Strength and Viscosity Effects on Perturbed Shock Front Stability in Metals

Computational modeling and experimental measurements on metal samples subject to a laser-driven, ablative Richtmyer-Meshkov instability showed differences between viscosity and strength effects. In particular, numerical and analytical solutions, coupled with measurements of fed-through perturbations, generated by perturbed shock fronts onto initially flat surfaces, show promise as a validation method for models of deviatoric response in the postshocked material. Analysis shows that measurements of shock perturbation amplitudes at low sample thickness-to-wavelength ratios are not enough to differentiate between strength and viscosity effects, but that surface displacement data of the fed-through perturbations appears to resolve the ambiguity. Additionally, analytical and numerical results show shock front perturbation evolution dependence on initial perturbation amplitude and wavelength is significantly different in viscous and materials with strength, suggesting simple experimental geometry changes should provide data supporting one model or the other.

Figure 1

Illustration of a rippled shock target with example VISAR and TIDI data used to measure shock feedthrough and imprint. The shock ripple oscillation frequency and growth of the imprint at the breakout surface are used to validate strength models that may soon be used in ICF designs to predict ablation front feedthrough in 1st shock solid ablators.

Figure 2

Shock front perturbation amplitude experimental data and their comparison to inviscid (Hydro), viscous (10 Pa s), elastic-plastic (400 MPa), and PTW material models. Simulations are for a $150\mu \mathrm{m}$ wavelength and a ${\mathrm{A}}_0=6\mu \mathrm{m}$ initial amplitude.

Figure 3

Comparison of shear stresses after trailing shock front breakout. (a) 10 Pa s, (b) elastic-plastic, and (c) PTW. Stress contour plots ($\pm 231\mathrm{MPa}$) are linear with units of Pascals.