A dislocation kinetic model of the formation and propagation of intense shock waves in crystals

Analytical expressions for the front of a shock plastic wave and the plastic relaxation region behind the front have been obtained and a relation of the wave parameters to the pressure in the wave has been determined in the framework of the dislocation kinetic approach based on kinetic relationships and equations for the density of dislocations. Within this approach, the physical mechanism of the origin and the universality of the Swegle–Grady empirical relationship for crystals in the form of a power-law dependence of the plastic strain rate $P$ : $\dot{\varepsilon}\sim P^4$ on the pressure in the wave $P$, that is, $\dot{\varepsilon}\sim P^4$, have been discussed. The principal contribution to this dependence comes from the power-law (cubic) dependence of the density of dislocations generated in the wave front on the pressure. The universality of the Swegle–Grady relationship is based on the invariance of the dissipative action $A$. An explicit expression for the dissipative action has been derived: $A = SBV_0/3\beta$. As follows from this expression, the dissipative action is determined by fundamental parameters for shock wave loading of crystals, such as the dislocation viscous drag coefficient $B$ and the adiabaticity factor $S$ (here, $V_0$ is the specific volume and $\beta$ is a coefficient of the order of 10$^{-3}$–10$^{-2}$). In light of the revealed circumstances, such phenomenological notions as the Hugoniot elastic limit and the elastic precursor have been critically examined.