Critical Stresses for Twinning, Slip, and Transformation in Ti-Based Shape Memory Alloys

Abstract

We investigate the effect of Nb and Ta contents on the (i) critical resolved shear stress (CRSS) for the β − α″ transformation, (ii) the CRSS for austenite slip, and (iii) the CRSS for twin nucleation in martensite (α″ phase) that govern shape memory and superelasticity in Ti-based alloys. The critical stresses for slip and twinning are achieved with a modified Peierls Nabarro formalism utilizing generalized stacking fault energy and the generalized planar fault energy (GPFE), respectively, obtained from first-principles density functional theory (DFT) calculations. During the calculation of the twinning stress, we show the importance of the shuffling process in stabilizing and lowering the GPFE curve. Similarly, the transformation stress is obtained with heterogeneous martensite nucleation mechanism incorporating the energy barriers associated with the transformation process. Here, we point to the role of dislocations in the shuffling process during the early stage of transformation. We show that the increase of Ta content raises the CRSS more effectively for the case of slip compared to twinning or transformation. The slip stress and twin stress magnitudes increase with an increase in the unstable fault energy $$\left( {\gamma_{\text{us}} } \right)$$ and unstable twinning fault energy $$\left( {\gamma_{\text{ut}} } \right),$$ respectively. In summary, as the Ta composition increases, the difference between martensite/austenite slip resistance and the transformation/twinning stress widens showing the efficacy of Ta alloying additions.