Mechanism of formation of cellular dislocation structures during propagation of intense shock waves in crystals

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

“…DEPENDENCES OF THE PARAMETERS β AND ξ ON THE PRESSURE As already mentioned above, the parameters β and ξ determine the character of a dislocation structure formed in the crystal after the passage of a shock wave: for the parameters β > 1 and ξ > 1, the dislocations are nonuniformly distributed and concentrated within the boundaries of dislocation cells; for β < 1 and ξ < 1, they are uniformly distributed over the crystal [14]. In this section, we determined the dependence of the above parameters on the pressure and showed that the first type of dislocation structure is formed in the crys tal at relatively low pressures, whereas at relatively high pressures, the crystal has the second type of disloca tion structure.…”

“…The purpose of this work is to analyze the influence of the stacking fault energy on the critical stress of the transition from a cellular distribution of dislocations in a shock wave to a uniform distribution of dislocations with stacking faults. As was done in the previously per formed analysis of the influence of the grain size and density of precipitates on the aforementioned transi tion [7], the present analysis is based on the kinetic equation for the density of dislocations and on the critical conditions of the formation of their cellular distribution [14]. This paper is organized as follows.…”

“…In [7,14], the influence of the pressure, grain size, and volume density of precipitates on the transition from a cellular dislocation structure to a uniform dis tribution of dislocations behind the shock wave front was analyzed using the model equation for the disloca tion density in the following form [15,16]: (1) where ρ(y, t) is the density of mobile dislocations; y is the coordinate along the normal to the dislocation slip plane; t is the time; u is the dislocation velocity; D m is the coefficient of the diffusion of screw segments of dislocation loops through the double cross slip mech anism; λ m and δ f ρ 1/2 are the mean free paths of dislo cations between the events of their multiplication at obstacles of the nonstrain and strain (forest of disloca tions with density ρ f = ρ) origins, respectively; δ f ≈ 10 ⎯2 is the coefficient determining the intensity of the latter process; and h a is the characteristic distance of the annihilation of screw segments of dislocation loops through the cross slip mechanism [17]. In equation (1), the parameters ξ and β determine the type of dis location structure formed in the material.…”

“…In equation (1), the parameters ξ and β determine the type of dis location structure formed in the material. For the parameters ξ < 1 and β < 1, the propagation of a shock wave results in the formation of a spatially homoge neous dislocation structure; for ξ > 1 and β > 1, this process leads to the formation of an inhomogeneous (cellular) dislocation structure [7,14]. The specific (1), as applied to the problem of the origin and propagation of plastic shock waves, is that some of the coefficients and parameters of this equation depend on the pressure in the shock wave.…”

“…The deviatoric component of the stress τ is related to the pressure σ at the shock wave front (elastic pre cursor) by the expression (11) The processing [14] of experimental data [3], as well as the results of computer simulation [19,20], showed that the numerical coefficient in expression (11), which relates the shear stress behind the shock wave front to the pressure, is one to two orders of magnitude smaller and, for Cu and Ni crystals, lies in the range of 0.002-0.020. This decrease in the shear stress behind the shock wave front is associated with the strong relaxation of the deviatoric stress component [21] due to the generation of geometrically necessary disloca tions at the shock front.…”