Dynamic Behavior of Two Parallel Symmetry Cracks in Magneto-Electro-Elastic Composites Under Harmonic Anti-Plane Waves

ZHOU Zhen-gong; WANG Biao

Volume 27 Issue 5

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(5): 519-526

ZHOU Zhen-gong, WANG Biao. Dynamic Behavior of Two Parallel Symmetry Cracks in Magneto-Electro-Elastic Composites Under Harmonic Anti-Plane Waves[J]. Applied Mathematics and Mechanics, 2006, 27(5): 519-526.

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Dynamic Behavior of Two Parallel Symmetry Cracks in Magneto-Electro-Elastic Composites Under Harmonic Anti-Plane Waves

ZHOU Zhen-gong¹,
WANG Biao²

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

Received Date: 2004-07-31
Rev Recd Date: 2006-01-10
Publish Date: 2006-05-15

Abstract

Abstract

The dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied by Schmidt method. By using the Fourier trans-form, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surface were expanded in a series of Jacobi polynomials. The relations among the electric filed, the magnetic flux and the stress field were obtained. From the results, it can be obtained that the singular stresses in piezoelectric/piezomagnetic materials carry the same forms as those in a general elastic material for the dynamic anti-plane shear fracture problem. The shielding effect of two parallel cracks was also discussed.
- magneto-electro-elastic composites,
- crack,
- harmonic waves,
- dual integral equations,
- intensity factor

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References(15)

References

[1]	Wu T L，Huang J H.Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases[J].International Journal of Solids and Structures,2000,37(21):2981—3009. doi: 10.1016/S0020-7683(99)00116-X
[2]	Sih G C, Song Z F, Magnetic and electric poling effects associated with crack growth in BaTiO3-CoFe2O4 composite[J].Theoretical and Applied Fracture Mechanics,2003,39(3):209—227.
[3]	Wang B L,Mai Y W.Crack tip field in piezoelectric/piezomagnetic media[J].European Journal of Mechanics A/Solid,2003,22(4):591—602. doi: 10.1016/S0997-7538(03)00062-7
[4]	Gao C F,Tong P, Zhang T Y.Interfacial crack problems in magneto-electroelastic solids[J].International Journal of Engineering Science,2003,41(18):2105—2121. doi: 10.1016/S0020-7225(03)00206-4
[5]	Liu J X, Liu X L,Zhao Y B.Green's functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack[J].International Journal of Engineering Science,2001,39(12):1405—1418. doi: 10.1016/S0020-7225(01)00005-2
[6]	Gao C F, Kessler H, Balke H.Crack problems in magnetoelectroelastic solids， Part Ⅰ:exact solution of a crack[J].International Journal of Engineering Science,2003,41(9):969—981. doi: 10.1016/S0020-7225(02)00323-3
[7]	Wang B L,Mai Y W.Fracture of piezoelectromagnetic materials[J].Mechanics Research Communications,2004,31(1):65—73. doi: 10.1016/j.mechrescom.2003.08.002
[8]	Van Suchtelen J.Product properties: a new application of composite materials[J].Phillips Research Reports,1972,27(1):28—37.
[9]	Morse P M, Feshbach H.Methods of Theoretical Physics[M].New York:McGraw-Hill,1958,926—940.
[10]	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 Mechanics. A/Solid,2000,19(10):961—977. doi: 10.1016/S0997-7538(00)01107-4
[11]	Gradshteyn I S, Ryzhik I M.Table of Integrals, Series and Products[M].New York:Academic Press,1980,1035—1037.
[12]	Erdelyi A.Tables of Integral Transforms[M].New York:McGraw-Hill,1954,34—89.
[13]	周振功，王彪.双Ⅰ-型裂纹断裂动力学问题的非局部理论解[J].应用数学和力学，2001,22(7):682—690.
[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]	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

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