Evolution of yield surface in the 2D and 3D stress spaces

Initial and subsequent yield surfaces for 6061 aluminum, determined by a method of automated yield stress probing, are presented in the 2D ( σ zz − σ θz ) and 3D ( σ θθ − σ zz − σ θz ) stress spaces. In the ( σ zz − σ θz ) space, yield surfaces at small pre-strains show the noses and unapparent cross effect. At larger pre-strains, they become ellipses with positive cross effect. In the ( σ θθ − σ zz − σ θz ) space, the initial yield surface is not well described by von Mises yield criterion due to material anisotropy. The yield surfaces of various torsional pre-strains show obvious rotation around the σ zz axis but they do not rotate when subjected to axial pre-strains. Therefore, the rotation behavior of yield surface is pre-strain path dependent. The rotation of yield surfaces in the 3D space is the emphasis of the present paper. Coupled axial–torsional behavior subjected to torsion after axial pre-strain are also presented for the same material that is used to determine the yield surfaces. This information is useful for verification of constitutive models.