1.

TRANSIENT RESPONSE OF COPLANAR INTERFACIAL CRACKS BETWEEN TWO DISSIMILAR PIEZOELECTRIC STRIPS UNDER ANTIPLANE MECHANICAL AND INPLANE ELECTRICAL IMPACTS





RayK.L.Su FengWenjie LiuJinxi ZouZhenzhu《Acta Mechanica Solida Sinica》,2003年第16卷第4期


The dynamic response of multiple coplanar interface cracks between two dissimilar piezoelectric strips subjected to mechanical and electrical impacts is investigated. Solutions to two kinds of electric boundary conditions on crack surfaces, i.e. electric impermeable and electric permeable, are obtained. Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations,which can be solved numerically. The effects of electrical load, geometry criterion of piezoelectric strips, relative location of cracks and material properties on the dynamic energy release rate are examined.

2.

Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips 被引次数：1





M. S. Matbuly《Acta Mechanica Sinica》,2008年第24卷第4期


The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bistrip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using GaussChebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.

3.

STRESS INTENSITY FACTOR OF AN ANTIPLANE CRACK PARALLEL TO THE WEAK/MICRODISCONTINUOUS INTERFACE IN A BIFGM COMPOSITE





YongDong Li Wei Tan Kang Yong Lee《Acta Mechanica Solida Sinica》,2008年第21卷第1期


The problem considered is a mode Ⅲ crack lying parallel to the interface of an exponentialtype functional graded material （FGM） strip bonded to a lineartype FGM substrate with infinite thickness. By applying the Fourier integral transform, the problem was reduced as a Cauchy singular integral equation with an unknown dislocation density function. The collocation method based on Chebyshev polynomials proposed by Erdogan and Gupta was used to solve the singular integral equation numerically. With the numerical solution, the effects of the geometrical and physical parameters on the stress intensity factor （SIF） were analyzed and the following conclusions were drawn： （a） The region affected by the interface or free surface varies with the material rigidity, and higher material rigidity will lead to bigger affected region. （b） The SIF of the crack in the affected region and parallel to the microdiscontinuous interface is lower than those of the weak discontinuous cases. Reducing the weakdiscontinuity of the interface will be beneficial to decrease the SIF of the interfaceparallel crack in the region affected by the interface. （c） The effect of the free surface on SIF is more remarkable than that of the interface, and the latter is still more notable than that of the material rigidity. When the effects of the interface and free surface are fixed, increase of the material rigidity will enhance the value of SIF.

4.

FRACTURE ANALYSIS OF AN ANNULAR CRACK IN A PIEZOELECTRIC LAYER





Yansong Li Wei Wang《Acta Mechanica Solida Sinica》,2015年第1期


A flat annular crack in a piezoelectric layer subjected to electroelastic loadings is investigated under electrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. With the aid of GaussChebyshev integration technique, the integral equations are further reduced to a system of algebraic equations. The field intensity factor and energy release rate are determined. Numerical results reveal the effects of electric loadings and crack configuration on crack propagation and growth. The results seem useful for design of the piezoelectric structures and devices of high performance.

5.

ON THE MATHEMATICAL PROBLEMS OF COMPOSITE MATERIALS WITH A DOUBLY PERIODIC SET OF CRACKS 被引次数：1





李星《应用数学和力学(英文版)》,1993年第14卷第12期


In this paper,the mathematical problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated,and the interface are arbitrary smooth closed contours.At first,we establish mathematical models by using Muskhelisvili complex variable methods,change the primitive problems into searching complex stress functions which satisfy four boundary value problems and construct forms of the solution,then,under some general restrictions it is reduced to normal type singular integral equation,the unique solvability is proved mathematically

6.

PERIODICAL INTERFACIAL CRACKS IN ANISOTROPIC ELASTOPLASTIC MEDIA





肖万伸 周建平 唐国金《应用数学和力学(英文版)》,2003年第24卷第11期


By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .

7.

Investigation of the dynamic behavior of two collinear antiplane shear cracks in a piezoelectric layer bonded to two half spaces by a new method





Zhou Zhengong and Wang Biao《应用数学和力学(英文版)》,2003年第24卷第1期


The dynamic behavior of two collinear antiplane shear cracks in a piezoelectric layer bonded to two half spaces subjected to the harmonic waves is investigated by a new method. The cracks are parallel to the interfaces in the midplane of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved by using Schmidt’s method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of cracks, the frequency of the incident wave, the thickness of the piezoelectric layer and the constants of the materials upon the dynamic stress intensity factor of cracks.

8.

ANALYSIS OF TWO DISSIMILAR FUNCTIONALLY GRADED STRIPS CONTAINING INTERFACE CRACK UNDER PLANE DEFORMATION





Haiyang Li Xingtao Zhang Zhanqi Cheng Danying Gao Zheng Zhong《Acta Mechanica Solida Sinica》,2013年第26卷第1期


In this paper the plane elasticity problem of two bonded dissimilar functionally graded strips containing an interface crack is studied.The governing equation in terms of Airy stress function is formulated and exact solutions are obtained for several special variations of material properties in Fourier transformation domain.The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically.Numerical results show that fracture toughness of materials can be greatly improved by graded variation of elastic modulus and the influence of the specific form of elastic modulus on the fracture behavior of FGM is limited.

9.

SCATTERING OF HARMONIC ANTIPLANE SHEAR STRESS WAVES BY A CRACK IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS 被引次数：1





Liang Jun《Acta Mechanica Solida Sinica》,2007年第20卷第1期


In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.

10.

ANALYSIS OF A CRACK IN A FUNCTIONALLY GRADED STRIP WITH A POWER FORM SHEAR MODULUS





Jinju Ma Zheng ZhongChuanzeng Zhang《Acta Mechanica Solida Sinica》,2009年第22卷第5期


The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy＇s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at cracktip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the influence of the material gradation models and the crack sizes on the modeI and modeII stress intensity factors. The dependence of the critical kinkangle on the crack size is examined and it is found that the crack kinkangle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crackline while it is much easier for a shorter crack to deviate from the original crackline.

11.

Fracture analysis of modeII crack perpendicular to imperfect bimaterial interface





钟献词 张克实《应用数学和力学(英文版)》,2012年第33卷第3期


The problem of a modeII crack close to and perpendicular to an imperfect interface of two bonded dissimilar materials is investigated.The imperfect interface is modelled by a linear spring with the vanishing thickness.The Fourier transform is used to solve the boundaryvalue problem and to derive a singular integral equation with the Cauchy kernel.The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation.Several special cases of the modeII crack problem with an imperfect interface are studied in detail.The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically.The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.

12.

CRACK PROPAGATING IN FUNCTIONALLY GRADED COATING WITH ARBITRARILY DISTRIBUTED MATERIAL PROPERTIES BONDED TO HOMOGENEOUS SUBSTRATE





Zhanqi Cheng Danying Gao Zheng Zhong《Acta Mechanica Solida Sinica》,2010年第23卷第5期


In this paper, a finite crack with constant length （Yoffe type crack） propagating in a functionally graded coating with spatially varying elastic properties bonded to a homogeneous substrate of finite thickness under antiplane loading was studied. A multilayered model is employed to model arbitrary variations of material properties based on two linearlydistributed material compliance parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. The numerical results show that the graded parameters, the thicknesses of the interfacial layer and the two homogeneous layers, the crack size and speed have significant effects on the dynamic fracture behavior.

13.

Investigation of the crack problem in nonlocal piezoelectric materials under combined electromechanical loadings





Qun Li Yiheng Chen《Acta Mechanica Sinica》,2009年第25卷第2期


The present investigation of the crack problem in piezoelectric materials is performed based on the nonlocal theory. After some manipulations, the impermeable crack, the permeable crack （the crack gap is full of NaCI solution）, and the semipermeable crack （the crack gap is full of air or silicon oil） are reduced to a uniform formulation by assuming the normal electric displacement on the crack surfaces to be an unknown variable. Thus, a triple integral equation with the unknown normal electric displacement is established. By using the Newton iterative method and solving the triple integral equation, it is found that the normal electric displacement on the crack surfaces is no longer a constant as determined by previous studies, rather, it depends upon the remote combined electromechanical loadings. Numerical results of the stresses and electric displacement fields show that there are no singularities at the crack tips so that the stresses remain finite. It is of great significance that the concrete electric boundary condition on the crack surfaces exerts significant influence on the neartip fields and in this way plays an important role in evaluating the crack stability in the nonlocal piezoelectric materials. More specifically, the impermeable crack model always overestimates the finite stresses at the crack tips, whereas the permeable crack model always underestimates them.

14.

INVESTIGATION OF BEHAVIOR OF MODEI INTERFACE CRACK IN PIEZOELECTRIC MATERIALS BY USING SCHMIDT METHOD





周振功 王彪《应用数学和力学(英文版)》,2006年第27卷第7期


The behavior of a ModeⅠinterface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.

15.

INVESTIGATION OF BEHAVIOR OF MODEⅠ INTERFACE CRACK IN PIEZOELECTRIC MATERIALS BY USING SCHMIDT METHOD





周振功 王彪《应用数学和力学(英文版)》,2006年第27卷第7期


The behavior of a ModeⅠ interface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.

16.

ELECTROELASTIC INTENSIFICATION NEAR ANTIPLANE CRACK IN A FUNCTIONALLY GRADIENT PIEZOELECTRIC CERAMIC STRIP





HuKeqiang ZhongZheng JinBo《Acta Mechanica Solida Sinica》,2003年第16卷第3期


Following the theory of linear piezoelectricity, we consider the electroelastic problems of a finite crack in a functionally gradient piezoelectric ceramic strip. By the use of Fourier transforms we reduce the problem to solving two pairs of dual integral equations. The solution to the dual integral equations is then expressed in terms ofa Fredholm integral equation of the second kind. Numerical calculations are carried out for piezoelectric ceramics. The electric field intensity factors and the energy release rate are shown graphically, and the electroelastic interactions are illustrated.

17.

ELECTROELASTIC INTENSIFICATION NEAR ANTIPLANE CRACK IN A FUNCTIONALLY GRADIENT PIEZOELECTRIC CERAMIC STRIP





Hu Keqiang Zhong Zheng Jin Bo 《Acta Mechanica Solida Sinica》,2003年第3期


Following the theory of linear piezoelectricity,we consider the electroelastic problems of a finite crack in a functionally gradient piezoelectric ceramic strip.By the use of Fouriertransforms we reduce the problem to solving two pairs of dual integral equations.The solution tothe dual integral equations is then expressed in terms of a Fredholm integral equation of the secondkind.Numerical calculations are carried out for piezoelectric ceramics.The electric field intensityfactors and the energy release rate are shown graphically,and the electroelastic interactions areillustrated.

18.

Influence of residual surface stress on the fracture of nanoscale piezoelectric materials with conducting cracks





NAN HaiShun WANG BaoLin《中国科学:物理学 力学 天文学(英文版)》,2014年第57卷第2期


In this paper,we analyze the stress and electric field intensity factors affected by residual surface stress for conducting cracks in piezoelectric nanomaterials.The problem is reduced to a system of nonlinear singular integral equations,whose solution is determined by iteration technique.Numerical results indicate that the residual surface stress can significantly alter the crack tip fields at nanometer length scales.Due to the residual surface stress,281he electric field can produce stress around crack tip.This suggests a strong electromechanical coupling crack tip field for nanoscale piezoelectric materials.Such a finding is considerably different from the classical fracture mechanics results.A transit electric field to stress load ratio is identified,for which influences of residual surface stresses vanish.The research is useful for the applications of nanoscale piezoelectric devices.

19.

CRACK PROBLEM FOR AN INHOMOGENEOUS PLANE BONDED BY TWO DIFFERENT INHOMOGENEOUS HALFPLANES





汤任基《应用数学和力学(英文版)》,1991年第12卷第2期


In this paper the crack problem.for two bonded inhomogeneous halfplanes isconsidered.It is assumed that the different materials have the same Poisson ratio v.butgenerally speaking,both Young s moduli vary exponentially with the coordinate x indifferent form.Using the single crack solution of the inhomogeneous plane problem andFourier transform technique.the problem is reduced to a Cauchytype singular integralequation.Several numerical examples to calculate the stress intensity factors are carriedout.

20.

Pennyshaped interfacial crack between dissimilar magnetoelectroelastic layers





YanSong Li · ZengHe Xu · WenJie Feng Institute of Engineering Mechanics Northeastern University Shenyang China Department of Engineering Mechanics Shijiazhuang Tiedao University Shijiazhuang China《Acta Mechanica Sinica》,2011年第27卷第3期


A pennyshaped interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectromechanical loads is investigated,where the magnetoelectrically impermeable crack surface condition is adopted. By using Hankel transform technique,the mixed boundary value problem is firstly reduced to a system of singular integral equations,which are further reduced to a system of algebraic equations. The field intensity factors and energy release rate are finally derived. Numerical results elucidate the eects of crack configuration,electric and/or magnetic loads,and material parameters of the magnetoelectroelastic layers on crack propagation and growth. This work should be useful for the design of magnetoelectroelastic composite structures.
