Exploration of the Partial Transformation Behaviour of Shape Memory Alloys and its Effect on Actuation Performance

Multiple applications of shape memory alloys (SMA) involve operation under partial transformation (PT), where reversal of the transformation direction takes place while the material is in a mixed phase state. Typical applications of SMAs include: actuators in adaptive/morphing structures which should repeatedly reach various target shapes or to follow time trajectories at higher time rates; dampers vibrating pseudo-elastically under varying amplitudes of dynamic loads. While the thermo-mechanically coupled behavior of SMAs under full transformation has been studied during the past and various models have been proposed, their response under PT has yet to receive the required attention to fully unravel the potential of these materials. In this paper, an experimental study of SMA wires under PT is presented along with a modified constitutive model. The physical constitutive model of Lagoudas et al.,(1) is combined with a new expression of the hardening function to enable the accurate and efficient prediction of PT behaviour. The predicted PT response is correlated with isobaric, thermally induced PT cycle experiments. Very good agreement is obtained with measured partial cycles, especially for PT cycles formed near the middle of the major hysteresis loop. The new constitutive equations are included into a finite element framework to investigate the effect of PT on SMA actuation function in morphing airfoils for active load alleviation in large wind turbine blades, and numerical results are correlated with experimental data. The correlations prove the importance of PT behavior in the actuator performance of SMAs, resulting in substantially more accurate predictions in deformation, stress and temperature.