### Abstract

The elastostatic problem of a surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions 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 crack surfaces are subjected to arbitrary loadings which give rise to mixed fracture modes which can be uncoupled due to the fact that the crack axis is parallel to the material gradient. Therefore, the opening and sliding mode problems may be formulated separately. For each problem, the solution of the composite medium may be determined by obtaining the solution of the homogeneous substrate and that of the graded layer. The latter solution may be expressed as the sum of two solutions, namely an infinite graded medium with a crack and a graded strip without a crack. The resulting mixed-boundary value problem is reduced to a set of two uncoupled singular integral equations which are solved numerically using Jacobi polynomials. The main objective of the paper is to study the effect of the layer thickness and nonhomogeneity parameter on the crack tip mixed-mode stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

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

Pages (from-to) | 1331-1353 |

Number of pages | 23 |

Journal | Journal of Mechanics of Materials and Structures |

Volume | 2 |

Issue number | 7 |

Publication status | Published - Sep 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Graded coating
- Mixed-mode loading
- Singular integral equations
- Stress intensity factor
- Surface crack

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials

### Cite this

*Journal of Mechanics of Materials and Structures*,

*2*(7), 1331-1353.

**A surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions.** / El-Borgi, Sami; Abdelmoula, Radhi; Dag, Serkan; Lajnef, Nizar.

Research output: Contribution to journal › Article

*Journal of Mechanics of Materials and Structures*, vol. 2, no. 7, pp. 1331-1353.

}

TY - JOUR

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

AU - El-Borgi, Sami

AU - Abdelmoula, Radhi

AU - Dag, Serkan

AU - Lajnef, Nizar

PY - 2007/9

Y1 - 2007/9

N2 - The elastostatic problem of a surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions 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 crack surfaces are subjected to arbitrary loadings which give rise to mixed fracture modes which can be uncoupled due to the fact that the crack axis is parallel to the material gradient. Therefore, the opening and sliding mode problems may be formulated separately. For each problem, the solution of the composite medium may be determined by obtaining the solution of the homogeneous substrate and that of the graded layer. The latter solution may be expressed as the sum of two solutions, namely an infinite graded medium with a crack and a graded strip without a crack. The resulting mixed-boundary value problem is reduced to a set of two uncoupled singular integral equations which are solved numerically using Jacobi polynomials. The main objective of the paper is to study the effect of the layer thickness and nonhomogeneity parameter on the crack tip mixed-mode stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

AB - The elastostatic problem of a surface crack in a graded coating bonded to a homogeneous substrate under general loading conditions 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 crack surfaces are subjected to arbitrary loadings which give rise to mixed fracture modes which can be uncoupled due to the fact that the crack axis is parallel to the material gradient. Therefore, the opening and sliding mode problems may be formulated separately. For each problem, the solution of the composite medium may be determined by obtaining the solution of the homogeneous substrate and that of the graded layer. The latter solution may be expressed as the sum of two solutions, namely an infinite graded medium with a crack and a graded strip without a crack. The resulting mixed-boundary value problem is reduced to a set of two uncoupled singular integral equations which are solved numerically using Jacobi polynomials. The main objective of the paper is to study the effect of the layer thickness and nonhomogeneity parameter on the crack tip mixed-mode stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

KW - Graded coating

KW - Mixed-mode loading

KW - Singular integral equations

KW - Stress intensity factor

KW - Surface crack

UR - http://www.scopus.com/inward/record.url?scp=34548700869&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548700869&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34548700869

VL - 2

SP - 1331

EP - 1353

JO - Journal of Mechanics of Materials and Structures

JF - Journal of Mechanics of Materials and Structures

SN - 1559-3959

IS - 7

ER -