Effects of statistics of cell’s size and shape irregularity on mechanical properties of 2D and 3D Voronoi foams

Abstract

In the study of the mechanical properties of metallic foam, the relative density (or porosity) and the average size of cells are two key parameters of the meso-geometry, but it is also well known experimentally that the two parameters alone are not enough since the mechanical properties of metallic foams are different even with the same initial relative density and average cell size. In this paper, we have classified the irregularity of cells into two types to describe polygonal and polyhedral cells in 2D and 3D metallic foams, which are called size irregularity and shape irregularity, respectively. The former reflects the deviation of the size of a cell from the average cell size in the foam and the latter reflects the deviation of the shape of a cell from a circle with the same area (2D) or a globe with the same volume (3D). With the two kinds of definitions, effects of the irregularity of cells in aluminum foam on mechanical properties are investigated using the Voronoi tessellation technique and the finite element method. The well- designed 2D and 3D Voronoi models are constructed, of which the statistic distributions of size and shape irregularity are presented. The compression simulations of Voronoi-based models indicate that the yield stress of metallic foam is seldom affected by the size irregularity, but significantly affected by the shape irregularity. The more regular the foams, the higher will be their yield plateau at constant overall relative density and average cell size.