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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
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The interaction of a general plane P wave and an elastic cylindrical inclusion of infinite length partially debonded from
its surrounding viscoelastic matrix of infinite extension is investigated. The debonded region is modeled as an arc-shaped
interface crack between inclusion and matrix with non-contacting faces. With wave functions expansion and singular integral
equation technique, the interaction problem is reduced to a set of simultaneous singular integral equations of crack dislocation
density function. By analysis of the fundamental solution of the singular integral equation, it is found that dynamic stress
field at the crack tip is oscillatory singular, which is related to the frequency of incident wave. The singular integral
equations are solved numerically, and the crack open displacement and dynamic stress intensity factor are evaluated for various
incident angles and frequencies.
The project supported by the National Natural Science Foundation of China (19872002) and Climbing Foundation of Northern Jiaotong
University 相似文献
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与两相材料界面接触的裂纹对SH波的散射 总被引:1,自引:0,他引:1
利用积分变换方法得出了两相材料中作用简谐集中力时的格林函数.根据所得的格林函数并利用Betti-Rayleigh互易定理得出了与界面接触裂纹的散射波场.裂纹的散射波场可分解为两部分,一部分为奇异的散射场,另一部分为有界的散射场.利用分解后的散射场,可得裂纹在SH波作用下的超奇异积分方程.根据裂纹散射场的奇异部分和Cauchy型奇异积分的性质得出了裂纹和界面接触点处的奇性应力指数和接触点角形域内的奇性应力.利用所得的奇性应力定义了裂纹和界面接触点处的动应力强度因子.对所得超奇异积分方程的数值求解可得裂纹端点和接解点处的应力强度因子。 相似文献
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X.-F. Li 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,72(10):745-758
Summary The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform
electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral
equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and
the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results
are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results
reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors
depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results
reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied
stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack
in a piezoelectric strip.
Received 14 August 2001; accepted for publication 24 September 2002
The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported
by the National Natural Science Foundation of China under Grant 70272043. 相似文献
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The scattering of Love waves by an interface crack between a piezoelectric layer and an elastic substrate is investigated
by using the integral transform and singular integral equation techniques. The dynamic stress intensity factors of the left
and the right crack tips are determined. It is found from numerical calculation that the dynamic response of the system depends
significantly on the crack configuration, the material combination and the propagating direction of the incident wave. It
is expected that specifying an appropriate material combination may retard the growth of the crack for a certain crack configuration.
Project supported by the National Natural Science Foundation of China (No. 19891180), the Fundamental Research Foundation
of Tsinghua University (JZ 2000.007) and the Fund of the Education Ministry of China. 相似文献
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Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack 总被引:1,自引:0,他引:1
Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a
cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and
the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip
are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular
stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since
the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and
its numerical results coincide with those in references. Thus the method proposed here is verified.
The project supported by National Natural Science Foundation of China 相似文献
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折线型裂纹对SH波的动力响应 总被引:1,自引:0,他引:1
利用Fourier积分变换方法,得出了无限平面中用裂纹位错密度函数表示的单裂纹散射场.根据无穷积分的性质,把单裂纹的散射场分解为奇异部分和有界部分.利用单裂纹的散射场建立了折线裂纹在SH波作用下的Cauchy型奇异积分方程.根据折线裂纹散射场和所得的积分方程讨论了裂纹在折点处的奇性应力及折点处的奇性应力指数.利用所得的奇性应力定义了折点处的应力强度因子.对所得Cauchy型奇积分方程的数值求解,可得裂纹端点和折点处的动应力强度因子。 相似文献
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By using the finite-part integral concepts and limit technique, the hypersingular integrodifferential equations of three-dimensional
(3D) planar interface crack were obtained; then the dominant-part analysis of 2D hypersingular integral was further used to
investigate the stress fields near the crack front theoretically, and the accurate formulae were obtained for the singular
stress fields and the complex stress intensity factors. After that, a numerical method is proposed to solve the hypersingular
integrodifferential equations of 3D planar interface crack, and the problem of elliptical planar crack is then considered
to show the application of the method. The numerical results obtained are satisfactory.
Project supported by the Foundation of Solid Mechanics Open Research Laboratory of State Education Commission at Tongji University
and the National Natural Science Foundation. 相似文献
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The transient fracture behavior of a functionally graded layered structure subjected to an in-plane impact load is investigated. The studied structure is composed of two homogeneous layers and a functionally graded interlayer with a crack perpendicular to the boundaries. The impact load is applied on the face of the crack. Fourier transform and Laplace transform methods are used to formulate the present problem in terms of a singular integral equation in Laplace transform domain. Considering variations of parameters such as the nonhomogeneity constant, the thickness ratio and the crack length, the dynamic stress intensity factors (DSIFs) in time domain are studied and some meaningful conclusions are obtained.The project supported by the National Science Foundation for Excellent Young Investigators (10325208), the National Natural Science Foundation of China (10432030) and the China Postdoctoral Science Foundation (2004036018)The English text was polished by Ron Marshall. 相似文献
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A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely
isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic
induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform,
the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were
gained by making use of Fourier transform and adopting electro-magneto impermeable boundary conditions. The closed form expression
for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations
using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around
the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic
stress intensity factor.
Contributed by SHEN Ya-peng
Foundation item: the National Natural Science Foundation of China (10132010, 50135030)
Biographies: DU Jian-ke (1970∼) 相似文献
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《International Journal of Solids and Structures》2003,40(13-14):3571-3588
The transient response of a piezoelectric strip with an eccentric crack normal to the strip boundaries under applied electromechanical impacts is considered. By using the Laplace transform, the mixed initial-boundary-value problem is reduced to triple series equations, then to a singular integral equation of the first kind by introducing an auxiliary function. The Lobatto–Chebyshev collocation technique is adopted to solve numerically the resulting singular integral equation. Dynamic field intensity factors and energy release rate are obtained for both a permeable crack and an impermeable crack. The effects of the crack position and the material properties on the dynamic stress intensity factor are examined and numerical results are presented graphically. 相似文献
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Sei Ueda 《European Journal of Mechanics - A/Solids》2003,22(6):431-942
In this study, the dynamic response of a coated piezoelectric strip containing a crack vertical to the interfaces under normal impact load is considered. Based on the superposition principle and the integral transform techniques, the solution in the Laplace transformed plane is obtained in terms of a singular integral equation. The order of stress singularity around the tip of the terminated crack is also obtained. The singular integral equation is solved by using the Gauss–Jacobi integration formula, and the numerical Laplace inversion is then carried out to obtain the resulting dynamic stress and electric displacement intensities. The effects of the material properties and the geometric parameters on the dynamic stress intensity factor and the dynamic energy density factors are shown graphically. 相似文献
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Doo-Sung Lee 《International Journal of Solids and Structures》2009,46(2):433-439
This paper deals with the problem of finding the stress distribution in the neighborhood of a peripheral edge crack in a spherical cavity. The crack is excited by a torsional standing wave.The problem is solved by using integral transforms and is reduced to the solution of a singular integral equation. The solution of this equation is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors are displayed graphically. 相似文献
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The penny-shaped cracks periodically distributed in infinite elastic body are studied. The problem is approximately simplified
to that of a single crack embedded in finite length cylinder and the stress intensity factor is obtained by solving a Fredholm
integral equation. Numerical results are given and the effects of crack interaction on the stress intensity factor are discussed.
The project suppoted by National Natural Science Foundation of China 相似文献
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Mohammad R. Torshizian Mohammad H. Kargarnovin Cyrus Nasirai 《Mechanics Research Communications》2011,38(3):164-169
In this paper, a two dimensional functionally graded material (2D-FGM) under an anti-plane load with an internal crack is considered. The crack is oriented in an arbitrary direction. The material properties are assumed to vary exponentially in two planar directions. The problem is analyzed and solved by two different methods namely Fourier integral transforms with singular integral equation technique, and then by the finite element method. The effects of crack orientation, material non-homogeneity, and other parameters on the value of stress intensity factor (SIF) are studied. Finally, the obtained results for Mode III stress intensity factor of different methods are compared. 相似文献