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金属学报  2025, Vol. 61 Issue (6): 941-952    DOI: 10.11900/0412.1961.2023.00174
  研究论文 本期目录 | 过刊浏览 |
六重对称合金枝晶生长场变量扩散元胞自动机模型
汤思璠1,2, 魏晶晶1, 岳怡心1, 李鹏宇1, 姚曼1, 王旭东1,2()
1 大连理工大学 材料科学与工程学院 大连 116024
2 大连理工大学 辽宁省凝固控制与数字化制备技术重点实验室 大连 116024
Field-Variable Diffusion Cellular Automaton Model for Dendritic Growth with Sixfold Symmetry Alloys
TANG Sifan1,2, WEI Jingjing1, YUE Yixin1, LI Pengyu1, YAO Man1, WANG Xudong1,2()
1 School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China
2 Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), Dalian University of Technology, Dalian 116024, China
引用本文:

汤思璠, 魏晶晶, 岳怡心, 李鹏宇, 姚曼, 王旭东. 六重对称合金枝晶生长场变量扩散元胞自动机模型[J]. 金属学报, 2025, 61(6): 941-952.
Sifan TANG, Jingjing WEI, Yixin YUE, Pengyu LI, Man YAO, Xudong WANG. Field-Variable Diffusion Cellular Automaton Model for Dendritic Growth with Sixfold Symmetry Alloys[J]. Acta Metall Sin, 2025, 61(6): 941-952.

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摘要: 

在合金凝固枝晶生长元胞自动机(CA)模型中,正方形元胞、邻胞构造、尖锐界面模型固有特性引起的各向异性,给枝晶择优取向生长的模拟研究带来了诸多限制,特别是难以模拟六重对称合金的枝晶生长行为。本工作在借鉴相场弥散界面模型中相场变量梯度能项建模与求解方法的基础上,构建和推导了考虑元胞状态变量的场变量梯度泛函及场变量扩散方程,提出了一种新的场变量扩散元胞自动机(FCA)模型。模型考虑了成分过冷和Gibbs-Thomson效应,采用“浓度势法”处理溶质扩散和再分配,依据杠杆定理处理界面凝固的生长动力学,通过引入场变量扩散项修正界面元胞的生长速率,并利用不同条件下Mg-6%Al (质量分数)合金的枝晶生长结果对模型进行了验证。在正方形网格离散方式下,六重对称Mg-6%Al合金的枝晶尖端稳态特征和生长动力学与LGK模型的预测结果基本吻合,模型能够呈现多重合金枝晶形貌的对称性以及枝晶的随机择优取向生长,还原凝固过程的枝晶臂生长、竞争和粗化等行为。

关键词 场变量扩散元胞自动机六重对称枝晶生长随机择优取向    
Abstract

The cellular automaton (CA) model exhibits a notable disadvantage of substantial anisotropy, triggered by the square cells, adjacent cell structures, and intrinsic features of the sharp interface model. This disadvantage leads to limitations in simulating dendritic growth with random preferred orientations during the solidification of alloys, particularly in the context of sixfold symmetric alloys. In the present study, drawing inspiration from the processing concept of diffuse interfaces and the gradient energy term in the phase field model, a function concerning the gradient of the field variable associated with the cell state is constructed and the diffusion equation for the field variable is derived. Consequently, a novel field-variable diffusion CA (FCA) model is proposed, which addresses the growth kinetics of the solid-liquid interface in accordance with the lever rule. The proposed model considers constitutional supercooling and the Gibbs-Thomson effect, employing the concentration potential method to manage solute diffusion and redistribution. The growth rate of interface cells is modulated by introducing a field-variable diffusion term. The analysis reveals that within the square-grid discretization mode, the model demonstrates validation under various conditions, focusing on the steady-state characteristics of the dendritic tip and growth kinetics of the sixfold symmetric Mg-6%Al (mass fraction) alloy. The findings are consistent with the predictions of the LGK model, suggesting that the FCA model can effectively emulate dendritic morphology with multifold symmetry and random preferred orientations, and elucidate critical dendritic arm behaviors, such as competitive dendritic growth and coarsening.

Key wordsfield variable diffusion    cellular automaton    six-fold symmetry    dendritic growth    random preferred orientation
收稿日期: 2023-04-18     
基金资助:国家自然科学基金项目(51974056);国家自然科学基金项目(51474047)
通讯作者: 王旭东,hler@dlut.edu.cn,主要从事连铸过程模型化与质量控制、凝固过程的微观组织预测研究
Corresponding author: WANG Xudong, associate professor, Tel: (0411)84707347, E-mail: hler@dlut.edu.cn
作者简介: 汤思璠,女,1998年生,博士生
图1  Von Neumann型邻胞2种模型模拟结果
图2  Moore型邻胞2种模型模拟结果
图3  场变量扩散枝晶生长CA模型计算流程
ParameterValueUnit
Diffusivity of alloy elements in liquid DL1.8 × 10-9m2·s-1
Diffusivity of alloy elements in solid DS1.0 × 10-13m2·s-1
Liquidus temperature TL901K
Partition coefficient k0.4-
Liquidus slope mL-5.5K·%-1 (% for mass fraction)
Gibbs-Thomson coefficient Γ2.0 × 10-7K·m
Kinetic anisotropy δk0.5-
Thermodynamic anisotropy δ0.03-
Accommodation coefficient γ1.25-
Degree of anisotropy n6-
表1  计算采用的Mg-6%Al合金热物性参数[13]
图4  不同择优取向的Mg-6%Al在凝固时间为0.455 s时的枝晶形貌
图5  不同择优生长方向的枝晶形貌对比
图6  Mg-6%Al合金枝晶形貌模拟与水平方向主枝晶臂浓度
图7  Mg-6% Al合金枝晶尖端特征参数随时间变化
图8  Mg-6%Al合金枝晶尖端半径和速率与LGK预测结果对比
图9  Mg-6%Al合金枝晶形貌及溶质浓度随时间演化
图10  Mg-6%Al合金等轴晶形貌及溶质浓度分布随时间演化
图11  Mg-6%Al合金定向凝固柱状晶形貌随时间的模拟结果
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