## 3 Results  
All experimental runs showed a strain value greater than 2% and less than 8%, which are the strain limits that the proposed ISO-3630 standard considers valid [7]. Table 3 details the NCF, strain, and fragment length for the four selected instruments when tested at their manufacturer's recommended settings. TRN showed the highest NCF with the lowest values for strain and fragment lengths, whereas PTU showed the lowest NCF and the highest values for strain and fragment lengths. Three-dimensional modeling of the instruments showed three distinct geometries, as seen in Figure 3.  
PTU, PTG, and VB showed a cross-section that was convex triangular, whereas TRN was presented as an off-centered parallelogram cross-sectional design [15]. The overall geometry of the working portion of the instruments was also modeled, with only a small portion of the shaft (Figure 4). A mesh of the fatigue rig was also successfully obtained after adjustments in the SolidWorks software (Figure 4). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instrument** &
\begin{tabular}{c} **NCF** \\ **(Dimensionless)** \\ \end{tabular} & **Strain (\%)** & **Fragment (mm)** \\ \hline ProTaper Universal (PTU) & 600.90 \(\pm\) 80.86 & 6.29 \(\pm\) 0.47 & 5.36 \(\pm\) 0.79 \\ ProTaper Gold (PTG) & 1944.64 \(\pm\) 189.86 & 5.98 \(\pm\) 1.11 & 4.92 \(\pm\) 1.80 \\ Vortex Blue (VB) & 1882.18 \(\pm\) 353.35 & 4.66 \(\pm\) 0.28 & 3.59 \(\pm\) 0.47 \\ TruNatomy (TRN) & 2027.94 \(\pm\) 452.50 & 4.49 \(\pm\) 0.23 & 3.26 \(\pm\) 0.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: NCF, strain, and fragment data from cyclic fatigue testing for PTU, PTG, VB, and TRN. Figure 3: Top images showing geometries of the instrument tip for PTU/PTG, VB, and TRN (left to right) from _STL 3D models, viewed in Materialise MiniMagics 23.5 (Materialise, Leuven, Belgium). Bottom images show SEM microscopy at 800\(\times\) magnification of the corresponding instrument tips. All four simulations for PTU, PTG, VB, and TRN were completed successfully until the end of the step at 1 s. A plot for both the maximum von Mises stress and the maximum principal stress was reported for the entire insertion step of the simulation, but those values differed minimally (Figures 5A-D and 6). All plotted values remained below the ultimate tensile strength of the respective NiTi constituents. In general, there was an initial linear increase in von Mises stress in the first 0.2 s of insertion. PTG, VB, and TRN showed plateaus in stress values during 0.35-0.55 s, 0.55-0.85 s, and 0.30-0.60 s, respectively, whereas PTU did not exhibit this behavior. Figure 4: **(Top)**: PTG F2 instrument with its.STL counterpart, viewed from Materialise MiniMagics 23.5. **(Bottom)**: Comparison of VB instrument under light microscopy **(left)** vs. FE model **(right)**. Figure 5: _Cont._  
Figure 5: **(A)** PTU: Comparison of von Mises and maximum principal stress values during insertion. **(B)** PTG: Comparison of von Mises and maximum principal stress values during insertion. **(C)** VB: Comparison of von Mises and maximum principal stress values during insertion. **(D)** TRN: Comparison of von Mises and maximum principal stress values during insertion. Comparison of von Mises and maximum principal stress values during insertion. Figure 6: Comparison of von Mises stress values during insertion for PTU, PTG, VB, and TRN. The locations of both maximum von Mises and principal stresses were identified at the end of the insertion (Table 4). To identify the distance, the query function for distance was applied to the node at the tip, the highest stress node, and then calibrated to millimeters (Figure 7). In step 2, the mesh models of the instruments were allowed to rotate freely in the canal of the fatigue device. The stress values during this step did not change for all four instruments, however, the tensile-compressive actions of the instruments were observed as stress distributions alternated as the instruments rotated in the fatigue device.