Dynamic Shear Bands in Metals under High Strain Rates

Abstract

Adiabatic shear bands have been observed for a long time to occur under different conditions in many applications. Analysis of these localizations highly depends on the selection of the constitutive model. Hence, two constitutive models that take temperature and strain rate effect into account are proposed. The first model is a physically based model that depends on basic physical quantities, such as dislocation densities, Burgers vector, and activation energy. The second model is a simple empirical power model with a softening term. The empirical constitutive law is seen to be more successful in capturing the mechanical behavior of steel alloy under different temperatures and strain rates, and therefore is used in the finite element analysis. Generally in finite element analysis, a finer mesh will yield results that are more accurate, but on the other hand will increase the computational cost. One way to handle this issue is through using a nonlocal gradient theory that is associated with a material length scale. Experimental procedure is utilized to obtain the length scale for steel alloys. To capture the rate sensitivity of the length scale, two models are proposed for the material dynamic hardness; a simple power law model, and a physically based model. The power law is chosen to be implemented in a finite element subroutine to be used to simulate adiabatic shear banding. Explicit finite element analysis is used to solve different problems of adiabatic shear banding. Three examples include adiabatic shear bands due to material inhomogeneities as well as due to deformation gradients are presented. The simulation results of the steel penetration problem are seen to be in a very good agreement with available experimental data. It is also noticed that deformation mode changes significantly in the steel beam impact problem at different impact velocities.