**3. Results**

The mean times to fracture and standard deviations for the PTU, PTG, and PTN instruments are presented in Table 4. The CF behaviors of the PTU, PTG, and PTN series are presented in Figure 4. Comparing the instruments with similar D5 ±0.01 mm, one-way ANOVA and Tukey's post-hoc tests showed that PTG F1 and F2 had significantly higher CF resistance than PTU F1 and PTN X2, and PTU F2 and PTN X3, respectively. PTN X2 showed a significantly higher CF resistance than PTU F1. However, there was no significant difference between PTU F2 and PTN X3 in terms of CF resistance.



SD: standard deviation. Weibull calculations included the Weibull modulus (m), the coefficient of determination (R-squared), and the predicted time in seconds for 99% survivability.

**Figure 4.** The mean time to fracture (s), standard deviation (SD) and D5 (mm) for PTU, PTG, and PTN.

Probabilistic modeling of fatigue failure and reliability assessment has been done for various engineering components such as turbine blades [19], turbine disc [20], and railway axles [21], which are subjected to variable loading conditions. Reliability analysis is important for the establishment of suitable safety levels for any device or system.

Weibull reliability analysis results and the probabilities of survival calculated for the PTU, PTG, and PTN instruments are presented in Table 4. The PTG series showed higher reliability than the PTU and PTN series. PTG S1 showed the longest resistance, with 181 s at 99% survival. Regarding the instruments with similar diameters at 5 mm from the tip, rotation for 152 s was predicted for PTG F1 at 99% reliability compared with 78 and 62 s for PTN X2 and PTU F1, respectively. Additionally, rotation for 145 s was predicted for PTG F2 at 99% reliability compared with 49 and 48 s for PTN X3 and PTU F2, respectively.

Figure 5 shows the fractography analysis of the PTU S1 sample. Two distinct regions were noticed: one with fatigue striations (Region a) and another with a dimpled surface (Region b) (Figure 5A). The crack initiates at the edge and propagates to the fatigue striations (Figure 5B). Micro-voids produced coalesce with each other and weakens the material (Figure 5C), after which ductile fracture occurs, which is evident from the dimpled surface in Figure 5D, until failure. The round dimples indicate normal rupture caused by tensile stresses.

**Figure 5.** SEM analysis of PTU S1 sample. ( **A**) Overall cross-sectional view (**B**) Crack initiation ( **C**) micro-voids. ( **D**) Dimpled structures.
