Abstract
In this paper, the problem of a functionally graded piezoelectric strip with a constant-velocity Yoffe-type moving crack is considered. By using the Fourier transforms, the problem is first reduced to dual integral equations and then into Fredholm integral equations of the second kind. The electroelastic field near the crack tip is obtained for electrical impermeable boundary conditions and electrical permeable boundary conditions, respectively. The results obtained show that the gradient of the material properties can increase or decrease the magnitudes of the stress intensity factors, and the velocity can disturb the stress distribution near the crack tip.
Similar content being viewed by others
References
Z.T. Chen S.W. Yu (1997) ArticleTitleAntiplane Yoffe crack problem in piezoelectric materials International Journal of Fracture 84 L41–L45
E.T. Copson (1961) ArticleTitleOn certain dual integral equations Proceedings of the Glasgow Mathematical Association 5 19–24
Deeg, W.F. (1980). “The analysis of dislocation, crack, and inclution problems in piezoelectric solids,” Ph.D. Thesis, Stanford University.
B. Jin Z. Zhong (2002) ArticleTitleA moving mode-III crack in functionally graded piezoelectric material: permeable problem Mechanics Research Communications 29 217–224 Occurrence Handle10.1016/S0093-6413(02)00259-8
S. Kumar R.N. Singh (1996) ArticleTitleCrack propagation in piezoelectric materials under combined mechanical and electrical loadings Acta Materialia 44 173–200 Occurrence Handle1:CAS:528:DyaK28XhvFWmtQ%3D%3D
S.M. Kwon J.S. Lee K.Y. Lee (2002) ArticleTitleMoving eccentric crack in a piezoelectric strip bonded to elastic half planes International Journal of Solids and Structures 39 4395–4406 Occurrence Handle10.1016/S0020-7683(02)00338-4
X.F. Li T.Y. Fan X.F. Wu (2000) ArticleTitleA moving mode-III crack at the interface between two dissimilar piezoelectric materials International Journal of Engineering Science 38 1219–1234 Occurrence Handle1:CAS:528:DC%2BD3cXksFSkurg%3D
McHenry, K.D. and Koepke, B.G. (1983). In: R.C. Bradt, D.P. Hasselman and F.F. Lange (eds.), Fracture Mechanics of Ceramics, Vol. 5, Plenum Press, New York, 1983. pp. 337–352.
S.A. Meguid Z.T. Chen (2001) ArticleTitleTransient response of finite piezoelectric strip containing coplanar insulating cracks under electromechanical impact Mechanics of Materials 33 85–96 Occurrence Handle10.1016/S0167-6636(00)00052-1
F. Narita Y. Shindo (1998) ArticleTitleDynamic anti-plane shear of a cracked piezoelectric ceramic Theoretical and Applied Fracture Mechanics 29 169–180 Occurrence Handle10.1016/S0167-8442(98)00028-7 Occurrence Handle1:CAS:528:DyaK1cXkslCqsbY%3D
Y.E. Pak (1990) ArticleTitleCrack extension force in a piezoelectric material Journal of Applied Mechanics 57 647–653
V.Z. Parton (1976) ArticleTitleFracture mechanics of piezoelectric materials Acta Astronautica 3 671–683 Occurrence Handle10.1016/0094-5765(76)90105-3
W.F. Shelly S. Wan K.J. Bowman (1999) ArticleTitleFunctionally graded piezoelectric ceramics Materials Science Forum 308–311 515–520
Y. Shindo K. Watanabe F. Narita (2000) ArticleTitleElectroelastic analysis of a piezoelectric ceramic strip with a central crack International Journal of Engineering Science 38 1–19 Occurrence Handle10.1016/S0020-7225(99)00015-4 Occurrence Handle1:CAS:528:DyaK1MXotFaisbk%3D
G.C. Sih G.T. Embley (1972) ArticleTitleSudden Twisting of a Penny-Shaped Crack ASME Journal of Applied Mechanics 39 395–400
Z. Suo C.M. Kuo D.M. Barnett J.R. Willis (1992) ArticleTitleFracture mechanics for piezoelectric ceramics Journal of the Mechanics and Physics of Solids 40 IssueID4 739–765 Occurrence Handle10.1016/0022-5096(92)90002-J
X.Y. Wang S.W. Yu (2000) ArticleTitleTransient response of a crack in piezoelectric strip subjected to the mechanical and electrical impacts: mode-III problem International Journal of Solids and Structures 37 5795–5808
C.M. Wu M. Kahn W. Moy (1996) ArticleTitlePiezoelectric ceramics with functional gradients: A new application in material design Journal of the American Ceramic Society 79 IssueID3 809–812 Occurrence Handle1:CAS:528:DyaK28XhvVCrtr4%3D
E.H. Yoffe (1951) ArticleTitleThe moving Griffith crack Philosophical Magazine 42 739–750
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 Handle10.1016/0020-7683(95)00073-9
X. Zhu Q. Wang Z. Meng (1995) ArticleTitleA functionally gradient piezoelectric actuator prepared by power metallurgical process in PNN-PZ-PT system Journal of Materials Science Letters 14 516–518 Occurrence Handle1:CAS:528:DyaK2MXltVantrk%3D
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hu, K., Zhong, Z. A Moving Mode-III Crack in a Functionally Graded Piezoelectric Strip. Int J Mech Mater Des 2, 61–79 (2005). https://doi.org/10.1007/s10999-005-4443-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10999-005-4443-6