×

On contact zone models for an electrically limited permeable interface crack in a piezoelectric bimaterial. (English) Zbl 1273.74444

Summary: An electrically limited permeable crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric spaces under the action of a remote electromechanical loading is considered. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the contact zone length and the fracture mechanical parameters. Assuming the electric displacement constant inside the open region of the crack, the problem is reduced to a combined Dirichlet-Riemann and Hilbert boundary value problems which have been solved exactly. Stress and electric displacement intensity factors as well as the crack tip energy release rate are found in a clear analytical form. Furthermore, transcendental equations for the determination of the real contact zone length have been obtained for a general case and for a small contact zone length in an especially simple form. The dependencies of the mentioned values on the intensities of the electromechanical loading are presented in tables and associated diagrams.

MSC:

74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Beom HG, Atluri SN (1996) Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media. Int J Fract 75: 163–183
[2] Beom HG (2003) Permeable cracks between two dissimilar piezoelectric materials. Int J Solids Struct 40: 6669–6679 · Zbl 1054.74039
[3] Comninou M (1977) The interface crack. ASME J Appl Mech 44: 631–636 · Zbl 0369.73092
[4] Deeg WF (1980) The analysis of dislocation, crack and inclusion problem in piezoelectric solids. Ph.D.dissertation, Standford University
[5] Dundurs J, Gautesen AK (1988) An opportunistic analysis of the interface crack. Int J Fract 36: 151–159. doi: 10.1007/BF00017793
[6] Dunn ML (1994) The effects of crack face boundary conditions on the fracture mechanics of piezoelectric solids. Eng Fract Mech 48: 25–39. doi: 10.1016/0013-7944(94)90140-6
[7] Dunn ML, Taya M (1994) Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids. ASME J Appl Mech 61: 474–475
[8] Gao CF, Wang MZ (2000) Collinear permeable cracks between dissimilar piezoelectric materials. Int J Solids Struct 37: 4969–4986 · Zbl 1090.74658
[9] Govorukha VB, Kamlah M (2005) Investigation of an interface crack with a contact zone in a piezoelectric biomaterial under limited permeable electric boundary conditions. Acta Mech 178: 85–99 · Zbl 1116.74416
[10] Govorukha VB, Loboda VV, Kamlah M (2006) On the influence of the electric permeability on an interface crack in a piezoelectric biomaterial compound. Int J Solids Struct 43: 1979–1990. doi: 10.1016/j.ijsolstr.2005.04.009 · Zbl 1121.74363
[11] Gruebner O, Kamlah M, Munz D (2003) Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Eng Fract Mech 70: 1399–1413. doi: 10.1016/S0013-7944(02)00117-0
[12] Hao TH, Shen ZY (1994) A new electric boundary condition of electric fracture mechanics and its applications. Eng Fract Mech 47: 793–802. doi: 10.1016/0013-7944(94)90059-0
[13] Herrmann KP, Loboda VV (2000) Fracture-mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by considerations of various contact zone models. Arch Appl Mech 70: 127–143. doi: 10.1007/s004199900052 · Zbl 1030.74042
[14] Herrmann KP, Loboda VV, Govorukha VB (2001) On contact zone models for an electrically impermeable interface crack in a piezoelectric biomaterial. Int J Fract 111: 203–227. doi: 10.1023/A:1012269616735
[15] Kharun IV, Loboda VV (2003) A set of interface cracks with contact zones in a combined tension-shear field. Acta Mech 166: 43–56. doi: 10.1007/s00707-003-0044-3 · Zbl 1064.74153
[16] Kemmer G (2000) Berechnung von elektromechanischen Intensitätsparametern bei Rissen in Piezokeramiken. Dissertation, VDI Verlag Düsseldorf Nr. 261 Reihe 18
[17] Landis CM (2004) Energetically consistent boundary conditions for electromechanical fracture. Int J Solids Struct 41: 6291–6315 · Zbl 1120.74755
[18] Lapusta Y, Loboda V (2009) Electro-mechanical yielding for a limited permeable crack in an interlayer between piezoelectric materials. Mech Res Commun 36: 183–192. doi: 10.1016/j.mechrescom.2008.09.001 · Zbl 1258.74189
[19] Li Q, Chen YH (2007) Solution for a semi-permeable interface crack between two dissimilar piezoelectric material. ASME J Appl Mech 74: 833–844. doi: 10.1115/1.2711232
[20] Li Q, Chen YH (2008) Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials. ASME J Appl Mech 75: 0110101–01101013. doi: 10.1115/1.2745397
[21] Li W, McMeeking RM, Landis CM (2008) On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rates. Eur J Mech A Solids 27: 285–301 · Zbl 1154.74378
[22] Liu Y, Chen YH (2005) An analytical solution for a cracked piezoelectric plate according to the PKHS electric boundary condition. Acta Mech 180: 233–244. doi: 10.1007/s00707-004-0103-4 · Zbl 1093.74052
[23] Ma LF, Chen YH (2001) Weight functions for interface cracks in dissimilar anisotropic piezoelectric materials. Int J Fract 110: 263–279
[24] McMeeking RM (1999) Crack tip energy release rate for a piezoelectric compact tension speciment. Eng Fract Mech 64: 217–244. doi: 10.1016/S0013-7944(99)00068-5
[25] McMeeking RM (2001) Towards a fracture mechanics for brittle piezoelectric and dielectric materials. Int J Fract 108: 25–41. doi: 10.1023/A:1007652001977
[26] McMeeking RM (2004) The energy release rate for a Griffith crack in a piezoelectric material. Eng Fract Mech 71: 1149–1163. doi: 10.1016/S0013-7944(03)00135-8
[27] Muskhelishvili NI (1953) Some basic problems of mathematical theory of elasticity. Noordhoff, Groningen · Zbl 0052.41402
[28] Nakhmein EL, Nuller BM (1986) Contact between an elastic half-plane and a partly separated stamp. J Appl Math Mech 50: 507–515. doi: 10.1016/0021-8928(86)90017-1 · Zbl 0624.73123
[29] Ou ZC, Chen YH (2005) On approach of crack tip energy release rate for a semi-permeable crack when electromechanical loads become very large. Int J Fract 133: 89–105. doi: 10.1007/s10704-005-3123-8 · Zbl 1196.74207
[30] Ou ZC, Chen YH (2007) Re-examination of the PKHS crack model in piezoelectric materials. Euro J Mech A Solids 26: 659–675. doi: 10.1016/j.euromechsol.2006.09.007 · Zbl 1188.74049
[31] Pak YE (1992) Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fract 54: 79–100. doi: 10.1007/BF00040857
[32] Park SB, Sun CT (1995) Fracture criteria for piezoelectric ceramics. J Am Ceram Soc 78: 1475–1480. doi: 10.1111/j.1151-2916.1995.tb08840.x
[33] Parton VZ (1976) Fracture mechanics of piezoelectric materials. Acta Astronaut 3: 671–683. doi: 10.1016/0094-5765(76)90105-3 · Zbl 0351.73115
[34] Parton VZ, Kudryavtsev BA (1988) Electromagnetoelasticity. Gordon and Breach Science Publishers, New York
[35] Ricoeur A, Enderlein M, Kuna M (2005) Calculation of the J-integral for limited permeable cracks in piezoelectrics. Arch Appl Mech 74: 536–549. doi: 10.1007/s00419-004-0370-5 · Zbl 1119.74563
[36] Ricoeur A, Kuna M (2009) Electrostatic tractions at dielectric interfaces and their implication for crack boundary conditions. Mech Res Commun 36: 330–335 · Zbl 1258.74076
[37] Rogowski B (2007) The limited electrically permeable crack model in linear piezoelasticity. Int J Press Vess Piping 84: 572–581. doi: 10.1016/j.ijpvp.2007.04.006
[38] Scherzer M, Kuna M (2004) Combined analytical and numerical solution of 2D interface corner configurations between dissimilar piezoelectric materials. Int J Fract 127: 61–99 · Zbl 1187.74200
[39] Suo Z, Kuo CM, Barnett DM, Willis JR (1992) Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 40: 739–765. doi: 10.1016/0022-5096(92)90002-J · Zbl 0825.73584
[40] Tian WY, Rajapakse RKND (2006) Fracture parameters of a penny-shaped crack at the interface of a piezoelectric bi-material system. Int J Fract 141: 37–48 · Zbl 1197.74134
[41] Wang BL, Mai YW (2003) On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics. Int J Eng Sci 41: 633–652. doi: 10.1016/S0020-7225(02)00149-0
[42] Williams ML (1959) The stresses around a fault or crack in dissimilar media. Bull Seismol Soc Am 49: 199–204
[43] Wippler K, Ricoeur A, Kuna M (2004) Towards the computation of electrically permeable cracks in piezoelectrics. Eng Fract Mech 71: 2567–2587. doi: 10.1016/j.engfracmech.2004.03.003
[44] Xu XL, Rajapakse RKND (2001) On plane crack in piezoelectric solids. Int J Solids Struct 38: 7643–7658. doi: 10.1016/S0020-7683(01)00029-4 · Zbl 1020.74035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.