Evaluation of yield function including effects of third stress invariant and initial anisotropy

Abstract

By means of combining Drucker's yield function with Hill's quadratic yield function, the anisotropic yield function of the sixth degree is proposed. It is able to include the effects of the third deviatoric stress invariant and initial anisotropy. The experimental evaluation is made on thin-walled cylindrical specimens of mild steel (in the fully annealed condition and the stress-relief annealed condition after a tensile pre-strain) and 2024 aluminum alloy (in the -0 and -T₆ tempered conditions). By applying proportional combined loadings of axial load, internal pressure, and torsion to the specimens, a change of yield stress with a rotation of the principal stress axes and a difference between the directions of the principal stress and principal strain increment are examined Under tension–internal pressure and tension–torsion, the yield surfaces and strain behaviour are determined. The fully annealed steel is almost isotropic for yielding although it reveals the effect of the third deviatoric stress invariant. The stress-relief annealed steel and the 2024–0 and -T₆ aluminum alloys exhibit axi-symmetric anisotropy. All of the yield surfaces can be expressed precisely by the proposed yield function. In addition, the normality rule is obeyed in strain behaviour.