Simulating percolation in multiphase materials

This paper introduces a multi-scale approach for modeling percolation, using representative volume elements at the microscale and grid-based percolation analysis at the macroscale. In a first scenario, the transition from open to closed porosity during solid-state sintering is studied yielding a sharp percolation threshold at 95% relative density for homogeneous microstructure. Initial inhomogeneity shifts the threshold to lower density and broadens the transition range. As second scenario, electrical conductivity in dense particulate composites with a dielectric and a conductive phase is studied depending on the grain size ratio. Applying Voronoi structures, the conduction threshold falls below 10% volume fraction of the conductive phase when its grains are considerably smaller than those of the insulating phase. Finite element analyses of the macroscopic conductivity of Al₂O₃-TiN composites were done as an example. The model also enables analyzing the size of non-contacted regions on the macroscale, being relevant, e.g., for electroerosive machining.