Skip to main content
SpringerLink
Log in

Influence of Initial Stresses on the Fracture of Composite Material Weakened by a Subsurface Mode III Crack

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

By using the relations of linearized mechanics of deformable solids, we study the space problem of fracture of prestressed semibounded composites weakened by subsurface disk-shaped torsion (mode-III) cracks. With the help of representations of the general solutions of linearized equilibrium equations in terms of harmonic potential functions and Hankel integral transforms, we reduce the problem to a system of dual integral equations and then to the resolving Fredholm integral equation of the second kind. From the analysis of the stress distribution in the vicinity of the crack, we obtain the values of the stress intensity factors and study their dependences on the initial stresses, mechanical characteristics of the components of the composite, and geometric parameters of the problem.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. L. Bohdanov, “Influence of initial stresses on the stressed state of a composite with a periodic system of parallel coaxial normal tensile cracks,” Mat. Met. Fiz.-Mekh. Polya, 54, No. 3, 99–110 (2011); English translation: J. Math. Sci., 186, No. 1, 1–13 (2012).

    Article  Google Scholar 

  2. V. L. Bohdanov, “Nonaxisymmetric problem of the stress-strain state of an elastic half-space with a subsurface circular crack under the action of loads along it,” Mat. Met. Fiz.-Mekh. Polya, 52, No. 4, 173–190 (2009); English translation: J. Math. Sci., 174, No. 3, 341–366 (2011).

    Article  Google Scholar 

  3. V. L. Bohdanov, “On the interaction of a periodic system of parallel coaxial radial-shear cracks in a prestressed composite,” Mat. Met. Fiz.-Mekh. Polya, 54, No. 4, 59–70 (2011); English translation: J. Math. Sci., 187, No. 5, 606–619 (2012).

    Article  MathSciNet  Google Scholar 

  4. V. L. Bohdanov, “On a circular shear crack in a semiinfinite composite with initial stresses,” Fiz.-Khim. Mekh. Mater., 43, No. 3, 27–34 (2007); English translation: Mater. Sci., 43, No. 3, 321–330 (2007).

    Article  Google Scholar 

  5. V. L. Bohdanov, A. N. Guz’, and V. M. Nazarenko, “Stress-strain state of a material under forces acting along a periodic set of coaxial mode II penny-shaped cracks,” Prikl. Mekh., 46, No. 12, 3–16 (2010); English translation: Int. Appl. Mech., 46, No. 12, 1339–1350 (2010).

    Article  Google Scholar 

  6. V. L. Bohdanov, A. N. Guz’, and V. M. Nazarenko, “Fracture of semiinfinite material with a circular surface crack in compression along the crack plane,” Prikl. Mekh., 28, No. 11, 3–22. (1992); English translation: Int. Appl. Mech., 28, No. 11, 687–704 (1992).

    Article  Google Scholar 

  7. V. L. Bohdanov, A. N. Guz’, and V. M. Nazarenko, “Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem,” Prikl. Mekh., 45, No. 2, 3–18 (2009); English translation: Int. Appl. Mech., 45, No. 2, 111–124 (2009).

    Article  Google Scholar 

  8. A. N. Guz’, “On the linearized theory of fracture of brittle bodies with initial stresses,” Dokl. Akad. Nauk SSSR, 252, No. 5, 1085–1088 (1980).

    MathSciNet  Google Scholar 

  9. A. N. Guz’, “Mechanics of crack propagation in materials with initial (residual) stresses (review),” Prikl. Mekh., 47, No. 2, 3–75 (2011); English translation: Int. Appl. Mech., 47, No. 2, 121–168 (2011).

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  11. A. N. Guz’, “A criterion for the fracture of rigid bodies under compression along cracks. Three-dimensional problem,” Dokl. Akad. Nauk SSSR, 261, No. 1, 42–45 (1981).

    MathSciNet  Google Scholar 

  12. 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 

  13. A. N. Guz’, V. M. Nazarenko, and V. A. Nikonov, “Torsion of a prestressed half space with a disk-shaped crack at the surface,” Prikl. Mekh., 27, No. 10, 24–30 (1991); English translation: Int. Appl. Mech., 27, No. 10, 948–954 (1991).

    Google Scholar 

  14. A. A. Kaminskii and O. S. Bohdanova, “Long-term crack resistance of an orthotropic viscoelastic plate with a crack under biaxial loading. Safe loads,” Prikl. Mekh., 31, No. 9, 66–72 (1995); English translation: Int. Appl. Mech., 31, No. 9, 747–753 (1995).

    Article  Google Scholar 

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

    Google Scholar 

  16. L. P. Khoroshun, B. P. Maslov, E. N. Shikula, 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 

  17. 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 

  18. V. L. Bohdanov, “Effect of residual stresses on fracture of semi-infinite composites with cracks,” Mech. Adv. Mater. Struct., 15, No. 6–7, 453–460 (2008).

    Article  Google Scholar 

  19. V. L. Bohdanov, “Influence of initial stresses on fracture of composite materials containing interacting cracks,” J. Math. Sci., 165, No. 3, 371–384 (2010).

    Article  Google Scholar 

  20. A. N. Guz’, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer, Berlin (1999).

    Book  MATH  Google Scholar 

  21. A. N. Guz’, “On some non-classical problems of fracture mechanics taking into account the stresses along cracks,” Int. Appl. Mech., 40, No. 8, 937–941 (2004).

    Article  MathSciNet  Google Scholar 

  22. A. N. Guz’, V. M. Nazarenko, and V. L. Bohdanov, “Fracture under initial stresses acting along cracks: Approach, concept and results,” Theor. Appl. Fract. Mech., 48, No. 3, 285–303 (2007).

    Article  Google Scholar 

  23. M. K. Kassir and G. C. Sih, Mechanics of Fracture. Three-Dimensional Crack Problems, Vol. 2, Netherlands Noordhoff Int. Publ., Leyden (1975).

    Google Scholar 

  24. V. M. Nazarenko, V. L. Bohdanov, and H. Altenbach, “Influence of initial stress on fracture of a half space containing a penny-shaped crack under radial shear,” Int. J. Fract., 104, No. 3, 275–289 (2000).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Timoshenko Institute of Mechanics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    V. L. Bohdanov

Authors
  1. V. L. Bohdanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 3, pp. 110–121 July–October, 2013.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bohdanov, V.L. Influence of Initial Stresses on the Fracture of Composite Material Weakened by a Subsurface Mode III Crack. J Math Sci 205, 621–634 (2015). https://doi.org/10.1007/s10958-015-2270-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-015-2270-3

Keywords

Search

Navigation