Dislocation Patterns and Work-Hardening in Crystalline Plasticity

We propose a continuum model for the evolution of the total dislocation densities in fcc crystals, in the framework of rate-independent plasticity. The basic physical features which are taken into account are: (i) the role of dislocations in hardening; (ii) the relations between the slip velocity and dislocation mobility; (iii) the energetics of self and mutual interactions between dislocations; (iv) nonlocal effects in the interaction between dislocations. A set of reaction–diffusion equations is obtained, with mobilities depending on the slip velocities, which is able to describe the formation of dislocation walls and cells. To this effect, the results of numerical simulations in two special cases are presented.Mathematics Subject Classifications (2000) 74C15, 74C20.