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.

The scattering of the harmonic anti-plane shear stress waves by two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material half-infinite planes dynamic loading

2006 ◽  
Vol 220 (2) ◽  
pp. 137-148 ◽  
Author(s):  
Z-G Zhou ◽  
B Wang
Keyword(s):  
Shear Stress ◽  
Magnetic Flux ◽  
Electric Displacement ◽  
Stress Waves ◽  
Functionally Graded ◽  
Plane Shear ◽  
Interface Cracks ◽  
Unknown Variable ◽  
Dynamic Stress Field ◽  
Functionally Graded Piezoelectric

In this paper, the dynamic behaviour of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material half-infinite planes subjected to the harmonic anti-plane shear stress waves is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By using the Fourier transform technique, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the jump of the displacements across the crack surfaces. These equations are solved by using the Schmidt method. The relations among the electric field, the magnetic flux field, and the dynamic stress field near the crack tips can be obtained. Numerical examples are provided to show the effect of the functionally graded parameter, the distance between two interface cracks, and the circular frequency of the incident waves upon the stress, the electric displacement, and the magnetic flux intensity factors of cracks.

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.

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