## 4 Results and Discussion
### Fatigue Life Analysis  
Once the residual shear stress and residual normal stress were determined, fatigue tests were performed to explore the effect on fatigue life. Under the same fatigue testing condition, the fatigue life of a specimen with different levels of residual shear stress and residual normal stress are presented in Figure 6a-c. The fatigue test results illustrated that no evident fatigue life evolution tendencies were observed with the increase in the residual normal and shear stresses. It is suggested that the fatigue life of a specimen was not directly dependent upon only residual shear stress or residual normal stresses. Figure 5: Residual normal and shear stresses calculated using the cos\(\alpha\) method. Consequently, it can be deduced that residual stress in only one direction would not be a suitable indicator for evaluating the effect of residual stress on fatigue life. Figure 6d illustrates the relationship between the equivalent stress and fatigue life. Compared with the residual shear stress and residual normal stress, the equivalent stress significantly influenced the fatigue life of the specimen. It is clear from Figure 6d that there was a linear relationship between the equivalent stress and fatigue life. The longest and shortest fatigue lives (mean value) of the machined specimens were 59,765 cycles and 36,236 cycles which correspond to the equivalent stress at the levels of 1248 MPa and 1317 MPa, respectively. As the equivalent stress decreased from 1317 to 1248 MPa, the fatigue life tended to increase from 36,236 cycles to 59,765 cycles, a 39.4% increase (see Figure 6d). Figure 6: _Cont._  
To further understand the effect of residual stress on fatigue life, a comparison was made between the equivalent stress calculated by Equation (22) and the total stresses calculated by Equation (20) according to [PERSON] et al. [16; 17]. The relationship between the calculated total stresses and the fatigue life were plotted in Figure 7. It is observed that the results of the total stresses were depicted as a function of fatigue life. The maximum total stress calculated by Equation (20) was nearly 1400 MPa, which exceeded the yield strength (\(\sigma_{0.2}=1360.5\) MPa) of the material. However, the maximum total stress calculated by the proposed model was less than the yield strength, which corresponded to a fatigue life of \(3.6\times 10^{4}\) cycles. From Figure 7, it is noted that the higher total stress calculated by Equation (22) gave rise to the lower fatigue life of the machined specimen. However, as the total stress calculated by Equation (20) increased, there was no evident tendency of the fatigue life to diminish gradually. This phenomenon was not consistent with [PERSON] et al. [16; 17] who reported  
Figure 6: Fatigue life at different stresses: (**a**) residual normal stress \(\sigma_{xx}\), (**b**) residual normal stress \(\sigma_{yy}\), (**c**) residual shear stress \(\tau_{xy}\), and (**d**) equivalent stress \(\sigma_{y}\). that the maximum value of residual stress at the surface was a good indicator for evaluating fatigue performance as summarized in Figure 8. In the figure, it can be found that the fatigue life increased with the decrease in the maximum local stress. Nevertheless, it was found in detail that the longest fatigue life did not occur at the largest compressive residual stress. (e.g., the fatigue life induced by the compressive stress of Specim 4 was much shorter than that induced by Specim 1, and Specim 17 generated a longer fatigue life than Specim 3). Thus, this indicated that the residual stress at the surface in only one direction might not be enough to accurately evaluate fatigue performance. In the present work, the fatigue tests revealed that there was no clear and orderly tendency of the residual stress at the surface to directly impact on fatigue life. The residual stress at the surface in one direction could not fully describe the effect of residual stress on fatigue life.