 | | 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
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| In English (Mech. Solids): | | 4760 |
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| R. V. Goldstein and N. M. Osipenko, "Beam Approximation in Problems of Delamination of Thin Coatings," Mech. Solids. 38 (5), 127-135 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
5 |
Pages |
127-135 |
| Title |
Beam Approximation in Problems of Delamination of Thin Coatings |
| Author(s) |
R. V. Goldstein (Moscow)
N. M. Osipenko (Moscow) |
| Abstract |
Multi-layer structural elements and systems with single- or multi-layer coatings are acquiring an ever increasing importance in modern technologies. Fracture of such structural elements and coatings is often connected with the development of cracks near the interfaces. modeling of adhesive strength and fracture is one of the topical problems of fracture mechanics. In this connection, it would be interesting to construct models utilizing relatively simple mathematical tools while giving a deeper understanding of adhesion fracture processes and the related mechanical effects. Beam models seem to meet these requirements. Among the relevant references, we should mention [1-3] and also [4, 5], where solutions were obtained for some problems of crack propagation along the layer boundaries in the beam approximation. In the present paper, a beam approximation is proposed for modeling resistance to adhesive fracture in the case of delamination of thin coatings, with the size of the delamination end-region being larger than the coating thickness. A representative element of the coating in the end-region is replaced by an effective beam of unit width loaded by a system of bonds inside the end-region. The external loads are represented by a longitudinal force and a concentrated bending moment applied to the free end on the beam. We discuss the conditions of fixation, assuming that there is no specific energy dissipation in the delamination end-region regarded as an effective crack with external loads compensated by adhesion forces. We consider some examples which demonstrate how the approach proposed here can be used for solving coating delamination problems for various types of bonds between the base and the coating. |
| References |
| 1. | L. I. Slepyan, Mechanics of Cracks [in Russian], Sudostroenie, Leningrad, 1981. |
| 2. | V. M. Entov and R. L. Salganik,
"On the beam approximation in the theory of cracks," Izv. AN SSSR.
Mekhanika, No. 5, pp. 95-102, 1965. |
| 3. | J. G. Williams,
"On the calculation of energy release rates for cracked laminates,"
Intern. J. Fracture, Vol. 36, No. 2, pp. 101-119, 1988. |
| 4. | A. V. Dyskin, L. N. Germanovich, and K. B. Ustinov,
"Asymptotic analysis of crack interaction with free boundary,"
Intern. J. Solids and Structures, Vol. 37, No. 6, pp. 857-886, 2000. |
| 5. | K. Hellan, Introduction to Fracture Mechanics [Russian translation], Mir, Moscow, 1988. |
| 6. | G. I. Barenblatt,
"Mathematical theory of equilibrium cracks formed in the process of brittle fracture," Zh. Prikl. Mechaniki i Tekhn. Fiziki, No. 4, pp. 3-56, 1961. |
| 7. | V. I. Feodos'ev, Strength of Materials [in Russian], Nauka, Moscow, 1986. |
| 8. | R. V. Goldstein and Yu. V. Zhitnikov, "Equilibrium of cavities and crack cuts with regions of overlapping and opening in an elastic medium,"
PMM [Applied Mathematics and Mechanics], Vol. 50, No. 5, pp. 826-834, 1986. |
| 9. | R. V. Goldstein and M. B. Konovalov,
"Asymptotic analysis of delamination in a bi-layered plate,"
C. R. Acad. Sci. Paris, Vol. 324, Ser. II b, No. 7, pp. 419-426, 1997. |
| 10. | R. V. Goldstein and M. B. Konovalov,
"Asymptotic analysis of the 3D problem on a crack-delamination in a two-layer plate,"
Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 62-71, 1996. |
|
| Received |
06 March 2003 |
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