Complex patterning in jerky flow from time series analysis and numerical simulation

The paper is a tribute to Ladislas P. Kubin's long-standing work on the collective behavior of dislocations in jerky flow. In a first part, it reviews his contributions to the statistical, dynamical and multifractal analyses carried out on stress-time series recorded from both single crystals and polycrystalline samples of dilute alloys subjected to tensile tests at constant strain rate. Various spatio-temporal dynamical regimes were found as the applied strain rate was varied. Type C static bands were associated with quasi-random collective behavior, the hopping type B and propagating type A bands could be shown to correspond to chaotic and self-organized critical dynamics, respectively. The crossover between the A and B regimes was characterized by a large spread in the multifractal spectrum of stress drops, associated with heterogeneity of the dynamics. In a second part, the paper reviews the nonlocal models Ladislas inspired to interpret these results from numerical solutions of the boundary value problem, on the basis of dynamic strain aging, the incompatibility stresses associated with dislocations, their plastic relaxation and the spatial couplings they inherently involve. Eventual developments of this research, rooted in the same ideas, on the statistical and multifractal analyses of the accompanying acoustic emission are reviewed and discussed in terms of the synchronization of small-scale plastic events.