 | | 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
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| V. V. Glagolev and A. A. Markin, "A model of the process of steady separation of a material layer," Mech. Solids. 39 (5), 97-104 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
5 |
Pages |
97-104 |
| Title |
A model of the process of steady separation of a material layer |
| Author(s) |
V. V. Glagolev (Tula)
A. A. Markin (Tula) |
| Abstract |
The mechanical separation of a deformable body is suggested
to be described on the basis of equations that relate the deformation and loading processes for the representative volume of the material. Let δ0 be the initial linear dimension of this volume. We consider the stable and unstable (according to Drucker) stages of the deformation. The transition from the stable stage to the unstable stage occurs when the maximum principal tensile component of the strain tensor attains its lower critical value. This critical value is a material constant. This approach is a development of the fracture concept of [1]. It is known that the formation of micropores and cracks at the pre-fracture stage leads to softening of the material. From the point of view of continuum mechanics, this effect manifests itself by the presence of the descending segment on the complete deformation curve. Experimental techniques for constructing complete deformation curves are presented in [2, 3].
In the present paper, we consider the separation of a material layer under an external load symmetric with respect to the plane of the separation. A layer of thickness δ0 formed by the material transforming to the softening stage is considered. A phenomenological definition of the surface energy of the material is given on the basis of the fundamental thermodynamic relationship [4]. On the basis of the physical definitions of the surface energy given in [5-7], the thickness of the interaction layer is evaluated in terms of the interatomic spacing, Young's modulus, and the limit of elasticity.
On the basis of the thermodynamic analysis of the quasi-reversible separation, when the behavior of the material outside the interaction layer is assumed to be elastic, a representation for the invariant contour integral is obtained. Unlike the traditional approaches of [8, 9], in which the crack is regarded as a mathematical cut, the proposed approach does not lead to singularities and infinite stresses. Proceeding from this concept, we establish the relationship between the familiar fracture criteria (Griffith, Irwin, Cherepanov-Rice, and Leonov-Panasyuk-Dugdale ones) and the critical values of the specific free energy and dissipation. To obtain specific values for these criteria within the concept under consideration, it suffices to have the complete tension diagram and know the thickness of the interaction layer. |
| References |
| 1. | A. M. Lin'kov, "Fracture as the loss of stability: Some new effects, methods, and results,"
in Nonlinear Problems of Mechanics and Physics of Solids.
Collected Works of the Scientific School of Academician
V. V. Novozhilov [in Russian], No. 4, pp. 13-31, Izd-vo SPbGU, St. Petersburg,
2001. |
| 2. | A. A. Lebedev and N. G. Chausov,
"An installation for material tests with the construction of completely equilibrium deformation curves,"
Problemy Prochnosti, No. 12, pp. 104-106, 1981. |
| 3. | A. A. Lebedev, N. G. Chausov, and Yu. L. Evitskii,
"A technique for constructing complete deformation curves
for sheet materials,"
Problemy Prochnosti, No. 9, pp. 29-32, 1986. |
| 4. | A. A. Il'yushin, Continuum Mechanics
[in Russian], Izd-vo MGU, Moscow, 1990. |
| 5. | G. P. Cherepanov,
Mechanics of Brittle Fracture
[in Russian], Nauka, Moscow, 1974. |
| 6. | N. F. Morozov, Mathematical Issues of the Theory of Cracks
[in Russian], Nauka, Moscow, 1984. |
| 7. | A. H. Cottrell, Tewksbury Symposium on Fracture,
University of Melbourne, 1963. |
| 8. | G. P. Cherepanov, "On the propagation of cracks in a continuous
medium,"
PMM [Applied Mathematics and Mechanics], Vol. 31, No. 3, pp. 476-488, 1967. |
| 9. | V. M. Alexandrov and I. I. Kudish,
"Asymptotic methods in the Griffith problem,"
PMM [Applied Mathematics and Mechanics], Vol. 53, No. 4, pp. 665-671, 1989. |
| 10. | V. V. Panasyuk,
Mechanics of Quasi-brittle Fracture of Materials
[in Russian], Naukova Dumka, Kiev, 1991. |
| 11. | V. Z. Parton and E. M. Morozov,
Mechanics of Elastoplastic Fracture
[in Russian], Nauka, Moscow, 1985. |
|
| Received |
26 December 2002 |
| << Previous article | Volume 39, Issue 5 / 2004 | Next article >> |
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