The Parametrization of Thermoelastic Martensite Phase Transformations at Constant Stress in Shape Memory Alloys Using a Sigmoidal Boltzmann Function

The parametrization of the thermomechanical behavior of shape memory alloys (SMAs) under constant load is described in terms of their functional properties. The deformation–temperature–stress behavior of SMAs from various alloy systems—such as Ni-Ti, Ni-Ti-Cu, and Ni-Mn-Ga—was parametrized using a sigmoidal function. This approach enables the characterization of phase transformation parameters, including transformation temperatures, kinetic parameters, and the relationship between recoverable deformation and applied stress. It is shown that the sigmoid function can serve as a universal descriptor of thermoelastic phase transformations across different alloy systems and transformation types, such as B2–R–B19′–R–B2 (Ni-Ti-Cu), B2–R–B19′–B2 (Ni-Ti), and B2 (L21)–B19′ (L20)–B2 (L21). A correlation coefficient of approximately 0.99 was achieved. The present work extends the theoretical framework of diffuse martensitic transitions in SMAs, for which the sigmoid function has been theoretically derived to describe phase fractions. The article’s novelty lies in shifting from pure mathematical approximation (curve fitting) to physical parametrization of SMA behavior specifically under constant stress (actuator mode).