On the crack-tip stress singularity of interfacial cracks in transversely isotropic piezoelectric bimaterials

Ou, Zhuo-Cheng; Wu, X.D.

doi:10.1016/j.ijsolstr.2003.08.021

Cited by 58 publications

(35 citation statements)

References 23 publications

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“…The satisfaction of the conditions (13), (14) by means of the expressions (15), (16) leads to the inhomogeneous combined Dirichlet-Riemann boundary value problem…”

Section: An Interface Crack Under a Concentrated Loadingmentioning

confidence: 99%

“…Stress singularities of an interface crack in a piezoelectric bimaterial have been explicitly studied in [13,14] with respect to various boundary conditions on the crack faces. Analytical investigations of near-tip fields in dissimilar piezoelectric media have been performed in [15,16]. A crack terminating at a piezoelectric bimaterial interface was studied in [17].…”

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confidence: 99%

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Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field

2015

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A plane problem for an electrically permeable tunnel crack between two piezoelectric half-spaces under concentrated loading applied to the crack faces and remote mixed-mode loading is studied. The elastic displacement and potential jumps as well as the stresses and electrical displacement along the interface are represented via sectionally holomorphic vector functions. At the crack tip, we assume closed crack faces with frictionless contact at the crack tip. The problem is reduced to combined Dirichlet-Riemann boundary value problems that are solved analytically. From these solutions, clear analytical expressions for characteristics of the electromechanical field at the interface are derived. A transcendental equation, which determines the point of separation of the open and closed section of the crack, is found. The stress intensity factors at the crack tip and the energy release rate are calculated. The influence of the magnitude and the locations of the applied concentrated loading upon the contact zone length and the associated fracture mechanical parameters is considered.

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“…The satisfaction of the conditions (13), (14) by means of the expressions (15), (16) leads to the inhomogeneous combined Dirichlet-Riemann boundary value problem…”

Section: An Interface Crack Under a Concentrated Loadingmentioning

confidence: 99%

mentioning

confidence: 99%

Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field

2015

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“…It can be noted that the sum of the highly converged λ 2 and λ 3 equals −1. The exact solutions are obtained by repeating the analytical calculation of Ou and Wu [14]. As seen in Fig.…”

Section: Interfacial Crack In Bimorphmentioning

confidence: 99%

“…In this context, Stroh's formalism, eigenfunction expansion and complex variable techniques have been employed/developed to determine the electromechanical stress (stress + electric displacement) singularities at cracks and interfacial cracks (see, e.g., [3,11,14,23,27]). Analytical derivation of the eigensolutions not only requires a high level of mathematical competence but also mostly results in a system of equations which can only be solved numerically.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Electromechanical Stress Singularity in Piezoelectrics by Computed Eigensolutions and Hybrid-trefftz Finite Element Models

2006

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This paper concerns the determination of singular electromechanical stress field in piezoelectrics. A one-dimensional finite element procedure is generalized to compute the eigensolutions of the singular electromechanical field. The generalized procedure is capable of taking differently poled piezoelectrics, cracks and ultra-thin electrodes into account.To determine the strength of the singular electromechanical stress field, the hybrid-Trefftz finite element method is adopted. The independently assumed electromechanical stress modes are extracted from the eigensolutions previously computed from the one-dimensional procedure. Since the eigensolutions satisfy all the balance conditions, the hybridTrefftz models can be constructed by boundary integration. This feature enables the models to be interfaced compatibly with conventional finite element models. To illustrate the efficacy of the present approach, the eigensolutions and/or parameters directly related to the electromechanical stress intensity in crack, interfacial crack and bimorph with embedded electrode are considered. The predictions are in good agreement with the reference solutions reported in the literature or computed by using over 10,000 conventional finite elements.

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“…In addition to increasing applications for the analysis composites [5][6][7], cracking has recently been investigated in conjunction with microelectronics [8][9][10][11], and piezoelectric bimaterials [12] as well as thin film interfaces [13]. Also, cracks that develop at the fiber-matrix interface in composites [14].…”

Section: Introductionmentioning

confidence: 99%

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Krueger

Shivakumar

Raju

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Recent developments in fracture mechanics analyses of the interfacial crack problem are reviewed. The intent of the review is to renew the awareness of the oscillatory singularity at the crack tip of a bimaterial interface and the problems that occur when calculating mode mixity using numerical methods such as the finite element method in conjunction with the virtual crack closure technique. Established approaches to overcome the nonconvergence issue of the individual mode strain energy release rates are reviewed. In the recent literature many attempts to overcome the nonconvergence issue have been developed. Among the many approaches found only a few methods hold the promise of providing practical solutions. These are the resin interlayer method, the method that chooses the crack tip element size greater than the oscillation zone, the crack tip element method that is based on plate theory and the crack surface displacement extrapolation method. Each of the methods is validated on a very limited set of simple interface crack problems. However, their utility for a wide range of interfacial crack problems is yet to be established.

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On the crack-tip stress singularity of interfacial cracks in transversely isotropic piezoelectric bimaterials

Cited by 58 publications

References 23 publications

Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field

Influence of concentrated loading on opening of an interface crack between piezoelectric materials in a compressive field

Analysis of Electromechanical Stress Singularity in Piezoelectrics by Computed Eigensolutions and Hybrid-trefftz Finite Element Models

Fracture Mechanics Analyses for Interface Crack Problems - A Review

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