Geometrically non-linear modeling of the Portevin-Le Chatelier effect

In this work we investigate the plastic instabilities associated with the Portevin-Le Chatelier (PLC) effect in Al alloy 2024. A semiphenomenological approach is taken. A simple geometrically non-linear elastic-viscoplastic constitutive model is proposed for simulation of material response under various applied strain rates. Using the model we determine numerically the relation between the critical strain for the onset of discontinuous yielding and the applied strain rate. The results obtained are in very good quantitative agreement with the available experimental data and cover both the normal and the inverse behavior of the critical strain. The simulations are performed using non-linear finite element method. Additional verification of the proposed constitutive framework was carried out using statistical analysis of the simulated stress-time series. A transition from a non-linear chaotic regime to self-organized critical behaviour of the localized strain bands were predicted in terms of the temporal two-point correlation function of the stress-time series. Finally we investigated the influence of different factors, such as the geometry of the specimen, its orientation with respect to the rolling direction and loading conditions (strain rate), on the type of PLC instabilities and the critical conditions for their onset.