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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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研究蠕变加载条件下线黏弹性材料接触界面端附近的奇异应力场问题.考虑接触界面的摩擦,假设界面端的滑移方向不改变,相对滑移量微小,且其与位移同量级,由此线性化局部边界条件,根据对应原理得到Laplace变换域中的界面端应力场,导出时域中奇异应力场的卷积积分表达式.对卷积积分核函数进行数值反演,考虑接触材料的两类组合,一是持久模量具有量级上的差异,另一是持久模量接近相同.算例结果证实核函数可以用准弹性法求得的解析式较准确地近似.在此基础上,利用积分中值定理,并引入各应力分量的修正系数,得到黏弹性奇异应力场的简化式.结合核函数的数值反演结果分析修正系数表达式的取值范围,得到如下结论,若两相接触材料的持久模量相差很大,可以采用准弹性解的解析式较准确地描述界面端的奇异应力场;一般情况下,应力场不存在统一的奇异值和应力强度系数,当采用类似于准弹性解的表达式近似给出黏弹性应力场时,可以估计此近似描述的误差限.文中最后采用有限元分析黏弹性板端部嵌入部位的应力场,算例包括了黏弹性板与弹性金属支承、黏弹性板与黏弹性垫层所形成的滑移接触界面端,利用黏弹性有限元的数值结果验证理论分析所得结论的有效性. 相似文献
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M.H. Kargarnovin C. NasiraiM.R. Torshizian 《Theoretical and Applied Fracture Mechanics》2011,56(1):42-48
The fracture problem of a crack in a functionally graded strip with its properties varying in a linear form along the strip thickness under an anti-plane load is considered. The embedded anti-plane crack is located in the middle of strip half way through the thickness. The third mode stress intensity factor is derived using two different methods. In the first method, by employing Fourier integral transforms, the governing equation is converted to a singular integral equation, which is subsequently solved numerically by the collocation method based on Chebyshev polynomials. Then, the problem is solved by means of finite element method in which quadrilateral 8-node singular elements around each crack tip are used. After inspecting the validity of the solution technique, effects of crack geometry and non-homogeneous material parameter on the stress intensity, energy release and energy density are studied and the results of analytical and FEM solutions are compared. 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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功能梯度材料的黏弹性断裂问题 总被引:2,自引:2,他引:0
功能梯度材料(FGM)是一种不同于传统复合材料的新型工程复合材料 [1], 国内外关于FGM的断裂力学方面的研究发展非常迅速. 关于FGM静态裂纹问题,学者们研究了不同类型裂纹尖端场的应力强度因子 [2-5], 探讨了有限长裂纹在不用载荷作用下的传播等问题. 而关于动态裂纹问题,也已经取得很大成就 [6-9]. FGM一个很重要的应用是高温结构材料,在强大的热环境中,很多材料都呈现出黏弹性. 因此,研究FGM的黏弹性断裂力学非常具有实际价值.对此,众多研究 [10-14]提出不同的分析模型,并在不同受载条件,通过理论计算,分析了黏弹性裂纹尖端场的力学 行为.本文考查了功能梯度材料板条中界面裂纹垂直于梯度方向时的黏弹性断裂问题,首先利用有限元法求解线弹性功能梯度材料板条的裂纹尖端场,然后根据黏弹性的对应性原理,求解出黏弹性功能梯度材料板条裂纹问题的应力场强度因子. 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
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Discussed is the fracture behavior of a cracked smart actuator on a substrate under thermal load. The actuator is made of piezoelectric material with functionally graded material (FGM) properties. Integral transform method is used to reduce the problem to the solution of a set of singular integral equations and is solved numerically. This paper is completed by including graphical plots of the thermal flow, stress and electric displacement intensity factors around the crack for different crack positions and material gradients. Directions of crack initiation are also predicted by using the energy density criterion. 相似文献
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针对组分材料体积含量任意分布的黏弹性功能梯度材料裂纹问题建立有限元分析途径. 通过Laplace变换,将黏弹性问题转化到象空间中求解,基于反映材料非均匀的梯度单元和裂纹尖端奇异特性的奇异单元计算象空间中的位移、应力和应变场,应用虚拟裂纹闭合方法得到应变能释放率,分别由应力和应变能释放率确定应力强度因子. 给出这些断裂参量在物理空间和象空间之间的对应关系,由数值逆变换求出其在物理空间的相应值. 文中分析两端均匀受拉的黏弹性边裂纹板条,首先针对松弛模量表示为空间函数和时间函数乘积的特殊梯度材料进行计算,结合对应原理验证方法的有效性. 然后分析组分材料体积含量具有任意梯度分布的情形,由Mori-Tanaka方法预测象空间中的等效松弛模量. 计算结果表明,蠕变加载条件下,应变能释放率随时间增加,其增大程度与黏弹性组分材料体积含量相关. 由于梯度材料的非均匀黏弹性性质,产生应力重新分布,导致应力强度因子随时间变化,其变化范围与组分材料的体积含量分布方式有关. 相似文献
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Modelling of crack opening and surface sliding in an orthotropic viscoelastic material is made by introducing two coefficients: one for the surface displacement and surface friction. The material possesses orthotropy in two dimensions and viscoelastic property consisting of a Kelvin element in series with a spring. The method of Laplace transform is applied to obtain a closed form solution to the problem. Explicit expressions of Mode I and II stress intensity factors are computed together with crack surface opening. Trade-off between the Mode I and II stress intensity factors depends on the nature of material orthotropy. 相似文献
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研究两种材料界面上的刚性线与其它任意位置处直线裂纹弹性干涉的反平面问题。基于界面上刚性线与任意位置处螺型位错干涉的基本解,运用连续位错密度模型法将问题转化为奇异积分方程。用半开型积分法求解奇异积分方程,得到位错密度函数的离散值,计算裂纹尖端处的应力强度因子。算例说明该方法可用于工程实际问题。 相似文献
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Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load 总被引:3,自引:0,他引:3
Summary The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular
crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The
problem is formulated as a system of integral equations with r
−3-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product
of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite
body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results
and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along
the crack front is presented for various crack shapes and different Poisson's ratio.
Received 5 March 2002; accepted for publication 2 July 2002 相似文献
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V. G. Popov 《Mechanics of Solids》2013,48(2):194-202
The paper presents a solution of the problem of determining the stress state in an elastic isotropic half-space with a crack intersecting its boundary under harmonic longitudinal shear vibrations. The vibrations are excited by a regular action of a harmonic shear load on the crack shores. The solution method is based on the use of the discontinuous solution of the Helmholtz equation, which allows one to reduce the original problem to a singular integro-differential equation for the unknown jump of the displacement on the crack surface. The solution of this equation is complicated by the existence of a fixed singularity of its kernel. Therefore, one of the main results is the development of an efficient approximate method for solving such equations, which takes into account the true asymptotics of the unknown function. The latter allows one to obtain a high-precision approximate formula for calculating the stress intensity factor. 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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This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters. 相似文献
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根据线弹性断裂力学理论,V形切口处的应力场具有奇异性,应力值趋于无穷大,峰值应力不能直接用于评定疲劳强度。通过引入了奇异强度因子“as”,单边缺口应力分布和缺口应力强度因子(N-SIF)的半解析公式被推导。考虑张开角和几何尺寸等因素,基于奇异强度因子拟合得到了切口应力评估的简易公式,可用于切口应力场和N-SIF值的快速评估。将简易公式评估结果与有限元结果以及传统文献结果进行对比分析,结果表明,本文简易公式可以准确地预报拉伸载荷下单边V型切口角平分线上的应力场和N-SIF值,实现了切口试样应力场的快速评估。 相似文献
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《ournal of non Newtonian Fluid Mechanics》1987,24(1):97-119
We report on the use of a numerical method to solve the (inertia-less) squeeze-film flow problem for a viscoelastic fluid. The method is based on a Boundary Element formulation and relies on a time-marching scheme. The viscoelastic fluid is modelled by a constitutive law that allows for a shear stress overshoot mechanism in a suddenly started shear flow. The results show convincingly that the load enhancement sometimes observed experimentally is due to stress overshoot. A simple explanation for the enhancement is suggested; the stress overshoot appears quickly and takes a long time to die away, so that steady-state viscous behaviour is not very relevant. 相似文献