Scale transitions in the dynamic analysis of jerky flow

Abstract

Jerky flow or the Portevin - Le Chatelier effect is observed in polycrystals submitted to velocity controlled unidirectional tests. Complementary statistical, multifractal and dynamical analysis have been carried out on stress vs. time series recorded during unstable plastic flow. Along with the characterization of the statistical distributions of stress drops, the paper investigates their clustering in time as well as the multifractality of their singularity spectrum. By embedding the stress time series in a higher dimensional phase space, dynamic properties such as the fractal dimension and Lyapunov exponents of the reconstructed attractor are exhibited. These methods allow to show that a Self Organized Critical dynamics is present at a high strain rate in strongly annealed polycrystals, whereas a chaotic regime is observed in cold-rolled polycrystals at lower strain rates. Infinitely many degrees of freedom are required to account for SOC, whereas chaotic dynamics is fully captured by a limited number of variables. Therefore, a dramatic reduction in the dimensionality of the phenomenon is observed at a crossover strain rate. This result has significant implications for the multiscale modeling of the phenomenon. Models limited to a few mesoscopic modes are proved unable to account for the high strain rate behavior.