Statistical dynamics of dislocations in simple models of plastic deformation: Phase transitions and related phenomena

Dislocation assemblies in crystalline substrates are a beautiful example of the broad class of systems that are governed by the presence of kinematical constraints induced by interactions, geometry, and/or disorder. The interactions between dislocation lines of different type together with the dynamic constraints which tie the motion of the dislocations to their slip planes lead to the possibility of forming metastable jammed configurations even in the absence of any disorder in the material. However, general dislocation assemblies will also be affected by the presence of disorder-induced pinning forces. In this paper we study several aspects concerning the dynamics of dislocation assemblies in simple models of plastic deformation that we believe we can successfully address with the conceptual and technical tools provided by Statistical Mechanics. In particular, we discuss the yielding (or jamming) transition between stationary and moving states in these models, the intermittent and globally slow relaxations observed around this transition, and the stress-strain relationships measured in the steady regime of deformation. We also briefly describe the main implications of sample geometry and of quenched disorder in dislocation assemblies present in the vortex lattice of type II superconductors, where we obtain some of the statistical dynamic properties of experimental interest.