Anisotropic yield criteria in σ-τ stress space for materials with yield asymmetry

In this study, yield behavior of an extruded magnesium alloy is investigated experimentally and analytically. A precise definition of yield is established for the extruded AZ31 magnesium alloy by deforming several specimens to certain levels of strain and measuring the residual strains after unloading. The material is then subjected to different loading conditions (uniaxial to multiaxial) at four different plastic strains. Multiaxial loading is comprised of free-end torsion and combined axial-torsion loading. Therefore, yield response is measured in σ-τ space. Several yield criteria are studied to predict yield response of extruded AZ31. The developed model by Cazacu et al. (2006), CPB06, which uses a fourth-order linear transformation, is calibrated through optimization of initial guesses. Despite the reasonable accuracy of CPB06 in prediction of experimental results, it shows that its precision significantly depends on initial guesses, which make the calculation complicated and time consuming. The asymmetrical quadratic model developed by Khan et al. (2012) presents a less accuracy in prediction of yield response of the highly textured AZ31. This study proposes an asymmetrical fourth-order polynomial yield function. Unlike CPB06, material constants in this model can be directly calculated using mechanical measurements. Convexity of the proposed model is discussed, and the domains of variation for the material parameters such that convexity holds are determined.