Selection of calculation methods for accounting complex stress-strain state and mean cycle stress for the origin of fatigue crack in elastic clamp localisation

Introduction. The authors conducted valid accounting methods choice of complex stress-strain state and mean stress in the calculations of elastic clamps of intermediate rail fastenings nodes connected with the localisation of potentially critical sites under the condition of fatigue durability. Methods that enable to most accurately localise places of fatigue fractures has been determined.
Materials and methods. The elastic clamp CP 369.102 (clamp ZhBR-65) was chosen as the clamp under study. The selection of potential methods for accounting complex stress-strain state and mean cycle stress for the origin of a fatigue crack in an elastic clamp localisation was carried out through a review and analysis of existing approaches. A finite element model of the elastic clamp was developed for conducting virtual tests. Full-scale fatigue tests of the elastic clamps were performed according to the developed test procedure. In order to compare the results of the full-scale fatigue tests and the virtual experiments, 3D scanning of the fractured clamp fragments was employed.
Results. It was established that samples of the elastic clamp CP 369.102, when subjected to full-scale fatigue life tests, failed in two distinct zones with probabilities of 5 % and 95 %, respectively. The results of calculations performed using combined methods for accounting complex stress-strain states and the influence of mean cycle stress demonstrated satisfactory correlation with the experimentally determined locations of fatigue crack initiation in the clamps.
Discussion and conclusion. Combinations of methods for accounting for complex stress-strain states and the influence of mean cycle stress were identified, which allow to localise potentially critical zones of the elastic clamp in terms of fatigue durability during calculations. Further research is planned and aimed at developing a model for the elastic clamp that would enable a sufficiently accurate assessment of its service life based on the current results.

1. Park Y.-C., An C., Sim H.-B., Kim M., Hong J.-K. Failure ana­lysis of fatigue cracking in the tension clamp of a rail fastening system. International Journal of Steel Structures. 2019;19(5):1570–1577. https://doi.org/10.1007/s13296-019-00231-5. EDN: https://elibrary.ru/oiozcc.

2. Xiao H., Guo X., Wang H., Ling X., Wu S. Fatigue damage analysis and life prediction of e-clip in railway fasteners based on ABAQUS and FE-SAFE. Advances in Mechanical Engineering. 2018;10(3):1–12. https://doi.org/10.1177/1687814018767249.

3. Kim S.-H., Fang X.-J., Park Y.-C., Sim H.-B. Evaluation of structural behavior and fatigue performance of a KR-type rail clip. Applied Sciences. 2021;11(24):12074. https://doi.org/10.3390/app112412074. EDN: https://elibrary.ru/dpczcv.

4. Cho J.-G., Kim J.-W., Koo J.-S. A study on fatigue strength impro­ vement for tension clamp of railway using work hardening. IOP Conf. Series: Materials Science and Engineering. 2019;491:012028. https://doi.org/10.1088/1757-899X/491/1/012028.

5. Wang Y.-X., Xiao W.-J., Wang Z.-F., Liu Y., Wang E.-B., Chang H.‑T. Fracture behavior analysis and fatigue assessment of the spring clip in heavy-haul railway. Fatigue and Fracture of Engineering Materials and Structures. 2024;47(10):3658–3672. https://doi.org/10.1111/ffe.14401. EDN: https://elibrary.ru/xcqxop.

6. Liu Y., Jiang X., Li Q., Liu H. Failure analysis and fatigue life prediction of high-speed rail clips based on DIC technique. Advances in Mechanical Engineering. 2021;13(12):1–13. https://doi.org/10.1177/16878140211066225. EDN: https://elibrary.ru/hykfco.

7. Liu Y., Li Q., Jiang X., Liu H., Yuan X., Zhu Z. The effect of material static mechanical properties on the fatigue crack initiation life of rail fastening clips. Advances in Civil Engineering. 2021;2021(1):1366007. https://doi.org/10.1155/2021/1366007. EDN: https://elibrary.ru/tmxhjs.

8. Ferreño D., Casado J. A., Carrascal I. A., Diego S., Ruiz E., Saiz M., Sainz-Aja J. A., Cimentada A. I. Experimental and finite element fatigue assessment of the spring clip of the SKL-1 railway fastening system. Engineering Structures. 2019;188:553–563. https://doi.org/10.1016/j.engstruct.2019.03.053.

9. Liu Z., Tsang K. S., Liu Y., Pang J. H. L. Finite element and experimental study on multiaxial fatigue analysis of rail clip failures. Fatigue and Fracture of Engineering Materials and Structures. 2020;43(10):2390–2401. https://doi.org/10.1111/ffe.13310. EDN: https://elibrary.ru/fnemrs.

10. Xie M., Wei K., Liu Y., Li J., Zhao Z., Wang P. Fatigue life prediction and verification of railway fastener clip based on critical plane method. International Journal of Applied Mechanics. 2024;16(05):2450053. https://doi.org/10.1142/s1758825124500534. EDN: https://elibrary.ru/beereu.

11. Papuga J., Vízková I., Lutovinov M., Nesládek M. Mean stress effect in stress-life fatigue prediction re-evaluated. MATEC Web of Confe­ rences. 2018;165:10018. https://doi.org/10.1051/matecconf/201816510018.

12. Strizhius V. E. Methods for fatigue life analysis of aircraft structural elements under multi-axis loading. Civil Aviation High Technologies. 2013;187:65–73. (In Russ.). EDN: https://www.elibrary.ru/pxqkhn.

13. Findley W. N. A theory for the ef fect of mean stress on fatigue of me­tals under combined torsion and axial load or bending. Journal of Engi­neering for Industry. 1959;81(4):301–305. https://doi.org/10.1115/1.4008327.

14. Brown M. W., Miller K. J. A theory for fatigue failure under multiaxial stress-strain conditions. Proceedings of the Institution of Mecha­ni­cal Engineers. 1973;187(1):745–755. https://doi.org/10.1243/PIME_PROC_1973_187_161_02.

15. Fatemi A., Socie D. F. A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue and Fracture of Engineering Materials and Structures. 1988; 11(3):149–165. https://doi.org/10.1111/j.1460-2695.1988.tb01169.x.

16. Kim J.-H., Park Y.-C., Kim M., Sim H.-B. A fatigue reliability assessment for rail tension clamps based on field measurement data. Applied Sciences. 2022;12(2):624. https://doi.org/10.3390/app12020624.EDN: https://elibrary.ru/dltxjo.

17. Glinka G., Wang G., Plumtree A. Mean stress ef fects in multi­ axial fatigue. Fatigue and Fracture of Engineering Materials and Struc­ tures. 1995;18(7–8):755–764. https://doi.org/10.1111/j.1460-2695.1995.tb00901.x.

18. Ali R., Shehbaz T., Felicis D. D., Sebastiani M., Bemporad E. Investigations into fatigue failure in e-type fastening clips used in railway tracks. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2020;235(7):898–905. https://doi.org/10.1177/0954409720967802. EDN: https://elibrary.ru/beddby.

19. Hasap A., Noraphaiphipaksa N., Kanchanomai C. Influence of malposition on the performance of elastic rail clip: Toe load, stress, and friction. Structures. 2020;28:2661–2670. https://doi.org/10.1016/j.istruc.2020.10.073. EDN: https://elibrary.ru/buusua.

20. Xiao H., Wang J.-B., Zhang Y.-R. The fractures of e-type fastening clips used in the subway: Theory and experiment. Engineering Failure Ana­ lysis. 2017;81:57–68. https://doi.org/10.1016/j.engfailanal.2017.07.006.

21. Ballard P., Dang Van K., Deperrois A., Papadopoulos Y. V. High cycle fatigue and a finite element analysis. Fatigue and Fracture of Engineering Materials and Structures. 1995;18(3):397–411. https://doi.org/10.1111/j.1460-2695.1995.tb00886.x.

22. McDiarmid D. L. A general criterion for high cycle multiaxial fatigue failure. Fatigue and Fracture of Engineering Materials and Structures. 1991;14(4):429–453. https://doi.org/10.1111/j.1460-2695.1991.tb00673.x.

23. Bourago N. G., Zhuravlev A. B., Nikitin I. S. Models of multiaxial fatigue fracture and service life estimation of structural elements. Mecha­ nics of Solids: A Journal of Russian Academy of Sciences. 2011;(6):22–23. (In Russ.). EDN: https://www.elibrary.ru/pepwlh.

24. Yu Z.-Y., Zhu S.-P., Liu Q., Liu Y. A new energy-critical plane damage parameter for multiaxial fatigue life prediction of turbine blades. Materials. 2017;10(5):513. https://doi.org/10.3390/ma10050513.

25. Berezin V. O., Zamukhovsky A. V., Ef imov A. A., Grechanik A. V. Validation of finite-element model of clamp of rail fastening system. Russian Railway Science Journal. 2025;84(2):113–125. (In Russ.). EDN: https://elibrary.ru/qyogfn.

26. Chu C.-C., Conle F. A., Bonnen J. Multiaxial stress-strain mo­deling and fatigue life prediction of SAE axle shafts. Advances in Multi­ axial Fatigue, ASTM STP 1191. American Society for Testing and Materials. 1993;1191:37–54. https://doi.org/10.1520/STP1191‑EB.

27. Dowling N. E., Calhoun C. A., Arcari A. Mean stress ef fects in stress-life fatigue and the Walker equation. Fatigue and Fracture of En­ gineering Materials and Structures. 2009;32(3):163–179. https://doi.org/10.1111/j.1460-2695.2008.01322.x.

28. Tamagawa S., Kataoka H., Deshimaru T. A Fatigue Limit Diagram For Plastic Rail Clips. Computers in Railways XIV. 2014;135:839–848. https://doi.org/10.2495/CR140701.