The Voigt bound of the stress potential of isotropic viscoplastic FCC polycrystals

Abstract

The Voigt bound of the stress potential of face-centered cubic (fcc) polycrystals without texture is numerically determined for all types of strain rate states. The numerical findings reveal the dependence of the stress potential on both the second and the third principal invariant of the strain rate deviator. The dependence on the determinant vanishes only for a linear viscoplastic behavior. Due to the dependence of the stress potential on the third principal invariant, the determinant, the viscoplastic flow is generally nonproportional to the stress deviator. A simple analytical expression is found, which reproduces the numerical findings over the full range of strain rate sensitivities.