Thermo-mechanically coupled deformation of pseudoelastic NiTi SMA helical spring

• Thermo-mechanically coupled deformation of NiTi SMA helical spring is investigated by experiment. • A 3D constitutive model considering two-step phase transition and thermo-mechanical coupling effect is constructed. • An extended analytical model of helical spring is developed by simultaneously considering torsion, bending deformation modes and curvature effect. • Deformation behavior and temperature evolution of the spring are well captured. • Influences of geometrical parameters and ambient temperature on thermo-mechanical responses of helical spring are discussed. Based on the cyclic tension-unloading tests with various displacements (40, 60 and 80mm) and at different loading rates (0.3mm/s, 1mm/s and 5mm/s), the thermo-mechanically coupled deformation and temperature evolution of pseudoelastic NiTi shape memory alloy (SMA) helical spring are investigated. Experimental results reveal that the phase transition between austenite (A) and martensite (M) phases undergoes a two-step process involving an intermediate phase, that is, rhombohedral (R) phase; the force-displacement responses of the spring depend on the loading rate strongly, which originates from Clausius-Clapeyron relation between the critical stresses of phase transitions (including R and M transformations), and the competition between the internal heat generation and heat exchange. Then, a three-dimensional phenomenological constitutive model is developed by addressing three possible phase transition processes (that is, A→R→M, A→mixed A+R→M and A→M) and thermo-mechanical coupling effect. Generalized thermodynamic forces for the phase transitions and the evolution equation of temperature are derived based on the second and first laws of thermodynamics, respectively. To accurately describe the loading amplitude-dependent dissipation and hardening behavior of MT, new dissipation and hardening laws are proposed. Furthermore, a new analytical model of helical spring is developed by simultaneously considering the torsion and bending deformation modes, curvature effect and the coupling effect between the deformation and temperature evolution. Finally, the developed model is validated by comparing the simulated results with the experimental data, and the influences of geometrical parameters and ambient temperature on the thermo-mechanical responses of the spring are also predicted and discussed.