Yield properties of closed-cell aluminum foam under triaxial loadings by a 3D Voronoi model

Considering the lack of abundant experimental data on metal foams under tensile triaxial loadings, characterization of the yield surface of metallic foam is controversial. In this paper, we explore a numerical method to study the yield properties of closed-cell aluminum (Al) foam under triaxial loadings using a three-dimensional (3D) Voronoi model. The finite element model was verified by a uniaxial compressive experiment with optimized modeling and computing parameters. Three normal stresses (including tension and compression) were proportionally applied on the cubic Voronoi foam to conduct numerical simulation experiments, in which each stress proportion of the von Mises stress over the mean stress includes at least three different combinations of triaxial loadings. Results indicated that the yield surface, covering the entire spectrum of stress paths from hydrostatic compression to hydrostatic tension in the plane of the von Mises stress and the mean stress, could be approximately depicted by a parabola or ellipse, but it is not symmetric about the zero mean stress. Owing to the asymmetry of the yield surface in the compressive and tensile states, the yield surfaces should be normalized by compressive and tensile uniaxial yield stresses, respectively, which leads to the conclusion that normalized yield surfaces are almost independent of both relative density and thickness distribution of the cell wall. Moreover, the scatter in the same proportion of the von Mises stress over the mean stress, but different triaxial stress combinations, shows that it might not be sufficient to depict the yield surface only by the von Mises stress and the mean stress.