In the small sample fatigue test space, in order to obtain the master S-N curves of each reliability of the titanium alloy welded structures. Firstly, the Bootstrap method is combined with the equivalent structural stress to determine the minimum number of samples under each level of equivalent structural stress, and the appropriate resampling times are obtained through residual analysis. Secondly, based on the fatigue test data of titanium alloy welded joints with different plate thicknesses, materials, types and stress ratios, the linear regression model of master S-N curves are determined by using the traditional group method and Bootstrap method, and its reliability is 99%, 95%, 84%, and 50% respectively. Finally, the comparative analysis shows that the titanium alloy fatigue test samples obtained by Bootstrap method tends to be more stable, which improves the fitting degree of the titanium alloy fatigue life test data and the accuracy of the fatigue life prediction when the sample is small. A more accurate regression model of the master S-N curves of titanium alloy welded structures was obtained and verified.

Purpose: This paper aims to study and modify the notch equivalent stress method, as well as to establish the notch equivalent stress range S–N curve and apply it to the fatigue assessment of engineering examples.Design/methodology/approach: This paper studies the notch equivalent stress method and puts forward the concept of “singular equivalent crack”. Combined with the fatigue test results, by proposing to consider the singular coefficient of the transition angle of the welded structure and the introduction of material correction factors, this paper derives the notch equivalent stress equation for commonly used welded joints applicable to steel, and finally establishes the notch equivalent stress range of the S–N curve.Findings: The obtained results show that the dispersion of fatigue data is 65.6 and 75.4% for T-joints and transverse cross-joints, respectively, under S–N curves using notched equivalent stress compared to the nominal stress range. The fatigue evaluation error of the modified notch equivalent stress equation for transverse cross welded joints improved by 50.65%, 53.1 and 39.6% on average, respectively, compared to the original other methods. The fatigue evaluation error for T-joints improved by 13.4 and 13.9%, respectively, compared to the original other methods.Originality/value: There are relatively few studies on the fatigue assessment of notch equivalent stress method. In this paper, the notch equivalent stress method is studied and modified to improve the accuracy of fatigue assessment of welded structures with singular stresses.

Purpose: In order to extend the application of the original octagonal Goodman–Smith fatigue limit diagram, which is commonly used for the evaluation of structure fatigue stress in engineering, a modification of it is proposed for the structure made of S355 steel (commonly used in high-speed electric multiple units (EMUs) bogie frame).Design/methodology/approach: The modification is made based on Deutscher Verband für Schweißen und verwandte Verfahren e. V. (DVS) 1612 standard and the γ-P-S-N curve, with consideration of the fatigue evaluation requirements of different survival rates and confidence levels. The verification of the modification is performed for three welded joints and for the comparison with the experimental data.Findings: The results indicate that the design survival rate, the design safety margin and the fatigue stress evaluation of welded joint types are all improved by using the modified diagram.Originality/value: There are relatively few studies on modifying octagonal Goodman–Smith fatigue limit diagram. In this paper, a modified diagram is proposed and applied in order to ensure the safety and durability of key welded structures of rail vehicles.

With the continuous increase in high-speed train operation speeds, lightweight bogie design has become a key means to enhance dynamic performance, which also increases the risk of structural fatigue. High-frequency wheel–rail excitations are transmitted to the bogie frame and couple with its higher-order modes at around 200 Hz, inducing local high-frequency resonance. This coupling markedly increases the stress amplitude within the affected frequency range and accelerates vibration-induced fatigue damage. This study investigates the vibration fatigue characteristics of a bogie frame with an inner axle box under high-speed operation and wheel polygon wear conditions. Using a high-speed wheel–rail interaction test rig, dynamic stresses and the vibration acceleration of the bogie frame are measured under different speeds and polygon orders. Based on modal analysis and vibration fatigue methods, a high-frequency vibration fatigue assessment method for the bogie is developed. Wheel polygon significantly amplifies mid-to-high-frequency vibration energy, and for the bogie frame with an inner axle box, pronounced modal coupling is observed at around 200 Hz. In particular, under the 11th-order polygon condition, the equivalent stress at critical locations such as the traction motor seat weld seam exceeds the fatigue limit, while the effect of the 20th-order polygon is relatively mitigated. The proposed vibration fatigue assessment method provides a theoretical basis for the safe design and operational maintenance of high-speed trains with bogie frames with inner axle boxes.

In order to reduce the potential safety hazards in the operation of rail vehicles, a new parameter table optimization algorithm based on the particle swarm optimization algorithm is proposed to carry on the failure assessment and fatigue life calculation of welded joints. This algorithm reduces the number of iterations by adding connection pools to connect the parameter selection database. In addition, based on this algorithm, combined with Python language and BS7910 standard, a calculation program for failure assessment and fatigue crack growth life is written. The algorithm program is validated by taking the commonly used T-type, butt, and lap joints as examples. In terms of failure assessment, the calculation results of the algorithm program are securer and more conservative, and the safety accuracy of the algorithm program is improved by 8%–12%. In terms of fatigue crack growth life, the error between the calculated value of the algorithm program and the test data is within the engineering allowable range. At the same time, the algorithm program can give the evaluation calculation results more intuitively and quickly, which provides a reference for the failure assessment and life calculation of the welded structure.