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金属学报  2018, Vol. 54 Issue (8): 1204-1214    DOI: 10.11900/0412.1961.2017.00478
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基于序参量梯度的改进相场模型及对大尺度体系马氏体相变的模拟研究
魏铖1,2, 柯常波2, 马海涛1,3, 张新平2()
1 华南理工大学土木与交通学院 广州 510640
2 华南理工大学材料科学与工程学院 广州 510640
3 广州大学工程抗震研究中心 广州 510405
A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System
Cheng WEI1,2, Changbo KE2, Haitao MA1,3, Xinping ZHANG2()
1 School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China
2 School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China
3 Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou 510405, China;
引用本文:

魏铖, 柯常波, 马海涛, 张新平. 基于序参量梯度的改进相场模型及对大尺度体系马氏体相变的模拟研究[J]. 金属学报, 2018, 54(8): 1204-1214.
Cheng WEI, Changbo KE, Haitao MA, Xinping ZHANG. A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System[J]. Acta Metall Sin, 2018, 54(8): 1204-1214.

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摘要: 

基于序参量变化在界面区域远大于非界面区域的特性,构造了全局修正函数,建立了适用于可调尺度体系马氏体相变模拟的相场模型。在不改变界面能密度的情况下,通过调整界面区域的体积自由能密度差与梯度能系数,有效增大了原相场模型中的界面宽度,实现了大尺度下的高效模拟,并能很好地表征马氏体相变。结果表明,改进后的相场模型能很好地解决原相场模型在大尺度体系模拟时存在的如生长速率过快、位向关系不合理及组织形貌杂乱无序等问题,模拟结果与实验结果符合较好。

关键词 马氏体相变序参量梯度界面宽度相场法    
Abstract

The materials design and fabrication based on predicting microstructure have been drawn increasing attention from scientists and engineers. Martensite microstructure, which is well observed in many materials, has significant influence on physical and mechanical properties of the materials. Some experimental studies have been launched to understand the featured microstructure and its evolution in martensitic transformations (MT). Meantime, numerical approaches are often employed to assist the experimental studies due to the complex and nonlinear nature of MT. The phase field method is one of the most powerful tools in predicting microstructure. Due to the diffuse-interface description, phase field method can be used to simulate arbitrary morphologies without tracking the interface. As a consequence, the interface must contain enough elements to obtain reasonable results by using finite element method. On the other hand, the width of the interface is several orders smaller than its real counterpart. More computational resources are required to resolve the phase field variables at the interface with the system size increased. Therefore, the simulation is restricted in smaller system even with state-of-the-art computer power. For arbitrary model formulations, the interfacial energy depends on the interfacial width and other specific properties of materials. However, the phase field models of martensitic transformation do not have enough degrees of freedom to increase the interfacial width without changing the interfacial energy. In the present study, a scalable phase field model by introducing a global modified function is constructed to study MT, the modified function takes into account the inhomogeneous nature of order parameter gradient across the interfacial region. Through adjusting the free energy density and gradient coefficient, meanwhile keeping the interfacial energy density unchanged, the interfacial width and system size are increased, yet the MT feature can be fully characterized. The simulation results show that the modified phase field model can well solve the drawbacks such as fast growth rate of martensite, artificial orientation relationship between the variants of martensite, and disordered martensite microstructure in large scale system.

Key wordsmartensitic transformation    order parameter gradient    interfacial width    phase field method
收稿日期: 2017-11-15     
ZTFLH:  TF777.1  
基金资助:国家自然科学基金项目No.51205135和广东省自然科学基金重点项目No.S2013020012805资助
作者简介:

作者简介 魏 铖,男,1987年生,博士生

图1  全局修正函数gp随等效梯度νp的变化曲线(λm/λ=8和λm/λ=10)
图2  新相在不同尺度体系中的演化过程和等效半径变化
图3  引入全局修正函数后新相在不同尺度体系中的演化过程和等效半径变化
图4  2个R相变体在不同尺度体系中的位向关系及应变能密度变化
图5  修正函数后2个R相变体在不同尺度体系中的位向关系及应变能密度变化
图6  R相4个变体分别在(001)面上形成2种界面示意图
图7  B2-R相变在不同尺寸体系中的演化过程及应变能密度变化
图8  修正后B2-R相变在不同尺寸体系中的演化过程及应变能密度变化
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