Crossover behavior of self-similar wave solutions in polymer metal composites

Shock propagation in composite materials is intrinsically dependent on the length scales that are introduced by the microstructural details of the material. Here we investigate shock propagation in a composite material composed of a bulk polymer with embedded tungsten micron sized spheres. Experimental data for a range of sample widths shows that the composite material particle speed profile reaches a steady-state flow that is dependent on the tungsten particle volume fraction. Building on previous work, we developed self-similarity solutions of a one dimensional two-phase flow hydrodynamic model that depends on the particle volume fraction and diameter. We use these solutions to examine the crossover from non-equilibrium to steady wave propagation.