Shape memory alloys (SMAs) show a unique thermomechanical behavior, given by the shape memory effect and the pseudoelasticity according to the working temperature, resulting from a thermal or stress-induced thermoelastic phase transformation allowing large strain recovery. SMAs find applications in many sectors, including medical devices, actuators, energy absorption systems, and vibration dampers, with Ni-Ti cardiovascular devices dominating the market. Since most SMA components undergo significant thermomechanical cycles throughout their lifespan, SMA fatigue and fracture have been extensively studied, mainly adopting an experimental perspective. The research in modeling of damage in SMAs is still in its early stages due to the intricate nature of the material, with just a few studies proposed in the literature. This work proposes a 1-D phase-field model of fracture combining a SMA constitutive model with a gradient damage model, following the rationale of previous work focused on plasticity. A variational approach is adopted by defining the total energy of the system and applying irreversibility, stability, and energy balance to solve the evolution problem, coupling damage with the phase transformation. The model was calibrated exploiting experimental tensile tests on Ni-Ti multi-wire samples, studying the non-homogeneous damage response. Numerically, we adopted an alternate minimization algorithm. Additionally, tensile fatigue tests on Ni-Ti samples at several mean and alternate strains were simulated by exploiting the inherent structure of the model allowing for damage accumulation under cyclic loads. Promising fatigue life predictions matching the experiments were obtained, capturing both run-out conditions and the increase in fatigue resistance with mean strain that characterizes SMAs in the transformation strain range. Further investigations will allow to establish an accurate predictive tool to lower the burden of experimental campaigns and reduce the device failure risk.