A 3D numerical study of mixed-mode (I and II) stationary notch tip fields in shape memory alloys

In this work, the 3D nature of stationary mixed-mode (I & II) notch tip fields in shape memory alloys, initially in austenite phase, under small scale transformation and yielding conditions is studied through finite element simulations. An isotropic constitutive model which represents the combined effects of superelasticity and plasticity is employed. The effects of the above factors and temperature on the evolution of transforming and plastic zones as well as the spatial distribution of near-tip stresses, plastic strain and martensite volume fraction are analyzed. The results show that at a temperature above the austenite finish temperature, \(A_f\), plasticity occurs before phase transformation takes place near the tip, whereas it does so only in the fully transformed martensite phase at a temperature well below \(A_f\). By contrast, the transforming zone is much smaller at higher temperature, which is attributed to impediment caused by plastic deformation. Under mixed-mode loading, hydrostatic stress is tensile near the stretched or blunted part of the notch, and compressive close to its sharpened portion. The plastic strain and martensite volume fraction are higher at the latter side. The thickness variations of field quantities become insignificant at distances from the tip of 0.25 to 0.5 of the specimen thickness.