Crack Opening Displacement Intensity Factor Research Articles

Fracture analysis of an infinite 1D hexagonal piezoelectric quasicrystal plate with a penny-shaped dielectric crack

This article studies the electroelastic behavior induced by a penny-shaped dielectric crack lying at the midplane of a one-dimensional (1D) hexagonal piezoelectric quasicrystal plate of finite thickness. Semi-permeable crack boundary conditions are given. By using the Hankel transform technique, an associated mixed boundary value problem is reduced to two coupled Fredholm integral equations of the second kind. Singular electric and elastic fields around the crack front along with their intensity factors in the phonon and phason fields near the crack front are obtained. The intensity factors of crack opening displacement (COD) across the crack faces are calculated and presented graphically. The influence of electric field and phason field on the COD intensity factors is analyzed. Permeable and impermeable cracks are two limit cases of the present.

Transient thermal fracture analysis of a penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder

ABSTRACTThe problem of penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder is investigated under thermal shock load. The problem is reduced to solve three coupled Fredholm integral equations. The field intensity factors are derived. Numerical results of crack opening displacement intensity factors are presented, and the effects of thermal shock time, crack configuration, and magnetoelectrical crack surface conditions on crack propagation and growth are evaluated. Among others, the larger cylinder's radius, the easier to propagate the crack is. For a fixed crack configuration, magnetoelectrical crack surface conditions have different effects on crack propagation as well.

Fracture analysis of a penny-shaped dielectric crack in a piezoelectric cylinder

Electroelastic behavior induced by a penny-shaped dielectric crack in a piezoelectric cylinder (i.e., a finite piezoelectric body in the radius direction) is considered in this paper. Two coupled Fredholm integral equations are derived by employing the Hankel transform technique with the introduction of certain auxiliary functions. The intensity factors of stress, electrical displacement and crack opening displacement (COD) are obtained in closed forms. The effects of the radius of the piezoelectric cylinder, the applied electrical field and permittivity of the crack interior on the COD intensity factor are illustrated numerically. The results of both the electrically permeable and impermeable boundary conditions are simultaneously displayed as special cases.

A penny‐shaped magnetically dielectric crack in a magnetoelectroelastic cylinder under magnetoelectromechanical loads

In this paper the fracture behaviors of magnetoelectroelastic cylinder induced by a penny‐shaped magnetically dielectric crack are investigated. By employing the Hankel transform technique and introducing three auxiliary functions, the complex question is transformed to solve three coupled nonlinear Fredholm integral equations. The intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) are derived in closed forms. The effects of the radius of the cylinder, applied electric field and magnetic field, dielectric permittivity and magnetic permeability of the crack interior on the COD intensity factor are illustrated numerically. The results corresponding to magnetoelectrically permeable and impermeable boundary conditions are only the special cases of the present model.

Closed-form solutions for two collinear dielectric cracks in a magnetoelectroelastic solid

The problem of two collinear electromagnetically dielectric cracks in a magnetoelectroelastic material is investigated under in-plane electro-magneto-mechanical loadings. The semi-permeable crack-face boundary conditions are adopted to simulate the case of two collinear cracks full of a dielectric interior. Utilizing the Fourier transform technique, the boundary-value problem is reduced to solving singular integral equations with Cauchy kernel, which then are solved explicitly. The intensity factors of stress, electric displacement, magnetic induction, crack opening displacement (COD) and the energy release rates near the inner and outer crack tips are determined in closed forms for two cases of possible far-field electro-magneto-mechanical loadings respectively. Numerical results for a BaTiO 3–CoFe 2O 4 composite are carried out to show the effects of applied mechanical loadings on the crack-face electric displacement and magnetic induction, the stress intensity factor and the COD intensity factor, respectively. The obtained results reveal that when the applied mechanical loading is stress, applied electromagnetic loadings have no influences on the stress intensity factor. When the applied mechanical loadings is train, the applied positive electromagnetic loadings decrease the intensity factors of stress and COD, and the applied negative ones increase the intensity factors of stress and COD. The variations of energy release rates are also given to show the effects of the geometry of two collinear dielectric cracks.

Thickness effects for a penny-shaped dielectric crack in a magnetoelectroelastic layer

The problem of a penny-shaped dielectric crack in a magnetoelectroelastic layer is considered within the theory of linear magnetoelectroelasticity. Under the assumption of mode-I magnetoelectromechanical loadings, the semipermeable crack-face electromagnetic boundary conditions are applied to describe the case of an opening penny-shaped crack. In order to solve the boundary-value problem, the Hankel transform technique is utilized and three coupled Fredholm integral equations are further derived. The intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) are further determined by the composite Simpson's rule. Thickness effects of a magnetoelectroelastic layer on the electric displacement and magnetic induction of the crack interior, and the field intensity factors are illustrated through numerical computations for a BaTiO3-CoFe2O4 composite. The obtained results reveal that an increase of the ratio of the layer thickness and the crack radius h/a increases the electric displacement and magnetic induction of a dielectric crack interior, and decreases the field intensity factors regardless of the permeability of the crack interior. Based on the COD intensity factor, the influences of applied electric and magnetic fields on the growth of a dielectric crack are further investigated and presented graphically.

Analysis of a dielectric crack in a magnetoelectroelastic layer

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto-electrically dielectric Griffith crack embedded in a magnetoelectroelastic layer is investigated under in-plane magneto-electro-mechanical loadings. The semi-permeable crack-face magnetoelectric boundary conditions are utilized to simulate the case of an opening dielectric crack. Applying the Fourier transform technique, the boundary-value problem is reduced to solving three coupling singular integral equations. Field intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) are further determined by the Lobatto-Chebyshev collocation method. The electric displacement and magnetic induction of crack interior are discussed in detail. The obtained results reveal that the magnetoelectric field inside the crack is dependent on the material properties, applied loadings, the dielectric permeability of crack interior, and the ratio of the crack length and the layer width. Numerical computations are carried out to present that the volume fraction of piezoelectric phase in BaTiO 3 – CoFe 2 O 4 composites has great influences on the magnetoelectric field inside the dielectric crack. Based on the COD intensity factor, the analysis for the growth of a dielectric crack in a magnetoelectroelastic layer is examined. The proposed procedure can be reduced to dealing with the case of a dielectric crack in a piezoelectric layer and the obtained results can be verified by the experimental observations.

Study of a propagating finite crack in functionally graded piezoelectric materials considering dielectric medium effect

This paper provides a study of the problem of a propagating finite crack under in-plane loading in functionally graded piezoelectric materials (FGPMs). The analytical formulations are developed by Fourier transforms and the resulting singular integral equations are solved by using Chebyshev polynomials. By using a dielectric crack model with deformation-dependent electric boundary condition, numerical simulations are made to show the effects of the dielectric medium, the gradient of material properties and the speed of crack propagation on the fracture parameters, such as the stress, electric displacement and crack opening displacement intensity factors. A critical state for the electromechanical loading applied to the FGPMs is observed, which determines whether the traditionally impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric model. The validity of this dielectric crack model is also examined by comparing the results of different existing crack models.

Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer

The assumptions of impermeable and permeable cracks give rise to significant errors in determining electro-elastic behavior of a cracked piezoelectric material. The former simply imposes that the permittivity or electric displacement of the crack interior vanishes, and the latter neglects also the effects of the dielectric of an opening crack interior. Considering the presence of the dielectric of an opening crack interior and the permeability of the crack surfaces for electric field, this paper analyzes electro-elastic behavior induced by a penny-shaped dielectric crack in a piezoelectric ceramic layer. In the cases of prescribed displacement or prescribed stress at the layer surfaces, the Hankel transform technique is employed to reduce the problem to Fredholm integral equations with a parameter dependent nonlinearly on the unknown functions. For an infinite piezoelectric space, a closed-form solution can be derived explicitly, while for a piezoelectric layer, an iterative technique is suggested to solve the resulting nonlinear equations. Field intensity factors are obtained in terms of the solution of the equations. Numerical results of the crack opening displacement intensity factors are presented for a cracked PZT-5H layer and the effect of applied electric field on crack growth are examined for both cases. The results indicate that the fracture toughness of a piezoelectric ceramic is affected by the direction of applied electric fields, dependent on the elastic boundary conditions.