搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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

Simulation of dendritic growth for ternary alloys based on modified cellular automaton model

Shi Yu-Feng, Xu Qing-Yan, Liu Bai-Cheng
PDF
导出引用
  • 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.
    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.
    • 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.
    • 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).
    [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]

  • [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]

  • [1] 张颖, 吴文华, 王建元, 翟薇. 超声场中气泡稳态空化对枝晶生长过程的作用机制. 物理学报, 2022, 71(24): 244303. doi: 10.7498/aps.71.20221101
    [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. 物理学报, 2019, 68(16): 166401. doi: 10.7498/aps.68.20190603
    [3] 沙莎, 王伟丽, 吴宇昊, 魏炳波. 深过冷条件下Co7Mo6金属间化合物的枝晶生长和维氏硬度研究. 物理学报, 2018, 67(4): 046402. doi: 10.7498/aps.67.20172156
    [4] 李路远, 阮莹, 魏炳波. 液态三元Fe-Cr-Ni合金中快速枝晶生长与溶质分布规律. 物理学报, 2018, 67(14): 146101. doi: 10.7498/aps.67.20180062
    [5] 魏绍楼, 黄陆军, 常健, 杨尚京, 耿林. 液态Ti-Al合金的深过冷与快速枝晶生长. 物理学报, 2016, 65(9): 096101. doi: 10.7498/aps.65.096101
    [6] 段培培, 邢辉, 陈志, 郝冠华, 王碧涵, 金克新. 镁基合金自由枝晶生长的相场模拟研究. 物理学报, 2015, 64(6): 060201. doi: 10.7498/aps.64.060201
    [7] 潘诗琰, 朱鸣芳. 双边扩散枝晶生长的定量相场模型. 物理学报, 2012, 61(22): 228102. doi: 10.7498/aps.61.228102
    [8] 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. 物理学报, 2012, 61(9): 098104. doi: 10.7498/aps.61.098104
    [9] 王明光, 赵宇宏, 任娟娜, 穆彦青, 王伟, 杨伟明, 李爱红, 葛洪浩, 侯华. 相场法模拟NiCu合金非等温凝固枝晶生长. 物理学报, 2011, 60(4): 040507. doi: 10.7498/aps.60.040507
    [10] 朱昌盛, 王军伟, 王智平, 冯力. 受迫流动下的枝晶生长相场法模拟研究. 物理学报, 2010, 59(10): 7417-7423. doi: 10.7498/aps.59.7417
    [11] 李胜斌, 李晓娜, 董闯, 姜辛. 基于β-FeSi2的(Fe, M)Si2三元合金相形成规律. 物理学报, 2010, 59(6): 4267-4278. doi: 10.7498/aps.59.4267
    [12] 孙东科, 朱鸣芳, 杨朝蓉, 潘诗琰, 戴挺. 强制对流和自然对流作用下枝晶生长的数值模拟. 物理学报, 2009, 58(13): 285-S291. doi: 10.7498/aps.58.285
    [13] 朱昌盛, 冯力, 王智平, 肖荣振. 三维枝晶生长的相场法数值模拟研究. 物理学报, 2009, 58(11): 8055-8061. doi: 10.7498/aps.58.8055
    [14] 龙文元, 吕冬兰, 夏春, 潘美满, 蔡启舟, 陈立亮. 强迫对流影响二元合金非等温凝固枝晶生长的相场法模拟. 物理学报, 2009, 58(11): 7802-7808. doi: 10.7498/aps.58.7802
    [15] 臧渡洋, 王海鹏, 魏炳波. 深过冷三元Ni-Cu-Co合金的快速枝晶生长. 物理学报, 2007, 56(8): 4804-4809. doi: 10.7498/aps.56.4804
    [16] 龙文元, 蔡启舟, 魏伯康, 陈立亮. 相场法模拟多元合金过冷熔体中的枝晶生长. 物理学报, 2006, 55(3): 1341-1345. doi: 10.7498/aps.55.1341
    [17] 杨 弘, 张清光, 陈 民. 热扰动对过冷熔体中二次枝晶生长影响的相场法模拟. 物理学报, 2005, 54(8): 3740-3744. doi: 10.7498/aps.54.3740
    [18] 龙文元, 蔡启舟, 陈立亮, 魏伯康. 二元合金等温凝固过程的相场模型. 物理学报, 2005, 54(1): 256-262. doi: 10.7498/aps.54.256
    [19] 李 强, 李殿中, 钱百年. 元胞自动机方法模拟枝晶生长. 物理学报, 2004, 53(10): 3477-3481. doi: 10.7498/aps.53.3477
    [20] 于艳梅, 杨根仓, 赵达文, 吕衣礼, A. KARMA, C. BECKERMANN. 过冷熔体中枝晶生长的相场法数值模拟. 物理学报, 2001, 50(12): 2423-2428. doi: 10.7498/aps.50.2423
计量
  • 文章访问数:  5684
  • PDF下载量:  1083
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-08-09
  • 修回日期:  2012-05-28
  • 刊出日期:  2012-05-05

/

返回文章
返回