Skip to main content
SpringerLink
Log in

Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials is carried out. Continuously distributed dislocations are used to simulate the crack. The simulation will cause singular integral equations with Cauchy kernel. By solving the singular integral equations numerically, the effects of crack depth (distance from the interface to the crack middle point) and Dundurs’ parameters on the Mode I stress intensity factor are investigated systematically. Then, based on the Dugdale model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings are investigated. The effects of uniform loadings, crack depth, and Dundurs’ parameters on the plastic zone size and the crack tip opening displacement are examined. Numerical results show that when the crack is embedded in a stiffer material, the values of both the normalized plastic zone size and the normalized crack tip opening displacement are larger than 1. On the contrary, if the crack is embedded in a softer material, the values of both the normalized plastic zone size and the crack tip opening displacement are less than 1.

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. England A.H.: A crack between dissimilar media. J. Appl. Mech. 32, 400–402 (1965)

    Article  Google Scholar 

  2. Comninou M.: Interface crack. J. Appl. Mech. 44, 631–636 (1977)

    Article  MATH  Google Scholar 

  3. Rice J.R.: Elastic fracture-mechanics concepts for interfacial cracks. J. Appl. Mech. 55, 98–103 (1988)

    Article  Google Scholar 

  4. Suo Z.G., Hutchinson J.W.: Interface crack between two elastic layers. Int. J. Fract. 43, 1–18 (1990)

    Article  Google Scholar 

  5. He M.Y., Evans A.G., Hutchinson J.W.: Crack deflection at an interface between dissimilar elastic materials—role of residual stresses. Int. J. Solids Struct. 31, 3443–3455 (1994)

    Article  MATH  Google Scholar 

  6. 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 

  7. Lu H., Lardner T.J.: Mechanics of subinterface cracks in layered material. Int. J. Solids Struct. 29, 669–688 (1992)

    Article  Google Scholar 

  8. Yang M.F., Kim K.S.: The behavior of subinterface cracks with crack-face contact. Eng. Fract. Mech. 44, 155–165 (1993)

    Article  Google Scholar 

  9. Xiao Z.M., Fan H., Sun Y.M.: On the contact zone of a subinterfacial Zener-Stroh crack. Acta. Mech. 142, 133–148 (2000)

    Article  MATH  Google Scholar 

  10. Huang G.Y., Wang Y.S., Gross D.: Fracture analysis of functionally graded coatings: antiplane deformation. Eur. J. Mech. A Solids 21, 391–400 (2002)

    Article  MATH  Google Scholar 

  11. Bogy D.B.: Plane elastostatic problem of a loaded crack terminating at a material interface. J. Appl. Mech. 38, 911–918 (1971)

    Article  MATH  Google Scholar 

  12. Hills D.A., Kelly P.A., Dai D.N., Korsunsky A.M.: Solution of Crack Problems: The Distributed Dislocation Technique. Springer, New York (1996)

    MATH  Google Scholar 

  13. Cook T.S., Erdogan F.: Stresses in bonded materials with a crack perpendicular to interface. Int. J. Eng. Sci. 10, 677–697 (1972)

    Article  MATH  Google Scholar 

  14. Erdogan F., Biriciko V.: Two bonded half planes with a crack going through interface. Int. J. Eng. Sc. 11, 745–766 (1973)

    Article  MATH  Google Scholar 

  15. Lin K.Y., Mar J.W.: Finite-element analysis of stress intensity factors for cracks at a bi-material interface. Int. J. Fract. 12, 521–531 (1976)

    Google Scholar 

  16. Suo Z.: Singularities interacting with interfaces and cracks. Int. J. Solids Struct. 25, 1133–1142 (1989)

    Article  Google Scholar 

  17. Wang W.C., Chen J.T.: Theoretical and experimental reexamination of a crack perpendicular to and terminating at the bimaterial interface. J. Strain Anal. Eng. Des. 28, 53–61 (1993)

    Article  Google Scholar 

  18. Wang T.C., Stahle P.: Stress state in front of a crack perpendicular to bimaterial interface. Eng. Fract. Mech. 59, 471–485 (1998)

    Article  Google Scholar 

  19. Guo L.C., Wu L.Z., Ma L., Zeng T.: Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface—part 1: static problem. Int. J. Fract. 127, 21–38 (2004)

    Article  MATH  Google Scholar 

  20. Zhang W., Deng X.: Elastic fields around the cohesive zone of a Mode III crack perpendicular to a bimaterial interface. J. Appl. Mech. 74, 1049–1052 (2007)

    Article  Google Scholar 

  21. Dugdale D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)

    Article  Google Scholar 

  22. Hoh H.J., Xiao Z.M., Lou J.: On the plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a circular inclusion. Acta Mech. 210, 305–314 (2010)

    Article  MATH  Google Scholar 

  23. Hoh H.J., Xiao Z.M., Luo J.: Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion. Philos. Mag. 90, 3511–3530 (2010)

    Article  Google Scholar 

  24. Yi D.K., Xiao Z.M., Zhuang J. et al.: On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate. Philos. Mag. 91, 3456–3472 (2011)

    Article  Google Scholar 

  25. Erdogan F., Gupta G.D.: Numerical solution of singular integral-equations. Q. Appl. Math. 29, 525–534 (1972)

    MathSciNet  MATH  Google Scholar 

  26. Dundurs J.: Effect of elastic constants on stress in a composite under plane deformation. J. Compos. Mater. 1, 310–322 (1967)

    Google Scholar 

  27. Korsunsky A.M., Hills D.A.: The solution of plane crack problems by dislocation dipole procedures. J. Strain Anal. Eng. Des. 30, 21–27 (1995)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Singapore

    D. K. Yi & Z. M. Xiao

  2. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, Singapore

    S. K. Tan

Authors
  1. D. K. Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. M. Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. K. Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. M. Xiao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yi, D.K., Xiao, Z.M. & Tan, S.K. Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials. Acta Mech 223, 1031–1045 (2012). https://doi.org/10.1007/s00707-012-0620-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0620-5

Keywords

Search

Navigation