Model for resistance evolution in shape memory alloys including R-phase

The electrical resistance behavior of a shape memory alloy (SMA) wire can be used for sensing the state of an SMA device. Hence, this study investigates the resistance evolution in SMAs. A lumped parameter model with cosine kinetics to capture the resistance variation during the phase transformation is developed. Several SMA materials show the presence of trigonal or rhombohedral (R) phase as an intermediate phase, apart from the commonly recognized austenite and martensite phases. Most of the SMA models ignore the R-phase effect in their prediction of thermomechanical response. This may be acceptable since the changes in thermomechanical response associated with the R-phase are relatively less. However, the resistivity related effects are pronounced in the presence of the R-phase and its appearance introduces non-monotonicity in the resistivity evolution. This leads to additional complexities in the use of resistance signal for sensing and control. Hence, a lumped model is developed here for resistance evolution including the R-phase effects. A phase-diagram-based model is proposed for predicting electro-thermomechanical response. Both steady state hysteretic response and transient response are modeled. The model predictions are compared with the available test data. Numerical studies have shown that the model is able to capture all the essential features of the resistance evolution in SMAs in the presence of the R-phase.