Abstract
This paper considers the non-axisymmetric three-dimensional problem of a penny-shaped crack with permeable electric conditions imposed on the crack surfaces, subjected to a pair of point normal forces applied symmetrically with respect to the crack plane. The crack is embedded in an infinite transversely isotropic piezoelectric body with the crack face perpendicular to the axis of material symmetry. Applying the symmetry of the problem under consideration then leads to a mixed–mixed boundary value problem of a half-space, for which potential theory method is employed for the purpose of analysis. The cases of equal eigenvalues are also discussed. Although the treatment differs from that for an impermeable crack reported in literature, the resulting governing equation still has a familiar structure. For the case of a point force, exact expressions for the full-space electro-elastic field are derived in terms of elementary functions with explicit stress and electric displacement intensity factors presented. The exact solution for a uniform loading is also given.
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References
P. Bisegna F. Maceri (1996) ArticleTitleAn exact three-dimensional solution for simply supported rectangular piezoelectric plate Journal of Applied Mechanics 63 628–638 Occurrence Handle0886.73054
W.Q. Chen H.J. Ding (2004) ArticleTitlePotential theory method for 3D crack and contact problems of multi-field coupled media: a survey Journal of Zhejiang University (SCIENCE) 5 1009–1021
W.Q. Chen H.J. Ding P.F. Hou (2001a) ArticleTitleExact solution of an external circular crack in a piezoelectric solid subjected to shear loading Journal of Zhejiang University (SCIENCE) 2 9–14 Occurrence Handle1068.74597 Occurrence Handle1:CAS:528:DC%2BD3MXhvVKkurc%3D Occurrence Handle10.1631/jzus.2001.0009
W.Q. Chen T. Shioya (1999a) ArticleTitleFundamental solution for a penny-shaped crack in a piezoelectric medium Journal of the Mechanics and Physics of Solids 47 1459–1475 Occurrence Handle0959.74019 Occurrence Handle1999JMPSo..47.1459C Occurrence Handle1686643
W.Q. Chen T. Shioya (1999b) ArticleTitleGreen’s functions of an external circular crack in a transversely isotropic piezoelectric medium JSME International Journal A 42 73–79 Occurrence Handle1:CAS:528:DyaK1MXitlGgsLc%3D
W.Q. Chen T. Shioya (2000) ArticleTitleComplete and exact solutions of a penny-shaped crack in a piezoelectric solid: antisymmetric shear loadings International Journal of Solids and Structures 37 2603–2619 Occurrence Handle0974.74050
W.Q. Chen T. Shioya H.J. Ding (2000) ArticleTitleA penny-shaped crack in piezoelectrics: Resolved International Journal of Fracture 105 49–56 Occurrence Handle1:CAS:528:DC%2BD3cXot1ahsb4%3D
W.Q. Chen T. Shioya H.J. Ding (2001b) ArticleTitleAn antisymmetric problem of a penny-shaped crack in a piezoelectric medium Archive of Applied Mechanics 71 63–73 Occurrence Handle1057.74032 Occurrence Handle1:CAS:528:DC%2BD3MXot1Ogur4%3D Occurrence Handle10.1007/s004190000111
Y.H. Chen T.J. Lu (2003) ArticleTitleCracks and fracture in piezoelectrics Advances in Applied Mechanics 39 121–215 Occurrence Handle1993454
H.J. Ding B. Chen J. Liang (1996) ArticleTitleGeneral solutions for coupled equations for piezoelectric media International Journal of Solids and Structures 33 2283–2298 Occurrence Handle0899.73453
H.J. Ding B. Chen J. Liang (1997) ArticleTitleOn the Green’s functions for two-phase transversely isotropic piezoelectric media International Journal of Solids and Structures 34 3041–3057 Occurrence Handle0942.74555
H.J. Ding W.Q. Chen (2001) Three Dimensional Problems of Piezoelasticity Nova Science Publishers New York
M.L. Dunn M. Taya (1994) ArticleTitleElectroelastic field concentrations in and around inhomogeneities in piezoelectric solids Journal of Applied Mechanics 61 474–475
V.I. Fabrikant (1986) ArticleTitleA new approach to some problems in potential theory ZAMM 66 363–368 Occurrence Handle0604.73110 Occurrence Handle864491
V.I. Fabrikant (1989) Applications of Potential Theory in Mechanics: A Selection of New Results Kluwer Academic Publishers Dordrecht Occurrence Handle0744.73016
V.I. Fabrikant (1991) Mixed Boundary Value Problem of Potential Theory and Their Applications in Engineering Kluwer Academic Publishers Dordrecht
P.F. Hou H.J. Ding F.L. Guan (2001) ArticleTitleA penny-shaped crack in an infinite piezoelectric body under antisymmetric point loads Journal of Zhejiang University (SCIENCE) 2 146–151 Occurrence Handle10.1631/jzus.2001.0146 Occurrence Handle1057.74010
L. Kogan C.Y. Hui V. Molkov (1996) ArticleTitleStress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezoelectric material International Journal of Solids and Structures 33 2719–2737 Occurrence Handle0903.73062
X.F. Li K.Y. Lee (2004) ArticleTitleElectro-elastic behavior induced by an external circular crack in a piezoelectric material International Journal of Fracture 126 17–38 Occurrence Handle1187.74187
D. Royer E. Dieulesaint (2000) Elastic Waves in Solids I. Free and Guided Propagation Springer-Verlag Berlin Occurrence Handle0960.74002
G.A. Schneider F. Felten R.M. McMeeking (2003) ArticleTitleThe electrical potential difference across cracks in PZT measured by Kelvin Probe Microscopy and the implications for fracture Acta Materialia 51 2235–2241 Occurrence Handle1:CAS:528:DC%2BD3sXisVGgsLs%3D
Z.K. Wang B.L. Zheng (1995) ArticleTitleThe general solution of three-dimensional problems in piezoelectric media International Journal of Solids and Structures 31 105–115
J.H. Yang K.Y. Lee (2001) ArticleTitlePenny-shaped crack in a three-dimensional piezoelectric strip under in-plane normal loadings Acta Mechanica 148 187–197 Occurrence Handle0987.74057
J.H. Yang K.Y. Lee (2002) ArticleTitleThree-dimensional non-axisymmetric behavior of a penny-shaped crack in a piezoelectric strip subjected to in-plane loads European Journal of Mechanics, A/Solids 21 223–237 Occurrence Handle1023.74039 Occurrence Handle1:CAS:528:DC%2BD38XotFeitrc%3D Occurrence Handle2002EJMS...21..223Y
J.H. Yang K.Y. Lee (2003) ArticleTitlePenny-shaped crack in a piezoelectric cylinder surrounded by an elastic medium subjected to combined in-plane mechanical and electric loads International Journal of Solids and Structures 40 573–590 Occurrence Handle1087.74617
T.Y. Zhang C.F. Gao (2004) ArticleTitleFracture behaviors of piezoelectric materials Theoretical and Applied Fracture Mechanics 41 339–379 Occurrence Handle1:CAS:528:DC%2BD2cXisVymt70%3D Occurrence Handle2067096
T.Y. Zhang P. Tong (1996) ArticleTitleFracture mechanics for a mode-III crack in a piezoelectric material International Journal of Solids and Structures 33 343–359 Occurrence Handle0919.73225
T.Y. Zhang M.H. Zhao P. Tong (2002) ArticleTitleFracture of piezoelectric ceramics Advances in Applied Mechanics 38 147–289 Occurrence Handle10.1016/S0065-2156(02)80104-1
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Chen, W.Q., Lim, C.W. 3D point force solution for a permeable penny-shaped crack embedded in an infinite transversely isotropic piezoelectric medium. Int J Fract 131, 231–246 (2005). https://doi.org/10.1007/s10704-004-4195-6
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DOI: https://doi.org/10.1007/s10704-004-4195-6