A novel fracture mechanics approach for shape memory alloys with trilinear stress-strain behavior

The high values of local stresses arising near the crack tip in Nickel–Titanium based shape memory alloys (SMAs) causes a stress-induced martensitic transformation. Previous studies have demonstrated that this micro-structural evolution plays a significant role in the fracture and fatigue properties of SMAs, as it significantly changes the crack tip stress distribution with respect to common engineering metals. In this investigation a novel analytical model is proposed, which is based on the small scale yielding condition and on modified elastic-plastic fracture mechanics concepts, to predict the extent of the crack tip transformation region together with the resulting stress distribution. In particular, based on the general framework of a recent literature approach, a newmodel has been developed in order to overcome one of the major limitation of the previous one, i.e. the assumption of constant stress during phase transformation. In fact, the proposed approach uses a trilinear stress–strain constitutive behavior, i.e. it is able to analyze SMAs with not constant transformation stress. The model has been applied to some case studies, in order to analyze the effects of several thermo-mechanical parameters and loading conditions on the crack tip transformation region and stress distribution.