In this paper, a finite crack propagating at constant speed in a functionally graded piezoelectric material (FGPM) is studied. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential gradients along the thickness of the strip, and that the strip is under anti-plane shear mechanical and in-plane electrical loads. The analysis is conducted on the electrically unified (natural) crack boundary condition, which is related to the ellipsoidal crack parameters. By using the Fourier transform, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, crack propagation speed, electric field, FGPM gradation, crack length, and electromechanical coupling coefficient. It reveals that there are considerable differences between traditional electric crack models and the present unified crack model.

On the dynamic propagation of an anti-plane shear crack in a functionally graded piezoelectric strip

The generalized plane problem of a finite Griffith crack moving with constant velocity in an anisotropic piezoelectric material is investigated. The combined mechanical and electrical loads are applied at infinity. Based on the extended Stroh formalism, the closed-form expressions for the electroelastic fields are obtained in a concise way. Numerical results for PZT-4 piezoelectric ceramic are given graphically. The effects on the hoop stress of the velocity of the crack and the electrical to mechanical load ratios are analyzed. The propagation orientation of a moving crack is also predicted in terms of the criterion of the maximum tensile stress. When the crack speed vanishes, the results of the present paper are in good agreement with those given previously in the literature.

On a moving Griffith crack in anisotropic piezoelectric solids

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 impermea...

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

Fracture analysis of an orthotropic strip with imperfect piezoelectric coating containing multiple defects

In this study, a functionally graded orthotropic layer sandwiched between two magneto-electro-elastic layers under anti-plane time-harmonic mechanic and in-plane electromagnetic loadings is studied. This paper examines the modeling of cracks by distribution of strain nuclei along crack lines. During this investigation, the Volterra-type screw dislocation is employed in the FGM orthotropic layer and the magneto-electro-elastic coating. The material properties of the strip are considered to obey exponential variations. To solve the dislocation problem, the complex Fourier transform is applied. One merit of this technique is the possibility of determination of the stress intensity factors for multiple smooth cracks. The system of equations is derived by considering the distribution of line dislocation on the crack. These equations are of Cauchy singular type in the location of dislocation, which can be solved numerically to obtain the dislocation density on the faces of the cracks. Various examples are solved, and the dynamic stress intensity factors are obtained. The effect of the cracks configuration, bonding constant, angular frequency and material properties on the mode III stress intensity factor is studied, and the validity of the analysis is checked.

Fracture Analysis in an Imperfect FGM Orthotropic Strip Bonded Between Two Magneto-Electro-Elastic Layers

An analysis is performed for the problem of a finite Griffith crack moving with constant velocity along the interface of a two-layered strip composed of a piezoelectric ceramic and an elastic layers. The combined out-of-plane mechanical and in-plane electrical loads are applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic stress intensity factor(DSIF) is determined, and numerical results show that DSIF depends on the crack length, the ratio of stiffness and thickness, and the magnitude and direction of electrical loads as well as the crack speed. In case that the crack moves along the interface of piezoelectric and elastic half planes, DSIF is independent of the crack speed.

Moving interfacial crack between piezoelectric ceramic and elastic layers

This paper provides the problem of an interfacial crack moving along the interface between a piezoelectric and two orthotropic materials under electromechanical longitudinal shear loadings Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations, which are then reduced to a Fredholm integral equation of the second kind The dynamic field intensity factors are determined in terms of a Fredholm integral equation of the second kind To show the geometrical and electromechanical effects on the dynamic stress intensity factor for various material combinations, some numerical examples are presented The numerical results show that the dynamic stress intensity factor depends on the crack length, the ratios of stiffness and thickness, and the magnitude and direction of electrical loads as well as crack speed

Anti-plane interfacial Yoffe-crack between a piezoelectric and two orthotropic layers

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Moving interfacial crack between piezoelectric ceramic and elastic layers

Anti-plane interfacial Yoffe-crack between a piezoelectric and two orthotropic layers