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IssuesArchive of Issues2001-2pp.85-89

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S. Yu. Veselkov and Yu. M. Dal', "Shear strength of metals in stress concentration regions," Mech. Solids. 36 (2), 85-89 (2001)
Year 2001 Volume 36 Number 2 Pages 85-89
Title Shear strength of metals in stress concentration regions
Author(s) S. Yu. Veselkov (St. Petersburg)
Yu. M. Dal' (St. Petersburg)
Abstract V. V. Novozhilov's brittle strength criterion [1] has been investigated and widely applied in the works published in Russia on the static and the dynamic strength of structural materials. These works are mainly concerned with tensile cracks spontaneously spreading in elastic bodies with an ideal crystal lattice [2] or a simple Bravais lattice with one or two vacancies near the crack tip [3].

The present paper is dedicated to the analysis of plastic shear appearing in metals near stress concentrators. The investigation is based on the Frenkel-Kontorova model [4, 5], which is adapted by the authors to the case of large tangential stress gradients, the presence of defects in the form of isolated edge dislocations or dislocation ensembles, and large displacements of atoms (in comparison with the lattice parameters). Following the V. V. Novozhilov's concept, we take into account in the model the discrete character of forces responsible for the plastic shear of atoms.
References
1.  V. V. Novozhilov, "On a necessary and sufficient criterion of brittle strength," PMM [Applied Mathematics and Mechanics], Vol. 33, No. 2, pp. 212-222, 1969.
2.  N. F. Morozov and M. V. Paukshto, Discrete and Combined Models in Fracture Mechanics [in Russian], Izd-vo SPbGU, St. Petersburg, 1995.
3.  V. N. Kornev and Yu. V. Tikhomirov, "Deformation and instability of a segment of an atomic chain near a crack tip", Zh. Prikl. Mech. i Tekhn. Fiziki, No. 3, pp. 160-172, 1993.
4.  Ya. I. Frenkel', Introduction to the Theory of Metals [in Russian], Nauka, Leningrad, 1972.
5.  A. I. Mel'ker and S. V. Govorov, "On dislocations in two-dimensional crystals", Izv. AN SSSR. Fizika Tverdogo Tela, Vol. 30, No. 12, pp. 3597-3604, 1988.
6.  A. Yu. Ishlinskii (Editor), Atomistics of Fracture [Russian translations], Mir, Moscow, 1987.
7.  A. N. Orlov (Editor), Topical Issues in the Theory of Dislocations [Russian translations], Mir, Moscow, 1968
8.  V. L. Indenbom, "Mobility of dislocations in the Frenkel-Kontorova model", Kristallografiya, Vol. 3, No. 2, pp. 197-205, 1958.
9.  A. K. Head, "The interaction of dislocations with boundaries and surface films", Austral. J. Phys., Vol. 13, No. 2A, pp. 278-283, 1960.
10.  G. V. Uzhik, Rupture Resistance and Strength of Metals [in Russian], Izd-vo AN SSSR, Moscow, Leningrad, 1950.
11.  Physics of Metals [in Russian], Izd-vo Metallurgia, Moscow, 1987.
Received 12 January 1998
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