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.

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.

In this paper, a new fatigue life evaluation method, namely augmented-reverse notch equivalent stress method, is proposed for titanium alloy welded structures with stress singularities. First, a new three-parameter power function model is proposed in this paper, and the notch stress equivalent value method with correction factor is deduced. Combining the two, the theoretical framework of the augmented-reverse notch equivalent stress method is obtained. Within this framework, the fatigue test data of four titanium alloy welded joints with the same grade were used for analysis, and a new three-parameter power function model of titanium alloy welded structure was established. According to the calculation method of the notch equivalent stress correction factor, the correction factor suitable for the titanium alloy welded structure was obtained. Finally, the fatigue test data, different from the above titanium alloy welded structure, are used to verify the augmented-reverse notch equivalent stress method. The verification results show that the augmented-reverse notch equivalent stress method improves the effectiveness and accuracy of fatigue life evaluation and establishes a new life evaluation method for titanium alloy welded structures with stress singularities.

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.

Purpose: The stress ratio has a significant effect on the fatigue crack growth rate (FCGR). The traditional stress ratio normalization model has problems due to incomplete consideration of correction coefficients and an unsatisfactory normalization effect at high stress ratio. Design/methodology/approach: This paper proposes an improved stress ratio normalization model. By correcting the slope and translation intercept of the FCGR curves at different stress ratios, the unknown parameters were solved and optimized by combining them with the genetic algorithm (GA). Under the small range yield condition, the scope of application of the improved model was extended to the range of elastic-plastic mechanics. Findings: Titanium alloys, aluminum alloys and steels were used as research objects. The effects of stress ratio normalization of traditional and improved models were compared in the range of linear elastic mechanics. The improved model can effectively gather the FCGR data at high and low stress ratios on the same straight line. The coefficients of determination R2 of the linear fits to the data were all raised to 0.98 after normalization. The improved models in the elastic-plastic mechanics range exhibited the same normalization effect. The coefficients of determination R2 were 0.98, 0.97 and 0.98, respectively. Originality/value: The results show that the improved model based on the GA exhibits good stress ratio normalization effect and wide applicability. It provides a new theoretical basis and reference for variable amplitude fatigue crack growth (FCG) life prediction.