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     

Stress intensity factors for curved and kinked cracks in plane extension

A singular integral equation containing the crack opening displacement (COD) is developed for solving plane elasticity problems. The crack may contain any number of kinks at different intervals and orientations, such as a saw-tooth shape. Cracks in the form of a sine wave can also be treated. The crack tip stress intensity factors are evaluated for a variety of crack shapes and the results are displayed graphically. The distance between the crack tips is found to be a dominant factor on the crack tip stress intensity while the angle between the tangent to the crack tip and load direction determines the proportion of Mode I and II stress intensity factors.     

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     

Stress intensity factors for asymmetric branched cracks in plane extension by using crack-tip displacement discontinuity elements

Stress intensity factors are important in the analysis of cracked materials. They are directly related to the fracture propagation and fatigue crack growth criteria. Based on the analytical solution (Crouch, S.L., 1976. Solution of plane elasticity problems by displacement discontinuity method, Int. J. Numer. Methods Eng. 10, pp. 301–343; Crouch, S.L., Starfield, A.M., 1983. Boundary Element Method in Solid Mechanics, with Application in Rock Mechanics and Geological Mechanics, London, Geore Allon and Unwin, Bonton, Sydney) to the problem of a constant discontinuity in displacement over a finite line segment in the x, y plane of an infinite elastic solid, recently, the crack-tip displacement discontinuity element which can be classified as the left and right crack-tip displacement discontinuity elements are developed by the author Yan, X., (in press. A special crack-tip displacement discontinuity element, Mechanics Research Communications) to model the crack-tip fields to more accurately compute the stress intensity factors of cracks in general plane elasticity. In the boundary element implementation the left or the right crack-tip displacement discontinuity element is placed locally at the corresponding left or right crack tip on top of the ordinary non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. To prove further the efficiency of the suggested approach and provide more results of the stress intensity factors, in this study, analysis of an asymmetric branched crack bifurcated from a main crack in plane extension is carried out.     

Dynamic stress intensity factors around two rectangular cracks in an infinite elastic plate under impact load

A dynamic problem for two equal rectangular cracks in an infinite elastic plate is considered. The two cracks are placed perpendicular to the plane surfaces of the plate. An incoming shock tensile stress is returned by the cracks. In the Laplace transform domain, the boundary conditions at the two sides of the plate are satisfied using the Fourier transform technique. The mixed boundary conditions are reduced to dual integral equations. Crack displacement is expanded in a series of functions which are zero outside of the cracks. The unknown coefficients in the series are determined by the Schmidt method. The stress intensity factors are defined in the Laplace transform domain and these are inverted using a numerical method.     

An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks

The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors (SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole (a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.     

Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks

In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener–Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution.The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.     

Stress concentration and stress intensity factors fop an infinite plane with several rows of elliptic holes and cracks

This paper deals with the stress concentration in plane with swveral arbitrarily distributed elliptic holes. By using the functions of complex variables, the stress functions in which the interactions of neighbouring holes are taken into consideration can be constructed. By applying the conformed mapping method to satisfy the boundary conditions of each hole, the governing equations can then be transformed into a set of simultaneous equations through boundary integrals. Moreover, the problems with crack can be derived by changing the elliptical rates of the ellipses, thereby an approximate solution of cracking problem may be obtained. Some computing examples are given in the paper.     

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。     

A study on stress intensity factors and singular stress fields of three-dimensional interface crack

By using the finite-part integral concepts and limit technique, the hypersingular integrodifferential equations of three-dimensional (3D) planar interface crack were obtained; then the dominant-part analysis of 2D hypersingular integral was further used to investigate the stress fields near the crack front theoretically, and the accurate formulae were obtained for the singular stress fields and the complex stress intensity factors. After that, a numerical method is proposed to solve the hypersingular integrodifferential equations of 3D planar interface crack, and the problem of elliptical planar crack is then considered to show the application of the method. The numerical results obtained are satisfactory. Project supported by the Foundation of Solid Mechanics Open Research Laboratory of State Education Commission at Tongji University and the National Natural Science Foundation.     

压电界面裂纹裂尖强度因子的显式计算公式

对常见横观各向同性压电材料(TIP)中界面裂纹的裂纹面与压电材料的极化方向成任意夹角的一般情况进行了研究,通过推导得到了计算裂尖强度因子的显式外推公式,同时给出了裂纹面与极化方向垂直的典型情况下的外推公式.这些显式计算公式为常见数值方法如有限元法及边界元法在压电材料断裂力学中的应用提供了便利.     

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

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Convolution of the impact three-dimensional elasto-dynamics and dynamic stress intensity factor for an elliptic cracks

This paper presents a formulation for three-dimensional elastodynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method. The project supported by the National Natural Science Foundation of China (K19672007)     

On computations of stress intensity factors for stiffened half planes with imperfections and cracks

In this paper we consider uniform extension problems for joined two half-planes with different thickness and material behavior and one of which contains an elliptical hole, the other contains a crack. Along the boundary of these half-planes there is a stiffening stringer. Computational formulas are given in power series form by complex variable—pertubation method. Results obtained here give extension to those of Handbook of stress intensity factors. Numerical results of special cases in this paper coincide with those of refs. [1], [3].     

A Self-Similar Crack Expansion method for three-dimensional cracks in an infinite or semi-infinite medium

The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks are in good agreement with other analytical solutions.     

WEIGHT FUNCTION FOR STRESS INTENSITY FACTORS IN ROTATING THICK-WALLED CYLINDER

The equation of stress intensity factors(SIF) of internally pressurized thick- walled cylinder was used as the reference case.SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method.The weight fumction formulas were worked out and can be used for all kinds of depth of cracks,rotating speed,material,size of thick-walled cylinder to calculate the stress intensity factors.The results indicated the validity and effectiveness of these formulas.Meanwhile,the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied.The studies are valuable to engineering application.     

Elastoplastic near field solution for mode II crack loaded by remote shear stress in an infinite plate

A suitable elastic stress field near the crack line which satisfied the far field boundary conditions and the boundary conditions of the crack surfaces has been obtained and successful analysis has been made of a near crack line field for an infinite elastic-perfectly plastic medium containing a quasi-statically propagating plane stress crack subjected to far field shear stress. It is shown that the solutions of the problem of mode II crack loaded by remote shear stress from the Westergaard method in some previous papers is used as the elastic stress field near the crack line, are inappropriate.     

An improved numerical method for computation of stress intensity factors along 3D curved non-planar cracks in FGMs

A simplified strategy based on the interaction energy integral is implemented in the finite element framework to evaluate mixed mode Stress Intensity Factors (SIFs) in 3D non-planar cracks. The proposed approach does not require any a priori information about crack front and crack surface curvatures, therefore different arbitrary non-planar cracks can be easily investigated. In particular, both conical and lens-shaped cracks in homogeneous materials are considered as case studies in order to demonstrate the accuracy of the present approach. Finally, the computational strategy is extended to Functionally Graded Materials (FGMs) and the effect of graded material properties (Young’s modulus and Poisson’s ratio) on the SIFs is studied in detail.