Irreversible Thermodynamic Modeling of Shape Memory Alloys for Elastocaloric Refrigeration

Solid-state refrigeration offers a sustainable alternative to traditional cooling technologies, with elastocaloric effect (ECE) materials emerging as promising candidates due to their ability to release or absorb heat through stress-induced phase transformations. The performance of systems based on the ECE are currently limited by 1) the identification of materials that most efficiently convert mechanical work into thermal energy and 2) the prediction of their response around various refrigeration cycles. Addressing these challenges requires a precise understanding of the thermomechanical response of ECE materials to external stimuli. Shape Memory Alloys (SMAs), known to exhibit the ECE, encounter additional complexities due to hysteresis and their microstructural dependence on the stress-temperature conditions during the transition from austenite to martensite. When evaluating the effectiveness of these materials in refrigeration applications, performance metrics such as coefficient of performance (COP) and cooling power are crucial.
These metrics depend on a material’s entropy and strain response to a specific stress-temperature path, which is governed by the intrinsic material properties of elastocaloric SMAs. However, the microstructural dependence on the stress-temperature conditions during the phase transition result in different strain outputs, meaning strain – typically considered to be a state variable (path independent) – can no longer be considered such due to a path dependence. Combining this path dependence with the complexities from hysteresis, an accurate thermodynamic description of the system becomes non-trivial. This work develops a predictive path-dependent irreversible thermodynamic model capable of capturing these complexities for a model NiTi alloy system. A Presaich formalism (mathematical description of hysteresis) is adopted to track the phase fraction in the system while a new variable is created to account for the path dependence of strain in the system. This variable is representative of the relative alignment of martensite variants in the microstructure. By developing this thermodynamic model, we are able to predict the entropy and strain response of the NiTi alloy system for any arbitrary refrigeration cycle, allowing the determination of key refrigeration performance metrics.