Modeling the Interaction Between Localized Transformation and Functional Fatigue in Shape Memory Alloys

NiTi shape memory alloys (SMAs) are widely utilized in various engineering applications due to their unique properties, such as superelasticity and shape memory effect. The operational lifespan of SMAs in most of the applications involves enduring cyclic mechanical/thermal loadings, which highlights the great importance of identifying their fatigue behavior. Due to the martensitic transformation, fatigue in SMAs is mainly classified into two aspects. The first aspect is known as functional fatigue, which involves the degradation of functional properties such as recoverable strain, transformation stress, and the area of the hysteresis loop. The second aspect is referred to as structural fatigue, which pertains to the evolution of damage within the material. In superelastic NiTi, stress-induced martensitic transformation typically proceeds in a localized manner through propagation of diffuse interfaces (macroscopic transformation front) that separate low-strain austenite from high-strain martensite. In view of the high strain incompatibilities that exist within the transformation front, and thus large local stresses, it can be inferred that transformation localization plays a key role in the fatigue behavior of the material. Experimental studies have shown that repeated nucleation and propagation of localized bands accelerate superelastic degradation and promote earlier fatigue crack initiation and failure, highlighting a direct link between localization and fatigue performance. While existing constitutive models capture general degradation trends, they fail to distinguish the fatigue evolution in homogeneous versus non-homogeneous (localized) transformations. To address this limitation, this study presents a novel functional fatigue model that integrates the effect of localized transformation into the fatigue constitutive description. The model adopts a gradient-enhanced formulation, in which the gradient of the martensite volume fraction is included to represent the interfacial energy associated with the transformation front. The evolution of fatigue-related variables, namely the irreversible volume fraction of martensite and plastic strain, is explicitly coupled to transformation localization. This coupling is introduced by enriching their evolution laws with the gradient of the martensite volume fraction, so that localized transformation fronts accelerate their accumulation and thereby intensify functional degradation. A representative numerical study investigates the influence of specimen geometry on fatigue behavior, specifically comparing thin and thick NiTi strips. Experimental observations indicate that, as specimen thickness increases, the transformation front becomes more diffuse, whereas thinner specimens tend to exhibit a sharper transformation front with more branching. It has been revealed that the thicker specimen maintains a higher fatigue life. The developed model is capable of capturing these important morphology-dependent localization effects and their implications for functional degradation effects.