Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials

Abstract

The method of the dual plastic potentials is used to derive convenient formulas for calculating yield loci of rate insensitive anisotropic materials. For rate sensitive materials, equipotential surfaces are obtained instead of yield surfaces. Emphasis is on the theory needed to identify the plastic potentials to certain functions that (in the case of single phase materials) can directly be calculated from the crystallographic texture. The resulting formulas are kept as simple as possible, which means that the influence of the magnitude of stress or strain rate on the one hand, and of the mode (or direction) of stress or strain rate on the other hand, are separated into multiplicative factors. In addition, the theory was also applied to the von Mises and Hill yield loci, for which strain rate sensitive versions were proposed. The theory could also be applied to the well-known viscoplastic model for the plastic deformation of crystals.