  We present a new phase field framework for modelling fracture and fatigue in
Shape Memory Alloys (SMAs). The constitutive model captures the superelastic
behaviour of SMAs and damage is driven by the elastic and transformation strain
energy densities. We consider both the assumption of a constant fracture energy
and the case of a fracture energy dependent on the martensitic volume fraction.
The framework is implemented in an implicit time integration scheme, with both
monolithic and staggered solution strategies. The potential of this formulation
is showcased by modelling a number of paradigmatic problems. First, a boundary
layer model is used to examine crack tip fields and compute crack growth
resistance curves (R-curves). We show that the model is able to capture the
main fracture features associated with SMAs, including the toughening effect
associated with stress-induced phase transformation. Insight is gained into the
role of temperature, material strength, crack density function and fracture
energy homogenisation. Secondly, several 2D and 3D boundary value problems are
addressed, demonstrating the capabilities of the model in capturing complex
cracking phenomena in SMAs, such as unstable crack growth, mixed-mode fracture
or the interaction between several cracks. Finally, the model is extended to
fatigue and used to capture crack nucleation and propagation in biomedical
stents, a paradigmatic application of nitinol SMAs.
