 | | 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
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 52, Issue 5 / 2017 | Next article >> |
| N.A. Gorbushin and G.S. Mishuris, "Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice," Mech. Solids. 52 (5), 541-548 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
5 |
Pages |
541-548 |
| DOI |
10.3103/S0025654417050090 |
| Title |
Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice |
| Author(s) |
N.A. Gorbushin (Aberystwyth University, Penglais Campus, Penglais, Aberystwyth SY23 3FL, UK)
G.S. Mishuris (Aberystwyth University, Penglais Campus, Penglais, Aberystwyth SY23 3FL, UK, ggm@aber.ac.uk) |
| Abstract |
In this paper, the authors return to the classical problem of crack propagation in a lattice. The authors study the problems concerned with the possible regimes of stable steady-state crack propagation in an anisotropic lattice. They show that the steady-state crack propagation is impossible for some relations between the strength and elastic properties of the lattice. The authors also discuss the possibility of stable crack propagation at low speeds. |
| Keywords |
dynamic fracture of the lattice, stable crack propagation |
| References |
| 1. | A. A. Griffith,
"The Phenomena of Rupture and Flow in Solids,"
Philos. Trans. Roy. Soc. Ser. A
221, 163-198 (1921). |
| 2. | J. D. Eshelby,
"The Force on an Elastic Singularity,"
Philos. Trans. Roy. Soc.
244, 87-112 (1951). |
| 3. | 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)]. |
| 4. | 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)]. |
| 5. | R. Thompson, C. Hsieh, and V. Rana,
"Lattice Trapping of Fracture Cracks,"
J. Appl. Phys.
42 (8), 3154-3160 (1971). |
| 6. | L. I. Slepyan,
"Crack Propagation in High-frequency Lattice Vibration,"
Dokl. Akad. Nauk SSSR
260 (3), 566-569 (1981)
[Sov. Phys. Dokl. (Engl. Transl.)
26, 900-902 (1981)]. |
| 7. | L. I. Slepyan,
"On Discrete Models in Fracture Mechanics,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 46-59 (2010)
[Mech. Solids (Engl. Transl.)
45 (6), 803-814 (2010)]. |
| 8. | L. I. Slepyan and L. V. Troyankina,
"Fracture Wave in a Chain Structure,"
Zh. Prikl. Mekh. Tekhn. Fiz.,
No. 6, 128-134 (1984)
[J. Appl. Mech. Phys. (Engl. Transl.)
25 (16), 921-927 (1984)]. |
| 9. | S. A. Kulakhmetova, V. A. Saraikin, and L. I. Slepyan,
"Plane Problem of a Crack in a Lattice,"
Mech. Solids
19, 102-108 (1984). |
| 10. | A. J. Rosakis, O. Samudrala, and D. Coker,
"Cracks Faster then the Shear Wave Speed,"
Science
284 (5418), 1337-1340 (1999). |
| 11. | H. Gao, Y. Huang, and F. F. Abraham,
"Continuum and Atomic Studies of Intersonic Crack Propagation,"
J. Mech. Phys. Solids
49, 2113-2132 (2001). |
| 12. | G. S. Mishuris, A. V. Movchan, and L. I. Slepyan,
"Dynamics of a Bridged Crack in a Discrete Lattice,"
Quart. J. Mech. Appl. Math.
61 (2), 151-160 (2008). |
| 13. | N. Gorbushin and G. Mishuris,
"Analysis of Dynamic Failure of the Discrete Chain Structure with Nonlocal Interactions,"
Math. Mech. Appl. Sci.,
No. 23 (2016). |
| 14. | G. S. Mishuris, A. V. Movchan, and L. I. Slepyan,
"Localized Knife Waves in a Structured Interface,"
J. Mech. Phys. Solids
57, 1958-1979 (2009). |
| 15. | L. I. Slepyan,
Models and Phenomena in Fracture Mechanics
(Springer, Berlin, 2002). |
| 16. | L. Slepyan, A. Cherkaev, and E. Cherkaev,
"Transition Waves in Bistable Structures. II.
Analytical Solution: Wave Speed and Energy Dissipation,"
J. Mech. Phys. Solids
53 (2), 407-436 (2005). |
| 17. | L. Truskinowsky and A. Vainchtein,
"Kinetics of Martensite Phase Transitions: Lattice Model,"
SIAM J. Appl. Math.
66 (2), 533-553 (2005). |
| 18. | J. Fineberg and M. Marder,
"Instability in Dynamics Fracture,"
Phys. Rep.
313 (1), 1-108 (1999). |
| 19. | L. Pechnik, H. Levinem, and D. A. Kessler,
"Steady-State Mode I Cracks in a Viscoelastic Triangular Lattice,"
J. Mech. Phys. Solids
50 (3), 583-613 (2002). |
| 20. | K. Ravi-Chandar,
"Dynamic Fracture of Nominally Brittle Materials,"
Int. J. Fract.
90 (1), 83-102 (1998). |
| 21. | J. R. Wills and A. V. Movchan,
"Dynamic Weight Functions for a Moving Crack. I. Mode I Loading,"
J. Mech. Phys. Solids
43, 319-341 (1995). |
| 22. | A. V. Movchan and J. R. Wills,
"Dynamic Weight Functions for a Moving Crack. II. Shear Loading,"
J. Mech. Phys. Solids
43 (9), 1369-1383 (1995). |
| 23. | A. Picclroaz, G. Mishuris, and A. V. Movchan,
"Perturbation of Mode III Interfacial Cracks,"
Int. J. Fract.
166, 41-51 (2010). |
| 24. | X. P. Xu and A. Needleman,
"Numerical Simulations of Fast Crack Growth in Brittle Solids,"
J. Mech. Phys. Solids
42 (9), 1397-1434 (1994). |
| 25. | M. Marder,
"Simple Models of Rapid Fracture,"
Physica D
66, 125-134 (1993). |
| 26. | L. I. Slepyan, A. B. Movchan, and G. S. Mishuris,
"Crack in a Lattice Waveguide,"
Int. J. Fract.
162 (1-2), 91-106 (2010). |
| 27. | L. I. Slepyan, M. V. Ayzenberg-Stepanenko, and G. Mishuris,
"Forerunning Mode Transition in a Continuous Waveguide,"
J. Mech. Phys. Solids
78, 32-45 (2015). |
| 28. | K. Ravi-Chandar, and W. G. Knauss,
"An Experimental Investigation into Dynamic Fracture: III.
On Steady-State Crack Propagation and Crack Branching,"
Int. J. Fract.
26, 141-154 (1984). |
| 29. | M. Marder and S. Grass,
"Origin of Crack Tip Instabilities,"
J. Mech. Phys. Solids
43 (1), 1-48 (1995). |
| 30. | N. Gorbushin and G. Mishuris,
"Dynamic Fracture of a Discrete Media under Moving Load,"
2017.arXiv preprint arXiv:1701.02725. |
| 31. | M. V. Ayzenberg-Stepanenko, G. Mishuris, and L. I. Slepyan,
"Brittle Fracture in a Periodic Structure with Internal Potential Energy.
Spontaneous Crack Propagation,"
Proc. Roy. Soc. London. Ser. A
470 (2167), 20140121 (2014). |
| 32. | N. F. Morozov and M. V. Paukshto,
Discrete and Hybrid Models of Fracture Mechanics
(SPbGU, St. Petersburg, 1995)
[in Russian]. |
| 33. | N. F. Morozov and M. V. Paukshto,
"On the Crack Simulation and Solution in the Lattice,"
ASME J. Appl. Mech.
58, 290-292 (1991). |
| 34. | N. Gorbushin and G. Mishuris,
"On Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice,"
2017.arXiv preprint arXiv:1701.04818. |
|
| Received |
06 April 2017 |
| Link to Fulltext |
|
| << Previous article | Volume 52, Issue 5 / 2017 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English