaiser, I.

Polosukhin, Attention is all you need, Advances in neural information processing systems, 2017,

pp. 5998-6008.

[128] J. Devlin, M.-W. Chang, K. Lee, K. Toutanova, Bert: Pre-training of deep bidirectional

transformers for language understanding, arXiv preprint arXiv:1810.04805 (2018).