Numerical simulation of systems of shear bands in ductile metal with inclusions

Abstract

We develop a method for numerical simulations of high strain-rate loading of mesoscale samples of ductile metal with inclusions. Because of its small-scale inhomogeneity, the composite material is prone to localized shear deformation (adiabatic shear bands). This method employs the Generalized Method of Cells of Paley and Aboudi [Mech. Materials, vol. 14, pp. 127–139, 1992] to ensure that the micro mechanical behavior of the metal and inclusions is reflected properly in the behavior of the composite at the mesoscale. To find the effective plastic strain rate when shear bands are present, we extend and apply the analytic and numerical analysis of shear bands of Glimm, Plohr, and Sharp [Mech. Materials, vol. 24, pp. 31–41, 1996]. Our tests of the method focus on the stress/strain response in uniaxial-strain flow, both compressive and tensile, of depleted uranium metal containing silicon carbide inclusions. We use the Preston-Tonks-Wallace viscoplasticity model [J. Appl. Phys., vol. 93, pp. 211–220, 2003], which applies to the high strain-rate regime of an isotropic viscoplastic solid. In results, we verify the elevated temperature and thermal softening at shear bands in our simulations of pure DU and DU/SiC composites. We also note that in composites, due the asymmetry caused by the inclusions, shear band form at different times in different subcells. In particular, in the subcells near inclusions, shear band form much earlier than they do in pure DU.