Negative strain rate sensitivity and the critical nature of type A bands in the Portevin-Le Chatelier effect

Abstract

Describing spatio-temporal features of the Portevin-Le Chatelier (PLC) effect is a particularly difficult task as it arises from the interaction of the collective modes that have widely separated time scales. Using a dynamical approach we provide a new interpretation for the two most important features of the PLC effect, namely the negative Strain Rate Sensitivity (SRS) of the flow stress and the critical nature of type A band that is reflected in the power law statistics for stress drops in this region. Within the scope of Ananthakrishna's model, using the slow manifold approach applicable to multiple time scale dynamical systems, we show that the two stable branches of the negative SRS can be identified with two subset of dislocation mechanisms that have physically appealing meaning. The method also allows us to visualize dislocation configurations corresponding to the different band types. While most dislocations are in the pinned state corresponding to type C and B bands, that for the type A are at the edge of unpinning thus explaining the origin of its critical nature of the propagating band.