Bistability, negative strain rate sensitivity and visualization of dislocation configurations

Abstract

Describing spatio-temporal features of the Portevin-Le Chatelier effect is known to be a difficult task as they emerge due to collective behavior of dislocations. In this article, we describe a dynamical approach to understand three aspects of the phenomenon, namely, the bistable nature of stress envelope, the negative strain rate sensitivity and visualization of dislocation configurations in different regimes of strain rate. We shall use some special dynamical techniques such as the reductive perturbative technique and slow manifold approach to understand these features. Using a reductive perturbative technique, we derive Stuart-Landau equation for the complex order parameter representing the amplitude and the phase of the limit cycle solution in the neighbourhood of the Hopf bifurcation. The slow manifold technique is used to map different parts of the slow manifold with the different branches of the negative SRS. More importantly, the method allows us to visualize the dislocation configurations in the regions of the bands.