Variation of the stress intensity factor along the crack front of interacting semi-elliptical surface cracks

Summary  In this study, the interaction between two semi-elliptical co-planar surface cracks is considered when Poisson's ratio ν = 0.3. The problem is formulated as a system of singular integral equations, based on the idea of the body force method. In the numerical calculation, the unknown density of body force density is approximated by the product of a fundamental density function and a polynomial. The results show that the present method yields smooth variations of stress intensity factors along the crack front very accurately, for various geometrical conditions. When the size of crack 1 is larger than the size of crack 2, the maximum stress intensity factor appears at a certain point, β₁=177^∘, of crack 1. Along the outside of crack 1, that is at β₁=0∼90^∘, the interaction can be negligible even if the two cracks are very close. The interaction can be negligible when the two cracks are spaced in such a manner that their two closest points are separated by a distance exceeding the small crack's major diameter. The variations of stress intensity factor of a semi-elliptical crack are tabulated and charted. Received 30 August 1999; accepted for publication 22 February 2000     

The 3-D stress intensity factor for a half plane crack in a transversely isotropic solid due to the motion of loads on the crack faces

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results. The project supported by the Guangdong Provincial Natural Science Foundation and the Science Foundation of Shantou University     

Electro-mechanical analysis of an interfacial crack between a piezoelectric and two orthotropic layers

Summary  The problem of an interfacially cracked three-layered structure constructed of a piezoelectric and two orthotropic materials is analyzed using the theory of linear piezoelectricity and fracture mechanics. Anti-plane shear loading is considered, and the integral transform technique is used to determine the stress intensity factor. Numerical examples show the electro-mechanical effects of various material combinations and layer thicknesses on the stress intensity factor. Interesting results are obtained in comparison with earlier solutions for interfacially cracked piezoelectric structures. Received 29 December 2000; accepted for publication 3 May 2001     

Effect of crack position on stress intensity factor in particle-reinforced metal-matrix composites

In this study, a numerical model was developed to study the effects of mechanical properties of the particle and matrix materials, the crack position (in particle/in matrix) and loading conditions (mode 1 and mixed-mode) in particle-reinforced metal-matrix composites. The finite element technique was used to calculate the stress intensity factors for crack at and near-interface. The Displacement Correlation Method was used to calculate the stress intensity factors K₁ and K₂. In the present model, the particle and matrix materials were modeled in linear elastic conditions. The interface crack was considered between the particle and matrix, without the presence of the interface. For near-interface crack problem, two different crack positions (in particle/in matrix) were selected. The obtained results show the key role on the stress intensity factors played by the relative elastic properties of the particle and matrix. The results also show that loading condition has an important effect on the K₂ stress intensity factor and the crack deflection angle.     

Impact response of an interface crack in a hybrid piezoelectric laminate

Summary  In a hybrid laminate containing an interfacial crack between piezoelectric and orthotropic layers, the dynamic field intensity factors and energy release rates are obtained for electro-mechanical impact loading. The analysis is performed within the framework of linear piezoelectricity. By using integral transform techniques, the problem is reduced to the solution of a Fredholm integral equation of the second kind, which is obtained from one pair of dual integral equations. Numerical results for the dynamic stress intensity factor show the influence of the geometry and electric field. Received 29 June 2001; accepted for publication 3 December 2001     

3D dynamic stress intensity factors at three rectangular cracks in an infinite elastic medium subjected to a time-harmonic stress wave

Summary Dynamic stresses around three coplanar cracks in an infinite elastic medium are determined in the paper. Two of the cracks are equal, rectangular and symmetrically situated on either side of the centrally located rectangular crack. Time-harmonic normal traction acts on each surface of the three cracks. To solve the problem, two kind of solutions are superposed: one is a solution for a rectangular crack in an infinite elastic medium, and the other one is that for two rectangular cracks in an infinite elastic medium. The unknown coefficients in the combined solution are determined by applying the boundary conditions at the surfaces of the cracks. Finally, stress intensity factors are calculated numerically for several crack configurations. Received 14 July 1998; accepted for publication 2 December 1998     

Generalized stress intensity factors in the interaction within a rectangular array of rectangular inclusions

Summary To evaluate the mechanical strength of fiber-reinforced composites, it is necessary to consider singular stresses at the end of fibers because they cause crack initiation, propagation, and final failure. A square array of rectangular inclusions under longitudinal tension is considered in this paper. The body-force method is applied to a unit cell region. Then, the problem is formulated as a system of singular integral equations, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. The unknown functions are expressed as piecewise-smooth functions using power series and two types of fundamental densities which express singular stresses. Generalized stress intensity factors at the corners of inclusions are systematically calculated with varying the shape and spacing of a square array of square and rectangular inclusions.     

Analytical solution for bending stress intensity factor in an orthotropic elastic plate containing a crack and subjected to concentrated moments

The problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an orthotropic elastic plate of constant thickness subjected to out-of-plane concentrated moments is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in a closed form for the case in which there is a single crack in an infinite plate subjected to symmetric concentrated moments.     

Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes

Summary  In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact. Received 4 December 2001; accepted for publication 9 July 2002 This work is supported by the National Natural Science Foundation of China through Grant No. 10132010.     

Determination of mixed-mode stress intensity factors, fracture toughness, and crack turning angle for anisotropic foam material

A numerical and experimental investigation for determining mixed-mode stress intensity factors, fracture toughness, and crack turning angle for BX-265 foam insulation material, used by NASA to insulate the external tank (ET) for the space shuttle, is presented. BX-265 foam is a type of spray-on foam insulation (SOFI), similar to the material used to insulate attics in residential construction. This cellular material is a good insulator and is very lightweight. Breakup of segments of this foam insulation on the shuttle ET impacting the shuttle thermal protection tiles during liftoff is believed to have caused the space shuttle Columbia failure during re-entry. NASA engineers are interested in understanding the processes that govern the breakup/fracture of this material from the shuttle ET. The foam is anisotropic in nature and the required stress and fracture mechanics analysis must include the effects of the direction dependence on material properties. Material testing at NASA Marshall Space Flight Center (MSFC) has indicated that the foam can be modeled as a transversely isotropic material. As a first step toward understanding the fracture mechanics of this material, we present a general theoretical and numerical framework for computing stress intensity factors (SIFs), under mixed-mode loading conditions, taking into account the material anisotropy. We present SIFs for middle tension – M(T) – test specimens, using 3D finite element stress analysis (ANSYS) and FRANC3D fracture analysis software. SIF values are presented for a range of foam material orientations. Mode I fracture toughness of the material is determined based on the SIF value at failure load. We also present crack turning angles for anisotropic foam material under mixed-mode loading. The results represent a quantitative basis for evaluating the strength and fracture properties of anisotropic foam insulation material.     

3D dynamic stress intensity factors around two parallel square cracks in an infinite elastic medium under impact load

Summary  Transient stresses around two parallel cracks in an infinite elastic medium are investigated in the present paper. The shape of the cracks is assumed to be square. Incoming shock stress waves impinge upon the two cracks normal to tzheir surfaces. The mixed boundary value equations with respect to stresses and displacements are reduced to two sets of dual integral equations in the Laplace transform domain using the Fourier transform technique. These equations are solved by expanding the differences in the crack surface displacements in a double series of a function that is equal to zero outside the cracks. Unknown coefficients in the series are calculated using the Schmidt method. Stress intensity factors defined in the Laplace transform domain are inverted numerically to the physical space. Numerical calculations are carried out for transient dynamic stress intensity factors under the assumption that the shape of the upper crack is identical to that of the lower crack. Received 2 February 2000; accepted for publication 10 May 2000     

焊接节点半椭圆表面裂纹应力强度因子的权函数计算

本文采用一种改进的权函数法来计算焊接节点半椭圆表面裂纹应力强度因子ＫＩ值，并给出了相应的数值处理方法，就Ｔ型板节点进行了数值验算。     

内部压力作用下矩形板中源于椭圆孔的分支裂纹应力强度因子的一种数值分析

应用一种边界元方法来研究内部压力作用下矩形板中源于椭圆孔的分支裂纹。该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者最近提出的裂尖位移不连续单元构成。在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界。本数值结果进一步证实这种数值方法对计算有限大板中复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示裂纹体几何对应力强度因子的影响。     

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy.     

Crack initiation at the rectangular step notch surface under combined loading

Summary  Under external forces acting on the face of a notch, cracks originate at corners, and the system is liable to fail. An analysis is presented of the stress field in the neighborhood of the notch tips, based on the integral representation of the biharmonic solution and on numerical methods. Computations were performed for constant loading or constant displacement distributed along one face of the notch. The coefficients in the principal terms of the asymptotic formulae for the circumferential and shear stresses depend on the angle and height of the notch face and on the boundary conditions. The maximal values of these coefficients determine the stress intensity factors for the opening and shear modes. The angles corresponding to the maximal values of the intensity factors indicate the directions of initiation of opening and sliding cracks. Received 30 May 2000; accepted for publication 3 April 2001     

基于子模型法的带有表面裂纹钢丝应力强度因子研究

钢丝裂纹应力强度因子是进行钢丝疲劳断裂寿命评估、疲劳裂纹扩展分析和钢丝断裂强度评估等工作的重要参数。本文首先介绍了裂纹扩展分析软件FRANC3D,然后基于子模型法模拟研究了拉伸荷载作用下带有表面裂纹钢丝的应力强度因子,裂纹种类包括直线形裂纹和半圆形裂纹,最后拟合得到拉伸荷载作用下带表面裂纹钢丝的应力强度因子形状修正系数表达式,分析了利用该公式进行承载力评估时产生误差的原因。研究结果表明,利用子模型模拟分析拉伸荷载作用下带有表面裂纹的钢丝应力强度因子时计算精度高,计算速度快,对计算机硬件要求低;利用该方法得到的钢丝裂纹应力强度因子,在进行索承式桥梁吊索安全性能评估时,评估结果更精确。     

Analysis of stress intensity factor in orthotropic bi-material mixed interface crack

Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With consideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial differential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit,undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship between the bi-material stress intensity factor and the ratio of bi-material Young's modulus are given in the numerical analysis.     

Mode-III interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials

Summary  The problem of an interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials is considered under the conditions of anti-plane shear and in-plane electric loading. The crack surfaces are assumed to be impermeable to the electric field. An integral transform technique is employed to reduce the problem under consideration to dual integral equations. By solving the resulting dual integral equations, the intensity factors of the stress and the electric displacement and the energy release rate as well as the crack sliding displacement and the electric voltage across the crack surfaces are obtained in explicit form for the case of concentrated forces and free charges at the crack surfaces and at the boundary. The derived results can be taken as fundamental solutions which can be superposed to model more realistic problems. Received 10 November 2000; accepted for publication 28 March 2001     

残余应力下厚壁筒表面裂纹的应力强度因子计算

本文首先介绍了边界元法计算裂纹尖端应力强度因子的基本理论,接着利用边界元法计算了在残余应力下不同厚壁筒内表面椭圆裂纹的应力强度因子,研究了其大不随椭圆裂纹不同而变化的规律,为厚壁筒结构的设计,制造以及疲劳寿命分析提供了许多有价值的参考资料。     

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.