# A New Method for Fatigue Evaluation of Titanium Alloy Welded Structures
## 1 Introduction  
Titanium alloy is favored by more and more people because of its high specific strength, low density, and many other excellent properties [1]. With the gradual maturity of titanium alloy welding technology, it is also widely used in the field of rail transit. The use of titanium alloy to make rail vehicle parts reduces the weight of the vehicle to a certain extent. It can achieve the purpose of saving energy, so this method has great potential [2; 3; 4]. However, when the titanium alloy welded structure is under load, stress concentration will occur at the structural abrupt change position of the weld, and fatigue cracks will be initiated, resulting in fatigue fracture [5; 6; 7; 8; 9]. One of the main reasons for fatigue failure of welded structures is the generation of stress concentration [10]. Therefore, it is very important to study the stress concentration phenomenon at the cross-section of the titanium alloy welded structure, and the important factors affecting the degree of stress concentration of titanium alloy welded structures are the type and size of the welded structure. Therefore, the selection of the type and size of the welded joints of the key stress parts needs to be carefully considered so that the titanium alloy welded joints can meet the static strength and fatigue strength requirements under the condition of a reasonable structure. In recent years, many scholars have studied the fatigue phenomenon of metal welded structures with stress singularity. [PERSON] et al. [11] are based on the linear elastic fracture mechanics method, the average strain energy density method, and the microstructure sensitive strain method. The fatigue life prediction of welded joints with different geometric types and different plate thicknesses was carried out, respectively. The predicted resultswere compared with the test results, and it was found that the difference between the predicted life of the microstructure sensitive strain method and the test results was the smallest. [PERSON] et al. [12] conducted fatigue tests on 4 mm thick laser welded joints of different sizes. Based on the structural hot spot stress, they compared the test results of full-scale and small-scale specimens and found that the two slopes of the S-N curves of the samples were the same. [PERSON] et al. [13] studied the crack propagation of stainless steel microstructure based on the digital image correlation method. Combined with the fatigue test data, it is demonstrated that the crack growth rate is correlated with the accumulated strain. [PERSON] et al. [14] conducted fatigue tests on different types of welded joints, found that the change of stress gradient at the weld toe was greatly affected by the radius of the weld toe, and proposed a fatigue life prediction method that is insensitive to the joint type. [PERSON] et al. [15] measured the fatigue limit of titanium alloy welded joints of two materials, TC11 and TC17, by linear friction welding. It was found that with the increase in the amplitude and frequency of the applied vibration, the fatigue limit showed a trend of high first and then low, and the correction parameters for the determination of the fatigue limit were proposed. [PERSON] et al. [16] applied the finite element method to calculate the nodal forces and bending moments and obtained the structural stress at the welding position based on the free-body section method. Fracture mechanics is used as the theoretical basis, and stress parameters related to fatigue life are incorporated. Not only the effect of load action mode and plate thickness on fatigue strength is considered, but also the effect of stress concentration on fatigue strength at the sudden change of position of the welded structure is studied. After synthesizing the above influencing factors, the calculation formula of equivalent structural stress \(\Delta Ss\) is derived. [PERSON] et al. [17] analyzed the stress singularity inside the steel and the overall singular mode shape through the finite element analysis method.