Micromechanical modeling of NiTi shape memory alloys including austenite, R-phase, and martensite

摘要

The special features in the material behavior of shape memory alloys (SMAs) are due to their ability to spontaneously transform between different crystallographic phases. In order to reproduce this material behavior, the elastic energy is formulated separately for each crystallographic phase and variant in the model described in this work. The microstructure of different crystallographic phases and variants that is formed for a given load is then captured by an estimate of the quasiconvexification of the resulting energy landscape. In this work, we focus our attention to the case of the commercially most successful SMA, NiTi. The downside of this material with respect to micromechanical modeling is the elevated number of 17 different variants of cubic austenite, monoclinic martensite, and the intermediate rhombohedral R-phase. Compared to the formation or re-orientation of martensite, a transformation between austenite and R-phase or between different variants of the latter implies a relatively small change in crystal structure. It is therefore assumed that austenite and R-phase may transform spontaneously and without losing energy, whereas a dissipation ansatz homogeneous of first order is assumed for the evolution of martensite. Sample computations and comparison with experimental data show that using this approach leads to a realistic estimate of the material behavior of NiTi. Especially, modeling the stress-strain relation for a tensile test exhibits the typical slope reduction before the onset of the stress plateau.