## 5 Calculation Method for Torsional Fatigue Life of Titanium Alloy Turning Surface
### Titanium Alloys Fatigue Life Solution Results  
This study establishes a torsional fatigue life analysis procedure for TC6 titanium alloy turned workpieces based on the fatigue life analysis function of FE-SAFE, with a detailed examination of its key components. The FE-SAFE fatigue analysis is conducted using ABAQUS simulation results as input data. Therefore, the initial modeling must be performed in ABAQUS to generate and export the necessary stress and strain parameters. In the subsequent FE-SAFE analysis, the Rainflow counting algorithm is applied at each nodal point to determine fatigue cycle counts and predict fatigue life. During the FE-SAFE preprocessing phase, surface roughness and residual stress are incorporated as boundary conditions for the workpiece. The material constitutive model is calibrated using the Seeger algorithm, with key mechanical properties including elastic modulus and torsional strength being explicitly defined. A dedicated S-N curve is established to characterize the material's fatigue behavior. Following the material property definition, the stress-strain results from the final torsional state are imported into FE-SAFE. The fatigue life assessment of TC6 titanium alloy turned workpieces is then performed using the S-N curve algorithm. The variation curves of fatigue life with torque for different surfaces are shown in Figure 21.  
As can be seen from Figure 21, when the torque is 90 N m, the fatigue life of the ideal smooth surface titanium alloy specimens shows a significant decrease, and at this torque,  
Figure 21: Variation curves of fatigue life with torque for different surfaces. Figure 20: Maximum torque and torsional fracture points of Groups 10 and 11.  
the fatigue life of each group differs greatly, which is easier to analyze, verifying the validity of the selection of 90 N m torque as mentioned in the previous section. The fatigue life of each point \(a_{1}\)-\(a_{5}\) of the current turning surface is solved, and the results are shown in Figure 22.  
Figure 22 presents the calculated maximum torque and fatigue life values at characteristic points \(a_{1}\)-\(a_{5}\) on the machined turning surface. The results demonstrate substantial spatial variations in both mechanical properties across different axial positions of the titanium alloy workpiece. A clear correlation emerges between proximity to the fracture location and reduced performance metrics, with nearer points showing systematically lower maximum torque and fatigue life values. Although points \(a_{1}\)-\(a_{5}\) display limited consistency under identical processing conditions, the overall variation remains considerable. Most significantly, point \(a_{4}\) exhibits a markedly reduced fatigue life (approximately X% lower than the average of other points), indicating potential localized processing defects or non-uniform parameter distribution that warrant further investigation. By analyzing the fatigue life of different characteristic points at corresponding angles, their degree of unevenness was obtained, as shown in Figure 22. The calculation results indicate that the fatigue lives of points \(a_{3}\) and \(a_{4}\) exhibit obvious fluctuations, suggesting poor distribution consistency. It can be seen from the solution results that the fatigue life distribution of different feature points along the axial direction on the machined surface of titanium alloy is still quite different, and the fatigue life of the feature points close to the fracture position is lower. According to the results, although feature points \(a_{1}\)-\(a_{5}\) show some consistency under the same process parameters, the overall consistency is not high, and the fatigue life of feature point \(a_{4}\) is significantly lower than that of other points, which indicates potential processing problems and uneven distribution. The fatigue life at points \(a_{3}\) and \(a_{4}\) shows obvious fluctuations and poor distribution consistency, as shown by the solution results.