 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| I. M. Dunaev and V. I. Dunaev, "An energy-based fracture condition for thermoelastic solids," Mech. Solids. 38 (6), 55-64 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
6 |
Pages |
55-64 |
| Title |
An energy-based fracture condition for thermoelastic solids |
| Author(s) |
I. M. Dunaev (Krasnodar)
V. I. Dunaev (Krasnodar) |
| Abstract |
On the basis of thermodynamics of thermoelastic deformation, an energy-based condition of Griffith type is proposed as a criterion of brittle fracture of solid bodies subjected to single loading. This condition is examined in the case of plane stress (strain) state for two known models of an isolated defect. In the first model, the stresses prescribed on the external (remote) surface of the body with a defect coincide with those in the same body without defects. In the second model, displacements are prescribed on the outer surface of the body with a defect; these displacements correspond to the load applied to the body before the appearance of the defect (crack). In both these models, the crack surfaces are stress-free. It is shown that the first model, in the case of isothermal deformation, leads to the Griffith condition. This implies that the critical tensile stresses have the same absolute values as the critical compressive stresses, which does not agree with experimental data. The second model corresponds to an energy-based condition of Griffith type. From this condition, combined with certain additional assumptions on the crack shape and conditions of isotropy and convexity, we obtain a fracture curve (a macroscopic fracture criterion) in the form of an ellipse in the space of principal stresses and determine the crack orientation. The coefficients of the fracture curve explicitly depend on the elastic constants, the temperature, the linear heat expansion coefficient, and the crack size. |
| References |
| 1. | A. A. Griffith, "The phenomena of rupture and flow in solids,"
Philos. Trans. Roy. Soc., Ser. A 221, pp. 163-198, 1921. |
| 2. | A. A. Griffith, "The theory of rupture,"
Proc. Intern. Congr. Appl. Mech., pp. 55-63, J. Waltman, Delft, 1925. |
| 3. | B. Pol, "Macroscopic criteria of plastic flow and brittle fracture,"
in H. Liebowitz (Editor), Fracture. Volume 2 [Russian translation], pp. 336-520, Mir, Moscow, 1975. |
| 4. | W. Nowacki, Theory of Elasticity [Russian translation], Mir, Moscow, 1975. |
| 5. | A. A. Il'yushin, Continuum Mechanics [in Russian], Izd-vo MGU, Moscow, 1990. |
| 6. | G. M. Fikhtengol'ts, A Course in Differential and Integral Calculus.
Volume 3 [in Russian], Nauka, Moscow, 1969. |
| 7. | I. M. Dunaev and V. I. Dunaev,
"On an energy-based condition of fracture of solids,"
Doklady AN, Vol. 372, No. 1, pp. 43-45, 2000. |
| 8. | J. Goodier, "Mathematical theory of equilibrium cracks,"
in H. Liebowitz (Editor), Fracture. Volume 2 [Russian translation], pp. 71-89, Mir, Moscow, 1975. |
| 9. | N. I. Muskhelishvili,
Some Basic Problems in Mathematical Elasticity [in Russian], Nauka, Moscow, 1966. |
| 10. | I. I. Privalov, An Introduction to the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow, 1984. |
| 11. | G. C. Sih and H. Liebowitz,
"On the Griffith energy criterion for brittle fracture,"
Int. J. Solids Struct., Vol. 3, pp. 1-22, 1967. |
| 12. | P. M. Ogibalov, V. A. Lomakin, and B. P. Kishkin,
Mechanics of Polymers [in Russian], Izd-vo MGU, Moscow, 1975. |
|
| Received |
06 June 2002 |
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