自适应有限元法对合金定向倾斜枝晶生长的相场法模拟

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (3): 15-22.

自适应有限元法对合金定向倾斜枝晶生长的相场法模拟

朱昶胜^*1,2, 高宏伟¹, 马芳兰¹, 冯力², 雷鹏³

1.兰州理工大学计算机与通信学院, 甘肃兰州 730050;
2.兰州理工大学省部共建有色金属先进加工与再利用国家重点实验室, 甘肃兰州 730050;
3.兰州理工大学网络与信息中心, 甘肃兰州 730050

收稿日期:2020-12-22 出版日期:2021-06-28 发布日期:2021-07-19
通讯作者: 朱昶胜(1972-),男,甘肃秦安人,教授,博导.Email:zhucs_2008@163.com
基金资助:
国家自然科学基金(51661020,11364024,11504149)

Phase field method study on oriented tilted dendrite growth of alloy by adaptive finite element method

ZHU Chang-sheng^1,2, GAO Hong-wei¹, MA Fang-lan¹, FENG Li², LEI Peng³

1. College of Computer and Communication, Lanzhou Univ. of Tech., Lanzhou 730050, China;
2. State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metal, Lanzhou Univ. of Tech., Lanzhou 730050, China;
3. Network & Information Center, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2020-12-22 Online:2021-06-28 Published:2021-07-19

摘要/Abstract

摘要： 建立了合金定向倾斜枝晶生长的相场模型,采用非均匀网格的自适应有限元法求解薄界面层厚度条件下的相场模型,研究了Al-Cu(w(Cu)=4%)合金的倾斜枝晶演化过程,定量分析了冷却速率、主晶间距对凝固组织的影响.结果表明:冷却速率、主晶间距和抽拉速度可以控制倾斜枝晶的生长角度,随着冷却速率的增加,枝晶的生长会偏离择优取角向温度梯度方向偏转,反之主晶间距和抽拉速度增大,枝晶的生长角度逐渐从温度梯度方向朝着晶体择优方向偏转.此外,自适应有限元法相较于均匀网格法在CPU的运行时间上降低了一个数量级,并且随着计算域的增大,自适应有限元法的计算效率越高.

关键词: 相场模拟, 自适应有限元, 定向凝固, Al-Cu(w(Cu)=4%)合金

Abstract: The article established a phase field model that is an oriented tilted dendrite of alloy, and used a non-uniform grid adaptive finite element method to solve the phase field model of thin interface layer thickness. The thesis also researched the evolution process of the tilting dendrite of Al-Cu(w(Cu)=4%) alloy, and quantitatively analyzed the effect of cooling rate and the main crystal spacing on solidification structure. The results demonstrated that the cooling rate and the main crystal spacing and the pulling speed can control the growth angle of the tilting dendrite. With the increase of the cooling rate, the growth of dendrite will deviate from the preferred direction to the direction of temperature gradient. On the contrary, with the increase of main crystal spacing and pulling speed, the growth angle of dendrite will gradually deviate from the temperature gradient direction to the preferred crystal direction. In addition, compared with the uniform grid method, the adaptive finite element method reduces the running time of the CPU by an order of magnitude. And as the computational domain increases, the computational efficiency of the adaptive finite element method is higher.

Key words: phase field simulation, adaptive finite element, directional solidification, Al-4wt.%Cu alloy

中图分类号:

TG111

朱昶胜, 高宏伟, 马芳兰, 冯力, 雷鹏. 自适应有限元法对合金定向倾斜枝晶生长的相场法模拟[J]. 兰州理工大学学报, 2021, 47(3): 15-22.

ZHU Chang-sheng, GAO Hong-wei, MA Fang-lan, FENG Li, LEI Peng. Phase field method study on oriented tilted dendrite growth of alloy by adaptive finite element method[J]. Journal of Lanzhou University of Technology, 2021, 47(3): 15-22.

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