### Abstract

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

Pages (from-to) | 394-413 |

Number of pages | 20 |

Journal | Journal of Thermal Stresses |

Volume | 32 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Condensed Matter Physics
- Materials Science(all)

### Cite this

*Journal of Thermal Stresses*,

*32*(4), 394-413. https://doi.org/10.1080/01495730802637209

**A surface crack in a graded coating bonded to a homogeneous substrate under transient thermal loading.** / Gharbi, M.; El-Borgi, Sami; Chafra, M.

Research output: Contribution to journal › Article

*Journal of Thermal Stresses*, vol. 32, no. 4, pp. 394-413. https://doi.org/10.1080/01495730802637209

}

TY - JOUR

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

AU - Gharbi, M.

AU - El-Borgi, Sami

AU - Chafra, M.

PY - 2009/4

Y1 - 2009/4

N2 - 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.

AB - 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.

KW - Dynamic stress intensity factor

KW - Graded coating

KW - Singular integral equation

KW - Surface crack

KW - Transient thermal loading

UR - http://www.scopus.com/inward/record.url?scp=70449553350&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449553350&partnerID=8YFLogxK

U2 - 10.1080/01495730802637209

DO - 10.1080/01495730802637209

M3 - Article

VL - 32

SP - 394

EP - 413

JO - Journal of Thermal Stresses

JF - Journal of Thermal Stresses

SN - 0149-5739

IS - 4

ER -