Skip to main content
Log in

Mutual influence of two parallel coaxial cracks in a composite material with initial stresses

  • Published:
Materials Science Aims and scope

Abstract

By using the approaches of three-dimensional linearized mechanics of deformed bodies, we study the axisymmetric problem of two parallel coaxial circular cracks in an infinite composite material with initial stresses acting in the planes of the cracks. The resolving system of Fredholm integral equations of the second kind is deduced and the representations of the stress intensity factors in the vicinity of the crack tips are obtained. The dependences of the stress intensity factors on the initial stresses and the distance between the cracks are determined. For two types of composite materials, namely, for a layered composite with isotropic layers and a composite with stochastic reinforcement by short ellipsoidal fibers, the stress intensity factors are computed and their dependences on the initial stresses, physicomechanical characteristics of the composites, and geometric parameters of the problem are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. A. Shul'ga and V. T. Tomashevskii, Technological Stresses and Strains in Materials, in: A. N. Guz' (editor), Mechanics of Composites [in Russian], Vol. 6, A.S.K. Kiev (1997).

    Google Scholar 

  2. A. N. Guz', Mechanics of Brittle Fracture of Materials with Initial Stresses [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  3. A. N. Guz', Brittle Fracture of Materials with Initial Stresses, in: A. N. Guz' (editor), Nonclassical Problems of Fracture Mechanics [in Russian], Vol. 2, Naukova Dumka, Kiev (1991).

    Google Scholar 

  4. A. N. Guz, “On the development of brittle-fracture mechanics of materials with initial stress,” Int. Appl. Mech., 32, No. 4, 316–323 (1996).

    Article  MATH  Google Scholar 

  5. A. N. Guz, N. Sh. Dyshel', and V. M. Nazarenko, “Fracture and stability of materials and structural members with cracks: Approaches and results,” Int. Appl. Mech., 40, No. 12, 1323–1359 (2004).

    Article  Google Scholar 

  6. A. N. Guz, V. M. Nazarenko, and V. L. Bogdanov, “Fracture under initial stresses acting along cracks: Approach, concept, and results,” Theor. Appl. Fract. Mech., 48, 285–303 (2007).

    Article  Google Scholar 

  7. A. N. Guz', “Dynamic problems in the mechanics of brittle fracture of materials with initial stresses for propagating cracks. 1. Statement of the problems and general relations,” Prikl. Mekh., 34, No. 12, 3–15 (1998).

    MathSciNet  Google Scholar 

  8. V. P. Silovanyuk, “Cracks and cracklike defects in prestressed bodies,” Fiz.-Khim. Mekh. Mater., 31, No. 2, 22–35 (1995).

    CAS  Google Scholar 

  9. V. L. Bogdanov, “Axisymmetric problem of a subsurface mode I crack in a composite material with residual stresses,” Mat. Met. Fiz.-Mekh. Polya, 50, No. 2, 45–54 (2007).

    MATH  MathSciNet  Google Scholar 

  10. V. L. Bogdanov, “On a circular shear crack in a semiinfinite composite with initial stresses,” Fiz.-Khim. Mekh. Mater., 43, No. 3, 27–34 (2007).

    Google Scholar 

  11. V. L. Bogdanov, “Effect of residual stresses on the fracture of semiinfinite composites with cracks,” Mech. Adv. Mater. Struct., 15, No. 6, 453–460 (2008).

    Article  CAS  Google Scholar 

  12. L. P. Khoroshun, B. P. Maslov, E. N. Shykula, and L. V. Nazarenko, Statistical Mechanics and Effective Properties of Materials, in: A. N. Guz' (editor), Mechanics of Composites [in Russian], Vol. 3, Naukova Dumka, Kiev (1993).

    Google Scholar 

  13. Ya. S. Uflyand, Method of Coupled Equations in Problems of Mathematical Physics [in Russian], Nauka, Leningrad (1977).

    Google Scholar 

  14. Van Fo Fy, Theory of Reinforced Plastics [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  15. B. P. Maslov, Investigation of Stochastic Composites with Nonlinear and Anisotropic Properties of the Components [in Russian], Author's Abstract of the Doctor-Degree Thesis (Physics and Mathematics), Kiev (1983).

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 4, pp. 58–67, July–August, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bohdanov, V.L. Mutual influence of two parallel coaxial cracks in a composite material with initial stresses. Mater Sci 44, 530–540 (2008). https://doi.org/10.1007/s11003-009-9113-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11003-009-9113-7

Keywords

Navigation