Abstract
This paper studies a penny-shaped crack in a finite thickness piezoelectric material layer. The piezoelectric medium is subjected to a thermal flux on its top and bottom surfaces. Both thermally insulated crack and heated crack are considered. Numerical solution for the finite layer thickness is obtained through the solution of a pair of dual integral equations. The result reduces to the closed form solution when the thickness of the piezoelectric layer becomes infinite. Exact expressions for the stress and electric displacement at the crack border are given as a function of the stress intensity factor, which is determined by the applied thermal flux. This paper is useful for the reliability design of piezoelectric materials in thermal environments.
Similar content being viewed by others
References
Bermejo R, Grunbichler H, Kreith J, Auer C (2010) Fracture resistance of a doped PZT ceramic for multilayer piezoelectric actuators: effect of mechanical load and temperature. J Eur Ceramic Soc 30: 705–712
Chen CD (2006) On the singularities of the thermo-electro-elastic fields near the apex of a piezoelectric bonded wedge. Int J Solids Struct 43: 957–981
Chen WQ, Shioya T (1999) Fundamental solution for a penny-shaped crack in a piezoelectric medium. J Mech Phys Solids 47: 1459–1475
Dunn ML (1994) The effects of crack face boundary conditions on the fracture of piezoelectric solids. Eng Fract Mech 48: 25–39
Fulton CC, Gao H (2001) Effect of local polarization switching on piezoelectric fracture. J Mech Phys Solids 49: 927–952
Gao H, Barnett DM (1996) An invariance property of local energy release rate in a strip saturation model of piezoelectric fracture. Int J Fract 79: R25–R29
Gao H, Zhang T-Y, Tong P (1997) Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J Mech Phys Solids 45: 491–510
Gradshteyn IS, Ryzhik IM (1965) Tables of integrals, series and products. Academic Press, New York
Kirilyuk VS (2008) Thermostressed state of a piezoelectric body with a plane crack under symmetric thermal load. Int Appl Mech 44: 320–330
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
Kuna M (2010) Fracture mechanics of piezoelectric materials—where are we right now?. Eng Fract Mech 77: 309–326
Li YD, Lee KY, Feng FX (2011) Magnetostrictive/electrostrictive fracture of the piezomagnetic and piezoelectric layers in a multiferroic composite: anti-plane case. Int J Solids Struct 48: 1311–1317
Lucato S, Lupascu DC, Kamlah M, Rodel J, Lynch CS (2001) Constraint-induced crack initiation at electrode edges in piezoelectric ceramics. Acta Mater 49: 2751–2759
Narita F, Shindo Y, Hirama M (2010) Electric delayed fracture and localized polarization switching of cracked piezoelectric ceramics in three-point bending. Int J Damage Mech 19: 285–300
Noda N, Kimura S (1998) Deformation of a piezothermoelectric composite plate considering the coupling effect. J Therm Stress 21: 359–379
Ootao Y, Tanigawa Y (2002) Transient piezothermoelasticity for a cylindrical composite panel composed of angle-ply and piezoelectric laminae. Int J Solids Struct 39: 5737–5752
Park SB, Sun CT (1995) Effect of electric field on fracture of piezoelectric ceramics. Int J Fract 70: 203–216
Qin QH, Mai Y-W (1997) Crack growth prediction of an inclined crack in a half-plane thermopiezoelectric solid. Theor Appl Fract Mech 26: 185–191
Rao BN, Kuna M (2010) Interaction integrals for thermal fracture of functionally graded piezoelectric materials. Eng Fract Mech 77: 37–50
Shang FL (2002) Analytical solutions for two penny-shaped crack problems in thermo-piezoelectric materials and their finite element comparisons. Int J Fract 117: 113–128
Shang F, Wang Z, Li Z (1996) Thermal stresses analysis of a three-dimensional crack in a thermopiezoelectric solid. Eng Fract Mech 55: 737–750
Shang F, Kuna M, Kitamura T (2003) Theoretical investigation of an elliptical crack in thermopiezoelectric material. Part I: Analytical development. Theor Appl Fract Mech 40: 237–246
Shindo Y, Narita F, Horiguchi K, Magara Y, Yoshida M (2003) Electric fracture and polarization switching properties of piezoelectric ceramic PZT studied by the modified small punch test. Acta Mater 51: 4773–4782
Sosa H (1992) On the fracture mechanics of piezoelectric solids. Int J Solids Struct 29: 2613–2622
Suo Z, Kuo C-M, Barnett DM, Willis JR (1992) Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 40: 739–765
Ueda S, Kondo H (2008) Transient intensity factors for a parallel crack in a plate of a functionally graded piezoelectric material under thermal shock loading conditions. J Therm Stress 31: 211–232
Verhoosel CV, Remmers JJC, Gutierrez M (2010) A partition of unity-based multiscale approach for modelling fracture in piezoelectric ceramics. Int J Numer Methods Eng 82: 966–994
Wang BL, Mai Y-W (2006) Near-tip fields for penny-shaped cracks in magnetoelectroelastic media. Key Eng Mater 312: 41–46
Wang BL, Noda N (2001) Design of a smart functionally graded thermopiezoelectric composite structure. Smart Mater Struct 10: 189–193
Wang BL, Noda N (2001) Thermally induced fracture of a smart functionally graded composite structure. Theor Appl Fract Mech 35: 93–109
Wang BL (2004) Exact electroelastic solutions for penny-shaped cracks under prescribed temperature or thermal flow. Appl Phys Lett 85: 2800–2802
Wang BL, Noda N (2004) Exact thermoelectroelasticity solution for a penny-shaped crack in piezoelectric materials. J Therm Stress 27: 241–251
Wang BL, Noda N, Han JC, Du SY (2002) Surface thermal shock fracture of a semi-infinite piezoelectric medium (poling axis parallel to the crack plane). Mech Mater 34: 135–144
Wang ZK (1994) Penny-shaped crack in transversely isotropic piezoelectric materials. Acta Mech Sin 10: 49–60
Zhang TY, Gao CF (2004) Fracture behaviors of piezoelectric materials. Theor Appl Fract Mech 41: 339–379
Zhang TY, Zhao MH, Tong P (2002) Fracture of piezoelectric ceramics. Adv Appl Mech 38: 147–289
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, B.L., Sun, Y.G. & Zhu, Y. Fracture of a finite piezoelectric layer with a penny-shaped crack. Int J Fract 172, 19–39 (2011). https://doi.org/10.1007/s10704-011-9643-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-011-9643-5