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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.
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Keywords:
- modified cellular automation /
- ternary alloys /
- dendrite growth
[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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[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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