基于元胞自动机方法的定向凝固枝晶竞争生长数值模拟

陈瑞; 许庆彦; 柳百成

doi:10.7498/aps.63.188102

摘要

通过耦合温度场模型、溶质扩散方程以及枝晶生长动力学方程等重要因素，建立了一种改进的元胞自动机模型. 该模型通过采用偏心算法消除网格各向异性，实现了二维尺度上任意角度枝晶生长的模拟，同时适用于模拟三维尺度上枝晶的生长过程. 利用建立的模型开展了定向凝固枝晶竞争生长过程的数值模拟. 为了体现本模型的有效性，模拟了透明合金的竞争生长过程，并与实验结果符合良好. 镍基高温合金汇聚竞争和发散竞争的模拟结果清楚地展现了不同抽拉速度和枝晶优先生长角度下枝晶的竞争生长过程，并且模拟结果与理论模型相符合. 三维枝晶生长的模拟结果表明本模型可以用来模拟三维枝晶一次臂间距的调整过程.

关键词:

Abstract

Investigating the dendritic competitive growth mechanism is of great importance for directional solidification, and the numerical simulation technique is regarded as an effective approach to a description of microstructural evolution. Therefore, a modified cellular automaton model with decentered square algorithm is developed for quantitatively simulating the dendritic competitive growth process. The model takes into account the simplified thermal field, solute diffusion, growth kinetics, etc., and the solid fraction increment calculation is achieved through local level rule method. The model is successfully used to describe the dendrites with various growth orientations and its availability in simulating dendritic competitive growth is verified by comparing with the experimental results of transparent alloy. For the nickel-based superalloy, the simulated results reveal that in the case of converging dendrites, the unfavorably oriented dendrite is able to overgrow the favorably oriented dendrite, which is dependent on the preferential growth angle. For the divergence case, the favorably oriented dendrite can overgrow the unfavorably oriented dendrite through side branching at the grain boundary. The competitive growth process is mainly controlled by the pulling rate and the preferential growth angle. Furthermore, the model is successfully extended to the simulation of three-dimensional dendritic competitive growth.

Keywords:

作者及机构信息

1.
清华大学材料学院, 先进成形制造教育部重点实验室, 北京 100084

基金项目: 国家重点基础研究发展计划（批准号：2011CB706801）、国家自然科学基金（批准号：51374137，51171089）、国家高技术研究发展计划（批准号：2007AA04Z141）和国家科技重大专项（批准号：2012ZX04012-041-04，2011ZX04014-052）资助的课题.

Authors and contacts

1.
School of Materials Science and Engineering, Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Tsinghua University, Beijing 100084, China

Funds: Project supported by the National Basic Research Program of China (Grant No. 2011CB706801), the National Natural Science Foundation of China (Grant Nos. 51374137, 51171089), the High Technology Research and Development Program of China (Grant No. 2007AA04Z141) and the National Science and Technology Major Projects, China (Grant Nos. 2012ZX04012-041-04, 2011ZX04014-052).

参考文献

[1]	Boettinger W J, Corell S R, Greer A L, Karam A, Kura W, Rappaz M, Trivedi R 2000 Acta Mater. 48 43
[2]	Shi Y F 2013 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)[石玉峰 2013 博士学位论文 (北京: 清华大学)]
[3]	Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[4]	Gandin C A, Rappaz M 1994 Acta Mater. 42 2233
[5]	Yang X L, Dong H B, Wang W, Lee P D 2004 Mater. Sci. Eng. A 386 129
[6]	Dong H B, Lee P D 2005 Acta Mater. 53 659
[7]	Dong H B, Yang X L, Lee P D, Wang W 2004 J. Mater. Sci. 39 7207
[8]	Sanches L B, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[9]	Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[10]	Shi Y F, Xu Q Y, Gong M, Liu B C 2011 Acta Metall. Sin. 47 620(in Chinese)[石玉峰, 许庆彦, 龚铭, 柳百成 2011 金属学报 47 620]
[11]	Walton D, Chalmers B 1959 Trans. Metall. Soc. AIME 215 447
[12]	Zhou Y Z, Volek A, Green N R 2008 Acta Mater. 56 2631
[13]	Zhou Y Z, Jin T, Sun X F 2010 Acta Metall. Sin. 46 1327(in Chinese)[周亦胄, 金涛, 孙晓峰 2010 金属学报 46 1327]
[14]	Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478
[15]	Wang Y Q, Wang J C, Li J J 2012 Acta Phys. Sin. 61 118103(in Chinese)[王雅琴, 王锦程, 李俊杰 2012 物理学报 61 118103]
[16]	Yu H L, Lin X, Li J J, Wang Y Q, Huang W D 2013 Acta Metal. Sin. 49 58(in Chinese)[宇红雷, 林鑫, 李俊杰, 王理林, 黄卫东 2013 金属学报 49 58]
[17]	Nastac L 1999 Acta Mater. 47 4253
[18]	Pan S Y, Zhu M F 2009 Acta Phys. Sin. 58 S278(in Chinese)[潘诗琰, 朱鸣芳 2009 物理学报 58 S278]
[19]	Pan S Y, Zhu M F 2010 Acta Mater. 58 340
[20]	Li B 2013 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)[李斌 2013 博士学位论文 (北京: 清华大学)]
[21]	Esaka H, Shinozuka K, Tamura M 2005 Mater. Sci. Eng. A 413-414 151
[22]	Hunt J D, Lu S Z 1996 Metall. Mater. Trans. A 27 611
[23]	D'souza N, Ardakani M G, Wagner A, Shollock B A, Mclean M 2002 J. Mater. Sci. 37 481
[24]	Zhu M F, Hong C P 2001 ISIJ Int. 41 436
[25]	Yang C B, Liu L, Zhao S B, Wang N, Zhang J, Fu H Z 2013 J. Alloys. Comp. 573 170
[26]	Zhang X L, Zhou Y Z, Jin T, Sun X F, Liu L 2013 J. Mater. Sci. Technol. 29 879
[27]	Lee P D, Chirazi A, Atwood R C, Wang W 2004 Mater. Sci. Eng. A 365 57
[28]	D'Souza N, Jennings P A, Yang X L, Dong H B, Lee P D, Mclean M 2005 Metall. Mater. Trans. B 36B 657

施引文献

[1]	Boettinger W J, Corell S R, Greer A L, Karam A, Kura W, Rappaz M, Trivedi R 2000 Acta Mater. 48 43
[2]	Shi Y F 2013 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)[石玉峰 2013 博士学位论文 (北京: 清华大学)]
[3]	Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[4]	Gandin C A, Rappaz M 1994 Acta Mater. 42 2233
[5]	Yang X L, Dong H B, Wang W, Lee P D 2004 Mater. Sci. Eng. A 386 129
[6]	Dong H B, Lee P D 2005 Acta Mater. 53 659
[7]	Dong H B, Yang X L, Lee P D, Wang W 2004 J. Mater. Sci. 39 7207
[8]	Sanches L B, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[9]	Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[10]	Shi Y F, Xu Q Y, Gong M, Liu B C 2011 Acta Metall. Sin. 47 620(in Chinese)[石玉峰, 许庆彦, 龚铭, 柳百成 2011 金属学报 47 620]
[11]	Walton D, Chalmers B 1959 Trans. Metall. Soc. AIME 215 447
[12]	Zhou Y Z, Volek A, Green N R 2008 Acta Mater. 56 2631
[13]	Zhou Y Z, Jin T, Sun X F 2010 Acta Metall. Sin. 46 1327(in Chinese)[周亦胄, 金涛, 孙晓峰 2010 金属学报 46 1327]
[14]	Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478
[15]	Wang Y Q, Wang J C, Li J J 2012 Acta Phys. Sin. 61 118103(in Chinese)[王雅琴, 王锦程, 李俊杰 2012 物理学报 61 118103]
[16]	Yu H L, Lin X, Li J J, Wang Y Q, Huang W D 2013 Acta Metal. Sin. 49 58(in Chinese)[宇红雷, 林鑫, 李俊杰, 王理林, 黄卫东 2013 金属学报 49 58]
[17]	Nastac L 1999 Acta Mater. 47 4253
[18]	Pan S Y, Zhu M F 2009 Acta Phys. Sin. 58 S278(in Chinese)[潘诗琰, 朱鸣芳 2009 物理学报 58 S278]
[19]	Pan S Y, Zhu M F 2010 Acta Mater. 58 340
[20]	Li B 2013 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)[李斌 2013 博士学位论文 (北京: 清华大学)]
[21]	Esaka H, Shinozuka K, Tamura M 2005 Mater. Sci. Eng. A 413-414 151
[22]	Hunt J D, Lu S Z 1996 Metall. Mater. Trans. A 27 611
[23]	D'souza N, Ardakani M G, Wagner A, Shollock B A, Mclean M 2002 J. Mater. Sci. 37 481
[24]	Zhu M F, Hong C P 2001 ISIJ Int. 41 436
[25]	Yang C B, Liu L, Zhao S B, Wang N, Zhang J, Fu H Z 2013 J. Alloys. Comp. 573 170
[26]	Zhang X L, Zhou Y Z, Jin T, Sun X F, Liu L 2013 J. Mater. Sci. Technol. 29 879
[27]	Lee P D, Chirazi A, Atwood R C, Wang W 2004 Mater. Sci. Eng. A 365 57
[28]	D'Souza N, Jennings P A, Yang X L, Dong H B, Lee P D, Mclean M 2005 Metall. Mater. Trans. B 36B 657

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