We study the problem of contact interaction of two elastic isotropic half planes (one of which contains a shallow groove) made of identical materials with regard for the local friction slip. First, the bodies are pressed to each other by normal forces up to their full contact and then monotonically increasing shear forces are applied to these bodies which leads to their partial slip. The problem is reduced to a singular integral equation with Cauchy kernel for the relative tangential shift of the boundaries of half planes in the slip zone. The sizes of this zone are found from the condition of boundedness of tangential stresses on its edges. We also obtain analytic solutions of the problem for some profiles of the groove and analyze the dependences of the length of slip zone and contact stresses on the applied loads.
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I. V. Kragel’skii, M. N. Dobychin, and V. S. Kombalov, Foundations of the Numerical Analyses of Friction and Wear [in Russian], Mashinostroenie, Moscow (1977).
K. L. Johnson, Contact Mechanics, Cambridge Univ. Press, Cambridge (1985).
D. A. Hills and D. Nowell, Mechanics of Fretting Fatigue, Kluwer Acad. Publ., Dordrecht (1994).
I. G. Goryacheva, Mechanics of Friction Interaction [in Russian], Nauka, Moscow (2001).
G. Urriolagoitia Sosa and D. A. Hills, “Origins of partial slip in fretting—a review of known and potential solutions,” J. Strain Anal. Eng. Design., 34, 175–181 (1999).
J. Barber and M. Ciavarella, “Contact mechanics,” Int. J. Solids Struct., 37, 29–43 (2000).
O. I. Zhupanska, “On the analytical approach to Galin’s stick-slip problem. A survey,” J. Elasticity, 90, 315–333 (2008).
V. V. Panasyuk, O. P. Datsyshyn, and R. B. Shchur, “Residual service life of solids operating in contact under the conditions of fretting fatigue,” Fiz.-Khim. Mekh. Mater., 36, No. 2, 5–19 (2000).
O. P. Datsyshyn and V. M. Kadyra, “A fracture mechanics approach to prediction of pitting under fretting fatigue conditions,” Int. J. Fatigue, 28, No. 4, 375–385 (2006).
A. R. Mijar and J. S. Arora, “Review of formulations for elastostatic friction contact problems,” Struct. Multidisc. Optim., 20, 167– 189 (2000).
R. M. Shvets, R. M. Martynyak, and A. A. Kryshtafovych, “Discontinuous contact of an anisotropic half-plane and rigid base with disturbed surface,” Int. J. Eng. Sci., 34, No. 2, 183–200 (1996).
G. S. Kit and B. E. Monastyrsky, “A contact problem for a half-space and a rigid base with an axially symmetric recess,” J. Math. Sci., 107, No. 1, 3545–3549 (2001).
A. Kaczyński and B. Monastyrsky, “Contact problem for periodically stratified half-space and rigid foundation possessing geometrical surface defect,” J. Theor. Appl. Mech., 40, 985–999 (2002).
B. E. Monastyrs’kyi and R. M. Martynyak, “Contact of two half spaces one of which contains an annular groove. Part 1. Singular integral equation,” Fiz.-Khim. Mekh. Mater., 39, No. 2, 51–57 (2003).
B. Monastyrskyy and A. Kaczyński, “Contact between an elastic layer and an elastic semispace bounded by a plane with axially symmetric smooth dip,” Electronic J. Polish Agricult. Univ., Civil Eng., 8, Issue 4 (2005) (online: http://www.ejpau.media.pl).
R. Martynyak and A. Kryshtafovych, “Friction contact of two elastic semiplanes with wavy surfaces,” Friction Wear, 21, No. 5, 1– 8 (2000).
A. A. Kryshtafovych and S. J. Matysiak, “Frictional contact of laminated elastic half-spaces allowing interface cavities. Part 1: Analytical treatment. Part 2: Numerical results,” Int. J. Numer. Anal. Meth. Geomech., 25, 1077–1099 (2001).
R. M. Martynyak, N. I. Malanchuk, and B. E. Monastyrs’kyi, “Elastic interaction of two half planes for the local shift of their boundaries in the zone of intercontact gap,” Mat. Metody Fiz.-Mekh. Polya, 48, No. 3, 101–109 (2005).
R. M. Martynyak, N. I. Malanchuk, and B. E. Monastyrs’kyi, “Shift of half planes pressed to each other and containing a surface groove. Part 1. Full contact,” Fiz.-Khim. Mekh. Mater., 41, No. 2, 39–44 (2005).
N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).
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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol.48, No.1, pp.64–71, January–February, 2012.
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Malanchuk, N.I., Kaczyński, A. Friction interaction of two half planes in the presence of a surface groove. Mater Sci 48, 65–75 (2012). https://doi.org/10.1007/s11003-012-9473-2
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DOI: https://doi.org/10.1007/s11003-012-9473-2