An axisymmetric problem of an embedded crack in a graded layer bonded to a homogeneous half-space.

*(English)*Zbl 1194.74311Summary: In an attempt to simulate non-uniform coating delamination, the elasto-static problem of a penny shaped axisymmetric crack embedded in a functionally graded coating bonded to a homogeneous substrate subjected to crack surface tractions is considered. The coating’s material gradient is parallel to the axisymmetric direction and is orthogonal to the crack plane. The graded coating is modeled as a non-homogeneous medium with an isotropic constitutive law. Using Hankel transform, the governing equations are converted into coupled singular integral equations, which are solved numerically to yield the crack tip stress intensity factors. The Finite Element Method was additionally used to model the crack problem. The main objective of this paper is to study the influence of the material non-homogeneity and the crack position on the stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.

##### MSC:

74R10 | Brittle fracture |

74G70 | Stress concentrations, singularities in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

##### Keywords:

graded coating; stress intensity factor; surface crack; mixed-mode loading; singular integral equations; finite elements method and singular elements
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\textit{M. Rekik} et al., Int. J. Solids Struct. 47, No. 16, 2043--2055 (2010; Zbl 1194.74311)

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