The effect of material heterogeneity on the shock response of layered systems in plate impact tests

In the study of shock wave propagation in solids, scattering, dispersion, and attenuation play a critical role in determining the thermomechanical response of the media. These phenomena can be attributed to a number of nonlinearities arising from the wave characteristics, loading conditions, material heterogeneity (measured at various spatial scales ranging from nanometers to a few millimeters). The nonlinear effects in general can be ascribed to impedance (and geometric) mismatch present at various length scales as often encountered in composite material systems, apart from material nonlinearities arising from inelastic effects, void nucleation and growth, cracking, and delamination. However, in nearly brittle material systems, elastic effects dominate and is the only effect considered here. Uniaxial strain experiments on the S-2 glass/polymer composite system display markedly different behavior than that observed in monolithic metallic systems [6] and this motivated the present work. Stress profiles measured at various locations along the direction of wave propagation in the plate impact experiments showed that the shock wave rise time increased with propagation in addition to the reduction of peak stress. In this work, we specifically address the issue of shock wave rise time in a simplified multi-layered system. A careful analysis of wave propagation in heterogeneous medium is performed by considering the elastic/acoustic properties of individual lamina in a layered system. An analytical model has been developed to describe the scattering process (reflection/transmission) at various layer interfaces of multilayer composite system. FEM results are then used to compare with the analytical predictions. These results show that the rise time can be a consequence of multiple internal reflections and transmissions occurring at the heterogeneous interfaces, it is further shown that the rise time depends on the magnitude of impedance mismatch and the number of layers.