Phase-field Simulation Of Grain Growth By The Finite Element Method

The dendritic growth, such as the formation of snowflake and the nuclei growth in alloy, is a significant topic in the area of phase transformation. It is very important to investigate the effect of all factors in the microstructure through numerical simulation, which can also provide theoretical guidance in the manufacture of crystal. The phase-field model developed in recent years is the most important method to quantitatively simulate grain growth. However, since the method involves different physical scales, resulting in expensive computational cost in numerical implementation, which has greatly limited its application in the simulation of grain growth. Therefore, the most urgent difficulty encountered in the previous problem is to find an efficient method to solve high-dimensioned problems, with cheap computational cost and storage.In this thesis, we study the dendritic growth of a binary alloy in two dimensions, based on the WBM phase field model which is governed by the evolution of concentration and phase-field equations. During the numerical simulation, some adaptive finite element method and adaptive mesh technology are used to reduce the computational cost greatly. For the above problem, the effects of initial nuclei shapes on the solid/liquid interface are discussed, which shows that the grain morphologies are sentitive to the initial nuclei shapes, the anisotropy strength of interface energy and the symmetry of the initial nuclei.