Stress intensification near an elliptical crack border

Wang, Z.K.; Huang, Shan

doi:10.1016/0167-8442(94)00061-5

Cited by 32 publications

(21 citation statements)

References 5 publications

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“…The crack is described by an ellipse with its major and minor semiaxes c, a and the parametric angle φ. This configuration has been investigated theoretically in [51] and later corrected in [41]. The derived exact expressions of stress and electric field intensity factors have the form…”

Section: The Iterative Capacitor Analogy (Ica) Methodsmentioning

confidence: 99%

Finite element analyses of cracks in piezoelectric structures: a survey

Kuna

2006

Arch Appl Mech

105

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Piezoelectric materials have widespread applications in modern technical areas such as mechatronics, smart structures or microsystem technology, where they serve as sensors or actuators. For the assessment of strength and reliability of piezoelectric structures under combined electrical and mechanical loading, the existence of cracklike defects plays an important role. Meanwhile, piezoelectric fracture mechanics has been established quite well, but its application to realistic crack configurations and loading situations in piezoelectric structures requires the use of numerical techniques as finite element methods (FEM) or boundary element methods (BEM). The aim of this paper is to review the state of the art of FEM to compute the coupled electromechanical boundary value problem of cracks in 2D and 3D piezoelectric structures under static and dynamic loading. In order to calculate the relevant fracture parameters very precisely and efficiently, the numerical treatment must account for the singularity of the mechanical and electrical fields at crack tips. The following specialized techniques are presented in detail: (1) special singular crack tip elements, (2) determination of intensity factors K I -K IV from near tip fields, (3) modified crack closure integral, (4) computation of the electromechanical J -integral, and (5) exploitation of interaction integrals. Special emphasis is devoted to a realistic modeling of the dielectric medium inside the crack, leading to specific electric crack face boundary conditions. The accuracy, efficiency, and applicability of these techniques are examined by various example problems and discussed with respect to their advantages and drawbacks for practical applications.Keywords Piezoelectric fracture mechanics · Finite element method · Crack analyses · Limited permeable cracks IntroductionPiezoelectric materials are now widely used in many fields of engineering. Thanks to their ability to convert electrical in mechanical energy and vice versa, they serve as sensors, actuators, and transducers. Piezoelectric components and materials are integrated into complex "smart" structures or embedded as layers or fibers into multifunctional composites. The interested reader is referred to recent conference proceedings [1,2] for further information. Under service conditions, piezoelectric structures are exposed to high mechanical and electrical loadings that originate from internal and external sources of static and dynamic nature. Therefore, besides their functional features, problems of strength, fracture, and fatigue play an important role for the optimum design, reliability, and durability of piezoelectric structures and composites. This holds especially for the relatively brittle piezoelectric ceramics, containing flaws, electrodes, and geometrical imperfections. For these reasons, the fracture behavior of piezoelctric structures has become the subject of emerging scientific interest in the last 15 years.

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Section: The Iterative Capacitor Analogy (Ica) Methodsmentioning

confidence: 99%

Finite element analyses of cracks in piezoelectric structures: a survey

Kuna

2006

Arch Appl Mech

105

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“…Wang and Huang [19,20] earlier solved the same problem analytically using ellipsoidal coordinate system and deduced the expressions for mechanical stress intensity factor and electric displacement intensity factor which are very complicated and could not be reduced to simpler form as mentioned by Shang et al [16] who also corrected the theoretical results of Wang and Huang [20].…”

Section: For Crackmentioning

confidence: 99%

“…• The results (83) and (84) does not follow from the corrected version of the analytical expressions of the intensity factors given by Wang and Huang [20] (same as [19]). • The corrected expressions of intensity factors used by Shang et al [16] and Kuna [7] earlier for comparison of numerical results obtained by FEM and by Qin et al [13] for comparison of numerical results obtained by BEM, matches with the analytical expressions of the same obtained by the present authors.…”

Section: Note Thatmentioning

confidence: 99%

“…(30) and (31) for an elliptical crack embedded in an unbounded piezoelectric media have been obtained through the following steps: Substituting χ j ( j = 1, 2, 3, 4), the solutions to the quasi-harmonic equations (14), given by (26) in (11), (12), and (13), one obtains the integral representations of the field components in terms of the unknown functions T j (ξ, η), ( j = 1, 2, 3, 4). Substituting the integral representations for σ zx and σ zy in the boundary condition (20) one obtains…”

Section: Appendix Amentioning

confidence: 99%

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Elliptical crack and punch problems solved by integral equation method for piezoelectric media

Saha¹,

Saha

2011

Arch Appl Mech

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The problem of an elliptical crack embedded in an unbounded transversely isotropic piezoelectric media with the crack-plane parallel to the plane of isotropy of the media and subjected to remote normal mechanical as well as electric loading is considered first. The problem has been successfully reduced to a pair of coupled integral equations that are suitable for the application of an integral equation method developed earlier for three-dimensional problems of LEFM. Solution to the mechanical displacement and electric potentials are obtained for prescribed uniform loadings and expressions for corresponding intensity factors and crack opening displacement are deduced. The above method has further been applied to solve the problem of a rigid flat-ended elliptical punch indenting a transversely isotropic piezoelectric half-space surface with the plane of isotropy parallel to the surface. Solutions to mechanical stress and electric displacement are obtained for prescribed constant normal displacement and constant electric potential interior to the elliptical region and expression for the total force required to maintain a prescribed indentation is deduced.

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“…Chen and Shioya (1999) presented a general three-dimensional analysis of a penny-shaped crack subjected to normal mechanical loads and electric charges symmetrically applied on the upper and lower surfaces. Wang (1992) and Wang and Huang (1995) considered an elliptical crack in a piezoelectric medium. Lee (2001, 2003) studied a penny-shaped crack in a piezoelectric strip and a cylinder.…”

mentioning

confidence: 99%

Fracture parameters of a penny-shaped crack at the interface of a piezoelectric bi-material system

Tian

Rajapakse

2006

Int J Fract

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A penny-shaped crack at the interface of a piezoelectric bi-material system is considered. Analytical general solutions based on Hankel integral transforms are used to formulate the mixed-boundary value problem corresponding to an interfacial crack and the problem is reduced to a system of singular integral equations. The integral equations are further reduced to two systems of algebraic equations with the aid of Jacobi polynomials and Chebyshev polynomials. Thereafter, the exact expressions for the stress intensity factors and the electric displacement intensity factor at the tip of a crack are obtained. Selected numerical results are presented for various bi-material systems to portray the significant features of crack tip fracture parameters and their dependence on material properties, poling orientation and electric loading.

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Stress intensification near an elliptical crack border

Cited by 32 publications

References 5 publications

Finite element analyses of cracks in piezoelectric structures: a survey

Finite element analyses of cracks in piezoelectric structures: a survey

Elliptical crack and punch problems solved by integral equation method for piezoelectric media

Fracture parameters of a penny-shaped crack at the interface of a piezoelectric bi-material system

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