scholarly journals Analysis of Mode I Conducting Crack in Piezo-Electro-Magneto-Elastic Layer

2013 ◽  
Vol 18 (1) ◽  
pp. 153-176
Author(s):  
B. Rogowski
Keyword(s):  
Boundary Conditions ◽  
Electric Displacement ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Intensity Factors ◽  
Permeable Crack ◽  
Crack Face ◽  
Field Intensity Factors ◽  
Dielectric Crack ◽  
Thickness Field

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

Three-Dimensional Electroelastic Analysis of a Piezoelectric Material With a Penny-Shaped Dielectric Crack

2004 ◽  
Vol 71 (6) ◽  
pp. 866-878 ◽  
Author(s):  
Xian-Fang Li ◽  
Kang Yong Lee
Keyword(s):  
Boundary Conditions ◽  
Piezoelectric Material ◽  
Field Intensity ◽  
Three Dimensional ◽  
Intensity Factors ◽  
Elementary Functions ◽  
Dual Integral Equations ◽  
Electroelastic Field ◽  
Field Intensity Factors ◽  
Dielectric Crack

Previous studies assumed that a crack is either impermeable or permeable, which are actually two limiting cases of a dielectric crack. This paper considers the electroelastic problem of a three-dimensional transversely isotropic piezoelectric material with a penny-shaped dielectric crack perpendicular to the poling axis. Using electric boundary conditions controlled by the boundaries of an opening crack, the electric displacements at the crack surfaces are determined. The Hankel transform technique is employed to reduce the considered problem to dual integral equations. By solving resulting equations, the results are presented for the case of remote uniform loading, and explicit expressions for the electroelastic field at any point in the entire piezoelectric body are given in terms of elementary functions. Moreover, the distribution of asymptotic field around the crack front and field intensity factors are determined. Numerical results for a cracked PZT-5H ceramic are evaluated to examine the influence of the dielectric permittivity of the crack interior on the field intensity factors, indicating that the electric boundary conditions at the crack surfaces play an important role in determining electroelastic field induced by a crack, and that the results are overestimated for an impermeable crack, and underestimated for a permeable crack.

Transient Dynamic Analysis of Cracked Multifield Solids with Consideration of Crack-Face Contact and Semi-Permeable Electric/Magnetic Boundary Conditions

2014 ◽  
Vol 618 ◽  
pp. 123-150
Author(s):  
Michael Wünsche ◽  
Andrés Sáez ◽  
Felipe García-Sánchez ◽  
Chuan Zeng Zhang ◽  
Jose Domínguez
Keyword(s):  
Intensity Factor ◽  
Boundary Conditions ◽  
Electric Displacement ◽  
Dynamic Crack ◽  
Intensity Factors ◽  
Crack Face ◽  
Transient Dynamic ◽  
Electric Displacement Intensity Factor ◽  
Non Linear ◽  
Crack Face Contact

Boundary element method (BEM) formulations for transient dynamic crack analysis intwo-dimensional (2D) multifield materials are reviwed in this paper. Both homogeneous and lin-ear piezoelectric as well as magnetoelectroelastic material models are considered. Special attentionis paid to properly modeling the non-linear crack-face contact and semi-permeable electric/magneticboundary conditions. Implementation of the corresponding time-domain BEM(TDBEM) is discussedin detail. The proposed TDBEM uses a Galerkin-method for the spatial discretization, whilst thecollocation method is considered for the temporal discretization. Iterative solution algorithms aredeveloped to compute the non-linear crack-face boundary conditions. Crack-tip elements that ac-count for the square-root local behavior of the crack opening displacements (CODs) at the crack-tipsare implemented. In this way, stress intensity factors (SIF), electric displacement intensity factor(EDIF) and magnetic induction intensity factor (MIIF) may be accurately evaluated from the nu-merically computed CODs at the closest nodes to the crack-tips. Numerical examples involving sta-tionary cracks in piezoelectric and magnetoelectroelastic solids under different combined (mechani-cal/electric/magnetic) impact loadings are investigated, in order to illustrate the effectiveness of theproposed approach and characterize the influence of the semi-permeable crack-face boundary condi-tions on the dynamic field intensity factors.

scholarly journals Nonuniformly Loaded Stack of Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
G. E. Tupholme
Keyword(s):  
Electric Displacement ◽  
Polar Angle ◽  
Antiplane Shear ◽  
Shear Cracks ◽  
Intensity Factors ◽  
One Dimensional ◽  
Isotropic Solid ◽  
Special Cases ◽  
Field Intensity Factors ◽  
Explicit Representations

Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed.

A Piezoelectric Screw Dislocation Interacting with a Dielectric Crack in a Hexagonal Piezoelectric Material

2005 ◽  
Vol 9 ◽  
pp. 183-190
Author(s):  
Jin Xi Liu ◽  
X.L. Liu
Keyword(s):  
Electric Field ◽  
Screw Dislocation ◽  
Electric Displacement ◽  
Image Force ◽  
Mapping Method ◽  
Piezoelectric Medium ◽  
Intensity Factors ◽  
Potential Jump ◽  
Piezoelectric Screw Dislocation ◽  
Dielectric Crack

This paper is concerned with the interaction of a piezoelectric screw dislocation with a semi-infinite dielectric crack in a piezoelectric medium with hexagonal symmetry. The solution of the considered problem is obtained from the dislocation solution of a piezoelectric half-plane adjoining a gas medium of dielectric constant ε0 by using the conformal mapping method. The intensity factors of stress, electric displacement and electric field and the image force on the dislocation are given explicitly. The effect of electric boundary conditions on the dislocation-crack interaction is analyzed and discussed in detail. The results show that ε0 only influences the electric displacement and electric field intensity factors and the image force produced by the electric potential jump.

Contact Analysis for Collinear Multiple Cracks in Residual Stress Field

1994 ◽  
Vol 116 (2) ◽  
pp. 169-174 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Infinite Plate ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Algebraic Equations ◽  
Intensity Factors ◽  
Residual Stress Field ◽  
Crack Face

A method is proposed for analyzing stress intensity factors and crack profiles for collinear multiple cracks perpendicular to welded joints in an infinite plate. Using the basic solution of a single crack and taking unknown density of fictitious tractions, Fredholm integral equations and algebraic equations are formulated based upon traction-free conditions and crack face displacements, respectively. These equations are solved simultaneously, considering the contact effect of crack surfaces. Using the derived density of fictitious tractions, the stress intensity factors and displacements of multiple cracks are determined. Some numerical examples are analyzed.

A Study of Crack-Face Boundary Conditions for Piezoelectric Strip Cut Along Two Equal Collinear Cracks

2016 ◽  
Vol 8 (4) ◽  
pp. 573-587 ◽  
Author(s):  
R. R. Bhargava ◽  
Pooja Raj Verma
Keyword(s):  
Boundary Conditions ◽  
Crack Opening ◽  
Electric Displacement ◽  
Potential Drop ◽  
Collinear Cracks ◽  
Crack Face ◽  
Plane Shear ◽  
Fracture Parameters ◽  
Analytic Expressions ◽  
Piezoelectric Strip

AbstractA problem of two equal, semi-permeable, collinear cracks, situated normal to the edges of an infinitely long piezoelectric strip is considered. Piezoelectric strip being prescribed out-of-plane shear stress and in-plane electric-displacement. The Fourier series and integral equation methods are adopted to obtain analytical solution of the problem. Closed-form analytic expressions are derived for various fracture parameters viz. crack-sliding displacement, crack opening potential drop, field intensity factors and energy release rate. An numerical case study is considered for poled PZT–5H, BaTiO3 and PZT–6B piezoelectric ceramics to study the effect of applied electro-mechanical loadings, crack-face boundary conditions as well as inter-crack distance on fracture parameters. The obtained results are presented graphically, discussed and concluded.

Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane

2017 ◽  
Vol 28 (19) ◽  
pp. 2823-2834 ◽  
Author(s):  
Mojtaba Ayatollahi ◽  
Mojtaba Mahmoudi Monfared ◽  
Mahsa Nourazar
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Field Intensity ◽  
Electric Displacement ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Mode Iii ◽  
Singular Stress ◽  
Field Intensity Factors

This study deals with the interaction of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane. The cracks are assumed to be either magneto-electrically impermeable or permeable. First, the singular stress, electric displacement, and magnetic induction fields in a half-plane with dislocations are obtained in closed form by the means of complex Fourier transform and then the problem is reduced to a system of singular integral equations in a set of unknown functions representing dislocation densities. These integral equations are Cauchy singular and are solved numerically to determine field intensity factors for multiple moving cracks. The results show that the crack velocity has great effect on the field intensity factors.

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

2014 ◽  
Vol 30 (4) ◽  
pp. 361-372 ◽  
Author(s):  
X.-C. Zhong ◽  
K.-Y. Lee
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Electric Fields ◽  
Stress Intensity Factors ◽  
Piezoelectric Layer ◽  
Intensity Factors ◽  
Crack Face ◽  
Closed Form Solutions ◽  
Electroelastic Fields ◽  
Crack Tips

AbstractWithin 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.

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

2020 ◽  
pp. 1045389X2096316
Author(s):  
MingHao Zhao ◽  
XinFei Li ◽  
Chunsheng Lu ◽  
QiaoYun Zhang
Keyword(s):  
Boundary Condition ◽  
Intensity Factor ◽  
Boundary Conditions ◽  
Crack Opening ◽  
Electric Displacement ◽  
Opening Displacement ◽  
Crack Face ◽  
Electric Boundary Condition ◽  
Electric Displacement Intensity Factor ◽  
Piezoelectric Semiconductors

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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