## Abstract

In this paper, a crack in a viscoelastic strip of a functionally graded material (FGM) is studied under tensile loading conditions. The extensional relaxation modulus is assumed as E = E_{0} exp(βy/h)f(t), where h is a scale length and f(t) is a nondimensional function of time t either having the form f(t) = E_{∞}/E_{0} + (1 - E_{∞}/E_{o}) exp(-t/t_{0}) for a linear standard solid or f(t) = (t_{0}/t)^{q} for a power law material model, where E_{0}, E_{∞}, β, t_{0} and q are material constants. An extensional relaxation function in the form E = E_{0} exp(βy/h)[t_{0} exp(δy/h)/t]^{q} is also considered, in which the relaxation time depends on the Cartesian coordinate y exponentially with δ being a material constant describing the gradation of the relaxation time. The Poisson's ratio is assumed to have the form v = v_{0}(1 + γy/h) exp(βy/h)g(t), where v_{0} and γ are material constants, and g(t) is a nondimensional function of time t. An elastic FGM crack problem is first solved and the "correspondence principle" is used to obtain both mode I and mode II stress intensity factors, and the crack opening/sliding displacements for the viscoelastic FGM considering various material models.

Original language | English (US) |
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Pages (from-to) | 1769-1790 |

Number of pages | 22 |

Journal | Engineering Fracture Mechanics |

Volume | 69 |

Issue number | 14-16 |

DOIs | |

State | Published - Sep 2002 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Materials Science
- Mechanics of Materials
- Mechanical Engineering

## Keywords

- Crack
- Functionally graded material
- Power law material
- Standard linear solid
- Stress intensity factor
- Viscoelasticity