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Mechanical properties, strength physics and plasticity
On the power-law pressure dependence of the plastic strain rate of crystals under intense shock wave loading
G. A. Malygina,
S. L. Ogarkovb,
A. V. Andriyashb a Ioffe Institute, St. Petersburg
b All-Russia Research Institute of Automatics named after N L Dukhov, Moscow
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
$\dot{\varepsilon}\sim P^4$ (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
$\rho\sim P^3$. In combination with the rate of viscous motion of dislocations, which varies linearly with pressure
$(u\sim P)$, this leads to the experimentally observed relationship
$\dot{\varepsilon}\sim P^4$ for a wide variety of materials with different types of crystal lattices in accordance with the Orowan relationship for the plastic strain rate
$\dot{\varepsilon}=b\rho u$ (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
$^{-4}$–10
$^{10}$ 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.
Received: 28.08.2012
Accepted: 26.09.2012
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