J. Phys. IV France 11 (2001) Pr5-135-Pr5-142
Scale transitions in the dynamic analysis of jerky flowG. Ananthakrishna1, M.S. Bharathi1, C. Fressengeas2, L.P. Kubin3 and M. Lebyodkin4
1 Materials Research Centre, Indian Institute of Science, Bangalore 560012, India
2 Laboratoire de Physique et Mécanique des Matériaux, Université de Metz, CNRS, Ile du Saulcy, 57045 Metz cedex 01, France
3 Laboratoire d'Étude des Microstructures, CNRS-ONERA (OM), 29 avenue de la Division Leclerc, BP. 72, 92232 Châtillon cedex, France
4 Institute of Solid State Physics, Russian Academy of Science, 142432 Chemogolovka, Moscow District, Russia
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.
© EDP Sciences 2001