Determination of stress intensity factors in half-plane containing several moving cracks

The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a single dislocation and without dislocation. An exact solution in a closed form to the stress fields and displacement is ob- tained. The Galilean transformation is used to transform between coordinates connected to the cracks. The stress components are of the Cauchy singular kind at the location of dislocation and the point of application of the the influence of crack length and crack running force. Numerical examples demonstrate velocity on the stress intensity factor.     

Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working conditions is an essential issue. In this paper, a comprehensive study of stress intensity factors(SIFs) in rotating disks containing three-dimensional(3D) semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical properties, rotational velocity, and orientation of cracks on SIFs in rotating disks under centrifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.     

Determination of stress-intensity factors for cracks in tubes under torsion

An experimental investigation by two-dimensional photoelastic technique is carried out to study the stress distribution and to determine the stress-intensity factors for arbitrarily oriented cracks in thin cylindrical shells subjected to torsion. A new method is employed to evaluate the pure and mixed-mode SIF's.     

The stress intensity factors near the tips of two collinear cracks in composite under in-plane shear

In this paper, the stress-intensity factors for two collinear cracks in a composite bonded by an isotropic and an anisotropic half-plane were calculated. The cracks are paralell to the interface, and the crack surfaces are loaded by uniform shear stresses. By using Fourier transform, the mixed boundary value problem is reduced to a set of singular integral equations. For solving the integral equations, the crack surface displacements are expanded in triangular series and the unknown coefficients in the series are determined by the Schmidt method. The stress intensity factors for the cracks in the boron-fibre plastics and aluminium joined composite and in carbon-fibre reinforced plastics were calculated numerically.     

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.     

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.     

The stress intensity factors in an isotropic elastic body weakened by equioriented disk cracks

A strict approach is proposed to analyze the stress intensity factors (SIFs) in an isotropic medium containing plane parallel cracks. The approach implies using a generalized periodic structural model and reducing the boundary-value problems formulated based on this model to a linear system of algebraic equations. An asymptotic analysis of the stress field near the crack apex is carried out, and the exact expressions for the SIF are obtained in the form of series. Numerical results that illustrate the effect of crack arrangement on the SIFs are presented and compared with known approximate theories. Institute of Superhard Materials. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 74–80, May, 2000.     

On the torsion of a cylinder with several cracks

In this paper, based on paper [1], the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations^[2,7] the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the creak-cutting method^[5] is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful. Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

Determination of stress intensity factors for cracks of complex shape in anisotropic plates

The application of analytical methods to the problem of fatigue crack propagation and branching is complicated by the shortage of information on the stress distribution near the tip of cracks of complex configuration. A discussion of this problem and a survey of the studies in this area can be found in [1], for example. Below we develop a method of solving a problem concerning a system of cracks of complex form in an anisotropic half-plane. An efficient algorithm for numerical solution of the problem is proposed. A study is made of the effect of anisotropy of the material, the free edge of the plate, and the curvature of the crack on the stress intensity factors at the tips of the cracks.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 124–128, November–December, 1986.     

Dynamic stress intensity factors of multiple cracks in a functionally graded orthotropic half-plane

In the present paper dynamic stress intensity factor and strain energy density factor of multiple cracks in the functionally graded orthotropic half-plane under time-harmonic loading are investigated. By utilizing the Fourier transformation technique the stress fields are obtained for a functionally graded orthotropic half-plane containing a Volterra screw dislocation. The variations of the material properties are assumed to be exponential forms which the equilibrium has an analytical solution. The dislocation solution is utilized to formulate integral equation for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determined stress intensity factor and strain energy density factors (SEDFs) for multiple smooth cracks under anti-plane deformation. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded orthotropic half-plane with multiple curved cracks.     

Mixed-mode stress intensity factors and critical angles of cracks in bolted joints by weight function method

Summary   Mechanical joints, such as bolted or riveted joints, are widely used in structural components. Reliable determination of stress intensity factors for cracks in bolted joints is required to evaluate their safety and fatigue life. The weight function method is an efficient technique to calculate stress intensity factors for various loading conditions by the stress analysis of an uncracked model. In this paper, the mixed-mode stress intensity factors for cracks in bolted joints are analyzed by the weight function method, and coefficients included in the weight function are determined by finite element analysis for reference loadings. The critical angle at which mode I stress intensity factor becomes maximum is determined, and the effects of the amount of clearance and crack length on the critical angle are investigated. Received 28 February 2001; accepted for publication 22 June 2001 RID=" ID=" The authors are grateful for the support provided by a grant from the Korea Science & Engineering Foundation (KOSEF) and Safety and Structural Integrity Research Center at the Sungkyunkwan University.     

A unified definition for stress intensity factors of interface corners and cracks

Based upon linear fracture mechanics, it is well known that the singular order of stresses near the crack tip in homogeneous materials is a constant value −1/2, which is nothing to do with the material properties. For the interface cracks between two dissimilar materials, the near tip stresses are oscillatory due to the order of singularity being −1/2 ± iε and −1/2. The oscillation index ε is a constant related to the elastic properties of both materials. While for the general interface corners, their singular orders depend on the corner angle as well as the elastic properties of the materials. Owing to the difference of the singular orders of homogeneous cracks, interface cracks and interface corners, their associated stress intensity factors are usually defined separately and even not compatibly. Since homogenous cracks and interface cracks are just special cases of interface corners, in order to build a direct connection among them a unified definition for their stress intensity factors is proposed in this paper. Based upon the analytical solutions obtained previously for the multibonded anisotropic wedges, the near tip solutions for the general interface corners have been divided into five different categories depending on whether the singular order is distinct or repeated, real or complex. To provide a stable and efficient computing approach for the general mixed-mode stress intensity factors, the path-independent H-integral based on reciprocal theorem of Betti and Rayleigh is established in this paper. The complementary solutions needed for calculation of H-integral are also provided in this paper. To illustrate our results, several different kinds of examples are shown such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials.     

Dislocation technique to obtain the dynamic stress intensity factors for multiple cracks in a half-plane under impact load

In this study, the transient response of multiple cracks subjected to shear impact load in a half-plane is investigated. At first, exact analytical solution for the transient response of Volterra-type dislocation in a half-plane is obtained by using the Cagniard-de Hoop method of Laplace inversion and is expressed in explicit forms. The distributed dislocation technique is used to construct integral equations for a half-plane weakened by multiple arbitrary cracks. These equations are of Cauchy singular type at the location of dislocation solved numerically to obtain the dislocation density on the cracks faces. The dislocation densities are employed to determine dynamic stress intensity factors history for multiple smooth cracks. Finally, several examples are presented to demonstrate the applicability of the proposed solution.     

The stress intensity factors for two collinear edge cracks in a rotating disc

Summary The problem of determining the stress intensity factors and the crack formation energy of two edge cracks of unequal length on the same diameter of a finite rotating elastic disc is reduced to the solution of two coupled singular integral equations. Numerical results are given.

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Zusammenfassung Das Problem der Bestimmung der Spannungsintensitätsfaktoren und der Rissbildungsenergie van zwei Kantenrissen ungleicher Länge auf denselben Durchmesser in einer endlichen rotierenden elastischen Scheibe wird auf die Lösung von zwei zusammengeschriebenen singulären Integralgleichnungen reduziert. Es werden numerische Resultate gegeben.

     

Determination of the stress intensity factors at the ends of two collinear transverse shear cracks under steady vibrations

International Applied Mechanics -     

Some stress intensity factors for self-similar cracks,derived from path-independent integrals

Summary A new method of computing stress intensity factors for self-similar cracks in the plane is discussed. It is based on some known path-independent integrals whose forms make them suited for use in elastic fields showing expansional invariance. General integral formulas for the various segments of a chosen integration contour are presented and also applied. The integrals generally express the total energy release rate at self-similar growth, but for the expansion loaded star crack and the symmetrically cracked wedge opened by concentrated forces the stress intensity factors are obtained in closed form.

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Zusammenfassung Ein neues Verfahren der Berechnung von Spannungsintensitätsfaktoren zugehörig selbstähnlichen Riss-systemen in der Ebene wird diskutiert. Es beruht auf einigen bekannten wegunabhängigen Integralen, deren Formen sie in expansionsinvariablen elastischen Feldern anwendbar machen. Die allgemeinen Integralformeln der verschiedenen Abschnitte eines speziell gewählten Integrationsweges werden sowohl vorgezeigt als angewandt. Gewöhnlicherweise drücken die Integrale die totale Energiefreisetzung eines Rissystems bei selbstähnlichem Zuwachs aus. Für den expansionsbelasteten Sternriss und für den symmetrisch gespaltenen Keil, der von Punktkräften geöffnet wird, werden aber die Spannungsintensitätsfaktoren in abgeschlossener Form erhalten.

     

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