About the influence of hydrostatic pressure on the yielding and flow of metallic polycrystals

• We investigate the overall response of a polycrystal aggregate of constituents obeying an extended Schmid law, sensitive to the hydrostatic component of the stress field.
• We find that the macro-rate of plastic deformation is still related to the yield surface via a generalized flow rule.
• If the elastic properties of the constituents enjoy deviatoric–volumetric uncoupling, the flow rule reduces to a normality rule in the deviatoric subspace.

We consider an aggregate of single crystals featuring pressure dependent yielding and deviatoric plastic response, and inquire about the overall response of the aggregate. Since this is one of the prototype examples of what is usually called non-associated plastic flow, the investigation is focused upon discerning the essential features of the resulting model at macro-scale: yield surface and flow rule. It is shown that a flow rule relates the macro-direction of plastic deformation, an additional macro-variable (which vanishes in the absence of pressure effects) and the exterior normal of the macro yield surface. Furthermore, if the constituent crystals feature uncoupled volumetric–deviatoric elastic response, then the plastic dilatancy is zero, the equivalent stress function is pressure-independent, and the flow rule reduces to the classical normality rule in the subspace of deviatoric stress tensors.