With the advancement of technology, applications of shape memory alloys have been considered in various industries such as aerospace, biomedical, automotive and robotics due to their unique properties, which is mainly due to phase transformation (austenite to martensite transformation or vice versa). These alloys are subjected to fatigue loading in various applications. Fatigue loads are applied as cyclic tensile, torsional, pure bending, rotary bending or combination of them. Rotary bending is more delicate compared to other one-dimensional loadings. One of the most commonly applications of these alloys under rotary bending fatigue is endofiles. Failure of these endofiles in the root canal occurres without any signs. Therefore, prediction of their fatigue life is very important. In this research, the low-cycle fatigue of shape memory alloys under pseudo-elastic rotary bending has been investigated. In fact, the reason of studying the low cycle fatigue in these alloys is that the occurrence of transformation has led to a distinct behavior compared to other metals, so these alloys should be investigated under the conditions in which they are transformed. On the other hand, this phase transformation causes significant changes in the temperature of the material; therefore, the frequency or, in other words, the loading rate affects the stress-strain response and the fatigue life of these materials. In the present study, a fully coupled thermomechanical model in the continuum mechanics framework is presented to obtain stress-strain response of SMA wires under rotary bending and pure bending cyclic loadings. Then, using the properties of nickel-titanium, stress, strain and temperature at each point of the wire cross section has been determined; then, the required bending moment in this loading has been obtained. Next, a relation between fatigue life and stabilized dissipated energy in rotary bending is presented. The results of the numerical solution presented in this study have been validated with experimental results presented in previous papers. At the end, using the developed model, the effects of factors such as loading speed, radius of curvature and wire diameter on fatigue life in rotary bending have been investigated. The results showed that increasing the rotational speed and wire diameter would reduce the fatigue life and increase the bending radius of curvature, resulting in longer fatigue life. Keywords: Shape memory alloys, Rotary bending, Fatigue life, Stabilized dissipated energy , Loading frequency.
