 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
|
| << Previous article | Volume 46, Issue 3 / 2011 | Next article >> |
| I.N. Dashevskii, "Model of Symmetric Crack Formation in a Plate and a Wedge under Bending by a Point Indenter," Mech. Solids. 46 (3), 425-433 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
3 |
Pages |
425-433 |
| DOI |
10.3103/S0025654411030095 |
| Title |
Model of Symmetric Crack Formation in a Plate and a Wedge under Bending by a Point Indenter |
| Author(s) |
I.N. Dashevskii (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, dash@ipmnet.ru) |
| Abstract |
The energy approach is used to propose a model of brittle fracture of a thin plate (and a wedge) under bending by a point indenter, which permits studying some possible mechanisms determining the number of sectors into which the plate breaks.
Since the energy necessary to form new cracks and the total elastic bending energy of the n triangular sectors-beams arising under bending vary in opposite directions with variation in both the crack length L and n, it follows that the total energy required to form n sectors has a minimum depending on L and n, and it is this minimum that determines the number n of the arising sectors.
In the simplest scheme, the number of developing cracks turns out to be independent of the plate physical-mechanical characteristics, and its thickness and varies from 2 to 4 as the wedge opening angle varies from 0 to 2π.
An analysis is performed and a qualitative interpretation of the obtained results is given. Possible refinements of the proposed model in various directions are discussed. |
| Keywords |
crack, crack formation, fracture, bending, plate, wedge, model, indenter |
| References |
| 1. | R. V. Goldstein and N. M. Osipenko,
"Fracture Mechanics and Several Problems of Ice Fracture,"
in Mechanics and Physics of Ice
(Nauka, Moscow, 1983),
pp. 65-94
[in Russian]. |
| 2. | E. M. Gramuzov, V. A. Zuev, and M. S. Yakovlev,
"Several Problems of Ice Fracture by River Ice-Breaker,"
in Theory of Strength of Ice-Breaking Ship, No. 2
(Izd-vo GPI, Gor'kii, 1980),
pp. 4-10
[in Russian]. |
| 3. | S. A. Vershinin, "Interaction between Sea Ice Fields and
Continental Shelf Structure Footings," in Mechanics and
Physics of Ice (Nauka, Moscow, 1983), pp. 38-57 [in Russian]. |
| 4. | K. N. Korzhavin, "Physical Picture of Interaction between River
Ice Cover and Engineering Structure Footings," in
Mechanics and Physics of Ice (Nauka, Moscow, 1983),
pp. 135-140 [in Russian]. |
| 5. | Yu. P. Doronin and D. E. Kheisin,
Sea Ice
(Gidrometeoizdat, Leningrad, 1975)
[in Russian]. |
| 6. | S. A. Vershinin, Interaction between Sea Ice Fields and Continental Shelf Structure Footings, Abstract of Doctoral
Dissertation in Technical Sciences (Moscow, 1980) [in Russian]. |
| 7. | S. A. Vershinin, Fracture and Deformation of Sea Ice Fields Interacting with Continental Shelf Objects Abstract of Doctoral Dissertation in Mathematics and Physics (Leningrad, 1984) [in Russian]. |
| 8. | Yu. A. Dvoichenko, "Ice Field Deformation and Breaking," in
Theory and Strength of Ice-Breaking Ship, No. 2 (Izd-vo
GPI, Gor'kii, 1980), pp. 38-44. |
| 9. | B. Audoly and S. Neukirch, "Fragmentation of Rods by Cascading
Cracks: Why Spaghetti Do not Break in Half," Phys. Rev. Lett.
95 (9), 095505 (1-4) (2005). |
| 10. | Ch. Sykes (Editor),
No Ordinary Genius: The Illustrated Richard Feynman,
(W. W. Norton, New York, 1994),
p. 181. |
| 11. | S. P. Timoshenko and J. M. Gere,
Mechanics of Materials
(Van Nostrand Reinhold Company, 1972; Mir, Moscow, 1976). |
| 12. | A. R. Rzhanitsyn,
Structural Mechanics
(Vysshaya Shkola, Moscow, 1991)
[in Russian]. |
| 13. | Yu. N. Rabotnov,
Mechanics of Deformable Solids
(Nauka, Moscow, 1979)
[in Russian]. |
| 14. | G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev,
Reference Book in Strength of Materials
(Naukova Dumka, Kiev, 1975)
[in Russian]. |
| 15. | V. E. Kuz'michev,
Physics Laws and Formulas, Reference book
(Naukova Dumka, Kiev, 1989)
[in Russian]. |
| 16. | G. P. Cherepanov,
Mechanics of Brittle Failure
(Nauka, Moscow, 1974)
[in Russian]. |
|
| Received |
25 December 2008 |
| Link to Fulltext |
|
| << Previous article | Volume 46, Issue 3 / 2011 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English