 | | 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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| R. V. Goldstein and G. A. Shatalov, "Brittle fracture in the one-dimensional model of atomistic crack," Mech. Solids. 38 (3), 107-117 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
3 |
Pages |
107-117 |
| Title |
Brittle fracture in the one-dimensional model of atomistic crack |
| Author(s) |
R. V. Goldstein (Moscow)
G. A. Shatalov (Moscow) |
| Abstract |
We consider a Thomson type atomistic model of cracks.
It is assumed that an interface crack separates two
semi-infinite atomic chains. The interaction between the atoms of
neighboring chains is modelled by bilinear bonding elements (springs)
working in tension. The interaction between the atoms of the same chain
is characterized by two springs with flexural rigidity. Tensile forces are
applied to the extreme atoms of the chains. It is assumed that
fracture initiation occurs near the crack-tip in an end-zone of
unknown length with nonlinearly deformed bonding elements.
Numerical-analytical modeling is used for obtaining estimates of the length
of the cohesive zone depending on the crack length and the parameters of
bonding elements. Lattice trapping conditions are discussed. |
| References |
| 1. | G. I. Barenblatt, "On equilibrium cracks in brittle bodies,"
Doklady AN SSSR, Vol. 127, No. 1, pp. 47-50, 1959. |
| 2. | D. S. Dugdale,
"Yielding of steel sheets containing slits,"
J. Mech. Phys. Solids, Vol. 8, No. 2, pp. 100-104, 1960. |
| 3. | M. Ya. Leonov and V. V. Panasyuk,
"Development of finest cracks in a solid,"
Prikl. Mekhanika, Vol. 5, No. 4, pp. 391-401, 1959. |
| 4. | B. N. Cox and D. B. Marshall,
"Concepts for bridged cracks in fracture and fatigue,"
Acta Metallurg. Materialia, Vol. 42, No. 2, pp. 341-363, 1994. |
| 5. | R. Goldstein and M. Perelmuter,
"Modelling of bonding at an interface crack,"
Intern. J. Fract., Vol. 99, No. 1-2, pp. 53-79, 1999. |
| 6. | P. Thomson, C. Hsieh, and V. Rana,
"Lattice trapping of fracture cracks," J. Appl. Phys, Vol. 72, No. 8,
pp. 3154-3160, 1971. |
| 7. | E. R. Fuller and R. M. Thomson,
"Lattice theories of fracture," in R. C. Brandt et al. (Editors),
Fracture Mechanics of Ceramics. Volume 4, pp. 507-548, Plenum Press, New
York, 1978. |
| 8. | R. Thomson, "Fracture physics," in
Atomistics of Fracture [in Russian], pp. 104-144, Mir, Moscow, 1987. |
| 9. | E. Smith, "The effect of the discreteness of the atomic structure
on cleavage crack extension: use of a simple one-dimensional model," Mat.
Sci. and Eng., Vol. 17, No. 1, pp. 125-130, 1975. |
| 10. | 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. |
| 11. | V. V. Novozhilov,
"On the principles of the theory of equilibrium cracks in solids,"
PMM [Applied Mathematics and Mechanics], Vol. 33, No. 5, pp. 797-812, 1969. |
| 12. | L. I. Slepyan, Mechanics of Cracks [in Russian],
Sudostroenie, Leningrad, 1990. |
| 13. | N. F. Morozov and M. V. Paukshto,
Discrete and Hybrid Models in Fracture Mechanics [in Russian],
Izd-vo SPbGU, St. Petersburg, 1995. |
| 14. | A. O. Gelfond, Finite-Difference Calculus [in Russian],
Nauka, Moscow, 1967. |
| 15. | Ch. Kittel, Introduction to Solid State Physics [Russian translation], Nauka,
Moscow, 1978. |
| 16. | G. J. Dienes and A. Paskin,
"Computer-aided modelling of cracks," in
Atomistics of Fracture [in Russian], pp. 177-212, Mir, Moscow, 1987. |
|
| Received |
20 February 2003 |
| << Previous article | Volume 38, Issue 3 / 2003 | Next article >> |
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