Dynamic shear instabilities in metallic sheets subjected to shear-compression loading

Abstract

This paper presents an investigation on the formation of adiabatic shear bands in metallic sheets subjected to dynamic shear-compression loading under plane-stress conditions. For that purpose, we have developed a theoretical model based on perturbation analysis, and have performed finite element calculations. The material behavior has been modeled with von Mises plasticity, and the evolution of the yield stress has been considered dependent on plastic strain, plastic strain rate, and temperature. The theoretical model extends the linear stability analysis for simple-shear formulated by Molinari (1997) to shear-compression loading. The numerical simulations have been performed in ABAQUS/Explicit (2016) using a unit-cell model based on the work of Rodríguez-Martínez et al. (2015) in which the shear band formation is favored introducing geometric and material imperfections. Moreover, we have developed a calibration procedure for the stability analysis that enables to make qualitative and quantitative comparisons with the finite element calculations. Both stability analysis predictions and finite element results display the same overall trends, and show that any small negative triaxiality has a profound stabilizing effect on the material behavior delaying, or even preventing, the formation of a shear band. This key outcome has been substantiated for a wide range of strain rates and for materials with different strain hardening coefficients, strain rate sensitivities, and thermal softening behaviors.