Engineering Model to Predict Behaviors of Shape Memory Alloy Wire for Vibration Applications

Abstract

An engineering model for predicting the behavior of shape memory alloy (SMA) wire is presented in this study. Piecewise linear relations between stress and strain at a given temperature are assumed and the mixture rule of Reuss bounds is applied to get the elastic modulus of the SMAs in the mixed phase. Critical stresses and strains of the start and finish of the phase transformation are calculated at a given temperature by means of a linear constitutive equation and a stress-temperature diagram. Transformation conditions based on the critical stresses are translated in terms of critical strains. Martensite volume fraction and stress at the end of the increment are calculated using the defined linear transformation path by algebraic manner. To consider the trained behavior and strain rate dependent behavior of SMA wire, model correlation with the experimental data was made for specific SMA material. A numerical example of vibration response of the SMA wire damped beam is presented to demonstrate the strain dependent behavior. System damping capacity is reduced by considering fast strain rate loading compared to the case of counting the quasi-static behavior of SMA wire.