Constitutive Modeling of Deformation-Induced Anisotropy in Superplastic Materials

摘要

The development of axial stresses during fixed-end torsion is indicative of deformation-induced anisotropy. Generally, these stresses can be associated with texture development. However, this cannot be said about the induced axial stresses in superplastic materials, since no or little texture is observed during superplastic deformation. In this work, we model the deformation-induced anisotropy by incorporating a generalized anisotropic dynamic yield function in a microstructure-based viscoplastic model. The anisotropic yield function is capable of describing the evolution of the initial state of anisotropy 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 it is initially identical to the Eulerian spin, and as deformation continues, it tends towards an orthotropic spin. Experimental data on the Pb-Sn alloy is 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.