Elasto-Plastic Behaviour of Transversely Isotropic Cellular Materials with Inner Gas Pressure

Abstract

The fabrication process of cellular materials, such as foaming, usually leads to cells elongated in one direction, but equiaxed in a plane normal to that direction. This study is aimed at understanding the elasto-plastic behaviour of transversely isotropic cellular materials with inner gas pressure. An idealised ellipsoidal-cell face-centred-cubic foam that is filled with gas was generated and modelled to obtain the uniaxial stress–strain relationship, Poisson’s ratio and multiaxial yield surface. The effects of the elongation ratio and gas pressure on the elasto-plastic properties for a relative density of 0.5 were investigated. It was found that an increase in the elongation ratio caused increases in both the elastic modulus and yield stress for uniaxial loading along the cell elongation direction, and led to a tilted multiaxial yield surface in the mean stress and Mises equivalent stress plane. Compared to isotropic spheroidal-cell foams, the size of the yield surface of the ellipsoidal-cell foam is smaller for high-stress triaxiality, but larger for low-stress triaxiality, and the yield surface rotates counter-clockwise with the Lode angle increasing. The gas pressure caused asymmetry of the uniaxial stress–strain curve (e.g., reduced tensile yield stress), and it increased the nominal plastic Poisson’s ratio for compression, but had the opposite effect for tension. Furthermore, the gas pressure shifted the yield surface towards the negative mean stress axis with a distance equal to the gas pressure. The combined effects of the elongation ratio and gas pressure are complicated, particularly for the elasto-plastic properties in the plane in which the cells are equiaxed.