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The multi-phase field model is employed to simulate the growth of tilted dendrites during directional solidification. In this simulation, the evolution of a single oriented dendritic array and the overgrowth behavior between two converging grains with different orientations are studied. The simulated results show that the dendritic tip undercooling increases with the tilt angle, which means that the tip position of tilted dendrite is always lower than that of the non-tilted in the same condition. The favorably oriented grain always blocks the unfavorably oriented one in the case of converging growth. However, when the pulling velocity is low, the growth of the preferred crystalline orientation dendrites at the grain boundary is lagged by the immediate unfavorably ones because of the solutal interaction, which may result in the fact that the unfavorably oriented grain overgrows the favorably oriented one.
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Keywords:
- phase field method /
- directional solidification /
- tip undercooling /
- growth direction
[1] Tiller W A, Jackson K A, Rutter J W 1953 Acta Metall. 1 428
[2] Mullins W W, Sekerka R K 1964 J. Appl. Phys. 35 444
[3] Warren J A, Langer J S 1993 Phys. Rev. E 47 2702
[4] Deschamps J, Georgelin M, Pocheau A 2008 Phys. Rev. E 78 011605
[5] Akamatsu S, Ihle T 1997 Phys. Rev. E 56 4479
[6] Zhou Y Z, Volek A, Green N R 2008 Acta Mater. 56 2631
[7] Zhou Y Z, Green N R 2008 Superalloys Champion, USA, September 14--18, 2008 p317
[8] 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]
[9] Okada T, Saito Y 1996 Phys. Rev. E 54 650
[10] Pocheau A, Deschamps J, Georgelin M 2007 JOM 59 71
[11] Pocheau A, Deschamps J, Georgelin M 2010 Phys. Rev. E 81 1539
[12] Yu Y M, Yang G C, Zhao D W, Lü Y L 2001 Acta Phys. Sin. 50 2423 (in Chinese) [于艳梅, 杨根仓, 赵达文, 吕衣礼 2001 50 2423]
[13] Karma A, Sarkissian A 1996 Metall. Mater. Trans. A 27 635
[14] Zhu Y C, Wang J C, Yang G C, Yang Y J 2007 Acta Phys. Sin. 56 5542 (in Chinese) [朱耀产, 王锦程, 杨根仓, 杨玉娟 2007 56 5542]
[15] Folch R, Plapp M 2003 Phys. Rev. E 68 010602
[16] Li J J, Wang J C, Xu Q, Yang G C 2007 Acta Phys. Sin. 56 1514 (in Chinese) [李俊杰, 王锦程, 许泉, 杨根仓 2007 56 1514]
[17] Steinbach I, Pezzolla F, Nestler B 1996 Phys. D 94 135
[18] Kim S G, Kim W T, Suzuki T 2004 J. Cryst. Growth 261 135
[19] Yang X L, Dong H B, Wang W 2004 Mater. Sci. Eng. A 386 129
[20] Walton D, Chalmers B 1959 Trans. Metall. Soc. AIME 215 447
[21] Burden M H, Hunt J D 1974 J. Cryst. Growth 22 99
[22] Huang W, Geng X, Zhou Y 1993 J. Cryst. Growth 134 105
[23] Trivedi R, Shen Y, Liu S 2003 Metall. Mater. Trans. A 34 395
[24] Souza N D, Aradakani M G, Wagner A 2002 J. Mater. Sci. 27 481
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[1] Tiller W A, Jackson K A, Rutter J W 1953 Acta Metall. 1 428
[2] Mullins W W, Sekerka R K 1964 J. Appl. Phys. 35 444
[3] Warren J A, Langer J S 1993 Phys. Rev. E 47 2702
[4] Deschamps J, Georgelin M, Pocheau A 2008 Phys. Rev. E 78 011605
[5] Akamatsu S, Ihle T 1997 Phys. Rev. E 56 4479
[6] Zhou Y Z, Volek A, Green N R 2008 Acta Mater. 56 2631
[7] Zhou Y Z, Green N R 2008 Superalloys Champion, USA, September 14--18, 2008 p317
[8] 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]
[9] Okada T, Saito Y 1996 Phys. Rev. E 54 650
[10] Pocheau A, Deschamps J, Georgelin M 2007 JOM 59 71
[11] Pocheau A, Deschamps J, Georgelin M 2010 Phys. Rev. E 81 1539
[12] Yu Y M, Yang G C, Zhao D W, Lü Y L 2001 Acta Phys. Sin. 50 2423 (in Chinese) [于艳梅, 杨根仓, 赵达文, 吕衣礼 2001 50 2423]
[13] Karma A, Sarkissian A 1996 Metall. Mater. Trans. A 27 635
[14] Zhu Y C, Wang J C, Yang G C, Yang Y J 2007 Acta Phys. Sin. 56 5542 (in Chinese) [朱耀产, 王锦程, 杨根仓, 杨玉娟 2007 56 5542]
[15] Folch R, Plapp M 2003 Phys. Rev. E 68 010602
[16] Li J J, Wang J C, Xu Q, Yang G C 2007 Acta Phys. Sin. 56 1514 (in Chinese) [李俊杰, 王锦程, 许泉, 杨根仓 2007 56 1514]
[17] Steinbach I, Pezzolla F, Nestler B 1996 Phys. D 94 135
[18] Kim S G, Kim W T, Suzuki T 2004 J. Cryst. Growth 261 135
[19] Yang X L, Dong H B, Wang W 2004 Mater. Sci. Eng. A 386 129
[20] Walton D, Chalmers B 1959 Trans. Metall. Soc. AIME 215 447
[21] Burden M H, Hunt J D 1974 J. Cryst. Growth 22 99
[22] Huang W, Geng X, Zhou Y 1993 J. Cryst. Growth 134 105
[23] Trivedi R, Shen Y, Liu S 2003 Metall. Mater. Trans. A 34 395
[24] Souza N D, Aradakani M G, Wagner A 2002 J. Mater. Sci. 27 481
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