Dynamic Length Scale and Weakest Link Behavior in Crystal Plasticity

Abstract: Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the validity of such an approach and the ideal choice for the size of the representative volume element for crystal plasticity in terms of a discrete dislocation model. We find that the number of links representing possible sources of plastic activity exhibits anomalous (super-extensive) scaling which tends to extensive scaling (often assumed in weakest-link models) if quenched short-range interactions are introduced. The reason is that the interplay between long-range dislocation interactions and short-range quenched disorder destroys scale-free dynamical correlations leading to event localization with a characteristic length-scale. Several methods are presented to determine the dynamic length-scale that can be generalized to other types of heterogeneous materials.