Dislocation mutual interactions mediated by mobile impurities and the conditions for plastic instabilities

Metallic alloys, such as Al and Cu or mild steel, display plastic instabilities in a well-defined range of temperatures and deformation rates, a phenomenon known as the Portevin-Le Chatelelier effect. The stick-slip behavior, or serration, typical of this effect is due to the discontinuous motion of dislocations as they interact with solute atoms. Here we study a simple model of interacting dislocations and show how the classical Einstein fluctuation-dissipation relation can be used to define the temperature over a range of model parameters and to construct a phase diagram of serration that can be compared to experimental results. Furthermore, by performing analytic calculations and numerically integrating the equations of motion, we clarify the crucial role played by dislocation mutual interactions in serration.