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IssuesArchive of Issues2004-1pp.81-87

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V. A. Belyakova and E. V. Lomakin, "Elastoplastic deformation of a dilatant medium subjected to a plane stress state near a crack tip," Mech. Solids. 39 (1), 81-87 (2004)
Year 2004 Volume 39 Number 1 Pages 81-87
Title Elastoplastic deformation of a dilatant medium subjected to a plane stress state near a crack tip
Author(s) V. A. Belyakova (Moscow)
E. V. Lomakin (Moscow)
Abstract The behavior of the structural microdefects in damaged media changes depending on the loading conditions. Therefore, materials with microcracks, inclusions or pores are characterized by the dependence of the deformation and strength properties on the stress state type. This complicates the description of the deformation process. The analysis of the experimental data shows the absence of a unified diagram for the dependence of the intensity of the tangential stresses on the strain intensity, the interdependence between the shear and volume strains, the appearance of irreversible volume strains, and a number of other specific features. Such properties are characteristic, for example, of engineering graphite, concrete, cast iron, some ceramic and composite materials, and rocks [1-7].

In the present paper, we investigate the influence of these specific features of the deformation on the character of asymptotic solutions near macrocracks in a hardening material. The case of plane stress state is considered. An approximation for material functions is suggested. This approximation allows one to describe the experimental strain diagrams with reasonable degree of accuracy. For specific material functions, the distributions of stresses, strains, and displacements near the crack tip are obtained. These distributions are compared with those following from the solution of a similar problem for a plastically incompressible medium. The conditions of the crack initiation are determined in terms of the invariant integral.
References
1.  M. Ya. Leonov, V. A. Panyaev, and K. N. Rusinko, "The stress-strain dependence for semi-brittle bodies," Inzh. Zh. MTT [Mechanics of Solids], No. 6, pp. 26-32, 1967.
2.  V. A. Panyaev, "Experimental study of the deformation of gray iron," in Complex Deformation of Solids [in Russian], pp. 126-135, Ilim, Frunze, 1969.
3.  A. V. Berezin, E. V. Lomakin, V. I. Strokov, and V. N. Barabanov, "The resistance of isotropic graphite materials subjected to a complex stress state to deformation and fracture," Problemy Prochnisti, No. 2, pp. 60-65, 1979.
4.  A. A. Lebedev, B. I. Koval'chuk, F. F. Giginyak, and V. P. Lamashevskii, Mechanical Properties of Structural Materials Subjected to a Complex Stress State [in Russian], Naukova Dumka, Kiev, 1983.
5.  A. N. Stavrogin and A. G. Protosenya, Plasticity of Rocks [in Russian], Nedra, Moscow, 1979.
6.  E. V. Lomakin, "Constitutive relations of the strain theory for dilatant media," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 66-75, 1991.
7.  E. V. Lomakin, "Nonlinear deformation of materials the strength of which depend on the stress-strain type," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 92-99, 1980.
8.  E. V. Lomakin, "Deformation of a dilatant medium near crack tip under plane stress conditions," Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 99-109, 1996.
9.  E. V. Lomakin, "The limiting state of composite and polymer materials as depending on the stress-state type. Part 1. Experimental data and constitutive relations," Mekhanika Kompositnykh Materialov, No. 1, pp. 3-9, 1988.
10.  V. V. Novozhilov, "The physical meaning of the stress invariants utilized in the theory of plasticity," PMM [Applied Mathematics and Mechanics], Vol. 16, No. 5, pp. 617-619, 1952.
11.  J. W. Hutchinson, "Singular behavior at the end of a tensile crack in a hardening material," J. Mech. and Phys. Solids, Vol. 16, No. 1, pp. 13-31, 1968.
12.  J. R. Rice and G. F. Rosengren, "Plane strain deformation near a crack tip in a power-law hardening material," J. Mech. and Phys. Solids, Vol. 16, No. 1, pp. 1-12, 1968.
13.  G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian], Nauka, Moscow, 1974.
Received 02 October 2003
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