Localization in elasto-plastic materials: Influence of an evolving yield surface in biaxial loading conditions

The influence of the plasticity yield surface – and of its evolution with plastic deformation – on the development of instabilities in metals is analyzed. Conditions for the activation of slip bands are taken as an instability criterion. They are exhibited in stress states identical to the ones encountered in a flat plate in biaxial tension. The classical bifurcation criterion is replaced by a criterion on the growth of a perturbation at a time scale comparable to the one of the homogeneous solution. This second criterion reveals less severe than the bifurcation one which is reached for the limit case of an infinite growth rate in the perturbation approach. The growth rate is a decreasing function of the biaxiality of the loading which is in agreement with previous studies. The possible destabilizing effect of texture evolution is also exhibited by using an evolving yield surface the curvature of which increases in the neighborhood of the homogeneous solution.