A Review of Meso-micro Modeling and Simulation Methods of Selective Laser Melting Process

doi:10.3901/JME.2022.05.239

Abstract

Abstract: The selective laser melting(SLM) process is a complex physical and chemical metallurgical process, which not only involves multi-scale issues such as macro part-scale, meso molten-pool-scale and micro metallographic-scale but also includes multi-physical behaviors such as phase change, fluid flow, heat transfer and mass transfer. Using experimental methods to directly observe the phenomenon online is not only extremely difficult but also of a long period and high cost. Therefore, a high-fidelity numerical simulation method has become an important means to reveal the mechanism of the SLM process and predict the forming quality. This study focused on the two aspects of mesoscopic powder molten pool evolution(powder laying, molten pool evolution kinetics) and microscopic solidification structure formation(crystal nucleation, dendrite growth) and discussed the modeling and simulation methods of the SLM process in detail. The features, advantages and applicability of the physical models and simulation methods were analyzed, and the simulation and application statuses of the mesoscopic molten pool and microstructure morphology of the SLM process were summarized. This review was ended up with the perspectives of the challenges and developments of the meso-micro numerical simulation technology for the SLM process.

Key words: selective laser melting, molten pool, microstructure, physical modeling, simulation method

CLC Number:

TH164

AO Xiao-hui, LIU Jian-hua, XIA Huan-xiong, HE Qi-yang, REN Ce. A Review of Meso-micro Modeling and Simulation Methods of Selective Laser Melting Process[J]. Journal of Mechanical Engineering, 2022, 58(5): 239-257.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://www.cjmenet.com.cn/EN/10.3901/JME.2022.05.239

http://www.cjmenet.com.cn/EN/Y2022/V58/I5/239

References

[1] CHEN R,XU Q,LIU B.Simulation of the dendrite morphology and microsegregation in solidification of Al-Cu-Mg aluminum alloys[J].Acta Metallurgica Sinica,2015,28(2):173-181.
[2] MEZA E S,BERTELLI F,GOULART P R,et al.The effect of the growth rate on microsegregation:Experimental investigation in hypoeutectic Al-Fe and Al-Cu alloys directionally solidified[J].Journal of Alloys and Compounds,2013,561:193-200.
[3] WANG Y,PENG L,JI Y,et al.Effect of cooling rates on the dendritic morphology transition of Mg-6Gd alloy by in situ X-ray radiography[J].Journal of Materials Science and Technology,2018,34:1142-1148.
[4] 魏雷,林鑫,王猛,等.金属激光增材制造过程数值模拟[J].航空制造技术,2017(13):16-25.WEI Lei,LIN Xin,WANG Meng,et al.Numerical simulation on laser additive manufacturing process for metal components[J].Aeronautical Manufacturing Technology,2017(13):16-25.
[5] 尹华,白培康,刘斌,等.金属粉末选区激光熔化技术的研究现状及其发展趋势[J].热加工工艺,2010,39(1):140-144.YIN Hua,BAI Peikang,LIU Bin,et al.Present situation and development trend of selective laser melting technology for metal powder[J].Hot Working Technology,2010,39(1):140-144.
[6] 吴勇毅,陈渊源.《中国制造2025》上的3D打印"国家战略"[J].上海信息化,2015(10):10-15.WU Yongyi,CHEN Yuanyuan.3D printing "National Strategy" on "Made in China 2025"[J].Shanghai Informatization,2015(10):10-15.
[7] VRANCKEN B,THIJS L,KRUTH J P,et al.Microstructure and mechanical properties of a novel βtitanium metallic composite by selective laser melting[J].Acta Materialia,2014,68:150-158.
[8] KANKO J A,SIBLEY A P,FRASER J M.In situ morphology-based defect detection of selective laser melting through inline coherent imaging[J].Journal of Materials Processing Technology,2016,231:488-500.
[9] HUSSEIN A,HAO L,YAN C,et al.Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting[J].Materials and Design,2013,52:638-647.
[10] ZHAO C,FEZZAA K,CUNNINGHAM R W,et al.Real-time monitoring of laser powder bed fusion process using high-speed X-ray imaging and diffraction[J].Scientific Reports,2017,7:3602.
[11] GUO Q,ZHAO C,ESCANO L I,et al.Transient dynamics of powder spattering in laser powder bed fusion additive manufacturing process revealed by in-situ high-speed high-energy X-ray imaging[J].Acta Materialia,2018,151:169-180.
[12] ESCANO L I,PARAB N,XIONG L,et al.Revealing particle-scale powder spreading dynamics in powder-bed-based additive manufacturing process by high-speed X-ray imaging[J].Scientific Reports,2018,8:15079.
[13] HE Q,XIA H,LIU J,et al.Modeling and numerical studies of selective laser melting:Multiphase flow,solidification and heat transfer[J].Materials and Design,2020,196:109115.
[14] MEAKIN P,JULLIEN R.Restructuring effects in the rain model for random deposition[J].Journal de Physique,1987,48(10):1651-1662.
[15] KÖRNER C,ATTAR E,HEINL P.Mesoscopic simulation of selective beam melting processes[J].Journal of Materials Processing Technology,2011,211:978-987.
[16] KÖRNER C,BAUEREIßA,ATTAR E.Fundamental consolidation mechanisms during selective beam melting of powders[J].Modelling and Simulation in Materials Science and Engineering,2013,21:085011.
[17] BAUEREIßA,SCHAROWSKY T,KÖRNER C.Defect generation and propagation mechanism during additive manufacturing by selective beam melting[J].Journal of Materials Processing Technology,2014,214:2522-2528.
[18] HAN Q,GU H,SETCHI R,et al.Discrete element simulation of powder layer thickness in laser additive manufacturing[J].Powder Technology,2019,352:91-102.
[19] LEE Y S,ZHANG W.Modeling of heat transfer,fluid flow and solidification microstructure of nickel-base superalloy fabricated by laser powder bed fusion[J].Additive Manufacturing,2016,12:178-188.
[20] 赵艳波,马麟,刘波,等.基于离散元法的纯铁粉振动填充密度分析[J].粉末冶金技术,2020,38(6):429-435.ZHAO Yanbo,MA Lin,LIU Bo,et al.Analysis on vibration packing density of pure iron powders based on discrete element method[J].Powder Metallurgy Technology,2020,38(6):429-435.
[21] ZHOU J,ZHANG Y,CHEN J K.Numerical simulation of random packing of spherical particles for powder-based additive manufacturing[J].Journal of Manufacturing Science and Engineering,2009,131:031004.
[22] LEE Y S,NANDWANA P,ZHANG W.Dynamic simulation of powder packing structure for powder bed additive manufacturing[J].The International Journal of Advanced Manufacturing Technology,2018,96:1507-1520.
[23] CHEN H,WEI Q,WEN S,et al.Flow behavior of powder particles in layering process of selective laser melting:Numerical modeling and experimental verification based on discrete element method[J].International Journal of Machine Tools and Manufacture,2017,123:146-159.
[24] 向召伟,殷鸣,邓珍波,等.增材制造技术粉床的数值模拟与分析[J].四川大学学报:工程科学版,2016,48(2):191-197.XIANG Zhaowei,YIN Ming,DENG Zhenbo,et al.Simulation and analysis of powder bed for additive manufacturing[J].Journal of Sichuan University:Engineering Science Edition,2016,48(2):191-197.
[25] CAO L.Study on the numerical simulation of laying powder for the selective laser melting process[J].The International Journal of Advanced Manufacturing Technology,2019,105:2253-2269.
[26] HAERI S,WANG Y,GHITA O,et al.Discrete element simulation and experimental study of powder spreading process in additive manufacturing[J].Powder Technology,2016,306:45-54.
[27] HIRT C W,NICHOLS B D.Volume of fluid (VOF) method for the dynamics of free boundaries[J].Journal of Computational Physics,1981,39(1):201-225.
[28] CAO L.Numerical simulation of the impact of laying powder on selective laser melting single-pass formation[J].International Journal of Heat and Mass Transfer,2019,141:1036-1048.
[29] 袁伟豪,陈辉,魏青松.反冲压力作用下激光选区熔化熔池热动力学行为[J].机械工程学报,2020,56(7):213-219.YUAN Weihao,CHEN Hui,WEI Qingsong.The role of recoil pressure in thermodynamic behaviors of molten pool during selective laser melting[J].Journal of Mechanical Engineering,2020,56(7):213-219.
[30] SHRESTHA S,CHOU K.A build surface study of powder-bed electron beam additive manufacturing by 3Dthermo-fluid simulation and white-light interfero-metry[J].International Journal of Machine Tools and Manufacture,2017,121:37-49.
[31] SIAO Y H,WEN C D.Examination of molten pool with Marangoni flow and evaporation effect by simulation and experiment in selective laser melting[J].International Communications in Heat and Mass Transfer,2021,125:105325.
[32] 曲睿智,黄良沛,肖冬明.基于数值模拟的选择性激光熔化过程中熔池演变与金属飞溅特性分析[J].航空学报,2022,43(1):425240.QU Ruizhi,HUANG Liangpei,XIAO Dongming.Study on the numerical simulation of melt pool evolution and metal spattering characterization during selective laser melting processing[J].Acta Aeronautica et Astronautica Sinica,2022,43(1):425240.
[33] ZHANG T,LI H,LIU S,et al.Evolution of molten pool during selective laser melting of Ti-6Al-4V[J].Journal of Physics D:Applied Physics,2019,52(5):055302.
[34] ZAKIROV A,BELOUSOV S,BOGDANOVA M,et al.Predictive modeling of laser and electron beam powder bed fusion additive manufacturing of metals at the mesoscale[J].Additive Manufacturing,2020,35:101236.
[35] CHO J H,FARSON D F,MILEWSKI J O,et al.Weld pool flows during initial stages of keyhole formation in laser welding[J].Journal of Physics D:Applied Physics,2009,42:175502.
[36] TANG C,TAN J L,WONG C H.A numerical investigation on the physical mechanisms of single track defects in selective laser melting[J].International Journal of Heat and Mass Transfer,2018,126:957-968.
[37] VOLLER V R,PRAKASH C.A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems[J].International Journal of Heat and Mass Transfer,1987,30(8):1709-1719.
[38] 陈嘉伟,熊飞宇,黄辰阳,等.金属增材制造数值模拟[J].中国科学:物理学、力学、天文学,2020,50(9):090007.CHEN Jiawei,XIONG Feiyu,HUANG Chenyang,et al.Numerical simulation of metal additive manufacturing[J].Science in China:Physics,Mechanics,Astronomy,2020,50(9):090007.
[39] YAN W,GE W,SMITH J,et al.Multi-scale modeling of electron beam melting of functionally graded materials[J].Acta Materialia,2016,115:403-412.
[40] MISHRA A K,KUMAR A.Numerical and experimental analysis of the effect of volumetric energy absorption in powder layer on thermal-fluidic transport in selective laser melting of Ti6Al4V[J].Optics and Laser Technology,2019,111:227-239.
[41] ANTONY K,ARIVAZHAGAN N,SENTHILKUMARANK.Numerical and experimental investigations on laser melting of stainless steel 316L metal powders[J].Journal of Manufacturing Processes,2014,16:345-355.
[42] PATIL R B,YADAVA V.Finite element analysis of temperature distribution in single metallic powder layer during metal laser sintering[J].International Journal of Machine Tools and Manufacture,2007,47:1069-1080.
[43] SIH S S,BARLOW J W.The prediction of the emissivity and thermal conductivity of powder beds[J].Particulate Science and Technology,2004,22:427-440.
[44] GUSAROV A V,LAOUI T,FROYEN L,et al.Contact thermal conductivity of a powder bed in selective laser sintering[J].International Journal of Heat and Mass Transfer,2003,46:1103-1109.
[45] BAYAT M,THANKI A,MOHANTY S,et al.Keyhole-induced porosities in Laser-based Powder Bed Fusion (L-PBF) of Ti6Al4V:High-fidelity modelling and experimental validation[J].Additive Manufacturing,2019,30:100835.
[46] KHAIRALLAH S A,MARTIN A A,LEE J R I,et al.Controlling interdependent meso-nanosecond dynamics and defect generation in metal 3D printing[J].Science,2020,368:660-665.
[47] KHAIRALLAH S A,ANDERSON A T,RUBENCHIKA,et al.Laser powder-bed fusion additive manufacturing:Physics of complex melt flow and formation mechanisms of pores,spatter,and denudation zones[J].Acta Materialia,2016,108:36-45.
[48] KHAIRALLAH S A,ANDERSON A.Mesoscopic simulation model of selective laser melting of stainless steel powder[J].Journal of Materials Processing Technology,2014,214:2627-2636.
[49] KING W E,ANDERSON A T,FERENCZ R M,et al.Laser powder bed fusion additive manufacturing of metals,physics,computational,and materials challenges[J].Applied Physics Reviews,2015,2:041304.
[50] MARTIN A A,CALTA N P,KHAIRALLAH S A,et al.Dynamics of pore formation during laser powder bed fusion additive manufacturing[J].Nature Communications,2019,10:1987.
[51] WEIRATHER J,ROZOV V,WILLE M,et al.A smoothed particle hydrodynamics model for laser beam melting of Ni-based alloy 718[J].Computers and Mathematics with Applications,2019,78:2377-2394.
[52] FÜRSTENAU J P,WESSELS H,WEIßENFELS C,et al.Generating virtual process maps of SLM using powder scale SPH simulations[J].Computational Particle Mechanics,2020,7:655-677.
[53] RUSSELL M A,SOUTO-IGLESIAS A,ZOHDI T I.Numerical simulation of laser fusion additive manufacturing processes using the SPH method[J].Computer Methods in Applied Mechanics and Engineering,2018,341:163-187.
[54] KRZYZANOWSKI M,SVYETLICHNYY D.Amultiphysics simulation approach to selective laser melting modelling based on cellular automata and lattice Boltzmann methods[J].Computational Particle Mechanics,2021.
[55] FRANCOIS M M,SUN A,KING W E,et al.Modeling of additive manufacturing processes for metals:Challenges and opportunities[J].Current Opinion in Solid State and Materials Science,2017,21(4):198-206.
[56] 赵九洲,李璐,张显飞.合金凝固过程元胞自动机模型及模拟方法的发展[J].金属学报,2014,50(6):641-651.ZHAO Jiuzhou,LI Lu,ZHANG Xianfei.Development of cellular automaton models and simulation methods for solidfication of alloys[J].Acta Metallurgica Sinica,2014,50(6):641-651.
[57] OLDFIELD W.A quantitative approach to casting solidification-freezing of casting iron[J].ASMTransaction,1966.
[58] AKRAM J,CHALAVADI P,PAL D,et al.Understanding grain evolution in additive manufacturing through modeling[J].Additive Manufacturing,2018,21:255-268.
[59] NIE P,OJO O A,LI Z.Numerical modeling of microstructure evolution during laser additive manufacturing of a nickel-based superalloy[J].Acta Materialia,2014,77:85-95.
[60] THÉVOZ P,DESBIOLIES J L,RAPPAZ M.Modeling of equiaxed microstructure formation in casting[J].Metallurgical and Materials Transactions A,1989,20A:311-321.
[61] WANG Z,LUO S,SONG H,et al.Simulation of microstructure during laser rapid forming solidification based on cellular automaton[J].Mathematical Problems in Engineering,2014,2014:627528.
[62] ZINOVIEV A,ZINOVIEVA O,PLOSHIKHIN V,et al.Evolution of grain structure during laser additive manufacturing simulation by a cellular automata method[J].Materials and Design,2016,106:321-329.
[63] SHI R,KHAIRALLAH S A,ROEHLING T T,et al.Microstructural control in metal laser powder bed fusion additive manufacturing using laser beam shaping strategy[J].Acta Materialia,2020,184:284-305.
[64] 杨鑫,王犇,谷文萍,等.金属激光3D打印过程数值模拟应用及研究现状[J].材料工程,2021,49(4):52-62.YANG Xin,WANG Ben,GU Wenping,et al.Applicationand research status of numerical simulation of metal laser 3D printing process[J].Journal of Materials Engineering,2021,49(4):52-62.
[65] 陈伟鹏,赵宇宏,张冰,等.金属凝固过程枝晶生长相场法模拟研究进展[J].材料导报,2018,32(S2):535-539.CHEN Weipeng,ZHAO Yuhong,ZHANG Bing,et al.Development of phase-field simulation of dendritic growth in metal solidification[J].Materials Review,2018,32(S2):535-539.
[66] 赵宇辉,程军,侯华,等.凝固过程微观组织数值模拟研究进展[J].中北大学学报,2006,27(4):372-376.ZHAO Yuhui,CHENG Jun,HOU Hua,et al.Advancement in numerical simulation of microstructure during solidification[J].Journal of North University of China,2006,27(4):372-376.
[67] KÖRNER C,MARKL M,KOEPF J A.Modeling and simulation of microstructure evolution for additive manufacturing of metals:A critical review[J].Metallurgical and Materials Transactions A,2020,51:4970-4983.
[68] WHEELER A A,BOETTINGER W J,MCFADDEN G B.Phase field model for isothermal phase transitions in binary alloys[J].Physical Review A,1992,45(10):7424-7439.
[69] SUZUKI T,ODE M,KIM S G.Phase-field model of dendritic growth[J].Journal of Crystal Growth,2002,237-239:125-131.
[70] FALLAH V,ALIMARDANI M,CORBIN S F,et al.Temporal development of melt-pool morphology and clad geometry in laser powder deposition[J].Computational Materials Science,2011,50:2124-2134.
[71] LIU P W,JI Y Z,WANG Z,et al.Investigation on evolution mechanisms of site-specific grain structures during metal additive manufacturing[J].Journal of Materials Processing Tech.,2018,257:191-202.
[72] RODGERS T M,MADISON J D,TIKARE V.Simulation of metal additive manufacturing microstructures using kinetic Monte Carlo[J].Computational Materials Science,2017,135:78-89.
[73] ZHU P,SMITH R W.Dynamic simulation of crystal growth by Monte Carlo method-II.Ingot microstructures[J].Acta Metallurgica et Materialia,1992,40(12):3369-3379.
[74] LEE H N,RYOO H S,HWANG S K.Monte Carlo simulation of microstructure evolution based on grain boundary character distribution[J].Materials Science and Engineering A,2000,281:176-188.
[75] RAPPAZ M,GANDIN C A.Probabilistic modelling of microstructure formation in solidification processes[J].Acta Metallurgica et Materialia,1993,41(2):345-360.
[76] GANDIN C A,RAPPAZ M.A 3D cellular automaton algorithm for the prediction of dendritic grain growth[J].Acta Materialia,1997,45(5):2187-2195.
[77] KURZ W,GIOVANOLA B,TRIVEDI R.Theory of microstructural development during rapid solidification[J].Acta Metallurgica,1986,34(5):823-830.
[78] NASTAC L,STEFANESCU D M.Stochastic modelling of microstructure formation in solidification processes[J].Modelling and Simulation in Materials Science and Engineering,1997,5:391-420.
[79] MULLIS A M.Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity[J].Physical Review E,2011,83:061601.
[80] LIPTON J,GLICKSMAN M E,KURZ W.Dendritic growth into undercooled alloy metals[J].Materials Science and Engineering,1984,65(1):57-63.
[81] CHEN R,XU Q,LIU B.Cellular automaton simulation of three-dimensional dendrite growth in Al-7Si-Mg ternary aluminum alloys[J].Computational Materials Science,2015,105:90-100.
[82] ZHU M,PAN S,SUN D,et al.Numerical simulation of microstructure evolution during alloy solidification by using cellular automaton method[J].ISIJ International,2010,50(12):1851-1858.
[83] LIPTON J,GLICKSMAN M E,KURZ W.Equiaxed dendrite growth in alloys at small supercooling[J].Metallurgical Transactions A,1987,18(A),341-345.
[84] NATSUME Y,OHSASA K.Three-dimensional cellular automaton model for the prediction of microsegregation in solidification grain structures[J].ISIJ International,2014,54(2):415-421.
[85] TAO P,LI H,HUANG B,et al.The crystal growth intercellular spacing and microsegregation of selective laser melted Inconel 718 superalloy[J].Vacuum,2019,159:382-390.
[86] ZHAN X,WEI Y,DONG Z.Cellular automaton simulation of grain growth with different orientation angles during solidification process[J].Journal of Materials Processing Technology,2008,208:1-8.
[87] CHEN R,XU Q,LIU B.A modified cellular automaton model for the quantitative prediction of equiaxed and columnar dendritic growth[J].Journal of Materials Science and Technology,2014,30(12):1311-1320.
[88] REUTHER K,RETTENMAYR M.A comparison of methods for the calculation of interface curvature in two-dimensional cellular automata solidification models[J].Computational Materials Science,2019,166:143-149.
[89] WEI L,CAO Y,LIN X,et al.Quantitative cellular automaton model and simulations of dendritic and anomalous eutectic growth[J].Computational Materials Science,2019,156:157-166.
[90] HUNT J D.Steady state columnar and equiaxed growth of dendrites and eutectic[J].Materials Science and Engineering,1984,65:75-83.
[91] GÄUMANN M,BEZENÇON C,CANALIS P,et al.Single-crystal laser deposition of superalloys:Processing microstructure maps[J].Acta Materialia,2001,49:1051-1062.
[92] LENART R,ESHRAGHI M.Modeling columnar to equiaxed transition in directional solidification of Inconel718 alloy[J].Computational Materials Science,2020,172:109374.
[93] WANG W,WANG Z,YIN S,et al.Numerical simulation of solute undercooling influenced columnar to equiaxed transition of Fe-C alloy with cellular automaton[J].Computational Materials Science,2019,167:52-64.
[94] ZHU M F,STEFANESCU D M.Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys[J].Acta Materialia,2007,55:1741-1755.
[95] KARAYAGIZ K,JOHNSON L,SEEDE R,et al.Finite interface dissipation phase field modeling of Ni-Nb under additive manufacturing conditions[J].Acta Materialia,2020,185:320-339.
[96] YIN H,FELICELLI S D.Dendrite growth simulation during solidification in the LENS process[J].Acta Materialia,2010,58:1455-1465.
[97] OMAR L B,URIEL M H,JOSÉR,et al.Two-dimensional simulation of grain structure growth within selective laser melted AA-2024[J].Materials and Design,2017,113:369-376.
[98] DEZFOLI A R A,HWANG W S,HUANG W,et al.Determination and controlling of grain structure of metals after laser incidence:Theoretical approach[J].Scientific Reports,2017,7:41527.
[99] YANG C,XU Q,LIU B.GPU-accelerated three dimensional phase-field simulation of dendrite growth in a nickel-based superalloy[J].Computational Materials Science,2017,136:133-143.
[100] NASTAC L.A multiscale transient modeling approach for predicting the solidification structure in VAR-processed alloy 718 ingots[J].Metallurgical and Materials Transactions B,2014,45:44-50.
[101] ROMANOVA V,BALOKHONOV R,ZINOVIEVA O,et al.Micromechanical simulations of additively manufactured aluminum alloys[J].Computers and Structures,2021,244:106412.
[102] YANG M,WANG L,YAN W.Phase-field modeling of grain evolutions in additive manufacturing from nucleation,growth,to coarsening[J].npj Computational Materials,2021,7:56.
[103] GANDIN C A,DESBIOLLES J L,RAPPAZ M,et al.A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures[J].Metallurgical and Materials Transactions A,1999,30:3153-3165.
[104] WANG Y,SHI J,LIU Y.Competitive grain growth and dendrite morphology evolution in selective laser melting of Inconel 718 superalloy[J].Journal of Crystal Growth,2019,521:15-29.
[105] ZINOVIEVA O,ZINOVIEV A,ROMANOVA V,et al.Three-dimensional analysis of grain structure and texture of additively manufactured 316L austenitic stainless steel[J].Additive Manufacturing,2020,36:101521.
[106] TAN W,BAILEY N S,SHIN Y C.A novel integrated model combining cellular automata and phase field methods for microstructure evolution during solidification of multi-component and multi-phase alloys[J].Computational Materials Science,2011,50:2573-2585.
[107] RAI A,MARKL M,KÖRNER C.A coupled cellular automaton-Lattice Boltzmann model for grain structure simulation during additive manufacturing[J].Computational Materials Science,2016,124:37-48.
[108] AO X,XIA H,LIU J,et al.Simulations of microstructure coupling with moving molten pool by selective laser melting using a cellular automaton[J].Materials and Design,2020,185:108230.
[109] LIAN Y,GAN Z,YU C,et al.A cellular automaton finite volume method for microstructure evolution during additive manufacturing[J].Materials and Design,2019,169:107672.
[110] XIONG F,HUANG C,KAFKA O L.Grain growth prediction in selective electron beam melting of Ti-6Al-4V with a cellular automaton method[J].Materials and Design,2021,199:109410.