Computer simulation of three-dimensional material microstructure and its application in the determination of mechanical behavior of polycrystalline materials and engineering structures

Voronoi tessellation has been used to simulate topologically equivalent microstructures for materials in three dimensions having random shape and size constituents. A complete statistical description of the topological and size properties of a cellular microstructure generated by a three-dimensional Poisson-Voronoi tessellation has been obtained by a rigorous computer simulation involving hundreds of thousands of cells. It has been found that a two-parameter gamma distribution gives an accurate fit to the distribution of faces, volumes, and surface areas of the cells. A finite element package (pre- and postprocessors) has been developed to use the Voronoi tessellation model to determine the effective elastic moduli of the polycrystalline materials. The effective elastic moduli predicted by the model always fall within the Voigt and Reuss limits. The calculated elastic moduli deviate between the Voigt and Reuss values systematically with the anisotropy of the single crystal. It has been found that the stress concentration at the grain boundary affects the elastic moduli of the polycrystalline material. The effect of random shape and size voids on the elastic moduli of alumina has also been determined. The model has been used to study the transient thermal stresses in a multilayer capacitor assuming anisotropy of the ceramic.