The Hosford yield function for weakly textured sheets of cubic crystal orthotropic metals in any stress state

Most rolled sheet metals are orthotropic aggregates of cubic crystallites. The texture coefficients, characterized by the preferred orientation of the crystallites, are important to set up the yield function. Although the Hosford yield function is more suitable than the Hill yield function for describing both the yielding and plastic deformation of orthotropic material, it suffers from the restriction that the three principal stresses must be coaxial with the orthotropy of materials. This paper proposes the new Hosford yield function for weakly textured sheets of cubic crystal orthotropic metals in any stress state by expanding the introduced orientation-dependent functions to its sixth-order Taylor series expansion. Also, the new yield function, which covers three material parameters and seven texture coefficients, is more general than the existing Hosford yield function. Finally, both the plastic anisotropy of the q-value and the yield stress obtained from the new yield function agree well with experimental results. This yield function can lay a theoretical foundation for analyzing the mechanical properties of metal materials.