Topological transitions during grain growth on a finite element mesh

TL;DR

This paper develops a method to enumerate and select topological transitions during grain growth in materials with complex boundary energies, using finite element simulations to better understand microstructure evolution.

Contribution

It introduces a procedure to enumerate all possible topological transitions in grain growth with general boundary energies within a finite element framework.

Findings

Exceptional transitions can be energetically similar to conventional ones.

The method is implemented as a parallel C++ library based on SCOREC.

Simulation results demonstrate the approach's effectiveness.

Abstract

The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general grain boundary energies in principle allow many more viable grain boundary configurations. A simulation of grain growth in such a material therefore requires a procedure to enumerate all possible topological transitions and select the most energetically favorable one. Such a procedure is developed and implemented here for a microstructure represented by a volumetric finite element mesh. As a specific example, all possible transitions for a typical configuration with five grains around a junction point are enumerated, and some exceptional transitions are found to be energetically similar to the conventional ones even for a uniform boundary energy. A general discrete formulation to calculate grain boundary velocities is used to simulate grain growth for an example microstructure. The method is implemented as a C++ library based on SCOREC, an open source massively parallelizable library for finite element simulations with adaptive meshing.