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This paper is concerned with the mechanical behavior of Shape Memory Alloys (SMA). A particular attention is paid to the behavior under multi-axial proportional and non-proportional loadings. A large experimental data-base, composed of tension-torsion tests, tension-internal pressure tests and bi-axial compressive tests is presented and reported. For each type of multi-axial tests, an emphasis is placed on the determination of the shape of the transformation outset surface and the transformation strain rate is determined for selected loading path. Finally, a generalized J 2 -J 3 criterion of transformation outset, based on experimental observations, is proposed and identified.

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 the recent biaxial compression loadings on Cu-Al-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.

Depuis une dizaine d'annees, des alliages a memoire de forme (AMF) sont sollicites, en chargement multiaxial, dans le domaine de la pseudoelasticite (transformation martensitique renversable induite sous contrainte) et de la pseudoplasticite (reorientation des plaquettes de martensite sous l'effet des contraintes externes). Les resultats experimentaux obtenus montrent que le choix du chemin de chargement multiaxial influe fortement sur la reponse mecanique de l'AMF. Actuellement, malgre les nombreux modeles proposes dans la litterature, la simulation des chargements nonproportionnels n'est pas tout a fait operatoire. C'est la raison pour laquelle un modele de comportement des AMF sous chargements proportionnels et nonproportionnels est propose dans ce papier. A cet effet, deux surfaces de transformation directe et inverse, une deformation et une contrainte equivalentes sont introduites dans le cadre de la thermodynamique des processus irreversibles. Pour un Cu-Al-Be polycristallin, la capacite de prediction du comportement sous sollicitation complexe est bonne avec un nombre faible de parametres materiau a identifier.