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本文基于MeshTV界面重构算法, 发展了二元合金凝固自由枝晶生长的元胞自动机 (cellular automaton, CA) 模型. 通过采用MeshTV界面重构算法, 在细化的界面元胞内重构出了固液界面的位置. 在此基础上, 发展了一种同时适合描述纯物质与合金凝固界面生长的动力学模型. 与非界面重构的CA模型相比, 本文所发展的模型可以在较大的网格尺寸下实现模型的收敛, 同时网格各向异性不明显, 且能够反映界面能各向异性参数 对自由枝晶生长的影响. 在 =0.02时, 通过与描述自由枝晶生长的LGK理论模型相比较, 发现计算的枝晶尖端速度与LGK理论模型的预测符合较好, 而计算的枝晶尖端半径比LGK理论预测值大于约20%.In this paper, cellular automata (CA) model for free dendritic growth of alloy is presented, in which the interface cell is refined by MeshTV interface reconstruction algorithm. In the present CA model, the growth kinetic for both pure material and alloy is used. The effect of interfacial energy anisotropy parameter is validated in the CA model. The dendrite tip growth velocity and tip radius are compared with those of the LGK theoretical model, when =0.02.
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Keywords:
- cellular automata /
- dendrite growth /
- anisotropy
[1] Boettinger W J, Coriell SR, Greer A L, Karma A, Kurz W, Rappaz M, Trivedi R 2000 Acta Metar. 48 43
[2] Asta M, Beckermann C, Karma A, Kurz W, Napolitano R, Plapp M, Purdy G, Rappaz M, Trivedi R 2009 Acta Mater. 57 941
[3] Huang S C, Glicksman M E 1981 Acta Metall. Mater. 29 701
[4] Langer J S 1980 Rev. Mod. Phys. 52 1
[5] Lipton J, Glicksman M E, Kurz W 1987 Metall. Trans. A 18A 341
[6] Huang W D, Geng X G, Zhou Y H 1993 J. Crystal Growth 134 105
[7] Lin X, Huang W D, Feng J, Li T, Zhou Y H 1999 Acta Mater. 47 3271
[8] McFadden G B, Wheeler A A, Braun R J, Coriell S R 1993 Phys. Rev. E 48 2016
[9] Ramirez J C, Beckermann C 2005 Acta Mater. 53 1721
[10] Nastac L 1999 Acta Mater. 47 4253
[11] Beltran Sanchez L, Stefanescu D M 2003 Metall. Mater. Trans. A 34 367
[12] Beltran Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[13] Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[14] Dong H B, Lee P D 2004 Acta Mate. 53 659
[15] Kremeyer K 1998 J. Computational Physics 142 243
[16] Zhu M F, Lee S Y, Hong C P 2004 Phys. Rev. E 69 061610
[17] Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[18] Shan B W, Lin X, Wei L, Huang W D 2007 Advan. Mater. Res. 26--28 957
[19] BROWN S G 1998 J. Mater. Sci. 33 4769
[20] Zhu M F, Yu J, Hong C P 2004 Engineering Science 6 8 (in Chinese) [朱鸣芳, 于金, 洪俊杓 2004 中国工程科学 6 8]
[21] Pan S Y, Zhu M F 2009 Acta Phys. Sinc. 58S278 (in Chinese) [潘诗琰, 朱鸣芳 2009 58 S278]
[22] Shan B W, Lin X, Wei L, Huang W D 2009 Acta Phys. Sin. 58 1132 (in Chinese) [单博炜, 林鑫, 魏雷, 黄卫东 2009 58 1132]
[23] Shan B W, Wei L, Lin X, Huang W D 2006 Foundry 55 439 (in Chinese) [单博炜, 魏雷, 林鑫, 黄卫东 2006 铸造 55 439]
[24] Wei L, Lin X, Shan B W, Huang W D 2007 Proceedings of the 5th Decennial International Conference on Solidification Processing Sheffield, England, July, 2007 p53
[25] Lin X, Wei L, Wang M, Huang W D 2010 Mater. Sci. Forum PRICM7 1528
[26] Wei L, Lin X, Wang M, Huang W D 2011 Applied Physics A 103 123
[27] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477 (in Chinese) [李强, 李殿中, 钱百年 2004 53 3477]
[28] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 S285 (in Chinese) [孙东科, 朱鸣芳, 杨朝蓉, 潘诗琰 2009 58 S285]
[29] Meredith J 2002 Genetic Algorithms and Genetic Programming at Stanford (Custom Publishing) p139
[30] Noh W F, Woodward P R 1976 Lecture Notes in Physics (Berlin/New York: Springer-Verlag) p330
[31] Parker B J, Youngs D L 1992 Technical Report 01/92 (Berkshire, U.K.: Atomic Weapons Establishment) p30
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[1] Boettinger W J, Coriell SR, Greer A L, Karma A, Kurz W, Rappaz M, Trivedi R 2000 Acta Metar. 48 43
[2] Asta M, Beckermann C, Karma A, Kurz W, Napolitano R, Plapp M, Purdy G, Rappaz M, Trivedi R 2009 Acta Mater. 57 941
[3] Huang S C, Glicksman M E 1981 Acta Metall. Mater. 29 701
[4] Langer J S 1980 Rev. Mod. Phys. 52 1
[5] Lipton J, Glicksman M E, Kurz W 1987 Metall. Trans. A 18A 341
[6] Huang W D, Geng X G, Zhou Y H 1993 J. Crystal Growth 134 105
[7] Lin X, Huang W D, Feng J, Li T, Zhou Y H 1999 Acta Mater. 47 3271
[8] McFadden G B, Wheeler A A, Braun R J, Coriell S R 1993 Phys. Rev. E 48 2016
[9] Ramirez J C, Beckermann C 2005 Acta Mater. 53 1721
[10] Nastac L 1999 Acta Mater. 47 4253
[11] Beltran Sanchez L, Stefanescu D M 2003 Metall. Mater. Trans. A 34 367
[12] Beltran Sanchez L, Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
[13] Zhu M F, Stefanescu D M 2007 Acta Mater. 55 1741
[14] Dong H B, Lee P D 2004 Acta Mate. 53 659
[15] Kremeyer K 1998 J. Computational Physics 142 243
[16] Zhu M F, Lee S Y, Hong C P 2004 Phys. Rev. E 69 061610
[17] Wang W, Lee P D, McLean M 2003 Acta Mater. 51 2971
[18] Shan B W, Lin X, Wei L, Huang W D 2007 Advan. Mater. Res. 26--28 957
[19] BROWN S G 1998 J. Mater. Sci. 33 4769
[20] Zhu M F, Yu J, Hong C P 2004 Engineering Science 6 8 (in Chinese) [朱鸣芳, 于金, 洪俊杓 2004 中国工程科学 6 8]
[21] Pan S Y, Zhu M F 2009 Acta Phys. Sinc. 58S278 (in Chinese) [潘诗琰, 朱鸣芳 2009 58 S278]
[22] Shan B W, Lin X, Wei L, Huang W D 2009 Acta Phys. Sin. 58 1132 (in Chinese) [单博炜, 林鑫, 魏雷, 黄卫东 2009 58 1132]
[23] Shan B W, Wei L, Lin X, Huang W D 2006 Foundry 55 439 (in Chinese) [单博炜, 魏雷, 林鑫, 黄卫东 2006 铸造 55 439]
[24] Wei L, Lin X, Shan B W, Huang W D 2007 Proceedings of the 5th Decennial International Conference on Solidification Processing Sheffield, England, July, 2007 p53
[25] Lin X, Wei L, Wang M, Huang W D 2010 Mater. Sci. Forum PRICM7 1528
[26] Wei L, Lin X, Wang M, Huang W D 2011 Applied Physics A 103 123
[27] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477 (in Chinese) [李强, 李殿中, 钱百年 2004 53 3477]
[28] Sun D K, Zhu M F, Yang C R, Pan S Y, Dai T 2009 Acta Phys. Sin. 58 S285 (in Chinese) [孙东科, 朱鸣芳, 杨朝蓉, 潘诗琰 2009 58 S285]
[29] Meredith J 2002 Genetic Algorithms and Genetic Programming at Stanford (Custom Publishing) p139
[30] Noh W F, Woodward P R 1976 Lecture Notes in Physics (Berlin/New York: Springer-Verlag) p330
[31] Parker B J, Youngs D L 1992 Technical Report 01/92 (Berkshire, U.K.: Atomic Weapons Establishment) p30
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