A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming

Spitzig and Richmond [Acta Metall. 32 (1984) 457] proposed that plastic yielding of both polycrystalline and single crystals of steel and aluminum alloys shows a significant sensitivity to hydrostatic pressure. They further showed that under the associated flow rule, this pressure sensitivity leads to a plastic dilatancy, i.e. permanent volume change, that is at least an order of magnitude larger than observed. Indeed, the plastic dilatancy for most materials is on the order of the measurement error and must be zero in the absence of phase change and significant void nucleation during plastic deformation. A non-associated flow rule based on a pressure sensitive yield criterion with isotropic hardening is proposed in this paper that is consistent with the Spitzig and Richmond data and analysis. The significance of this work is that the model distorts the shape of the yield function in tension and compression, fully accounting for the strength differential effect (SDE). This capability is important because the SDE is sometimes described through kinematic hardening models using only pressure insensitive yield criteria.