Skip to main content
Log in

Stressed state of a half plane with shallow edge crack under Hertzian loading (a survey)

  • Published:
Materials Science Aims and scope

Abstract

We present a survey of works dealing with the stress intensity factors (SIF) for shallow edge cracks formed in elastic half planes subjected to the action of Hertzian loads moving along the boundaries of the planes. The numerical data on the SIF obtained by the method of singular integral equations are compared with the results of the other authors. The best agreement is observed with the results obtained by Keer and Bower by using the dislocation approach. The agreement with the results obtained by the finite-element method is satisfactory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. M. Keer and M. D. Bryant, “A pitting model for rolling contact fatigue,” Trans. ASME: J. Lubric. Technol., 105, No. 2, 198–205 (1983).

    Google Scholar 

  2. Yu. V. Kolesnikov and E. M. Morozov, Mechanics of Contact Fracture [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  3. J. W. Ringsberg and A. Bergkvist, “On propagation of short rolling contact fatigue cracks,” Fatigue Fract. Eng. Mater. Struct., 26, No. 10, 969–983 (2003).

    Article  Google Scholar 

  4. U. Zerbst, K. Madler, and H. Hintze, “Fracture mechanics in railway application — an overview,” Eng. Fract. Mech., 72, 163–194 (2005).

    Article  Google Scholar 

  5. S. Way, “Pitting due to rolling contact,” Trans. ASME: J. Appl. Mech., 2, A49–A58 (1935).

    Google Scholar 

  6. L. A. Sosnovskii, N. A. Makhutov, and V. A. Shurinov, “Contact mechanical fatigue: basic principles (generalizing paper),” Zavod. Lab., 58, No. 11, 44–61 (1992).

    Google Scholar 

  7. D. F. Cannon and H. Pradier, “Rail contact fatigue research by the European Rail Research Institute,” Wear, 191, 1–13 (1996).

    Article  Google Scholar 

  8. M. Ishida, M. Akama, K. Kashiwaya, and A. Kapoor, “The current status of the theory and practice on rail integrity in Japanese railways-rolling contact fatigue and corrugations,” Fatigue Fract. Eng. Mater. Struct., 26, No. 10, 909–919 (2003).

    Article  Google Scholar 

  9. A. Ekberg and E. Kabo, “Fatigue of railway wheel and rails under rolling contact and thermal loading — an overview,” Wear, 258, 1288–1300 (2005).

    Article  Google Scholar 

  10. O. P. Datsyshyn, “Service life and fracture of solid bodies under the conditions of cyclic contact interaction,” Fiz.-Khim. Mekh. Mater., 41, No. 6, 5–25 (2005).

    Google Scholar 

  11. L. M. Keer, M. D. Bryant, and G. K. Haritos, “Subsurface and surface cracking due to Hertzian contact,” Trans. ASME: J. Lubric. Technol., 104, No. 3, 347–351 (1982).

    Google Scholar 

  12. Y. Murakami, M. Kaneta, and H. Yatsuzuka, “Analysis of surface crack propagation in lubricated rolling contact,” Trans. ASLE, 28, No. 1, 60–68 (1985).

    Article  Google Scholar 

  13. M. Kaneta and Y. Murakami, “Propagation of semi-elliptical surface crack in lubricated rolling/sliding elliptical contact,” J. Trib. ASME, 113, 270–275 (1991).

    Article  Google Scholar 

  14. M. D. Bryant, G. R. Miller, and L. M. Keer, “Line contact between a rigid indenter and a damaged elastic body,” Quart. J. Mech. Appl. Math., 37, No. 3, 468–478 (1984).

    Article  Google Scholar 

  15. A. F. Bower, “The influence of crack face friction and trapped fluid on surface initiated rolling contact fatigue cracks,” J. Trib. ASME, 110, No. 4, 704–711 (1988).

    Article  Google Scholar 

  16. R. S. Zhou, H. S. Cheng, and T. Mura, “Micropitting in rolling and sliding contact under mixed lubrication,” Trans. ASME: J. Tribol., 111, 605–613 (1989).

    Article  Google Scholar 

  17. N.-A. Noda, M. Yagishita, and T. Kihara, “Effect of crack shape, inclination angle, and friction coefficient in crack surface contact problems,” Int. J. Fract., 105, 367–389 (2000).

    Article  Google Scholar 

  18. W. L. Zang and P. Gudmudson, “Frictional contact problems of kinked cracks modelled by a boundary integral method,” Int. J. Numer. Meth. Eng., 31, 427–446 (1991).

    Article  Google Scholar 

  19. M. Akama and T. Mori, “Boundary element analysis of surface initiated rolling contact fatigue cracks in wheel/rail contact system,” Wear, 253, 35–41 (2002).

    Article  Google Scholar 

  20. M. Beghini, L. Bertini, and V. Fontanari, “Parametric study of oblique edge cracks under cyclic contact loading,” Fatigue Fract. Eng. Mater. Struct., 28, No. 1–2, 31–40 (2005).

    Google Scholar 

  21. O. P. Datsyshyn, R. E. Pryshlyak, S. V. Prykhods’ka, et al., “Influence of the shape of model contact loading on the stress intensity factors for the edge crack,” Probl. Trybol., No. 3, 3–16 (1998).

    Google Scholar 

  22. V. V. Panasyuk, O. P. Datsyshyn, and H. P. Marchenko, “Crack growth in rolling bodies under the conditions of dry friction and wetting,” Fiz.-Khim. Mekh. Mater., 37, No. 1, 7–16 (2001).

    Google Scholar 

  23. O. P. Datsyshyn, V. V. Panasyuk, R. E. Pryshlyak, and A. B. Terlets’kyi, “Paths of edge cracks in rolling bodies under the conditions of boundary lubrication,” Fiz.Khim. Mekh. Mater., 37, No. 3, 5–12 (2001).

    Google Scholar 

  24. O. P. Datsyshyn, and H. P. Marchenko, “Assessment of the period of growth of surface cracks according to the mechanism of shear in rolling contact,” Mashynoznavstvo, No. 7, 21–28 (2003).

  25. O. P. Datsyshyn, V. I. Tkachov, A. Yu. Glazov, and R. A. Khrunyk, “Prediction of the contact durability of backup rolls of forge-rolling mills according to the development of pitting,” Fiz.Khim. Mekh. Mater., 42, No. 6, 95–105 (2006).

    Google Scholar 

  26. V. V. Panasyuk, O. P. Datsyshyn, and A. Yu. Glazov, “Prediction of the contact durability of rails according to the development of pitting,” Mashynoznavstvo, No. 3, 3–10 (2007).

  27. S. Bogdanski, M. Olzak, and J. Stupnicki, “Numerical stress analysis of rail contact fatigue cracks,” Wear, 192, 14–24 (1996).

    Article  Google Scholar 

  28. S. Bogdanski, “The behaviour of kinked cracks in contact,” in: Proc. of the 14th Bienniel Conf. on Fracture “Fracture Mechanics beyond — ECF 14” (Cracow, September 2002), Vol. 1/3, EMAS Publ., Cracow, Poland (2002), pp. 289–296.

    Google Scholar 

  29. S. Bogdanski and M. Trajer, “A dimensionless multi-size finite element model of a rolling contact fatigue crack,” Wear, 258, 1265–1272 (2005).

    Article  Google Scholar 

  30. D. Benuzzi, E. Bormetti, and G. Donzella, “Stress intensity factor range and propagation mode of surface cracks under rolling-sliding contact,” Theor. Appl. Fract. Mech., 40, 55–74 (2003).

    Article  Google Scholar 

  31. Yu. Murakami (editor), Stress Intensity Factors. A Handbook [Russian translation], Vol. 2, Mir, Moscow (1990).

    Google Scholar 

  32. S. Bogdanski and M. W. Brown, “Modelling the three-dimensional behavior of shallow rolling fatigue cracks in rails,” Wear, 253, 17–25 (2002).

    Article  Google Scholar 

  33. V. V. Panasyuk, O. P. Datsyshyn, and H. P. Marchenko, “The crack propagation theory under rolling contact,” Eng. Fract. Mech., 52, No. 1, 179–191 (1995).

    Article  Google Scholar 

  34. M. Kaneta and Y. Murakami, “Effect of oil hydraulic pressure on surface crack growth in rolling/sliding contact,” Tribology Int., 20, 210–217 (1987).

    Article  Google Scholar 

  35. B. Zafošnik, Z. Ren, J. Flaške, and G. Mishuris, “Modelling of surface crack growth under lubricated rolling-sliding contact loading,” Int. J. Fract., 134, 127–149 (2005).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 1, pp. 23–34, January–February, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Datsyshyn, O.P., Marchenko, H.P. Stressed state of a half plane with shallow edge crack under Hertzian loading (a survey). Mater Sci 44, 22–34 (2008). https://doi.org/10.1007/s11003-008-9039-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11003-008-9039-5

Keywords

Navigation