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本文结合无限域上单根夹杂和单根裂纹的基本解,将裂纹与夹杂相互作用的问题归结为解一组柯西型奇异积分的积分方程组,使问题得到解决。本文还使用夹杂两侧的未知界面应力差,进一步推导了夹杂两侧的界面应力,并做了数值计算。有关这方面的计算可以作为研究与设计纤维与基体的联结强度的工程参考。 相似文献
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IntroductionUptonow ,thetechnicalliteratureonseparatecracks,voids,inclusionsandtheinteractionsbetweencracksandinclusionshavebeenquiteextensive.However,thecontactproblemsofcrack_inclusiondonotseemtobeaswidelystudied .Thispapercanberegardedasthefurtherrese… 相似文献
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IntroductionWhilewestudythestrengthandthecrackofpractisingcomponents,thematerialdefectionshouldbeconsidered .IntheopinionsofCrackMechanics,thematerialdefectioncanbereducedtoplanarcracksandinclusions.Besides,theproblemofshort_fibercompositematerialsuchas… 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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In this paper interfacial edge crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to those of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge interface crack in a bonded strip are newly obtained and compared with those of a single-edge interface crack for different forms of combination of material. It is found that the stress intensity factors should be compared in the three different zones of relative crack lengths. Different from the case of a cracked homogeneous strip, the results for the double edge interface cracks are found to possibly be bigger than those for a single edge interface crack under the same relative crack length. 相似文献
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The problem of a mode-II crack close to and perpendicular to an imperfect interface of two bonded dissimilar materials is investigated.The imperfect interface is modelled by a linear spring with the vanishing thickness.The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel.The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation.Several special cases of the mode-II crack problem with an imperfect interface are studied in detail.The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically.The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface. 相似文献
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The weakly singular integral equation used to solve the problem of the curved crack crossing the boundary of the antiplane
circular inclusion is presented. Using the principal part analysis method of the Cauchy type integral equation, the singular
stress index at the intersection and the singular stress of angular regions near the intersection are obtained. By using the
singular stress obtained, the stress intensity factor at the intersection is, defined. After the numerical solution of the
integral equation, the stress intensity factors at the end points of the crack and intersection are obtainable.
The research is supported by National Natural Science Foundation of China (No. 59879012) and is the project of Chinese Foundation
of State Education Commission (No. 98024832). 相似文献
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涉及两相正交各向异性体界面干涉问题的研究,多裂纹问题被分解为只含单裂纹的子问题,利用位错理论和裂面应力自由条件,列出一组可数值求解位错密度函数的奇异积分方程,从耐 注得应力强度因子。 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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对材料界面超高速自相似动态分层的反平面问题进行了解析分析。分层模拟为界面裂纹由零长度自相似扩展,扩展速度为蹭音速或超音速。首先考虑运动集中载荷作用下界面动态分层的情况,利用界面裂纹自相似扩展的运动位错模型将问题归结为奇异积分方程,并求得解析解,分析了裂纹尖端的应力奇性,获得了动应力强度因子。最后,利用叠加原理给出了x^n型载荷作用下界面动态分层的解。 相似文献
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采用材料力学的直杆和梁的变形假定,对平面线夹杂问题提出了一种能同时考虑夹杂两侧法向应力和剪应力间断的新的力学模型,然后通过集中力作用的Kelvin解答,求得了单夹杂问题的基本解。文中还导出了夹杂两侧的界面应力公式。最后对夹杂端点的应力强度因子及界面应力作了计算,结果令人满意 相似文献
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Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips 总被引:1,自引:1,他引:1
M. S. Matbuly 《Acta Mechanica Sinica》2008,24(4):433-438
The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor. 相似文献
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Crack problems for isotropic/orthotropic two-layered strips have been investigated. A system of two singular integral equations
can be derived by using Fourier integral transformation and boundary conditions of crack problems. After stress singularities
at crack tips or other special points are determined for internal and edge cracks, and for cracks terminating at and going
through the interface, the system of singular integral equations is solved numerically by Gauss-Jacobi or Gauss-Chebyshev
integration formulas for stress intensity factors at the tips and other singular points of cracks. Finally, possible crack
growth behavior for cracks approaching and going through the interface is discussed. 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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W.-J. Feng R.-J. Hao J.-X. Liu S.-M. Duan 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,74(10):649-663
Summary In this paper, the scattering of SH waves by a magneto-electro-elastic cylindrical inclusion partially debonded from its surrounding magneto-electro-elastic material is investigated by using the wavefunction expansion method and a singular integral equation technique. The debonding regions are modeled as multiple arc-shaped interface cracks with non-contacting faces. The magneto-electric impermeable boundary conditions are adopted. By expressing the scattered fields as wavefunction expansions with unknown coefficients, the mixed boundary-value problem is firstly reduced to a set of simultaneous dual-series equations. Then, dislocation density functions are introduced as unknowns to transform these dual-series equations to Cauchy singular integral equations of the first type,which can be numerically solved easily. The solution is valid for arbitrary number and size of the arc-shaped interface cracks. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond. The effects of incident direction, crack configuration and various material parameters on the dynamic stress intensity factors are discussed. The solution of this problem is expected to have applications in the investigation of dynamic fracture properties of magneto-electro-elastic materials with cracks.The work was supported by the National Natural Science Fund of China (Project No. 19772029) and the Research Fund for Doctors of Hebei Province, China (Project No. B2001213). 相似文献
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根据界面上应力和位移的连续条件,得到了单向拉伸状态下,含有椭圆夹杂的无限大双材料组合板的复势解。进一步通过求解Hilbert问题,得到了含有夹杂和半无限界面裂纹的无限大板的应力场,并由此给出了裂尖的应力强度因子K。计算了夹杂的形状、夹杂的位置、夹杂的材料选取以及上、下半平面材料与夹杂材料的不同组合对裂尖应力强度的影响。计算结果表明夹杂到裂尖的距离和夹杂材料的性质对K影响较大,对于不同材料组合,该影响有较大差异。夹杂距裂尖较近时,会对K产生明显屏蔽作用,随着夹杂远离裂尖,对K的影响也逐渐减小。另外,软夹杂对K有屏蔽作用,硬夹杂对K有反屏蔽作用,而夹杂形状对K几乎没有影响。 相似文献