Phenomenological Modeling of Shape Memory Alloys

Shape memory alloys exhibit two characteristic effects, viz., shape memory and superelasticity or pseudoelasticity, due to a reversible solid-solid transformation brought about by either temperature or stress or both. The two important aspects involved in modeling the macroscopic SMA behavior are the constitutive equation describing the stress-strain-temperature relationship and the evolution kinetics describing the phase transformation as a function of the driving forces. Phenomenological models for macroscopic behavior of SMAs are frequently used wherein the aforementioned aspects of SMA behavior are treated independently. Using empirical data, a phase diagram is constructed to describe evolution of martensitic phase fraction (x) as a function of stress and temperature. A constitutive equation is derived using the appropriate form of free energy. In this paper, salient aspects in phenomenological models are discussed and a robust model for SMA behavior is presented. Using a distance based memory parameter, rate based kinetics is provided along with a differential form of constitutive equation. Also, several critical issues in phenomenological modeling like prescribing consistent kinetics and catering to arbitrary thermomechanical loading are highlighted. Through numerical studies, it is shown that the proposed model provides consistent kinetics and caters to arbitrary thermomechanical loading.