基于改进元胞自动机模型的三元合金枝晶生长的数值模拟

石玉峰; 许庆彦; 柳百成

doi:10.7498/aps.61.108101

摘要

在二元合金元胞自动机模型的基础上,通过耦合多元合金热力学相平衡求解器PanEngine, 建立了三元合金改进的元胞自动机模型,可模拟初生相枝晶的生长过程. 模型考虑了曲率过冷和成分过冷对界面平衡溶质成分的影响,通过不同组元的无量纲溶质过饱和度方程和界面溶质守恒方程之间的耦合来求解界面生长速率,并通过PanEngine计算界面处的液相线温度. 采用本模型模拟了Al-7%Si-xMg三元合金自由枝晶的生长形态, 结果表明Mg含量的增加会抑制枝晶一次臂的生长和二次臂的产生.同时模拟了不同抽拉速度下 Al-7%Si-0.5%Mg合金柱状枝晶的竞争生长过程,随着抽拉速度的增大,柱状枝晶一次枝晶臂间距逐渐减小, 与Hunt理论模型符合较好.

关键词:

Abstract

Based on the binary cellular automaton method, a modified cellular automaton model for ternary alloys is developed to simulate dendrite growth controlled by solutal effects and microsegregation in the low Peclet number regime by coupling PanEngine, which is a multicomponent thermodynamic and equilibrium calculation engine. The model can be used to calculate the interfacial equilibrium composition by considering the influence of Gibbs-Thomson effect induced curvature undercooling, and multicomponents contributed constitutional undercooling. Meanwhile, the growth velocity of interface is determined by solving the solute conservation equation simultaneously with dimensionless solute supersaturation equation for each alloying element. Moreover, equilibrium liquidus temperature and equilibrium solid concentration at the interface are derived by PanEngine. Free dendrite growth of Al-7%Si-xMg ternary alloys is simulated by the present model, which shows that the increase of solute Mg can suppress the growths of both primary and secondary dendrite arms. Meanwhile, constrained columnar dendrite growth of Al-7%Si-0.5%Mg with the increases of pulling velocity and constant thermal gradient during directional solidification is calculated. The results reveal the competitive growth of columnar dendrites, and demonstrate that the primary dendrite arm spacing would decrease as the pulling velocity increases, which accords well with the Hunt model.

Keywords:

作者及机构信息

1.
清华大学机械工程系,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: 2005CB724105和2011CB706801)、国家自然科学基金(批准号: 10477010和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: 2009ZX04006-041-04和2011ZX04014-052)资助的课题.

Authors and contacts

1.
Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2005CB724105, 2011CB706801), the National Natural Science Foundation of China (Grant Nos. 10477010, 51171089), the National High Technology Research and Development Program of China (Grant No. 2007AA04Z141), and the Important National Science and Technology Specific Projects of China (Grant Nos. 2009ZX04006-041-04, 2011ZX04014-052).

参考文献

[1]	Scheil E 1942 Z. Metallkd 34 70
[2]	Brody H D, Flemings M C 1966 AIME Met. Soc. Trans. 236 615
[3]	Clyne T W, Kurz W 1981 Metall. Mater. Trans. A 12 965
[4]	Chen F Y, Jie W Q 2004 Acta Metall. Sin. 40 664 (in Chinese) [陈福义, 介万奇 2004 金属学报 40 664]
[5]	Lipton J, Glicksman M, Kurz W 1984 Mater. Sci. Eng. 65 57
[6]	Kurz W, Giovanola B, Trivedi R 1986 Acta Metall. 34 823
[7]	Kurz W, Fisher D J 1981 Acta Metall. 29 11
[8]	Hunt J D, Lu S Z 1996 Metall. Mater. Trans. A 27 611
[9]	Wheeler A A, Murrary B T, Schaefer R J 1993 Physica D 66 243
[10]	Kobayashi H, Ode M, Kim S G, Kim W T, Suzuki T 2003 Scripta Mater. 48 689
[11]	Suzuki T, Ode M, Kim S G, Kim W T 2002 J. Cryst. Growth 237-239 125
[12]	Zhang R J, Jing T, Jie W Q, Liu B C 2006 Acta Mater. 54 2235
[13]	Rappaz M, Gandin C A 1993 Acta Metall. 41 345
[14]	Gandin C A, Rappaz M 1994 Acta Metall. 42 2233
[15]	Nastac L 1999 Acta Mater. 47 4253
[16]	Beltran S L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[17]	Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[18]	Liu Y, Xu Q Y, Liu B C 2006 Tsinghua Sci. Tech. 11 495
[19]	Pan S Y, Zhu M F 2010 Acta Mater. 58 340
[20]	Zhu M F, Cao W, Chen S L, Hong C P, Chang Y A 2007 J. Phase Equilib. Diffus. 28 130
[21]	Dai T, Zhu M F, Chen S L, Cao W S, Hong C P 2008 Acta Metall. Sin. 44 1175 (in Chinese) [戴挺, 朱鸣芳, 陈双林, 曹伟生, 洪俊杓 2008 金属学报 44 1175]
[22]	Michelic S C, Thuswaldner J M, Bernhard C 2010 Acta Mater. 58 2738
[23]	Rappaz M, Boettinger W J 1999 Acta Mater. 47 3205
[24]	Trivedi R, Kurz W 1994 Int. Mater. Rev. 39 49
[25]	Du Q, Jacot A 2005 Acta Mater. 53 3479
[26]	Jie W Q, Fu H Z, Zhou Y H 2010 Mater. China 29 1 (in Chinese) [介万奇, 傅恒志, 周尧和 2010 中国材料进展 29 1]

施引文献

[1]	Scheil E 1942 Z. Metallkd 34 70
[2]	Brody H D, Flemings M C 1966 AIME Met. Soc. Trans. 236 615
[3]	Clyne T W, Kurz W 1981 Metall. Mater. Trans. A 12 965
[4]	Chen F Y, Jie W Q 2004 Acta Metall. Sin. 40 664 (in Chinese) [陈福义, 介万奇 2004 金属学报 40 664]
[5]	Lipton J, Glicksman M, Kurz W 1984 Mater. Sci. Eng. 65 57
[6]	Kurz W, Giovanola B, Trivedi R 1986 Acta Metall. 34 823
[7]	Kurz W, Fisher D J 1981 Acta Metall. 29 11
[8]	Hunt J D, Lu S Z 1996 Metall. Mater. Trans. A 27 611
[9]	Wheeler A A, Murrary B T, Schaefer R J 1993 Physica D 66 243
[10]	Kobayashi H, Ode M, Kim S G, Kim W T, Suzuki T 2003 Scripta Mater. 48 689
[11]	Suzuki T, Ode M, Kim S G, Kim W T 2002 J. Cryst. Growth 237-239 125
[12]	Zhang R J, Jing T, Jie W Q, Liu B C 2006 Acta Mater. 54 2235
[13]	Rappaz M, Gandin C A 1993 Acta Metall. 41 345
[14]	Gandin C A, Rappaz M 1994 Acta Metall. 42 2233
[15]	Nastac L 1999 Acta Mater. 47 4253
[16]	Beltran S L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[17]	Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[18]	Liu Y, Xu Q Y, Liu B C 2006 Tsinghua Sci. Tech. 11 495
[19]	Pan S Y, Zhu M F 2010 Acta Mater. 58 340
[20]	Zhu M F, Cao W, Chen S L, Hong C P, Chang Y A 2007 J. Phase Equilib. Diffus. 28 130
[21]	Dai T, Zhu M F, Chen S L, Cao W S, Hong C P 2008 Acta Metall. Sin. 44 1175 (in Chinese) [戴挺, 朱鸣芳, 陈双林, 曹伟生, 洪俊杓 2008 金属学报 44 1175]
[22]	Michelic S C, Thuswaldner J M, Bernhard C 2010 Acta Mater. 58 2738
[23]	Rappaz M, Boettinger W J 1999 Acta Mater. 47 3205
[24]	Trivedi R, Kurz W 1994 Int. Mater. Rev. 39 49
[25]	Du Q, Jacot A 2005 Acta Mater. 53 3479
[26]	Jie W Q, Fu H Z, Zhou Y H 2010 Mater. China 29 1 (in Chinese) [介万奇, 傅恒志, 周尧和 2010 中国材料进展 29 1]

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