Torsion of a cylinder with a shallow external crack

The torsional problem of a finite elastic cylinder with a circumferential edge crack is studied in this paper. An efficient solution to the problem is achieved by using a new form of regularization applied to dual Dini series equations. Unlike the Srivastav approach, this regularization transforms dual equations into a Fredholm integral equation of the second kind given on the crack surface. Hence, exact asymptotic expansions of the Fredholm equation solution, the stress intensity factor and the torque are derived for the case of a shallow crack. The asymptotic expansions are certain power-logarithmic series of the normalized crack depth. Coefficients of these series are found from recurrent relations. Calculations for a shallow crack manifest that the stress intensity factor exhibits the rather weak dependence upon the cylinder length when the torque is fixed and the triple length is larger than the diameter.     

A long circular cylinder with a circumferential edge crack subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in a long circular cylinder of isotropic elastic material with a circumferential edge crack when it is deformed by the application of a uniform shearing stress. The crack with its center on the axis of the cylinder lies on the plane perpendicular to that axis, and the cylindrical surface is stress-free. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of singular integral equations. This pair of singular integral equations is solved numerically, and the stress intensity factor due to the effect of the crack size is tabulated.     

Strip yield zones around ring-shaped crack in transversely isotropic thick layer

A ring-shaped crack under uniform load in an infinitely long elastic–perfectly plastic thick layer is considered. The problem is formulated for a transversely isotropic material by using integral transform technique. Due to the geometry of the configuration, Hankel integral transform technique was chosen and the problem was reduced to a singular integral equation which is solved numerically by using Gaussian Quadrature Formulae and the values were evaluated at discrete points. The plastic zone widths were obtained by using the plastic strip model after stress intensity factors were obtained. Numerical results are plotted for various ring-shaped crack sizes and transversely isotropic materials. It was found that the width of the plastic zone at the inner edge of the crack was greater than the outer one.     

考虑应力松驰复合型裂纹顶端塑性区分析

Ｓｈｉｈ［１］应用奇异单元，获得了不考虑应力松驰小范围屈服条件下复合型裂纹尖端塑性区形状。Ｚ．Ｚ．Ｚｕ等［２］采用Ｒｉｃｅ［５］给出的裂纹尖端应力关系式，利用有限元分析获得了不考虑应力松驰下复合型裂纹尖端塑性区，本文基于静力学中内力与外力平衡条件，用线弹性的全场解代替局部解，给出了考虑应力松驰下复合型裂纹尖端塑性区边界方程，获得了考虑应力松驰下的任意方向的塑性区尺寸及塑性区形状     

Stress intensity factors of the eccentric and edge cracked cylinders

Using the single crack solution and the regular solution of harmonic function,thetorsion problem of a cracked cylinder is reduced to solving a set of mixed-type integralequations which can be solved by combining the numerical method of singular integralequation with the boundary element method.Several numerical examples arecalculated and the stress intensity factors are obtained.     

Axisymmetric circumferential internal crack problem of a thick-walled cylinder with inner and outer claddings

The elastostatic axisymmetric problem for a long thick-walled cylinder containing an axisymmetric circumferential internal crack with two claddings is considered. The claddings having different elastic properties than the hollow cylinder are assumed to be bonded to inner and outer wall of the hollow cylinder. The problem is formulated in terms of a singular integral equation of a well known type, the derivative of the crack surface displacement being the density function, using the standard transform technique. By using appropriate quadrature formulas, the integral equation is reduced to a system of linear algebraic equations. This system is solved numerically and the related stress-intensity factors are calculated for the cases of hollow cylinder with two claddings bonded to inner and outer wall of the cylinder, a cladding bonded to inner wall of the cylinder, a cladding bonded to outer wall of the cylinder and no cladding under axial tensile load. The influence of the geometrical configuration, the claddings and internal crack length on the stress-intensity factors is shown graphically.     

Stress intensity factors for an oblique edge crack in a coating/substrate system with a graded interfacial zone under antiplane shear

This paper investigates the edge crack problem for a coating/substrate system with a functionally graded interfacial zone under the condition of antiplane deformation. With the interfacial zone being modeled by a nonhomogeneous interlayer having the continuously varying shear modulus between the dissimilar, homogeneous phases of the coated medium, the coating is assumed to contain an edge crack at an arbitrary angle to the interfacial zone. The Fourier integral transform method is used in conjunction with the coordinate transformations of basic field variables. Formulation of the proposed crack problem is then reduced to solving a singular integral equation with a generalized Cauchy kernel. The mode III stress intensity factors are defined and evaluated in terms of the solution to the integral equation. In the numerical results, the values of the stress intensity factors are plotted, illustrating the effects of the crack orientation angle for various material and geometric combinations of the coating/substrate system with the graded interfacial zone.     

Refined Dugdale plastic zones of an external circular crack

The refined Dugdale-type plastic zones ahead of an external circular crack, subjected to a uniform displacement at infinity, are evaluated both analytically and numerically. The analytical method utilizes potential theory in classical linear elasticity with emphasis on the contrast from the internal crack problem. A closed-form solution to the mixed boundary problem is obtained to predict the length of the plastic zone for a Tresca yield condition. The analytical solution is also used to benchmark the results obtained from the numerical method, which show good agreement. Through an iterative scheme, the numerical technique is able to estimate the size of crack tip plasticity zone, which is governed by the non-linear von Mises criterion. The relationships between the applied displacement and the length of the plastic zone are compared for the different yielding conditions. Computational modeling has demonstrated that the plastic constraint effect based on the true yield condition can significantly influence the load-bearing capacity. It is also discovered from the comparative study that the stress components predicted by the three different yield conditions may differ notably; however, the stress triaxiality in the ligament region has only small deviations. The proposed study may find applications in predicting the plastic flow in a circumferentially notched round bars under tension.     

The Problem of an External Circular Crack Under Asymmetric Loadings

ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎｔｈｅｂｏｕｎｄａｒｙｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｍｅｔｈｏｄｉｓａｐｐｌｉｅｄｔｏｃｒａｃｋａｎａｌｙｓｉｓ,ｏｎｌｙｎｕｍｅｒｉｃａｌｓｏｌｕｔｉｏｎｓｃａｎｂｅｏｂｔａｉｎｅｄ ,ｓｕｃｈａｓ:ｔｈｅｔｙｐｉｃａｌｗｏｒｋｓｏｆＳｎｙｄｅｒａｎｄＣｒｕｓｅ[1],Ｃｒｏｕｃｈ[2 ],Ｂｌａｎｄｆｏｒｄｅｔａｌ.[3],Ｐｏｒｔｅｌａｅｔａｌ.[4 ],Ｂｕｉ[5 ],Ｗｅａｖｅｒ[6 ]ａｎｄＷＡＮＧｅｔａｌ.[7- 9].Ｉｔｉｓｖｅｒｙｄｉｆｆｉｃｕｌｔｔｏａｐｐｌｙｔｈｅｂｏｕｎｄａｒ…     

Torsion of a long circular cylinder having a spherical cavity with a peripheral edge crack

The singular stress problem of a peripheral edge crack around a spherical cavity in a long circular cylinder under torsion is investigated. The problem is solved by using integral transforms and is reduced to the solution of two integral equations. The solution of these equations is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors, and crack opening displacements are displayed graphically.     

Anti-plane shear crack growth rate of piezoelectric ceramic body with finite width

The theory of linear piezoelectricity is applied to develop an anti-plane crack growth rate equation of a finite crack in a piezoelectric ceramic body with finite width. Plastic zone is assumed to be confined to a sheet ahead of both crack edges similar to the strip model for in-plane loading. The procedure consists of reducing a system of dual integral equations to a Fredholm integral equation of the second kind. The accumulated plastic displacement criterion is used for developing a solution for the crack growth rate. Numerical values of crack growth rate are obtained and the results are displayed graphically to exhibit the electroelastic interactions.     

Tension of a long circular cylinder having a spherical cavity with a peripheral edge crack

The singular stress problem of a peripheral edge crack around a spherical cavity in a long circular cylinder under tension is investigated. The problem is solved by using integral transforms and is reduced to the solution of three integral equations. The solution of these equations is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors are displayed graphically.     

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.      

A three-dimensional rectangular crack subjected to shear loading

In this paper a solution is derived to treat the three-dimensional elastostatic problem of a narrow rectangular crack embedded in an infinite elastic medium and subjected to equal and opposite shear stress distribution across its faces. Employing two-dimensional integral transforms and assuming a plane-strain solution across the width of the crack, the stress field ahead of the crack length is reduced to the solution of an integral equation of Fredholm type. A numerical solution of the integral equation and the corresponding mode II stress-intensity factor is obtained for several crack dimensions and Poisson's ratios of the material.     

Diffraction of torsional elastic waves by a peripheral edge crack around a spherical cavity

This paper deals with the problem of finding the stress distribution in the neighborhood of a peripheral edge crack in a spherical cavity. The crack is excited by a torsional standing wave.The problem is solved by using integral transforms and is reduced to the solution of a singular integral equation. The solution of this equation is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors are displayed graphically.     

SAINT-VENANT’S TORSION PROBLEM FOR A COMPOSITE CIRCULAR CYLINDER WITH ANINTERNAL EDGE CRACK

In this paper the writer uses Muskhelishvili single-layer potential function solutionand single crack solution for the torsion problem of a circular cylinder to discuss thetorsion problem of a composite cylinder with an internal crack,and the problem isreduced to a set of mixed-type integral equation with generalized Cauchy-kernel.Then,by using the integration formula of Gauss-Jacobi.the numerical method isestablished and several numerical examples are calculated.The torsional rigidity andthe stress intensity factors are obtained.The results of these examples fit the resultsobtained by the previous papers better.     

Boundary element method to solve torsion problem of cracked cylinder

Separating the discontinuous solution by use of the single crack solution, together with the regular solution of harmonic function, the torsion problem of a cracked cylinder is reduced to solving a set of mixed-type integral equations and its numerical technique is then proposed by combining the numerical method of singular integral equation with the boundary element method. Several numerical examples are calculated which will be useful to engineering practice. The method proposed is characterized by its fine accuracy and convenience for using, which can be extended to the cases of multiple crack.The project supported by National Natural Science Foundation of China.     

A Zener–Stroh crack interacting with a coated inclusion with generalized Irwin plastic zone correction

The elastic–plastic fracture behavior of a Zener–Stroh crack interacting with a coated inclusion in composite materials has been investigated with crack tip plastic zone corrections. With the distributed dislocation method, the crack problem is formulated into a set of singular integral equations which are solved numerically. The plastic zone sizes at the both crack tips are determined by a generalized Irwin model where Von Mises stress yielding criterion is used. The stress intensity factor (SIF), the plastic zone size (PZS), the crack tip opening displacement (CTOD) and the effective stress intensity factor have been evaluated. In the numerical examples, the influence of the inclusion shear modulus, the coating-layer thickness and shear modulus, as well as the distance between the crack and inclusion, on the SIF, the PZS and the CTOD are discussed in detail. Numerical examples show that increasing the shear modulus or the thickness of the coating phase, the influence of the inclusion on the normalized SIF and the normalized PZS will be shielded.     

A closed crack tip model for interface cracks inthermopiezoelectric materials

The interface crack problem of a bimaterial thermopiezoelectric solid was treated byapplying the extended version of Strohs formalism and singular integral equation approach. Theinterface crack considered is subjected to combined thermal, mechanical and electric loads.Under the applied loading, the interface crack is assumed to be partially opened. Formulation ofthe problem results in a set of singular integral equations which are solved numerically. Thestudy shows that the contact zone is extremely small in comparison with the crack length. Basedon the formulation, some physically meaningful quantities of interest such as stress intensityfactors and size of contact zone for a particular material group are analyzed.     

The approximate solution of penny-shaped cracks periodically distributed in infinite elastic body

The penny-shaped cracks periodically distributed in infinite elastic body are studied. The problem is approximately simplified to that of a single crack embedded in finite length cylinder and the stress intensity factor is obtained by solving a Fredholm integral equation. Numerical results are given and the effects of crack interaction on the stress intensity factor are discussed. The project suppoted by National Natural Science Foundation of China