Rate-sensitive shape memory constitutive model: Theory and experimental verification

Presented here are some extensions of a previously developed hysteretic model for shape memory alloys (SMAs) and other metallic hysteretic deforming materials, for use in vibrational analysis. This work was carried out to address the problem of the changing response of shape memory alloys with strain rate, which could be important in vibration problems involving rapid loading.;This work begins by modifying an existing rate-independent SMA constitutive model to eliminate some undesirable features. The SMA model was also simplified by reducing the number of parameters without sacrificing physically significant SMA characteristics. To enhance the ease of evaluating the model parameters, a systematic method for determining these parameters is developed and illustrated by example. This modified SMA constitutive model is then extended to a three-dimensional form. The responses to shear and nonproportional loading conditions are compared between the modified and the previously existing rate-independent SMA constitutive model.;The results of uniaxial tests designed to determine the strain-rate sensitivity of a Nickel-Titanium SMA are presented in this work. These tests include: ramp loading/hold, ramp unloading/hold, and cyclic ramp loading of Nitinol wire. The tests were performed at different strain rates. The trends of the rate-sensitivity seen in the test results are identified. In addition to the strain rate effects which are presented, the evolution of the stress-strain response of Nitinol with cyclic strain and dependency on strain range is also presented.;The identified characteristics of the rate-dependent response of Nitinol, are used to extend the one-dimensional rate-independent SMA constitutive model to include rate effects. Responses to different loading conditions are also examined. A procedure for determining the parameters of the rate-dependent SMA model from experimental data is presented and illustrated by example. The response of the developed rate-sensitive SMA model is compared with the experimental test results on Nitinol. Comparisons between model response and the experimental results included: energy absorbed in hysteresis loop, stress-strain curves under different loading conditions, and change in stress level under constant strain conditions.