## 4 Discussion  
Numerous studies have approached various aspects regarding the behavior of endodontic instruments, including the influence of lubricants on torsional loads [27], metallurgical features [28], comparison between manual instruments and NiTi files [29], influence of heat sterilization procedures [30] or of surface design [31]. During root canal preparation, endodontic instruments are exposed to torsional and flexural stresses, the former for straight root canals and the latter for curved ones [32]. These stresses contribute to  
Figure 9: Shear stresses \(\tau_{\text{max}}\) versus twist angles \(\theta\) of the Endostar, Reciproc and Protaper instruments: graphs obtained for samples that experience (a) low and (b) high torque and twist angle at failure. metal fatigue and failure [33]. Few studies have looked into the impact of cyclic fatigue preloading on torsional resistance [10; 34; 35] or into the impact of torsional preloads on cyclic fatigue resistance of traditional NiTi instrument [36; 37; 38]. In the present study, the effect of cyclic fatigue of three root canal type of instruments (and preparations) was considered, and then the maximum shear stresses obtained by torsion to failure of these (used) instruments were compared. In comparison to other studies, we did not consider the cycle fatigue in a dynamic regime [11], but rather in a static model [39]. While in other studies the simulated root canals were manufactured from stainless steel [40], in the present study, they were made from polycarbonate blocks. The first group of instruments is made out of conventional NiTi alloy (i.e., Endostar), while the other two groups of instruments are made of M-wire alloy (i.e., Reciproc and Protaper). The difference between the two systems made of M-wire alloy is the movement that the instrument develops inside the root canal, namely: Reciproc instruments use a reciprocating movement, while Protaper instruments uses a continuous rotational movement, similar to Endostar instruments. Torsional behavior of NiTi instruments can be affected by a variety of factors, including root canal anatomy, instrument size, taper, geometry, alloy chemical composition, and the thermomechanical method used during manufacturing [41]. The torsion test was used in the analysis performed in this work to determine maximum torsional strength and angle of twisting before failure (and after instrument wear in processing five simulated root canals). The 2 to 3 mm tips of the instruments were fastened in the chuck of the machine, and rotations in a clockwise direction were performed [42; 43; 44; 45; 46]. In previous studies, instruments with larger metal mass-volume and tip diameter have been found to have higher torsional strength and lower rotation angles to failure. The taper, cross-sectional shape and tip diameter of the instruments have been demonstrated to have a direct impact on the metal mass-volume [43; 45; 47; 48; 49]. Comparing the lengths of the considered instruments after fracture (\(L_{2}\), Figure 4a) to the total/initial lengths (\(L_{1}\), Figure 2a), it can be observed that the broken element has roughly a 2 to 3 mm length range. Thus, it belongs to the tip of the instrument. This confirms the clinical experience of rupture of instruments in dental canals or in the simulated root canals of polycarbonate blocks. In addition, it can be seen in Figure 4a that the breaking lengths of all the three types of instruments included in this experimental study are comparable, and that dimensional deviations of around 0.5 mm are obtained. Regarding the diameters of the instruments, [PERSON] et al. tested ProFile.04 tapered instruments for torsional stress and discovered that larger-diameter instruments had better torsional fatigue resistance [50]. [PERSON] et al. checked various tip sizes of ProFile.04 and.06 tapered files that had already been strained by cyclic fatigue (as considered in the present study, as well).