**4. Discussion**

In this study, the tested instruments were selected because they shared the same recommended scheme of instrumentation. Generally, compared with the PTU and PTN series, the PTG series in this study demonstrated favorable CF behavior. However, the PTU, PTG, and PTN instruments vary in their tapering schemes, cross sections, axes of rotations, and alterations in metallurgic processing. Therefore, comparisons were performed among instruments of similar diameter ( ±0.01 mm) at the center of the

curvature to minimize confounding factors. The PTG instruments were most resistant to CF, followed by PTN and PTU. However, the difference between PTN X3 and PTU F2 was not significant.

The higher CF resistance of the PTG and PTN instruments can be attributed to the thermomechanical treatment of these instruments [9]. Furthermore, instrument morphology is considered a significant determinant of CF behavior and can explain the greater CF resistance of the PTG instruments compared with that of the PTN instruments. Some studies have shown that instrument design is not an important determinant of CF resistance [22,23], whereas others have suggested that a different cross-sectional design is a main determinant of the CF resistance of different files [10,12,14,24,25]. Cheung et al. reported that instruments with a triangular cross-section demonstrated a higher fatigue resistance than those with a square cross section [26].

Yong et al. reported a favorable balanced relationship of flexibility, peak torque, and cyclic fatigue resistance of NiTi rotary instruments when compared to stainless steel instruments [27]. Furthermore, the thermomechanically treated NiTi instruments demonstrated greater flexibility and fatigue resistance than conventional SE NiTi instruments of similar diameter and geometry.

Several studies have compared the CF resistance of different NiTi rotary systems. Hieawy et al. tested the CF resistance of PTG and PTU instruments of sizes S1 to F3 using a 3-point bending device at a curvature of 40◦ with a 6 mm radius [7]. Their results showed that the PTG file had a significantly higher CF resistance than did the PTU file ( *P* < 0.001). In addition, the S1 and S2 files were more resistant to fatigue failure than the F1 to F3 files in both the PTG and PTU systems ( *P* < 0.001). PTG S1 showed the highest CF resistance among all files ( *P* < 0.001), whereas PTU F3 showed the lowest CF resistance. These findings agree with the results from the PTU and PTG series in this study.

Perez-Higueras et al. reported that PTN X2 and X3 were more resistant than were PTU F1 and F2, respectively, when tested in stainless-steel curved canals at a curvature of 60◦ with a 3 mm radius [28]. Nguyen et al. compared the CF among PTU and PTN instruments with a curvature of 90◦ and a 5 mm radius. Their results indicated that PTU F1/F2 had a higher CF resistance than PTN X2/X3, respectively; however, this difference was not significant [29].

Weibull analysis can predict a product's resistance and be used to compare the reliability of various product designs. Nguyen et al. discussed in detail the clinical relevance and the advantages of Weibull analysis in such cases when they compared CF with PTN, PTU, and Vortex Blue rotary instruments [29]. Weibull prediction can also provide the clinician with information about the time required for a rotating instrument in a canal to fracture.

Topographic features of the fracture surfaces of all broken instruments were analyzed using SEM. The findings of this study are in agreemen<sup>t</sup> with previous studies where the fracture surfaces of all groups showed typical features of CF with one or more crack initiation areas, fatigue striation, and a fast fracture zone with dimples [5,7].

The KT (Kitagawa–Takahashi) diagram represents the boundary in terms of crack size and stress range for infinite fatigue life [30]. The present work can be extended to define the KT diagram for fatigue life prediction based on various approaches such as the probabilistic S-N model, EIFS (equivalent initial flaw size), and fatigue crack growth models [18,31,32]. The experimental fatigue life data can then be plotted and compared with the KT diagram.
