Synergetic model of structure formation during plastic deformation of crystals

Abstract

A synergetic model of the band-structure formation in plastically deformed crystals is proposed that describes the behaviour of a defect system containing vacancies and vacancy-type agglomerates. The production of vacancies by jogged dislocations and the production (capture) of vacancy agglomerates are assumed to take place in crystals during loading. The agglomeration processes are simulated by simplified schemes which are like double irreversible chemical reactions. As a whole the defect system is described by a set of nonlinear partial differential equations. The linear local analysis of spatial homogeneous states of the defect system is carried out assuming that the agglomerates are geometrically similar to one another (this is true for lines, discs, spheres and fractal structures). The conditions for the appearance of instability with regard to spatially inhomogeneous disturbances are found. The parameters of the structure which appears are numerically evaluated. A novel explanation of the localization of vacancies and vacancy-type agglomerates is proposed on the basis of this model.