Skip to main content
SpringerLink
Log in

Mode III fracture problem of two arbitrarily oriented cracks located within two bonded functionally graded material strips

  • Original Article
  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

This paper shows the anti-plane crack problem of two bonded functionally graded material (FGM) strips. Each strip contains an arbitrarily oriented crack. The material properties of the strips are assumed in exponential forms varied in the direction normal to the interface. After employing the Fourier transforms, the unknowns are solved from the interface conditions, boundary conditions and the condition on the crack surfaces. The problem can then be reduced to a system of singular integral equations, which are solved numerically by applying the Gauss-Chebyshev integration formula to obtain the stress intensity factors at the crack tips. In the discussions, several degenerated problems are considered to demonstrate the influence of the non-homogeneous parameters, crack orientations, edge effects and the crack interactions on the normalized intensity factors. In general, the factors are larger when crack tips are located in stronger material. Also, the factors increase as the crack is oriented in the direction normal to the interface. The conclusions made in this research can be used to evaluate the safety of two bonded strips once the cracks exist inside the structure.

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. Erdogan F, Aksogan O (1974) Bonded half planes containing an arbitrarily oriented crack. Int J Solids Struct 10:569–585

    Article  MATH  Google Scholar 

  2. Erdogan F, Arin K (1975) A half plane and a strip with an arbitrarily located crack. Int J Fract 11:191–204

    Article  Google Scholar 

  3. Ashbaugh N (1975) Stress solution for a crack at an arbitrarily angle to an interface. Int J Fract 11:205–219

    Article  Google Scholar 

  4. Krenk S (1975) On the elastic strip with an internal crack. Int J Solids Struct 11:693–708

    Article  MATH  Google Scholar 

  5. Isida M, Noguchi H (1993) Arbitrary array of cracks in bonded half planes subjected to various loadings. Eng Fract Mech 46:365–380

    Article  Google Scholar 

  6. Kim HK, Lee SB (1996) Stress intensity factors of an obliqe edge crack subjected to normal and shear tractions. Theor Appl Fract Mech 25:147–154

    Article  Google Scholar 

  7. Beghini M, Bertini L, Fontanari V (1999) Stress intensity factors for an inclined edge crack in a semiplane. Eng Fract Mech 62:607–613

    Article  Google Scholar 

  8. Konda N, Erdogan F (1994) Mixed mode crack problem in a nonhomogeneous elastic medium. Eng Fract Mech 47:533–545

    Article  Google Scholar 

  9. Shbeeb N, Binienda WK, Kreider K (2000) Analysis of the driving force for a generally oriented crack in a functionally graded strip sandwiched between two homogeneous half planes. Int J Fract 104:23–50

    Article  Google Scholar 

  10. Long X, Delale F (2004) The general problem for an arbitrarily oriented crack in a FGM layer. Int J Fract 129:221–238

    Article  MATH  Google Scholar 

  11. Long X, Delale F (2005) The mixed mode crack problem in a FGM layer bonded to a homogeneous half-plane. Int J Solids Struct 42:3897–3917

    Article  MATH  Google Scholar 

  12. Shbeeb N, Binienda WK (1999) Analysis of the driving forces for multiple cracks in an infinite nonhomogeneous plate, part I: theoretical analysis. J Appl Mech 66:492–500

    Article  Google Scholar 

  13. Choi HJ (2001) The problem for bonded half-planes containing a crack at an arbitrary angle to the graded interfacial zone. Int J Solids Struct 38:6559–6588

    Article  MATH  Google Scholar 

  14. Ma L, Wu LZ, Guo LC, Zhou ZG (2005) Dynamic behavior of a finite crack in the functionally graded materials. Mech Mater 37:1153–1165

    Article  Google Scholar 

  15. Theotokoglou EE, Paulino GH (2005) A crack in the homogeneous half plane interacting with a crack at the interface between the nonhomogeneous coating and the homogeneous half plane. Int J Fract 134:11–18

    Article  Google Scholar 

  16. Zhou ZG, Wang B (2006) An interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Meccanica 41:79–99

    Article  MathSciNet  MATH  Google Scholar 

  17. Orakdögen E, Küçükarslan S, Sofiyev A, Omurtag MH (2010) Finite element analysis of functionally graded plates for coupling effect of extension and bending. Meccanica 45:63–72

    Article  MATH  Google Scholar 

  18. Chiba R (2009) Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients. Meccanica 44:159–176

    Article  MathSciNet  Google Scholar 

  19. Chen YJ, Chue CH (2009) Mode III crack problems for two bonded functionally graded strips with internal cracks. Int J Solids Struct 46:331–343

    Article  MATH  Google Scholar 

  20. Erdogan F (1985) The crack problem for bonded non-homogeneous materials under anti-plane shear loading. ASME J Appl Mech 52:823–828

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, No. 1, University Road, 70101, Tainan, Taiwan, ROC

    Ching-Hwei Chue & Chien-Nan Yeh

Authors
  1. Ching-Hwei Chue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chien-Nan Yeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ching-Hwei Chue.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chue, CH., Yeh, CN. Mode III fracture problem of two arbitrarily oriented cracks located within two bonded functionally graded material strips. Meccanica 46, 447–469 (2011). https://doi.org/10.1007/s11012-010-9326-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-010-9326-8

Keywords

Search

Navigation