Effects of Correlation Interaction of Dislocations During Plastic Deformation of Metals

Abstract

Based on the continuum theory for the dynamics of a deformable crystal with dislocations, we consider the effect of shielding their elastic field. Representing the dislocation ensemble as a plasma-like medium, we construct a theory of the correlation interaction of screw dislocations. It is shown that the radius of shielding of dislocations is the radius of their correlation. Using the theory being developed, self-consistent evolutionary equations of the dynamics of dislocations are formulated with allowance for their correlation interaction. The study of the corresponding system of equations has shown that in a dislocation ensemble for the total and excess density of dislocations (dislocation charge), under certain conditions, there is an instability of their homogeneous distribution due to the correlation interaction between them. Based on a linear analysis of the initial system, a criterion for this instability related to the critical density of dislocations, above which the instability develops, is obtained. A nonlinear theory for the formation of inhomogeneous cellular structures beyond the bifurcation point has been developed. Using the approach of the theory of dissipative structures, equations of order parameters are obtained. Their study has shown that cellular structures with different types of symmetry can be formed in the system, depending on the number of excited modes parameterized by the number N. As a result, it is shown that crystal-type (rhombic and hexagonal) structures are formed at N = 2, 3, while quasi-crystalline (octagonal, decagonal, etc.) structures are formed at N > 3.