Basic Solution of Two Parallel Non-Symmetric Permeable Cracks in Piezoelectric Materials

ZHOU Zhen-gong; WANG Biao

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(4): 379-390

ZHOU Zhen-gong, WANG Biao. Basic Solution of Two Parallel Non-Symmetric Permeable Cracks in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(4): 379-390.

Citation:

ZHOU Zhen-gong, WANG Biao. Basic Solution of Two Parallel Non-Symmetric Permeable Cracks in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(4): 379-390.

Citation:

ZHOU Zhen-gong, WANG Biao. Basic Solution of Two Parallel Non-Symmetric Permeable Cracks in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(4): 379-390.

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Basic Solution of Two Parallel Non-Symmetric Permeable Cracks in Piezoelectric Materials

ZHOU Zhen-gong¹,
WANG Biao²

1.
Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P. R. China;

Received Date: 2006-11-08
Rev Recd Date: 2007-01-25
Publish Date: 2007-04-15

Abstract

Abstract

The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading is studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations in which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.
- piezoelectric materials,
- parallel non-symmetric cracks,
- the dual-integral equations,
- intensity factor

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References(21)

References

[1]	Beom H G，Atluri S N. Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media[J].International Journal of Fracture,1996,75(2):163-183. doi: 10.1007/BF00034075
[2]	Gao H J, Zhang T Y,Tong P.Local and global energy rates for an elastically yielded crack in piezoelectric ceramics[J].Journal of Mechanics and Physics of Solids,1997,45(2):491-510. doi: 10.1016/S0022-5096(96)00108-1
[3]	Han X L, WANG Tzu-chiang. Interacting multiple cracks in piezoelectric materials[J].International Journal of Solids and Structures,1999,36(27):4183-4202. doi: 10.1016/S0020-7683(98)00187-5
[4]	Yu S W, Chen Z T. Transient response of a cracked infinite piezoelectric strip under anti-plane impact[J].Fatigue of Engineering Materials and Structures,1998,21(3):1381-1388. doi: 10.1046/j.1460-2695.1998.00108.x
[5]	Zhang T Y, Hack J E. Mode-III cracks in piezoelectric materials[J].Journal of Applied Physics,1992,71(4):5865-5870. doi: 10.1063/1.350483
[6]	Sih G C, Zuo J Z. Energy density formulation and interpretation of cracking behavior for piezoelectric ceramics[J].Theoretical and Applied Fracture Mechanics,2000,34(2):123-141. doi: 10.1016/S0167-8442(00)00031-8
[7]	Deeg W E F. The analysis of dislocation, crack and inclusion problems in piezoelectric solids[D].Ph D thesis.California:Stanford University,1980.
[8]	Pak Y E. Crack extension force in a piezoelectric material[J].Journal of Applied Mechanics,1990,57(3):647-653. doi: 10.1115/1.2897071
[9]	Han J J, Chen Y H. Multiple parallel cracks interaction problem in piezoelectric ceramics[J].International Journal of Solids and Structures,1999,36(6): 3375-3390. doi: 10.1016/S0020-7683(98)00149-8
[10]	Parton V S. Fracture mechanics of piezoelectric materials[J].Acta Astronautra,1976,3(4):671-683. doi: 10.1016/0094-5765(76)90105-3
[11]	Hao T H, Shen Z Y. A new electric boundary condition of electric fracture mechanics and its applications[J].Engineering Fracture Mechanics,1994,47(6): 793-802. doi: 10.1016/0013-7944(94)90059-0
[12]	Soh A K, Fang D N, Lee K L. Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading[J].European Journal of Mechchanics，A Solid,2000,19(6):961-977. doi: 10.1016/S0997-7538(00)01107-4
[13]	Zhou Z G, Wang B. The behavior of two parallel symmetry permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes[J].International Journal of Solids and Structures,2002,39(17):4485-4500. doi: 10.1016/S0020-7683(02)00347-5
[14]	周振功，王彪. 压电材料中两平行对称可导通裂纹断裂性能分析[J]. 应用数学和力学,2002,23(12):1211-1219.
[15]	孙建亮，周振功，王彪. 压电材料中两平行不相等界面裂纹的动态特性研究[J].应用数学和力学，2005,26(2):145-154.
[16]	Sun J L, Zhou Z G, Wang B. Dynamic behavior of unequal parallel permeable interface multi-cracks in a piezoelectric layer bonded to two piezoelectric materials half planes[J].European Journal of Mechanics，A Solids,2004,23(6): 993-1005. doi: 10.1016/j.euromechsol.2004.05.005
[17]	Morse P M, Feshbach H.Methods of Theoretical Physics[M].Vol 1.New York：McGraw-Hill,1958,828-930.
[18]	Gradshteyn I S,Ryzhik I M.Table of Integral, Series and Products[M].New York:Academic Press,1980,1035-1037.
[19]	Erdelyi A.Tables of Integral Transforms[M].Vol 1.New York：McGraw-Hill,1954, 34-89.
[20]	周振功，王彪. 压电压磁复合材料中一对平行裂纹对弹性波的散射[J].应用数学和力学,2006,27(5):519-526.
[21]	Ratwani M, Gupta G D. Interaction between parallel cracks in layered composites[J].International Journal of Solids and Structures,1974,10(7):701-708. doi: 10.1016/0020-7683(74)90034-1