Penny-shaped cracks in three-dimensional piezoelectric semiconductors via Green’s functions of extended displacement discontinuity

Zhao, Yanfei; Zhou, ChunGuang; Zhao, Minghao; Pan, Ernian; Fan, CuiYing

doi:10.1177/1045389x16679294

Cited by 17 publications

(8 citation statements)

References 23 publications

(27 reference statements)

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“…Tian et al (2020) introduced interface effect into PSC composites to provide possible extra tuning opportunities. Furthermore, fracture problem in PSCs has also received considerable attention in recent years (Hu et al, 2007;Sladek et al, 2014aSladek et al, , 2014bSladek et al, , 2015Zhao et al, 2016Zhao et al, , 2017Zhao et al, , 2018. More recently, a double iteration method was proposed to analyze the crack problem in a 2D piezoelectric semiconductor with more accurate and real electric boundary conditions (Zhao et al, 2020a).…”

Section: Introductionmentioning

confidence: 99%

Size effect in piezoelectric semiconductor nanostructures

Sládek

Repka

et al. 2021

Journal of Intelligent Material Systems and Structures

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A gradient theory is applied to the mechanical constitutive equations for piezoelectric semiconductor nanostructures. This is achieved by considering the strain gradients in the constitutive equation with high-order stresses and electric displacements in advanced continuum model. The C1 continuous interpolations of displacements or a mixed formulation is required in the finite element method (FEM) due to the presence of the second-order derivative on the elastic displacements. A mixed FEM is then developed from the principle of virtual work. Numerical examples clearly show the significant effect of flexoelectricity on the induced electric potential and electric current in the piezoelectric semiconductor nanostructures.

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Section: Introductionmentioning

confidence: 99%

Size effect in piezoelectric semiconductor nanostructures

Sládek

Repka

et al. 2021

Journal of Intelligent Material Systems and Structures

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“…In consideration of thermal-mechanical coupling effect, a central crack problem in thermal PSCs was studied by using the extended displacement discontinuity method (Zhao et al, 2017). A few of crack problems in three-dimensional (3D) PSCs were also investigated by using the extended displacement discontinuity method, such as, singularity indexes of near-border fields of a planar crack in 3D transversely isotropic PSCs (Zhao et al, 2016a), a penny shaped crack problem in 3D PSCs (Zhao et al, 2016c), and a penny shaped crack problem in 3D thermal PSCs (Zhao et al, 2018a). With these researches, it is seen that analytical methods can be used to solve simple crack problems like anti-plane cracks in infinite PSCs.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of a crack in 2D piezoelectric semiconductors with exact electric boundary conditions

Zhao

et al. 2020

Journal of Intelligent Material Systems and Structures

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In this paper, taking the exact electric boundary conditions into account, we propose a double iteration method to analyze a crack problem in a two-dimensional piezoelectric semiconductor. The method consists of a nested loop process with internal and outside circulations. In the former, the electric field and electron density in governing equations are constantly modified with the fixed boundary conditions on crack face and the crack opening displacement; while in the latter, the boundary conditions on crack face and the crack opening displacement are modified. Such a method is verified by numerically analyzing a crack with an impermeable electric boundary condition. It is shown that the electric boundary condition on crack face largely affects the electric displacement intensity factor near a crack tip in piezoelectric semiconductors. Under exact crack boundary conditions, the variation tendency of the electric displacement intensity factor versus crack size is quite different from that under an impermeable boundary condition. Thus, exact crack boundary conditions should be adopted in analysis of crack problems in a piezoelectric semiconductor.

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“…According to the finite element and boundary element methods, Fan et al [ 19 ] and Zhang et al [ 20 ] proposed a piezoelectric-conductor iterative approach for structural analysis of PSC with combined mechanical and electrical loading. Zhao et al [ 21 ] analyzed a penny-shaped crack in the isotropic plane of PSC and, based on Almansi’s theory, derived its general solutions.…”

Section: Introductionmentioning

confidence: 99%

Electric Current Dependent Fracture in GaN Piezoelectric Semiconductor Ceramics

Qin

Zhang

et al. 2018

Materials

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In this paper, the fracture behavior of GaN piezoelectric semiconductor ceramics was investigated under combined mechanical and electric loading by using three-point bending tests and numerical analysis. The experimental results demonstrate that, in contrast to traditional insulating piezoelectric ceramics, electric current is a key factor in affecting the fracture characteristics of GaN ceramics. The stress, electric displacement, and electric current intensity factors were numerically calculated and then a set of empirical formulae was obtained. By fitting the experimental data, a fracture criterion under combined mechanical and electrical loading was obtained in the form of an ellipsoid function of intensity factors. Such a fracture criterion can be extended to predict the failure behavior of other piezoelectric semiconductors or devices with a crack, which are useful in their reliability design and applications.

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Penny-shaped cracks in three-dimensional piezoelectric semiconductors via Green’s functions of extended displacement discontinuity

Cited by 17 publications

References 23 publications

Size effect in piezoelectric semiconductor nanostructures

Size effect in piezoelectric semiconductor nanostructures

Nonlinear analysis of a crack in 2D piezoelectric semiconductors with exact electric boundary conditions

Electric Current Dependent Fracture in GaN Piezoelectric Semiconductor Ceramics

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