A phenomenological model for a Cu-Al-Be shape memory alloy pseudoelasticity under complex loading

Abstract
For the recent years, some multiaxial loadings are performed on Shape Memory Alloys (SMA) in the range of pseudoelasticity (stress induced martensitic transformation). For instance the tension-torsion tests on Cu-Zn-Al tubes of Rogueda et al. [1], the triaxial proportional loadings of Gall et al. [2], the tension (compression) torsion tests on Ti-Ni tubes of Raniecki et al. [3] and thé recent biaxial compression loadings on Cu-AI-Be of Bouvet et al. [4]. These recent experimental results show that the mechanical behavior of SMA is affected by the multiaxiality of the stress tensor. Indeed, some comparisons between simulations with classical models and experimental results under nonproportional loadings permit to conclude that more work must be done to increase the accuracy of models. The aim of this paper is to present a new phenomenological modeling based on the thermodynamics framework of irreversible processes. This model uses two transformation surfaces, the first one controls the forward transformation (austenite phase transforms to martensite phase) and the second one the reverse transformation (martensite phase transforms to austenite phase). This model is shown to give good results for the prediction of complex multiaxial nonproportional tests.