Shakedown based model for high-cycle fatigue of shape memory alloys

Abstract

The paper presents a high-cycle fatigue criterion for shape memory alloys (SMAs) based on shakedown analysis. The analysis accounts for phase transformation as well as reorientation of martensite variants as possible sources of fatigue damage. In the case of high-cycle fatigue, once the structure has reached an asymptotic state, damage is assumed to become confined at the mesoscopic scale, or the scale of the grain, with no discernable inelasticity at the macroscopic scale. Using a multiscale approach, a high-cycle fatigue criterion analogous to the Dang Van model (Dang Van 1973) for elastoplastic metals is derived for SMAs obeying the Zaki–Moumni model for SMAs (Zaki and Moumni 2007a). For these alloys, a safe domain is established in stress deviator space, consisting of a hypercylinder with axis parallel to the direction of martensite orientation at the mesoscopic scale. Safety with regard to high-cycle fatigue, upon elastic shakedown, is conditioned by the persistence of the macroscopic stress path at every material point within the hypercylinder, whose size depends on the volume fraction of martensite. The proposed criterion computes a fatigue factor at each material point, indicating its degree of safeness with respect to high cycle fatigue.