## 2 Materials and Methods  
Four different proprietary rotary endodontic instruments (PTG, PTU, VB, and TRN) with varying NiTi alloy types were used (Table 1). Instruments were subjected to cyclic fatigue testing through a custom-built cyclic fatigue fixture proposed as an additional test for the ISO 3630-1 standard, the specifications of which are found in previously published works [7,12]. The instruments (n = 30) were run until failure according to the manufacturer's recommended settings in the R5 fixture, which has a radius of 5 mm with a maximum angle of curvature of 75\({}^{\circ}\) (Figure 1). A high-resolution video (30 frames per second) was recorded for each run. The number of cycles to failure (NCF) was determined using open-source video-analysis software (Kinovea 0.9.3, open-source software). The separated fragments were retrieved and measured with a micrometer to determine the location of the fracture, which was expressed as a distance from the tip of the instrument. NCF and the location of the fracture were used as dependent variables, and the strain (\(\varepsilon\)) was calculated using Equation (1) to ensure the tests were valid under an 8% strain. \[\varepsilon_{\mathrm{T}}=\frac{d}{(2r)} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**NiTi Wire Type** & \
\begin{tabular}{c} **Corresponding NiTi** \\ **Instrument** \\ \end{tabular} & **Size** &
\begin{tabular}{c} **Rotations per** \\ **Minute (rpm)** \\ \end{tabular} & **Torque (Ncm)** \\ \hline Stock & ProTaper UniversalTMF2, 25 mm (PTU) & 25/06v & 250 & 2.0 \\ Gold & ProTaper GoldTMF2, 25 mm (PTG) & 25/06v & 300 & 3.1 \\ Blue & Vortex BlueTM, 25 mm (VB) & 25/06v & 500 & 2.8 \\ Superflex & TruNatomyTM Prime, 25 mm (TRN) & 26/04v & 500 & 1.5 \\ \hline \end{tabular}
\end{table} 
Table 1: List of rotary NiTi endodontic instruments selected, with the corresponding wire specimen that matches the metallurgical properties. Micro-CT scans (\(\mu\)CT 40, Scanco Medical, Bruttisellen, Switzerland) of the PTU, VB, and TRN instruments were taken at 5.8 \(\mu\)m resolution, which generated three volume sets of DICOM data. As the PTU and PTG instruments have identical geometries, only a scan of the PTU instrument was required. Using specialized imaging software (InVesalius 3.1, CTI, Sao Paolo, Brazil), the DICOM data were processed into a 3D model in the form of a Standard Tessellation Language (.STL) format. The instruments were also viewed under scanning electron microscopy (SEM) at 800\(\times\) magnification as a confirmatory step for the cross-sectional geometry for PTU/PTG, VB, and TRN. The models were refined and repaired using SolidWorks 2016 (Dassault Systemes SE, Velizy-Villacoublay, France), and exported to ABAQUS 2016 software (Dassault Systemes SE). FEA was performed in ABAQUS/Explicit because of its capability of solving nonlinear behavior. The FE models were meshed using the solid continuum brick element (type: C3D4): PTU had 18,558 elements with 13,572 degrees of freedom (DOF), VB had 18,885 elements with 13,029 DOF, and TRN had 22,193 elements with 16,482 DOF. The.STL model of the R5 fatigue rig was supplied by Dentsply (Dentsply Maillefer Ballaguues, Switzerland). The in-house measured elastic moduli and transformation stress values from microtensile tests in a study conducted by [PERSON] et al., 2022, were implemented in ABAQUS through a user-defined material (VUMAT, ABQ_SUPER_ELASTIC_N3D) [13]. Material constants not determined from the experimental results in [PERSON] et al., 2022, were extracted from the previous publication of [PERSON] et al., 2022 [14]. The full list of material constants used is shown in Table 2.  
Figure 1: VB instrument set up with a cyclic fatigue rig with a thermocouple for tracking the temperature.