Simulation of grain structure evolution in Al-Si alloys during laser powder bed fusion

Ekaterina M. Dymnich, Varvara A. Romanova, Anzhelika Borodina, Ruslan R. Balokhonov

Author details

Ekaterina M. Dymnich
Institute of Strength Physics and Material Science SB RAS, Tomsk, Russian Federation; National Research Tomsk State University, Tomsk, Russian Federation
Varvara A. Romanova
Institute of Strength Physics and Material Science SB RAS, Tomsk, Russian Federation; National Research Tomsk State University, Tomsk, Russian Federation
Anzhelika Borodina
Institute of Strength Physics and Material Science SB RAS, Tomsk, Russian Federation; National Research Tomsk State University, Tomsk, Russian Federation
Ruslan R. Balokhonov
Institute of Strength Physics and Material Science SB RAS, Tomsk, Russian Federation; National Research Tomsk State University, Tomsk, Russian Federation

https://doi.org/10.15593/perm.mech/2025.5.01

This study focuses on the development and validation of a model for grain structure formation in the aluminum-silicon alloy AlSi10Mg during selective laser melting (SLM). The developed model incorporates calculations of the spatiotemporal evolution of thermal fields induced by laser action and establishes a direct correlation between local thermal history (temperature gradients, cooling rates) and grain structure formation processes. To address this challenge, we propose an integrated approach combining finite difference method for temperature field calculations and cellular automaton modeling of crystallization. A key feature of the model is its consideration of both epitaxial and competitive grain growth mechanisms, as well as nucleation processes in multiple melt pools. Within the cellular automaton framework, the growing dendrite morphology was approximated by an octahedral surface, consistent with the crystallographic characteristics of FCC alloy solidification. The developed model was applied to simulate grain structure formation under a bidirectional scanning strategy. Results demonstrate that the proposed model effectively reproduces characteristic solidification features observed in selective laser melting processes. We present validation results comparing geometric characteristics and crystallographic orientations of grains with experimental data. The comparison shows both qualitative and quantitative agreement, confirming the model's ability to accurately reproduce key geometric features of the grain structure.

Keywords

selective laser meltingaluminum-silicon alloysthermal fieldscrystallizationgrain structurecrystallographic textureEBSD analysisfinite difference methodcellular automata.

МОДЕЛИРОВАНИЕ ФОРМИРОВАНИЯ ЗЕРЕННОЙ СТРУКТУРЫ СПЛАВА AlSi10Mg В УСЛОВИЯХ СЕЛЕКТИВНОГО ЛАЗЕРНОГО СПЛАВЛЕНИЯ

Настоящая работа посвящена разработке и валидации модели формирования зеренной структуры алюминиево-кремниевого сплава AlSi10Mg в процессе селективного лазерного сплавления. Разработанная модель включает расчет пространственно-временной эволюции термических полей, вызванных действием лазера, и установление прямой связи между локальной термической историей (градиентами температуры, скоростями охлаждения) с процессом формирования зеренной структуры. Для решения этой задачи предложен подход, объединяющий расчет температурных полей методом конечных разностей и моделирование кристаллизации методом клеточных автоматов. Важной особенностью модели является учет процессов эпитаксиального и конкурирующего типов роста зерен, а также процесса зародышеобразования во множественных ваннах расплава. В рамках реализации метода клеточных автоматов форма растущего дендрита аппроксимировалась октаэдрической поверхностью в соответствии с кристаллографическими особенностями кристаллизации ПЦК сплавов. Разработанная модель была применена для моделирования формирования зеренной структуры при двунаправленной стратегии сканирования. Было показано, что предложенная модель способна адекватно воспроизводить характерные особенности кристаллизации в процессе селективного лазерного сплавления. Приведены результаты валидации построенной модели зеренной структуры сплава AlSi10Mg на основе сравнения геометрических характеристик и кристаллографических ориентаций зерен с экспериментальными данными. Сравнение результатов моделирования с экспериментальными данными показало качественное и количественное согласие, что свидетельствует о корректном воспроизведении геометрических особенностей зеренной структуры в модели.

Ключевые слова

селективное лазерное сплавлениеалюминиево-кремниевые сплавытермические полякристаллизациязеренная структуракристаллографическая текстураEBSD-анализметод конечных разностейметод клеточных автоматов.

Bibliography

1.Unravelling the multi-scale structure–property relationship of laser powder bed fusion processed and heat-treated AlSi10Mg / P. Van Cauwenbergh [et al.] // Scientific Reports. – 2021. – Vol. 11, no. 1. – 6423. DOI: 10.1038/s41598-021-85047-2 Scholar
2.Научные подходы к микро-, мезо- и макроструктурному дизайну объемных металлических и полиметаллических материалов с использованием метода электронно-лучевого аддитивного производства / Е.А. Колубаев, В.Е. Рубцов, А.В. Чумаевский, Е.Г. Астафурова // Физическая мезомеханика. – 2022. – T. 25 (4). – C. 5–18. Scholar
3.Effects of build orientation and heat treatments on the tensile and fracture toughness properties of additively manufactured AlSi10Mg / L.C. Araújo [et al.] // International Journal of Mechanical Sciences. – 2022. – Vol. 213. – 106868. DOI: 10.1016/j.ijmecsci.2021.106868 Scholar
4.Microstructure, porosity and mechanical properties of selective laser melted AlSi10Mg / J. Chen, W. Hou, X. Wang, S. Chu, Z. Yang // Chinese Journal of Aeronautics. – 2020. – Vol. 33, no. 7. – P. 2043–2054. DOI: 10.1016/j.cja.2019.08.017 Scholar
5.Evaluation of the stress-strain relationship of constituent phases in AlSi10Mg alloy produced by selective laser melting using crystal plasticity FEM / D-K. Kim, J-H. Hwang, E-Y. Kim, Y-U. Heo, W. Woo, S-H. Choi // Journal of Alloys and Compounds. – 2017. – Vol. 714. – P. 687–97. DOI: 10.1016/j.jallcom.2017.04.264 Scholar
6.Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior / E. Brandl, U. Heckenberger, V. Holzinger, D. Buchbinder // Materials & Design. – 2012. – Vol. 34. P. 159–69. DOI: 10.1016/j.matdes.2011.07.067 Scholar
7.Altenbach H., Öchsner A., editors. State of the Art and Future Trends in Material Modeling. vol. 100, Cham: Springer International Publishing; 2019. DOI: 10.1007/978-3-030-30355-6. Scholar
8.Maeshima, T. Solute clustering and supersaturated solid solution of AlSi10Mg alloy fabricated by selective laser melting / T. Maeshima, K. Ohishi // Heliyon. – 2019. – Vol. 5. – e01186. DOI: 10.1016/j.heliyon.2019.e01186 Scholar
9.Additive manufacturing of metallic components – Process, structure and properties / T. DebRoy, H.L. Wei, J.S. Zuback, T. Mukherjee, J.W. Elmer, J.O. Milewski, A.M. Beese, A. Wilson-Heid, A. De, W. Zhang // Progress in Materials Science. – 2018. – Vol. 92. – P. 112–224. DOI: 10.1016/j.pmatsci.2017.10.001 Scholar
10.3D printing of Aluminium alloys: Additive Manufacturing of Aluminium alloys using selective laser melting / N.T. Aboulkhair, M. Simonelli, L. Parry, I. Ashcroft, C. Tuck, R. Hague // Progress in Materials Science. – 2019. – Vol. 106. – 100578. DOI: 10.1016/j.pmatsci.2019.100578. Scholar
11.Effect of the Boundary Orientation of Melt Pool on Mechanical Property and Fracture Path in Selective-Laser-Melted AlSi10Mg Alloy / Z. Jiang, Y. Li, H. Luo, B. Zhou, Y. Liang, Y. Liang // Met. Mater Int. – 2022. – Vol. 28. – P. 2934–2946. DOI: 10.1007/s12540-022-01199-4 Scholar
12.Microstructural origin of anisotropic tensile ductility of Al-Si alloy manufactured by laser powder bed fusion / Y. Otani, N. Takata, A. Suzuki, M. Kobashi, M. Kato // Scripta Materialia. – 2023. – Vol. 226. – 115259. DOI: 10.1016/j.scriptamat.2022.115259 Scholar
13.Review on the correlation between microstructure and mechanical performance for laser powder bed fusion AlSi10Mg / L. Zhao, L. Song, J.G. Santos Macias, Y. Zhu, M. Huang, A. Simar, Z. Li // Additive Manufacturing. – 2022. – Vol. 56. – 102914. DOI: 10.1016/j.addma.2022.102914. Scholar
14.On the Selective Laser Melting (SLM) of the AlSi10Mg Alloy: Process, Microstructure, and Mechanical Properties / F. Trevisan, F. Calignano, M. Lorusso, J. Pakkanen, A. Aversa, E. Ambrosio, M. Lombardi, P. Fino, D. Manfredi // Materials. – 2017. – Vol. 10. – 76. DOI: 10.3390/ma10010076. Scholar
15.Microstructure of selective laser melted AlSi10Mg alloy / X. Liu, C. Zhao, X. Zhou, Z. Shen, W. Liu // Materials & Design. – 2019. – Vol. 168. – 107677. DOI: 10.1016/j.matdes.2019.107677 Scholar
16.Körner, C. Mesoscopic simulation of selective beam melting processes / C. Körner, E. Attar, P. Heinl // Journal of Materials Processing Technology. – 2011. – Vol. 211. – P. 978–987. DOI: 10.1016/j.jmatprotec.2010.12.016 Scholar
17.Discrete element simulation and experimental study of powder spreading process in additive manufacturing / S. Haeri, Y. Wang, O. Ghita, J. Sun // Powder Technology. – 2017. – Vol. 306. – P. 45–54. DOI: 10.1016/j.powtec.2016.11.002 Scholar
18.Metal additive-manufacturing process and residual stress modeling / M. Megahed, H-W. Mindt, N. N’Dri, H. Duan, O. Desmaison // Integr. Mater. Manuf. Innov. – 2016. – Vol. 5. – P. 61–93. DOI: 10.1186/s40192-016-0047-2. Scholar
19.Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones / S.A. Khairallah, A.T. Anderson, A. Rubenchik, W.E. King // Acta Materialia. – 2016. – Vol. 108. – P. 36–45. DOI: 10.1016/j.actamat.2016.02.014. Scholar
20.A Review of Computational Approaches to the Microstructure-Informed Mechanical Modelling of Metals Produced by Powder Bed Fusion Additive Manufacturing / O. Zinovieva, V.A. Romanova, E. Dymnich, A. Zinoviev, R. Balokhonov // Materials. – 2023. – Vol. 16, no. 19. – 6459. DOI: 10.3390/ma16196459 Scholar
21.Князева, А.Г. Уточнение базовых уравнений теории фазового поля для неизотермических условий / А.Г. Князева // Физическая мезомеханика. – 2024. – Т. 27(6). – С. 33–54. Scholar
22.Application of finite element, phase-field, and CALPHAD-based methods to additive manufacturing of Ni-based superalloys / T. Keller [et al.] // Acta Materialia. – 2017. – Vol. 139. – P. 244–253. DOI: 10.1016/j.actamat.2017.05.003 Scholar
23.Galenko, P., Phase-field model with relaxation of the diffusion flux in nonequilibrium solidification of a binary system // Physics Letters A. – 2001. – Vol. 287. – P. 190–197. Scholar
24.Lu, L-X. Phase field simulation of powder bed-based additive manufacturing / L-X. Lu, N. Sridhar, Y-W. Zhang // Acta Materialia. – 2018. – Vol. 144. – P. 801–809. DOI: 10.1016/j.actamat.2017.11.033 Scholar
25.On the primary spacing and microsegregation of cellular dendrites in laser deposited Ni–Nb alloys / S. Ghosh, L. Ma, N. Ofori-Opoku, J.E. Guyer // Modelling Simul. Mater. Sci. Eng. – 2017. – Vol. 25. – 065002. DOI: 10.1088/1361-651X/aa7369 Scholar
26.Gong, X. Phase-Field Modeling of Microstructure Evolution in Electron Beam Additive Manufacturing / X. Gong, K. Chou // JOM. – 2015. – Vol. 67. – P. 1176–1182. DOI: 10.1007/s11837-015-1352-5. Scholar
27.Sahoo, S. Phase-field simulation of microstructure evolution of Ti–6Al–4V in electron beam additive manufacturing process / S. Sahoo, K. Chou // Additive Manufacturing. – 2016. – Vol. 9. – P.14–24. DOI: 10.1016/j.addma.2015.12.005 Scholar
28.Phase-field simulation of solidification morphology in laser powder deposition of Ti–Nb alloys / V. Fallah, M. Amoorezaei, N. Provatas, S.F. Corbin, A.A. Khajepour // Acta Materialia. – 2012. – Vol. 60. – P. 1633–1646. DOI: 10.1016/j.actamat.2011.12.009 Scholar
29.The Origin of Microstructural Diversity, Texture, and Mechanical Properties in Electron Beam Melted Ti-6Al-4V / S.S. Al-Bermani, M.L. Blackmore, W. Zhang, I. Todd // Metallurgical and Materials Transactions A. – 2010. – Vol. 41, no. 13. – P. 3422–3434. DOI: 10.1007/s11661-010-0397-x Scholar
30.Antonysamy, A.A. Effect of build geometry on the β-grain structure and texture in additive manufacture of Ti6Al4V by selective electron beam melting / A.A. Antonysamy, J. Meyer, P.B. Prangnell // Materials Characterization. – 2013. – Vol. 84. – P. 153–168. DOI: 10.1016/j.matchar.2013.07.012 Scholar
31.Rodgers, T.M. Simulation of metal additive manufacturing microstructures using kinetic Monte Carlo / T.M. Rodgers, J.D. Madison, V. Tikare // Computational Materials Science. – 2017. – Vol. 135. – P. 78–89. DOI: 10.1016/j.commatsci.2017.03.053 Scholar
32.Influence of manufacturing geometric defects on the mechanical properties of AlSi10Mg alloy fabricated by selective laser melting / P. Wang, H. Lei, X. Zhu, H. Chen, D. Fang // Journal of Alloys and Compounds. – 2019. – Vol. 789. – P. 852–859. DOI: 10.1016/j.jallcom.2019.03.135. Scholar
33.Damage modeling of metallic alloys made by additive manufacturing / M. Taheri Andani, M. Ghodrati, M.R. Karamozov-Ravari, R. Mirzaeifar, J. Ni // Materials Science and Engineering: A. – 2019. – Vol. 743. – P. 656–664. DOI: 10.1016/j.msea.2018.11.125 Scholar
34.An integrated process–structure–property modeling framework for additive manufacturing / W. Yan [et al.] // Computer Methods in Applied Mechanics and Engineering. – 2018. – Vol. 339. – P. 184–204. DOI: 10.1016/j.cma.2018.05.004 Scholar
35.Evolution of grain structure during laser additive manufacturing. Simulation by a cellular automata method / A. Zinoviev, O. Zinovieva, V. Ploshikhin, V. Romanova, R. Balokhonov // Materials & Design. – 2016. – Vol. 106. – P. 321–329. DOI: 10.1016/j.matdes.2016.05.125 Scholar
36.Understanding grain evolution in additive manufacturing through modeling / J. Akram, P. Chalavadi, D. Pal, B. Stucker // Additive Manufacturing. – 2018. – Vol. 21. – P. 255–268. DOI: 10.1016/j.addma.2018.03.021 Scholar
37.Mohebbi, M.S. Implementation of nucleation in cellular automaton simulation of microstructural evolution during additive manufacturing of Al alloys / M.S. Mohebbi, V. Ploshikhin // Additive Manufacturing. – 2020. – Vol. 36. – 101726. DOI: 10.1016/j.addma.2020.101726 Scholar
38.Chen, R. Cellular automaton simulation of three-dimensional dendrite growth in Al-7Si-3Mg ternary aluminum alloys / R. Chen, Q. Xu, B. Liu // Computational Materials Science. – 2015. – Vol. 105. – P. 90–100. DOI: 10.1016/j.commatsci.2015.04.035 Scholar
39.Zinovieva, O. Three-dimensional modeling of the microstructure evolution during metal additive manufacturing / A. Zinoviev, O. Zinovieva, V. Ploshikhin // Computational Materials Science. – 2018. – Vol. 141. – P. 207–220. DOI: 10.1016/j.commatsci.2017.09.018 Scholar
40.Three-dimensional analysis of grain structure and texture of additively manufactured 316L austenitic stainless steel / O. Zinovieva, A. Zinoviev, V. Romanova, R. Balokhonov // Additive Manufacturing. – 2020. – Vol. 36. – 101521. DOI: 10.1016/j.addma.2020.101521. Scholar
41.Morel, V. The Critical Temperature of Aluminum / V. Morel, A. Bultel, B.G. Cheron // International Journal of Thermophysics. – 2009. – Vol. 30. – P. 1853–1863. DOI: 10.1007/s10765-009-0671-6 Scholar
42.Simulations of microstructure coupling with moving molten pool by selective laser melting using a cellular automaton / X. Ao, H. Xia, J. Liu, Q. He // Materials & Design. – 2020. – Vol. 185. – 108230. doi: 10.1016/j.matdes.2019.108230 Scholar
43.A physically-based computational approach for processing-microstructure-property linkage of materials additively manufactured by laser powder bed fusion / V. Romanova, M.S. Mohebbi, E. Dymnich, R. Balokhonov, V. Ploshikhin // International Journal of Mechanical Sciences. – 2022. – Vol. 219. – 107103. DOI: 10.1016/j.ijmecsci.2022.107103 Scholar
44.Gandin, Ch.-A. Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings / Ch.-A. Gandin, M. Rappaz, R. Tintillier // MTA. – 1993. – Vol. 24. – P. 467–479. DOI: 10.1007/BF02657334 Scholar
45.Rappaz, M. Probabilistic modelling of microstructure formation in solidification processes / M. Rappaz, Ch.-A. Gandin // Acta Metallurgica et Materialia. – 1993. – Vol. 41. – P. 345–360. DOI: 10.1016/0956-7151(93)90065-z Scholar
46.Shao, G. Prediction of phase selection in rapid solidification using time dependent nucleation theory / G. Shao, P. Tsakiropoulos // Acta Metallurgica et Materialia. – 1994. – Vol. 42, no. 9. – P. 2937–2942. DOI: 10.1016/0956-7151(94)90391-3 Scholar
47.Gandin, Ch.-A. A 3D Cellular Automaton algorithm for the prediction of dendritic grain growth / Ch.-A. Gandin, M. Rappaz // Acta Materialia. – 1997. – Vol. 45. – P. 2187–2195. DOI: 10.1016/s1359-6454(96)00303-5 Scholar
48.Kurz, W. Theory of microstructural development during rapid solidification / W. Kurz, B. Giovanola, R. Trivedi // Acta Metallurgica. – 1986. – Vol. 34, no. 5. – P. 823–830. Scholar
49.Strategy of computational predictions for mechanical behaviour of additively manufactured materials / O. Zinovieva, A. Zinoviev, V. Ploshikhin, V. Romanova, R. Balokhonov // Materials Science and Technology. – 2018. – Vol. 34, no. 3. – P. 1591–1605. DOI: 10.1080/02670836.2018.1489939 Scholar
50.A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures / Ch.-A. Gandin, J.-L. Desbiolles, M. Rappaz, Ph. Thevoz // Metallurgical and Materials Transactions A. – 1999. – Vol. 30, no. 12. – P. 3153–3165. Scholar
51.Rafique, M.M.A. Probabilistic Modelling of Microstructural Evolution in Zr Based Bulk Metallic Glass Matrix Composites during Solidification in Additive Manufacturing / M.M.A. Rafique // Engineering. – 2018. – Vol. 10, no. 04. – pp. 130–141. DOI: 10.4236/eng.2018.104010 Scholar
52.A cellular automaton finite volume method for microstructure evolution during additive manufacturing / Y. Lian, Z. Gan, C. Yu, D. Kats, W.-K. Liu, G.J. Wagner // Materials & Design. – 2019. – Vol. 169, no. 6. – 107672. DOI: 10.1016/j.matdes.2019.107672 Scholar
53.Knyazeva A. G. Sviazannaa model' sinteza na podlozhke // Matematicheskoe modelirovanie v estestvennykh naukah. – 2023. – № 1. – C. 166–169. Scholar
54.Zienkiewicz O.C. The finite element method: its basis and fundamentals / Zienkiewicz, R.L. Taylor, J.Z. Zhu. – Elsevier, Amsterdam Heidelberg, 2010. – 802 p. Scholar
55.Thijs L. Microstructure and Texture of Metal Parts Produced by Selective Laser Melting: doctoral thesis / L. Thijs – KU Leuven, Faculty of Engineering Science, 2014. – 294 p. Scholar
56.Microstructure evolution and thermal properties of an additively manufactured, solution treatable AlSi10Mg part / P. Yang, L.A. Deibler, D.R. Bradley, D.K. Stefan, J.D. Caroll, // Journal of Materials Research. – 2018. – Vol. 33, no. 23. – P. 4040–4052. DOI: 10.1557/jmr.2018.405 Scholar
57.Lathabai, S. Additive Manufacturing of Aluminium-Based Alloys and Composites // Fundamentals of Aluminium Metallurgy. – 2018. – P. 47–92. DOI: 10.1016/B978-0-08-102063-0.00002-3 Scholar
58.Influence of process-induced microstructure and imperfections on mechanical properties of AlSi12 processed by selective laser melting / S. Siddique, M. Imran, E. Wycisk // Journal of Materials Processing Technology. – 2015. – Vol. 221. – P. 205–213. doi: 10.1016/j.matprotec.2015.02.023 Scholar
59.Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder / L. Thijs, K. Kempen, J.-P. Kruth, J. Van Humbeeck // Acta Materialia. – 2013. – Vol. 61, no. 5. – P. 1809–1819. DOI: 10.1016/j.actamat.2012.11.052 Scholar
60.Solidification pattern, microstructure and texture development in Laser Powder Bed Fusion (LPBF) of Al10SiMg alloy / H. Qin, V. Fallah, Q. Dong, M. Brochu, M. Daymond, M. Gallerneault // Materials Characterization. – 2018. – Vol. 145. – P. 29–38. DOI: 10.1016/j.matchar.2018.08.025 Scholar
61.Change in microstructure of selectively laser melted AlSi10Mg alloy with heat treatments / N. Takata, H. Kodaira, K. Sekizawa, A. Suzuki, M. Kobashi // Materials Science and Engineering: A. – 2017. – Vol. 704, no. 67. – P. 218–228. DOI: 10.1016/j.msea.2017.08.029 Scholar
62.Influence on microstructure, strength and ductility of build platform temperature during laser powder bed fusion of AlSi10Mg / J.G. Santos Macias [et al.] // Acta Materialia. – 2020. – Vol. 201. – P. 231–243. DOI: 10.1016/j.actamat.2020.10.001 Scholar
63.Panwisawas, C. Metal 3D printing as a disruptive technology for superalloys / C. Panwisawas, Y.T. Tang, R.C. Reed // Nature Communications. – 2020. – Vol. 11, no. 1. – 2327. DOI: 10.1038/s41467-020-16188-7 Scholar
64.Anwar, A.B. Selective laser melting of AlSi10Mg: Effects of scan direction, part placement and inert gas flow velocity on tensile strength / A.B. Anwar, Q.-C. Pham // Journal of Materials Processing Technology. – 2017. – Vol. 240. – P. 388–396. DOI: 10.1016/j.matprotec.2016.10.015 Scholar
65.A Study of Deformation and Fracture of the Eutectic in an Additively Manufactured Al-Si Composite Alloy / A.V. Zemlyanov [et al.] // Physical Mesomechanics. – 2023. – Vol. 26, no. 6. – P. 678–690. DOI: 10.1134/S1029959923060073 Scholar

Article information

Published: 17 December 2025
Issue date: 17 December 2025
Issue: No. 5 (2025)