Critical behavior in dislocation systems: power-law relaxation below the yield stress

Plasticity of two-dimensional discrete dislocation systems is studied. It is shown, that at some threshold stress level the response becomes stress-rate dependent. Below this stress level the stress-plastic strain relation exhibits power-law type behavior. In this regime the plastic strain rate induced by a constant external stress decays to zero as a power-law, which stems from the scaling of the dislocation velocity distribution. The scaling is cut-off at a time only dependent on the system size and the scaling exponent depends on the external stress and on the initial correlations present in the system. These results show, that the dislocation system is in a critical state everywhere we studied below the threshold stress.