ISSN 3041-1815. Physicochemical Mechanics of Materials. 2025.
Volume 61, Issue 5

Fretting wear of elastic half-spaces with a groove in a frictional slip zone

Keywords

elastic half-spaces, groove, slip, fretting wear, limiting shape of the groove, singular integral equation, contact pressure.

Cite as

Malanchuk N. I., Martynyak R. M., and Kozachok O. P. Fretting wear of elastic half-spaces with a groove in a frictional slip zone. Physicochemical Mechanics of Materials. 2025. 61(5), 130-136.

https://doi.org/10.15407/pcmm2025.05.130

Abstract

A method for determining the limiting state after fretting wear of an elastic half-spaces with a groove in their complete contact under the action of alternating shear forces is developed. The limiting stress of bodies after the end of wear is given by the initial shape of the groove and the function of the thickness of the worn-out material in the slip zone. To determine the function of the thickness of the worn-out material, a singular integral equation with a Cauchy kernel is written and its analytical solution is obtained. The limiting shape of the groove and the contact pressure after wear for different values of shear loads, Poisson’s ratio, and width of wear zone are analyzed.

References

  1. D. A. Hills, A. Sackfield, and R. J. H. Paynter, “Simulation of fretting wear in halfplane geometries: Part 1 – The solution for long term wear,” J. Tribology, 131, 031401-1-031401-4 (2009) https://doi.org/10.1115/1.3118785
  2. M. Ciavarella, and D. A. Hills, “Brief note: Some observations on oscillating tangential forces and wear in general plane contacs,” Eur. J. Mechanics: A/Solids, 18, Is. 3, 491-497 (1999). https://doi.org/10.1016/S0997-7538(99)00117-5
  3. T. Liskiewicz, and D. Dini, Fretting Wear and Fretting Fatigue: Fundamental Principles and Applications, Elsevier, Amsterdam (2023).
  4. P. Kennedy, M. B. Peterson, and L. Stallings, “An evaluation of fretting at small slip amplitudes,” in Materials Evaluation under Fretting Conditions, ASTM Spec. Tech. Publ. (1982), pp. 30-48. https://doi.org/10.1520/STP29395S
  5. T. N. Farris, H. Murthy, and J. F. Matlik, “Fretting fatigue,” Comprehensive Structural Integrity, 4, 281-326 (2003). https://doi.org/10.1016/B0-08-043749-4/04080-5
  6. T. Yue, and M. A. Wahab, “A review on fretting wear mechanisms, models and numerical analyses,” Comput. Mater. Contin., 59, No. 2, 405-432 (2019). https://doi.org/10.32604/cmc.2019.04253
  7. M. Ciavarella, and G. Demelio, “A review of analytical aspects of fretting fatigue, with extension to damage parameters, and application to dovetail joints,” Int. J. Solids and Struct., 38, Is. 10, 1791-1811 (2001). https://doi.org/10.1016/S0020-7683(00)00136-0
  8. L. A. Blunt, X. Jiang, S. M. Barrans, L. T. Brown, and H. Zhang, “Understanding initiation and propagation of fretting wear on the femoral stem in total hip replacement,” Wear, 266, Iss. 5-6, 566-569 (2009). https://doi.org/10.1016/j.wear.2008.04.076
  9. J. F. Zheng, J. Luo, J. L. Mo, J. F. Peng, X. S. Jin, and M. H. Zhu, “Fretting wear behaviors of a railway axle steel,” Tribol. Int., 43, Iss. 5-6, 906-911 (2010). https://doi.org/10.1016/j.triboint.2009.12.031
  10. M. Antler, “Survey of contact fretting in electrical connectors,” IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 8, Is. 1, 87-104 (1985). https://doi.org/10.1109/TCHMT.1985.1136462
  11. E. Willert, “A Simple semi-analytic contact mechanical model for tangential and torsional fretting wear of axisymmetric contacts,” Symmetry, 13, Is. 9 (2021). Article number 1582. https://doi.org/10.3390/sym13091582
  12. A. V. Dimaki, A. I. Dmitriev, Y. S. Chai, and V. L. Popov, “Rapid simulation procedure for fretting wear on the basis of the method of dimensionality reduction,” Int. J. Solids Struct., 51, Iss. 25-26, 4215-4220 (2014). https://doi.org/10.1016/j.ijsolstr.2014.08.003
  13. M. Hess, “A study on gross slip and fretting wear of contacts involving a power-law graded elastic half-space,” Facta Universitatis Series: Mech. Eng., 17, Is. 1, 47-64 (2019). https://doi.org/10.22190/FUME190121010H
  14. D. Dini, A. Sackfield, and D. A. Hills, “An axi-symmetric Hertzian Contact subject to cyclic shear and severe wear,” Wear, 265, Iss. 11-12, 1918-1922 (2008). https://doi.org/10.1016/j.wear.2008.04.031
  15. V. L. Popov, “Analytic solution for the limiting shape of profiles due to fretting wear,” Sci. Reports. 4 (2014). Article namber 3749. https://doi.org/10.1038/srep03749
  16. Li Qiang, “Limiting profile of axisymmetric indenter due to the initially displaced dualmotion fretting wear,” Facta Universitatis Series: Mech. Eng., 14, Is. 1, 55-61 (2016). https://doi.org/10.22190/FUME1601055L
  17. X. Mao, W. Liu, Y. Ni, and V. L. Popov, “Limiting shape of profile due to dual-mode fretting wear in contact with an elastomer,” Proc. IMechE. Part C: J. Mech. Eng. Sci., 230, Is. 9, 1417-1423 (2016). https://doi.org/10.1177/0954406215619450
  18. R. M. Martynyak, N. I. Malanchuk, and B. E. Monastyrs’kyi, “Shear of two half planes pressed to each other and containing a surface groove. Part 1. Full contact,” Mater. Sci., 41, Is. 2, 178-185 (2005). https://doi.org/10.1007/s11003-005-0148-0
  19. R. M. Martynyak, R. M. Shvets’, and A. V. Glod, “Running in of moving half spaces in the case of partial wear of an asperity on the contact surface,” Mater. Sci., 39, Is. 1, 54-63 (2003). https://doi.org/10.1023/A:1026174428831
  20. O. P. Kozachok, and R. M. Martynyak, “Local wear of elastic half-spaces with protrusions,” in Contact mechanics. Roughness, Delamination and Wear of Surfaces [in Ukrainian], Viktoria Kundelska Publ. House, Lviv (2022), pp. 281-302 URL: www.researchgate.net/publication/366177313
  21. O. P. Kozachok, “Local friction wear of an elastic half space with protrusion,” Mater. Sci., 57, Is. 6, 797-804 (2022). https://doi.org/10.1007/s11003-022-00611-z
  22. N. I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen (1953).