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. This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20     

流体饱和弹性半空间裂隙对平面P_I波的衍射

采用间接边界元法,求解了饱和半空间裂隙对平面PI波的二维衍射问题。基于单层位势理论,将边界离散并直接在边界单元上施加虚拟荷载(水平作用力、竖向作用力和流量源的叠加)以构造散射波场,并由边界条件确定虚拟荷载密度,总波场由自由波场和散射波场共同组成。通过参数分析研究了入射波频率、入射倾角、埋深、孔隙率、边界渗透条件等因素对饱和半空间中裂隙对平面PI波衍射的影响规律。结果表明:裂隙随埋深增大,地表位移谱振荡加剧,峰值有所降低;随着入射频率增加,孔隙率影响逐渐增大;垂直入射时,水平位移的放大区域主要分布在裂隙两端,斜入射时,主要集中在裂隙正上方地表附近;透水和不透水两种情况下的地表位移幅值和相位差别较小,但干土情况与饱和情况下的位移幅值相差较大。     

Scattering of guided waves by circumferential cracks in composite cylinders

A somewhat generalized numerical procedure is used in this paper to study the problem of wave scattering by circumferential cracks in composite pipes. The study is motivated by the need to develop a model for the quantitative, ultrasonic non-destructive evaluation of cracks in pipes. For this purpose, a stiffness-based Rayleigh–Ritz type approach is employed first to obtain the approximate wave numbers and wave modes. Using the wave function expansions of the incident and scattered fields in the axial direction and decomposing the problem into separate symmetric and anti-symmetric problems, a three-dimensional wave scattering problem is reduced to two, independent two-dimensional problems over the circular cross-section. Both these problems can be reduced further to quasi-one-dimensions by discretizing the cross-section into finite elements and using a transfer matrix approach in the circumferential direction. This simplification greatly reduces the computational time. A comparison of the results for an isotropic pipe demonstrates the reliability and accuracy of the modified numerical procedure. Numerical results for the reflection and transmission coefficients of different incident wave modes are also presented for a 2-ply composite pipe with a crack. The crack may have an arbitrary circumferential length and radial depth. Simple extrapolations from one wave to another wave, separately incident on a crack, are demonstrated to be impossible due to different mode conversions by the crack.     

General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients

General electromechanical reciprocity relations are applied to the calculation of elastic wave scattering coefficients observed at the electrical terminals of the transducer used in performing an experiment. Both direct backscatter and two transducer geometries are considered. The general formulation is applicable to anisotropic media, but is applied as an example to Rayleigh wave scattering from a surface-breaking crack on an isotropic substrate. This method of analysis is applicable to both the Born and quasistatic approximations and is valid for bulk, Rayleigh and plate wave transducers using any single transduction mechanism.     

Surface acoustic wave measurements of small fatigue cracks initiated from a surface cavity

A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavity with two corner cracks is presented. It is applied to determine the depth of the small fatigue cracks initiated from a pit-type surface flaw. The general scattering formalism based on the elastodynamic reciprocity principle is employed. The effect of the cylindrical cavity on the surface wave reflection from cracks is considered using an approximate stress intensity factor for the corner cracks. In situ surface acoustic wave measurements have been performed during fatigue tests for an Al 2024-T3 sample. The surface wave signal was acquired continuously at different cyclic load levels. The model is verified by comparing calculated reflection signals and spectra with those from experiments. The depths of fully and partially open cracks are determined from the predicted and the measured surface wave reflections. The surface wave reflection is observed to be sensitive to crack closure.     

SH波在正交各向异性功能梯度无限长条中心裂缝处的散射

研究了正交各向异性功能梯度材料无限长条中心裂缝对SH波的散射问题,为方便起见,材料两个方向的剪切模量和密度假定为指数模型.通过Fourier积分变换,将问题转化为对偶积分方程的求解.然后,用Cop-son方法求解对偶积分方程,定义了标准动应力强度因子,通过数值算例,讨论了在SH波作用下,裂缝尖端的标准动应力强度因子与入射波的频率、材料参数之间的关系.     

有限散射信号下二维缺陷形状识别的罚函数方法

研究在有限照射角度和频带宽度下二维缺陷的形状识别问题。首先,通过引进介质参数扰动函数,建立介质参数扰动函数和弹性波散射场之间的非线性关系,并将所关心的缺陷的形状识别问题转化为关于扰动函数的反演;然后,利用变分技术和优化方法求解,为了弥补散射数据的不足,在总的目标函数中,采用附加度量函数作为罚函数;最后,对后场散射远场测量时有限照射角度和频带宽度下几种典型缺陷进行了模拟识别,表明了;表明了罚函数法的有效性。     

SH波在压电材料条中垂直界面裂纹处的散射

研究了SH波在压电材料条中裂纹处的散射.压电材料条两侧涂有相同梯度参数的两个半无限大功能梯度材料,裂纹垂直于界面.通过Fourier变换,利用边界条件把问题转化为柯西核奇异积分方程,然后利用Chebyshev多项式对奇异积分方程进行数值求解.通过数值计算,分析讨论了压电条的几何参数和SH波频率对标准动应力强度因子的影响.     

Sensitivity of a supersonic boundary layer to acoustic disturbances

The results obtained by the authors in [1] are extended to the case of arbitrary angles of incidence of the external wave. This is not a trivial generalization, since the acoustic scattering undergoes a qualitative change. It is possible to distinguish two excitation channels: the first is connected with the diffraction of the acoustic wave by the spatial inhomogeneity resulting from the displacing action of the boundary layer, and the second with the presence of concentrated acoustic field sources associated with the scattering of the wave at the leading edge. The latter makes the principal contribution to the initial amplitude of the unstable modes when the angles of incidence of the sound are substantially different from zero. At low angles of incidence there is a singularity which can be revealed by introducing narrow intervals in the neighborhood of the limiting values of the wave numbers, where the two excitation channels are approximately equivalent. It is possible to obtain composite expressions for the initial amplitudes of the unstable modes uniformly valid for all angles of incidence of the acoustic wave.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–47, January–February, 1992.     

Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack

Nonlinear scattering of ultrasonic waves by closed cracks subject to contact acoustic nonlinearity (CAN) is determined using a 2D Finite Element (FE) coupled with an analytical approach. The FE model, which includes unilateral contact with Coulomb friction to account for contact between crack faces, provides the near-field solution for the interaction between in-plane elastic waves and a crack of different orientations. The numerical solution is then analytically extended in the far-field based on a frequency domain near-to-far field transformation technique, yielding directivity patterns for all linear and nonlinear components of the scattered waves. The proposed method is demonstrated by application to two nonlinear acoustic problems in the case of tone-burst excitations: first, the scattering of higher harmonics resulting from the interaction with a closed crack of various orientations, and second, the scattering of the longitudinal wave resulting from the nonlinear interaction between two shear waves and a closed crack. The analysis of the directivity patterns enables us to identify the characteristics of the nonlinear scattering from a closed crack, which provides essential understanding in order to optimize and apply nonlinear acoustic NDT methods.     

Interaction between rigid-disc inclusion and penny-shaped crack under elastic time-harmonic wave incidence

Influence of a rigid-disc massive inclusion on a neighboring penny-shaped crack induced by the time-harmonic wave propagation in an infinite elastic matrix is investigated by the numerical solution of associated 3D elastodynamic problem. No restrictions on the mutual orientation of interacting objects and direction of wave incidence are assumed. The inclusion is perfectly bonded with a matrix and supposes the translations and rotations, the crack faces are load-free. Frequency-domain problem is reduced to a system of boundary integral equations (BIEs) relative to the interfacial stress jumps (ISJs) on the inclusion and the crack opening displacements (CODs). The subtraction technique in conjunction with mapping technique, under taking into account the structure of solution at the fronts of inclusion and crack, is applied for regularization of BIEs obtained. A discrete analogue of equations is constructed by using the collocation scheme. Numerical calculations are carried out for the grazing incidence of a plane P-wave on the crack, where the interacting inclusion is coplanar and perpendicular to the crack, and has the same radius. The shielding and amplification effects of inclusion are assessed by the analysis of mode-I stress intensity factor (SIF) in the crack vicinity depending on the wave number, incident wave direction, position of the crack front point, inclusion mass, crack-inclusion orientation and distance.     

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

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｌａｓｔｆｏｕｒｄｅｃａｄｅｓｈａｖｅｗｉｔｎｅｓｓｅｄｔｈｅｉｎａｕｇｕｒａｔｉｏｎｏｆａｎｏｖｅｌｔｈｅｏｒｙｏｆｍａｔｅｒｉａｌｂｏｄｉｅｓ,ｎａｍｅｄｔｈｅｎｏｎ＿ｌｏｃａｌｍｅｃｈａｎｉｃｓ.ＴｈｉｓｗａｓｄｏｎｅｐｒｉｍａｒｉｌｙｄｕｅｔｏｔｈｅｅｆｆｏｒｔｓｏｆＥｄｅｌｅｎ[1],Ｅｒｉｎｇｅｎ[2 ],ＧｒｅｅｎａｎｄＲｉｖｌｉｎ[3].Ａｃｃｏｒｄｉｎｇｔｏｔｈｅｎｏｎ＿ｌｏｃａｌｔｈｅｏｒｙ ,ｔｈｅｓｔｒｅｓｓａｔａｐｏｉｎｔＸｉｎａｂｏｄｙｄｅｐｅｎｄｓｎｏ…     

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。     

孔边裂纹对SH波的散射及其动应力强度因子

采用Ｇｒｅｅｎ函数法研究任意有限长度的孔边裂纹对ＳＨ波的散射和裂纹尖端场动应力强度因子的求解．取含有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解作为Ｇｒｅｅｎ函数,采用裂纹“切割”方法并根据连接条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．最后给出了孔边裂纹动应力强度因子的算例和结果,并讨论了圆孔的存在对动应力强度因子的影响     

Lamb wave scattering by a symmetric pair of surface-breaking cracks in a plate

The scattering problem of a Lamb wave incident on a symmetric pair of surface-breaking transverse cracks in a plate is considered. The Lamb wave is assumed to be obliquely incident on the crack plane. Since the cracks are part-through, the scattered field will contain reflected as well as transmitted waves. The energy of the incoming wave is partitioned into reflected and transmitted wave modes. Energy coefficients of the reflected and transmitted waves are calculated as a function of incident frequency and crack depth. The incidence angle of the incoming wave is also treated as a parameter. Both the reflected and transmitted wave fields are considered as linear superpositions of all real and complex wave modes in the plate. Decomposition of modes is achieved with the help of an orthogonality condition based on the principle of reciprocal work. Continuity of displacement and stress fields is imposed at the crack plane. Energy coefficients for reflection and transmission are obtained from the mode amplitudes. Energy coefficients are shown to be a strong function of incident frequency and crack depth. Experiments are conducted with a PZT transducer network interacting with a symmetric pair of machined cracks in an aluminum plate. Trends predicted by the analysis are reflected in the experimental results.     

Wave scattering from an interface crack in multilayered piezoelectric plate

This paper focuses on the theoretical basis for the study of wave scattering from an interface crack in multilayered piezoelectric media. The materials are taken to be anisotropic with arbitrary symmetry. Based on the Fourier transform technique together with the aid of the stiffness matrix approach, the boundary value problem of wave scattering is reduced to solving a system of Cauchy-type singular equations. The intensity factors and crack opening displacements are defined in terms of the solutions of the corresponding integral equations for any incident frequencies and incident angles. Numerical results are presented. The effects of incident frequencies and crack location on both the major and coupling intensity factors are illustrated. The influence of the piezoelectricity is also shown.     

Elastic wave scattering from a penny-shaped interface crack in coated materials

This paper is concerned with the elastic wave scattering induced by a penny-shaped interface crack in coated materials. Using the integral transform, the problem of wave scattering is reduced to a set of singular integral equations in matrix form. The singular integral equations are solved by the asymptotic analysis and contour integral technique, and the expressions for the stress and displacement as well as the dynamic stress intensity factors (SIFs) are obtained. Using numerical analysis, this approach is verified by the finite element method (FEM), and the numerical results agree well with the theoretical results. For various crack sizes and material combinations, the relations between the SIFs and the incident frequency are analyzed, and the amplitudes of the crack opening displacements (CODs) are plotted versus incident wavenumber. The investigation provides a theoretical basis for the dynamic failure analysis and nondestructive evaluation of coated materials.     

平面波对有部分脱胶衬砌的圆形孔洞的散射

将波函数展开法与奇异积分方程技术相结合研究了平面波对有部分脱胶衬砌的圆形孔洞的散射。将脱离区看作弧形裂纹并忽略裂纹表面的相互作用。将衬砌和基体中的波场展开成Fou-rier-Bessel级数,利用混合边界条件得到一组对偶级数方程组并进一步转化成Hilbert奇异积分方程。数值求解给出了脱离区大小和衬砌厚度对动应力强度因子(DSIF)和散射截面(SCS)的影响。结果显示由于脱胶,动应力强度因子和散射截面呈现明显的低频共振特性。     

Scattering of a longitudinal wave by a circular crack in a fluid-saturated porous medium

Physical properties of many natural and man-made materials can be modelled using the concept of poroelasticity. Some porous materials, in addition to the network of pores, contain larger inhomogeneities such as inclusions, cavities, fractures or cracks. A common method of detecting such inhomogeneities is based on the use of elastic wave scattering. We consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot’s equations of dynamic poroelasticity. The problem is formulated in cylindrical co-ordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave induced fluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has it’s maximum value when they are of the same order.