A phenomenological theory of transformation superplasticity

Abstract A phenomenological theory of transformation superplasticity is presented from the point of view of thermomechanics. The stretching tensor and entropy density are assumed to be decomposed into the elastic part and the part due to the superplastic process. The constitutive equations for the superplastic part are derived by means of a dissipation potential, while the elastic part is shown to be determined from the free energy as usual. The theory developed is applied to the transformation superplastic deformation of a thin-walled tubular specimen of pure iron which is subjected simultaneously to a constant shear stress and temperature cycling. The results clearly show the following characteristic: The increment of the superplastic strain per cycle is proportional to the applied stress. The maximum value of the rate of transformation superplastic strain during a cycle is proportional to the applied stress, as well as to the heating (cooling) rate.