Scattering of anti-plane shear waves by an interface crack between two bonded dissimilar functionally graded piezoelectric materials

2009 ◽  
Vol 465 (2104) ◽  
pp. 1249-1269 ◽  
Author(s):  
B.M Singh ◽  
J Rokne ◽  
R.S Dhaliwal ◽  
J Vrbik
Keyword(s):  
Integral Equations ◽  
Integral Transform ◽  
Piezoelectric Materials ◽  
Mass Density ◽  
Electric Displacement ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

In the present paper, the dynamic behaviour of a Griffith crack situated at the interface of two bonded dissimilar functionally graded piezoelectric materials (FGPMs) is considered. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPMs vary continuously as an exponential function of the x and y coordinates, and that the FGPMs are under anti-plane mechanical loading and in-plane electrical loading. By using an integral transform technique the problem is reduced to four pairs of dual integral equations, which are transformed into four simultaneous Fredholm integral equations with four unknown functions. By solving the four simultaneous Fredholm integral equations numerically the effects of the material properties on the stress and electric displacement intensity factors are calculated and displayed graphically.

Antiplane Crack Problem in Functionally Graded Piezoelectric Materials

2002 ◽  
Vol 69 (4) ◽  
pp. 481-488 ◽  
Author(s):  
Chunyu Li ◽  
G. J. Weng
Keyword(s):  
Integral Equations ◽  
Piezoelectric Material ◽  
Electric Fields ◽  
Crack Problem ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Functionally Graded Piezoelectric Material ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

In this paper the problem of a finite crack in a strip of functionally graded piezoelectric material (FGPM) is studied. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric permitivity of the FGPM vary continuously along the thickness of the strip, and that the strip is under an antiplane mechanical loading and in-plane electric loading. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. The near-tip singular stress and electric fields are obtained from the asymptotic expansion of the stresses and electric fields around the crack tip. It is found that the singular stresses and electric displacements at the tip of the crack in the functionally graded piezoelectric material carry the same forms as those in a homogeneous piezoelectric material but that the magnitudes of the intensity factors are dependent upon the gradient of the FGPM properties. The investigation on the influences of the FGPM graded properties shows that an increase in the gradient of the material properties can reduce the magnitude of the stress intensity factor.

Anti-Plane Moving Crack in Functionally Graded Piezoelectric Materials

2002 ◽  
Author(s):  
Bo Jin
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Equations ◽  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Dual Integral Equations ◽  
Moving Crack ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

This paper considers the anti-plane moving crack in functionally graded piezoelectric materials (FGPM). The governing equations for FGPM are solved by means of Fourier cosine transform. The mathematical formulation for the permeable crack condition is derived as a system of dual integral equations. By appropriate transformations, it is shown that the dual integral equations can be reduced to a Fredholm integral equation of the second kind. The results obtained indicate that the stress intensity factor of moving crack in FGPM depends only on the mechanical loading. The gradient parameter of the FGPM and the moving velocity of the crack do have significant influence on the dynamic stress intensity factor.

The Non-Local Theory Solution of a Crack in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves

2007 ◽  
Vol 353-358 ◽  
pp. 258-262
Author(s):  
Zhen Gong Zhou ◽  
Lin Zhi Wu
Keyword(s):  
Shear Stress ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Stress Waves ◽  
Functionally Graded ◽  
Local Theory ◽  
Plane Shear ◽  
Functionally Graded Piezoelectric Materials ◽  
Non Local ◽  
Functionally Graded Piezoelectric

In this paper, the non-local theory of elasticity was applied to obtain the dynamic behavior of a Griffith crack in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves. The problem can be solved with the help of a pair of dual integral equations. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips, thus allows us to use the maximum stress as a fracture criterion.

Interaction between a Rigid Cylinder with a Piezoelectric Half-Space with Partial Adhesion

2008 ◽  
Vol 33-37 ◽  
pp. 333-338 ◽  
Author(s):  
Zuo Rong Chen ◽  
Shou Wen Yu
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Contact Region ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Dual Integral Equations ◽  
Slip Region

An axisymmetric problem of interaction of a rigid rotating flat ended punch with a transversely isotropic linear piezoelectric half-space is considered. The contact zone consists of an inner circular adhesion region surrounded by an outer annular slip region with Coulomb friction. Beyond the contact region, the surface of the piezoelectric half-space is free from load. With the aid of the Hankel integral transform, this mixed boundary value problem is formulated as a system of dual integral equations. By solving the dual integral equations, analytical expressions for the tangential stress and displacement, and normal electric displacement on the surface of the piezoelectric half-space are obtained. An explicit relationship between the radius of the adhesion region, the angle of the rotation of the punch, material parameters, and the applied loads is presented. The obtained results are useful for characterization of piezoelectric materials by micro-indentation and micro-friction techniques.

The Higher Order Crack-Tip Fields for Anti-Plane Crack in Exponential Functionally Graded Piezoelectric Materials

2014 ◽  
Vol 989-994 ◽  
pp. 1212-1215
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Shi Min Li
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Crack Tip ◽  
Expansion Method ◽  
Elastic Stiffness ◽  
Functionally Graded ◽  
Plane Crack ◽  
Displacement Fields ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

The near-tip fields of an anti-plane crack in functionally graded piezoelectric materials (FGPMs) are investigated. To make the analysis tractable as usual, the elastic stiffness, piezoelectric parameter, and dielectric permittivity of FGPMs are assumed to be exponential functions of x parallel to the crack. The boundary conditions on crack surfaces are assumed to be the stress free and electrically impermeable. The high order crack tip stress and electric displacement fields are obtained by the eigen-expansion method. This study possesses fundamental significance as Williams’ solution to homogeneous materials.

The Higher Order Crack Tip Fields for Interfacial Crack between Linear Functionally Graded and Homogeneous Piezoelectric Materials

2014 ◽  
Vol 1015 ◽  
pp. 97-100
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Ying Chen
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Crack Tip Fields ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for an anti-plane crack situated in the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The mechanical and electrical properties of the FGPMs are assumed to be linear functions of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. By using the method of eigen-expansion, the higher order stress and electric displacement crack tip fields for FGPMs and HPMs are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

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