Skip to main content
SpringerLink
Log in

Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating-substrate structure

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The thermal fracture problem of an interface crack between a graded orthotropic coating and the homogeneous substrate is investigated by two different approaches. For the case that most of the material properties in the graded orthotropic coating are assumed to vary as an exponential function, the integral transform and singular integral equation technique is used to obtain some analytical results. In order to analyze the case with more complex material distribution, an interaction integral is presented to evaluate the thermal stress intensity factors of cracked functionally graded materials (FGMs), and then the element-free Galerkin method (EFGM) is developed to obtain the final numerical results. The good agreement is obtained between the numerical results and the analytical ones. In addition, the influence of material gradient parameters and material distribution on the thermal fracture behavior is also presented.

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

  • G. Anlas M.H. Santare J. Lambros (2000) ArticleTitleNumerical calculation of stress intensity factors in functionally graded materials International Journal of Fracture 104 131–143 Occurrence Handle10.1023/A:1007652711735

    Article  Google Scholar 

  • C. Baoxing Z. Xiangzhou (1988) ArticleTitleThermoelasticity problem of an orthotropic plate with two collinear cracks International Journal of Fracture 38 161–192

    Google Scholar 

  • C. Baoxing (1995) ArticleTitleOrthotropic thermoelasticity problem of an antisymmetric heat flow disturbed by three coplanar cracks International Journal of Fracture 70 267–273 Occurrence Handle10.1007/BF00012939

    Article  Google Scholar 

  • T. Belytschko Y. Krongauz D. Organ M. Fleming P. Krysl (1996) ArticleTitleMeshless methods: an overview and recent developments Computer Methods in Applied Mechanics and Engineering 139 3–47 Occurrence Handle10.1016/S0045-7825(96)01078-X

    Article  Google Scholar 

  • J. Chen L.Z. Wu S.Y. Du (2000) ArticleTitleElement-free Galerkin methods for fracture of functionally graded materials Key Engineering Materials 183-187 487–492

    Google Scholar 

  • J. Chen L.Z. Wu S.Y. Du (2000) ArticleTitleA modified J integral for functionally graded materials Mechanics Research Communications 27 IssueID3 301–306 Occurrence Handle10.1016/S0093-6413(00)00096-3

    Article  Google Scholar 

  • J. Chen Z.X. Liu Z.Z. Zou (2002) ArticleTitleTransient internal crack problem for a nonhomogeneous orthotropic strip (Mode I) International Journal of Engineering and Science 40 1761–1774 Occurrence Handle10.1016/S0020-7225(02)00038-1

    Article  Google Scholar 

  • Y.F. Chen F. Erdogan (1996) ArticleTitleThe interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate Journal of Mechanics Physics Solids 44 771–787 Occurrence Handle10.1016/0022-5096(96)00002-6

    Article  Google Scholar 

  • S. Dag S. Kadioglu O.S. Yashi (1999) ArticleTitleCircumferential crack problem for an FGM cylinder under thermal stresses Journal of Thermal Stresses 22 659–687 Occurrence Handle10.1080/014957399280698

    Article  Google Scholar 

  • F. Delala F. Erdogan (1983) ArticleTitleThe crack problem for a nonhomogeneous plane ASME Journal of Applied Mechanics 50 823–825

    Google Scholar 

  • J.E. Dolbow M. Gosz (2002) ArticleTitleOn the computation of mixed-mode stress intensity factors in functionally graded materials International Journal of Solids and Structures 39 IssueID9 2557–2574 Occurrence Handle10.1016/S0020-7683(02)00114-2

    Article  Google Scholar 

  • Erdogan, F. (1975). Complex function technique. In: Continuum Physics, Vol. 2. Academic Press, New York, pp. 523–603.

  • F. Erdogan (1995) ArticleTitleFracture mechanics of functionally graded materials Composite Engineering 5 753–770

    Google Scholar 

  • F. Erdogan B.H. Wu (1997) ArticleTitleThe surface crack problem for a plate with functionally graded properties ASME Journal of Applied Mechanics 64 449–456

    Google Scholar 

  • F. Erdogan T.C. Chiu (2003) ArticleTitlePlane strain and axisymmetric spallation of graded coatings under thermal load Journal of Thermal Stresses 26 497–523

    Google Scholar 

  • P. Gu M. Dao R.J. Asaro (1999) ArticleTitleA simplified method for calculating the crack tip field of functionally graded materials using the domain integral ASME Journal of Applied Mechanics 66 101–108

    Google Scholar 

  • T. Honein G. Herrmann (1997) ArticleTitleConservation laws in homogeneous plane elastostatics Journal of the Mechanics and Physic of Solids 45 IssueID5 789–805 Occurrence Handle10.1016/S0022-5096(96)00087-7

    Article  Google Scholar 

  • S. Itou (2000) ArticleTitleThermal stress intensity factors of an in.nite orthotropic layer with a crack International Journal of Fracture 103 279–291 Occurrence Handle10.1023/A:1007630808737

    Article  Google Scholar 

  • Z.H. Jin N. Noda (1994) ArticleTitleTransient thermal stress intensity factors for a crack in a semi-infinite plate of a functionally gradient material International Journal of Solids and Structural 31 203–218 Occurrence Handle10.1016/0020-7683(94)90050-7

    Article  Google Scholar 

  • W.A. Kaysser B. Ilschner (1995) ArticleTitleFGM research activities in Europe MRS Bulletin 20 IssueID1 22–26

    Google Scholar 

  • J.K. Kim G.H. Paulino (2003) ArticleTitleMixed-mode J-integral formulation and implementation using graded elements for fracture analysis of nonhomogeneous orthotropic materials Mechanics of Materials 35 107–128 Occurrence Handle10.1016/S0167-6636(02)00159-X

    Article  Google Scholar 

  • N. Konda F. Erdogan (1994) ArticleTitleThe mixed mode crack problem in a nonhomogeneous elastic medium Engineering of Fracture Mechanics 47 533–545 Occurrence Handle10.1016/0013-7944(94)90253-4

    Article  Google Scholar 

  • P.R. Marur H.V. Tippur (2000) ArticleTitleNumerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient International Journal of Solids and Structures 37 5353–5370 Occurrence Handle10.1016/S0020-7683(99)00207-3

    Article  Google Scholar 

  • N. Noda Z.H. Jin (1993) ArticleTitleThermal stress intensity factors for a crack in a strip of a functionally gradient material International Journal of Solids and Structural 30 1039–1056 Occurrence Handle10.1016/0020-7683(93)90002-O

    Article  Google Scholar 

  • N. Noda (1999) ArticleTitleThermal stresses in functionally graded materials Journal of Thermal Stresses 22 477–512 Occurrence Handle10.1080/014957399280841

    Article  Google Scholar 

  • M. Ozturk F. Erdogan (1993) ArticleTitleThe axisymmetric crack problem in a nonhomogeneous medium ASME Journal of Applied Mechanics 60 406–413

    Google Scholar 

  • M. Ozturk F. Erdogan (1997) ArticleTitleMode I crack problem in an inhomogeneous orthotropic medium International Journal of Engineering Science 35 869–883 Occurrence Handle10.1016/S0020-7225(97)00014-1

    Article  Google Scholar 

  • M. Ozturk F. Erdogan (1999) ArticleTitleThe mixed mode crack problem in an inhomogeneous orthotropic medium International Journal of Fracture 98 243–261 Occurrence Handle10.1023/A:1018352203721

    Article  Google Scholar 

  • B.N. Rao S. Rahman (2003) ArticleTitleMesh-free analysis of cracks in isotropic functionally graded materials Engineering Fracture Mechanics 70 1–27 Occurrence Handle10.1016/S0013-7944(02)00038-3

    Article  Google Scholar 

  • J.R. Rice (1968) ArticleTitleA path independent integral and the approximate analysis of strain concentration by notches and cracks ASME Journal of Applied Mechanics 35 379–386

    Google Scholar 

  • S. Sampath H. Herman N. Shimoda T. Saito (1995) ArticleTitleThermal spray processing of FGMs MRS Bulletin 20 IssueID1 27–31

    Google Scholar 

  • N. Sukumar B. Moran T. Belytschko (1998) ArticleTitleThe natural element method in solid mechanics International Journal of Numerical Methods in Engineering 43 839–887 Occurrence Handle10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R

    Article  Google Scholar 

  • B.H. Wu F. Erdogan (1996) ArticleTitleCrack problems in FGM layers under thermal stresses Journal of Thermal Stresses 19 237–265

    Google Scholar 

  • B.L. Wang J.C. Han S.Y. Du (2000) ArticleTitleThermoelastic fracture mechanics for nonhomogeneous material subjected to unsteady thermal Load ASME Journal of Applied Mechanics 67 87–95 Occurrence Handle10.1115/1.321153

    Article  Google Scholar 

  • B. Yildirim F. Erdogan (2004) ArticleTitleEdge crack problems in homogeneous and functionally graded material thermal barrier coatings under uniform thermal load Journal of Thermal Stresses 27 311–329

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai, 200030, P.R. China

    Jian Chen

Authors
  1. Jian Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, J. Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating-substrate structure. Int J Fract 133, 303–328 (2005). https://doi.org/10.1007/s10704-005-4728-7

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-005-4728-7

Keywords

Search

Navigation