Phase field modelling of fracture and fatigue in Shape Memory Alloys

Abstract: 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.