Strain localization in polycarbonates deformed at high strain rates

Abstract

We studied three-dimensional transient large coupled thermomechanical deformations of a polycarbonate (PC) plate with a through-the-thickness inhomogeneity at its centroid. The PC exhibits strain softening followed by strain hardening and its elastic moduli are taken to be functions of strain rate and temperature. The inhomogeneity is either a void or a region of initial temperature higher than that of the rest of the plate. The nonlinear initial-boundary-value problem is solved numerically by the finite element method. It is found that deformations localize into narrow regions that we call bands. For a plate deformed in tension, the maximum principal stretch within the band is almost twice that of the maximum shear strain and for a plate deformed in shear the two have approximately the same magnitude. For the PC deformed in uniaxial compression, we call the minimum slope of the effective stress vs. the effective strain curve in the strain softening regime as the softening modulus, E_s, and find values of E_s and the defect strength needed for the deformations to localize. These values are found to be different for the plate deformed in shear from that deformed in tension and the minimum value of E_s for the localization of deformation also depends upon the defect type and the defect strength (e.g., the ratio of the major to the minor axes of the elliptic void).