Repeated yield drop phenomena as a cooperative effect

Abstract

We present a theoretical model of repeated yielding (RY) which reproduces many experimentally observed features, apart from showing how the temporal behaviour of the phenomenon emerges as a consequence of the cooperative behaviour of defects. We first consider the case of step-like creep curves. Our model leads to a coupled set of nonlinear differential equations which admit limit cycle solutions, and thence jumps on the creep curve. Approximate closed form solutions for the limit cycles and the steps on the creep curve are obtained. The model is then extended to the constant strain rate experiment by including the machine equation. The temporal ordering of RY is shown to follow, as well as several other features characteristic of RY. Chaotic flow is also exhibited: the model has a sequence of period-doubling bifurcations with an exponent equal to that of the quadratic map. Finally, we have analysed the fluctuations during the onset of RY using nonlinear Langevin equations. Fluctuations in the periodic (RY) phase are also investigated. We conclude that RY is another example of a dissipative structure.