Constitutive modeling of multiaxial deformation and induced anisotropy in superplastic materials

The multiaxial deformation of supeiplastic materials is modeled within a continuum theory of viscoplasticity using a generalized anisotropic dynamic yield function. The anisotropic dynamic yield function is capable of describing the evolution of the initial anisotropic state of the yield potential through the evolution of unit vectors defining the direction of anisotropy. The evolution of the direction of anisotropy is represented by a constitutive spin such that initially it is identical to the Eulerian spin and as deformation continues, it tends towards an orthotropic spin. Experiments on the model Pb-Sn alloy were conducted and used to calibrate and verify the constructed model. It is shown that the model in conjunction with the anisotropic dynamic yield function is capable of predicting the actual trend of the induced axial stresses recorded in fixed-end torsion experiments.