Diffusion Generated Motion for Recrystallization and Grain Growth

A new numerical approach for the efficient computation of grain boundary motion is used to simulate normal grain growth and recrystallization in three dimensions with high accuracy. The method is based on the diffusion of signed distance functions and shares similarities with level set methods. The Herring angle condition at junctions and topological transitions are naturally captured with this formulation. In addition, this approach offers significant advantages over existing numerical methods and accurate computational results are presented on scales not previously possible. For example, a fully-resolved simulation of normal grain growth initially containing over 100,000 grains in three dimensions is presented. It is shown that the average grain radius grows as the square root of time and the grain size distribution is self-similar. This numerical approach is easily extended to include recrystallization. Simulations of recrystallization for physically relevant parameter values are displayed. These are quite difficult to obtain via kinetic Monte Carlo approaches, commonly used for this problem.