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 ba 00 transformation, (ii) the CRSS for austenite slip, and (iii) the CRSS for twin nucleation in martensite (a 00 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 c us ð Þ and unstable twinning fault energy c ut ð Þ; 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.

Crystallography Study on the Internal Twinning of Ti–Nb‐Based Shape Memory Alloys

“…In literature, it is proposed that the twinning mode with a low value of critical resolved shear stress forms preferentially in the Ti–Nb‐based alloys. For a certain alloy, the value of critical resolved shear stress is reversely proportional to the magnitude of Burgers vector for twinning dislocation . According to the theory for interfacial defects reported in references, the admissible interfacial dislocations for martensite twins can be identified clearly using the associated dichromatic pattern.…”

“…Numerous possible deformation twins of α″ martensite, such as {111} type I, (011) compound, and (021) compound, are proposed based on the theory of deformation twinning, while actually, only one or several of them are observed as the LIS for a certain alloy during the experimental observation . The migration of twin boundaries, both intervariant and substructural, plays an important role in the deformation of martensite, and the value of critical resolved shear stress, which is quite different for different twinning systems, governs the shape memory and superelasticity behavior . Thus, a thorough understanding of the internal twinning is essential for revealing the deformation mechanism and optimizing the shape memory functionality of the Ti–Nb‐based alloys.…”

Non-Schmid response of Fe3Al: The twin-antitwin slip asymmetry and non-glide shear stress effects

“…Extension of this generalized yield criterion for varying 3-D stress states promoting the activation of different glide systems induces significant asymmetries in the shape of convex yield hyper surface in the principal stress space owing to the TA asymmetry and NGS  component effects [34,35,41]. The effects of non-planar core structure of screw dislocations are not only limited with the non-Schmid character of the yield surfaces.…”

“…The term  represents the GSFE landscape of the system on either {1 1 0} or {1 1 2} slip planes along the slip direction and is written as a function of the atomistic disregistry function, () fx, which is also a function of x coordinate on the glide plane perpendicular to the dislocation lines [21,41]. The  values are attained by utilizing the control box method [42,43].…”

A review on shape memory metallic alloys and their critical stress for twinning

“…A. Ojha, et al [98] carried out first-principles calculations for Ti-Ta alloys and they studied the effect of Nb and Ta additions on (i) the 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). Their calculations showed that an increase in Ta content from 0 to 37.5 at.% increases the CRSS for austenite and martensite slip by more than 90 %, while the twinning stress increases by 25 %, and the transformation stress by…”