Abstract
A contact problem in elasticity theory for an isotropic half-plane with a set of curvilinear cracks, into which a rigid punch with the foundation of convex shape is indented, is considered. Coulomb friction is assumed to exist between the punch and the half-plane, while the crack faces are under conditions of either stick or smooth contact on contact parts. On the basis of integral representation for Kolosov-Muskhelishvili complex potentials by derivatives of displacement discontinuities along the crack contours and pressure under the punch, the problem is reduced to a system of complex Cauchy type singular integral equations of first and second kind. An algorithm is proposed to find solution of these equations by the method of mechanical quadratures using an iterative procedure. Two numerical examples are presented.
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Avetisian, Ye.P., Khachatrian, O.Kh. and Shaginian, S.S. (1983). On a mixed boundary value problem in elasticity theory for a half-plane weakened by an internal rectilinear cut. Uchenyie Zapiski Yerevanskogo Universiteta, Yestestvenyie Nauki 1, 28–33.
Boyadzhi, A.H., Buryshkin, M.L. and Radiollo, M. V. (1988). On action of a rigid punch on a half-plane weakened by a regular set of cracks. Prikladnaya Matematika i Mekhanika 52, 856–860.
Datsyshyn, O.P. and Marchenko, H.P. (1984). Interaction between curvilinear cracks and the boundary of an elastic half-plane. Physicochemical Mechanics of Materials 20(5), 64–71.
Erdogan, F., Gupta, G.D. and Cook, T.S. (1973). The numerical solutions of singular integral equations. Methods of Analysis and Solutions of Crack Problems(Edited by G.S. Sih), Noordhoff International Publishing, Leyden, 368–425.
Hasebe, N. (1981). An edge crack in a semi-infinite plate welded to a rigid stiffener. Proceedings of Japan Civil Engineers 314, 149–157.
Hasebe, N., Okumura, M. and Nakamura, T. (1989). Frictional punch and crack in plane elasticity. Journal of Engineers Mechanics 115, 1137–1149.
Hasebe, N. and Qian, J. (1995). Circular inclined punch problem with two corners to contact with a half-plane with a surface crack. Proceedings of the 2nd International Conference on Computational Methods in Contact Mechanics, Computational Mechanics Publications, Southampton, Boston, 159–166.
Hasebe, N. and Qian, J. (1997). Circular rigid punch with one smooth and another sharp ends on a half-plane with edge crack. Journal of Applied Mechanics 64, 73–79.
Hills, D.A. and Nowell, D. (1994). Mechanics of Fretting Fatigue, Kluwer Academic Publishers, Dordrecht.
Kudish, I.I. (1986). Contact problem in elasticity theory for bodies with cracks. Prikladnaya Matematika i Mekhanika 50, 1020–1033.
Melkumian, S.A. (1972). Contact problem for a half-plane with a vertical finite cut. Doklady Akademii Nauk Arnlianskoy SSR 55, 87–93.
Minasian, A.F. (1975). Asymmetric contact problem for a half-plane with a vertical cut. Doklady Akademii Nauk Armianskoy SSR 61, 82–89.
Minasian, A.F. and Tonoyan, V.S. (1985). Contact problem for a half-plane with a vertical cut in stick. Mechanics of Deformable Bodies and Structures, Akademiya Nauk Armianskoy SSR, Yerevan, 286–297.
Muskhelishvili, N.I. (1975). Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff International Publishing, Leiden.
Okumura, M., Hasebe, N. and Nakamura, T. (1990). Crack due to wedge-shaped punch with friction. Journal of Engineers Mechanics 116, 2173–2185.
Panasyuk, V.V., Datsyshyn, O.P. and Marchenko, H.P. (1995). Contact problem for a half-plane with cracks under action of a rigid punch on its boundary. Physicochemical Mechanics of Materials 31(6), 7–16.
Panasyuk, V.V., Datsyshyn, O.P. and Marchenko, H.P. (1996). On punch pressure on a half-plane with cracks. Proceedings of the 9th Conference on Strength and Plasticity, Vol. 1, Profservis, Moscow, 150–155.
Panasyuk, V.V., Datsyshyn, O.P. and Marchenko, H.P. (1998). An internal crack under a punch in an elastic solids. Fracture Mechanics and Physics of Construction Materials and Structures(Edited by O.Ye. Andreikiv and J.J. Luchko), Issue 3, Kameniar, Lviv, 170–177.
Panasyuk, V.V., Savruk, M.P. and Datsyshyn, O.P. (1976). Stress Distribution Around Cracks in Plates and Shells
Naukova Dumka, Kyiv. Panasyuk, V.V., Savruk, M.P. and Datsyshyn, O.P. (1977). A general method of solution of two-dimensional problems in the theory of cracks. Engineering Fracture Mechanics 9, 481–497.
Qian, J. and Hasebe, N. (1997). Circular rigid punch on a semi-infinite plane with an oblique edge crack subjected to concentrated forces or point deslocations. Proceedings of Japan Civil Engineers 570, 149–159.
Sarkisian, V.S., Hrihorian, E.Kh. and Shaginian, S.S. (1980). On two boundary value problems in elasticity theory for a half-plane weakened by an internal rectilinear cut. Uchenyie Zapiski Yerevanskogo Universiteta, Yestestvenyie Nauki 2, 49–58.
Savruk, M.P. (1981). Two-Dimensional Problems of Elasticity for Bodies with Cracks, Naukova Dumka, Kyiv.
Tonoyan, V.S. and Melkumian, S.A. (1970). Contact problem for a half-plane with a vertical cut. Doklady Akademii Nauk Annianskoy SSR 51, 144–149.
Tonoyan, V.S. and Melkumian, S.A. ( 1973). On symmetric indentation of two rigid similar punches into an elastic half-plane with a vertical semi-infinite cut. Doklady Akademii Nauk Annianskoy SSR 57, 282–288.
Tonoyan, V.S. and Minasian, A.F. (1975). Asymmetric contact problem for a half-plane with a vertical finite cut. Doklady Akademii Nauk Annianskoy SSR 61, 289–297.
Tonoyan, V.S. and Minasian, A.F. (1976). On symmetric indentation of two rigid similar punches into an elastic half-plane with a vertical finite cut. Doklady Akademii Nauk Annianskoy SSR 62, 36–42.
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Panasyuk, V., Datsyshyn, O. & Marchenko, H. Stress state of a half-plane with cracks under rigid punch action. International Journal of Fracture 101, 347–363 (2000). https://doi.org/10.1023/A:1007530123470
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DOI: https://doi.org/10.1023/A:1007530123470