Termination of Elastic Range of Pressure Insensitive Materials—Isotropic and Anisotropic Initial Yield Criteria

Abstract

In this chapter basic features of isotropic versus anisotropic initial yield criteria are discussed. Two ways to account for anisotropy are presented: the explicit and implicit formulations. The explicit description of anisotropy is rigorously based on well-established theory of common invariants (Sayir, Goldenblat–Kopnov, von Mises, Hill). The implicit approach involves linear transformation tensor of the Cauchy stress that accounts for anisotropy to enhance the known isotropic criteria to be able to capture anisotropy, hydrostatic pressure insensitivity, and asymmetry of the yield surface (Barlat, Plunckett, Cazacu, Khan). The advantages and differences of both formulations are critically presented. Possible convexity loss of the classical Hill’48 yield surface in the case of strong orthotropy is examined and highlighted in contrast to unconditionally stable von Mises–Hu–Marin’s criterion. Various transitions from the orthotropic yield criteria to the transversely isotropic ones are carefully distinguished in the light of irreducibility or reducibility to the isotropic Huber–von Mises criterion in the transverse isotropy plane and appropriate symmetry class of tetragonal symmetry (classical Hill’s formulation) or hexagonal symmetry (hexagonal Hill’s or von Mises–Hu–Marin’s). The new hybrid formulation applicable for some engineering materials based on additional bulge test is also proposed.