Constitutive modeling of superplastic deformation. Part I: Theory and experiments

In this work, we investigate the mechanical behavior of superplastic materials under various loading conditions and examine the nature of anisotropy. This and other phenomena are modeled within a continuum theory of viscoplasticity which includes an overstress function, 'yield surface' and internal variables. Anisotropic hardening is represented by an internal stress tensor whose evolution (including plastic spin) consists of hardening, dynamic recovery, and static recovery terms. The 'dynamic' yield surface (within a viscoplasticity formulation) is assumed to be isotropic and depends on both J₂ and J₃. Various experiments on a Pb-Sn superplastic alloy including tension, jump test, stress relaxation, fixed-end torsion, and combined tension-torsion -tests were performed and the results are used to calibrate and verify the theoretical model. It is shown that the isotropic dynamic surface can successfully model the uniaxial behavior of super-plastic deformation, including stress relaxation, and produces axial stresses in fixed-end torsion.