Chaotic and power law states in the Portevin - Le Chatelier effect

– Recent studies on the Portevin Le Chatelier effect report an intriguing crossover phenomenon from a low dimensional chaotic to an infinite dimensional scale invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as a function of strain rate. We devise a fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero. The Portevin-Le Chatelier (PLC) effect, discovered at the turn of the last century [1], is a striking example where collective behaviour of defects leads to complex spatio-temporal patterns [2, 3, 4]. The PLC effect manifests itself as a series of serrations on the stress-strain curves when samples of dilute alloys are deformed under constant strain rate, ǫ̇a (actually constant pulling speed). The effect is observed only in a window of strain rates and temperatures. Each stress drop is associated with the formation and often the propagation of a dislocation band. In polycrystals, at low ǫ̇a, the randomly nucleated type C bands with large stress drop amplitudes are seen. At intermediate strain rates, one finds the spatially correlated ’hopping’ type B bands moving in a relay race manner with smaller stress drop amplitudes. At high strain rates, propagating type A bands with small amplitudes are observed. (In single crystals such a clear classification does not exist.) These different types of PLC bands are believed to represent distinct correlated states of dislocations in the bands. It is this rich spatio-temporal dynamics that has recently attracted the attention of physicists as well [8,9]. Indeed, the PLC effect is a good example of slow-fast dynamics commonly found in many stick-slip systems such as frictional sliding [5], fault dynamics [6] and peeling of an adhesive tape [7]. Recent efforts have shown that surprisingly large body of information about the nature of dynamical correlations is hidden in the stress-strain curves [10, 11, 12, 13]. More recently, an intriguing crossover phenomenon from a chaotic regime occurring at low and medium strain rates to a power law regime at high strain rates has been detected in experiments on the PLC