Skip to main content
SpringerLink
Log in

Steady-state mode III delamination crack in a periodically layered medium

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

A non-homogeneous layered space with a semi-infinite interface crack is considered. Isotropic elastic layers having dissimilar thicknesses and shear moduli are arranged periodically and the antiplane stress state is produced by a shear loading applied to the crack faces. Application of the representative cell method based on the discrete Fourier transform allows to reduce the initial problem to the problem for a single bi-layered cell in the transform space and to formulate the Wiener–Hopf equation. The final result is presented in the form of triple quadratures. A parametric study of the stress intensity factor revealed some qualitative differences in its behavior for the cases of equal and non-equal layers thicknesses. The obtained analytical result is employed to derive of the closed form eigensolution corresponding to the traction free crack faces and vanishing remote loading. In addition to the local near tip square root asymptote this solution has also the remote one on a macroscale. The influence of the problem parameters on the ratio of the near to the far stress intensity factor is investigated and expressed by a simple algebraic formula which is confirmed by energy considerations. It is found that when the thin layers are more compliant this ratio is always less than unity, while in the opposite case the local stress singularity may exceed the remote one.

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. Chen E.P., Sih G.C.: Interfacial delamination of a layered composite under anti-plane strain. J. Compos. Mater. 5, 12–23 (1971)

    Article  Google Scholar 

  2. Hutchinson J.W., Suo Z.: Mixed mode cracking in layered materials. In: Hutchinson, J.W., Wu, T.Y. (eds) Advances in Applied Mechanics, vol. 29, pp. 63–191. Academic Press, San Diego (1991)

    Chapter  Google Scholar 

  3. Erdogan F., Gupta G.: Layered composites with an interface flaw. Int. J. Solids Struct. 7, 1089–1107 (1971)

    Article  MATH  Google Scholar 

  4. Sih G.C., Chen E.P.: Cracks in composite materials. In: Sih, G.C. (eds) Mechanics of Fracture, vol. 6, Martinus Nijhoff, The Hague (1981)

    Google Scholar 

  5. Kaczyński A., Matysiak S.: On crack problems in periodic two-layered elastic composites. Int. J. Fract. 37, 31–45 (1988)

    Article  Google Scholar 

  6. Charalambides P.G.: Steady-state mechanics of delamination cracking in laminated ceramic–matrix composites. J. Am. Ceram. Soc. 74, 3066–3080 (1991)

    Article  Google Scholar 

  7. Slepyan, L.: Crack in a layered medium. In: Selected Problems of Applied Mechanics, pp. 657–664, Viniti, Moscow (in Russian) (1974)

  8. Ryvkin M.: Antiplane deformation of a periodically layered composite with a crack. A non-homogenization approach. Int. J. Solids Struct. 35, 511–526 (1998)

    Article  MATH  Google Scholar 

  9. Kucherov L., Ryvkin M.: Interface crack in periodically layered bimaterial composite. Int. J. Fract. 117, 175–194 (2002)

    Article  Google Scholar 

  10. Nuller, B., Ryvkin, M.: On the boundary value problems for elastic domains of the periodical structure deformed by arbitrary loads. In: Proceedings of the State Hydraulic Institute, vol. 136, pp. 49–55, Energia, Leningrad (in Russian)(1980)

  11. Kucherov L., Ryvkin M.: Elastic solutions for periodically layered strip with perfect bonding or with an interface crack. Int. J. Solids Struct. 41, 4551–4565 (2004)

    Article  MATH  Google Scholar 

  12. Nuller B.: On the elastic deformation of a layered plate and a half-space. Proc. All-Union Res. Inst. Hydraul. Eng. (VNIIG) 151, 25–30 (1981) (in Russian)

    Google Scholar 

  13. Ryvkin M.: Mode III crack in a laminated medium. Int. J. Solids Struct. 33, 3611–3625 (1996)

    Article  MATH  Google Scholar 

  14. Atkinson S.: Dynamic crack problems in dissimilar media. In: Sih, G.C. (eds) Mechanics of Fracture 4, Elastodynamic Crack Problems, pp. 213–238. Noordhoff, Leyden (1977)

    Google Scholar 

  15. Slepyan L.I.: Models and Phenomena in Fracture Mechanics. Springer, Berlin (2002)

    MATH  Google Scholar 

  16. Ryvkin M., Slepyan L., Banks-Sills L.: On the scale effect in the thin layer delamination problem. Int J Fract 71, 247–271 (1995)

    Article  Google Scholar 

  17. Ryvkin M.: K-dominance zone for a semi-infinite Mode I crack in a sandwich composite. Int. J. Solids Struct. 37, 4825–4840 (2000)

    Article  MATH  Google Scholar 

  18. Hutchinson J.W., Mear M.E., Rice J.R.: Crack paralleling an interface between dissimilar materials. J. Appl. Mech. 54, 828–832 (1987)

    Article  Google Scholar 

  19. Postma G.W.: Wave propagation in stratified medium. Geophysics 20, 780–806 (1955)

    Article  ADS  Google Scholar 

  20. Ryvkin M., Kucherov L.: An inverse shielding effect in a periodically layered composite. Int. J. Fract. 108, L3–L8 (2001)

    Article  Google Scholar 

  21. Barthelat F., Espinosa H.D.: An experimental investigation of deformation and fracture of nacre-mother of pearl. Exp. Mech. 47, 311–324 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tel Aviv University, Ramat Aviv, Israel

    Michael Ryvkin

Authors
  1. Michael Ryvkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Ryvkin.

Additional information

Communicated by Prof. Rohan Abeyaratne.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ryvkin, M. Steady-state mode III delamination crack in a periodically layered medium. Continuum Mech. Thermodyn. 22, 635–646 (2010). https://doi.org/10.1007/s00161-010-0157-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-010-0157-6

Keywords

Search

Navigation