Circumferential Edge Crack in a Cylindrical Cavity

1977 ◽  
Vol 44 (2) ◽  
pp. 250-254 ◽  
Author(s):  
L. M. Keer ◽  
V. K. Luk ◽  
J. M. Freedman
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Cylindrical Cavity ◽  
Edge Crack ◽  
Numerical Scheme ◽  
Crack Opening ◽  
Integral Transforms ◽  
Intensity Factors ◽  
Physical Quantities ◽  
Elastostatic Problem

The elastostatic problem of a circumferential edge crack in a cylindrical cavity is investigated. The problem is formulated by means of integral transforms and reduced to a singular integral equation. The numerical scheme of Erdogan, Gupta, and Cook is used to obtain the relevant physical quantities and the stress-intensity factors, and crack opening displacements are computed for several values of crack length.

Stress Analysis for Bonded Layers

1974 ◽  
Vol 41 (3) ◽  
pp. 679-683 ◽  
Author(s):  
L. M. Keer
Keyword(s):  
Stress Intensity ◽  
Stress Analysis ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Numerical Scheme ◽  
Singular Integral Equations ◽  
Integral Transforms ◽  
Theory Of Elasticity ◽  
Intensity Factors ◽  
Plane Theory Of Elasticity

The problem of a line bond between two layers is solved by techniques appropriate to the plane theory of elasticity. Integral transforms are used to reduce the problem to singular integral equations. Numerical results are obtained for the case of identical layers and the numerical scheme of Erdogan and Gupta proved to be effective for this case. Stress-intensity factors and bond stresses for several types of loading are calculated.

Stress Intensity Factor of Peripheral Edge Crack around a Spherical Cavity under Internal Pressure Corrected

2011 ◽  
Vol 137 ◽  
pp. 77-81
Author(s):  
Shaofang Shi ◽  
Qi Zhi Wang ◽  
Ping Jun Li
Keyword(s):  
Stress Intensity ◽  
Internal Pressure ◽  
Spherical Cavity ◽  
Edge Crack ◽  
Integral Transforms ◽  
Intensity Factors ◽  
Singular Stress ◽  
Annular Crack ◽  
Triple Integral Equations ◽  
Special Cases

The singular stress problem of a flat annular crack around a spherical cavity subjected to internal pressure is investigated. By application of an integral transforms and the theory of triple integral equations, the problem is reduced to the solution of a singular integral equation of the first kind. The equations gotten for the case of peripheral edge crack around a spherical cavity is solved numerically, and the stress intensity factors are shown graphically. The results in this paper are basically consistent with the existing literature in special cases.

Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

1988 ◽  
Vol 110 (3) ◽  
pp. 408-413 ◽  
Author(s):  
L. J. Ghosn
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Roller Bearing ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

Experimental Determination of KI for Short Internal Cracks

2001 ◽  
Vol 68 (6) ◽  
pp. 937-943 ◽  
Author(s):  
K. Bearden ◽  
J. W. Dally ◽  
R. J. Sanford
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Edge Crack ◽  
Series Solution ◽  
Experimental Studies ◽  
Experimental Methods ◽  
Internal Crack ◽  
Intensity Factors ◽  
Mode Stress

Since the pioneering discussion by Irwin, a significant effort has been devoted to determining stress intensity factors (K) using experimental methods. Techniques have been developed to determine stress intensity factors from photoelastic, strain gage, caustics, and moire´ data. All of these methods apply to a relatively long single-ended-edge crack. To date, the determination of K for internal cracks that are double-ended by experimental methods has not been addressed. This paper describes a photoelastic study of tension panels with both central and eccentric internal cracks. The data recorded in the experiments was analyzed using a new series solution for the opening-mode stress intensity factor for an internal crack. The data was also analyzed using the edge-crack series solution, which is currently employed in experimental studies. Results indicated that the experimental methods usually provided results accurate to within three to five percent if the series solution for the internal crack was employed in an overdeterministic numerical analysis of the data. Comparison of experimental results using the new series for the internal crack and the series for an edge crack showed the superiority of the new series.

Edge Crack in an Elastic Strip on a Liquid Foundation

1989 ◽  
Vol 33 (03) ◽  
pp. 214-220
Author(s):  
Paul C. Xirouchakis ◽  
George N. Makrakis
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Fourier Transform ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Edge Crack ◽  
Applied Pressure ◽  
Theory Of Elasticity ◽  
Elastic Strip ◽  
Pressure Loading

The behavior of a long elastic strip with an edge crack resting on a liquid foundation is investigated. The faces of the crack are opened by an applied pressure loading. The deformation of the strip is considered within the framework of the linear theory of elasticity assuming plane-stress conditions. Fourier transform techniques are employed to obtain integral expressions for the stresses and displacements. The boundary-value problem is reduced to the solution of a Fredholm integral equation of the second kind. For the particular case of linear pressure loading, the stress-intensity factor is calculated and its dependence is shown on the depth of the crack relative to the thickness of the strip. Application of the present results to the problem of flexure of floating ice strips is discussed.

scholarly journals Interaction between line cracks in an orthotropic layer

2002 ◽  
Vol 29 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Subir Das
Keyword(s):  
Fourier Transform ◽  
Stress Intensity ◽  
Finite Thickness ◽  
Intensity Factors ◽  
Orthotropic Layer ◽  
Finite Hilbert Transform ◽  
Crack Tips ◽  
The Fourier Transform ◽  
Analytical Expressions ◽  
Elastostatic Problem

We deal with the interaction between three coplanar Griffith cracks located symmetrically in the mid plane of an orthotropic layer of finite thickness2h. The Fourier transform technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have been solved by using the finite Hilbert transform technique and Cooke's result. The analytical expressions for the stress intensity factors at the crack tips are obtained for largeh. Numerical values of the interaction effect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to each other and crack tip spacing as well as the thickness of the layer.

The Axisymmetric Crack Problem in a Nonhomogeneous Medium

1993 ◽  
Vol 60 (2) ◽  
pp. 406-413 ◽  
Author(s):  
M. Ozturk ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Shear Modulus ◽  
Mixed Mode ◽  
Crack Opening ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Nonhomogeneous Medium ◽  
Intensity Factors ◽  
Simple Simulation ◽  
Graded Properties

In this paper, the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by μ = μ0eαz. This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed-mode problem and is formualated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a function of the nonhomogeneity parameter a for various loading conditions. Also given are some sample results showing the crack opening displacements.

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