Material yielding and irreversible deformation mediated by dislocation motion

We study the collective behavior of dislocation assemblies in simplified models of plastic deformation. We first review several numerical results on long range dislocation interactions with simplified dislocation motion constraints. These typically give rise to a yielding transition separating stationary and moving dislocation phases. Furthermore, we discuss the intermittent relaxation of the plastic strain-rate observed around this transition at mesoscopic scales, and how this intermittent behavior gives rise to an average slow power law relaxation in time known in the literature as Andrade's creep. We analyze the coherent dynamics and the average stress-strain relationship in the steady regime of plastic deformation. In this steady regime, plastic deformation proceeds in the form of plastic avalanches whose size and duration are broadly distributed and statistically characterized. One signature of the time correlations of this heterogeneous collective dislocation dynamics is a power spectrum scaling with frequency as f(-alpha) with an exponent alpha close to 1.5. This feature appears to be peculiar of dislocation and grain boundary motion as has been observed in other physical situations in the vicinity of a yielding transition.