High-velocity plate impact of metal foams

The ballistic impact of a massive, effectively 1-D plate on an initially stationary foam layer is considered. It is shown that four discrete velocity regimes must be considered. Two of these regimes are of major interest for ballistic impact studies. Regime 2 considers the case when the initial velocity of the plate is lower than the sound velocity of the constitutive material of the foam, but higher than the linear sound velocity of foam. Regime 3 considers the case when the initial plate velocity is lower than the linear sound velocity of the foam; but remains higher than the effective sound velocity for a perturbation in which the amplitude lies in the so-called “plateau region” of the static stress–strain diagram. Analytical solutions for dynamic deformation and energy absorption of foam materials under the plate impact condition for Regimes 2 and 3 are developed. It has been shown that in both cases, a compressive shock wave appears. The physical difference between these two regimes entails not only the creation of a shock front associated with the collapsing foam, but also an acoustic precursor in the case of Regime 3. As a result, the efficiency of energy absorption in Regime 2 depends only on the initial density of the foam, the density of the constitutive material of the foam, and the areal mass of the impacting plate, whereas the efficiency of energy absorption for Regime 3 also depends on the Mach number and the critical stress of the foam. Numerical plate impact simulations have been carried out in impact Regime 2. Explicit finite element analysis is performed using LS-DYNA 960. The time history of dynamic deformation and energy of the impact plate is presented. The numerical prediction is found to be in good agreement with the analytical results.