摘要
【目的】材料微结构中界面能异性和弹性应变能是产生各向异性的主要因素,本文主要研究含弹性应变能的各向异性相场模型的紧致指数时间差分方法。【方法】在紧致指数时间差分方法框架下引入了界面能异性和弹性应变能的计算,将界面能异性和弹性应变能归于指数时间差分方法的非线性项统一处理,为二者设计了算子分裂格式。【结果】从数学上证明了算子分裂格式能够保证能量稳定,并进行了镍基合金以及Zr的氢化物的材料腐蚀相场模型的数值实验,验证了含弹性应变能的各向异性相场模型的指数时间差分方法的能量稳定性。【局限】本文仅得到了指数时间差分方法的一阶和二阶求解格式,更高阶的求解格式有待进一步探索。【结论】设计了能量稳定的含弹性应变能的各向异性相场模型的指数时间差分方法。
[Objective]The interface energy and elastic strain energy are the main factors of anisotropy in the microstructure of materials.In this paper,the compact Exponential Time Difference method of anisotropic phase field model with elastic strain energy is studied.[Methods]In the framework of the compact Exponential Time Difference method,the calculation of interface energy and elastic strain energy is introduced.The interface energy and elastic strain energy are treated as the nonlinear terms of the Exponential Time Difference method,and the operator splitting scheme is designed for them.[Results]It is mathematically proved that the operator splitting scheme can guarantee the energy stability,and the numerical experiments of the corrosion phase field model of Ni-based alloy and Zr-hydride are carried out,which verify the energy stability of the Exponential Time Difference method of the anisotropic phase field model with elastic strain energy.[Limitations]In this paper,only the first-order and second-order solutions of the Exponential Time Difference method are obtained,and the higher-order solutions need to be further explored.[Conclusions]The Exponential Time Difference method of energy stable anisotropic phase field model with elastic strain energy is designed.
作者
王姗姗
张鉴
Wang Shanshan;Zhang Jian(Computer Network Information Center,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China)
出处
《数据与计算发展前沿》
2020年第3期113-125,共13页
Frontiers of Data & Computing
基金
国家重点研发计划项目(2016YFB0201100,2017YFB0202803)
国家自然科学基金资助项目(11871454,91630204,61531166003)
中国科学院战略性先导科技专项(B类)(XDB22020102)
中国科学院信息化专项(XXH13506-204)。
关键词
相场模型
紧致指数时间差分方法
界面能异性
弹性应变能
phase field model
Compact Exponential Time Difference Method
interfacial anisotropy
elastic strain energy