Some advances in study of crack identification problems

In the present paper, the crack identification problems are investigated. This kind of problems belong to the scope of inverse problems and are usually ill-posed on their solutions. The paper includes two parts: (1) Based on the dynamic BIEM and the optimization method and using the measured dynamic information on outer boundary, the identification of crack in a finite domain is investigated and a method for choosing the high sensitive frequency region is proposed successfully to improve the precision. (2) Based on 3-D static BIEM and hypersingular integral equation theory, the penny crack identification in a finite body is reduced to an optimization problem. The investigation gives us some initial understanding on the 3-D inverse problems.

郭永怀文集

Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading

In this paper the problem of a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered. The shear modulus and the mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial cylinders. This mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) is also obtained by a numerical Laplace inversion technique. The DSIF is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation. The influences of the crack location, the FGM interlayer thickness and the relative magnitudes of the adjoining material properties are examined. It is found among others that, by increasing the FGM gradient, the DSIF can be greatly reduced.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

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.

Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces art assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density,function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically, and using a numerical Laplace inversion technique, the dynamic stress intensity factors art obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading .2. The crack going through the bimaterial interface into the fiber

The axisymmetric problem of an elastic fiber perfectly bonded to a nonhomogeneous elastic matrix which contains an annular crack going through the interface into the fiber under axially symmetric shear stress is considered. The nature of the stress singularity is studied. It is shown that at the irregular point on the interface, whether the shear modulus is continuous or discontinuous the stresses are bounded. The problem is formulated in terms of a singular integral equation and can be solved by a regular method. The stress intensity factors and crack surface displacement are given.

3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

Magnetohydrodynamics equilibrium of a self-confined elliptic plasma ball

A variational principle is applied to the problem of magnetohydrodynamics (MHD) equilibrium of a self-contained elliptical plasma ball, such as elliptical ball lightning. The principle is appropriate for an approximate solution of partial differential equations with arbitrary boundary shape. The method reduces the partial differential equation to a series of ordinary differential equations and is especially valuable for treating boundaries with nonlinear deformations. The calculations conclude that the pressure distribution and the poloidal current are more uniform in an oblate self-confined plasma ball than that of an elongated plasma ball. The ellipticity of the plasma ball is obviously restricted by its internal pressure, magnetic field, and ambient pressure. Qualitative evidence is presented for the absence of sighting of elongated ball lightning.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.

A contact crack problem in an infinite plate

The problem of an infinite plate with crack of length 2a loaded by the remote tensile stress P and a pair of concentrated forces Q is discussed. The value of the force Q for the initial contact of crack face is investigated and the contact length elevated, while the Q force increases. The problem is solved assuming that the stress intensity factor vanishes at the end point of the contact portion. By the Fredholm integral equation for the multiple cracks, the reduction of stress intensity factor due to Q is found. (C) 1999 Elsevier Science Ltd. All rights reserved.

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.

Gain saturation effects of a flowing chemical oxygen-iodine laser

A new oxygen-iodine medium gain model is developed to include pumping and deactivation of the upper laser levels of the iodine atoms, hyperfine and translation relaxation, as well as the flowing effect. The rate equations for gain of a supersonic flowing cw oxygen-iodine laser (COIL) are described when the medium is stimulated by a single-mode field. The general solution of the self-consistency integral equation is obtained. The result shows that the saturation behaviour in low pressure of the COIL differs from both the inhomogeneous and homogeneous broadening, and exhibits an 'anomalous' saturation phenomenon.

在激波波面中氧分子的非平衡离解

对强激波作用下双原子分子振动与离解耦合的非平衡离解过程进行了理论计算.本工作的特点是将计算起点建立在分子基本参数上,采用主方程理论处理振动与离解的耦合,振动跃迁几率用SSH理论计算,在离解限附近考虑多量子数跃迁并计及原子复合的影响.对O2-Ar体系,计算给出了在正激波后O2分子振动能级分布、振动弛豫时间、离解孕育时间、离解产物浓度、离解速率系数等物理量随时间的演化.计算结果分别与Camac和Wray的实验相符.计算显示,在激波作用的后期,有准稳态的振动能级布居分布.计算结果显示,Park模型低估了非平衡离解速率系数,Hansen模型则高估了非平衡离解速率系数.

粘弹性材料界面裂纹的瞬态响应和散射研究

本文研究粘弹性材料界面裂纹对冲击载荷的瞬态响应和对广义平面波的稳态散射。相对于已有广泛研究的弹性材料裂纹瞬态响应和稳态散射问题，本文的研究有三个突出特点：1）粘弹性材料；2）界面裂纹；3）广义平面波入射。粘弹性材料界面裂纹对冲击载荷的瞬态响应和对广义平面波的散射尚无开展研究，本文在弹性材料相应问题的研究基础上，首先开展了这一问题的研究。对于冲击载荷下粘弹性界面裂纹的瞬态响应问题，利用Laplace积分变换方法，将粘弹性材料卷积型本构方程转化为Laplace变换域内的代数型本构方程，从而可以在Laplace变换域内象处理弹性材料的冲击响应一样，将相应的混合边值问题归结为关于裂纹张开位移COD的对偶积分方程，并进一步引入裂纹位错密度函数CDD （Crack Dislocation Density），将对偶积分方程化成关于CDD的奇异积分方程（SIE）。用数值方法求解奇异积分方程得到变换域内的动应力强度因子数值解，最后利用Laplace积分逆变换数值方法得到时间域内的动应力强度因子的时间响应。理论分析考虑了两种裂纹模型，即Griffith界面裂纹和柱面圆弧型界面裂纹。考虑的载荷包括反平面冲击载荷和平面冲击载荷。对于平面冲击载荷，通过对裂尖应力场的奇性分析，首次发现粘弹性界面裂纹裂尖动应力场奇性指数不是常数0.5，而是与震荡指数一样依赖材料参数。针对反平面冲击载荷给出了一个算例，计算了裂尖动应力强度因子的时间响应，并与弹性材料的结果作了比较，发现粘弹性效应的影响不仅使过冲击峰值降低，而且使峰值点后移。粘性效应较大时，过冲击现象甚至不出现。关于粘弹性界面裂纹对广东省义平面波的散射问题，首先研究广义平面波在无裂纹存在的理想界面的反射和透射，再研究由于界面裂纹的存在而产生的附加散射场。利用粘弹性材料的复模量理论，可将粘弹性材料的卷积型相构方程化成频率域内的代数型本构方程。类似弹性平面波的处理，在频率域内将问题最终归结为关于裂纹位错密度CDD的奇异积分方程。数值方法求解奇异积分方程即可得到频率域内的散射场，并进而得到裂尖动应力强度因子和远场位移型函数和散射截面。理论分析考虑了两种裂纹模型：Griffith界面裂纹和柱面圆弧型界面裂纹。研究的入射波有广义的SH波和P波。对于广义平面P波入射的情况，通过对裂尖应力场的奇性分析，同样发现粘弹性界面裂纹裂尖动应力场奇性指数不地常数0.5，而是与震荡指数一样依赖于材料参数。对柱面裂纹散射远场的渐近分析，发现远场位移和应力除含有几何衰减因子外，都含有一个材料衰减速因子。散射截面由于材料衰减因子的存在也成为依赖散射半径的量。为了使散射截面仍有意义，文中提出一种修正办法。对Griffith界面裂纹，给出了一个广义平面SH波入射的算例；对柱面界面裂纹，给出了一个广义平面P波入射的算例。计算了不同入射角和入射频率下裂纹的张开位移和动就应力强度因子，并分析了其依赖关系。求解奇异积分方程的数值方法和Laplace积分逆变换数值方法是本文的基本数值方法。本文对这两种方法作了大量的调研和系统的研究。在对比分析的基础上，对现有的各种方法从原理，适用范围，计数效率，优势及特点进行了归纳总结。并尝试了奇异积分方程的最新数值方法--分片连续函数法，证实了其适用性和方便性．