A new level set-finite element formulation for anisotropic grain boundary migration

TL;DR

This paper introduces a novel level set-finite element method for modeling anisotropic grain boundary migration, providing the first analytical solution for such boundary configurations and demonstrating its convergence and advantages over previous models.

Contribution

The paper presents the first analytical solution for anisotropic grain boundary migration and develops a new level set-finite element formulation validated through convergence analysis.

Findings

Analytical solution for anisotropic boundary migration derived

Convergence properties of the numerical model demonstrated

Enhanced modeling of grain boundary energy anisotropy

Abstract

Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats an aspect of the anisotropic grain growth problem. By applying the first principles of thermodynamics and mechanics, an expression for the velocity field of a migrating grain boundary with an inclination dependent energy density is expressed. This result is used to generate the first, to the authors' knowledge, analytical solution (for both the form and kinetics) to an anisotropic boundary configuration. This new benchmark is simulated in order to explore the convergence properties of the proposed level set finite element numerical model in an anisotropic setting. Convergence of the method being determined, another configuration, using a more general grain boundary energy density, is investigated in order to show the added value of the new formulation.