Two-wave structure of plastic relaxation waves in crystals under intense shock loading

The mechanism of formation of a two-wave structure of plastic relaxation waves at shock wave stresses $\sigma>$ 1 GPa (plastic strain rates $\dot{\varepsilon}>10^6$ s$^{-1}$) has been theoretically considered using the dislocation kinetic equations and relationships. It has been shown that, under intense shock loading, two plastic relaxation waves are generated in the crystal. Initially, there arises the first wave (in the traditional terminology, it is an elastic precursor) associated with the generation of geometrically necessary dislocations at the boundary between the compressed and uncompressed parts of the crystal. Then, there arises the second wave due to the dislocation multiplication on geometrically necessary dislocations of the first wave in the form of forest dislocations. The dependences of the stresses on the plastic strain rate $\sigma\sim\dot{\varepsilon}^{1/4}$ in the first wave and $\sigma\sim\dot{\varepsilon}^{2/5}$ in the second wave, as well as the dependences of the stresses on the thickness of the target $D$, i.e., $\sigma\sim D^{-1/3}$ and $\sigma\sim D^{-2/3}$, respectively, have been determined by solving the relaxation equations. The obtained relationships have been confirmed by the experimental data available in the literature.