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1.
Summary The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a penny-shaped crack
parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip
vary continuously along the thickness direction of the strip, and that the strip is under time-dependent electric load. Integral
transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of
singular integral equations. The stress and electric displacement intensity factors versus time are presented for various
values of dimensionless parameters representing the crack size, the crack location and the material nonhomogeneity. 相似文献
2.
S. Ueda 《Engineering Fracture Mechanics》2007,74(8):1255-1273
The mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip with a penny-shaped crack is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under thermal loading. The crack faces are supposed to be insulated thermally and electrically. The thermal and electromechanical problems are reduced to singular integral equations and solved numerically. The stress and electric displacement intensity factors are presented for different crack size, crack position and material nonhomogeneity. 相似文献
3.
A mixed-mode thermoelectroelastic fracture problem of a functionally graded piezoelectric material strip containing two parallel axisymmetric cracks, such as penny-shaped or annular cracks, is considered in this study. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip and that the strip is under thermal loading. The crack faces are supposed to be insulated thermally and electrically. Using integral transform techniques, the problem is reduced to that of solving two systems of singular integral equations. Systematic numerical calculations are carried out, and the variations of the stress and electric displacement intensity factors are plotted for various values of dimensionless parameters representing the crack size, the crack location and the material non-homogeneity. 相似文献
4.
S. Ueda 《Engineering Fracture Mechanics》2006,73(11):1455-1471
The dynamic fracture problem for a functionally graded piezoelectric strip containing a center crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the medium vary continuously in the thickness direction, and that the strip is under in-plane mechanical and electric impact loadings. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the material nonhomogeneity and the loading combination. 相似文献
5.
Summary. The dynamic behavior of a crack in a functionally graded piezoelectric material (FGPM) strip bonded to two half dissimilar piezoelectric material planes subjected to combined harmonic anti-plane shear wave and in-plane electrical loading was studied under the limited permeable and permeable electric boundary conditions. It was assumed that the elastic stiffness, piezoelectric constant and dielectric permittivity of the functionally graded piezoelectric layer vary continuously along the thickness of the strip. By using the Fourier transform, the problem can be solved with a set of dual integral equations in which the unknown variables are the jumps of the displacements and the electric potentials across the crack surfaces. In solving the dual integral equations, the jumps of the displacements and the electric potentials across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical results illustrate the effects of the gradient parameter of FGPM, electric loading, wave number, thickness of FGPM strip and electric boundary conditions on the dynamic stress intensity factors (SIFs). 相似文献
6.
The Dugdale plastic zone ahead of a penny-shaped crack in a piezoelectric material, subjected to electric and axisymmetric mechanical loadings, is evaluated analytically. Hankel transform is employed to reduce the mixed boundary-value problem of the penny-shaped crack to dual integral equations, which are solved exactly under the assumption of electrically permeable crack face conditions. A closed-form solution to the mixed boundary-value problem is obtained to predict the relationship between the length of the plastic zone and the applied loading. The stress distribution in and outside of the yield zone has been derived analytically, and the crack opening displacement has been investigated. The electric displacement has a constant value in the strip yield zone. The current Dugdale crack model leads to non-singular stress and electric fields near the crack front, and it is observed that the material properties affect the crack opening displacement. 相似文献
7.
In this paper the dynamic anti-plane problem for a functionally graded piezoelectric strip containing a central crack vertical to the boundary is considered. The crack is assumed to be electrically impermeable or permeable. Integral transforms and dislocation density functions are employed to reduce the problem to Cauchy singular integral equations. Numerical results show the effects of loading combination parameter, material gradient parameter and crack configuration on the dynamic response. With the permeable assumption, the electric impact has no contribution to the crack tip field singularity. With the impermeable assumption, the direction of applied electric impact loading plays a great role in the behavior of dynamic stress intensity factor, and the existence of electric load always enhances the crack propagation. However, the crack is easier to propagate under the negative electric load than that under the positive electric load. 相似文献
8.
On the dynamic propagation of an anti-plane shear crack in a functionally graded piezoelectric strip 总被引:8,自引:0,他引:8
S. M. Kwon 《Acta Mechanica》2004,167(1-2):73-89
Summary. 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. 相似文献
9.
Summary The problem of an anti-plane shear crack embedded in a magnetoelectroelastic strip is investigated. The crack is assumed to
be normal to the strip edges. By using the finite Fourier transform, the associated mixed boundary-value problem is reduced
to triple series equations, then to singular integral equations. Solving the resulting equations analytically, the field intensity
factors and energy release rates at the crack tips can be determined in explicit form. The influences of applied electric
and magnetic loadings on the normalized energy release rate and mechanical strain energy release rate are presented graphically.
Obtained results reveal that applied electric and magnetic loadings affect crack growth, depending on their directions and
adopted fracture criteria. The derived solution is applicable to other cases including two collinear cracks distributed symmetrically
in a magnetoelectroelastic strip, and a periodic array of collinear cracks in a magnetoelectroelastic plane. 相似文献
10.
Robert M. McMeeking 《International Journal of Fracture》2001,108(1):25-41
A theoretical fracture mechanics for brittle piezoelectric and dielectric materials is developed consistent with standard features of elasticity and dielectricity. The influence of electric field and mechanical loading is considered in this approach and a Griffith style energy balance is used to establish the relevant energy release rates. Results are given for a finite crack in an infinite isotropic dielectric and for steady state cracking in a piezoelectric strip. In the latter problem, the effect of charge separation in the material and discharge in the crack are considered. Observations of crack behavior in piezoelectrics under combined mechanical and electrical load are discussed to assess which features of the theory are useful. 相似文献
11.
Summary A laminate model is employed to solve the elastodynamic problem of a collinear crack in an inhomogeneous material. The inhomogeneous material is treated as a series of thinner layer. The Laplace and Fourier transforms are used to reduce the problem to a set of singular integral equations that is solved numerically. Numerical results of two collinear cracks in a functionally graded material strip are obtained to show the influence of material inhomogeneity and crack position on crack tip field intensities. 相似文献
12.
Singular stress and electric fields of a piezoelectric ceramic strip with a finite crack under longitudinal shear 总被引:11,自引:0,他引:11
Summary Following the theory of linear piezoelectricity, we consider the problem of determining the singular stress and electric fields in an orthotropic piezoelectric ceramic strip containing a Griffith crack under longitudinal shear. The crack is situated symmetrically and oriented in a direction parallel to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for piezoelectric ceramics are obtained, and the results are graphed to display the influence of the electric field. 相似文献
13.
《Engineering Analysis with Boundary Elements》2005,29(5):466-476
Using the fundamental solutions and the Somigliana identity of piezoelectric medium, the boundary integral equations are obtained for a conductive planar crack of arbitrary shape in three-dimensional transversely isotropic piezoelectric medium. The singular behaviors near the crack edge are studied by boundary integral equation approach, and the intensity factors are derived in terms of the displacement discontinuity and the electric displacement boundary value sum near the crack edge on crack faces. The boundary integral equations for two dimensional crack problems are deduced as a special case of infinite strip planar crack. Based on the analogy of the obtained boundary integral equations and those for cracks in conventional isotropic elastic material and for contact problem of half-space under the action of a rigid punch, an analysis method is proposed. As an example, the solution to conductive Griffith crack is derived. 相似文献
14.
15.
In this paper, the Fourier integral transform–singular integral equation method is presented for the problem of a periodic array of cracks in a functionally graded piezoelectric strip bonded to a different functionally graded piezoelectric material. The properties of two materials, such as elastic modulus, piezoelectric constant and dielectric constant, are assumed in exponential forms and vary along the crack direction. The crack surface condition is assumed to be electrically impermeable or permeable. The mixed boundary value problem is reduced to a singular integral equation over crack by applying the Fourier transform and the singular integral equation is solved numerically by using the Lobatto–Chebyshev integration technique. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived. The effects of the loading parameter λ, material constants and the geometry parameters on the stress intensity factor, the energy release ratio and the energy density factor are studied. 相似文献
16.
In Wang et al. (2002), the mode I crack problem has been analyzed for a functionally graded material strip with arbitrarily
distributed properties. For the completeness of the research, this paper provides an analysis method for the mode II in plane
and mode III anti-plane elastic crack problems for a functionally graded material (FGM) strip containing a crack along the
gradient direction. In the analysis, the gradient region is treated as a number of homogeneous layers stacked along the gradient
direction. The analytical models developed in this paper for the modes II and III problems, together with the model developed
in Wang et al. (2002) for the mode I crack problem complete the analysis of the mixed-mode crack problem for functionally
graded materials with a crack parallel the gradient direction. Those analytical models allow the material properties be any
continuous functions along the thickness direction of the strip. 相似文献
17.
18.
The problem of a uniformly propagating finite crack in a strip of elastic material is solved using the dynamic equations of elasticity in two-dimensions. Two specific conditions of loading on the strip with finite width are discussed. In the first case, the rigidly clamped edges are pulled apart in the opposite directions. The second case considers equal and opposite tractions applied to the crack surface. By varying the strip width to the crack length ratio, the amplitude of the dynamic stresses ahead of the running crack is determined as a function of the crack velocity. The local dynamic stresses are found to be lower than the corresponding static values for the displacement loading condition and higher for the stress loading condition. This effect becomes increasingly more important as the crack length to strip width ratio is enlarged. Numerical results for the dynamic crack opening displacement are also presented. 相似文献
19.
《International Journal of Engineering Science》2006,44(3-4):256-272
The strip dielectric breakdown (DB) model introduced by Zhang and Gao [T.Y. Zhang, C.F. Gao, Fracture behavior of piezoelectric materials, Thero. Appl. Fract. Mech. 41 (2004) 339–379] is used to study the generalized 2D problem of a conductive crack and an electrode in an infinite piezoelectric material. The energy release rate and stress intensity factors are derived based on the Stroh formalism, and then they are applied as failure criteria to predict the critical fracture loads. It is found that the DB strip may take the shielding effect on a conductive crack or electrode. For the case of an electrode, the local energy release rate and stress intensity factor become zero when DB happens ahead of the electrode tip. For the case of a mode-I conductive crack in a transversely isotropic piezoelectric solid, the results based on the DB model show that the critical stress intensity factor linearly increases as the applied electric field parallel to the poling direction increases, while it linearly decreases as the applied electric field anti-parallel to the poling direction increases. Finally, the upper and lower bounds of the actual critical fracture loads are proposed for a conductive crack in a piezoelectric material under combined mechanical–electrical loads. 相似文献
20.
This paper is concerned with the thermal fracture problem of a functionally graded orthotropic strip, where the crack is situated parallel to the free edges. All the material properties are assumed to be dependent only on the coordinate y (perpendicular to the crack surfaces). By using Fourier transform, the thermoelastic problem is reduced to those that involve a system of singular integral equations. Numerical results are presented to show the effects of the crack position and the material distribution on the thermal stress intensity factors. 相似文献