In-plane analysis of a cracked orthotropic half-plane

The stress fields in an orthotropic half-plane containing Volterra type climb and glide edge dislocations under plane stress condition are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surface of smooth cracks embedded in the half-plane under in-plane loads. The integral equations are of Cauchy singular type which are solved numerically. The dislocation density functions are employed to evaluate modes I and II stress intensity factors for multiple cracks with different configurations.     

In-plane stress analysis of an orthotropic plane containing multiple defects

The solution of Volterra type climb and glide edge dislocations is utilized to formulate integral equations for an orthotropic homogeneous infinite plane weakened by multiple smooth cracks and/or cavities. Cavities are considered as closed curved cracks without singularity. The integral equations are of Cauchy singular type which are converted to hypersingular integral equations. These equations are then solved numerically to determine stress intensity factors for cracks and hoop stress on the cavities. The results for isotropic and orthotropic planes are compared with available solutions in literature and excellent agreement is observed. The formulation allows stress analysis of orthotropic planes with several arbitrarily oriented cracks and cavities.     

Mixed mode axisymmetric annular cracks in a finite layer: Off angle crack initiation

The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions.     

Elastodynamic analysis of a plane weakened by several cracks

The stress fields in an infinite plane containing Volterra type climb and glide edge dislocations under time-harmonic excitation are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type which are solved numerically for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.     

AN INVESTIGATION ON TWO CRACKS PERPEN DICULAR TO THE INTERFACES IN A PIEZOE LECTRIC LAYER BONDED TO TWO HALF SPACES BY THE SCHMIDT METHOD

The behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the imerfaces 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 using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks.     

Analysis of Two Collinear Cracks in a Piezoelectric Layer Bonded to Two Half Spaces Subjected to Anti-plane Shear

In this paper, the behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by a new method for the impermeable crack face conditions. The cracks are parallel to the interfaces in the mid-plane 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 using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks.     

INVESTIGATION OF THE DYNAMIC BEHAVIOR OF TWO COLLINEAR ANTI-PLANE SHEAR CRACKS IN A PIEZOELECTRIC LAYER BONDED TO TWO HALF SPACES BY A NEW METOHD

IntroductionItiswell_knownthatpiezoelectricmaterialsproduceanelectricfieldwhendeformedandundergodeformationwhensubjectedtoanelectricfield .Thecouplingnatureofpiezoelectricmaterialshasattractedwideapplicationsinelectro_mechanicalandelectricdevices,suchaselectro_mechanicalactuators,sensorsandstructures.Whensubjectedtomechanicalandelectricalloadsinservice,thesepiezoelectricmaterialscanfailprematurelyduetodefects,e .g .,cracks,holds,etc.arisingduringtheirmanufactureprocess.Therefore,itisofgreatimp…     

Three-dimensional crack analysis

A method is presented for the stress analysis of plane cracks of any shape in a stressed three-dimensional linear elastic space. The approach utilizes a system of integral equations which is defined over the crack area only. When these equations are solved for the unknown dislocations, all other quantities related to the crack and the space can then be found. The text contains sections concerning equation system derivation, numerical procedures, stress intensity factors, rectangular cracks, and earthquake control.     

Weakly-singular,weak-form integral equations for cracks in three-dimensional anisotropic media

Singularity-reduced integral relations are developed for displacement discontinuities in three-dimensional, anisotropic linearly elastic media. An isolated displacement discontinuity is considered first, and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity. The singularity-reduced relation for the stress is particularly important since it is in a form which allows a weakly-singular, weak-form traction integral equation to be readily established. The integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations; the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context. Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established. These integral equations can be combined to obtain a final formulation which is in a symmetric form, and in this way they serve as the basis for a weakly-singular, symmetric Galerkin boundary element method suitable for analysis of cracks in anisotropic media.     

Multi-interface cracks in a piezoelectric layer bonded to two half-piezoelectric spaces under anti-plane shear loading

The behavior of four parallel symmetry permeable interface cracks in a piezoelectric layer bonded to two half-piezoelectric spaces under anti-plane shear loading is investigated. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. These equations are solved by the Schmidt method. This process is quite different from that papers adopted previously. The normalized stress and electrical displacement intensity factors are determined for different geometric and property parameters for permeable crack surface conditions. Numerical examples are provided to show the effect of the geometry of the interacting cracks, the thickness and the materials constants of the piezoelectric layer upon the stress and electric displacement intensity factors of the cracks. It is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than the results for the impermeable crack surface conditions.     

An investigation on two cracks perpen-dicular to the interfaces in a piezolectric layer bonded to two half spaces by the schmidt method

The behavior of two collinear anti-plane shear cracks in'a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces 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 using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks. Project supported by the Post Doctoral Science Foundation of Heilongijang Province, the Natural Science Foundation of Heilongjing Province and the Science Research Foundation of Harbin Institute of Technology(HIT. 2000. 30).     

层状介质垂直界面有限裂纹问题的积分变换解

层状弹性材料包含垂直于界面有限裂纹时，可运用富里叶变换及引用位错密度函数，导出了反映裂纹尖端奇异性的奇异积分方程组，并使用Ｌｏｂａｔｔｏ－ｃｈｅｂｙｓｈｅｖ方法解此方程组，最后得到裂纹尖端应力强度因子，为检验方法的正确性，对某两层含裂实际结构进行了计算，结果是满意的。     

Analysis of multiple axisymmetric annular cracks in a piezoelectric medium

An axisymmetric annular electric dislocation is defined. The solution of axisymmetric electric and Volterra climb and glide dislocations in an infinite transversely isotropic piezoelectric domain is obtained by means of Hankel transforms. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks with so-called permeable and impermeable electric boundary conditions on the crack faces where the domain is under axisymmetric electromechanical loading. These equations are solved numerically to obtain dislocation densities on the crack surfaces. The dislocation densities are employed to determine field intensity factors for a system of interacting annular and/or penny-shaped cracks.     

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

The dynamic behavior of two collinear anti-plane 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 mid-plane 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.     

Interaction between a circular inclusion and a symmetrically branched crack

The interaction problem between a circular inclusion and a symmetrically branched crack embedded in an infinite elastic medium is solved. The branched crack is modeled as three straight cracks which intersect at a common point and each crack is treated as a continuous contribution of edge dislocations. Green's functions are used to reduce the problem into a system of singular equations consisting of the distributions of Burger's dislocation vectors as unknown functions through the superposition technique. The resulting integral equations are solved numerically by the method of Gauss-Chebychev quadrature. The proposed integral equation approach is first verified for two limiting cases against the literature. More effort is paid on the effect of inclusion on both the Mode I and Mode lI stress intensity factors at the branch tips. The effect of inclusion on the branching path is also investigated.     

Hypersingular integral equation for multiple curved cracks problem in plane elasticity

The complex variable function method is used to formulate the multiple curved crack problems into hypersingular integral equations. These hypersingular integral equations are solved numerically for the unknown function, which are later used to find the stress intensity factor, SIF, for the problem considered. Numerical examples for double circular arc cracks are presented.     

Dynamic stress intensity factors for two parallel interface cracks between a nonhomogeneous bonding layer and two dissimilar elastic half-planes subject to an impact load

Some composite materials are constructed of two dissimilar half-planes bonded by a nonhomogeneous elastic layer. In the present study, a crack is situated at the interface between the upper half-plane and the bonding layer of such a material, and another crack is located at the interface between the lower half-plane and the bonding layer. The material properties of the bonding layer vary continuously from those of the lower half-plane to those of the upper half-plane. Incoming shock stress waves impinge upon the two interface cracks normal to their surfaces. Fourier transformations were used to reduce the boundary conditions for the cracks to two pairs of dual integral equations in the Laplace domain. To solve these equations, the differences in the crack surface displacements were expanded in a series of functions that are zero-valued outside the cracks. The unknown coefficients in the series were solved using the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors were defined in the Laplace domain and were inverted numerically to physical space. Dynamic stress intensity factors were calculated numerically for selected crack configurations.     

Dynamic behavior of two collinear anti-plane shear cracks in a functionally graded layer bonded to dissimilar half planes

In recent years, the functionally graded materials (FGMs) have been widely applied in extremely high temperate environment. In this paper, the dynamic behavior of two collinear cracks in FGM layer bonded to dissimilar half planes under anti-plane shear waves is studied by the Schmidt method. By using the Fourier transform technique, the present problem can be solved with a dual integral equation. These equations are solved using the Schmidt method. The present method is used to illustrate the fundamental behavior of the interacting cracks in FGMs under dynamic loading. Furthermore, the effects of the geometry of the interacting cracks, the shear stress wave velocity of the materials and the frequency of the incident wave on the Dynamic Stress Intensity Factor are investigated.     

SOLUTION OF MULTIPLE CRACKS IN A FINITE PLATE OF AN ELASTIC ISOTROPIC MATERIAL WITH THE DISTRIBUTED DISLOCATION METHOD

This paper presents a numerical solution to model multiple cracks in a finite plate of an elastic isotropic material. Both the boundaries and the cracks are modeled by distributed dislocations. This method results in a system of singular integral equations with Cauchy kernels which can be solved by Gauss-Chebyshev quadrature method. Four examples are provided to assess the capability of this method.     

层状磁电复合材料界面共线裂纹平面问题分析

本文研究了面内电磁势载荷作用下双层压电压磁复合材料中共线界面裂纹问题．考虑了压电材料的导磁性质和压磁材料的介电性质,引入了界面电位移和磁感强度的连续性条件．利用Fourier 变换得到一组第二类Cauchy 型奇异积分方程．进一步导出了相应问题的应力强度因子、电位移强度因子和磁感强度强度因子的表达式,给出了应力强度因子的数值结果．结果表明电磁载荷会导致界面裂纹尖端I、II 混合型应力奇异性,同时还伴随着电位移和磁感强度的奇异性．比较了双裂纹左右端的应力强度因子,发现在面内极化方向上施加面内磁势载荷时共线裂纹内侧尖端区域的两个法向应力场发生互相干涉增强．