Rotary bending fatigue analysis of shape memory alloys

Rotary bending is a kind of cyclic loading in which a straight beam is bent into a curved shape and is forced to rotate around its longitudinal axis. Thus, each point of the sample section is subjected to repeated tension-compression cycles until fracture occurs as a result of fatigue failure. Rotary bending fatigue (RBF) behavior of shape memory alloys (SMAs) is a fascinating research field especially in endodontic rotary files. In the present work, one dimensional constitutive model is used to study RBF behavior of SMA beams. The stress and strain distributions in a beam section are driven numerically for both pure bending and rotary bending to show the basic differences between the two loading fashions. In order to verify the numerical results, tests were performed on NiTi specimens with an imposed bending angle using a bending apparatus. Since the specimens show significant stress plateau for forward and backward transformation in their stress-strain response, an enhanced stress-temperature phase diagram is proposed in which different slopes are considered for the start and finish of each transformation strip. In order to study low cycle fatigue of SMAs during rotary bending, the stabilized dissipated energy is calculated from numerical solution. A power law for variations of the fatigue life with the stabilized dissipated energy is obtained for the studied specimens to predict their fatigue life. The numerical predictions of the present approach are shown to be in a good agreement with the experimental findings for rotary bending fatigue.