Dislocation dynamics and chaos

Abstract

We consider the model proposed earlier by us for explaining the phenomenon of multiple yield drop. The model consists of three types of dislocations interacting nonlinearly producing oscillatory solutions. These solutions arise due to bifurcation with respect several physically relevent drive parameters. The model reproduces a large number of experimentally observed features. The model alsoexhibits chaotic behaviour under the action of drive parameters such as the strain rate and the velocity exponent m. For m=2, it exhibits a period doubling as also period undoubling bifurcation as a function of the starin rate. The nature of convergence is sensitive to the velocity exponent m. When m=2, the convergence of the bifurcation sequence is rapid giving b=4.66 for both the period doubling and period halving sequences. The bifurcation diagram and the nature of the strange attractor are also studied for various values of m. Since the theory is of dynamical origin, it prediets that the yield drops are due to a few degree of freedom interacting nonlinearly in contrast to noise where a large number of degrees of freedom are involved and in priciple can distinguish these two. We outline and discuss various methods to varify whether the multiple yield drop is of dynamic origin. We also discuss possible limitation in obtaining and analysing the experimental data.