### Abstract

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 language | English |
---|---|

Pages (from-to) | 176-194 |

Number of pages | 19 |

Journal | Journal of Thermal Stresses |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

- 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

*Journal of Thermal Stresses*,

*31*(2), 176-194. https://doi.org/10.1080/01495730701737886

**A surface crack in a graded coating bonded to a homogeneous substrate under thermal loading.** / El-Borgi, Sami; Djemel, M. F.; Abdelmoula, R.

Research output: Contribution to journal › Article

*Journal of Thermal Stresses*, vol. 31, no. 2, pp. 176-194. https://doi.org/10.1080/01495730701737886

}

TY - JOUR

T1 - A surface crack in a graded coating bonded to a homogeneous substrate under thermal loading

AU - El-Borgi, Sami

AU - Djemel, M. F.

AU - Abdelmoula, R.

PY - 2008/2

Y1 - 2008/2

N2 - 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.

AB - 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.

KW - Graded coating

KW - Singular integral equation

KW - Stress intensity factor

KW - Surface crack

KW - Thermal loading

UR - http://www.scopus.com/inward/record.url?scp=39749117939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39749117939&partnerID=8YFLogxK

U2 - 10.1080/01495730701737886

DO - 10.1080/01495730701737886

M3 - Article

VL - 31

SP - 176

EP - 194

JO - Journal of Thermal Stresses

JF - Journal of Thermal Stresses

SN - 0149-5739

IS - 2

ER -