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.
Similar content being viewed by others
References
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).
Yu. V. Kolesnikov and E. M. Morozov, Mechanics of Contact Fracture [in Russian], Nauka, Moscow (1989).
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).
U. Zerbst, K. Madler, and H. Hintze, “Fracture mechanics in railway application — an overview,” Eng. Fract. Mech., 72, 163–194 (2005).
S. Way, “Pitting due to rolling contact,” Trans. ASME: J. Appl. Mech., 2, A49–A58 (1935).
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).
D. F. Cannon and H. Pradier, “Rail contact fatigue research by the European Rail Research Institute,” Wear, 191, 1–13 (1996).
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).
A. Ekberg and E. Kabo, “Fatigue of railway wheel and rails under rolling contact and thermal loading — an overview,” Wear, 258, 1288–1300 (2005).
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).
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).
Y. Murakami, M. Kaneta, and H. Yatsuzuka, “Analysis of surface crack propagation in lubricated rolling contact,” Trans. ASLE, 28, No. 1, 60–68 (1985).
M. Kaneta and Y. Murakami, “Propagation of semi-elliptical surface crack in lubricated rolling/sliding elliptical contact,” J. Trib. ASME, 113, 270–275 (1991).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
S. Bogdanski, M. Olzak, and J. Stupnicki, “Numerical stress analysis of rail contact fatigue cracks,” Wear, 192, 14–24 (1996).
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.
S. Bogdanski and M. Trajer, “A dimensionless multi-size finite element model of a rolling contact fatigue crack,” Wear, 258, 1265–1272 (2005).
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).
Yu. Murakami (editor), Stress Intensity Factors. A Handbook [Russian translation], Vol. 2, Mir, Moscow (1990).
S. Bogdanski and M. W. Brown, “Modelling the three-dimensional behavior of shallow rolling fatigue cracks in rails,” Wear, 253, 17–25 (2002).
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).
M. Kaneta and Y. Murakami, “Effect of oil hydraulic pressure on surface crack growth in rolling/sliding contact,” Tribology Int., 20, 210–217 (1987).
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).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 1, pp. 23–34, January–February, 2008.
Rights 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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11003-008-9039-5