Numerical Simulation and Experimental Study of a Simplified Force-Displacement Relationship in Superelastic SMA Helical Springs

This paper proposes a new force-displacement model for superelastic shape memory alloy (SMA) springs under complex loading and unloading. For the SMA wires used to make superelastic springs, a new multilinear constitutive model based on a modification of the 1D Motahari model is developed. In the modified model, the stress-strain relation curves are changed to fit the experimental results. Furthermore, the established force-displacement relationship of the springs considers the impact of not only the torque but also the moment on the cross sections of the SMA wires. Afterwards, a series of tension tests are performed on four NiTi helical spring specimens under various loading conditions. From the numerical simulations and experimental results, it is shown that, compared with the force-displacement curves for the SMA springs simulated by the Motahari model, those simulated by the proposed model can better approximate the experimental results. The new model inherits the advantage of simple computation of the multilinear constitutive model and can predict the force-displacement relation for superelastic SMA springs very well. Furthermore, due to the self-sensing properties of the SMA springs, the new model is very significant for establishing a new strategy for measuring the displacements or forces of SMA springs under complex loading and unloading.