A physically-based model was developed here in order to address slip in polycrystalline metals and alloys subjected to very high rates of deformation (104–108/s). Constitutive relations were provided for the kinematics, kinetics, and substructure of face-centered cubic metals with micron-scale grains. The main innovative feature of this work was the treatment of the dislocation substructure in the weak shock loading regime. Here, the mobile and immobile dislocation densities were assigned as internal state variables and path-dependent differential equations were formulated for their evolution. This enables physical descriptions of slip resistance and the plastic flow rate. The constitutive model was applied to 6061-T6 Al alloy and the viscoplastic relations were employed in steady plastic wave calculations that enable comparison of the model to experiments. For shock stress amplitudes of 2 to 10GPa 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 were also in agreement with measurements of material strength on the Hugoniot for shock stresses up to some 15GPa. 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 was suggested to bring the model into better agreement with experiments at higher shock stresses.

A Dislocation-Based Constitutive Model for Viscoplastic Deformation of FCC Metals at Very High Strain Rates. R.A.Austin, D.L.McDowell: International Journal of Plasticity, 2011, 27[1], 1-24