A surface crack in a graded coating bonded to a homogeneous substrate under transient thermal loading

M. Gharbi, Sami El-Borgi, M. Chafra

Research output: Contribution to journalArticle

3 Citations (Scopus)


The elastodynamic problem of a surface crack in a graded coating bonded to a homogeneous substrate under transient heat flux is considered. The coating is graded along the thickness direction and modelled as a nonhomogeneous medium with an isotropic stress-strain law. The problem is solved under the assumption of plane strain or generalized plane stress conditions. The resulting crack problem is of mode I because the orientations of the crack axis, the material gradient and the heat-flux are all parallel. The equivalent crack surface tractions are first obtained and substituted in the plane elasticity equations which are then converted analytically using appropriate integral transforms into a singular integral equation. The resulting equation is solved numerically using orthogonal Jacobi polynomials to yield the Mode I stress intensity factor. The main objective of the research is to study the effect of the layer thickness and nonhomogeneity parameters on the dynamic crack tip stress intensity factor for the purpose of gaining better understanding on the behavior of graded coatings under transient thermal loading.

Original languageEnglish
Pages (from-to)394-413
Number of pages20
JournalJournal of Thermal Stresses
Issue number4
Publication statusPublished - Apr 2009
Externally publishedYes



  • Dynamic stress intensity factor
  • Graded coating
  • Singular integral equation
  • Surface crack
  • Transient thermal loading

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Materials Science(all)

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