×

Numerical methods for microstructural evolutions in laser additive manufacturing. (English) Zbl 1443.80011

Summary: Different methods are developed for simulation of microstructural evolution in metals and alloys subject to Laser Additive Manufacturing. The Monte Carlo (MC) method is combined with a new proposed two scales strategy for simulation of the solidification and the subsequent solid-state phase transformation in Ti-6Al-4V. The Cellular Automaton (CA) method shows its higher efficiency in comparison with MC method. Moore neighbor type with energy barrier is recommended for the CA simulation of grain growth of Al 6061. The phase field (PF) model shows that different temperature gradients lead to different columnar grains in different layers of Ti-32wt.%Nb. The computed structures are related to experimental observations.

MSC:

80-10 Mathematical modeling or simulation for problems pertaining to classical thermodynamics
65C05 Monte Carlo methods
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Zhu, Z. C.; Dhokia, V.; Nassehi, A.; Newman, S. T., Investigation of part distortions as a result of hybrid manufacturing, Robot. Comput.-Integr. Manuf., 37, 23-32 (2016)
[2] Gao, W.; Zhang, Y.; Ramanujan, D.; Ramania, K.; Chen, Y.; Williams, C. B.; Wang, ., C. C., L.; Shin, Y. C.; Zhang, S.; Zavattieri, P. D., The status, challenges, and future of additive manufacturing in engineering, Comput. Aided Des., 69, 65-89 (2015)
[3] Frazier, W. E., Metal additive manufacturing: A review, J. Mater. Eng. Perform., 23, 1917-1928 (2014)
[4] Dong, L.; Makradi, A.; Ahzi, S.; Remond, Y., Three-dimensional transient finite element analysis of the selective laser sintering process, J. Mater Process. Technol., 209, 700-706 (2009)
[5] Michaleris, P., Modeling metal deposition in heat transfer analyses of additive manufacturing processes, Finite Elem. Anal. Des., 86, 51-60 (2014)
[6] Xiong, J.; Lei, Y.; Li, R., Finite element analysis and experimental validation of thermal behavior for thin-walled parts in GMAW-based additive manufacturing with various substrate preheating temperatures, Appl. Therm. Eng., 126, 43-52 (2017)
[7] Goldak, J., Computational welding mechanics as a coupled problem, (Rappaz, M.; Ozgu, M. R.; Mahin, K. W., Modelling of Casting, Welding and Advanced Solidification Processes V (1991), The Minerals, Metals & Materials Society)
[8] Fisk, M.; Ion, J. C.; Lindgren, L.-E., Flow stress model for IN718 accounting for evolution of strengthening precipitates during thermal treatment, Comput. Mater. Sci., 82, 531-539 (2014)
[9] Zhang, Z.; Wan, Z. Y.; Lindgren, L. E.; Tan, Z. J.; Zhou, X., The simulation of precipitation evolutions and mechanical properties in friction stir welding with post weld heat treatments, J. Mater. Eng. Perform., 26, 12, 5731-5740 (2017)
[10] Liu, Y. F.; Cheng, L. F.; Zeng, Q. F.; Feng, Z. Q.; Zhang, J.; Peng, J. H.; Xie, C. W.; Guan, K., Monte Carlo simulation of polycrystalline microstructures and finite element stress analysis, Mater. Des., 55, 740-746 (2014)
[11] Wang, S.; Holm, E. A.; Suni, J.; Alvi, M. H.; Kalu, P. N.; Rollett, A. D., Modeling the recrystallized grain size in single phase materials, Acta Mater., 59, 3872-3882 (2011)
[12] Tan, Y.; Maniatty, A. M.; Zheng, C.; Wen, J. T., Monte Carlo grain growth modeling with local temperature gradients, Modelling Simulation Mater. Sci. Eng., 25, Article 065003 pp. (2017)
[13] Wei, H. L.; Elmer, J. W.; DebRoy, T., Three-dimensional modeling of grain structure evolution during welding of an aluminum alloy, Acta Mater., 126, 413-425 (2017)
[14] Kim, T. H.; Park, J. K., Austenite grain coarsening of V-microalloyed medium carbon steel during high frequency induction heating: Monte Carlo simulation study, Mater. Sci. Technol., 29, 1414-1422 (2013)
[15] Grujicic, M.; Ramaswami, S.; Snipes, J. S.; Avuthu, V.; Galgalikar, R.; Zhang, Z., Prediction of the grain-microstructure evolution within a Friction Stir Welding (FSW) joint via the use of the Monte Carlo simulation method, J. Mater. Eng. Perform., 24, 3471-3486 (2015)
[16] Zhang, Z.; Wu, Q.; Grujicic, M.; Wan, Z. Y., Monte Carlo simulation of grain growth and welding zones in friction stir welding of AA6082-T6, J. Mater. Sci., 51, 1882-1895 (2016)
[17] Wu, Q.; Zhang, Z., Precipitation induced grain growth simulation in friction stir welding, J. Mater. Eng. Perform., 26, 5, 2179-2189 (2017)
[18] Zhang, Y. Q.; Jiang, S. Y.; Hu, L.; Zhao, Y. N.; Sun, D., Investigation of primary static recrystallization in a NiTiFe shape memory alloy subjected to cold canning compression using the coupling crystal plasticity finite element method with cellular automaton, Modelling Simulation Mater. Sci. Eng., 25, Article 075008 pp. (2017)
[19] Deng, Y. S.; Xiu, S., Research on microstructure evolution of austenitization in grinding hardening by cellular automata simulation and experiment, Int. J. Adv. Manuf. Technol., 93, 2599-2612 (2017)
[20] Dobravec, T.; Mavrič, B.; Šarler, B., A cellular automaton – finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement, J. Comput. Phys., 349, 351-375 (2017) · Zbl 1380.65194
[21] Hu, Y. Y.; Xie, J.; Liu, Z. X.; Ding, Q. G.; Zhu, W. H.; Zhang, J. Y.; Zhang, W., CA method with machine learning for simulating the grain and pore growth of aluminum alloys, Comput. Mater. Sci., 142, 244-254 (2018)
[22] Badillo, A.; Beckermann, C., Phase-field simulation of the columnar-to-equiaxed transition in alloy solidification, Acta Mater., 54, 2015-2026 (2006)
[23] Tourret, D.; Karma, A., Growth competition of columnar dendritic grains: A phase-field study, Acta Mater., 82, 64-83 (2015)
[24] Takaki, T.; Shimokawabe, T.; Ohno, M.; Yamanaka, A.; Aoki, T., Unexpected selection of growing dendrites by very-large-scale phase-field simulation, J. Cryst. Growth, 382, 21-25 (2013)
[25] Zinovieva, O.; Zinoviev, A.; Ploshikhin, V., Three-dimensional modeling of the microstructure evolution during metal additive manufacturing, Comput. Mater. Sci., 141, 207-220 (2018)
[26] Lopez-Botello, O.; Martinez-Hernandez, U.; Ramirez, J.; Pinna, C.; Mumtaz, K., Two-dimensional simulation of grain structure growth within selective laser melted AA-2024, Mater. Des., 113, 369-376 (2017)
[27] Rai, A.; Markl, M.; Korner, C., A coupled cellular automaton-lattice Boltzmann model for grain structure simulation during additive manufacturing, Comput. Mater. Sci., 124, 37-48 (2016)
[28] Acharya, R.; Sharon, J. A.; Staroselsky, A., Prediction of microstructure in laser powder bed fusion process, Acta Mater., 124, 360-371 (2017)
[29] Rodgers, T. M.; Madison, J. D.; Tikare, V., Simulation of metal additive manufacturing microstructures using kinetic Monte Carlo, Comput. Mater. Sci., 135, 78-89 (2017)
[30] Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E., Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087-1092 (1653) · Zbl 1431.65006
[31] Gilmer, G., Computer models of crystal growth, Science, 208, 355-363 (1980)
[32] Chatterjee, A.; Vlachos, D. G., An overview of spatial microscopic and accelerated kinetic Monte Carlo methods, J. Computer-Aided Mater. Design, 14, 253-308 (2007)
[33] Vlachos, D. G.; Schmidt, L. D.; Aris, R., Kinetics of faceting of crystals in growth, etching, and equilibrium, Phys. Rev. B, 47, 4896-4909 (1993)
[34] DeVita, J. P.; Sander, L. M.; Smereka, P., Multiscale kinetic Monte Carlo algorithm for simulating epitaxial growth, Phys. Rev. B, 72, Article 205421 pp. (2005)
[35] Rappaz, M.; Gandin, C. A., Probabilistic modelling of microstructure formation in solidification processes, Acta Metall. Mater., 41, 345-360 (1993)
[36] Zhang, Z.; Hu, C. P., 3D Monte Carlo simulation of grain growth in friction stir welding, J. Mech. Sci. Technol., 32, 1287-1296 (2018)
[37] Gao, J. H.; Thompson, R. G., Real time – temperature models for Monte Carlo simulations of normal grain growth, Acta Mater., 44, 4565-4570 (1996)
[38] Dezfoli, A. R.A.; Hwang, W. S., Monte Carlo simulation of TI-6AL-4V grain growth during fast heat treatment, CMC: Comput. Mater. Continua, 49, 1-11 (2015)
[39] Sha, W.; Malinov, S., Titanium Alloys: Modelling of Microstructure, Properties and Applications (2009), Woodhead Publishing Limited: Woodhead Publishing Limited Cambridge
[40] Z. Zhang, P. Ge, Z.Y. Wan, C.P. Hu, Z.J. Tan, Q. Wu, Computational modelling of heat generations and microstructural evolutions in advanced manufacturing technology, in: A Workshop on Predictive Theoretical, Computational and Experimental Approaches for Additive Manufacturing, Dalian, China, Oct 17-19, 2016.; Z. Zhang, P. Ge, Z.Y. Wan, C.P. Hu, Z.J. Tan, Q. Wu, Computational modelling of heat generations and microstructural evolutions in advanced manufacturing technology, in: A Workshop on Predictive Theoretical, Computational and Experimental Approaches for Additive Manufacturing, Dalian, China, Oct 17-19, 2016.
[41] Li, G. C.; Li, J.; Tian, X. J.; Cheng, X.; He, B.; Wang, H. M., Microstructure and properties of a novel titanium alloy Ti-6Al-2V-1.5 Mo-0.5 Zr-0.3 Si manufactured by laser additive manufacturing, Mater. Sci. Eng. A, 684, 233-238 (2017)
[42] Song, K. J.; Wei, Y. H.; Dong, Z. B.; Zhan, X. H.; Zheng, W. J.; Fang, K., Numerical simulation of \(\beta\) to \(\alpha\) phase transformation in heat affected zone during welding of TA15 alloy, Comput. Mater. Sci., 72, 93-100 (2013)
[43] Wolfram, S., Computation theory of cellular automata, Comm. Math. Phys., 96, 1, 15-57 (1984) · Zbl 0587.68050
[44] Liu, Y.; Baudin, T.; Penelle, R., Simulation of normal grain growth by cellular automata, Scr. Mater., 34, 11, 1679-1683 (1996)
[45] Ding, H. L.; He, Y. Z.; Liu, L. F.; Ding, W. J., Cellular automata simulation of grain growth in three dimensions based on the lowest-energy principle, J. Cryst. Growth, 293, 2, 489-497 (2006)
[46] Kobayashi, R., Modeling and numerical simulations of dendritic crystal growth, Physica D, 63, 410-423 (1993) · Zbl 0797.35175
[47] Barber, Z., Introduction to Materials Modelling (2005), Maney Publishing: Maney Publishing London
[48] Boettinger, W. J.; Warren, J. A.; Beckermann, C.; Karma, A., Phase-field Simulation of Solidification, Annu. Rev. Mater. Res., 32, 163-194 (2002)
[49] Provatas, N.; Elder, K., Phase-field methods in materials science and engineering (2010), John Wiley & Sons
[50] Echebarria, B.; Folch, R.; Karma, A.; Plapp, M., Quantitative phase-field model of alloy solidification, Phys. Rev. E, 70, Article 061604 pp. (2004)
[51] Karma, A., Phase-field formulation for quantitative modeling of alloy solidification, Phys. Rev. Lett., 87, Article 115701 pp. (2001)
[52] Takaki, T.; Ohno, M.; Shibuta, Y.; Sakane, S.; Shimokawabe, T.; Aoki, T., Two-dimensional phase-field study of competitive grain growth during directional solidification of polycrystalline binary alloy, J. Cryst. Growth, 442, 14-24 (2016)
[53] Lin, J. J.; Lv, Y. H.; Liu, Y. X.; Sun, Z.; Wang, K. B.; Li, Z. G.; Wu, Y. X.; Xu, B. S., Microstructural evolution and mechanical property of Ti-6Al-4V wall deposited by continuous plasma arc additive manufacturing without post heat treatment, J. Mech. Behav. Biomed. Mater., 69, 19-29 (2017)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.