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IssuesArchive of Issues2001-3pp.105-111

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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
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