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

Sami El-Borgi, M. F. Djemel, R. Abdelmoula

Research output: Contribution to journalArticle

5 Citations (Scopus)


The elastostatic problem of a surface crack in a graded coating bonded to a homogeneous substrate under steady-state heat flux is considered. The coating is graded along the thickness direction and modeled 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 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 article is to study the effect of the layer thickness and nonhomogeneity parameters on the crack tip stress intensity factor for the purpose of gaining better understanding on the behavior of graded coatings under thermal loading.

Original languageEnglish
Pages (from-to)176-194
Number of pages19
JournalJournal of Thermal Stresses
Issue number2
Publication statusPublished - Feb 2008
Externally publishedYes



  • Graded coating
  • Singular integral equation
  • Stress intensity factor
  • Surface crack
  • Thermal loading

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physical and Theoretical Chemistry
  • Fluid Flow and Transfer Processes

Cite this