Comprehensive shape memory alloys constitutive models for engineering application

[Display omitted] •Accurate shape memory alloys (SMA) constitutive models considering incomplete phase transformation are proposed.•The model parameters are easy to obtain by experiments, and the constitutive models are more applicable in engineering.•Differences between shape memory effect SMA and super elasticity SMA are fully considered in the constitutive model.•Tensile tests and loading-unloading cycles experiments verified the constitutive models’ results. The current shape memory alloys (SMA) constitutive models have the problems of complicated calculation, inaccurate results, measuring difficult parameters, and inconvenient application, which brings about challenges for designing, analyzing, and simulating SMA’s macroscopic behavior in engineering. This paper proposed practical SMA constitutive models for accurate engineering calculation, which apply to both the single loading-unloading process and the multiple loading-unloading cycles. The more accurate SMA theoretical tensile curve and temperature-stress phase transformation diagram is introduced to derive the constitutive model. The more accurate calculation method of elastic modulus, phase transformation modulus, and critical phase transformation stress is proposed in this paper. The proposed constitutive model considers the incomplete phase transformation phenomenon and the variation of critical phase transformation stress under multiple loading and unloading conditions. It can accurately evaluate the critical phase transformation stress and stress-strain relationships at various temperatures. Tensile tests under various working conditions were conducted. The results demonstrated that the proposed constitutive model could well simulate the SMA’s macroscopic mechanical behavior at various temperatures, loads, and multiple loading-unloading cycles with accuracy, practicality, and efficiency.