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Investigation of anti-plane shear behavior of a Griffith crack in a piezoelectric material by using the non-local theory

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Abstract

In this paper, the behavior of a Griffith crack in a piezoelectric material under anti-plane shear loading is investigated by using the non-local theory for impermeable crack surface conditions. By using the Fourier transform, the problem can be solved with two pairs of dual integral equations. These equations are solved using Schmidt method. Numerical examples are provided. Contrary to the previous results, it is found that no stress and electric displacement singularity is present at the crack tip.

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References

  • Amemiya, A. and Taguchi, T. (1969). Numerical Analysis and Fortran. Maruzen, Tokyo.

  • Chen, Z.T. and Karihaloo, B.I. (1999). Dynamic response of a cracked piezoelectric ceramic under arbitrary electro-mechanical impact. International Journal of Solds and Structures 36, 5125–5133.

    Google Scholar 

  • Deeg, W.E.F. (1980). The analysis of dislocation, crack and inclusion problems in piezoelectric solids, Ph.D. thesis, Stanford University.

  • Erdelyi, A. (ed.) (1954). Tables of Integral Transforms, Vol. 1. McGraw-Hill, New York.

    Google Scholar 

  • Eringen, A.C. (1974). Non-Local Elasticity andWaves. Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics (Edited by P. Thoft-Christensen), Kluwer Academic Publishers, Dordrecht, Holland, 81–105.

    Google Scholar 

  • Eringen, A.C., Speziale, C.G. and Kim, B.S. (1977a). Crack tip problem in non-local elasticity. Journal of Mechanics and Physics of Solids 25, 339–355.

    Google Scholar 

  • Eringen, A.C. (1977b). Continuum mechanics at the atomic scale. Crystal Lattice Defects 7, 109–130.

    Google Scholar 

  • Eringen, A.C. (1978). Linear crack subject to shear. International Journal of Fracture 14, 367–379.

    Google Scholar 

  • Eringen, A.C. (1979). Linear crack subject to antiplane shear. Engineering Fracture Mechanics 12, 211–219.

    Google Scholar 

  • Eringen, A.C. (1983). Interaction of a dislocation with a crack. Journal of Applied Physics 54, 6811.

    Google Scholar 

  • Gao, H., Zhang, T.Y. and Tong, P. (1997). Local and global energy rates for an elastically yielded crack in piezoelectric ceramics, Journal of Mechanics and Physics of Solids 45, 491–510.

    Google Scholar 

  • Gradshteyn, I.S. and Ryzhik, I.M. (1980). Table of Integral, Series and Products. Academic Press, New York.

    Google Scholar 

  • Han, Xue-Li and Wang, Tzuchiang (1999). Interacting multiple cracks in piezoelectric materials. International Journal of Solids and Structures 36, 4183–4202.

    Google Scholar 

  • Itou, S. (1978). Three dimensional waves propagation in a cracked elastic solid. ASME Journal of Applied Mechanics 45, 807–811.

    Google Scholar 

  • Itou, S. (1979). Three dimensional problem of a running crack. International Journal of Engineering Science 17, 59–71.

    Google Scholar 

  • Morse, P.M. and Feshbach, H. (1958). Methods of Theoretical Physics, Vol. 1. McGraw-Hill, New York.

    Google Scholar 

  • Narita, K. and Shindo, Y. (1998). Anti-plane shear crack growth rate of piezoelectric ceramic body with finite width. Theoretical and Applied Fracture Mechanics 30, 127–132.

    Google Scholar 

  • Pak, Y.E. (1990). Crack extension force in a piezoelectric material. Journal of Applied Mechanics 57, 647–653.

    Google Scholar 

  • Pak, Y.E. (1992). Linear electro-elastic fracture mechanics of piezoelectric materials. International Journal of Fracture 54, 79–100.

    Google Scholar 

  • Park, S.B. and Sun, C.T. (1995a). Effect of electric field on fracture of piezoelectric ceramics. International Journal of Fracture 70, 203–216.

    Google Scholar 

  • Park, S.B. and Sun, C.T. (1995b). Fracture criteria for piezoelectric ceramics. Journal of American Ceramics Society 78, 1475–1480.

    Google Scholar 

  • Shindo, Y., Narita, K. and Tanaka, K. (1996). Electroelastic intensification near anti-plane shear crack in orthotropic piezoelectric ceramic strip. Theoretical and Applied Fracture Mechanics 25, 65–71.

    Google Scholar 

  • Sosa, H. (1992). On the fracture mechanics of piezoelectric solids. International Journal of Solids and Structures 29, 2613–2622.

    Google Scholar 

  • Sosa, H., Khutoryansky, N. (1999). Transient dynamic response of piezoelectric bodies subjected to internal electric impulses. International Journal of Solids and Structures 36, 5467–5484.

    Google Scholar 

  • Suo, Z. (1993). Models for breakdown-resistant dielectric and ferroelectric ceramics. Journal of the Mechanics and Physics of Solids 41, 1155–1176.

    Google Scholar 

  • Suo, Z., Kuo, C.-M., Barnett, D.M. and Willis, J.R. (1992). Fracture mechanics for piezoelectric ceramics. Journal of Mechanics and Physics of Solids 40, 739–765.

    Google Scholar 

  • Wang, B. (1992). Three dimensional analysis of a flat elliptical crack in a piezoelectric material. International Journal of Engineering Science 30, 781–791.

    Google Scholar 

  • Yu, S.W. and Chen, Z.T. (1998). Transient response of a cracked infinite piezoelectric strip under anti-plane impact. Fatigue and Engineering Materials and Structures 21, 1381–1388.

    Google Scholar 

  • Zhang, T.Y. and Tong, P. (1996). Fracture mechanics for a mode III crack in a piezoelectric material. International Journal of Solids and Structures 33, 343–359.

    Google Scholar 

  • Zhang, T.Y., Qian, C.F. and Tong, P. (1998). Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material. International Journal of Solids and Structures 35, 2121–2149.

    Google Scholar 

  • Zhou, Z.G., Wang, Biao and Du, S.Y. (1998). Investigation of the scattering of harmonic elastic anti-plane shear waves by a finite crack using the non-local theory. International Journal of Fracture 91, 13–22.

    Google Scholar 

  • Zhou, Z.G., Han, J.C. and Du, S.Y. (1999). Two collinear Griffith cracks subjected to uniform tension in infinitely long strip. International Journal of Solids and Structures 36, 5597–5609.

    Google Scholar 

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Zhou, ZG., Du, SY. & Wang, B. Investigation of anti-plane shear behavior of a Griffith crack in a piezoelectric material by using the non-local theory. International Journal of Fracture 111, 105–117 (2001). https://doi.org/10.1023/A:1012201923151

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