Variational phase-field modeling of fracture and fatigue in shape memory alloys: a one-dimensional study

We propose a novel variational phase-field model for fracture and fatigue in pseudoelastic shape memory alloys (SMAs). The model, developed in a one-dimensional setting, builds upon the Auricchio-Petrini constitutive formulation for SMAs and couples damage evolution with phase transformation. We study analytically and numerically the homogeneous and localization responses of a bar under both monotonic and cyclic loading, and we investigate various macroscopic behaviors by tuning the constitutive parameters. A key feature of the model is the introduction of a transformation strain limit, beyond which the material is fully martensitic and behaves elastically. This leads to a distinctive behavior in which the region of localized damage widens, yielding a delay of fracture. The capability of the model to predict the fatigue performance is assessed by simulating the uniaxial response of Ni-Ti multi-wire samples under different loading conditions. The results show that the model discriminates between safe and critical loading scenarios, capturing the experimental trend of increased fatigue resistance with higher mean strain at a fixed strain amplitude. Ongoing efforts are aimed at further evaluating its reliability for quantitative fatigue life prediction.