### 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 language | English (US) |
---|---|

Pages (from-to) | 127-136 |

Number of pages | 10 |

Journal | International Journal of Solids and Structures |

Volume | 110-111 |

DOIs | |

State | Published - Apr 1 2017 |

### Fingerprint

### 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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*International Journal of Solids and Structures*, vol. 110-111, pp. 127-136. https://doi.org/10.1016/j.ijsolstr.2017.01.034

**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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dynamic stress intensity factor (Mode I) of a permeable penny-shaped crack in a fluid-saturated poroelastic solid

AU - Song, Yongjia

AU - Hu, Hengshan

AU - Rudnicki, John W

PY - 2017/4/1

Y1 - 2017/4/1

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.

KW - Biot's theory

KW - Dynamic stress intensity factor

KW - Penny-shaped crack

KW - Poroelasticity

UR - http://www.scopus.com/inward/record.url?scp=85011072130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011072130&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2017.01.034

DO - 10.1016/j.ijsolstr.2017.01.034

M3 - Article

AN - SCOPUS:85011072130

VL - 110-111

SP - 127

EP - 136

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

ER -