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

Abstract

There are multiple controversies regarding the yield surface of metallic forms, and the primary cause is that the characterizations are summarized by notably scarce yield points in the plane of effective stress and mean stress. In order to solve these controversies, experiments and numerical simulations were carried out to obtain sufficient yield points for metallic foams covering the entire permissible principal-stress space and principal-strain space to study properties of yield surfaces essentially. In experiments, uniaxial and biaxial tests were implemented to learn properties of metallic foams in yield and brittle fracture. In numerical simulations, 3D Voronoi models were built to simulate closed-cell aluminum foams with meso-structures, in which only the material parameters of aluminum were needed. The Voronoi models were verified first by uniaxial and biaxial tests. With the initial yield criterion of metallic foams under multi-axial loading proposed in the view of dissipation energy, sufficient yield points were obtained for metallic foams, which directly represent the global topology of yield surfaces in principal-stress space and principal-strain space. In addition, the yield surface was characterized by the yield points in principal-stress space and in principal-strain space respectively; moreover, the yield lines determined by the yield points having the same Lode angle were presented. It was observed that yield lines with different Lode angles in the plane of the von Mises stress and the mean stress were not coincident, which is why the controversial characterizations of the yield surface of metallic foams exist. However, the yield lines were nearly identical in the plane of effective strain and mean strain, suggesting that it is better to characterize the yield surface of metallic foams in principal-strain space than that in principal-stress space. Furthermore, effects of the initial density of metallic foams on yield surfaces were investigated. It was found that the asymmetry of tension and compression increases as relative density increases, but the asymmetry was eliminated when using two parameters to normalize the yield surfaces.