Calculation of grain boundary normals directly from 3D microstructure images

Abstract

The determination of grain boundary normals is an integral part of the characterization of grain boundaries in polycrystalline materials. These normal vectors are difficult to quantify due to the discretized nature of available microstructure characterization techniques. The most common method to determine grain boundary normals is by generating a surface mesh from an image of the microstructure, but this process can be slow, and is subject to smoothing issues. A new technique is proposed, utilizing first order Cartesian moments of binary indicator functions, to determine grain boundary normals directly from a voxelized microstructure image. To validate the accuracy of this technique, the surface normals obtained by the proposed method are compared to those generated by a surface meshing algorithm. Specifically, the local divergence between the surface normals obtained by different variants of the proposed technique and those generated from a surface mesh of a synthetic microstructure constructed using a marching cubes algorithm followed by Laplacian smoothing is quantified. Next, surface normals obtained with the proposed method from a measured 3D microstructure image of a Ni polycrystal are used to generate grain boundary character distributions (GBCD) for Σ3 and Σ9 boundaries, and compared to the GBCD generated using a surface mesh obtained from the same image. The results show that the proposed technique is an efficient and accurate method to determine voxelized fields of grain boundary normals.