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1.
Pei-Wei Zhang Zhen-Gong Zhou Zeng-Tao Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(6):411-430
The basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials was studied in this
paper using the generalized Almansi’s theorem. To make the analysis tractable, it was assumed that the shear modulus varies
exponentially along the horizontal axis parallel to the crack. The problem was formulated through a Fourier transform into
two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve
the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi
polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at
the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials;
however, the magnitudes of intensity factors depend on the gradient of functionally graded piezoelectric material properties.
It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials. 相似文献
2.
Zhen-Gong Zhou Pei-Wei Zhang Lin-Zhi Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(12):861-882
The solutions of a limited-permeable crack (case I) or two collinear limited-permeable cracks (case II) in piezoelectric/piezomagnetic materials subjected to a uniform tension loading were investigated in this paper using the
generalized Almansi’s theorem. At the same time, the electric permittivity and the magnetic permeability of air in crack were
firstly considered. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations,
in which the unknown variables were jumps of displacements across crack surfaces, not the dislocation density functions or
the complex variable functions. To solve the dual integral equations, the jumps of displacements across crack surfaces were
directly expanded in a series of Jacobi polynomials to obtain the relations among electric displacement intensity factors,
magnetic flux intensity factors and stress intensity factors at crack tips. 相似文献
3.
Jun Liang 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(6):443-464
The dynamic behavior of two parallel symmetric cracks in functionally graded piezoelectric/piezomagnetic materials subjected
to harmonic antiplane shear waves is investigated using the Schmidt method. The present problem can be solved using the Fourier
transform and the technique of dual integral equations, in which the unknown variables are jumps of displacements across the
crack surfaces, not dislocation density functions. To solve the dual integral equations, the jumps of displacements across
the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the electric, magnetic
flux, and dynamic stress fields near crack tips can be obtained. Numerical examples are provided to show the effect of the
functionally graded parameter, the distance between the two parallel cracks, and the circular frequency of the incident waves
upon the stress, electric displacement, and magnetic flux intensity factors at crack tips. 相似文献
4.
Consider two bonded functionally graded piezoelectric material (FGPM) with finite height. Each material contains an arbitrary oriented crack. The material properties are assumed in exponential forms in the direction normal to the interface. The crack surface condition is assumed to be electrically impermeable or permeable. Using the Fourier transform technique, the problem can be reduced to a system of singular integral equations, which are then solved numerically by applying the Gauss-Chebyshev integration formula to obtain the stress intensity factors at the crack tips. Numerical calculations are carried out to obtain the energy density factor S and the energy release rate G. In impermeable case, the energy release rate has been shown to be negative as the electric loads are applied. The positive definite characteristic of the energy density factor makes it possible for predicting the fracture behavior of the cracked structure. The influences of the non-homogeneous parameters and crack orientation on the energy density factors at the crack tips are discussed in detail. The results show that the energy density factor at the crack tip will be increased when the crack tip is located within the softer material. 相似文献
5.
The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves 总被引:1,自引:0,他引:1
In this paper, the dynamic interaction of two parallel cracks in functionally graded materials (FGMs) is investigated by means
of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially
with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used
instead of a two-dimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier
transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables
are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements
across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is
found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress
at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing
material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such
as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident
waves and the lattice parameter of materials.
The project supported by the National Natural Science Foundation of China (90405016, 10572044) and the Specialized Research
Fund for the Doctoral Program of Higher Education (20040213034).
The English text was polished by Yunming Chen. 相似文献
6.
The fracture behavior of a cracked strip under antiplane mechanical and inplane electrical loading is studied. A functionally graded piezoelectric strip with exponential material gradation is under consideration. The mechanical and electrical loading is combined via loading coupling factor. The problem of a graded piezoelectric strip containing a screw dislocation is solved. This solution results in stress and electric displacement components with Cauchy singularity. Based on the solution achieved for the dislocation, the distributed dislocation technique (DDT) is utilized to form any geometry of multiple cracks and analyze the behavior of a cracked strip under antiplane mechanical and inplane electrical loading. This technique is capable of the analysis of a strip with a system of interacting cracks. Several examples including strips with single crack, two straight cracks and two curved cracks are presented. 相似文献
7.
Studied is the problem of a periodic array of cracks in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric material. The properties of the functionally graded piezoelectric strip, 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. Integral transform and dislocation density functions are employed to reduce the problem to the solution of a system of singular integral equations. The effects of the periodic crack spacing, 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
8.
The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading 总被引:6,自引:0,他引:6
Summary In this paper, the behavior of a crack in functionally graded piezoelectric/piezomagnetic materials subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using a Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. These equations are solved using the Schmidt method. The relations among the electric displacement, the magnetic flux and the stress field near the crack tips are obtained. Numerical examples are provided to show the effect of the functionally graded parameter on the stress intensity factors of the crack.The authors are grateful for financial support from the Natural Science Foundation of Hei Long Jiang Province (A0301), the National Natural Science Foundation of China (50232030, 10172030), the Natural Science Foundation with Excellent Young Investigators of Hei Long Jiang Province(JC04-08) and the National Science Foundation with Excellent Young Investigators (10325208). 相似文献
9.
In this paper, the basic solution of a mode-I crack in functionally graded piezoelectric materials was investigated by using
the generalized Almansi’s theorem. In the analysis, the electric permittivity of air inside the crack were considered. To
make the analysis tractable, it was assumed that the shear modulus, piezoelectric constants and dielectric constants vary
exponentially with coordinate parallel to the crack. The problem was formulated through Fourier transform into two pairs of
dual integral equations, in which the unknown variables are jumps of displacements across the crack surfaces. To solve the
dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi
polynomials. The solution of the present paper shows that the effects of the electric boundary conditions on the electric
displacement fields near the crack tips can not be ignored. Simultaneously, the solution of the present paper will revert
to a closed form one when the functionally graded parameter equals to zero. 相似文献
10.
The dynamic interaction of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips subjected to the anti-plane shear harmonic stress waves was investigated. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is jump of displacement across the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter, the circular frequency of the incident waves and the thickness of the strip upon stress, electric displacement and magnetic flux intensity factors of cracks. 相似文献
11.
X. Y. Li Z. K. Wang S. H. Huang 《International Journal of Solids and Structures》2004,41(26):310-7328
To investigate the features of Love waves in a layered functionally graded piezoelectric structure, the mathematical model is established on the basis of the elastic wave theory, and the WKB method is applied to solve the coupled electromechanical field differential equation. The solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate. The dispersion relations of Love waves are deduced for electric open and short cases on the free surface respectively. The actual piezoelectric layer–elastic substrate systems are taken into account, and some corresponding numerical examples are proposed comparatively. Thus, the effects of the gradient variation about material constants on the phase velocity, the group velocity, the coupled electromechanical factor and the cutoff frequency are discussed in detail. So the propagation behaviors of Love waves in inhomogeneous medium is revealed, and the dispersion and the anti-dispersion are analyzed. The conclusions are significant both theoretically and practically for the surface acoustic wave devices. 相似文献
12.
In this paper a moving mode-III crack in functionally graded piezoelectric materials (FGPM) is studied. The crack surfaces are assumed to be permeable. 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 set of dual integral equations, which, in turn, are 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. 相似文献
13.
In this article, we study the axisymmetric tor-sional contact problem of a half-space coated with func-tionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thick-ness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral trans-form technique and reduce the problem to a singular integral equation, and then numerically determine the unknown con-tact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress. 相似文献
14.
Yu Jiangong Wu Bin Chen Guoqiang 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(9):807-824
Based on linear three-dimensional piezoelasticity, the Legendre orthogonal polynomial series expansion approach is used for
determining the wave characteristics in hollow cylinders composed of the functionally graded piezoelectric materials (FGPM)
with open circuit. The displacement and electric potential components, expanded in a series of Legendre polynomials, are introduced
into the governing equations along with position-dependent material constants so that the solution of the wave equation is
reduced to an eigenvalue problem. Dispersion curves for FGPM and the corresponding non-piezoelectric hollow cylinders are
calculated to show the piezoelectric effect. The influence of the ratio of radius to thickness is discussed. Electric potential
and displacement distributions are used to show the piezoelectric effect on the flexural torsional mode. The influence of
the polarizing direction on the piezoelectric effect is illustrated. For the radial and axial polarization, the piezoelectric
effect reacts mostly on the longitudinal mode. For circumferential polarization, the piezoelectric effect reacts mostly on
the torsional mode. In the FGPM hollow cylinder, piezoelectricity can weaken the guided wave dispersion. 相似文献
15.
Summary A finite crack propagating at constant speed in a functionally graded piezoelectric strip (FGPS) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPS vary exponentially across the thickness of the strip, and that the bimaterial strip is under combined anti-plane mechanical shear and in-plane electrical loads. The analysis is conducted for the electrically unified crack boundary condition, which includes both the traditional permeable and the impermeable ones. By using the Fourier transform, the problem is reduced to the solution of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and the crack sliding displacement are presented to show the influences of the crack propagation speed, electric loads, FGPS gradation, crack length, electromechanical coupling coefficient, properties of the bonded homogeneous piezoelectric strip and crack location. 相似文献
16.
The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks. 相似文献
17.
B. L. Wang 《Mechanics Research Communications》2003,30(2):151
This paper considers the mode III crack problem in functionally graded piezoelectric materials. The mechanical and the electrical properties of the medium are considered for a class of functional forms for which the equilibrium equations have an analytical solution. The problem is solved by means of singular integral equation technique. Both a single crack and a series of collinear cracks are investigated. The results are plotted to show the effect of the material inhomogeneity on the stress and the electric displacement intensity factors. 相似文献
18.
Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes 总被引:3,自引:0,他引:3
Summary In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through
a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular
integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution
and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of
the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of
applied electric impact.
Received 4 December 2001; accepted for publication 9 July 2002
This work is supported by the National Natural Science Foundation of China through Grant No. 10132010. 相似文献
19.
This paper studies the mode III crack problem of two bonded functionally graded piezoelectric half planes which contain a
crack respectively. These two cracks are located normal to the interface. All the material properties are assumed to vary
along the direction of the crack line. A system of singular integral equations for electrically impermeable and permeable
cracks is derived and solved numerically by using the Gauss–Chebyshev integration formula. The influence of the nonhomogeneous
parameters and the dependence of the crack interactions on the stress and electric displacement intensity factors are investigated. 相似文献
20.
Jian Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,75(2-3):138-152
The static and dynamic anti-plane problem for a functionally graded coating–substrate structure containing a periodic array
of parallel cracks, which are perpendicular to the boundary, is considered. Integral-transform techniques are employed to
reduce the problem to the solution of an integral equation with hypersingular kernels. Numerical results are presented to
show the influence of geometry, material properties and material gradient parameter on the fracture behavior. 相似文献