Modeling functional fatigue of SMA using a more accurate subdivision of martensite volume fractions

Functional fatigue happens when SMA is subjected to thermal and/or mechanical cyclic loadings. Experiments found functional fatigue of SMA mainly exhibits as the accumulation of the plastic strain, the evolution of the maximum transformation strain and transformation temperatures. In particular, experiments have also indicated that functional fatigue does not occur uniformly in the five phase transformations of SMA (A→M^d, M^d→A, A→M^t, M^t→A and M^t→M^d). To account for this issue, this paper introduces a more accurate subdivision of martensite volume fractions as internal variables to control the evolution of every variable in the relevant transformation. Based on the new subdivision, the free energy, thermodynamic forces, transformation functions, and evolution laws are improved. A simple procedure is also introduced in detail to identify the parameters of the model. Finally, numerical simulations using an explicit time-integration procedure are performed. The functional fatigue of a SMA wire under four typical mechanical and/or thermal loading cases are simulated, including (1) axial tension under various temperatures, (2) detwinning followed by subsequent free-recovery and self-accommodation, (3) thermal cycling under constant stress, and (4) mechanical cycling in the superelastic regime. The results indicate that the model can simulate the functional fatigue of SMA correctly.