Micro-plasticity and intermittent dislocation activity in a simplified micro-structural model

Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics (DD) algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The sinusoidal function, defined by a periodic length and a shear-stress amplitude, is interpreted to represent a pre-existing micro-structure. These model parameters, along with the mobile dislocation density, are found to admit a diversity of micro-plastic behaviour involving intermittent plasticity in the form of a scale-free avalanche phenomenon, with an exponent and scaling-collapse for the strain-burst magnitude distribution that is in agreement with mean-field theory and similar to that seen in experiment and more complex DD simulations.