弹性波与单侧界面裂纹相互作用问题的边界元法

借助边界元法设计了一种迭代修正方法来求解单侧界面裂纹模型与弹性波的相互作用问题,作为对算法的检验,用这种方法我们具体地分析了平面简谐弹性波对一个单侧界面裂纹的入射,给出了裂纹面的接触形态及应力场.     

薄膜涂层材料中币形界面裂纹的弹性波散射

研究了薄膜涂层材料中币形界面裂纹的弹性波散射问题,建立了含有币形界面裂纹的覆层半空间模型,采用Hankel积分变换,将裂纹对弹性波散射的问题转化为求解矩阵形式的奇异积分方程。结合渐近分析和围道积分技术得到积分方程的解,进一步推导了散射波的应力场和位移场,以及动应力强度因子的理论计算公式。在数值算例中,分析了不同材料组合和裂纹尺寸情况下动应力强度因子与入射波频率的关系,并给出了裂纹张开位移的结果。为薄膜涂层材料的动态破坏分析提供了一定的理论基础。     

黏弹性界面断裂分析的增量“加料”有限元法

提出了一种适用于黏弹性界面裂纹问题的增量“加料” 有限元方法. 利用弹性界面裂纹尖端位移场的解答,通过对应原理和拉普拉斯逆变换近似方法,得到了黏弹性界面裂纹的尖端位移场. 用该位移场构造了黏弹性界面裂纹“加料” 单元和过渡单元位移模式,推导了增量“加料” 有限元方程,求解有限元方程可获得应力强度因子和应变能释放率等断裂参量. 建立了典型黏弹性界面裂纹平面问题“加料” 有限元模型,计算结果表明,对于弹性/黏弹性界面裂纹和黏弹性/黏弹性界面裂纹,该方法都能得到相当精确地断裂参量,并能很好地反映蠕变和松弛特性,可推广应用于黏弹性界面断裂问题的计算分析.      

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的散射

本文研究一类粘着型界面裂纹的弹性波散射问题．文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组．采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组．最后本文给出裂纹尖端粘着区的大小和界面应力的数值结果．     

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的…

本文研究一类粘着型界面裂纹的弹性波散射问题。文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程。采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组。最后本文给出裂纹尖端站着区的大小和界面应力的数值结果。     

热释电材料问题的通解与界面裂纹

该文讨论了热释电材料中的热弹性问题的一般解，进而求解了共线界面裂纹问题．利用Ｓｔｒｏｈ方法，把热释电材料的热弹性界面裂纹问题化为一向量形式的Ｈｉｌｂｅｒｔ问题，求出这一Ｈｉｌｂｅｒｔ问题的通解，进而求得了热释电材料热弹性界面裂纹的闭合解，得到了温度、热流、位移、电势、应力和电位移的全场解，得到了裂纹张开位移及电势差的精确表达式．在此基础上，还求得了均匀热释电体中单个热弹性裂纹裂尖场，单个界面裂纹裂尖场以及点热源与界面裂纹的作用．此外，该文还对界面裂纹顶点附近的端部场作了渐近分析．     

各向异性介质的弹性波散射问题的边界元方法

本文引用加权残数法建立了各向异性介质内含任意形式异质夹杂时的散射问题的边界积分方程式,导出了相应的辐射条件,计算了内含圆柱体,椭圆柱体、界面裂纹情形下对SH 波的散射位移场、应力场以及散射横截面.数值结果表明本方法用于解答各向异性介质的弹性波散射问题具有良好的精度和应用前景.     

SH波对浅埋弹性圆柱及裂纹的散射与地震动

采用Green函数、复变函数和多极坐标等方法研究含圆柱形弹性夹杂的弹性半空间中任意位置、任意方位有限长度裂纹对SH波的散射与地震动. 构造了含圆柱形弹性夹杂的半空间对SH波的散射波,并求解了适合本问题Green函数,即含有圆柱形弹性夹杂的半空间内(表面)任意一点承受时间谐和的出平面线源载荷作用时位移函数的基本解答. 利用裂纹``切割'方法在任意位置构造任意方位的裂纹,可以得到基体中圆柱形弹性夹杂和裂纹同时存在条件下的位移场与应力场. 通过数值算例,讨论各种参数对夹杂上方地表位移的影响.      

SH波入射时半空间界面裂纹与圆形衬砌的相互作用

利用复变函数和Green函数法研究了双相介质半空间界面裂纹及界面附近圆形衬砌对SH 波的 散射与动应力集中问题。首先,采用映像思想构造满足自由边界条件的散射波表达式,进而求解所需的 Green函数;其次,采用裂纹切割技术构造裂纹,并根据连续性条件建立了求解该问题的无穷代数方程组; 最后,给出了不同入射波数时界面裂纹与衬砌的相互作用。结果表明,裂纹的存在显著放大了衬砌界面的动 应力集中。     

界面断裂力学简介与展望

界面断裂力学是目前国际力学界的前沿研究课题.本文对这门新兴分支学科的发展背景,近期进展及未来展望作了简要介绍.主要分析了各向同性及各向异性弹性材料间的界面裂纹;界面裂纹的力学模型;界面裂纹的弹塑性场及界面裂纹的断裂观念.讨论了界面断裂力学未来热门课题。     

Contact zone assessment for a fast growing interface crack in an anisotropic bimaterial

Summary A plane strain problem for a crack with a frictionless contact zone at the leading crack tip expanding stationary along the interface of two anisotropic half-spaces with a subsonic speed under the action of various loadings is considered. The cases of finite and infinite-length interface cracks under the action of a moving concentrated loading at its faces are considered. A finite-length crack for a uniform mixed-mode loading at infinity is considered as well. The associated combined Dirichlet-Riemann boundary value problems are formulated and solved exactly for all above-mentioned cases. The expressions for stresses and the derivatives of the displacement jumps at the interface are presented in a closed analytical form for an arbitrary contact zone length. Transcendental equations are obtained for the determination of the real contact zone length, and the associated closed form asymptotic formulas are found for small values of this parameter. It is found that independently of the types of the crack and loading, an increase of the crack tip speed leads to an increase of the real contact zone length and the correspondent stress intensity factor. The latter increase significantly for an interface crack tip speed approaching the Ragleigh wave speed.     

Dynamically induced fracture

Expressions are presented for the stresses generated in the vicinity of a crack tip when a plane transient tension-stress wave, which is incident under an arbitrary angle, is diffracted by the crack. The effect of ductility effects on the combined Mode I and Mode II fractures is examined by assuming that yielding is restricted to a thin strip in the plane of the crack. Within this zone of yielding the normal stress in a certain defined direction is set equal to a yield stress of the material. It is shown that for a step-stress wave the leading edge of the zone of yielding initially moves at a constant speed, which is computed. The time for rupture at the trailing edge of the zone of yielding is also determined.     

Interaction of general plane P wave and cylindrical inclusion partially debonded from its viscoelastic matrix

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     

考虑应力松驰复合型裂纹顶端塑性区分析

Ｓｈｉｈ［１］应用奇异单元，获得了不考虑应力松驰小范围屈服条件下复合型裂纹尖端塑性区形状。Ｚ．Ｚ．Ｚｕ等［２］采用Ｒｉｃｅ［５］给出的裂纹尖端应力关系式，利用有限元分析获得了不考虑应力松驰下复合型裂纹尖端塑性区，本文基于静力学中内力与外力平衡条件，用线弹性的全场解代替局部解，给出了考虑应力松驰下复合型裂纹尖端塑性区边界方程，获得了考虑应力松驰下的任意方向的塑性区尺寸及塑性区形状     

The propagation and arrest of an edge crack in anti-plane shear

The motion of an edge crack extending non-uniformly in an elastic half-space under conditions of anti-plane shear is investigated, taking the first reflected stress wave into account. An expression for the stress intensity factor at the crack tip is obtained, and an energy-balance crack propagation criterion is used to find the equation of motion of the tip. On solving this equation numerically, it is found that crack arrest occurs before the second reflected wave reaches the tip.     

Boundary Integral Analysis of the Symmetric Dynamic Problem for an Infinite Bimaterial Solid with an Embedded Crack

The symmetric frequency domain problem for two ideally bonded elastic half-spaces with a perpendicular plane crack is considered. It is reduced to the boundary integral equation (BIE) with integration over the limited crack region. The contact conditions on the bimaterial interface are satisfied identically in the initial stage of obtaining the equation. After boundary element solution of the equation, the stress concentration in the vicinity of a penny-shaped crack under time-harmonic loading of constant amplitude is studied. The mode I stress intensity factors as functions of angular coordinate of a crack front point and wave number for various relations between the material parameters are computed. The crack depth relative to the bimaterial interface is determined, when the effect of the material dissimilarity on the crack can be neglected.     

An analytically-numerical approach for the analysis of an interface crack with a contact zone in a piezoelectric bimaterial compound

An interface crack with an artificial contact zone at the right-hand side crack tip between two dissimilar finite-sized piezoelectric materials is considered under remote mixed-mode loading. To find the singular electromechanical field at the crack tip, an asymptotic solution is derived in connection with the conventional finite element method. For mechanical loads, the stress intensity factors at the singular points are obtained. As a particular case of this solution, the contact zone model (in Comninou’s sense) is derived. A simple transcendental equation and an asymptotic formula for the determination of the real contact zone length are derived. The dependencies of the contact zone lengths on external load coefficients are illustrated in graphical form. For a particular case of a short crack with respect to the dimensions of the bimaterial compound, the numerical results are compared to the exact analytical solutions, obtained for a piezoelectric bimaterial plane with an interface crack.     

Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory

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Edge dislocations generated from blunt crack tip in viscoelastic material under residual stress

The 2D model of edge dislocations generation from blunt crack tip in viscoelastic material under residual stress has been proposed, the solution of stress field and displacement field are solved by using complex potential method, conformal mapping and Laplace inverse transformation. The explicit expressions of stress intensity factor, strain energy density and crack tip slide displacement are obtained in closed form. The principle of compatibility of blunt crack to edge dislocations has been used to evaluate the dislocations number and dimensionless ratio α. Numerical results present that the number of edge dislocations first increases and then decreases with increase of zone size ratio of the dislocations zone and none-dislocations zone, but it can be reduced by higher configurations ratio of semi-minor axis and semi-major axis. In addition, it increases with time and tends to be a constant quickly. The normalized multiplier α first increases and then decreases with increase of zone size ratio. In addition, it decreases with time and the increase of crack configurations ratio. Both normalized micro-volume SED and normalized dislocation-volume SED decrease with increase of distance from crack tip and tend to vanish. But the dislocation-volume SED decreases more quickly than micro-volume SED does, because of its stronger singularity. Moreover, they increase with time and decrease of configurations ratio.