A thermodynamically consistent phase-field model of martensitic nano-twin evolution in NiTi alloys: effects of stress, temperature, and elastic anisotropy

This research presents a three-dimensional, thermodynamically consistent phase-field model for nanoscale martensitic transformation in NiTi (B2 → B19′) implemented in a finite-element COMSOL framework. The novelty of this work lies in its physics-based approach to modeling the martensitic transformation and nano-twin evolution in NiTi alloys. We incorporate elastic anisotropy and surface stress using 2-3-4-5 polynomial energy functions characterized by physically meaningful parameters for energy contributions. Furthermore, to enhance computational efficiency in solving these complex equations, we employ a reduced-order parameter approach where three order parameters represent six martensitic variants in two-dimensional simulations. In contrast to models calibrated against macroscopic data, our physical parameters are derived directly from NiTi's strain-energy landscape. This approach ensures an accurate representation of the transformation energy barriers and stresses, thereby enabling a thermodynamically consistent analysis of fundamental mechanisms such as nucleation barrier and variant interactions. This study successfully reproduces both the banded and herringbone morphologies frequently observed in experimental studies. Elastic anisotropy is identified as the dominance driver of variant selection and the formation of banded and herringbone patterns. Furthermore, the results indicate that a higher associated driving force promotes the growth of dominant, preferentially oriented variants. Specifically, higher stress increases the phase concentration and promotes the formation of wider martensitic variant bands, while a lower cooling temperature increases the nucleation rate, thereby resulting in thinner bands. This thermodynamically consistent model accurately predicts nano-scale NiTi martensite evolution, which is critical for designing microstructures with enhanced functional stability and performance.