Stress-Induced Martensite in Front of Crack Tips in NiTi Shape Memory Alloys: Modeling Versus Experiments

NiTi-based shape memory alloys (SMAs) exhibit an unusual stress distribution at the crack tip as compared to common engineering materials, due to a stress-induced martensitic transformation resulting from highly localized stresses. Understanding the fracture mechanics of NiTi-based SMAs is critical to many of their applications. Here, we develop an analytical model, which predicts the boundaries of the transformation region in the crack tip vicinity of NiTi-based SMAs. The proposed model is based on a recent analytical approach which uses modified linear elastic fracture mechanics concepts to predict the crack tip stress distribution and transformation region in SMAs but, unfortunately, it applies only to the plane stress condition. To overcome this limitation, the proposed model accounts for stress triaxiality, which plays an important role in restricting crack tip plastic deformations in common ductile metals as well as the stress-induced martensite in NiTi SMAs. The effects of triaxial stress at the crack tip are taken into account by including a new parameter, the transformation constraint factor, which is based on the plastic constraint factor of elasto-plastic materials. The predictions of the model are compared with synchrotron x-ray micro-diffraction observations and satisfactory agreement is observed between the two results. Finally, the evolution of crack tip transformation boundaries during fracture tests of miniature compact tension specimens is predicted and the effects of applied load and crack length are discussed.