Localization of plastic flow at high-rate simple shear

This study numerically investigates the influence of the initial perturbations of temperature or dislocation density in metals and of the stress concentrators on the plastic flow localization. The high-rate simple shear of micro-sample is simulated in two-dimensional formulation with use of the continuum mechanics and the dislocation plasticity model. The calculations are performed for the pure aluminum and the aluminum alloy, which differ by the yield stress values and by its temperature dependences. The considered perturbations of temperature or dislocation density lead to restricted localization of the plastic deformation, but they cannot initiate instability of the plastic flow as a self-sustained and increasing process. The more effective reason of the localization is the stress concentration, caused, for example, by boundary conditions. The plastic deformation rate is maximal in the shear stress localization areas and it can be close to zero outside these areas. Analytical estimation of the localization degree is constructed, which is in qualitative agreement with the numerical data; this estimation reveals that the localization degree grows linearly with time at the constant strain rate.