Cause Analysis and Solution of Premature Fracture of Suspension Rod in Metro Gear Box

Abstract

Through the appearance observation of suspension rod in the metro gearbox, macro and micro observation of the fracture and quantitative analysis of the fracture, combined with the metallographic and hardness examination results of the boom, the finite element model was established and the force analysis of suspension rod was carried out to explore the causes of the fracture of the gearbox boom. The results show that the nature of suspension rod fracture is fatigue. The cause of its fatigue fracture is related to the low fatigue tolerance for booms in metro operation, and the surface shallow decarburization plays a role in promoting the fatigue fracture of suspension rod. The life of fatigue crack growth in the boom is 819 stations (or 1210 km), and the fatigue initiation life is 522,452 km.

1. Introduction

The gearbox is a key component in metro vehicles and its main function is to transmit the power output from the traction motor to the wheel pairs to drive the vehicle [1]. The gearbox is connected to the lifting base on the bogie frame using a spreader bar. The spreader bar device carries the loads that occur during the operation of the gearbox, including those caused by traction and braking, vibration shocks and loads caused by short circuits in the traction motor [2,3].

The gearbox boom is a traction device installed on the bogie of a rail vehicle to improve the efficiency of traction and braking force transfer between the locomotive and the bogie [2]. The installation of the boom enables the gearbox to withstand the vibration impact from the wheelset during vehicle operation. If there is a relative movement between the wheelset and the bogie frame during operation, the rubber nodes on the boom device will enable the gearbox mounted on the wheelset to move consistent with the displacement of the wheelset so as not to affect other components [4,5,6]. The boom plays a key role in the safe operation of the gearbox and the vehicle.

F. CURÀ et al. [7] carried out numerical simulations using the three-dimensional extended finite element method to investigate the relationship between the rim crack expansion path and the thickness of the web during bending fatigue failure of thin-sided gears, showing that the thickness of the web affects the rim crack expansion state and the form of failure. Giovanni Meneghetti [8] and others carried out single tooth fatigue tests on gears with hardened tooth surfaces, predicted their fatigue life based on the test results and compared it with that of unhardened gears and found that the sample-based method had the same accuracy as the baseline gear-based method, provided that the material notch sensitivity factor was properly calibrated. Edoardo Conrado et al. [9] compared the flexural fatigue strength of carburized gears with that of nitrided gears. Single tooth flexural fatigue (STBF) tests were carried out on gears of the two different processes, and S-N curves were obtained for both processes to estimate their fatigue limits. The S-N curves for both processes were obtained and the fatigue limits were estimated.

In this paper, the appearance of the fractured boom was inspected, and the fracture was analyzed by macroscopic and microscopic observation, chemical composition check and mechanical properties evaluation, etc. The fracture mechanism of the boom was determined, and the causes of its production were analyzed qualitatively and quantitatively, to provide analytical methods and references for avoiding the recurrence of such incidents.

2. Materials and Processing Methods

A line metro was inspected and three pieces of gearbox boom were found to be fractured in different units of the vehicle, as shown in Figure 1. The boom material is C45E4 steel, processed in the following steps: raw materials-forging-heat treatment-shot blasting (Φ2 mm steel balls, time about 25–30 min)-magnetic particle testing-primer coating-Machining-Galvanizing (threaded rod section)-Inventory inspection-Finish coating (paint thickness required ≥120 μm). The heat treatment system is as follows: normalizing temperature 870–890 °C, air cooling, quenching temperature 840–860 °C, water cooling, tempering temperature 530–600 °C, air cooling. The technical requirements for the mechanical properties of the boom material are shown in Table 1.

3. Result Analysis

3.1. Macroscopic Observation

The fracture occurred at the bend transition of the boom structure [10]. Typical fatigue beach marks and extended radial marks are visible in the fracture, and the origin of the fracture can be judged from the direction of convergence of the prisms to be located on the lateral side of the boom width, and the crack is extended along the boom width. From the origin of the fracture to about 24 mm from the origin of the fracture, the fracture surface in the early-term propagation area is flat and the fracture fatigue beach mark is not obvious. From 24 mm to 47 mm from the origin of the fracture, the obvious fatigue beach mark feature is visible in the section. From 47 mm to 82 mm from the origin of the fracture, the fatigue feature is visible in the width of about 4 mm on both sides, and the section in the middle of the width direction is a rough tearing area. From 82 mm to 90 mm from the origin of the fracture, the obvious fatigue beach mark feature is visible in the section. The obvious fatigue beach mark can be seen from 82 mm to 90 mm from the origin of the fracture. Finally, after 90 mm from the origin of the fracture, the section is rough and is a transient fracture zone; see Figure 2 and Figure 3.

3.2. SEM Images of Fracture Surfaces

The boom fracture was ultrasonically cleaned with acetone and then analyzed in a scanning electron microscope for observation [11,12,13]. The origin of the boom fracture is located on the surface, no metallurgical defects are seen, fatigue beach marks and a large number of fine fatigue striations are visible during the cracking process, and the width of the fatigue beach marks from 24 mm to the origin of the fracture to about 90 mm from the origin of the fracture is about 0.1~0.14 mm, and the transient fracture area is characterized by dimples, see Figure 4.

3.3. Metallography Analysis

A longitudinal metallographic specimen was taken from the origin of the boom fracture and sent for inspection [14,15], with the metallographic grinding surface perpendicular to the fracture surface, and the macroscopic morphology after etching with 4% nitric acid in alcohol is shown in Figure 5.

It can be observed from Figure 6 that in the unetched high magnification morphology of the origin of the boom fracture sent for inspection, the area can be seen containing fine cracks and small surface pits, and no obvious coarse inclusions and other defects exist. The microstructure of the origin of the fracture after etching is fully decarburized, with a thickness of approximately 0.25 mm, and a small amount of plastic deformation in the local area below the origin of the fracture near the inner surface of the boom.

When the inner surface of the boom on the fatigue source side of the fracture was observed, cracks (Crack 1, Crack 2 and Crack 3) were found extending from the inner surface of the boom in a vertical direction to the interior, with crack lengths of approximately 0.13 mm, 1.95 mm and 1 mm respectively, and distances to the fracture of approximately 0.5 mm, 5 mm and 10.5 mm respectively, as shown in Figure 7. It is also seen that the thickness of the fully decarburized layer near the inner surface of the boom has an overall decreasing trend from the origin of the fracture downwards (0.25–0.05 mm), but local areas can be thick or narrow.

Near the origin of the fracture, five different microstructure areas (I, II, III, IV and V) can be seen from the inner surface of the boom to the core of the boom, as shown in Figure 8, with micro-Vickers hardness values of approximately 137.0 HV0.2 (Microstructure I), 246.0 HV0.2 (Microstructure II), 265.0 HV0.2 (Microstructure III), 250.0 HV0.2 (Microstructure IV), 252.0 HV0.2 (Microstructure V), 250.0 HV0.2 (Microstructure IV) and 252.0 HV0.2 (Microstructure V). The microstructure of the inner surface of the spreader bar to the core gradually transitions from fully decarburized (microstructure I) to tempered sorbite and white ferrite with a reticulated distribution, with some of the ferrite developing needle-like into the grain (microstructure II), and then to tempered sorbite that maintains the martensitic phase (microstructure III). The white ferrite in microstructure IV is slightly more severe than in microstructure V. Microstructures I and II are known as the transition zone. Below the origin of the fracture, the transition zone from the inner surface of the boom to the core of the boom becomes progressively narrower. The microstructure of the fractured boom is finer-grained, with microstructure I (fully decarburized) having a grain size of 8.5 and microstructures II to V having a grain size of 9.

The non-metallic inclusions in the gearbox boom were assessed in accordance with method A of GB/T 10561-2005 “Method for the determination of non-metallic inclusions in steel” and the non-metallic inclusions in type A (sulfides), B (alumina), C (silicates) and D (spherical oxides) of the fracture boom were recognized as coarse inclusions, the level is less than 0.5 [16].

3.4. Chemical Composition Test Results

The chemical composition of the fracture boom was tested according to the “Gearbox Boom Procurement Standard Book” provided by the client, and the test method was GB/T 4336-2002 “Carbon steel and low and medium alloy spark source yard emission spectroscopy method (conventional method)”. The results are shown in Table 2. The chemical composition of the fracture boom sent for testing met the technical requirements provided by the commissioner.

3.5. Mechanical Performance Testing

The tensile test, hardness test and impact test were carried out on the boom test according to the relevant standards respectively [17,18,19]. Hardness tests were carried out on the surface and core hardness of the boom. Specimens were taken in the positions shown in Figure 1 and subjected to tensile and impact tests, and the results are shown in Table 3. It can be seen that the yield strength of the fracture boom sent for inspection is lower than the technical requirements provided by the commissioner, while the tensile strength, axial elongation and area reduction in the tensile test meet the relevant technical requirements. The average hardness of the surface decarburization layer is 167 HB, which is much lower than the technical requirements (201~269 HB). The average hardness of the core is 230 HB, which meets the technical requirements (201~269 HB). The impact performance of the boom meets the technical requirements provided by the commissioning party.

4. Finite Element Analysis

In the gearbox transmission system, the gearbox is suspended from the bogie frame by means of a boom connection. The boom is not only subjected to tensile and compressive loads during the use of the gearbox but also to various impact loads during operation [20]. In order to analyze whether the strength of the boom meets the design requirements and analyze the stress distribution of the boom and make suggestions and recommendations for design improvements, a calculation of the static strength of the boom is required.

4.1. Model Simplification

In this paper, the finite element calculations are carried out using Pro/Engineer software for 3D modeling, and the model is imported into the finite element software for finite element analysis calculations.

The boom is first analyzed under different operating conditions to derive its maximum force load and thus its stress distribution under this load. The boom is subjected to a force of $Fr$, the pinion end is driven by the motor and the torque applied is $Md$. The torque at the large gear end is $Md\times i$, as can be seen from the transmission relationship between the large and small gears.

The input parameters of the motor, without regard to vibration, are as follows:

• The rated torque of the motor is: 955 Nm;

• The maximum traction (braking) torque of the motor is: 1361 Nm;

• Short-circuit torque of the motor is: 8000 Nm;

• Transmission ratio $i$: 7.69;

• $L$ is the distance from the boom centerline to the axle centerline, 421.68 mm;

• Then the torque balance gives $F_r=Md\times (1+i)/L$;

• At rated operation: $F_{r1}=955\times (7.69 + 1)/421.68$ = 19.68 kN;

• At start-up: $F_{r2}=1361\times (7.69+1)/421.68$ = 28.05 kN.

The input parameters for the case where vibration (vertical) is considered are as follows.

• $W$ is the mass of the case, 131 kg;

• $W_P$ + $Wc/2$ is the pinion weight and half coupling mass, 20.6 kg;

• $W_r$ is the boom mass, 15.7 kg;

• Maximum vertical vibration acceleration at the boom, ±15 g;

• Vibration force: $Fa=(W/3+Wp+Wc/2+Wr)\times 15 \mathrm{g}$ = 11.77 kN.

Boom force load:

• Rated working condition: $F1=Fr1+Fa$ = 31.45 kN;

• Start-up condition: $F2=Fr2+Fa$ = 39.82 kN.

The boom finite element model is shown in Figure 9.

4.2. Calculation Results

The stress distribution of the boom under the two working conditions is obtained by calculation, respectively, see Figure 10 (stresses in MPa).

As can be seen from the calculation results, in the rated and start-up two calculation conditions: boom maximum stress value is: 132.5 MPa, 167.8 MPa, maximum stress values are less than the boom material yield strength (≥490 MPa).

4.3. Fatigue Strength Assessment Methods

According to the relevant standards UIC 615-4 and TB/T 3548-2019, the Goodman diagram method is mainly used for fatigue strength assessment [21,22]. Fatigue strength assessment: select each node on the boom finite element model, simplify the stress state at each point into a uniaxial stress state based on the direction of the maximum principal stress for each working condition, calculate the stress value at each point σ_max and the minimum σ_min and calculate the equivalent average stress and equivalent force amplitude at each point according to the following formula:

(1)${\sigma }_{\mathrm{m}}=\frac{{\sigma }_{\max }+{\sigma }_{\min }}{2}$

(2)${\sigma }_a=\frac{{\sigma }_{\max }-{\sigma }_{\min }}{2}$

For each working condition, the relatively dangerous nodes on the boom are selected, and the maximum and minimum stress values of these nodes are calculated under the positive and negative rotation of the gearbox and different vibration loads. The average stress and stress amplitude of each point is calculated according to the above method, and the equivalent average stress and equivalent stress amplitude of each node are put into the Goodman diagram [23] for fatigue strength assessment. The fatigue strength assessment results of each node are shown in Figure 11, which shows that the nodes selected on the boom fall within the Goodman fatigue limit, and the fatigue strength of the boom meets the design requirements.

5. Quantitative Fracture Analysis

The technique of studying the fracture surface of metal components is also one of the basic tasks and important methods of failure analysis [24]. The quantitative analysis of the fracture surface is used to determine the fatigue crack propagation rate of the component in actual operation, to provide a reasonable estimate of the life of fatigue crack growth in the component and to provide a reference for determining the cause of component failure [25].

The force analysis of the boom is mainly subjected to torque and vibration stresses. As the metro starts to stop (each stop), the torque increases first, smoothly in the middle and then decreases in a changing pattern, and the torque state of the metro running at each stop can be equated to a trapezoidal wave. The vibration stress during boom operation is a random fluctuation and can be equated to a triangular wave. Therefore, the stress variation curve of the boom can be equated to a trapezoidal wave superimposed on a triangular wave, see Figure 12.

Combined with the observation results of the boom fracture, the boom fracture shows the shape of fatigue beach marks and fatigue striations, which correspond to the torque and vibration stresses that the boom is subjected to. Therefore, the fatigue beach marks on the fracture are used to quantitatively analyze the life of fatigue crack growth in the boom [26].

The fatigue beach marks on the fracture were observed and analyzed, and the statistical results are shown in Table 4. A total of 819 fatigue beach marks were analyzed using the mean value method for the life of fatigue crack growth in the boom, and the number of fatigue beach marks in the extended phase of the boom was 819.

The metro line has a total of 18 stations and a route length of 26.6 km, with an average distance of approximately 1.5 km per station. Quantitative analysis of fractures gives 819 fatigue beach marks for failed boom fractures, with a life of fatigue crack growth of 819 stations running, corresponding to a running distance of 819 stations ÷ 18 stations × 26.6 km = 1210 km.

6. Discussion

Through the above analysis, it can be seen that:

(1) The boom fractures at the transition of the structural bend, the origin of the fracture, are located at the inner edge of the bend, and typical fatigue beach marks and fatigue striations are visible in the extended area. From this, the nature of the fracture of the boom can be judged as fatigue.

(2) The boom originates at the inner edge of the bend, indicating a relatively high initial stress on the boom. A large number of rapid tearing features are also visible in the middle and late stages of the spreader bar fracture extension, also indicating high stress on the spreader bar. According to the commissioner, the metro line has high motor power and is subject to higher forces, approximately 10% to 20% higher than other lines, and three same-mode failures occurred between 360,000 km and 560,000 km of operation (the line runs a total of 39 trains), which was analyzed as possibly being a low boom fatigue tolerance in the line operating condition. From the metallographic analysis, it can be seen that there is a decarburization layer in the range of 0.3 mm on the surface of the boom, with a hardness of 167 HB in the decarburization zone, much lower than the hardness of the core (230 HB), which plays a role in promoting fatigue cracking of the boom.

(3) By finite element calculation, the maximum stress point of the boom under the rated and start-up conditions is located at the fracture corner. The maximum stress values of the boom under the rated and start-up conditions are 132.5 MPa and 167.8 MPa respectively, and the maximum stress values are less than the yield strength of the boom material (≥490 MPa).

(4) The results of the quantitative analysis of the fracture indicate that the life of fatigue crack growth in the boom is 819 stations (equivalent to 1210 km), according to the fatigue initiation life is equal to the total life minus the life of fatigue crack growth, it is known that the fatigue initiation life of the boom is (523,662 − 1210) km = 522,452 km.

7. Conclusions

The fatigue life margin of the boom is low, which is the main reason for fatigue fracture. The decarburization of the shallow surface also promotes the fatigue fracture of the suspension rod in the metro gearbox.

The recurrence of this boom fracture problem can be avoided from the following aspects.

In order to prevent decarburization and not affect the performance of the boom, the machining allowance at the corner of the boom is increased so that the depth of the decarburized layer is less than the machining allowance and can be completely cut off when mechanical machining is carried out. The correct heat treatment process operation can then be strictly implemented.

In order to reduce the magnetic particle testing cycle of the boom in service, the boom with fatigue cracks was replaced in time and all the booms of the batch were replaced during the subsequent overhaul period.

Author Contributions

Z.X. conducted the research and analyzed the results under the supervision of X.L. and W.L. Z.X. contributed to the design of experiments and morphology analysis during the research activities. Z.X. and H.L. contributed to image processing and data calculation. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Appearance of booms. (a) Sampling areas; (b) Appearance of fractured booms.

Figure 2. Macroscopic view of boom fracture (Unit: mm).

Figure 3. Boom fracture body view. (a) Pre-extension region; (b) Mid-term propagation area; (c) Late-term propagation area; (d) Transient fracture zone.

Figure 4. Boom fracture microscopy. (a) Early-term propagation area; (b) Mid-term propagation area fatigue beach marks and fatigue striations; (c) Late-term propagation area fatigue beach marks and fatigue striations; (d) Characteristics of the transient fracture zone of the dimple.

Figure 5. The macroscopic metallographic surface of the origin of the boom fracture sent for inspection.

Figure 6. Unetched high magnification morphology of the origin of the boom fracture sent for inspection.

Figure 7. Crack characteristics of the sending boom near the inner surface (below the origin of the fracture). (a) Crack 1; (b) Crack 2; (c) Crack 3.

Figure 8. Microstructure of the boom near the fatigue source from the inner surface of the boom to the core.

Figure 9. Boom finite element model.

Figure 10. Stress distribution in the boom under two operating conditions. (a) Stress nephogram of the boom at rated working conditions; (b) Stress nephogram of the boom at start-up.

Figure 11. Fatigue strength assessment of booms.

Figure 12. Boom force analysis per station.

Table 1

Technical requirements for the mechanical properties of the boom.

Yield Strength/MPa	Tensile Strength/MPa	Elongation/%	Area Reduction in Tensile Test/%	Impact Value/J/cm2	Hardness/HB
≥490	≥690	≥17	≥45	≥78	201~269

Table 2

Test results for the chemical composition of gearbox boom sent for inspection (mass, %).

Ingredient	C	Si	Mn	P	S
Composition	0.462	0.230	0.667	0.006	0.001

Table 3

Gearbox boom mechanical properties test results.

Specimen	Tensile Test				Brinell Hardness		Impact Value (J)
	Yield Strength (MPa)	Tensile Strength (MPa)	Axial Elongation (%)	Area Reduction in Tensile Test (%)	Surface Decarburization	Core Hardness
AVG	476	753.3	22.8	67.3	167	230	83.3
STD	7.21	6.66	1.44	0.58	7.94	4.00	4.62

Table 4

Data relating to fatigue beach mark spacing at the boom break.

No.	Length from the Origin of the Fracture an (mm)	Average Distance between Beach Marks (mm)	N i
1	0~24	0.10	240
2	24~47	0.10	230
3	47~82	0.12	292
4	82~90	0.14	57
5	-	-	ΣNn = 819

References

1. Ruobing, K.; Zhigang, K. Structural Strength Analysis of High Current Connector for Rail Transit. J. Phys. Conf. Ser.; 2021; 2095, 012013.

2. Mejuto Diego, G. Theorizing nation-building through high-speed rail development: Hegemony and space in the Basque Country, Spain. Environ. Plan. A Econ. Space; 2022; 54, pp. 554-571. [DOI: https://dx.doi.org/10.1177/0308518X211061747]

3. Wangang, Z.; Wei, S.; Hao, W. Vibration and Stress Response of High-Speed Train Gearboxes under Different Excitations. Appl. Sci.; 2022; 12, 712. [DOI: https://dx.doi.org/10.3390/app12020712]

4. Li, X.; Yang, Y.; Wu, Z.; Yan, K.; Shao, H.; Cheng, J. High-accuracy gearbox health state recognition based on graph sparse random vector functional link network. Reliab. Eng. Syst. Saf.; 2022; 218, 108187. [DOI: https://dx.doi.org/10.1016/j.ress.2021.108187]

5. Feng, Y.; Xiaochun, Z.; Chunyu, L.; Jun, L. Analysis and Research on Fracture Cause of Fixed Shaft of Torsion Arm of Wind Turbine Gearbox. J. Phys. Conf. Ser.; 2021; 2133, 012039. [DOI: https://dx.doi.org/10.1088/1742-6596/1993/1/012039]

6. Hu, Z.; Yang, J.; Yao, D.; Wang, J.; Bai, Y. Subway Gearbox Fault Diagnosis Algorithm Based on Adaptive Spline Impact Suppression. Entropy; 2021; 23, 660. [DOI: https://dx.doi.org/10.3390/e23060660] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/34070261]

7. Curà, F.; Mura, A.; Rosso, C. Effect of rim and web interaction on crack propagation paths in gears by means of XFEM technique. Fatigue Fract. Eng. Mater. Struct.; 2015; 10, pp. 1237-1245. [DOI: https://dx.doi.org/10.1111/ffe.12308]

8. Meneghetti, G.; Dengo, C.; Lo Conte, F. Bending fatigue design of case-hardened gears based on test specimens. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.; 2018; 11, pp. 1953-1969. [DOI: https://dx.doi.org/10.1177/0954406217712278]

9. Conrado, E.; Gorla, C.; Davoli, P.; Boniardi, M. A comparison of bending fatigue strength of carburized and nitrided gears for industrial applications. Eng. Fail. Anal.; 2017; 78, pp. 41-54. [DOI: https://dx.doi.org/10.1016/j.engfailanal.2017.03.006]

10. Shukla, A.; Rai, P. Finite element based modelling and analysis of dragline boom structure. J. Mines Met. Fuels; 2020; 68, pp. 50-56.

11. Zalaznik, A.; Nagode, M. Experimental, theoretical and numerical fatigue damage estimation using a temperature modified dirlik method. Eng. Struct.; 2015; 96, pp. 56-65. [DOI: https://dx.doi.org/10.1016/j.engstruct.2015.03.026]

12. Irisarri, A.M.; Pelayo, A. Failure analysis of an open die forging drop hammer. Eng. Fail. Anal.; 2009; 16, pp. 1727-1733. [DOI: https://dx.doi.org/10.1016/j.engfailanal.2008.12.008]

13. Lu, Y.; Ripplinger, K.; Huang, X.J.; Mao, Y.; Detwiler, D. A new fatigue life model for thermally-induced cracking in H13 steel dies for die casting. J. Mater. Process. Technol.; 2019; 271, pp. 444-454. [DOI: https://dx.doi.org/10.1016/j.jmatprotec.2019.04.023]

14. Mellouli, D.; Haddar, N.; Köster, A.; Ayedi, H.F. Thermal fatigue failure of brass die-casting dies. Eng. Fail. Anal.; 2012; 20, pp. 137-146. [DOI: https://dx.doi.org/10.1016/j.engfailanal.2011.11.006]

15. Cui, Z.; Bhattacharya, S.; Green, D.E.; Alpas, A.T. Mechanisms of die wear and wear-induced damage at the trimmed edge of high strength steel sheets. Wear; 2019; 427, pp. 1635-1645. [DOI: https://dx.doi.org/10.1016/j.wear.2019.01.113]

16. General Administration of Quality SupervisionInspection and Quarantine of the People’s Republic of China. GB/T 10561-2005 Determination of the Content of Non-Metallic Inclusions in Steel Standard Rating Chart Microscopic Test Method; 1st ed. China Standard Publishing House: Beijing, China, 2015.

17. China Iron and Steel Industry Association. GB/T 228.1-2021 Metallic Materials—Tensile Testing—Part 1: Method of Test at Room Temperature; 1st ed. China Standard Publishing House: Beijing, China, 2021.

18. China Iron and Steel Industry Association. GB/T 231.1-2018 Metallic Materials—Brinell Hardness Test—Part 1: Test Method; 1st ed. China Standard Publishing House: Beijing, China, 2018.

19. China Iron and Steel Industry Association. GB/T 229-2020 Metallic Materials—Charpy Pendulum Impact Test Method; 1st ed. China Standard Publishing House: Beijing, China, 2020.

20. Statharas, D.; Sideris, J.; Chicinas, I.; Medrea, C. Microscopic examination of the fracture surfaces of a cold working die due to premature failure. Eng. Fail. Anal.; 2011; 18, pp. 759-765. [DOI: https://dx.doi.org/10.1016/j.engfailanal.2010.12.007]

21. International Union of Railways. UIC 615-4 Motive Power Units-Bogies and Running GearBoige Frame Structure Strength Tests; 1st ed. International Union of Railways: Paris, France, 2003.

22. China Railway Bureau. TB/T 3548-2019 General Rules for Strength Design and Test Qualification Specifications for Rolling Stock; 1st ed. China Standards Publishing House: Beijing, China, 2019.

23. Institute of Metals and ChemistryMinistry of Railways Scientific Research Institute. The p-s-N Curves and Goodman’s Atlas for Materials Commonly Used in Railways; 1st ed. Research Report of the Academy of Railway Sciences: Beijing, China, 1999.

24. Liao, Z.; Wenfeng, Z.; Hai, Y. Application of quantitative fracture analysis in assessing the fatigue life of components. Mater. Eng.; 2000; 4, pp. 45-48.

25. Xinling, L.; Weifang, Z.; Chunhu, T. Comparison of fatigue life models for quantitative analysis of different fractures. Mech. Eng. Mater.; 2008; 5, pp. 4-6.

26. Xin, W.; Chunling, X.; Xing, C.; Dianyin, H.; Bo, H.; Rengao, H.; Yuanxing, G.; Zhihui, T. Effect of cold expansion on high-temperature low-cycle fatigue performance of the nickel-based superalloy hole structure. Int. J. Fatigue; 2021; 151, 106377.