Modeling of Polycrystalline Material Microstructure with 3D Grain Boundary Based on Laguerre-Voronoi Tessellation

Voronoi tessellations are shown to be statistically representative of polycrystalline microstructures, which have been widely accepted for the modeling of microstructures of metallurgic and ceramic materials. In this paper, a new implementation of the Voronoi diagram in Laguerre geometry is presented for the generation of numerical models of polycrystalline microstructures, where the size and shape of the grains can be controlled, and the 3D grain boundaries can be modeled with a specified thickness. The distribution of grain sizes in the models is fitted to a lognormal distribution, compared with the normal distribution in the Voronoi tessellation methods. Finally, statistical analyses of grain face and grain size distribution are performed with the models, and the macroscopic elastic properties of polycrystalline ceramic materials are simulated to verify the capability of the presented method.

Automated summary

This paper presents a new implementation of Voronoi diagram in Laguerre geometry for generating numerical models of polycrystalline microstructures. The method allows control over grain size and shape, and the modeling of 3D grain boundaries with specified thickness. The distribution of grain sizes in the models is fitted to a lognormal distribution instead of the normal distribution in traditional Voronoi tessellation methods. Statistical analyses and simulations are conducted to verify the effectiveness of the proposed method in modeling polycrystalline ceramic materials.