On the asymmetric yield surface of plastically orthotropic materials: A phenomenological study

Hill's (1948) yield criterion for plastically orthotropic solids is extended to include materials whose tensile and compressive yield stresses, obtained from uniaxial loading tests, are different. First, we review and discuss the classic yield criteria in plasticity theory including plastically isotropic and anisotropic materials. Then, we present a yield criterion for plastic anisotropic solids whose initial yield surface may not be symmetric about the origin in stress space. The new criterion is based on the criterion given by Hill (Proc. Roy. Soc. London A, 1948, 193, 281) for anisotropic solids and the criterion proposed by Drucker and Prager (Q. Appl. Math., 1952, 10, 157) for soil whose tensile and compressive strengths are far apart. The coefficients that appear in the new criterion can be determined from uniaxial tension and compression, and simple shearing tests. The formulae for the determination of those coefficients are given. Specifically, the new criterion is applied to the yielding of thin sheets where a plane stress condition prevails. Finally, the prediction of the criterion is compared with the experimental data obtained by Lee and Backofen (Trans. Metall. Soc. AIME, 1966, 236, 1966) on titanium alloy sheets,