 | | 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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| << Previous article | Volume 41, Issue 4 / 2006 | Next article >> |
| R. V. Goldstein and G. A. Shatalov, "Modeling of rupture processes in the framework of the generalized model of atomistic normal separation cracks," Mech. Solids. 41 (4), 118-129 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
4 |
Pages |
118-129 |
| Title |
Modeling of rupture processes in the framework of the generalized model of atomistic normal separation cracks |
| Author(s) |
R. V. Goldstein (Moscow)
G. A. Shatalov (Moscow) |
| Abstract |
We propose a generalized atomic model of a Thomson type crack. We assume
that an edge crack separates four half-infinite chains of atoms. The
interaction between atoms within each of the chains is characterized by
springs with flexural rigidity, while the interaction between atoms in
neighboring chains is modeled by bilinear bonds (springs) working in
tension. The loading is realized by lumped tensile forces acting on the
extreme atoms in the chains. We perform analytical-numerical modeling of
the deformation and bond rupture processes near the crack tip and obtain an
estimate for the dimensions of the adhesion region depending on the crack
length and the bond parameters. We analyze the role of the additional
(compared with the Thomson model) atomic chains and their influence on the
redistribution of stresses and displacements in the adhesion region as well
as the dimensions of the adhesion region itself. |
| References |
| 1. | G. I. Barenblatt, "On equilibrium cracks formed in the process of brittle
fracture," PMM [Applied Mathematics and Mechanics], Vol. 23, No. 3, pp. 434-444 (General
ideas and hypothesis. Axially symmetric cracks); No. 4, pp. 706-721 (Rectilinear cracks in
plane plates); No. 5, pp. 893-900 (Stability of isolated cracks. Relationship between
energy theories), 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 cracks in solids," PM [Applied
Mechanics], Vol. 5, No. 4, pp. 391-401, 1959. |
| 4. | R. Thomson, "Physics of Fracture," in R. V. Goldstein (Editor), Atomistics of
Destruction [in Russian], pp. 104-144, Mir, Moscow, 1987. |
| 5. | E. R. Fuller and R. M. Thomson, "Lattice theories of fracture," in R. C. Brandt
(Editor), Fracture Mechanics of Ceramics, Vol. 4, pp. 507-548, Plenum Press, New York,
1978. |
| 6. | N. F. Morozov and M. V. Paukshto, Discrete and Hybrid Models of
Fracture [in Russian], Idz-vo SPbGU, St. Petersburg, 1995. |
| 7. | R. V. Goldstein and G. A. Shatalov, "On the coupling domain near
the crack edge in the process of brittle fracture," Doklady RAN, Vol. 389,
No. 5, pp. 608-610, 2003. |
| 8. | R. V. Goldstein and G. A. Shatalov, "Brittle fracture in the one-dimensional model
of atomistic crack," Izv. RAN. MTT [Mechanics of Solids], No. 3, pp. 135-147, 2003. |
| 9. | R. Thomson, C. Hsiek, and V. Rana, "Lattice trapping of fracture cracks," J. Appl.
Phys., Vol. 42, No. 8, pp. 3154-3160, 1971. |
| 10. | A. O. Gelfond, Calculus of Finite Differences [in Russian], Nauka,
Moscow, 1967. |
| 11. | R. V. Goldstein and G. A. Shatalov, Modeling Destruction Processes in Atomistic
Normal Separation Crack. Preprint No. 710 [in Russian], In-t Problem Mekhaniki RAN, Moscow,
2002. |
|
| Received |
20 July 2005 |
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