A viscoelastic functionally graded strip containing a crack subjected to in-plane loading

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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 = E0 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/E0 + (1 - E/Eo) exp(-t/t0) for a linear standard solid or f(t) = (t0/t)q for a power law material model, where E0, E, β, t0 and q are material constants. An extensional relaxation function in the form E = E0 exp(βy/h)[t0 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 = v0(1 + γy/h) exp(βy/h)g(t), where v0 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 languageEnglish (US)
Pages (from-to)1769-1790
Number of pages22
JournalEngineering Fracture Mechanics
Issue number14-16
StatePublished - Sep 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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


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