| ||Mechanics of Solids|
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936
Archive of Issues
|Total articles in the database:|| ||10864|
|In Russian (Èçâ. ÐÀÍ. ÌÒÒ):|| ||8009|
|In English (Mech. Solids):|| ||2855|
|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)|
||Elastoplastic deformation of a dilatant medium subjected to a plane stress state near a crack tip|
||V. A. Belyakova (Moscow)|
E. V. Lomakin (Moscow)
||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
|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
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.|
||02 October 2003|