The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Zhou, Zhen-Gong; Wu, Linzhi; Wang, Biao

doi:10.1007/s00419-004-0369-y

Cited by 59 publications

(28 citation statements)

References 20 publications

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“…Since then, most research results published were obtained recently in references [1,[12][13][14][15][16][17][19][20][21][22][23][24]. Recently, the static fracture behaviors of a crack or two cracks in piezoelectric/piezomagnetic materials had been investigated in references [25][26][27][28] by the Schmidt method [29] until recent years, but they just concentrated on the anti-plane shear fracture problems in magnetoelectroelastic composite materials.…”

Section: Introductionmentioning

confidence: 98%

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

Zhou

Zhang

2007

Arch Appl Mech

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The solutions of a limited-permeable crack (case I) or two collinear limited-permeable cracks (case II) in piezoelectric/piezomagnetic materials subjected to a uniform tension loading were investigated in this paper using the generalized Almansi's theorem. At the same time, the electric permittivity and the magnetic permeability of air in crack were firstly considered. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were jumps of displacements across crack surfaces, not the dislocation density functions or the complex variable functions. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials to obtain the relations among electric displacement intensity factors, magnetic flux intensity factors and stress intensity factors at crack tips.

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Section: Introductionmentioning

confidence: 98%

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

Zhou

Zhang

2007

Arch Appl Mech

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“…In order to determine the possible singular behavior of Eq. (20), the behavior of the kernels i j for large values of s needs to be examined. It can be seen from Eq.…”

Section: The Integral Equationsmentioning

confidence: 99%

“…Tian and Rajapakse [19] presented theoretical study of a magnetoelectroelastic composite plane with a single conducting crack. Zhou et al [20] investigated the behavior of a crack in functionally graded piezoelectric/piezomagnetic materials subjected to an anti-plane shear loading. Gao et al [21] investigated an anti-plane crack in a magnetoelectroelastic solid.…”

Section: Introductionmentioning

confidence: 99%

A periodic array of cracks in a transversely isotropic magnetoelectroelastic material

2007

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Magnetoelectroelastic materials are inherently brittle and prone to fracture. Therefore, it is important to evaluate the fracture behavior of these advanced materials. In this paper, a periodic array of cracks in a transversely isotropic magnetoelectroelastic material is investigated. Hankel transform is applied to solve elastic displacements, electric potential and magnetic potential. The problem is reduced into a system of integral equations. Both impermeable and permeable crack-face electromagnetic boundary conditions assumptions are investigated. Quantities of the stress, electric displacement and magnetic induction and their intensity factor are obtained. Effect of the crack spacing on these quantities is investigated in details.

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“…Li and Weng [9] first considered the static anti-plane problem of a finite crack in a functionally graded piezoelectric material strip. More recently, Zhou and Wang [11,12] first studied the static ant-plane shear problems of two parallel cracks and a crack in functionally graded piezoelectric/piezomagnetic materials by using Schmidt method [13].…”

Section: Introductionmentioning

confidence: 99%

Basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials

2007

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The basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials was studied in this paper using the generalized Almansi's theorem. To make the analysis tractable, it was assumed that the shear modulus varies exponentially along the horizontal axis parallel to the crack. The problem was formulated through a Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials; however, the magnitudes of intensity factors depend on the gradient of functionally graded piezoelectric material properties. It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials.

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The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Cited by 59 publications

References 20 publications

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

A periodic array of cracks in a transversely isotropic magnetoelectroelastic material

Basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials

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