Diffusion Generated Motion for Large Scale Simulations of Grain Growth and Recrystallization

A polycrystalline material consists of many crystallites called grains that are differentiated by their varying orientation. These materials are very common, including most metals and ceramics. The properties of the network of grains making up these materials influence macroscale properties, such as strength and conductivity. Hence, understanding the statistics of the grain network and how it evolves is of great interest.

We describe new, efficient numerical algorithms for simulating with high accuracy on uniform grids the motion of grain boundaries in polycrystals. These algorithms are related to the level set method, but generate the desired geometric motion of a network of curves or surfaces (along with the appropriate boundary conditions) by alternating two very simple operations for which fast algorithms already exist: Convolution with a kernel, and the construction of the signed distance function to a set. Motions that can be treated with these algorithms include grain growth under misorientation dependent surface energies, and various models of recrystallization. We will present simulations with hundreds of thousands of fully resolved grains in 3D. Joint work with Matt Elsey and Peter Smereka.

Selim Esedoglu, University of Michigan

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