Dynamic stress–strain states for metal foams using a 3D cellular model

Dynamic uniaxial impact behaviour of metal foams using a 3D cell-based finite element model is examined. At sufficiently high loading rates, these materials respond by forming 'shock or consolidation waves' (Tan et al., 2005a, Tan et al., 2005b). However, the existing dynamic experimental methods have limitations in fully informing this behaviour, particularly for solving boundary/initial value problems. Recently, the problem of the shock-like response of an open-cell foam has been examined by Barnes et al. (2014) using the Hugoniot-curve representations. The present study is somewhat complementary to that approach and additionally aims to provide insight into the 'rate sensitivity' mechanism applicable to cellular materials. To assist our understanding of the 'loading rate sensitivity' behaviour of cellular materials, a virtual 'test' method based on the direct impact technique is explored. Following a continuum representation of the response, the strain field calculation method is employed to determine the local strains ahead of and behind the resulting 'shock front'. The dynamic stress–strain states in the densification stage are found to be different from the quasi-static ones. It is evident that the constitutive behaviour of the cellular material is deformation-mode dependent. The nature of the 'rate sensitivity' revealed for cellular materials in this paper is different from the strain-rate sensitivity of dense metals. It is shown that the dynamic stress–strain states behind a shock front of the cellular material lie on a unique curve and each point on the curve corresponds to a particular 'impact velocity', referred as the velocity upstream of the shock in this study. The dynamic stress–strain curve is related to a layer-wise collapse mode, whilst the equivalent quasi-static curve is related to a random shear band collapse mode. The findings herein are aimed at improving the experimental test techniques used to characterise the rate-sensitivity behaviour of real cellular materials and providing data appropriate to solving dynamic loading problems in which cellular metals are utilised.