Methods: We used a new mathematical model for the deformation of Ni-Ti material, showing that the maximal stress in a bent Ni-Ti endodontic instrument is not necessarily at the outer layer of the instrument. On the basis of this observation we modified Coffin-Manson relation so that a parameter corresponding to the position of the maximal stress within the instrument is introduced. Experiments were performed to determine coefficients in the modified Coffin-Manson relation. Twenty Ni-Ti rotary endodontic instruments BioRaCe (BR3 FKG Dentaire S.A., Chaux-de-Fonds, Switzerland) with tip size 25, 0.06 taper were subjected to the rotating-bending fatigue in an artificial root canals manufactured for cyclic fatigue test with two different curvatures; group I (27° angle of curvature and radius of curvature of 40 mm) and group II (35° angle of curvature and radius of curvature of 13 mm). Mean values were then calculated. Data were subjected to an independent sample t-test (p < 0.05).
Results: A highly statistically significant difference in the average number of cycles to failure (p < 0.05) was noted between instruments of groups I and II confirming that the increase of bending curvature to which instruments are subjected reduces their resistance to cyclic fatigue.
Conclusions: The results of mathematical modeling indicated that the number of cycles to failure was influenced by the curvature of the canal and the arc length.
Acknowledgements: This research was supported by the Ministry of Science Grant No 174005.