A novel 3D anisotropic Voronoi microstructure generator with an advanced spatial discretization scheme

Abstract

At the microstructural scale, Voronoi tessellations are commonly used to represent a polycrystalline morphology. However, due to spherical growth of nuclei, an anisotropic tessellation with spatially varying elongated grain directions, which is present in many applications, cannot be obtained. In this work, a novel 3D anisotropic Voronoi algorithm is presented, together with its implementation and two application cases. The proposed algorithm takes into account preferred grain growth directions, aspect ratios and sizes in the definition of an ellipsoidal growth velocity field defined per grain. For applications in which a predetermined mesh is used, e.g. voxel-mesh based simulations, the grains are extracted in a straight-forward manner. In cases where a fully grain conforming discretization is desired, e.g. finite element simulations, a hexahedral mesh generator is incorporated to arrive at a discretization which can be directly used in microstructural modeling simulations. Two application cases are studied (a wire + arc additively manufactured and a magnesium alloy microstructure) in which the algorithm’s capability for curved, non-convex, periodic domains is shown. Furthermore, the resulting grain morphology is compared to experimental data in terms of grain size, grain aspect ratio and grain columnar direction distribution. In both cases, the algorithm adequately produces a representative volume element with convincing representativeness of the experimental data. The 3D anisotropic Voronoi algorithm is highly versatile in a wide range of application cases, specifically suitable for the generation of polycrystalline microstructures that include grains with spatially varying elongated directions.