## 5 Calculation Method for Torsional Fatigue Life of Titanium Alloy Turning Surface  
### Construction Method of Torsional Strength and Fatigue Life Analysis Model of Titanium Alloys  
In the titanium alloy machining surface performance assessment, its fatigue life is an important basis for assessment; the machining surface performance directly determines the fatigue life of the titanium alloy workpiece machining surface. Fatigue life not only reflects the endurance performance of the material under dynamic loading but also reveals the influence of surface properties on the long-term reliability of the material. Therefore, by combining surface properties and fatigue life research, the performance of titanium alloys in practical applications can be more accurately predicted and optimized to ensure their reliability and durability under high-stress and complex environments.  
Using the results of processing surface morphology correction in Sections 3.4 and 4.3 and the results of superficial sub-surface layer performance parameter solving and taking into account the non-uniformity of the distribution of each characteristic parameter on the machined surface of titanium alloys, the titanium alloy torsion model shown in Figure 13 is constructed by taking the cross-section where a4 is located as an example.  
Figure 12: Work hardening rate distribution across characteristic points within the cross-section: (**a**) \(a_{1}\) Cross-section rate of work hardening; (**b**) \(a_{2}\) Cross-section rate of work hardening; (**c**) \(a_{3}\) Cross-section rate of work hardening; (**d**) \(a_{4}\) Cross-section rate of work hardening; (**e**) \(a_{5}\) Cross-section rate of work hardening.  
Figure 13 illustrates three key distribution functions along the depth direction: \(g_{1}\) represents the plastic strain distribution, \(g_{2}\) denotes the residual stress distribution, and \(g_{3}\) characterizes the work-hardening rate distribution. Additionally, \(G_{4}\)(\(x\),\(y\),\(z\)) defines the mathematical formulation of the turning transition surface associated with characteristic point \(a_{4}\).  
Using ABAQUS, a torsional dynamics simulation is performed on the corrected surface under the conditions of applied initial performance parameters. The maximum stress of the frame before torsional fracture is extracted as 670 MPa, recorded as the torsional strength, and the corresponding maximum torque under the current conditions is 360 N m. When the workpiece undergoes torsion, the nominal shear stress it experiences is approximately 167.5 MPa (\(\approx\)\(\tau_{\max}\)/4 [23]). When the nominal shear stress is 167.5 MPa, the torque T is approximately 90 N m. Therefore, in fatigue life analysis, a torque of 90 N m is uniformly selected for finite element simulation. Under the action of the maximum torque, the equivalent stress, plastic strain, and torsion process of the corrected surface are shown in Figures 14 and 15, while the torsion process of the simulated surface of the titanium alloy under the maximum torque is shown in Figure 16.  
Figure 14: Equivalent stress in the torsion process of the corrected surface under initial performance parameter conditions.  
Figure 13: Initial application of performance parameters for titanium alloy workpieces.  
Based on the results of the analysis of the torsion process, it is clear that the non-uniformity in the distribution of the machined surface morphology and the superficial sub-surface property parameters leads to significant differences in the location of the torsional fracture, which results in a deviation from the center of the workpiece.