Synergetics of the interaction of mobile and immobile dislocations in the formation of dislocation structures in a shock wave. Effect of the stacking fault energy

Abstract

A kinetic equation for the density of dislocations, which reflects the main stages of the formation of dislocation structures of different types in a shock wave, has been formulated based on the analysis of the interaction of two kinetic processes described by reaction-diffusion type equations for densities of mobile dislocations and dislocations forming immobile dipoles, respectively. It has been shown that an inhomogeneous (cellular) dislocation structure is formed at relatively low pressures behind the front of a shock wave, whereas a uniform distribution of the dislocation density with stacking faults appears at high pressures. The transition from a cellular dislocation density distribution to a uniformly distributed dislocations with stacking faults depends on the stacking fault energy γ _D of the metal: the lower is the stacking fault energy, the lower is the pressure in the shock wave σ _c at which the cellular dislocation structure transforms into the structure with a uniform dislocation density distribution. It has been found that the dependence of the critical pressure on the stacking fault energy γ _D is described by the law σ _c ∼ (γ _D /μb)^2/3 (where μ is the shear modulus and b is the Burgers vector), which is confirmed in the experiment.