Dynamic stress intensity factor (Mode I) of a permeable penny-shaped crack in a fluid-saturated poroelastic solid

Yongjia Song, Hengshan Hu*, John W Rudnicki

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a permeable penny-shaped crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow on the dynamic stress intensity factor is analyzed. The Hankel integral transform technique in conjunction with Helmholtz potential theory is used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. Using appropriate transforms, the dual integral equations can be reduced to a Fredholm integral equation of the second kind. The phenomenon of fluid flow along the crack surface has significant influences upon the frequency-dependent behavior of the dynamic stress intensity factor. The stress intensity factor monotonically decreases with increasing frequency, declining the fastest when the crack radius and the slow wave wavelength are of the same order. Such near-field information is of particular importance in predicting the crack strength subjected to oscillating loads. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack radius decreases.

Original languageEnglish (US)
Pages (from-to)127-136
Number of pages10
JournalInternational Journal of Solids and Structures
Volume110-111
DOIs
StatePublished - Apr 1 2017

Fingerprint

Dynamic Stress Intensity Factor
stress intensity factors
Stress intensity factors
Crack
cracks
Cracks
Fluid
Fluids
fluids
Integral equations
integral equations
Stress Intensity Factor
Fluid Flow
Integral Equations
Radius
fluid flow
Flow of fluids
Decrease
Mixed Boundary Value Problem
Surface Crack

Keywords

  • Biot's theory
  • Dynamic stress intensity factor
  • Penny-shaped crack
  • Poroelasticity

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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title = "Dynamic stress intensity factor (Mode I) of a permeable penny-shaped crack in a fluid-saturated poroelastic solid",
abstract = "A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a permeable penny-shaped crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow on the dynamic stress intensity factor is analyzed. The Hankel integral transform technique in conjunction with Helmholtz potential theory is used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. Using appropriate transforms, the dual integral equations can be reduced to a Fredholm integral equation of the second kind. The phenomenon of fluid flow along the crack surface has significant influences upon the frequency-dependent behavior of the dynamic stress intensity factor. The stress intensity factor monotonically decreases with increasing frequency, declining the fastest when the crack radius and the slow wave wavelength are of the same order. Such near-field information is of particular importance in predicting the crack strength subjected to oscillating loads. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack radius decreases.",
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Dynamic stress intensity factor (Mode I) of a permeable penny-shaped crack in a fluid-saturated poroelastic solid. / Song, Yongjia; Hu, Hengshan; Rudnicki, John W.

In: International Journal of Solids and Structures, Vol. 110-111, 01.04.2017, p. 127-136.

Research output: Contribution to journalArticle

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AU - Hu, Hengshan

AU - Rudnicki, John W

PY - 2017/4/1

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N2 - A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a permeable penny-shaped crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow on the dynamic stress intensity factor is analyzed. The Hankel integral transform technique in conjunction with Helmholtz potential theory is used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. Using appropriate transforms, the dual integral equations can be reduced to a Fredholm integral equation of the second kind. The phenomenon of fluid flow along the crack surface has significant influences upon the frequency-dependent behavior of the dynamic stress intensity factor. The stress intensity factor monotonically decreases with increasing frequency, declining the fastest when the crack radius and the slow wave wavelength are of the same order. Such near-field information is of particular importance in predicting the crack strength subjected to oscillating loads. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack radius decreases.

AB - A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a permeable penny-shaped crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow on the dynamic stress intensity factor is analyzed. The Hankel integral transform technique in conjunction with Helmholtz potential theory is used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. Using appropriate transforms, the dual integral equations can be reduced to a Fredholm integral equation of the second kind. The phenomenon of fluid flow along the crack surface has significant influences upon the frequency-dependent behavior of the dynamic stress intensity factor. The stress intensity factor monotonically decreases with increasing frequency, declining the fastest when the crack radius and the slow wave wavelength are of the same order. Such near-field information is of particular importance in predicting the crack strength subjected to oscillating loads. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack radius decreases.

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