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1.
This research is concerned with the fracture mechanics of a laminated composite medium, which contains a central layer sandwiched
by two outer layers. There is a periodic array of cracks in the central layer along the central axis of the medium. Fourier
transform is used to reduce the problem to the solution of a system of dual integral equations, which are solved by the singular
integral equation technique. Rigorous fracture mechanics analysis, which exactly satisfies all boundary conditions of the
problem, is conducted. Numerical solutions for the crack tip field and the stress in the medium are obtained for various values
such as crack length, crack spacing and layer thickness. Results are also given for the reduction of the equivalent Young’s
modulus of the laminate due to multiple cracking. The cases of axial extension and residual temperature change of the composite
medium are accounted for. 相似文献
2.
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
3.
B.L. Wang Y.G. Sun H.Y. Zhang 《International Journal of Solids and Structures》2008,45(14-15):4032-4048
This paper is concerned with the fracture of a fiber embedded in a matrix of finite radius. There is a periodic array of cracks in the fiber along the central axis of the medium. The paper accounts for the cases of axial extension and residual temperature change of the composite medium. Fourier and Hankel transforms are used to reduce the problem to the solution of a system of dual integral equations, which are solved by the singular integral equation technique. Rigorous fracture mechanics analysis, which exactly satisfies all boundary conditions of the problem, is conducted. Numerical solutions for the crack tip field and the stress in the fiber are obtained for various values such as crack radius, crack spacing and fiber volume fraction. 相似文献
4.
《European Journal of Mechanics - A/Solids》2006,25(5):867-875
The problem of a Griffith crack of constant length propagating at a uniform speed in a plane non-homogeneous medium under uniform load is investigated. The equilibrium equations for the non-homogeneous medium are solved by using the Fourier transforms and then the problem is reduced to the solution of dual integral equations. Solving the dual integral equations we obtain the expression for the dynamic stress intensity factor at the edge of the crack. Finally the numerical results for the stress intensity factor are obtained which are displayed graphically to show the effect of the material non-homogeneity on the stress intensity factor. 相似文献
5.
《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
6.
《International Journal of Solids and Structures》2003,40(3):573-590
The fracture problem of a penny shaped crack in a piezoelectric ceramic cylinder surrounded by an infinite elastic medium under in-plane normal mechanical and electrical loads is considered with the electric continuous boundary conditions on the crack surface. By using the potential theory and Hankel transform, a system of dual integral equations is obtained, and expressed to a Fredholm integral equation of the second kind. The mechanical and electrical field equations and all sorts of field intensity factors of mode I are obtained, and the numerical values of various field intensity factors for PZT-6B piezoelectric ceramic surrounded by several different elastic media are graphically shown for a uniform load and a ring-shaped load, respectively. And the effects of the size of the piezoelectric cylinder and the elastic material properties on various field intensity factors are obtained. 相似文献
7.
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
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.
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
10.
《European Journal of Mechanics - A/Solids》2001,20(3):457-468
The dynamic field intensity factors and energy release rates in a rectangular piezoelectric ceramic medium containing a center crack are obtained for boundary conditions of a permeable and an impermeable crack under electro-mechanical impact loading. An integral transform method is used to reduce the problem to two pairs of dual integral equations, which are then expressed as Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate are obtained to show the dependences upon the geometry and electric field. 相似文献
11.
12.
《International Journal of Solids and Structures》2007,44(2):419-435
In this paper, the behavior of a Mode-I crack in the piezoelectric/piezomagnetic materials subjected to a uniform tension loading is investigated by the generalized Almansi’s theorem. Through 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 displacement jumps are directly expanded in a series of Jacobi polynomials. Then the closed form solution of this problem can be obtained. 相似文献
13.
P. Malits 《International Journal of Solids and Structures》2009,46(16):3061-3067
The torsional problem of a finite elastic cylinder with a circumferential edge crack is studied in this paper. An efficient solution to the problem is achieved by using a new form of regularization applied to dual Dini series equations. Unlike the Srivastav approach, this regularization transforms dual equations into a Fredholm integral equation of the second kind given on the crack surface. Hence, exact asymptotic expansions of the Fredholm equation solution, the stress intensity factor and the torque are derived for the case of a shallow crack. The asymptotic expansions are certain power-logarithmic series of the normalized crack depth. Coefficients of these series are found from recurrent relations. Calculations for a shallow crack manifest that the stress intensity factor exhibits the rather weak dependence upon the cylinder length when the torque is fixed and the triple length is larger than the diameter. 相似文献
14.
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
15.
The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack. 相似文献
16.
IntroductionThediscoveryofquasicrystalaround 1 984 [1,2 ,3]issignificantbreakthroughforcondensedmatterphysicsinrecentyears.Thequasiperiodicsymmetryofsolidpresentsgreattheoreticalsignificance .Numerousquasicrystallinematerialswithstablepropertywereproduced ,thi… 相似文献
17.
In this paper the anti-plane problem for an interface crack between two dissimilar magneto-electro-elastic plates subjected
to anti-plane mechanical and in-plane magneto-electrical loads is investigated. The interface crack is assumed to be either
magneto-electrically impermeable or permeable, and the position of the interface crack is arbitrary. The finite Fourier transform
method is employed to reduce the mixed boundary-value problem to triple trigonometric series equations. The dislocation density
functions and proper replacement of the variables are introduced to reduce these series equations to a standard Cauchy singular
integral equation of the first kind. The resulting integral equation together with the corresponding single-valued condition
is approximated as a system of linear algebra equations which can be easily solved. Field intensity factors and energy release
rates are determined numerically and discussed in detail. Numerical results show the effects of crack configuration and loading
combination parameters on the fracture behaviors of crack tips according to energy release rate criterion. The study of this
problem is expected to have applications to the investigation of dynamic fracture properties of magneto-electro-elastic materials
with cracks. 相似文献
18.
In this paper, the behavior of a Griffith crack at the interface of a layer boned to a half plane subjected to a uniform tension is investigated by use of the Schmidt method under the assumptions that the effect of the crack surface overlapping very near the crack tips is negligible and also there is a sufficiently large component of mode-I loading so that the crack essentially remains open. 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 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 thickness of the material layer and the materials constants upon the stress intensity factor of the crack. As a special case in our solution, we also give the solution of the ordinary crack in homogeneous materials. Contrary to the previous solution of the interface crack problem, it is found that the stress singularities of the present interface crack solution are similar with ones for the ordinary crack in homogeneous materials. 相似文献
19.
In this paper, the behavior of an interface crack for a functionally graded strip sandwiched between two homogeneous layers
of finite thickness subjected to an uniform tension is resolved using a somewhat different approach, named the Schmidt method.
The Fourier transform technique is applied and a mixed boundary value problem is reduced to two pairs of dual integral equations
in which the unknown variables are the jumps of the displacements across the crack surface. To solve the dual integral equations,
the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite
different from those adopted in previous works. Numerical examples are provided to show the effects of the crack length, the
thickness of the material layer and the materials constants upon the stress intensity factor of the cracks. It can be obtained
that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation
method. As a special case, when the material properties are not continuous through the crack line, an approximate solution
of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near
the crack tips is negligible. Contrary to the previous solution of the interface crack, it is found that the stress singularities
of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. 相似文献
20.
IntroductionDuetotheintrinsiccouplingcharacteristicsbetweenelectricandelasticbehaviors,thatis,appliedmechanicalloadingproduceselasticdeformation ,aswellaselectricfield ,andconverselyelectricfieldcangiverisetoelasticdeformation ,piezoelectricmaterialshave… 相似文献