Summary
The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a penny-shaped crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under time-dependent electric load. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location and the material nonhomogeneity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen Z. T. and Meguid S. A. (2000). The transient response of a piezoelectric strip with a vertical crack under electromechanical impact load. Int. J. Solids Struct. 37: 6051–6062
Chen Z. T. and Worswick M. J. (2000). Antiplane mechanical and inplane electric time-dependent load applied to two coplanar cracks in piezoelectric ceramic. Theor. Appl. Fract. Mech. 33: 173–184
Ueda S. (2002). Impact response of a piezoelectric layered composite plate with a central crack. Theor. Appl. Fract. Mech. 38: 221–242
Ueda S. (2003). Enhancement of surface layer to a cracked piezoelectric half-plane under impact. Smart Mat. Struct. 12: 249–259
Ueda S. (2003). Normal impact of a piezoelectric strip with an off-center crack perpendicular to interface. Theor. Appl. Fract. Mech. 39: 259–273
Ueda S. (2003). Transient dynamic response of a coated piezoelectric strip with a vertical crack. Europ. J. Mech. A/Solids 22: 925–942
Ueda S. (2003). Transient response of sandwiched piezoelectric strip with crack normal to interface under impact. Theor. Appl. Fract. Mech. 40: 211–223
Wu C. M., Kahn M. and Moy W. (1996). Piezoelectric ceramics with functionally gradients: A new application in material design. J. Am. Ceram. Soc. 79: 809–812
Li C. and Weng G. J. (2002). Yoffe-type moving crack in a functionally graded piezoelectric material. Proc. Royal Soc. A 458: 381–399
Chen J., Liu Z. X. and Zou Z. Z. (2003). Electromechanical impact of a crack in a functionally graded piezoelectric medium. Theor. Appl. Fract. Mech. 39: 47–60
Ueda S. (2005). Impact response of a functionally graded piezoelectric plate with a vertical crack. Theor. Appl. Fract. Mech. 44: 329–342
Ueda S. (2006). Transient response of a center crack in a functionally graded piezoelectric strip under electromechanical impact. Engng. Fract. Mech. 73: 1455–1471
Ueda S. (2007). Electromechanical impact of an impermeable parallel crack in a functionally graded piezoelectric strip. Europ. J. Mech. A/Solids 26: 123–136
Erdogan F. and Wu B. H. (1997). The surface crack problem for a plate with functionally graded properties. Trans. ASME, J. Appl. Mech. 64: 449–456
Erdogan, F., Gupta, G. D., Cook, T. S.: Methods of analysis and solution of crack problems (Sih, G. C., ed.), p. 368. Leyden: Noordhoff 1972.
Miller M. K. and Guy W. T. (1966). Numerical inversion of the Laplace transform by use of Jacobi polynomials. SIAM J. Num. Anal. 3: 624–635
Wang B. L. and Mai Y. W. (2004). Impermeable crack and permeable crack assumptions, which one is more realistic? Trans. ASME, J. Appl. Mech. 71: 575–578
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ueda, S., Ashida, F. Transient response of a functionally graded piezoelectric strip with a penny-shaped crack under electric time-dependent loading. Acta Mechanica 194, 175–190 (2007). https://doi.org/10.1007/s00707-007-0463-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-007-0463-7