Influence of system size on spatiotemporal dynamics of a model for plastic instability:Projecting low-dimensional and extensive chaos

摘要

This work is a continuation of our efforts to quantify the irregular scalar stress signals from the Ananthakrishnanmodel for the Portevin–Le Chatelier instability observed under constant strain rate deformation conditions. Stressnrelated to the spatial average of the dislocation activity is a dynamical variable that also determines the timenevolution of dislocation densities. We carry out detailed investigations on the nature of spatiotemporal patternsnof the model realized in the form of different types of dislocation bands seen in the entire instability domain andnestablish their connection to the nature of stress serrations. We then characterize the spatiotemporal dynamicsnof the model equations by computing the Lyapunov dimension as a function of the drive parameter. The latternscales with the system size only for low strain rates, where isolated dislocation bands are seen, and at high strainnrates, where fully propagating bands are seen. At intermediate applied strain rates corresponding to the partiallynpropagating bands, the Lyapunov dimension exhibits two distinct slopes, one for small system sizes and anothernfor large. This feature is rationalized by demonstrating that the spatiotemporal patterns for small system sizesnare altered from the partially propagating band types to isolated burst type. This in turn allows us to reconfirmnthat low-dimensional chaos is projected from the stress signals as long as there is a one-to-one correspondencenbetween the bursts of dislocation bands and the stress drops. We then show that the stress signals in the regimenof partially to fully propagative bands have features of extensive chaos by calculating the correlation dimensionndensity.We also show that the correlation dimension density also depends on the system size. A number of issuesnrelated to the system size dependence of the Lyapunov dimension density and the correlation dimension densitynare discussed.