A model for instability growth in accelerated solid metals

Abstract

We present an approximate analytical dispersion relationship for elastic–plastic acceleration-driven instability growth. In this model, the accelerated solid behaves like a viscoplastic after its elastic yield strength is exceeded, with the viscosity inversely proportional to the strain rate. We have applied this model, or a 1993 model of shock-driven viscous instability growth, where applicable, to perturbation growth measurements made in three separate types of experiments: High-explosive (HE)-driven planar Al plates, HE-driven implosions of steel cylinders, and planar Al foils driven indirectly by Lawrence Livermore National Laboratory’s Nova laser. We have also compared the analytical modeling of these experiments with simulations done with a two-dimensional Lagrangian radiation-hydrodynamics computer code containing an elastic–plastic constitutive model. We find that for the moderate strain rates of the HE experiments, the simulations and analytical modeling of perturbation growth agree with each other and with the data, using an equivalent plastic viscosity consistent with the von Mises plasticity criterion. For the high strain rates of the Nova experiments, on the other hand, the early-time growth data is consistent with viscoplastic growth, with viscosity ten to a hundred times less than the von Mises plastic viscosity for nominal strength. This observed initial material weakening is followed by a transition to a strengthened state to match the late-time growth data, which we show to be consistent with a “relaxation” hypothesis in which plastic flow at high strain rate is confined to discrete shear bands. We also show under what conditions the perturbation growth is independent of initial amplitude.