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.

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.

scholarly journals The Static Stress Intensity Factor around the Antiplane Crack in an Infinite FGM Strip

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wen-bin Zhao ◽  
Zhi-xin Hu ◽  
Xue-xia Zhang ◽  
Hai-ling Xie
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Euler Equation ◽  
Integral Equations ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Static Stress ◽  
Dual Integral Equations ◽  
Graded Material

The problem of the static stress intensity factor around antiplane crack in an infinite strip functionally graded material was studied by using the method of integral transform-dual integral equations in this paper. The shear modulus in the two principal directions of the functionally graded material was assumed to vary proportionately as gradient model of double parameters index function. The partial differential equation was first reduced to Euler equation with Fourier cosine transform. By solving dual integral equations that were derived by applying the solution of Euler equation with the method of Copson, stress intensity factor around the crack tip was derived. And the variation curves of the dimensionless stress intensity factor with the strip height, crack length, gradient parameter, and inhomogeneous coefficient are obtained by using the numerical calculation.

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.

Intervallic Coiflets for Numerical Calculation of Dynamic Stress Intensity Factor

2012 ◽  
Vol 562-564 ◽  
pp. 668-671
Author(s):  
Jian Ping Xuan ◽  
Yuan Feng Liu ◽  
Tie Lin Shi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Equations ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
High Accuracy ◽  
Fredholm Integral Equations ◽  
Wavelet Expansion ◽  
Dual Integral Equations

There are lots of practical problems which are related to the solution of Fredholm integral equations of the second kind. The present work proposes intervallic Coiflets for solving the equations. Illustrative problem involving dynamic stress and electric fields of a cracked piezoelectric excited by anti-plane shear wave is addressed. Permeable boundary condition has been used to obtain a pair of dual integral equations of the symmetric and antisymmetric parts which can be reduced to the solutions of two Fredholm integral equations of the second kind. The dynamic stress intensity factor is expressed in terms of the right-end values of two unknown functions in Fredholm integral equations. The two unknown functions are solved by intervallic Coiflets which have less the endpoints error. And intervallic Coiflets have low calculation cost and high accuracy due to the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations. The calculation results agree well with the existing method, which show the high accuracy of the estimation and demonstrate validity and applicability of the method.

The Static Stress Intensity Factor around the Anti-Plane Crack in an Orthotropic Functionally Graded Material

2013 ◽  
Vol 275-277 ◽  
pp. 208-214
Author(s):  
Xue Xia Zhang ◽  
Zhi Xin Hu ◽  
Wen Bin Zhao ◽  
Chan Li
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Shear Modulus ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Plane Crack ◽  
Dual Integral Equations ◽  
Dimensionless Stress ◽  
Graded Material

The problem of anti-plane crack in infinity orthotropic functionally graded materials is studied by using of integral transforms-dual integral equations. The shear modulus in the two principal directions of the functionally graded material was assumed to vary proportionately as gradient model of double parameters. And the variation curves of the dimensionless stress intensity factor with the orthogonal parameter and the crack length have been obtained by using the mathematical software .The results shows that stress intensity factor increases with the increasing of and a. It means that stress intensity factor decreases as the shear modulus of perpendicular to crack direction increased.

Fracture Dynamics of a Mode III Moving Crack Impacted by Elastic Wave in Functionally Graded Materials

2010 ◽  
Vol 105-106 ◽  
pp. 683-686
Author(s):  
Xin Gang Li ◽  
Zhen Qing Wang ◽  
Nian Chun Lü
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Functionally Graded Materials ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Functionally Graded ◽  
Moving Crack ◽  
Graded Materials ◽  
Sh Waves

The dynamic stress field under the SH-waves at the moving crack tip of functionally graded materials is analyzed, and the influences of parameters such as graded parameter, crack velocity, the angle of the incidence and the number of the waves on dynamic stress intensity factor are also studied. Due to the same time factor of scattering wave and incident wave, the scattering model of the crack tip can be constructed by making use of the displacement function of harmonic load in the infinite plane. The dual integral equation of moving crack problem subjected to SH-waves is obtained through Fourier transform with the help of the exponent model of the shear modulus and density, then have some process on the even and odd term of the integral kernel. The displacement is expanded into series form using Jacobi Polynomial, and then the semi-analytic and numerical solutions of dynamic stress intensity factor are derived with Schmidt method.

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