 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| V.V. Glagolev and A.A. Markin, "Models of Strain and Separation Process," Mech. Solids. 45 (2), 275-283 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
2 |
Pages |
275-283 |
| DOI |
10.3103/S0025654410020135 |
| Title |
Models of Strain and Separation Process |
| Author(s) |
V.V. Glagolev (Tula State University, pr-t Lenina 92, Tula, 300600 Russia, vadim@tsu.tula.ru)
A.A. Markin (Tula State University, pr-t Lenina 92, Tula, 300600 Russia, markin@uic.tula.ru) |
| Abstract |
We consider models of strain and separation processes of rigid bodies, which are based on the use of the well-known scheme of mathematical cut [1, 2] and the concept of interaction layer developed in [3, 4].
We obtain a thermomechanical condition for the separation of a deformable body in the framework of physical and mathematical cut models. This condition allows us to obtain the general expression for the surface energy as the product of the interaction layer thickness by the critical free energy, which holds for the reversible (elastic) and irreversibly deformable materials. When using the mathematical cut model in an elastic body, the expressions of the surface energy is reduced to the classical Irwin-Orowan representation [1, 5].
On the basis of semidiscrete and discrete models of the interaction layer, we state the problem of determining the subcritical state of a plane loaded by a physical cut under symmetric loading by lumped forces and an end load. We compare the results obtained by the discrete model with the asymptotic solution obtained in [6] in a specific case.
It follows from the proposed fracture criterion that an increase in the end load may result in the critical state attained at a certain distance from the end surface. This effect was observed in the experiment described in the monograph [7]. |
| References |
| 1. | G. P. Cherepanov,
Mechanics of Brittle Fracture
(Nauka, Moscow, 1974; McGraw-Hill, New York, 1979). |
| 2. | N. I. Muskhelishvili,
Some Fundamental Problems of Mathematical Elasticity Theory
(Nauka, Moscow, 1966)
[in Russian]. |
| 3. | V. V. Glagolev and A. A. Markin,
"On a Method for the Establishment of Relations between the Critical Values of the Characteristics of Steady-State Material Separation Process,"
Probl. Prochn.,
No. 2, 47-58 (2006)
[Strength of Materials (Engl. Transl.)
38 (2), 141-149 (2006)]. |
| 4. | V. V. Glagolev, K. A. Kuznetsov, and A. A. Markin,
"A Model of Splitting of Solids,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 61-68 (2003)
[Mech. Solids (Engl. Transl.)
38 (6), 49-54 (2003)]. |
| 5. | G. R. Irwin,
"Analysis of Stresses and Strain near the End of a Crack Traversing a Plate,"
J. Appl. Mech.
24 (3), 361-364 (1958).
("Discussion," J. Appl. Mech. 25 (2), 299-303 (1958)) |
| 6. | V. M. Entov and R. L. Salganik,
"On the Prandtl Brittle Fracture Model,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 6, 87-99 (1968)
[Mech. Solids (Engl. Transl.)]. |
| 7. | A. Nadai,
Theory of Flow and Fracture of Solids
(McGraw-Hill, New York, 1950; Mir, Moscow, 1969). |
| 8. | A. A. Il'yushin,
Continuum Mechanics
(Izd-vo MGU, Moscow, 1990)
[in Russian]. |
| 9. | N. F. Morozov and Yu. V. Petrov,
"Quantum Nature and Dual Character of Fracture Dynamics in Solids,"
Dokl. Ross. Akad. Nauk
382 (2), 206-209 (2002)
[Dokl. Phys. (Engl. Transl.)
47 (1), 85-88 (2002)]. |
| 10. | R. V. Goldstein and A. V. Chentsov,
"Discrete-Continuous Model of a Nanotube,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 57-74 (2005)
[Mech. Solids (Engl. Transl.)
40 (4), 45-59 (2005)]. |
| 11. | G. P. Cherepanov,
"Supercritical Deformations,"
Probl. Prochn.,
No. 8, 3-8 (1985)
[Strength of Materials (Engl. Transl.)
17 (8), 1029-1036 (1985)]. |
| 12. | V. V. Novozhilov,
"On a Necessary and Sufficient Criterion for Brittle Strength,"
Prikl. Mat. Mekh.
33 (2), 212-222 (1969)
[J. Appl. Math. Mech. (Engl. Transl.)
33 (2), 201-210 (1969)]. |
| 13. | V. V. Novozhilov,
"On the Foundations of a Theory of Equilibrium Cracks in Elastic Solids,"
Prikl. Mat. Mekh.
33 (5), 797-812 (1969)
[J. Appl. Math. Mech. (Engl. Transl.)
33 (5), 777-790 (1969)]. |
| 14. | B. V. Kostrov,
"Unsteady Propagation of Longitudinal Shear Cracks,"
Prikl. Mat. Mekh.
30 (6), 1042-1049 (1966)
[J. Appl. Math. Mech. (Engl. Transl.)
30 (6), 1241-1248 (1966)]. |
| 15. | B. V. Kostrov, L. V. Nikitin, and L. M. Flitman,
"The Mechanics of Brittle Fracture,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 3, 112-125 (1969)
[Mech. Solids (Engl. Transl.)
4 (3), 105-117 (1969)]. |
| 16. | A. I. Lurie,
The Theory of Elasticity
(Nauka, Moscow, 1970)
[in Russian]. |
| 17. | S. Crouch and A. Starfield,
Boundary Element Methods in Solid Mechanics
(Allen & Unwin, London, 1983; Mir, Moscow, 1987). |
|
| Received |
19 June 2007 |
| Link to Fulltext |
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