Development of a Strain-Rate Dependent Model for Uniaxial Loading of SMA Wires

Abstract

This paper describes a modeling approach to incorporate the effects of nonquasistatic loading on the extensional behavior of an SMA wire. Experimental results under a variety of loading conditions indicate that the instantaneous temperature of the material is closely related to the applied strainrate in the material. In order to predict this behavior, a coupled thermo-mechanical analysis with the rate form of SMA constitutive models is formulated. The temperatures and temperature rates are not prescribed, but are derived from energy conservation of the material. The stress rate is simultaneously derived using the rate form of SMA constitutive models. Important parameters governing heat transfer such as specific heat, heat transfer and latent heat are modeled and validated with experimental data. For the material tested (0.38 mm diameter SMA wire), the quasistatic strain rate below which no significant deviation in material characteristics are observed was empirically determined to be about 0.0005/s. At a strain rate of 0.01/s, the transformation stresses in the material are increased by approximately 0.5 × 10 8 Pa, accompanied by an increase in temperature of about 2°C over the quasistatic values. The predictions for the stress-strain curves are compared with experimental data at different strain rates over a range of environmental temperatures, and are found to be in good qualitative agreement. The model is also shown to be in good qualitative agreement with the experimental behavior under more complex loading conditions involving two different strain rates of loading. Parametric variation of the model coefficients is discussed. Although the qualitative aspects of the model are in good agreement with experimental data, it is argued that more comprehensive estimation of the model parameters is required to assess the quantitative aspects of the model. The model described in the paper uses the rate forms of the Brinson model. However, it is equally applicable with a modified rate-dependant form of any other quasistatic model describing SMA behavior.