On the self-consistent, energetically consistent, and electrostatic traction approaches in piezoelectric fracture mechanics

Fan, CuiYing; Zhao, Minghao; Meng, Li-Cheng; Gao, Cun‐Fa; Zhang, Tong‐Yi

doi:10.1016/j.engfracmech.2011.05.006

Cited by 16 publications

(4 citation statements)

References 20 publications

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“…As we know, several other boundary conditions are also frequently used in piezoelectric solids besides the electrically impermeable condition, for example, electrically permeable, semi-permeable [29], self-consistent approach [30,31], energetically consistent boundary conditions [32] and the electrostatic tractions [33]. These results demonstrated that the boundary conditions on crack faces in piezoelectric solids have an important influence on the solutions.…”

Section: Analysis Of a Center Crack In A Rectangular Piezoelectric Sementioning

confidence: 87%

Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method

Fan

Yan

et al. 2016

Engineering Fracture Mechanics

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Section: Analysis Of a Center Crack In A Rectangular Piezoelectric Sementioning

confidence: 87%

Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method

Fan

Yan

et al. 2016

Engineering Fracture Mechanics

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“…One can find that the dielectric permittivity of crack interior has great influences on the crack opening displacement. The observations reveal theoretically that the effects of the dielectric inside a crack on the crack growth of piezoelectric solids should not be disregarded [26–29].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Recently, the electrostatic traction acting on the crack faces has been calculated [27, 28] and the energetically consistent boundary conditions have been proposed [27]. Unfortunately, applied positive and negative electrical loadings always decrease the stress intensity factor or retard the crack growth using the energetically consistent boundary conditions for a linear dielectric crack in a piezoelectric solid [29, 30], which is also inconsistent with the known experimental results. From the above analysis, the fracture toughness variations of piezoelectric ceramics should be further illustrated within the framework of linear piezoelectricity.…”

Section: Introductionmentioning

confidence: 99%

An analytical model for a bridged crack in piezoelectric ceramics

Zhong

2013

Mathematics and Mechanics of Solids

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A Griffith crack centrally bridged by a single grain in piezoelectric ceramics is modeled and investigated theoretically. Applying the Fourier transform method and the semi-permeable crack-face boundary conditions, various fracture parameters involving the stress intensity factors, the jumps of electrical potential and elastic displacement across the crack, and the energy release rate are given in closed forms. The total force and the electric potential acting on the bridging grain are obtained explicitly. Numerical results are calculated to show the effects of applied electrical fields and the permittivity of crack interior on the fracture parameters of concern. Under the assumption that the crack growth depends on the pull-out of the bridging grain, the obtained results reveal that applied positive electrical loadings enhance the crack growth and applied negative ones retard the crack growth. When one measures the crack length, applied positive electrical loadings will decrease the crack length and applied negative ones may increase the crack length. The above phenomena show that the crack-face bridging grains have contributions to various effects of applied electrical fields on the crack growth of piezoelectric solids.

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“…Eskandari et al [25] have made an electroelastic analysis of an energetically consistent annular crack in a piezoelectric solid. Using the self-consistent and the energetically consistent approaches, Fan et al [26] have compared the observations for cracked piezoelectric ceramics. Zhong [27] has addressed the problem of an eccentric penny-shaped crack embedded in a piezoelectric layer by using the energetically consistent boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Electroelastic Fields Induced by Two Collinear and Energetically Consistent Cracks in a Piezoelectric Layer

Zhong

Lee

2014

J. mech.

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Within the framework of linear piezoelectricity, the problem of two collinear electrically dielectric cracks in a piezoelectric layer is investigated under inplane electro-mechanical loadings. The energetically consistent crack-face boundary conditions are utilized to address the effects of a dielectric inside the cracks on the crack growth. The Fourier transform technique is applied to solve the boundary-value problem. Under the consideration of two-case electromechanical loadings, the electroelastic fields near the inner and outer crack tips are obtained through the Lobatto-Chebyshev collocation method. The special case of two collinear energetically consistent cracks in an infinite piezoelectric solid is analyzed and the closed-form solutions of the crack-tip electroelastic fields are further determined. Numerical results show the variations of stress intensity factors and energy release rates near the inner and outer crack tips on the applied electric fields, the geometry of cracks and the width of the piezoelectric layer in graphics. The observations reveal that the stress intensity factors are dependent not only on the adopted crack-face boundary conditions, but also on the applied mechanical loading.

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On the self-consistent, energetically consistent, and electrostatic traction approaches in piezoelectric fracture mechanics

Cited by 16 publications

References 20 publications

Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method

Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method

An analytical model for a bridged crack in piezoelectric ceramics

Electroelastic Fields Induced by Two Collinear and Energetically Consistent Cracks in a Piezoelectric Layer

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