Multiaxial Shape Memory Effect and Superelasticity

Abstract

WOSInternational audienceThe specific behaviour of shape memory alloys (SMA) is due to a martensitic transformation. This transformation consists mainly in a shear without volume change and is activated either by stress or temperature. The superelastic behaviour and the one-way shape memory effect are both due to the partition between austenite and martensite. The superelastic effect is obtained for fully austenitic SMA: loaded up to 5% strain, a sample recovers its initial shape after unloading with a hysteretic loop. The oneway shape memory effect is obtained when a martensitic SMA, plastically deformed, recovers its initial shape by simple heating. Superelasticity and one-way shape memory effect are useful for several three-dimensional applications. Despite all these phenomena are well known and modelled in 1D, the 3D behaviour, and especially the one-way shape memory effect, remains quite unexplored. Actually, the development of complex 3D applications requires time-consuming iterations and expensive prototypes. Predictive phenomenological models are consequently crucial objectives for the design and dimensioning of SMA structures. Therefore, a series of 2D proportional and non-proportional, isothermal and non-isothermal tests have been performed. This database will be used to build a phenomenological model within the framework of irreversible processes

Stochastic multiscale modeling of the thermomechanical behavior of polycrystalline shape memory alloys

“…The associated maximum eigenvalue of transformation matrix for R phase is around max 2%, which explains the maximum value for permanent strain observed during OWSME cycle. Despite some few differences of stress threshold, results of the modelling are in very good agreement with the experimental results reported in [20].…”

“…Transformation thresholds under biaxial loading are available in literature [22] [20]. They are always defined using a deformation criterium.…”

In-situ strain induced martensitic transformation measurement and consequences for the modeling of medium Mn stainless steels mechanical behavior

“…Equivalent stress σ eq for phase transformation would have to be defined. The reader can refer to the work of [59] where such equivalent stress has been proposed. Since only uniaxial stress conditions are met in the experimental part of the work, this point has not been developed further, by considering it out of the scope of the paper.…”

Yield criteria for quasibrittle and frictional materials: A generalization to surfaces with corners

“…1), in which case the conditions for convexity provided by Bigoni and Piccolroaz (2004) remain only necessary but not sufficient. 7 Since the convexity proposition is fundamental in developing new yield or phase-transformation criteria -and, generally speaking, convexity is the basis of extremum principles in mechanics (see for instance Duvaut and Lions, 1976;Noble and Sewell, 1972), it has immediately attracted a strong attention (Taillard et al, 2008;Laydi and Lexcellent, 2009;Lavernhe-Taillard et al, 2009;Saint-Sulpice et al, 2009;Valoroso and Rosati, 2009). Therefore, the convexity proposition is definitely important in analyzing yield criteria with corners, so that it becomes imperative a generalization to nonsmooth deviatoric yield surfaces, which is obtained in the present article (Theorem 4.3, Section 4).…”