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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.
The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations ip which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials. 相似文献
3.
In this paper, the interaction of two parallel Mode-I limited-permeable cracks in a functionally graded piezoelectric material was investigated by using the generalized Almansi's theorem. In the analysis, the electric permittivity of the air inside the crack was considered. The problem was formulated through 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 electric permittivity of the air inside the crack and the gradient parameter 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
4.
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
5.
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
6.
Zhen-Gong Zhou Pei-Wei Zhang Guoqiang Li 《European Journal of Mechanics - A/Solids》2009,28(4):728-737
In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric material plane subjected to anti-plane shear stress loading were studied by the Schmidt method. The problem was formulated through Fourier transform into 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 were directly expanded as a series of Jacobi polynomials. Finally, the relation between the electric field and the stress field near the crack tips was obtained. The results show that the stress and the electric displacement intensity factors at the crack tips depend on the lengths and spacing of the cracks. It is also revealed that the crack shielding effect presents in piezoelectric materials. 相似文献
7.
Pei-Wei Zhang Zhen-Gong Zhou Lin-Zhi Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(10):965-979
In this paper, the behavior of three parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic material plane
subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier
transform into three pairs of dual integral equations, in which 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. Finally, the relations among the electric displacement, the magnetic flux and the stress
fields near the crack tips can be obtained. The results show that the stress, the electric displacement and the magnetic flux
intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding
effect is present in piezoelectric/piezomagnetic materials. 相似文献
8.
The dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied by Schmidt method. By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surface were expanded in a series of Jacobi polynomials. The relations among the electric filed, the magnetic flux and the stress field were obtained. From the results, it can be obtained that the singular stresses in piezoelectric/piezomagnetic materials carry the same forms as those in a general elastic material for the dynamic anti-plane shear fracture problem. The shielding effect of two parallel cracks was also discussed. 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.
Dynamic behavior of unequal parallel permeable interface multi-cracks in a piezoelectric layer bonded to two piezoelectric materials half planes 总被引:2,自引:0,他引:2
Jian-Liang Sun Zhen-Gong Zhou Biao Wang 《European Journal of Mechanics - A/Solids》2004,23(6):993-1005
This study is concerned with the treatment of the dynamic behavior of interacting cracks in a piezoelectric layer bonded to two dissimilar piezoelectric half planes subjected to harmonic anti-plane shear waves. The permeable electric boundary condition is considered. By use of the Fourier transform technique, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in two series of Jacobi polynomials. The electromechanical behavior of two pairs of unequal parallel cracks was determined. Numerical examples are provided to show the effects of the geometry of the cracks, the frequency of the incident waves and materials properties upon the dynamic stress intensity factors (DSIFs) and the electric displacement intensity factors. 相似文献
11.
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
12.
The solutions of a 3-D rectangular permeable crack and two 3-D rectangular permeable cracks in a piezoelectric material were
investigated by using the generalized Almansi’s theorem and the Schmidt method. The problem was formulated through Fourier
transform into three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the
crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded
as a series of Jacobi polynomials. Finally, the effects of the shape of the rectangular crack and the distance between two
rectangular cracks on the stress and electric displacement intensity factors in a piezoelectric material were analyzed. These
results can be used for the strength and the coupling effect evaluation of cracked piezoelectric materials. 相似文献
13.
Dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes 总被引:1,自引:1,他引:0
IntroductionDuetotheintrinsicelectro_mechanicalcouplingbehavior,piezoelectricmaterialsareveryusefulinelectronicdevices.However,mostpiezoelectricmaterialsarebrittlesuchasceramicsandcrystals.Therefore ,piezoelectricmaterialshaveatendencytodevelopcriticalcracksduringthemanufacturingandthepolingprocesses.So ,itisimportanttostudytheelectro_elasticinteractionandfracturebehaviorsofpiezoelectricmaterials.Theincreasingattentiontothestudyofcrackproblemsinpiezoelectricmaterialshasledtoalotofsignificantw… 相似文献
14.
IntroductionItiswell_knownthatpiezoelectricmaterialsproduceanelectricfieldwhendeformedandundergodeformationwhensubjectedtoanelectricfield .Thecouplingnatureofpiezoelectricmaterialshasattractedwideapplicationsinelectric_mechanicalandelectricdevices,suc… 相似文献
15.
The solutions of a 3-D rectangular limited-permeable crack or two 3-D rectangular limited-permeable cracks in piezoelectric
materials were given by using the generalized Almansi’s theorem and the Schmidt method. At the same time, the electric permittivity
of the air inside the rectangular crack was considered. The problem was formulated through Fourier transform as three pairs
of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve
the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi
polynomials. Finally, the effects of the electric permittivity of the air inside the rectangular crack,the shape of the rectangular
crack and the distance between two rectangular cracks on the stress and electric displacement intensity factors in piezoelectric
materials were analyzed. 相似文献
16.
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
17.
《European Journal of Mechanics - A/Solids》2006,25(5):793-807
In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith crack in the piezoelectric materials subjected to a uniform tension loading. The permittivity of the air in the crack is considered. By means 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 the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the crack length, the materials constants, the electric boundary conditions and the lattice parameter on the stress and the electric displacement fields near the crack tips. It can be obtained that the effects of the electric boundary conditions on the electric displacement fields are large. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips, thus allowing us to use the maximum stress as a fracture criterion. 相似文献
18.
《International Journal of Solids and Structures》2003,40(3):747-762
In this paper, the dynamic behavior of two parallel symmetric cracks in piezoelectric materials under harmonic anti-plane shear waves is investigated by use of the non-local theory for permeable crack surface conditions. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the problem to obtain the stress occurs near the crack tips. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations that the unknown variables are the jumps of the displacement along the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided. Contrary to the previous results, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the frequency of the incident wave, the distance between two cracks and the lattice parameter of the materials, respectively. Contrary to the impermeable crack surface condition solution, it is found that the dynamic electric displacement for the permeable crack surface conditions is much smaller than the results for the impermeable crack surface conditions. The results show that the dynamic field will impede or enhance crack propagation in the piezoelectric materials at different stages of the dynamic load. 相似文献
19.
In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method.The problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces.To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials.Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained.The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks.It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials. 相似文献
20.
The dynamic behavior of two parallel symmetric cracks in a piezoelectric strip under harmonic anti-plane shear waves is studied
using the Schmidt method for permeable crack surface conditions. The cracks are parallel to the edge of the strip. By means
of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations
are solved using the schmidt method. The results show that the stress and the electric displacement intensity factors depend
on the geometry of the cracks, the frequency of incident waves, the distance between cracks and the thickness of the strip.
It is also found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller
than those for the impermeable crack surface conditions.
Project supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang
Province, the National Science Foundation with the Excellent Young Investigator Award (No. 19725209) and the Scientific Research
Foundation of Harbin Institute of Technology (HIT.2000.30). 相似文献