A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates

In this work a physically-based model is developed to address slip in polycrystalline metals and alloys subjected to very high rates of deformation (10(4)-10(8) s(-1)). Constitutive relations are provided for the kinematics, kinetics, and substructure of fcc metals with micron-scale grains. The main innovative feature of this work is the treatment of the dislocation substructure in the weak shock loading regime. Here, the mobile and immobile dislocation densities are assigned as internal state variables and path-dependent differential equations are formulated for their evolution. This enables physical descriptions of slip resistance and the plastic flow rate. The constitutive model is applied to 6061-T6 Al alloy and the viscoplastic relations are employed in steady plastic wave calculations that enable comparison of the model to experiments. For shock stress amplitudes of 2-10 GPa the model accurately reproduces direct measurements of material velocity and indirect measurements of the macroscopic shear stress and plastic rate of deformation in the shock front. Model results are also in agreement with measurements of material strength on the Hugoniot for shock stresses up to similar to 15 GPa. The accuracy of calculations in the weak shock loading regime indicates the proposed constitutive model may be useful in simulating high-strain-phenomena in a variety of technical applications, including dynamic material responses at small length scales. An improvement to the constitutive model is suggested to bring the model into better agreement with experiments at higher shock stresses. (C) 2010 Elsevier Ltd. All rights reserved.