A fast and easy-to-calibrate model for the cyclic material behavior of shape memory alloys

The phenomenon of functional fatigue occurs during cyclic loading of pseudoelastic shape memory alloys. We model this effect by considering an irreversible martensitic volume fraction in addition to the reversible amounts of austenite and martensite based on variational principles. The inclusion of irreversible martensitic volume fractions coincides with experimental observations and enables the model to be easily calibrated without any fitting functions. In our previous studies, we modeled the polycrystalline material structure by static discretization of a relatively large number of randomly chosen grain orientations, which required much numerical effort. In contrast, we now apply a dynamic representation of the orientation distribution function to the modeling of functional fatigue which has proven to be beneficial regarding the numerical performance. To this end, we take into account an averaged grain orientation parameterized by three Euler angles that serve as additional internal variables. This results in an extremely reduced numerical effort.

We present the variational material model based on the principle of the minimum of the dissipation potential. In addition, we show numerical results to prove our model's ability to predict the shape memory alloys' complex inner processes and compare them with the experimentally observed material behavior.