Three-dimensional digital approximations of grain boundary networks in polycrystals

Abstract

In this work, we offer a set of algorithms that convert a voxellated image to a conformal surface mesh that is targeted for polycrystalline materials containing grains with a wide range of sizes and complex shapes. More specifically, we propose a simple but effective algorithm for approximating the grain boundary networks that are implicit in three-dimensional digital images of polycrystals. The algorithm segments a three-dimensional digital image of a polycrystalline microstructure and then smoothes an interpolated conformal surface mesh of the grain boundary network while maintaining certain characteristic features of the microstructure. It is found that the proposed algorithm successfully approximates the grain boundary network based only on the digital, voxellated images of the polycrystal. Simulated microstructures are used to verify that the resulting mesh qualitatively and quantitatively approximates the true structure, in terms of the displacement of the nodes, the grain volume change and the dihedral angle distribution along triple junctions after smoothing. The effect of the use of the cubic grid for mapping digital microstructures on the grain boundary approximation is also discussed.