Dynamic material parameters of closed-cell foams under high-velocity impact

Abstract

Cellular materials under high-velocity impact have highly localized deformation with the cells layer-wise collapse, which is usually characterized by the propagation of shock wave. Researches have shown that the shock wave speed is strongly dependent on the impact velocity, but the effect of the meso-structural and base-material parameters is unclear. In this study, the dynamic material parameters of closed-cell foams are investigated with cell-based finite element models. The one-dimensional velocity distribution along the loading direction is used to capture the propagation of shock front. The shock wave speed is thus determined and it exhibits a linear relationship with impact velocity when the impact velocity is high enough. The difference between the shock wave speed and the impact velocity is a dynamic material parameter of cellular material and the effect of meso-structural and base-material parameters on this dynamic material parameter is investigated with dimensional analysis. An expression of the dynamic material parameter with respect to the relative density and the base-material parameters is obtained. It shows that the dynamic material parameter intensively relies on the relative density and increases linearly with the relative density. The investigation of dynamic stresses with the aid of a shock model shows that the initial crushing stress increases in a power-law tendency with the increase of relative density. As a result, a stress–strain relation involving the relative density of material cellular and the yield stress and density of base material is obtained for the closed-cell foams considered. The effects of hardening behaviors of cell-wall material and gas trapped within cells are also considered. It is found that the dynamic material parameter exhibits nearly linear increase with the increase of hardening parameters of base material and initial gas pressure, while the dynamic initial crushing stress is independent of the strain-hardening parameter and the entrapped gas pressure but increases with the strain-rate hardening parameter linearly. These findings may be helpful for guiding the crashworthiness design of cellular materials and structures.