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IssuesArchive of Issues2001-1pp.70-76

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V. M. Alexandrov and D. A. Pozharskii, "To the problem of a crack on the elastic strip-half-plane interface," Mech. Solids. 36 (1), 70-76 (2001)
Year 2001 Volume 36 Number 1 Pages 70-76
Title To the problem of a crack on the elastic strip-half-plane interface
Author(s) V. M. Alexandrov (Moscow)
D. A. Pozharskii (Moscow)
Abstract We study the plane problem of a crack on the interface between an elastic strip and an elastic half-plane made of another material. The strip adheres to the elastic half-plane and a normal load (concentrated force) is applied to the outer surface of this two-layer body. In order to solve the system of integral equations for the jumps of the displacements in the crack zone, we use a regular asymptotic method [1], which is effective if the crack is sufficiently narrow. On the basis of the solution obtained, it is proposed to use an integral fracture criterion of Novozhilov type [2] for evaluating the actual dimensions of the crack.

Previously, similar plane problems were considered for cracks on the interface between two elastic half-planes, for instance, in [3]. Problems of circular defects like cracks or inclusions on the plane between two regions with distinct elastic properties were investigated in [4, 5].
References
1.  V. M. Alexandrov, "On plane contact problems in elasticity with adhesion or friction," PMM [Applied Mathematics and Mechanics], Vol. 34, No. 2, pp. 246-257, 1970.
2.  N. F. Morozov, Mathematical Problems in the Theory of Cracks [in Russian], Nauka, Moscow, 1984.
3.  V. M. Alexandrov and M. A. Sumbatyan, "Periodic array of cracks on the contact boundary between two elastic half-planes," in Proc. 3rd Int. Conf. on Modern Problems in Continuum Mechanics. Volume 1 [in Russian], pp. 26-29, OOO MP Kniga, Rostov-on-Don, 1997.
4.  V. I. Mossakovskii, P. E. Berkovich, and V. M. Rybka, "Mixed axially symmetric problem of elasticity for a piecewise homogeneous space with a circular crack at the interface plane," Doklady AN Ukr.SSR, Ser. A, No. 9, pp. 812-816, 1978.
5.  V. V. Efimov, A. F. Krivoi, and G. Ya. Popov, "Problems on the stress concentration near a circular imperfection in a composite elastic medium," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 42-58, 1998.
6.  Ya. S. Uflyand, Integral Transforms in Elasticity Problems [in Russian], Izd-vo AN SSSR, Moscow, Leningrad, 1963.
7.  G. P. Aleksandrova, "Contact problems of bending of plates on an elastic foundation," Izv. AN. MTT [Mechanics of Solids]old, No. 1, pp. 97-106, 1973.
8.  V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol', Thin Stress Concentrators in Elastic Solids [in Russian], Nauka, Moscow, 1993.
9.  F. D. Gakhov, Boundary Value Problems [in Russian], Nauka, Moscow, 1977.
10.  N. I. Muskhelishvili, Some Basic Problems in Mathematical Elasticity [in Russian], Fizmatgiz, Moscow, 1966.
11.  V. V. Panasyuk, Limit Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kiev, 1966.
12.  V. M. Alexandrov, J. J. Kalker, and D. A. Pozharskii, "Three-dimensional contact problem for a two-layered elastic base with an unknown contact area," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 51-55, 1999.
13.  G. G. Gnesin and S. N. Fomenko, "Wear-resistant coatings on tool materials," Poroshkovaya Metallurgiya, No. 9/10, pp. 17-28, 1996.
Received 17 December 1999
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