Energy Criteria For Crack Propagation In Pre-Stressed Elastic Composites

Part of the Solid Mechanics And Its Applications book series (SMIA, volume 154)

We study the interaction of two unequal collinear cracks in a pre-stressed fiber reinforced elastic composite in Modes I and II of classical fracture. Using the theory of Riemann — Hilbert problem, Plemelj's function and the theory of Cauchy's integral we decide which tip of the crack will start to propagate first. We generalize Sih's fracture criterion for Modes I, II and we determine the direction of propagation for two transversally isotropic materials, graphite/epoxy and aramid/epoxy. The resonance phenomenon is studied in the case of unequal collinear cracks.

Keyword

collinear cracks pre-stressed elastic composite crack interaction Sih's fracture criterion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Craciun, E.M. (1999): Crack propagation conditions for a prestressed fiber — reinforced composite material acted by tangential forces. Vol. I. Theoretical analysis, Rev. Roum. Sci. Techn.-M«ec. Appl., 44, 2, pp. 149–164MathSciNetGoogle Scholar
  2. 2.
    Craciun, E.M. (1999): Crack propagation conditions for a prestressed fiber — reinforced composite material acted by tangential forces. Vol. II. Numerical analysis, Rev. Roum. Sci. Techn.-M«ec. Appl., 44, 4, pp. 435–446Google Scholar
  3. 3.
    Craciun, E.M., Soós, E. (1999): Sih's fracture criterion for anisotropic and pre-stressed materials. Rev. Roum. Sci. Techn.-M«ec. Appl., 44, 5, pp. 533–545Google Scholar
  4. 4.
    Craciun, E.M. (1999): Sih's energetical criterion and the second fracture mode. Rev. Roum. Sci. Techn.-Mec. Appl., Tome 45, 6, pp. 663–670Google Scholar
  5. 5.
    Guz, A.N. (1989): Fracture mechanics of composite materials acted by compression. Naukova Dumka, Kiev, in RussianGoogle Scholar
  6. 6.
    Guz A.N. (1983): Mechanics of brittle fracture of prestressed materials. Visha Schola, Kiev, in RussianGoogle Scholar
  7. 7.
    Guz A.N. (1986): The foundation of the three dimensional theory of the stability of deformable bodies. Visha Shcola, Kiev, in RussianGoogle Scholar
  8. 8.
    Guz A.N. (1991): Brittle fracture of materials with initial stresses. Naukova Dumka,Kiev, in RussianGoogle Scholar
  9. 9.
    Janke E., Emde F., Losch F. (1960): Tafeln höherer Functionen, Teubner, StuttgartGoogle Scholar
  10. 10.
    Kachanov, L.M. (1974): Fundamentals of fracture mechanics. Nauka, MoscowGoogle Scholar
  11. 11.
    Leblond, J.B. (1991): Mecanique de la rupture. Ecole Polytechnique, ParisGoogle Scholar
  12. 12.
    Muskhelishvili, N.I. (1953): Some basic problems of the mathematical theory of elasticity. Noordhoff Ltd., GroningenMATHGoogle Scholar
  13. 13.
    Rice, J.R. (1968): Mathematical theories of brittle fracture. H. Lebowitz (ed.) in Fracture — An advanced treatise, Vol. II. Mathematical fundamentals, pp. 192–314, Academic Press, New YorkGoogle Scholar
  14. 14.
    Sih G., Leibowitz H. (1968): Mathematical theories of brittle fracture. H. Lebowitz (ed.) in Fracture — An advanced treatise, Vol. II. Mathematical fundamentals, pp. 68–191, Academic Press, New YorkGoogle Scholar
  15. 15.
    Sih, G.C. (1973): Mechanics of fracture. G.C. Sih (ed.) in A special theory of crack propagation, Vol. I, pp. XXI–XLV, Norhoof Int. LeydenGoogle Scholar
  16. 16.
    Slepian L.I. (1981): Mechanics of cracks. Sudostroenie, LeningradGoogle Scholar
  17. 17.
    Sneddon, I.N., Lowengrub, M. (1969): Crack problems in the classical theory of elasticity. Wiley, Inc., New YorkMATHGoogle Scholar
  18. 18.
    Soós, E. (1996): Resonance and stress concentration in a pre-stressed elastic solid containing a crack. An apparent paradox. Int. J. Eng. Sci., 34, pp. 363–374MATHCrossRefGoogle Scholar
  19. 19.
    Tranter, C.J. (1961): The opening of a pair of coplanar Griffith's cracks under internal pressure. Quart. J. Mech. Appl. Math., 13, pp. 269–280MathSciNetGoogle Scholar
  20. 20.
    Willmore, T.J. (1969): The distribution of stress in the neighborhood of a crack. Quart. J. Mech. Appl. Math., II, pp. 53–60MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsOvidius University ConstantaRomania

Personalised recommendations