Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres

A type of diagram is proposed as microstructure model of polycrystalline materials, Voronoi diagram in the Laguerre geometry based on random closed packing of spheres (RCP-LV diagram), and discussed in detail. The volumes of spheres are set to serve lognormal distribution, which is strongly inherited by distribution of cell volumes in the RCP-LV diagram. The geometrical and topological properties in the RCP-LV diagram and the Poisson–Voronoi diagram (PV diagram) are compared with those properties of real polycrystalline materials, and it is found that the lognormal distribution is a better approximation to the cell volume and face number distribution in the RCP-LV diagram than in the PV diagram. It is also shown clearly that coefficient of variance of cell volumes in the RCP-LV diagram is controlled by coefficient of variance of sphere volumes. This makes it easy to simulate polycrystalline microstructure with different dispersion of grain volumes. The RCP-LV diagram is probably superior to the PV diagram for the simulation of polycrystalline materials.