Asymmetric yield function based on the stress invariants for pressure sensitive metals

A general asymmetric yield function is proposed with dependence on the stress invariants for pressure sensitive metals. The pressure sensitivity of the proposed yield function is consistent with the experimental result of Spitzig and Richmond (1984) for steel and aluminum alloys while the asymmetry of the third invariant is preserved to model strength differential (SD) effect of pressure insensitive materials. The proposed yield function is transformed in the space of the stress triaxaility, the von Mises stress and the normalized invariant to theoretically investigate the possible reason of the SD effect. The proposed plasticity model is further extended to characterize the anisotropic behavior of metals both in tension and compression. The extension of the yield function is realized by introducing two distinct fourth-order linear transformation tensors of the stress tensor for the second and third invariants, respectively. The extended yield function reasonably models the evolution of yield surfaces for a zirconium clock-rolled plate during in-plane and through-thickness compression reported by Plunkett et al. (2007). The extended yield function is also applied to describe the orthotropic behavior of a face-centered cubic metal of AA 2008-T4 and two hexagonal close-packed metals of high-purity α-titanium and AZ31 magnesium alloy. The orthotropic behavior predicted by the generalized model is compared with experimental results of these metals. The comparison validates that the proposed yield function provides sufficient predictability on SD effect and anisotropic behavior both in tension and compression. When it is necessary to consider r-value anisotropy, the proposed function is efficient to be used with non-associated flow plasticity by introducing a separate plastic potential for the consideration of r-values as shown in Stoughton and Yoon (2004, 2009).