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1.
用解析方法研究了非均匀弹性材料中反平面运动裂纹问题。首先采用余弦变换求解非均匀材料的基本方程,然后根据混合边值条件建立裂纹运动的对偶积分方程,再把对偶积分方程化为第二类Fredholm积分方程。给出了数值算例,计算结果表明材料的非均匀性对动应力强度因子有较大的影响。 相似文献
2.
The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the
dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems:
one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the
scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and
stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the
second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations.
Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction
of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous
function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the
end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material
parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic
effects cannot be ignored.
This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20 相似文献
3.
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
4.
M. Rekik M. Neifar S. El-Borgi 《International Journal of Solids and Structures》2010,47(16):2043-2055
In an attempt to simulate non-uniform coating delamination, the elasto-static problem of a penny shaped axisymmetric crack embedded in a functionally graded coating bonded to a homogeneous substrate subjected to crack surface tractions is considered. The coating’s material gradient is parallel to the axisymmetric direction and is orthogonal to the crack plane. The graded coating is modeled as a non-homogeneous medium with an isotropic constitutive law. Using Hankel transform, the governing equations are converted into coupled singular integral equations, which are solved numerically to yield the crack tip stress intensity factors. The Finite Element Method was additionally used to model the crack problem. The main objective of this paper is to study the influence of the material non-homogeneity and the crack position on the stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings. 相似文献
5.
Mohamed Ben-Romdhane Sami El-Borgi Malek Charfeddine 《International Journal of Solids and Structures》2013
In this paper, we consider the elasto-static problem of an embedded crack in a graded orthotropic coating bonded to a homogeneous substrate subject to statically applied normal and tangential surface loading. The crack direction is parallel to the free surface. The coating is graded in the thickness direction and is orthogonal to the crack direction. This coating is modelled as a non-homogeneous medium with an orthotropic stress–strain law. The equivalent crack surface stresses are first obtained and substituted in the plane elasticity equations. Using integral transforms, the governing equations are converted into singular integral equations which are solved numerically to yield the displacement field as well as the crack-tip stress intensity factors. This study presents a complete theoretical formulation for the problem in the static case. A numerical predictive capability for solving the singular integral equations and computing the crack-tip stress intensity factors is proposed. Since the loading is compressive, a previously developed crack-closure algorithm is applied to avoid interpenetration of the crack faces. The main objective of the paper is to investigate the effects of the material orthotropy and non-homogeneity of the graded coating on the crack-tip stress intensity factors, with and without using the crack-closure algorithm, for the purpose of gaining better understanding on the behavior and design of graded coatings. 相似文献
6.
A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudi-nal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity fac-tor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual inte-gral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor mono-tonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases. 相似文献
7.
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
8.
9.
An internal crack located within a functionally graded material (FGM) strip bonded with two dissimilar half-planes and under an anti-plane load is considered. The crack is oriented in an arbitrary direction. The material properties of strip are assumed to vary exponentially in the thickness direction and two half-planes are assumed to be isotropic. Governing differential equations are derived and to reduce the difficulty of the problem dealing with solution of a system of singular integral equations Fourier integral transform is employed. Semi closed form solution for the stress distribution in the medium is obtained and mode III stress intensity factor (SIF), at the crack tip is calculated and its validity was verified. Finally, the effects of nonhomogeneous material parameter and crack orientation on the stress intensity factor are studied. 相似文献
10.
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
11.
The problem of scattering of horizontal polarized shear waves by the two cracks in a uniform magnetostatic field is considered.
The magnetic field is assumed to be parallel to the crack surfaces as well as perpendicular to the crack surfaces. The elastic
medium under consideration is a homogeneous, isotropic and infinitely conducting one. The solution of the problem is reduced
into a pair of triple integral equations having trigonometrical kernels. Using the finite Hilbert transform technique, solution
of the pair of triple integral equations is obtained for the low frequencies. Finally, approximate formulae are derived for
the stress intensity factors. 相似文献
12.
A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases. 相似文献
13.
14.
《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
15.
研究功能梯度压电带中裂纹对SH波的散射问题,为了便于分析,材料性质假定为指数模型,并假设裂纹面上的边界条件为电渗透型的.根据压电理论得到压电体的状态方程,利用Fourier积分变换,问题转化为对偶积分方程的求解.用Copson方法求解积分方程.求得了裂纹尖端动应力强度因子、电位移强度因子的解析表达式,最后数值结果显示了标准动应力强度因子与入射波数、材料参数、带宽、波数以及入射角之间的关系. 相似文献
16.
DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL 总被引:2,自引:0,他引:2
IntroductionInrecentyears,greatattentionshavebeenpaidtotheresearchofFunctionallyGradedMaterials(FGM).Fromtheviewpointsofappliedmechanics,FGMarenon_homogeneoussolids.Thenon_homogeneityofFGMhasagreatinfluenceontheirmechanicalbehavior,especiallywhenthecomp… 相似文献
17.
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
18.
《European Journal of Mechanics - A/Solids》2007,26(2):325-336
Dynamic stress intensity factor for a Griffith crack in functionally graded orthotropic materials under time-harmonic loading is investigated in the present paper. By using the Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors of the functionally graded orthotropic materials with a Griffith crack. 相似文献
19.
The behaviors of an interface crack between dissimilar orthotropic elastic halfplanes subjected to uniform tension was reworked by use of the Schmidt method. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, of which the unknown variables are the jumps of the displacements across the crack surfaces. Numerical examples are provided for the stress intensity factors of the cracks. Contrary to the previous solution of the interface crack, it is found that the stress singularity of the present interface crack solution is of the same nature as that for the ordinary crack in homogeneous materials. When the materials from the two half planes are the same, an exact solution can be otained. 相似文献
20.
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