A Computationally Efficient Free Energy Model for Shape Memory Alloys - Experiments and Theory

Abstract

Shape memory alloys (SMA) belong to the class of active materials and have recently been considered as novel actuation and damping mechanisms in micro- and macro-scale applications. Combined with their advantageous lightweight and high work output characteristics is a complex, highly non-linear and hysteretic material behavior, which is also thermo-mechanically coupled. Due to this complexity, model development for SMA material behavior is a challenging task, and experimental data in particular about the inner hysteresis loops is necessary to gain further understanding and successfully design applications. In this thesis, a single crystal material model is presented and subsequently extended to the more realistic polycrystalline case considering material inhomogeneities, grain impurities and lattice imperfections. A first implementation, based on a stochastic homogenization procedure, provides a very accurate description of the observed phenomena, but also requires very high computation times. A reformulation of the underlying concept leads to a parameterization method, which preserves the advantages of the original method, but dramatically reduces the computation times. It is shown that the material behavior prediction of both models are identical, and the parameterization method is compared extensively to data from tensile experiments with a pseudoelastic SMA wire. Remarkably, the model is able to capture all facets of the material behavior including rate-dependence and minor loops. The versatility of the model also allows for the simulation of SMA actuator behavior including the electrical resistance. Finally, a MEMS device using polycrystalline SMA thin film actuators is experimentally investigated. As a first step, the material behavior of the SMA thin films is presented using strain-temperature and resistance-temperature measurements. Secondly, the performance of the MEMS device was determined for different driving frequencies.