Skip to main content
SpringerLink
Log in

Thermal stresses factors of orthotropic graded layers with a finite line bond

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In the paper, the problem of a finite line bond between two orthotropic functionally graded strips under thermal loading is considered. Considering some new boundary conditions, it is assumed that the temperature drop across the finite line bond is the result of the thermal conductivity index controlling heat conduction through the bond region. Using Fourier transforms technique, the therm-elastic mixed boundary value problems are reduced to a system of singular integral equations which can be solved approximately by applying the Chebyshev polynomials. The numerical results for the temperature and displacement field as well as the thermal stress intensity factors (TSIFs) are presented. The influence of the thickness of the layers and the thermo-elastic nonhomogeneity parameters on the temperature distribution and the TSIFs is discussed in detail. These results can be expected to be used for the purpose of gaining better understanding of the thermo-mechanical behavior of layered structures.

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. Williams M.L.: The Stress around a fault or crack in dissimilar media. Bull. Seismol. Soc. Am. 49, 199–204 (1959)

    Google Scholar 

  2. Erdogan F., Kaya A.C., Josehp P.F.: The crack problem in bonded non-homogeneous materials. J. Appl. Mech. 58, 410–418 (1991)

    Article  MATH  Google Scholar 

  3. Delale F., Erdogan F.: Interface crack in a non-homogeneous elastic medium. Int. J. Eng. Sci. 26, 559–568 (1988)

    Article  MATH  Google Scholar 

  4. Keer L.M., Guo Q.X.: Stress analysis for symmetrically loaded bonded layers. Int. J. Fract. 43, 69–81 (1990)

    Article  Google Scholar 

  5. Erdogan F., Wu B.H.: The surface crack problem for a plate with functionally graded properties. ASME J. Appl. Mech. 64, 449–456 (1997)

    Article  MATH  Google Scholar 

  6. El-Borgi S., Erdogan F., Benhatzra F.: Stress intensity factors for an interface crack between a functionally graded coating and a homogeneous substrate. Int. J. Fract. 123, 139–162 (2003)

    Article  Google Scholar 

  7. El-Borgi S., Erdogan F., Hidri L.: A partially insulated crack embedded in an infinite functionally graded medium under thermal-mechanical loading. Int. J. Eng. Sci. 42, 371–393 (2004)

    Article  Google Scholar 

  8. Chen J.: Determination of thermal stress intensity factors for interface crack in a graded orthotropic coating-substrate structure. Int. J. Fract. 133, 303–328 (2005)

    Article  MATH  Google Scholar 

  9. Zhou Y.T., Li X., Qin J.Q.: Transient thermal stress analysis of orthotropic functionally graded materials with a crack. J. Thermal Stress. 30, 1211–1231 (2007)

    Article  Google Scholar 

  10. Jin Z., Feng Y.: Thermal fracture resistance of a functionally graded coating with periodic edge crack. Surf. Coat. Technol. 202, 4189–4197 (2008)

    Article  Google Scholar 

  11. Zhou Y.T., Li X., Yu D.H.: A partially insulated interface crack between a graded orthotropic coating and a homogeneous orthotropic substrate under heat flux supply. Int. J. Solids Struct. 47, 768–778 (2010)

    Article  MATH  Google Scholar 

  12. Ding S.H., Li X.: Thermal stress intensity factors for an interface crack in a functionally graded layered structures. Arch. Appl. Mech. 81, 943–955 (2011)

    Article  Google Scholar 

  13. Erdogan F., Wu B.H.: Crack problems in FGM layers under thermal stresses. J. Thermal Stress. 19, 237–256 (1996)

    Article  Google Scholar 

  14. Itou S.: Thermal stress intensity factors of an infinite orthotropic layer with a crack. Int. J. Fract. 103, 279–291 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering and Water Conservancy, Ningxia University, Yinchuan, 750021, People’s Republic of China

    JunQiao Liu

  2. Faculty of Applied Mathematics, Yuncheng University, Yuncheng, 044000, People’s Republic of China

    JunQiao Liu

  3. School of Mathematics and Computer Science, Ningxia University, Yinchuan, 750021, People’s Republic of China

    Xing Li

  4. Beijing Military Representative Office of Land Activation, Army, Beijing, 100101, People’s Republic of China

    Peiyuan Liu

Authors
  1. JunQiao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peiyuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xing Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, J., Li, X. & Liu, P. Thermal stresses factors of orthotropic graded layers with a finite line bond. Arch Appl Mech 83, 939–954 (2013). https://doi.org/10.1007/s00419-013-0728-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-013-0728-7

Keywords

Search

Navigation