## 3 Results and Discussion
### Fatigue Properties of the FPP-Treated Ti-22V-4 Al Alloy  
Figure 9 shows the results of the rotating fatigue tests for the untreated and the FPP-treated specimens. In this figure, data points with an arrow indicate the run-out of the specimen, which was not failed until the number of stress cycles was 10\({}^{9}\). In each specimen, a fatigue limit was not clearly observed so that the _S-N_ curve was determined based on the curve of the _S-N_ model in the JSMS standard regression models [27]. Regression _S-N_  
Figure 8: (a) Residual stress and (b) FWHM values as a function of depth into the surface of FPP-treated specimen. Figure 7: Distribution of Vickers hardness at various cross-sectional depths for FPP-treated specimen. curves for the untreated and FPP-treated specimens are respectively expressed by the following formulae:  
\[\text{Untreated}:\sigma_{\text{a}}=\ 10^{(-0.80825\log{(N)}+5.7133)}+\ 505.30 \tag{2}\]  
\[\text{FPP-treated}:\sigma_{\text{a}}=\ 10^{(-0.50499\log{(N)}+4.1259)}+\ 591.95 \tag{3}\]  
where \(\sigma_{\text{a}}\) is the stress amplitude applied to the specimen surface (MPa), and \(N\) is the number of cycles. At high stress levels greater than 700 MPa, there is no improvement in fatigue life by FPP; nevertheless, a work-hardened layer and high compressive residual stress were generated at the specimen surface. As shown in Figure 3, SEM observation of the FPP-treated specimen surface indicated the rough surface formed by FPP. It is suggested that the asperity formed on the specimen surface can be a crack starter and deteriorate the fatigue life. On the other hand, at low stress levels lower than 700 MPa, the fatigue life of the FPP-treated specimen was longer than that of the untreated specimen. The FPP-treated specimen failed at \(\sigma_{\text{a}}\) = 600 MPa, the fatigue life was \(N_{\text{f}}\) = 1.0 \(\times\) 10\({}^{9}\) cycles, and the subsurface fracture mode was observed. In shot-peened specimens, fatigue crack initiated from the surface of the specimen at a high stress level, while at a low stress level, fatigue crack initiated from the subsurface [28,29]. The same phenomenon is assumed to have occurred in the FPP-treated specimen. Furthermore, if more fatigue tests are performed for the FPP-treated specimen, the duplex \(S\)-\(N\) characteristics [30] may appear. The fracture surfaces of all failed specimens were examined using SEM to determine the fatigue fracture mechanism. Figure 10 shows the SEM micrographs of the crack initiation site in each specimen failing at high and low stress levels. At a high stress level (\(\sigma_{\text{a}}\) = 800 MPa), a fatigue crack was initiated at the specimen surface in the untreated specimen. No defect was found at the crack initiation site, and the fatigue crack was caused by crystal grain slip. On the other hand, in the case of the FPP-treated specimen, a defect was found at the crack initiation site, and it was formed by the collision of HAp shot particles with the specimen surface during the process of FPP. Therefore, the reason the fatigue strength was not improved was that even though a work-hardened layer was generated, the high compressive residual stress caused the formation of defects during the FPP process, and they became crack starters. At a low stress level (\(\sigma_{\text{a}}\) = 600 MPa), in  
Figure 9: S–\(N\) diagram for untreated and FPP-treated specimens. the untreated specimen, a fatigue crack was initiated at the specimen surface, the same as when the specimen failed at a high stress level. In the case of the FPP-treated specimen that failed at a low stress level of 600 MPa, it seems that the crack initiated below the specimen surface. Thus, the subsurface-initiated fracture mode occurred in this case. However, no defect (inclusion or defect) was found at the crack initiation site. As can be seen in Figure 10, the FPP-treated specimens showed different failure modes at high and low stress levels. Figure 11 shows a schematic illustration of the fracture mechanism for the FPP-treated specimen.