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In this paper we propose a methodology for a fast numerical determination of low cycle fatigue lifetime of superelastic shape memory alloy structures. This method is based on the observation that generally, in low cycle fatigue, shape memory alloy (SMA) structures are subject to loadings that lead to a confined non-linear behaviour at stress concentration points, such as notches. Numerical fatigue lifetime prediction requires the computation of the mechanical state at critical points. However, classical computational methods, like the non-linear finite element method, lead to a prohibitive computation time in a non-linear cyclic framework. To overcome this issue, we propose to use fast prediction methods, based on localization laws. Following the determination of the stabilized behaviour, an energetic fatigue criterion is applied. The numerical fatigue life prediction model is validated experimentally on SMA endodontic instruments.

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Objectives: This study compared the cyclic fatigue resistance of One Curve (C wire) and F6 Skytaper (conventional austenite nickel-titanium [NiTi]), and 2 instruments with thermo-mechanically treated NiTi: Protaper Next X2 (M wire) and Hyflex CM (CM wire). Materials and Methods: Ten new instruments of each group (size: 0.25 mm, 6% taper in the 3 mm tip region) were tested using a rotary bending machine with a 60° curvature angle and a 5 mm curvature radius, at room temperature. The number of cycles until fracture was recorded. The length of the fractured instruments was measured. The fracture surface of each fragment was examined with a scanning electron microscope (SEM). The data were analyzed using one-way analysis of variance and the post hoc Tukey test. The significance level was set at 0.05. Results: At 60°, One Curve, F6 Skytaper and Hyflex CM had significantly longer fatigue lives than Protaper Next X2 (p < 0.05). No statistically significant differences were found in the cyclic fatigue lives of One Curve, F6 Skytaper, and Hyflex CM (p > 0.05). SEM images of the fracture surfaces of the different instruments showed typical features of fatigue failure. Conclusions: Within the conditions of this study, at 60° and with a 5 mm curvature radius, the cyclic fatigue life of One Curve was not significantly different from those of F6 Skytaper and Hyflex CM. The cyclic fatigue lives of these 3 instruments were statistically significantly longer than that of Protaper Next.

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OBJECTIVES: The objectives of this study were to compare numerically the bending and torsional mechanical behavior of 5 endodontic rotary Ni-Ti instruments with equivalent size and various designs for tapers, pitch, and cutting blades.First, the geometries of Hero (20/0.06), HeroShaper (20/0.06), ProFile (20/0.06), Mtwo (20/0.06), and ProTaper F1 were generated by finite element code. Then, the 2 most representative clinical loadings, i.e., bending and torsion, were studied with an ad hoc model for the superelasticity of Ni-Ti. Bending was generated by tip deflection and torsion by a constant twist-angle of the tip. RESULTS: Mechanical behavior of these 5 endodontic rotary Ni-Ti instruments could be evaluated and compared. Protaper F1 presented the greatest level of bending stress and torque. Hero and HeroShaper were more rigid than ProFile and Mtwo. CONCLUSIONS: This numerical comparison evaluated the effects of the geometrical parameters on the instrumental mechanical behavior. The 5 endodontic instruments, investigated in the present study, do not have the same bending and torsional mechanical behavior. Each clinician must be aware of these behavior differences so as to use the adequate file according to the clinical situation and to the manufacturer's recommendations.

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OBJECTIVES: The aim of this study was to develop a numeric method to study the mechanical behavior of an endodontic instrument during different loading paths and to demonstrate the importance of the behavior model in the finite element results. STUDY DESIGN: A numeric study of an endodontic instrument was carried out. At first, the geometry was meshed with a finite element code. Then, 3 among the most representative loadings in clinical use, i.e., bending, torsion, and nonproportional bending-torsion, were studied. Each of them was simulated by setting 3 different behaviors: elasticity, elastoplasticity, and an ad hoc model for the superelasticity. RESULTS: The simulations with nonproportional bending-torsion loading showed that the mechanical behavior of Ni-Ti shape memory alloy was strongly affected by change in the loading direction. Elastic and elastoplastic models were unable to consider this feature of Ni-Ti behavior. Only a superelastic model taking into account the effects of nonproportional loading proved to respect this crucial point. CONCLUSION: To realize valid simulations of the mechanical behavior of Ni-Ti instruments during different mechanical loading paths, it is necessary to use an ad hoc mechanical behavior model.

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