Multiaxial constitutive modelling for R-phase and M-phase transformations of TiNi shape memory alloys

A multiaxial constitutive model for describing the pseudoelastic and shape memory behaviour of a titanium-nickel (TiNi) shape memory alloy due to the stress-induced rhombohedral and martensitic transformations has been developed from a phenomenological point of view. First, the existing constitutive models proposed for shape memory alloys are reviewed in brief. On the basis of a comparison between these models, an expression prescribing the transformation strain range is proposed which depends on the applied stress and the current phase volume fraction. Then, the uniaxial Tanaka model for the rhombohedral and martensitic transformations of TiNi shape memory alloys is extended to a multiaxial form using the framework of the Boyd-Lagoudas model and the proposed expression of the transformation strain range. Finally, the capability of the present model to predict the pseudoelastic behaviour of TiNi shape memory alloys is examined through numerical simulations of stress-strain responses under uniaxial and multiaxial proportional/nonproportional loading-unloading conditions.