Modeling size effects on the transformation behavior of shape memory alloy micropillars

Abstract

The size dependence of the thermomechanical response of shape memory alloys (SMAs) at the micro and nano-scales has gained increasing attention in the engineering community due to existing and potential uses of SMAs as solid-state actuators and components for energy dissipation in small scale devices. Particularly, their recent uses in microelectromechanical systems (MEMS) have made SMAs attractive options as active materials in small scale devices. One factor limiting further application, however, is the inability to effectively and efficiently model the observed size dependence of the SMA behavior for engineering applications. Therefore, in this work, a constitutive model for the size-dependent behavior of SMAs is proposed. Experimental observations are used to motivate the extension of an existing thermomechanical constitutive model for SMAs to account for the scale effects. It is proposed that such effects can be captured via characteristic length dependent material parameters in a power-law manner. The size dependence of the transformation behavior of NiFeGa micropillars is investigated in detail and used as model prediction cases. The constitutive model is implemented in a finite element framework and used to simulate and predict the response of SMA micropillars with different sizes. The results show a good agreement with experimental data. A parametric study performed using the calibrated model shows that the influence of micropillar aspect ratio and taper angle on the compression response is significantly smaller than that of the micropillar average diameter. It is concluded that the model is able to capture the size dependent transformation response of the SMA micropillars. In addition, the simplicity of the calibration and implementation of the proposed model make it practical for the design and numerical analysis of small scale SMA components that exhibit size dependent responses.