A phase-field model of anisotropic polycrystalline system and computer simulation – Part I: Theory

A three-dimensional phase field model of anisotropic polycrystalline solids has been developed. In this model the system’s free energy is derived in a generalized form based on Ginzburg–Landau’s (GL) theory [1], which is a function of lattice’s parameters and electron density. A grain boundary in this model is viewed as a discontinuity of periodic atoms array, represented by the Read–Shockley dislocation representation [3]. The Peierls–Nabbaro’s dislocation potential [84] has been built into the model to characterize grain boundary’s adhesion. Therefore, the model establishes the links between lattice’s structure, sub-atomic quantum physics, and the evolutions of grains and grain-boundaries, leading to a meso-scopic constitutive law that governs grains’ nucleation, growth, and distortion in a polycrystalline system. This also provides a means to pursue analytical solutions of an alloy’s micro-structure’s evolution and establishes a framework for corresponding numerical analysis.