A dislocation kinetic model of the dislocation structure formation in a nanocrystalline material under intense shock wave propagation

A dislocation kinetic model of the formation and propagation of plastic shock waves in nanocrystalline materials (with a grain size of 1–100 nm) at pressures ranging from 1 to 50 GPa has been discussed theoretically. The model is based on a nonlinear equation of the reaction-diffusion type for the dislocation density, which includes the processes of multiplication, annihilation, and diffusion of dislocations with a strong absorption of the dislocations by nanograin boundaries. The solution of this equation is obtained in the form of a traveling dislocation density wave propagating with a constant velocity. The dependences of the dislocation density and dislocation front width on the nanograin size and pressure in the wave are determined. A comparison of the obtained dependences with the available results of the experiments and molecular dynamics simulations of shock-deformed nanocrystalline materials demonstrates their good quantitative agreement.