A New Constitutive Equation for Superelastic Deformation and Prediction of Martensite Volume Fraction in Titanium-Nickel-Cupper Shape Memory Alloy

Abstract

Our new model, “series combined model”, for the superelastic deformation in Ti–Ni–Cu shape memory alloy was proposed considering the mechanical deformation phenomenon in a L¨ uders deformation type of phase transformation in order to clarify the progressing behavior of the phase transformation and then the suitable physical formula for it in future. By assuming the competitive phenomenon between the phase transformation and the plastic deformation, this model was applied for transformation behavior progressing together with the local plastic deformation. In the application of the model, some significant transformation points in stress-strain curve were determined originally to be well fit for the superelastic deformation of shape memory alloy. The original constitutive equation, which based on this model, was used to calculate the martensite volume fraction at every point in one cycle of superelastic deformation by making the inverse analysis for the stress-strain data obtained experimentally under the various temperatures. The validity of this model and constitutive equation for superelastic deformation was confirmed by comparison between the experimental result of a half cycle and the prediction for the stress-strain curve based on the inverse analysis result in a full cycle. The prediction for temperature dependence of the volume fraction and the magnitude of plastic strain in the plastic deformed martensite phase could explain enough the temperature dependence of the irrecoverable strains obtained experimentally. The progressing rate of the martensite transformation as well as the reverse transformation, which was calculated by making the inverse analysis results, decreased depending on the increase of temperature.