Dynamic stress intensity factor of a crack perpendicular to the weak-discontinuous interface in a nonhomogeneous coating–substrate structure

A mechanical model was established for the antiplane dynamic fracture problem of a functionally graded coating–substrate structure with a coating crack perpendicular to the weak-discontinuous interface. The problem was reduced to a Cauchy singular integral equation by the methods of Laplace and Fourier integral transforms. Erdogan’s collocation method and the Laplace numerical inversion proposed by Miller and Guy were used to calculate the dynamic stress intensity factors. Three conclusions were drawn through parametric studies: (a) unlike the conclusion drawn for an interfacial crack, reducing the weak discontinuity of the interface will not necessarily decrease the dynamic stress intensity factor (DSIF) of the coating crack perpendicular to the interface; (b) increasing the stiffness of the substrate when that of the coating is fixed, or decreasing the stiffness of coating when that of the substrate is fixed, will be beneficial for the reduction of the DSIF of a coating crack perpendicular to the interface; and (c) the free surface has a greater influence on the DSIF than the interface does, and the effect of the interface on the DSIF is greater than that of the material stiffness in the crack-tip region.     

Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface

The mechanical model was established for the anti-plane dynamic fracture problem for two collinear cracks on the two sides of and perpendicular to a weak-discontinuous interface between two materials with smoothly graded elastic properties, as opposed to a sharp interface with discontinuously changing elastic properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. The integral equations were solved by Erdogan's collocation method and the dynamic stress intensity factors in the time domain were obtained through Laplace numerical inversion proposed by Miller and Guy. The influences of geometrical and physical parameters on the dynamic stress intensity factors were illustrated and discussed, based on which some conclusions were drawn: (a) to increase the thickness of the FGM strip on either side of the interface will be beneficial to reducing the DSIF of a crack perpendicular to a bi-FGM interface and embedded at the center of one of the FGM strips; (b) To increase the rigidity of the FGM strip where the crack is located will increase the DSIF. However, when the material in one side of the interface is more rigid, the DSIF of the interface-perpendicular embedded crack in the other side will be reduced; (c) To decrease the weak-discontinuity of a bi-FGM interface will not necessarily reduce the stress intensity factor of a crack perpendicular to it, which is different from the case of interfacial crack; (d) For two collinear cracks with equal half-length, when the distance between the two inner tips is less than about three times of the half-length, the interaction of them is intensified, however, when the distance is greater than this the interaction becomes weak.     

Dynamic stress intensity factor of the weak/micro-discontinuous interface crack of a FGM coating

The concepts and classification are brought forth for the strong-discontinuous interface, the weak-discontinuous interface, the micro-discontinuous interface and the all-continuous interface. The mechanical model is established for the dynamic fracture problem of the weak-discontinuous interface between a FGM coating and a FGM substrate. The Cauchy singular integral equation for the crack is derived by integral transform, and the allocation method is used to get the numerical solution. Analysis of the numerical solution indicates that the weak discontinuity is an important factor affecting the SIFs of the interfacial crack. To reduce the weak discontinuity is beneficial to the decrease of the SIFs. Contrast between the solution of the weak-discontinuous interface and that of the micro-discontinuous one shows that the micro-discontinuity is a kind of connection relation of mechanical property better than the weak discontinuity for the coating–substrate structure. To make the interface be micro-discontinuous is helpful to enhance the capacity of the functionally gradient coating–substrate interface to resist dynamic fracture. The first rank micro-discontinuity is enough to reduce the SIFs notably, however, the higher-rank micro-discontinuous terms, which is equal to or higher than the second rank, have less effect on the SIFs. In addition, the thickness of the coating and the substrate and the applied peel stress are also important factors affecting the dynamic SIFs.     

功能梯度夹层多个环形界面裂纹扭转冲击

研究位于功能梯度层和外部均匀材料之间多个环形界面裂纹的扭转冲击问题,功能梯度材料 (FGM)粘结在两种不同的弹性材料之间,功能梯度层和外部材料之间环形界面裂纹的数目是任意的．引进积分变换和位错密度函数将问题化为求解Laplace域里标准的Cauchy奇异积分方程,进而化为求解代数方程;应用Laplace数值反演技术,计算时域里的动应力强度因子(DSIF)．考查了结构几何尺度和材料特性对裂尖动态断裂特性的影响．数值结果表明,DSIF存在一个主峰,到达主峰后,在其相应的静态值附近波动并最终趋于稳定;增加FGM的梯度能减小DSIF的峰值．     

黏弹性体界面裂纹的冲击响应

研究两半无限大黏弹性体界面Griffith裂纹在反平面剪切突出载荷下,裂纹尖端动应力强度因子的时间响应,首先,运用积分变换方法将黏弹性混合黑社会问题化成变换域上的对偶积分方程,通过引入裂纹位错密度函数进一步化成Cauchy型奇异积分方程,运用分片连续函数法数值求解奇异积分方程,得到变换域内的动应力强度因子,再用Laplace积分变换数值反演方法,将变换域的解反演到时间域内,最终求得动应力强度因子的时间响应,并对黏弹性参数的影响进行分析。     

Moving interfacial crack between piezoelectric ceramic and elastic layers

An analysis is performed for the problem of a finite Griffith crack moving with constant velocity along the interface of a two-layered strip composed of a piezoelectric ceramic and an elastic layers. The combined out-of-plane mechanical and in-plane electrical loads are applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic stress intensity factor(DSIF) is determined, and numerical results show that DSIF depends on the crack length, the ratio of stiffness and thickness, and the magnitude and direction of electrical loads as well as the crack speed. In case that the crack moves along the interface of piezoelectric and elastic half planes, DSIF is independent of the crack speed.     

Dynamic fracture analysis of adhesive bonded material under normal loading

Dynamic fracture behavior of a Griffith crack along the interface of an adhesive bonded material under normal loading is studied. The singular integral equations are obtained by employing integral transformation and introducing dislocation density functions. By adopting Gauss-Jacobi integration formula, the problem is reduced to the solution of algebraic equations, and by collocation dots method. their solutions can be obtained Based on the parametric discussions presented in the paper, the following conclusions can be drawn： （1） Mode I dynamic stress intensity factor （DSIF） increases with increasing initial crack length and decreasing visco-elastic layer thickness, revealing distinct size effect; （2） The influence of the visco-elastic adhesive relaxation time on the DSIF should not be ignored.     

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。     

Fracture analysis on a piezoelectric sensor with a viscoelastic interface

Fracture analysis is performed on a layered piezoelectric sensor possessing a Kelvin-type viscoelastic interface. An electrically permeable anti-plane crack is situated in the piezoelectric layer and perpendicular to the interface. The crack problem is solved by the methods of integral transform and Cauchy singular integral equation. The variations of the dynamic stress intensity factor (DSIF) vs. physical and geometrical parameters are investigated. At the beginning of creep and relaxation, larger viscosity coefficient always induces smaller DSIF. With time elapsing, the effect of viscosity coefficient becomes weaker and weaker. When time approaches infinity, the viscous effect disappears, and the DSIF converges to a value corresponding to the case of an elastic interface. The effect of the viscoelastic interface on the fracture behavior of the piezoelectric layer also depends on the substrate thickness. To some extent, thicker substrate may intensify the effect of the interface.     

与两相材料界面接触的裂纹对SH波的散射

利用积分变换方法得出了两相材料中作用简谐集中力时的格林函数．根据所得的格林函数并利用Betti-Rayleigh互易定理得出了与界面接触裂纹的散射波场．裂纹的散射波场可分解为两部分，一部分为奇异的散射场，另一部分为有界的散射场．利用分解后的散射场，可得裂纹在SH波作用下的超奇异积分方程．根据裂纹散射场的奇异部分和Cauchy型奇异积分的性质得出了裂纹和界面接触点处的奇性应力指数和接触点角形域内的奇性应力．利用所得的奇性应力定义了裂纹和界面接触点处的动应力强度因子．对所得超奇异积分方程的数值求解可得裂纹端点和接解点处的应力强度因子。     

双材料中平片裂纹问题的超奇异积分方程解法

利用三维断裂力学的超奇异积分方程方法,对双材料空间中重直于界面的平片裂纹Ⅰ型问题进行了研究。首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位罗间断为未知函数的超奇异积分方程,并为其建立了数值法。在此基础上,讨论了用裂纹面位移问题计算应力强度因子的方法。最后用此计算了几个典型的Ⅰ型下片裂纹问题的应力强度因子,其数值结果令人满意。     

一种基于直接计算高阶奇异积分的断裂力学双边界积分方程分析法

相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.      

功能梯度双材料弱/微间断界面的冲击断裂分析

提出强间断、弱间断、微间断和全连续界面的概念与分类,建立功能梯度弹性双材料弱间断 界面冲击断裂问题的力学模型,采用积分变换法推导问题的Cauchy奇异积分方程,并用配 点法求得数值解. 分析表明,弱/微间断性对于FGMs界面裂纹应力强度因子有着重要影响, 而且微间断性是优于弱间断性的一种界面力学性能连接关系. 以FGMs界面某一侧 的力学性能函数在界面处的Taylor展开式的低阶项作为界面另一侧的力学性能函数,便可 以使FGMs界面成为``微间断'界面. 界面的一阶微间断对应力强度因子的减小作用较为明 显,而高阶(二阶及以上)微间断对应力强度因子的影响较小. 减小界面的弱间断程度或使 FGMs界面具备``微间断性',都将利于提高功能梯度双材料界面抗冲击断裂能力,在一定 程度上达到界面增韧的目的.     

The scattering of harmonic elastic anti-plane shear waves by a finite crack in infinitely long strip using the non-local theory

In this paper, the scattering of harmonic anti-plane shear waves by a finite crack in infinitely long strip is studied using the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual integral equations is solved using the Schmidt method instead of the first or the second integral equation method. A one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress occurring at the crack tips. Contraty to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the width of the strip and the lattice parameter. Supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang Province and the National Foundation for Excellent Young Investigators.     

Shrink fit of an elastic layer having a cylindrical cavity

Summary This paper deals with the problem of determining the stress distribution in an elastic layer with a cylindrical cavity when the mixed boundary conditions are prescribed on the curved surface of the cylinder. The problem is simplified to that of finding the solution of dual integral equations arising from the mixed boundary conditions. These dual integral equations are subsequently reduced to a singular integral equation. The solution of this integral equation is obtained numerically, and the quantities of physical interest are calculated.     

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     

Stress Analysis for an Elastic Semispace with Surface and Graded Layer Coatings under Induced Torsion

In this paper, the axisymmetric torsional problem of a coating structure consisting of a surface coating, a functionally graded layer and a substrate under a rigid cylindrical punch is investigated. The coating and substrate are homogeneous materials with distinct physical properties while the intermediate layer is inhomogeneous with its shear modulus changing exponentially along the thickness direction. The Hankel integral transform technique is employed to reduce the torsional problem to a singular integral equation with a Cauchy kernel. The circumferential shear stress and displacement fields in the coating structure are calculated by solving the integral equation numerically. The results show that the stiffness ratio has significant effect on the distribution of the circumferential stress and displacement at the interface.     

SHEAR WAVE SCATTERING FROM A PARTIALLY DEBONDED PIEZOELECTRIC CYLINDRICAL INCLUSION

I. INTRODUCTION Owing to the intrinsic coupling characteristics between electric and elastic behaviors, piezoelectricmaterials have been used widely in technology such as transducers, actuators, sensors, etc. Studieson electroelastic problems of a piezo…     

功能梯度材料裂纹尖端动态应力场

研究受反平面剪切作用的功能梯度材料动态裂纹问题,通过积分变换-对偶积分方程方法推出了裂纹尖端动态应力场,时间域内的动态应力强度因子由Laplace数值反演获得,研究结果表明功能梯度材料的梯度越大,相应的裂纹问题的动态应力强度因子值越低。     

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

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.