Global topology of failure surfaces of metallic foams in principal-stress space and principal-strain space studied by numerical simulations

Abstract Failure surfaces of foam materials in the principal-stress/strain space are quite different from those of dense materials. They cannot be deduced directly by several simple tests such as uniaxial loading and pure shear loading. However, it is difficult to carry out arbitrary proportional triaxial loading tests on materials, resulting in the global topology of failure surfaces of metallic foams remaining unknown. To overcome the difficulty of triaxial loading tests, we carried out numerical simulations by applying triaxial loadings on 3D Voronoi models, which have been used successfully to study the global topology of yield surfaces of metallic foams. In the numerical simulations, 3D Voronoi structures were used to simulate the meso–structures of metallic foams, and only the parameters of the matrix material (aluminum) are needed. Considering the influence of multi-axial effects on the failure of metallic foam, a new failure criterion for metallic foams based on the mass of failed elements was proposed, and sufficient failure points in the principal-stress/strain space were obtained to characterize the failure surfaces well. Results indicated that the failure surface in the in the principal-stress space looks more complicated than the failure surface in the principal-strain space, so it is better to depict the failure surface in the principal-strain space, which approaches an ellipsoid. Furthermore, self-similarity exists in failure surfaces of metallic foams with different relative densities. Because a metallic foam may not fail when the compressive loadings are dominant, the failure surface appears to be a “missing area” in the permissible principal-stress/strain space. The boundaries of missing areas were determined analytically and validated numerically.