### Abstract

In this paper, the problem of a functionally graded piezoelectric material (FGPM) with a constant-velocity Yoffe-type moving crack is considered. The strip is assumed to be under an anti-plane mechanical loading and an in-plane electric loading and its material properties, such as the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density, are assumed to vary continuously along the thickness of the strip. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. The closed forms of the singular stress, electric field and electric displacement are obtained from the asymptotic expansion of the stresses and electric fields around the crack tip. Different from the case of a stationary crack in an FGPM, it is found that at the tip of the crack the electric field also exhibits the singularity of the inverse square root, along with the stress and electric displacement singularities. It is also observed that increasing the gradient of the material properties can reduce the magnitudes of the stress and electric displacement intensity factors but it has little effect on the electric field intensity factor. When the crack moving velocity increases, both the stress and the electric displacement intensity factors decrease but the electric field intensity factor increases.

Original language | English (US) |
---|---|

Pages (from-to) | 381-399 |

Number of pages | 19 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 458 |

Issue number | 2018 |

DOIs | |

State | Published - Feb 8 2002 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

### Keywords

- Dynamic fracture
- Functionally graded piezoelectric materials
- Moving crack
- Piezoelectricity
- Stress and electric field intensity factors

### Cite this

}

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 458, no. 2018, pp. 381-399. https://doi.org/10.1098/rspa.2001.0873

**Yoffe-type moving crack in a functionally graded piezoelectric material.** / Li, Chunyu; Weng, G. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Yoffe-type moving crack in a functionally graded piezoelectric material

AU - Li, Chunyu

AU - Weng, G. J.

PY - 2002/2/8

Y1 - 2002/2/8

N2 - In this paper, the problem of a functionally graded piezoelectric material (FGPM) with a constant-velocity Yoffe-type moving crack is considered. The strip is assumed to be under an anti-plane mechanical loading and an in-plane electric loading and its material properties, such as the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density, are assumed to vary continuously along the thickness of the strip. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. The closed forms of the singular stress, electric field and electric displacement are obtained from the asymptotic expansion of the stresses and electric fields around the crack tip. Different from the case of a stationary crack in an FGPM, it is found that at the tip of the crack the electric field also exhibits the singularity of the inverse square root, along with the stress and electric displacement singularities. It is also observed that increasing the gradient of the material properties can reduce the magnitudes of the stress and electric displacement intensity factors but it has little effect on the electric field intensity factor. When the crack moving velocity increases, both the stress and the electric displacement intensity factors decrease but the electric field intensity factor increases.

AB - In this paper, the problem of a functionally graded piezoelectric material (FGPM) with a constant-velocity Yoffe-type moving crack is considered. The strip is assumed to be under an anti-plane mechanical loading and an in-plane electric loading and its material properties, such as the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density, are assumed to vary continuously along the thickness of the strip. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. The closed forms of the singular stress, electric field and electric displacement are obtained from the asymptotic expansion of the stresses and electric fields around the crack tip. Different from the case of a stationary crack in an FGPM, it is found that at the tip of the crack the electric field also exhibits the singularity of the inverse square root, along with the stress and electric displacement singularities. It is also observed that increasing the gradient of the material properties can reduce the magnitudes of the stress and electric displacement intensity factors but it has little effect on the electric field intensity factor. When the crack moving velocity increases, both the stress and the electric displacement intensity factors decrease but the electric field intensity factor increases.

KW - Dynamic fracture

KW - Functionally graded piezoelectric materials

KW - Moving crack

KW - Piezoelectricity

KW - Stress and electric field intensity factors

UR - http://www.scopus.com/inward/record.url?scp=33750901031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750901031&partnerID=8YFLogxK

U2 - 10.1098/rspa.2001.0873

DO - 10.1098/rspa.2001.0873

M3 - Article

AN - SCOPUS:33750901031

VL - 458

SP - 381

EP - 399

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2018

ER -