### Abstract

A crack in a viscoelastic functionally graded material (FGM) layer sandwiched between two dissimilar homogeneous viscoelastic layers is studied under antiplane shear conditions. The shear relaxation modulus of the FGM layer follows the power law of viscoelasticity, i.e., μ = μ_{0} exp(βy/h)[t_{0} exp(δy/h)/t]^{q}, where h is a scale length, and μ_{0}, t_{0}, β, δ and q are meterial constants. Note that the FGM layer has position-dependent modulus and relaxation time. The shear relaxation functions of the two homogeneous viscoelastic layers are μ = μ_{1}(t_{1}/t)^{q} for the bottom layer and μ = μ_{2}(t_{2}/t)^{q} for the top layer, where μ_{1} and μ_{2} are material constants, and t_{1} and t_{2} are relaxation times. An elastic crack problem of the composite structure is first solved and the 'correspondence principle' is used to obtain stress intensity factors (SIFs) for the viscoelastic system. Formulae for SIFs and crack displacement profiles are derived. Several examples are given which include interface cracking between a viscoelastic functionally graded interlayer and a viscoelastic homogeneous material coating. Moreover, a parametric study is conducted considering various material and geometric parameters and loading conditions.

Original language | English (US) |
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Pages (from-to) | 283-303 |

Number of pages | 21 |

Journal | International Journal of Fracture |

Volume | 111 |

Issue number | 3 |

DOIs | |

State | Published - Oct 2001 |

### Keywords

- Antiplane shear
- Correspondence principle
- Fracture
- Functionally graded material
- Stress intensity factor
- Viscoelasticity

### ASJC Scopus subject areas

- Computational Mechanics
- Modeling and Simulation
- Mechanics of Materials

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## Cite this

*International Journal of Fracture*,

*111*(3), 283-303. https://doi.org/10.1023/A:1012207008887