Characterization of initial and subsequent yield behaviors of closed-cell aluminum foams under multiaxial loadings

As one of widely-used multi-functional materials, metallic foams are often subjected to multiaxial stress states in practical applications; in which the yield behaviors under different stress states need to be better characterized. However, it is difficult to conduct multiaxial mechanical tests on foam materials, especially under arbitrarily proportional triaxial loadings. In this study, numerical modeling of the yield properties of aluminum (Al) foam is performed based upon 3D image-based models. Real structural models of the Al foam are reconstructed using microscopic X-ray computed tomography (micro-CT) technique for multiaxial characterization computationally. Numerical simulation reveals that plastic collapse and fracture of cell-walls first occur in a relatively weak zone under prescribed uni/tri-axial loadings, whereas happen in the central section under biaxial loadings. An initial yield criterion is defined based upon energy dissipation. A constant stress proportion coefficient can be obtained under the stress-controlled triaxial proportional loading and its effectiveness is also validated by comparing the stress-strain responses with those under velocity-controlled uniaxial and hydrostatic compressive loading. It is found that the initial yield points of foam specimens can be obtained in different stress states in the von Misesmean stress space. The normalized yield surface is approximately independent of relative density and can be well fitted to a parabolic or an elliptic function. Comparisons between the numerical yield surface and three typical theoretical yield criteria suggest that the Deshpande and Fleck's criterion provides more precise predictions than Gibson and Miller yield criteria when a proper plastic Poisson's ratio is adopted. Furthermore, it is shown that the early stage yield surface of metallic foams can be evolved in a geometrically self-similar manner.