## 4 Discussion  
Unlike most published endodontic literature on experimental cyclic fatigue, the present study aimed to use FEA to validate and explain experimental fatigue data rather than to compare the fatigue lives of various proprietary instrument brands. While the proposed ISO  
Figure 8: Stress contours viewed in the X-plane cross-section to observe differences in stress from instruments contacting the canal wall. standard is essentially a stationary fatigue test, this design has been recently criticized [3]. It should be noted that the stationary test was used for validating the finite element modeling, which in turn permits changes in experimental design, including selectable simulated instrument movements. Owing to the intricacy and asymmetrical nature of the instrument cross-sections, micro-CT is often advantageous in situations where numerical modeling is simply too complicated to perform or too time-consuming. However, imaging methods are often limited by the resolution and artifacts generated in the scans, whereas numerical modeling assumes a perfect model. SEM imaging confirmed that the 3D models generated in InVesalius 3.1 had reasonable resemblance when considering cross-sectional and overall geometry. With respect to the mesh models, a mesh convergence test could be considered to determine the optimum mesh size. The FEA results from the insertion and rotation processes explain the stress evolution and the fatigue failures observed in the in vitro tests. The von Mises criteria are normally applied to ductile materials, with a distortion energy failure theory used for combining multiaxial stresses (such as axial, bending, and torsional loads) into one equivalent stress, which is then compared to the yield stress of the material to judge the failure condition of the material [16; 17]. Given that the von Mises stress is presented as a single, easily calculated and visualized scalar value, it is not surprising that the von Mises stress has been a standard output for most FE software packages, with the assumption that the examined material is isotropic in nature [18]. However, previous studies have reported on the anisotropic nature of NiTi, which is believed to be a result of material processing or training procedures [19; 20; 21]. Maximum principal stress is a different failure indicator; based on the concept that if a material is exposed to a multiaxial stress system, fracture will occur where the stress anywhere in the component exceeds the local strength [22]. This theorem is also limited by the assumption of isotropy in the material [18]. In FEA, there exists no perfect stress evaluation method to account for all multiaxial stresses, and it is therefore, important to note that all calculations are a simplification of experimental phenomena. FEA verified that both the von Mises and maximum principal stresses occurred on the outer curve of the instrument (extrados). Repeated alternating stresses during cyclic rotation could lead to fatigue failure, since there were no increases in the stress distribution in the rotation step. Fractographic analysis of previous cyclic fatigue studies affirms that crack propagation begins in peripheral regions of the cross-sections, which validates the modeling of stress contours used in the present study [23; 24; 25; 26]. Arguably, the only two instruments that are directly comparable are the PTU and the PTG, as they have identical geometries and boundary load conditions. They differ only by the absolute values of the mechanical constants in the VUMAT subroutine. During insertion, von Mises and the maximum principal stresses of the selected elements were not significantly different. PTU had the highest peak von Mises stress at 742 MPa, whereas PTG had 702 MPa. Nevertheless, this difference is unlikely to explain the large disparity in experimental NCF (PTU: 601 NCF vs. PTG: 1944 NCF). For VB and TRN, the peak stress values recorded were significantly lower at 455 MPa and 406 MPa, respectively, which could explain the higher NCF values when compared to PTU.