Buckling of an orthotropic graded coating with an embedded crack bonded to a homogeneous substrate

W. Aloulou, B. Yildirim, Sami El-Borgi, A. Zghal

Research output: Contribution to journalArticle

3 Citations (Scopus)


To simulate buckling of nonuniform coatings, we consider the problem of an embedded crack in a graded orthotropic coating bonded to a homogeneous substrate subjected to a compressive loading. The coating is graded in the thickness direction and the material gradient is orthogonal to the crack direction which is parallel with the free surface. The elastic properties of the material are assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the crack orientation. The loading consists of a uniform compressive strain applied away from the crack region. The graded coating is modeled as a nonhomogeneous medium with an orthotropic stress-strain law. Using a nonlinear continuum theory and a suitable perturbation technique, the plane strain problem is reduced to an eigenvalue problem describing the onset of buckling. Using integral transforms, the resulting plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the critical buckling strain. The Finite Element Method was additionally used to model the crack problem. The main objective of the paper is to study the influence of material nonhomogeneity on the buckling resistance of the graded layer for various crack positions, coating thicknesses and different orthotropic FGMs.

Original languageEnglish
Pages (from-to)1890-1900
Number of pages11
JournalInternational Journal of Solids and Structures
Issue number9
Publication statusPublished - 1 May 2009
Externally publishedYes



  • Buckling
  • Finite element method
  • Instability load
  • Nonlinear continuum theory
  • Orthotropic graded coating
  • Perturbation technique
  • Singular integral equations

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Applied Mathematics
  • Modelling and Simulation
  • Condensed Matter Physics

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