Constitutive model for SMA considering arbitrary thermal-mechanical loading and loading history

Shape memory alloy (SMA) is capable of memorizing and regaining its original shape after being heated over its phase transformation temperature. Due to this so-called shape memory effect, SMAs are widely used as actuators in engineering. Over the last decade, with the development of SMA thin film technology, SMA has been used in MEMS devices like micro-grippers, micro-valves, and micro-pumps. For most applications, SMAs usually undergo arbitrary thermal and mechanical loadings, which lead to complex responses of SMAs. However, current SMA constitutive models mostly consider the response of SMA under an independent thermal or mechanical loading, only several models take proportional thermal-mechanical loading into account. Therefore, in order to further explore the application of SMA in MEMS, one great challenge is to predict the complex response of SMAs accurately under various thermal-mechanical loadings. As a result, this paper aims to develop a constitutive model capable of depicting responses of SMAs under arbitrary thermal-mechanical loading. The model is based on a former proposed SMA constitutive model, which was developed to consider cyclic degradation of SMA subjected to repeated thermal-mechanical loading. New hardening function and transformation function with non-constant parameters were proposed in the model to consider the shifting of transformation boundaries under four arbitrary loadings: in-strip fluctuation, minor loop, full transformation loop, and elastic fluctuation. Corresponding identification procedures for these non-constant parameters were also introduced. Finally, to validate the proposed model, simulations of the superelastic and shape memory behaviors of SMA under arbitrary loading paths like in-strip fluctuation, minor loop, and full transformation loop were performed. Good correlation between simulations and experiments demonstrates the ability of the model to depict both superelastic and shape memory behaviors of SMA under arbitrary loading.