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 inhomoge neous (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.

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“…Cell walls differ from grain boundaries as they exhibit lower misorientation and a different morphology [50]. At low strain, these cell structures are rather heterogeneous, but as further deformation is introduced into the material, a much more uniform distribution of dislocations is observed [6,[47][48][49]. It has also been reported that in low stacking fault energy materials, the deformation process/formation of cell structure, is accompanied by the formation of deformation induced martensite, first as ε martensite and then as α' martensite [6,47].…”

“…The heterogeneous stress state is due to the plastic deformation process that materials with low stacking fault energy, such as ASS [46], undergo. As plastic deformation is introduced into ASS, the planar dislocation structure evolves into stacking faults [6,[47][48][49]. As more deformation is induced, the stacking faults form a cell structure.…”