Crack propagation in piezoelectric materials under combined mechanical and electrical loadings

Kumar, Sanjeev; Singh, Rajeev

doi:10.1016/1359-6454(95)00175-3

Cited by 102 publications

(40 citation statements)

References 22 publications

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“…The ''negative'' means that the direction of applied electric load is opposite to the direction of poling. It can be observed that the crack tends to deviate from its straight line path under a purely electrical load for all the crack speeds, which is in agreement with the experimental observation in [36] and the theoretical investigations in [6] and [7] for the stationary crack in piezoelectric materials. On the other hand, Fig.…”

Section: Electroelastic Fields Near the Crack Tipsupporting

confidence: 92%

“…Especially, when the combined electrical and mechanical loads are applied, the positive electric load makes the crack tend to deviate from its original path and propagate in an oblique direction for higher crack velocity, which is impossible for a stationary crack. Finally, it should be pointed out that the stress distributions obtained for the case in which the crack velocity vanishes are consistent with those given in [6,7] for the stationary crack. Once a a have been obtained, b a can be computed from Eq.…”

Section: Discussionsupporting

confidence: 65%

“…Indeed, since the pioneering works [1] and [2], a number of analytical researches concerning the fracture problems of piezoelectric materials have been carried out and great progress has been made. References [3][4][5][6][7][8][9][10][11][12] give some examples of the plane and generalized plane crack problems in piezoelectric solids. It is worthwhile noting that these theoretical investigations were focused on the stress and electric fields induced by stationary cracks.…”

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confidence: 99%

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On a moving Griffith crack in anisotropic piezoelectric solids

Soh

Liu²,

Lee

et al. 2002

Archive of Applied Mechanics (Ingenieur Archiv)

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The generalized plane problem of a finite Griffith crack moving with constant velocity in an anisotropic piezoelectric material is investigated. The combined mechanical and electrical loads are applied at infinity. Based on the extended Stroh formalism, the closed-form expressions for the electroelastic fields are obtained in a concise way. Numerical results for PZT-4 piezoelectric ceramic are given graphically. The effects on the hoop stress of the velocity of the crack and the electrical to mechanical load ratios are analyzed. The propagation orientation of a moving crack is also predicted in terms of the criterion of the maximum tensile stress. When the crack speed vanishes, the results of the present paper are in good agreement with those given previously in the literature.

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Section: Electroelastic Fields Near the Crack Tipsupporting

confidence: 92%

Section: Discussionsupporting

confidence: 65%

mentioning

confidence: 99%

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On a moving Griffith crack in anisotropic piezoelectric solids

Soh

Liu²,

Lee

et al. 2002

Archive of Applied Mechanics (Ingenieur Archiv)

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“…Those quarter-point elements can be created (by collapsing one edge of a regular element and) shifting the mid-side nodes of the edges into the quarter position toward the crack front; see, e.g., [33,11,12] for mechanical analyses. This concept was first extended to piezoelectric crack problems by Kumar and Singh [34] and Kuna [35,36] for 2D cracks. CTE for 3D cracks were published in [37] and [38].…”

Section: Singular Electromechanical Crack-tip Elements (Cte)mentioning

confidence: 99%

Finite element analyses of cracks in piezoelectric structures: a survey

Kuna

2006

Arch Appl Mech

104

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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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“…Based on a simplified formulation of piezoelasticity, Spyropoulos [8] obtained the explicit expression of J em under different boundary conditions. However, for real piezoelectric materials, it is hard to get the exact solutions except few cases and the numerical method is often resorted to [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Bound theorem and implementation of dual finite elements for fracture assessment of piezoelectric materials

Lim

2005

Comput Mech

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Owing to the complexity of piezoelectric crack problems, derivation of closed-form solutions is virtually impossible and numerical solutions are largely resorted to. Hence, the upper and lower bound estimation for piezoelectric fracture parameters are of theoretical and practical values. An alternative assessment approach for electromechanical coupling cracked system is suggested in the paper. The dual path-independent integrals and the related bound theorems are presented. Consequently, the dual piezoelectric finite elements are formulated and implemented in bound analysis.

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Crack propagation in piezoelectric materials under combined mechanical and electrical loadings

Cited by 102 publications

References 22 publications

On a moving Griffith crack in anisotropic piezoelectric solids

On a moving Griffith crack in anisotropic piezoelectric solids

Finite element analyses of cracks in piezoelectric structures: a survey

Bound theorem and implementation of dual finite elements for fracture assessment of piezoelectric materials

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