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

The authors propose a variational phase-field model to study how pseudoelastic shape memory alloys (SMAs) fracture and fatigue. The model is set up in one dimension and extends an existing SMA constitutive formulation by coupling damage evolution with phase transformation. They analyze and simulate a bar under monotonic and cyclic loading to explore how different parameter choices change macroscopic responses. A key modeling feature is a transformation strain limit: once exceeded, the material becomes fully martensitic and then behaves elastically. The simulations show that this transformation strain limit affects fracture behavior by widening the localized damage region, which can delay fracture. For fatigue, the authors assess the model by simulating uniaxial responses of Ni-Ti multi-wire samples and report that it can distinguish safe versus critical loading scenarios and reproduce an experimental trend of higher fatigue resistance with higher mean strain at fixed strain amplitude.