A shakedown analysis of high cycle fatigue of shape memory alloys

• Investigation of SMA cyclic response under macroscopic elastic shakedown.
• Development of a general multiaxial failure criterion for SMAs.
• Derivation based on extension of the Dang Van high cycle fatigue criterion to SMA materials.
• Validation on experimental uniaxial data from the literature.

Shape memory alloys (SMAs) are exploited in several innovative applications, experiencing up to millions of cycles, and thus requiring a fully understanding of material fatigue and fracture resistance. However, experimental and methodological descriptions of SMA cyclic response are still incomplete. Accordingly, the present paper aims to investigate the cyclic response of SMAs under macroscopic elastic shakedown and to propose a criterion for the high cycle fatigue of SMAs. A multiaxial criterion based on a multiscale analysis of the phase transformation between austenite and martensite and using the rigorous framework of standard generalized materials is proposed. The criterion is an extension of the Dang Van high cycle fatigue criterion to SMAs. The criterion is applied to uniaxial experimental data taken from the literature. It distinguishes run out from failure tests in the infinite lifetime regime. The analysis permits a novel insight into the development of a general multiaxial failure criterion for SMA materials and also suggests further experimental investigations to completely understand the fatigue behavior of SMAs under elastic shakedown.