 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 36, Issue 3 / 2001 | Next article >> |
| I. M. Lavit, "Energy balance near a crack tip in an elastic-plastic medium," Mech. Solids. 36 (3), 105-111 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
3 |
Pages |
105-111 |
| Title |
Energy balance near a crack tip in an elastic-plastic medium |
| Author(s) |
I. M. Lavit (Tula) |
| Abstract |
The statement of energy relations for an elastic-plastic body with
a crack has been the subject matter of numerous investigations. The list of
works reviewed in [1] is far from completion. Almost all these studies
are concerned with a single crack model, namely, the Griffith crack [2]
whose edges do not interact. The efforts to give a more detailed
description of the stress-strain state in the vicinity of a crack tip
resulted in a model with a cohesive zone - the Barenblatt crack [3-7].
The growth of such cracks in elastic-plastic media is investigated in
[8-11]. The present study differs from the earlier ones mostly in a more
rigorous approach to the analysis of the initial assumptions and the
clarification of the conditions ensuring the equivalence of these two crack
models. |
| References |
| 1. | S. N. Atluri, "Application of energy methods and path
independent integrals in the mechanics of fracture," in
Numerical Methods in Fracture Mechanics
[Russian translation], pp. 129-179, Mir, Moscow. |
| 2. | A. A. Griffith, "The phenomenon of rupture and flow in solids,"
Phil. Trans. Roy. Soc. London. Ser. A, Vol. 221, pp. 163-198, 1920. |
| 3. | G. I. Barenblatt, "On equilibrium cracks in brittle bodies.
General ideas and hypotheses. Axially symmetric cracks,"
PMM [Applied Mathematics and Mechanics], Vol. 23, No. 3, pp. 434-444,
1959. |
| 4. | G. I. Barenblatt, "On equilibrium cracks in brittle bodies.
Rectilinear cracks in plates,"
PMM [Applied Mathematics and Mechanics], Vol. 23, No. 4, pp. 706-721,
1959. |
| 5. | G. I. Barenblatt, "On equilibrium cracks in brittle bodies.
Stability of isolated cracks. Relation to energy theories,"
PMM [Applied Mathematics and Mechanics], Vol. 23, No. 5, pp. 893-900,
1959. |
| 6. | M. Ya. Leonov and V. V. Panasyuk, "Cracks propagation in solids,"
Prikl. Mekh., Vol. 5, No. 4, pp. 391-401, 1959. |
| 7. | D. S. Dugdale, "Yielding of steel sheets containing slits,"
J. Mech. and Phys, Vol. 8, No. 2, pp. 100-104, 1960. |
| 8. | H. C. Strifors, "A generalized force measure of conditions
at crack tips," Intern J. Solids and Struct., Vol. 10, No. 12,
pp. 1389-1404, 1974. |
| 9. | M. E. Gurtin, "Thermodynamics and the cohesive zone in
fracture," ZAMP, Vol. 30, No. 6, pp. 991-1003. |
| 10. | I. M. Lavit and L. A. Tolokonnikov,
"Cohesive forces and the J-integral,"
Izv. Sev. Kavkaz. Nauchn. Tsentra Vyssh. Shkoly. Est. Nauki,
No. 1, pp. 28-30, 1985. |
| 11. | I. M. Lavit, "Cohesive forces in fracture mechanics,"
Izv. Tulskogo Un-ta, Mat., Mekh., Informat., Vol. 1, No. 2, pp. 80-89,
1995. |
| 12. | A. Freidental and H. Geiringer,
Mathematical Theories of Inelastic Continua [Russian translation],
Fizmatgiz, Moscow, 1962. |
| 13. | C. Truesdell, A First Course in Rational Continuum Mechanics
[Russian translation], Mir, Moscow, 1975. |
| 14. | B. M. Budak and S. V. Fomin, Multiple Integrals and Series [in Russian],
Nauka, Moscow, 1975. |
| 15. | J. Rice, Mathematical Methods in Fracture Mechanics. Fracture.
Volume 2 [Russian translation], Mir, Moscow, 1975. |
| 16. | K. Hellan, Introduction to Fracture Mechanics [Russian
translation], Mir, Moscow, 1988. |
| 17. | G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian], Nauka,
Moscow, 1974. |
| 18. | W. Prager, An Introduction to Continuum Mechanics [Russian translation],
Izd-vo Inostr. Lit-ry, Moscow, 1963. |
| 19. | G. R. Irwin, "Fracture dynamics," in Fracturing of Metals,
pp. 147-166, ASM, Clevelend, 1948. |
| 20. | E. Orowan, "Fundamentals of brittle behavior of metals,"
in N. M. Murray (Editor), Fatigue and Fracture of Metals, pp. 139-167,
Wiley, New York, 1952. |
| 21. | G. V. Klevtsov and L. R. Botvina,
"Micro- and macrozones of plastic strains as criteria
of the limit state of fracturing materials," Probl. Prochn., No. 4,
pp. 24-28, 1984. |
| 22. | G. I. Barenblatt, "On some general concepts of
the mathematical theory of brittle fracture," PMM [Applied Mathematics and Mechanics], Vol. 28, No. 4,
pp. 630-643, 1964. |
| 23. | I. M. Lavit, "On stable crack growth in an elasti-plastic
material," Probl. Prochn., No. 7, pp. 18-23, 1988. |
| 24. | A. A. Il'yushin, Plasticity. Part 1.
Elastic-Plastic Deformation [in Russian], Gostekhizdat,
Moscow, Leningrad, 1948. |
|
| Received |
18 September 1998 |
| << Previous article | Volume 36, Issue 3 / 2001 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English