Approximate yield criteria for anisotropic porous ductile sheet metals

Abstract An approximate macroscopic yield criterion for anisotropic porous sheet metals is developed under plane stress conditions in this paper. The metal matrices are assumed to be rigid perfectly plastic and incompressible. The Hill quadratic and non-quadratic anisotropic yield criteria are used to describe the matrix normal anisotropy and planar isotropy. The voids in sheet metals are assumed in the form of through-thickness holes. Under axisymmetric loading, a closed-form upper bound macroscopic yield criterion is derived as a function of the anisotropy parameter R , defined as the ratio of the transverse plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial loading conditions. The plane stress upper bound solutions for different in-plane strain ratios can be fitted well by the closed-form macroscopic yield criterion.