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1.
《International Journal of Solids and Structures》2006,43(5):887-898
In this paper, the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. The traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near the crack tips. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials. The magnitude of the finite stress field depends on the crack length, the distance between two cracks, the parameter describing the functionally graded materials and the lattice parameter of the materials. 相似文献
2.
A non-local theory of elasticity is applied to obtain the dynamic interaction between two collinear cracks in the piezoelectric materials plane under anti-plane shear waves for the permeable crack surface boundary conditions. Unlike the classical elasticity solution, a lattice parameter enters into the problem that make the stresses and the electric displacements finite at the crack tip. A one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and electric displacement near the crack tips. By means of the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations in which the unknown variable is the jump of the displacement across the crack surface. The solutions are obtained by means of the Schmidt method. Crack bifurcation is predicted using the strain energy density criterion. Minimum values of the strain energy density functions are assumed to coincide with the possible locations of fracture initiation. Bifurcation angles of ±5° and ±175° are found. The result of possible crack bifurcation was not expected before hand. 相似文献
3.
Zhou Zhengong Wang Biao Sun Yuguo 《Acta Mechanica Solida Sinica》2003,16(1):52-60
The dynamic behavior ofa Griffith permeable crack under harmonic anti-plane shearwaves in the piezoelectric materials is investigated by use of the non-local theory.To overcome themathematical difficulties,a one-dimensional non-local kernel is used instead of a two-dimensionalone for the anti-plane dynamic problem to obtain the stress and the electric displacement near thecrack tips.By means of Fourier transform,the problem can be solved with a pair of dual integralequations that the unknown variable is the jump of the displacement across the crack surfaces.These equations are solved with the Schmidt method and numerical examples are provided.Con-trary to the previous results,it is found that no stress and electric displacement singularities arepresent at the crack tip.The finite hoop stress and the electric displacement depend on the cracklength,the lattice parameter of the materials and the circle frequency of the incident waves.Thisenables us to employ the maximum stress hypothesis to deal with fracture problems in a naturalway. 相似文献
4.
In this paper, the dynamic interaction between two collinear cracks in a piezoelectric material plate under anti-plane shear
waves is investigated by using the non-local theory for impermeable crack surface conditions. By using the Fourier transform,
the problem can be solved with the help of two pairs of triple integral equations. These equations are solved using the Schmidt
method. This method is more reasonable and more appropriate. Unlike the classical elasticity solution, it is found that no
stress and electric displacement singularity is present at the crack tip. The non-local dynamic elastic solutions yield a
finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis.
The project supported by the Natural Science Foundation of Heilongjiang Province and the National Natural Science Foundation
of China(10172030, 50232030) 相似文献
5.
In this paper, the scattering of harmonic anti-plane shear waves by a finite crack in infinitely long strip is studied using
the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual
integral equations is solved using the Schmidt method instead of the first or the second integral equation method. A one-dimensional
non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress occurring
at the crack tips. Contraty to the classical elasticity solution, it is found that no stress singularity is present at the
crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture
criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length,
the width of the strip and the lattice parameter.
Supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang
Province and the National Foundation for Excellent Young Investigators. 相似文献
6.
In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material strip subjected to the harmonic anti-plane shear waves is investigated by use of the non-local theory for impermeable crack surface conditions. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near at the crack tip. 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. Contrary to the classical solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the thickness of the strip, the circular frequency of incident wave and the lattice parameter. 相似文献
7.
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
8.
《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
9.
《European Journal of Mechanics - A/Solids》2005,24(2):253-262
In this paper, the dynamic behavior of two collinear symmetric interface cracks between two dissimilar magneto-electro-elastic material half planes under the harmonic anti-plane shear waves loading is investigated by Schmidt method. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. To solve the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. Numerical solutions of the stress intensity factor, the electric displacement intensity factor and the magnetic flux intensity factor are given. The relations among the electric filed, the magnetic flux field and the stress field are obtained. 相似文献
10.
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
11.
《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
12.
Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory 总被引:1,自引:1,他引:0
IntroductionThelastfourdecadeshavewitnessedtheinaugurationofanoveltheoryofmaterialbodies,namedthenon_localmechanics.ThiswasdoneprimarilyduetotheeffortsofEdelen[1],Eringen[2 ],GreenandRivlin[3].Accordingtothenon_localtheory ,thestressatapointXinabodydependsno… 相似文献
13.
On anti-plane shear behavior of a Griffith permeable crack in piezoelectric materials by use of the non-local theory 总被引:3,自引:0,他引:3
In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith crack in the piezoelectric
materials under anti-plane shear loading for permeable crack surface conditions. By means of the Fourier transform the problem
can be solved with the help of a pair of dual integral equations with the unknown variable being the jump of the displacement
across the crack surfaces. These equations are solved by the Schmidt method. Numerical examples are provided. Unlike the classical
elasticity solutions, it is found that no stress and electric displacement singularity is present at the crack tip. The non-local
elastic solutions yield a finite hoop stress at 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 and the lattice parameter of the materials,
respectively.
The project supported by the National Natural Science Foundation of China (50232030 and 10172030) 相似文献
14.
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
15.
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
16.
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
17.
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
18.
《应用数学和力学(英文版)》2017,(2)
The dynamic behavior of a rectangular crack in a three-dimensional(3D)orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional(2D) Fourier transform is applied, and the mixedboundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves,and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite. 相似文献
19.
IntroductionCompositematerialconsistingofapiezoelectricphaseandapiezomagneticphasehasdrawnsignificantinterestinrecentyears,duetotherapiddevelopmentinadaptivematerialsystems .Itshowsaremarkablylargemagnetoelectriccoefficient,thecouplingcoefficientbetweenst… 相似文献
20.
SCATTERING OF HARMONIC ANTI-PLANE SHEAR STRESS WAVES BY A CRACK IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS 总被引:1,自引:0,他引:1
Liang Jun 《Acta Mechanica Solida Sinica》2007,20(1):75-86
In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials 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 the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack. 相似文献