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 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 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 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 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

[1]	张山, 张红伟, 苗淼, 冯苗苗, 雷洪, 王强. 高Cr铸铁中M₇C₃碳化物与奥氏体共生长的元胞自动机模拟. , 2021, 70(21): 218102. doi: 10.7498/aps.70.20210725
[2]	楚硕, 郭春文, 王志军, 李俊杰, 王锦程. 浓度相关的扩散系数对定向凝固枝晶生长的影响. , 2019, 68(16): 166401. doi: 10.7498/aps.68.20190603
[3]	方辉, 薛桦, 汤倩玉, 张庆宇, 潘诗琰, 朱鸣芳. 温度梯度区域熔化作用下熔池迁移的元胞自动机模拟. , 2019, 68(4): 048102. doi: 10.7498/aps.68.20181587
[4]	徐小花, 陈明文, 王自东. 各向异性表面张力对定向凝固中共晶生长形态稳定性的影响. , 2018, 67(11): 118103. doi: 10.7498/aps.67.20180186
[5]	蒋晗, 陈明文, 王涛, 王自东. 各向异性界面动力学与各向异性表面张力的相互作用对定向凝固过程中深胞晶生长的影响. , 2017, 66(10): 106801. doi: 10.7498/aps.66.106801
[6]	康永生, 赵宇宏, 侯华, 靳玉春, 陈利文. 相场法模拟Fe-C合金定向凝固的液相通道. , 2016, 65(18): 188102. doi: 10.7498/aps.65.188102
[7]	郭春文, 李俊杰, 马渊, 王锦程. 定向凝固过程中枝晶侧向分枝生长行为与强制调控规律. , 2015, 64(14): 148101. doi: 10.7498/aps.64.148101
[8]	魏雷, 林鑫, 王猛, 黄卫东. 激光立体成形中熔池凝固微观组织的元胞自动机模拟. , 2015, 64(1): 018103. doi: 10.7498/aps.64.018103
[9]	陈明文, 陈弈臣, 张文龙, 刘秀敏, 王自东. 各向异性表面张力对定向凝固中深胞晶生长的影响. , 2014, 63(3): 038101. doi: 10.7498/aps.63.038101
[10]	韩日宏, 董文超, 陆善平, 李殿中, 李依依. 宏微观耦合模拟熔池不同区域中枝晶竞争生长过程. , 2014, 63(22): 228103. doi: 10.7498/aps.63.228103
[11]	王贤斌, 林鑫, 王理林, 宇红雷, 王猛, 黄卫东. 液相对流对定向凝固胞/枝晶间距的影响. , 2013, 62(7): 078102. doi: 10.7498/aps.62.078102
[12]	王贤斌, 林鑫, 王理林, 白贝贝, 王猛, 黄卫东. 晶体取向对定向凝固枝晶生长的影响. , 2013, 62(10): 108103. doi: 10.7498/aps.62.108103
[13]	王雅琴, 王锦程, 李俊杰. 定向倾斜枝晶生长规律及竞争行为的相场法研究. , 2012, 61(11): 118103. doi: 10.7498/aps.61.118103
[14]	魏雷, 林鑫, 王猛, 黄卫东. 基于MeshTV界面重构算法的二元合金自由枝晶生长元胞自动机模型. , 2012, 61(9): 098104. doi: 10.7498/aps.61.098104
[15]	石玉峰, 许庆彦, 柳百成. 对流作用下枝晶形貌演化的数值模拟和实验研究. , 2011, 60(12): 126101. doi: 10.7498/aps.60.126101
[16]	单博炜, 林鑫, 魏雷, 黄卫东. 纯物质枝晶凝固的元胞自动机模型. , 2009, 58(2): 1132-1138. doi: 10.7498/aps.58.1132
[17]	黄锋, 邸洪双, 王广山. 用元胞自动机方法模拟镁合金薄带双辊铸轧过程凝固组织. , 2009, 58(13): 313-S318. doi: 10.7498/aps.58.313
[18]	王狂飞, 郭景杰, 米国发, 李邦盛, 傅恒志. Ti-45at.% Al合金定向凝固过程中显微组织演化的计算机模拟. , 2008, 57(5): 3048-3058. doi: 10.7498/aps.57.3048
[19]	王志军, 王锦程, 杨根仓. 各向异性作用下合金定向凝固界面稳定性的渐近分析. , 2008, 57(2): 1246-1253. doi: 10.7498/aps.57.1246
[20]	李梅娥, 杨根仓, 周尧和. 二元合金高速定向凝固过程的相场法数值模拟. , 2005, 54(1): 454-459. doi: 10.7498/aps.54.454

计量

文章访问数: 6994
PDF下载量: 845
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板