# Notch Effect on the Fatigue Behavior of a TC21 Titanium Alloy in Very High Cycle Regime
## 3 Results
### SEM Observation of the Fracture Surface  
Two different types of fatigue fracture of smooth specimens were observed. In Figure 6, the fatigue crack initiation occurs at the sample surface in the less than 10\({}^{6}\) cycles region, whereas subsurface crack initiation was exhibited in more than 10\({}^{6}\) cycles. The fine granular area (FGA) along the \(\alpha\) lamellar was at the crack initiation site (Figure 7). The similar morphology of the TC21 titanium alloy was observed in other high-strength titanium alloys [11]. The typical fatigue crack initiation models of the notched specimens are shown in Figures 8-11. Figure 8 shows that fatigue crack initiated from the specimen surface at a stress amplitude of 400 MPa, and multiple crack origins were displayed on specimen surface due to the high stress concentration at the notch root. A flat facets characteristics was observed at the crack initiation site as the stress amplitude decreased to 350 MPa (Figure 9). [PERSON] et al. [15] indicated the flat facets resulted from the dislocation arrays pile-up at the \(\alpha/\beta\) interfaces for titanium alloys with a lamellar microstructure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fatigue Life** & **Smooth Specimens** & **Notched Specimens** & \\ \hline
**(Cycles)** & **Fatigue Strength (MPa)** & **Fatigue Strength (MPa)** & **K\({}_{f}\)** \\ \hline \(1.25\times 10^{5}\) & 600 & 400 & 1.5 \\ \(3\times 10^{6}\) & 550 & 350 & 1.57 \\ \(2\times 10^{7}\) & 430 & 300 & 1.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fatigue notch factors in various fatigue lives. Figure 6: Fatigue fracture surface of TC21 titanium alloy at \(\sigma\) = 550 MPa and N = 2.37 \(\times\) 10\({}^{5}\) cycles: (**a**) fatigue crack initiation site, and (**b**) high magnification morphology of crack initiation site. Other subsurface crack initiation characteristics with \"facets + FGA\" were revealed in notched specimens under a low-stress amplitude (Figure 10). It was indicated that the flat facets were formed by the separation of the granular \(\alpha\) phase as the size of the flat facets were approximate to that of the granular \(\alpha\) phase (Figure 10,c). Furthermore, \(\alpha/\beta\) lamellar characteristics were present at the vicinity of the flat facet where the fine grains were distributed on the \(\alpha\) lamella (Figure 10). A similar characteristic at crack initiation site was observed in the notched specimen of a Ti-8 Al-1 Mo-1V alloy [8]. [PERSON]'s investigation [16] proposed that the morphology of the FGA can be formed regardless of materials when the next three conditions were satisfied: a vacuum environment, repeating contact of fracture surfaces, and long term loading over about \(10^{7}\) cycles. Furthermore, a wear process can take place due to the absence of oxygen, reducing the local crack closure effect. Thus, an arrested crack can propagate at a very slow rate. FGA characteristics of the specimens can result from the wear process. However, the surface initiation mode can also be observed at a low stress amplitude. Figure 11 shows the fatigue crack initiated from the notch surface under a 250 MPa stress amplitude, and the crack-propagation character was associated with \(\alpha/\beta\) lamellar microstructure that was generated by the subsequent low-stress fatigue. Figure 8: Fracture surface for the notch specimens at \(\sigma\) = 400 MPa and N = 1.25 \(\times\)\(10^{5}\) cycles: (**a**) macroscopic morphology, and (**b**) crack initiation morphology. Figure 7: Fatigue fracture surface of TC21 titanium alloy at \(\sigma\) = 460 MPa and N = 1.59 \(\times\)\(10^{7}\) cycles: (**a**) fatigue crack initiation site (remarked by red line), and (**b**) high magnification morphology of the crack initiation site. Figure 10: Fracture surface for the notch specimens at \(\sigma\) = 300 MPa and N = 2 \(\times\) 10\({}^{7}\) cycles: (a) fatigue crack initiation site (remarked by red line), (b) crack initiation morphology, (c) flat facet morphology, and (d) distribution of fine grains on the \(\alpha\) lamella.