## 4 Discussion
Fatigue fracture originates at the maximum bending point of the instrument during root canal shaping. Tensile stress amplitude increases with larger instrument diameter. The higher the tensile strain amplitude on the surface is, the lower cyclic fatigue resistance will be [47; 48]. In a study done by [PERSON] et al. [17], it was proven that a higher mass of alloy (i.e., a larger cross-section area) lowers cyclic fatigue resistance when using instruments from the same treated alloy with the same properties. However, in our study, the resistance of WaveOne Gold to cyclic fatigue was lower compared to Reciproc Blue and Unicone Plus, although its cross-sectional area is the smallest one. In the case of Unicone Plus and Reciproc Blue one can see that the latter, having a larger cross-sectional area, is more resistant to cyclic fatigue, though not statistically significantly. These results do not correlate with the last mentioned study [17]. Nevertheless, it should be stressed that other factors such as microstructure and phase composition have to be considered. In other words, the cross-sectional area is not the only parameter affecting or predetermining the performance of the NiTi endodontic instruments, as supported by comparison of Figures 2 and 3 for Unicone and Unicone Plus, for example. Although their cross-sectional areas are very similar, their performance differs significantly. Our results show that even small differences in manufacturing processes may have a great impact on the cyclic fatigue resistance of the instruments used in our study, in addition to cross-section area [16]. The cross-section shape is another plausible parameter, observable from the cross-sections in Figure 3, that correlates with our results. It is generally assumed that the S-shaped cross-section design, as in the case of Reciproc Blue,is more advantageous in terms of cyclic fatigue due to less blade engagement compared to instruments with a higher number of blades [49]. The process of cyclic fatigue fracture originates with the forming of nano and microcracks, predominantly initiated on the surface. In most cases surface imperfections created during the machining or any other technological operation are involved at the very beginning of crack formation. Surface and near subsurface microcracks and other voids act as stress concentrators, initiating the fracture process during mechanical loading. Once the crack is formed, it grows with each subsequent loading cycle. The gradual process of structural damage proceeds and the instrument is progressively weakened. This process continuous until the crack reaches its critical size and the catastrophic fracture ultimately takes place. Unfortunately, this happens suddenly and unexpectedly, with negative effects on the quality and course of endodontic treatment [50,51]. [PERSON] et al. [15] proved that lower surface roughness leads to increased cyclic fatigue resistance. However, this does not corelate with our results, where Unicone Plus had the lowest roughness but does not exhibit the highest resistance in cyclic fatigue tests, and WaveOne Gold, with the highest roughness, does not exhibit the lowest resistance; see Figure 2 and Table 2. This could be due to a higher effect of the other factors discussed in relation to cyclic fatigue compared to the surface roughness. Although high hardness is a suitable parameter against damage initiation due to the resistance to notching, it can be disadvantageous in fatigue tests. Materials of higher hardness are usually more brittle, which leads to rapid propagation and macroscopic cracking of the sample after the initial initiation of the microcrack [52, 53, 54]. This correlates well with the results of indentation tests, where Unicone has significantly higher hardness than other three samples, while also failing first during the fatigue test. The values of Elasticity modulus for all four samples are relatively similar. However, the increase between the 2 mm and 6.4 mm cross-sections is noticeable for each of the samples.