A closed crack tip model for interface cracks inthermopiezoelectric materials

Qin, Qing‐Hua; Mai, Yiu‐Wing

doi:10.1016/s0020-7683(98)00115-2

Cited by 82 publications

(35 citation statements)

References 30 publications

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“…The way of eliminating of such a phenomenon by means of contact zone considerations was suggested by Comninou [14] and further developed in an analytical way for isotropic bimaterials by Atkinson [15], Simonov [16], Dundurs and Gautesen [17] and others. For piezoelectric bimaterials a contact zone model for an interface crack was developed in an analytical way by Qin and Mai [18], Herrmann and Loboda [19] and Herrmann et al [20].…”

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confidence: 99%

An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

2009

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An interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric/piezomagnetic spaces under the action of a remote mechanical loading, magnetic and electric fluxes as well as concentrated forces at the crack faces is considered. Assuming that all fields are independent on the coordinate x 2 co-directed with the crack front, the stresses, the electrical and the magnetic fluxes as well as the derivatives of the jumps of the displacements, the electrical and magnetic potentials are presented via a set of analytic functions in the (x 1 , x 3 )-plane with a cut along the crack region. Two cases of magneto-electric conditions at the crack faces are considered. The first case assumes that the crack is electrically and magnetically permeable, and in the second case the crack is assumed electrically permeable while the open part of the crack is magnetically impermeable. For both these cases due to the above-mentioned representation the combined Dirichlet-Riemann boundary value problems have been formulated and solved exactly. Stress, electric and magnetic induction intensity factors are found in a simple analytical form. Transcendental equations and a closed form analytical formula for the determination of the real contact zone length have been derived for both cases of magnetic conditions in the crack region. For a numerical illustration of the obtained results a bimaterial BaTiO 3 -CoFe 2 O 4 with different volume fractions of BaTiO 3 has been used, and the influence of the mechanical loading and the intensity of the magnetic flux upon the contact zone length and the associated intensity factors as well as the energy release rate has been shown.

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confidence: 99%

An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

2009

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“…Assuming that all the field variables of the solid are dependent on zl and z2 only, the generalized displacement function vector u and the generalized stress function vector r can be expressed as [6], [7] u -2 Re [af(z,) + c9(zt)],…”

Section: Outline Of the Basic Formulationmentioning

confidence: 99%

“…Although the extension of the formulation of piezoelectric elasticity to that of thermopiezoelectric elasticity is straightforward, it is not easy to obtain an explicit solution to thermopiezoelectric problems, due to the mathematical complexity. On this subject, recently, several valuable solutions have been presented by some investigators, see, for example, the work of Shang et al [1] for a three-dimensional problem of a penny-shaped crack, Yu and Qin [2], Qin and Mai [3], Yang et al [4], Qin et al [5] for the plane crack problems, and also Shen and Kuang [6], Qin et al [7] for the case of interface cracks. However, it should be noted that the available studies are for the case of impermeable cracks, i.e., cracks are considered as impermeable slits, and thus the electric field inside the cracks is assumed to be zero.…”

Section: Introductionmentioning

confidence: 99%

A permeable interface crack between dissimilar thermopiezoelectric media

Gao

Wang

2001

Acta Mechanica

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Summary. This paper presents an explicit treatment of the generalized 2D thermopiezoelectric problem of an interfacial crack between two dissimilar thermopiezoelectric media by means of the extend Stroh formalism. In comparison with the other relevant studies, the present work has two features: one is that the crack is assumed to be a permeable slit across which the normal electric displacement and the tangential electric field are continuous. The other is that the heat loading is applied at infinity, rather than on the crack faces. As a result, the field intensity factors and the electric field inside the crack are obtained in explicit closed-forms, respectively. As examples, the solutions of several particular cases, including that of an impermeable crack and that of a homogeneous material with a crack are also presented. It is shown that the electric field inside a crack may be singular and oscillatory for the case of an interfacial crack, while for the case of a crack in a homogeneous medium it is linearly variable. Moreover, it is also found that for a homogeneous medium with a crack the stress intensity factors based on the impermeable model and permeable model are same, but the intensity factor of the electric displacement is not.

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“…To eliminate this phenomenon, a contact zone model for a crack between two isotropic materials was suggested by Comninou [1977]. It was developed further for interface cracks in piezoelectric bimaterials by Qin and Mai [1999], Herrmann and Loboda [2000] and Govorukha et al [2006]. Another way of removing crack tip singularities and modeling fracture processes for interface cracks was introduced by Needleman [1990], Tvergaard and Hutchinson [1996] and Tvergaard [2001] by means of a cohesive zone model.…”

Section: Introductionmentioning

confidence: 99%

Prefracture zone modeling for an electrically impermeable interface crack in a piezoelectric bimaterial compound

Govorukha

Kamlah

2008

JOMMS

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This work is concerned with the analytical characterization of the electromechanical nonlinear effects in the fields surrounding the tip of an interface crack located between two piezoelectric materials. It is assumed that a prefracture zone arises along a line segment in front of the crack tip. The prefracture zone is modeled by electrical displacement reaching a saturation limit and constant stress distribution. This reduces the problem to a linear interface crack analysis leading to a Hilbert problem, which is solved exactly. The prefracture zone length and the stress magnitude in this zone are found from algebraic and transcendental equations. The latter are derived from the requirement of stresses and electrical displacement to be finite at the end of prefracture zone towards the undamaged ligament. Numerical results for certain material combinations and remote loadings are presented and analyzed. In addition, energy release rate and crack opening displacements are introduced, which offers the possibility of formulating a fracture criterion based on the crack opening displacements.

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A closed crack tip model for interface cracks inthermopiezoelectric materials

Cited by 82 publications

References 30 publications

An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

A permeable interface crack between dissimilar thermopiezoelectric media

Prefracture zone modeling for an electrically impermeable interface crack in a piezoelectric bimaterial compound

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