Abstract
The problem of a penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer is investigated. The surfaces of the composite structure are subjected to both mechanical and electrical loads. The crack surfaces are assumed to be electrically impermeable. Integral transform method is employed to reduce the problem to a Fredholm integral equation of the second kind. The stress intensity factor, electric displacement intensity factor and energy release rate are derived, some typical numerical results are plotted graphically. The effects of electrical loads, material nonhomogeneity and crack configuration on the fracture behaviors of the cracked composite structure are analyzed in detail.
Similar content being viewed by others
References
Parton VZ (1976) Fracture mechanics of piezoelectric materials. Acta Astron 3:671–683
Deeg WF (1980) The analysis of dislocation, crack, inclusion problems in piezoelectric solids. PhD thesis, Stanford University
Kogan L, Hui CY, Molkov V (1996) Stress and induction field of a spherical inclusion or a penny-shaped crack in a transversely isotropic piezoelectric material. Int J Solids Struct 33:2719–2737
Karapetian E, Sevotianov I, Kachanov M (2000) Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading. Arch Appl Mech 70:201–229
Chen WQ, Shioya T (2000) Complete and exact solutions of a penny-shaped crack in a piezoelectric solid: antisymmetric shear loadings. Int J Solids Struct 37:2603–2619
Yang FQ (2004) General solutions of a penny-shaped crack in a piezoelectric material under opening mode-I loading. Q J Mech Appl Math 57:529–550
Eriksson K (2002) Energy release rates for the penny-shaped crack in a linear piezoelectric solid. Int J Fract 116:L23–L28
Yang JH, Lee KY (2003) Penny-shaped crack in a piezoelectric cylinder under electromechanical loads. Arch Appl Mech 73:323–336
Yang JH, Lee KY (2003) Penny-shaped crack in a piezoelectric cylinder surrounded by an elastic medium subjected to combined in plane mechanical and electrical loads. Int J Solids Struct 40:573–590
Wang BL, Noda N, Han JC, Du SY (2001) A penny-shaped crack in a transversely isotropic piezoelectric layer. Eur J Mech A/Solid 20:997–1005
Li XF, Lee KY (2004) Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer. J Mech Phys Solids 52:2079–2100
Feng WJ, Li YS, Ren DL (2006) Transient response of a piezoelectric layer with a penny-shaped crack under electrical-mechanical impacts. Struct Eng Mech 23:163–176
Zhu X, Wang Q, Meng Z (1995) A functionally gradient piezoelectric actuator prepared by power metallurgical process in PNN-PZ-PT system. J Mater Sci Lett 14:516–518
Wu CM, Kahn M, Moy W (1996) Piezoelectric ceramics with function gradients: a new application in material design. J Am Ceram Soc 79:809–812
Li C, Weng GJ (2002) Antiplane crack problem in functionally graded properties. J Appl Mech 69:481–488
Wang BL, Zhang XH (2004) A mode-III crack in functionally graded piezoelectric material strip. J Appl Mech 71:327–333
Ueda S (2003) Crack in functionally graded piezoelectric strip bonded to elastic surface layers under electromechanical loading. Theor Appl Fract Mech 40:225–236
Zhou ZG, Wu LZ (2006) Non-local theory solution for the anti-plane shear of two collinear permeable cracks in functionally graded piezoelectric materials. Int J Eng Sci 44:1366–1379
Kwon SM, Lee KY (2003) An anti-plane propagating crack in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric strip. Arch Appl Mech 73:348–366
Chen J, Liu ZX, Zou ZZ (2003) Electromechanical impact of a crack in a functionally graded piezoelectric medium. Theor Appl Fract Mech 39:47–60
Wang BL, Noda N (2001) Thermally induced fracture of a smart functionally graded composite structure. Theor Appl Fract Mech 35:93–109
Ueda S (2004) Thermally induced fracture of a functionally graded piezoelectric layer. J Therm Stresses 27:291–309
Ueda S (2006) Transient response of a center crack in a functionally graded piezoelectric strip under electromechanical impact. Eng Fract Mech 73:1455–1471
Ueda S (2007) A penny-shaped crack in a functionally graded piezoelectric strip under thermal loading. Eng Fract Mech 74:1255–1273
Copson ET (1961) On certain dual integral equations. Proc Glasg Math Assoc 5:19–24
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, Y.S., Feng, W.J. & Xu, Z.H. A penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer. Meccanica 44, 377–387 (2009). https://doi.org/10.1007/s11012-008-9177-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-008-9177-8