Multi-phase field simulation of competitive grain growth for directional solidification
Chang-Sheng Zhu(朱昶胜)1,2, Zi-Hao Gao(高梓豪)1,†, Peng Lei(雷鹏)3, Li Feng(冯力)2, and Bo-Rui Zhao(赵博睿)1
1 College of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, China; 2 State Key Laboratory of Gansu Advanced Processing and Recycling of Non-Ferrous Metal, Lanzhou University of Technology, Lanzhou 730050, China; 3 Network&Information Center, Lanzhou University of Technology, Lanzhou 730050, China
Abstract The multi-phase field model of grain competitive growth during directional solidification of alloy is established. Solving multi-phase field models for thin interface layer thickness conditions, the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt% camphor model alloy bi-crystals are investigated. The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed. The obtained results are shown below. In the competitive growth of convergent bi-crystals, when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large, the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite, blocking the unfavorably oriented dendrite, and the grain boundary is along the growth direction of the favorably oriented dendrite. When the pulling speed becomes small, the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite, eliminating the favorably oriented dendrite. In the process of competitive growth of divergent bi-crystal, when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small, the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains, and as the orientation angle of unfavorably oriented dendrites becomes larger, the unfavorably oriented grains are more likely to have stable secondary dendritic arms, which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space, but the grain boundary direction is still parallel to favorably oriented dendrites. In addition, the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes, this blocking of the tertiary dendritic arms has a random nature, which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.
(Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 52161002, 51661020, and 11504149), the Postdoctoral Science Foundation of China (Grant No. 2014M560371), and the Funds for Distinguished Young Scientists of Lanzhou University of Technology, China (Grant No. J201304). The authors thank Dr. Xing Hui for his helpful discussion in code.
Chang-Sheng Zhu(朱昶胜), Zi-Hao Gao(高梓豪), Peng Lei(雷鹏), Li Feng(冯力), and Bo-Rui Zhao(赵博睿) Multi-phase field simulation of competitive grain growth for directional solidification 2022 Chin. Phys. B 31 068102
[1] Stéphane Vernéde, Jonathan A, Dantzig and Michel Rappaz 2008 Acta Materialia57 01554 [2] Yue P T, Zhou C F and James J 2007 J. Comput. Physics223 1 [3] Zhu C S, Xu S, Feng L, et al. 2019 Computational Materials Science160 53 [4] Sakane S, Takaki T, Ohno M, et al. 2017 Journal of Crystal Growth483 147 [5] Walton D and Chalmers B 1959 Transactions of the American Institute of Mining and Metallurgical Engineers215 447 [6] Esaka H 1986 Dendrite growth and spacing in succinonitrile-acetone alloys, Ph. D. dissertation (Switzerland: Ecole Polytechnique Federale de Lausanne) [7] Rappaz M and Gandin C A 1993 Acta Metallurgica et Materialia41 345 [8] D'Souza N, Ardakani M G, Wagner A, et al. 2002 Journal of Materials Science37 481 [9] Zhou Y, Jin T and Sun X 2010 Acta Metallurgica Sinica46 1327 [10] Li J, Wang Z, Wang Y, et al. 2012 Acta Materialia60 1478 [11] Yu H, Li J, Xin L, et al. 2014 Journal of Crystal Growth402 210 [12] Zhao X B, Liu L, Zhang W G, et al. 2011 Rare Metal Materials and Engineering40 9 [13] Zhao Y H, Zhang B, Hou H, et al. 2019 Journal of Materials Science & Technology35 1044 [14] Xing H, Ji M Y, Dong X L, et al. 2020 Materials & Design185 108250 [15] Ofori-Opoku N and Provatas N 2010 Acta Mater58 2155 [16] Song Y, Akamatsu S, Bottin-Rousseau S and Karma A 2018 Phys. Rev. Mater.2 053403 [17] Karma A and Rappel W J 1998 Phys. Rev. E57 4323 [18] Karma A 2001 Phys. Rev. Lett.87 115701 [19] Echebarria B, Folch R, Karma A, et al. 2005 Phys. Rev. E70 061604 [20] Hu S, Yang W, Cui Q, et al. 2017 Materials Characterization125 152 [21] Tourret D and Karma A 2015 Acta Materialia82 64 [22] Takaki T, Ohno M, Shimokawabe T, et al. 2014 Acta Materialia81 272 [23] Dantzig J A and Rappaz M 2009 Solidifification (EFPL Press) [24] Gandin C A and Rappaz M 1994 Acta Metallurgica et Materialia42 2233 [25] Zhou Y Z, Volek A and Green N R 2008 Acta Materialia56 2631 [26] Zhou Y 2011 Scripta Materialia65 281 [27] Wagner A, Shollock B A and Mclean M 2004 Materials Science & Engineering A374 270
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