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

A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System

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。

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 compu-tational 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.