On the power-law pressure dependence of the plastic strain rate of crystals under intense shock wave loading

Abstract

The plastic deformation of metallic crystals under intense shock wave loading has been theoretically investigated. It has been experimentally found that the plastic strain rate $\dot \varepsilon$ and the pressure in the wave P are related by the empirical expression $\dot \varepsilon$ ∼ P ⁴ (the Swegle-Grady law). The performed dislocation-kinetic analysis of the mechanism of the origin of this relationship has revealed that its power-law character is determined by the power-law pressure dependence of the density of geometrically necessary dislocations generated at the shock wave front ρ ∼ P ³. In combination with the rate of viscous motion of dislocations, which varies linearly with pressure (u ∼ P), this leads to the experimentally observed relationship $\dot \varepsilon$ ∼ P ⁴ for a wide variety of materials with different types of crystal lattices in accordance with the Orowan relationship for the plastic strain rate $\dot \varepsilon$ = bρu (where b is the Burgers vector). In the framework of the unified dislocation-kinetic approach, it has been theoretically demonstrated that the dependence of the pressure (flow stress) on the plastic strain rate over a wide range from 10⁻⁴ to 10¹⁰ s⁻¹ reflects three successively developing processes: the thermally activated motion of dislocations, the viscous drag of dislocations, and the generation of geometrically necessary dislocations at the shock wave front.