The Mesoscale Velocity Distribution and Change of Regime of Shock Wave Propagation

Abstract

We consider the propagation of a plane elastic–plastic wave in a heterogeneous medium where the dynamic behaviour of the medium is determined by the high statistical moments of the velocity distribution function—the mesoparticle velocity dispersion and the asymmetry of the mesoparticle distribution function. In the case of an unsteady plastic wave, the rate of the plastic deformation upl is presented as the sum of the equilibrium and non-equilibrium parts: upl = \(u_{p}^{pl} + u_{{\mathcal{H}}}^{pl}\). The regime for the shock wave propagation changes when the rate of change of the mesoparticle velocity dispersion becomes higher the rate of change of the mean particle velocity. Physically, this means that the wave motion transits to a decaying regime. Thus, the condition for breaking the plastic front is determined by the ratio of the velocity variance and mean velocity and by the ratio of their rates of change. This means that in the dynamic processes, the rate of change of the particle velocity dispersion is the basic control parameter of the shock wave process. The obtained criterion has been applied to real experiments with the shock loaded materials, such as copper, aluminium alloys and steels. In experiments, the temporal behaviour of the velocity dispersion and mean particle velocity can be registered in real time in the processes of shock loading by using the interference technique. Shock tests of D16 aluminium alloy reveal the following features of dynamic response to shock loading: (1) The region of strain rates corresponding to impact velocities of 85–451 m/s is subdivided into two sub-regions at the impact velocity of 382 m/s. In the first sub-region (85–382 m/s), the velocity defect remains constant at ~20 m/s. In the second sub-region, corresponding to within impact velocity region of 382-451 m/s, the velocity defect grows with increasing impact velocity. This region corresponds to the irreversible regime of interscale momentum and energy exchange. (2) At the impact velocity of 382 m/s, the velocity variance equals the velocity defects, corresponding to the equality of the local strain rate and the macroscopic strain rate, just as that impact velocity corresponds to maximum spall strength of D16 Al alloy.