Numerical studies of self-organization of shear bands in one and two dimensions

In the present manuscript we perform a numerical analysis of the self-organization processes of adiabatic shear bands formation in depleted uranium, aluminum alloy, and high-strength steel in one- and two-dimensional cases. Since the processes of shear bands formation are strongly nonlinear, three materials with significantly different parameters considered allow us to generalize obtained dependencies. For all materials, we investigate the evolution of stress, temperature and velocity fields from initial to final stage of localization. It is well known that localization processes occur during the high shear rate loads in the presence of initial microstructural defects in metallic materials. Starting with a random distribution of initial stress, which models microstructural defects, we obtained new dependencies for such significant parameters of the problem considered such as localization time and spacing between shear bands. The influence of initial plastic strain rate on these parameters was also studied. We obtain the linear dependence of localization time on initial strain rate and show that spatial dimension significantly influences on its value. Also, we introduce the method of shear bands selection during computations and present new statistical distributions for band spacing. We show that the interaction between shear bands significant influences on the spacing between them. •The collective behavior of shear bands in 1D and 2D case is studied.•Numerical simulation of the shear bands formation in three metallic materials is performed.•Comparison of the adiabatic shear band spacing and localization time in 1D and 2D cases is performed.