Characterization and control of chaotic stress oscillations in a model for the Portevin-Le Châtelier effect

Abstract

The Portevin-Le Chatelier (PLC) effect, otherwise known as serrated yielding, repeated yielding, or jerky flow, has been a subject of investigation for many years. Modeling studies, and experiments have shown that the oscillatory PLC stress-strain dynamics can sometimes be a form of deterministic chaos. In such cases, the spontaneously occurring oscillations are aperiodic and are characterized by at least one positive Lyapunov exponent. However, whether they be chaotic or not, these oscillations are detrimental to the mechanical integrity of the material, so that some means by which they can be suppressed would be a desirable feature. In the work described below, a strategy for suppressing these oscillations is developed and applied to a model for the PLC effect. The strategy is physically realistic in the sense that it is based on the feedback of a control signal, obtained from a measurable quantity, to an accessible (i.e., controllable) parameter. Application is made here to a case for which the oscillations are chaotic, although the approach is applicable to periodic stress oscillations as well.