Crack Problem for a Semi-Infinite Solid With Heated Bounding Surface

1977 ◽  
Vol 44 (4) ◽  
pp. 637-642 ◽  
Author(s):  
H. Sekine
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Thermal Stresses ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Intensity Factors ◽  
Bounding Surface ◽  
Edge Dislocations

On the basis of the stationary two-dimensional theory of thermoelasticity, the thermal stresses near the tips of a thermally insulated line crack situated in a semi-infinite solid which is heated on a part of the bounding surface is considered. The crack is replaced by continuous distributions of temperature dislocations and edge dislocations. Then the integral equations are obtained as a system of singular integral equations with Cauchy kernels. By means of this method, the singular behavior of the thermal stresses around the crack tips is easily examined and the stress-intensity factors can be readily evaluated. Numerical results for the stress-intensity factors are plotted in terms of the geometrical parameters.

Stress Analysis for a Double Lap Joint

1975 ◽  
Vol 42 (2) ◽  
pp. 353-357 ◽  
Author(s):  
L. M. Keer ◽  
K. Chantaramungkorn
Keyword(s):  
Stress Intensity ◽  
Stress Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Lap Joint ◽  
Intensity Factors

The problem of a double lap joint is analyzed and solved by using integral transform techniques. Singular integral equations are deduced from integral transform solutions using boundary and continuity conditions appropriate to the problem. Numerical results are obtained for the case of identical materials for the cover and central layers. Stress-intensity factors are calculated and presented in the form of a table and contact stresses are shown in the form of curves for various values of geometrical parameters.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 2: Fully Anisotropic Materials

1984 ◽  
Vol 51 (4) ◽  
pp. 780-786 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Mathematical Problem ◽  
Stress Singularity ◽  
Interfacial Crack ◽  
Singular Integral Equations ◽  
Intensity Factors

Dynamic stress intensity factors for an interfacial crack between two dissimilar elastic, fully anisotropic media are studied. The mathematical problem is reduced to three coupled singular integral equations. Using Jacobi polynomials, solutions to the singular integral equations are obtained numerically. The orders of stress singularity and stress intensity factors of an interfacial crack in a (θ(1)/θ(2)) composite solid agree well with the finite element solutions.

Stress Intensity Factors for Fully Interacting Cracks in a Multicrack Solid

1994 ◽  
Vol 116 (2) ◽  
pp. 56-63 ◽  
Author(s):  
W. K. Binienda
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Damage Growth ◽  
Intensity Factors ◽  
Rigorous Solution ◽  
Damage State ◽  
Perturbation Problem ◽  
Solution Formulation

An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF). Here, a methodology and rigorous solution formulation for SIF of a multicracked plate, with fully interacting cracks, subjected to a far-field arbitrary stress state is presented. The fundamental perturbation problem is derived, and the steps needed to formulate the system of singular integral equations whose solution gives rise to the evaluation of the SIF are identified. This analytical derivation and numerical solution are obtained by using intelligent application of symbolic computations and automatic FORTRAN generation capabilities in form of symbolic/FORTRAN package, named SYMFRAC, that is capable of providing accurate SIF at each crack tip. The accuracy of the results has been validated for the two parallel interacting crack problem. Limits and sensitivity of the results for the problem of a horizontal notch interacting with ten microcracks have been analyzed.

Stress-Intensity Factors for Very Short Cracks in Arbitrary Pressurized Shells

1976 ◽  
Vol 43 (4) ◽  
pp. 657-662 ◽  
Author(s):  
J. G. Simmonds ◽  
M. R. Bradley
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fourier Transforms ◽  
Cylindrical Shells ◽  
Singular Integral Equations ◽  
Intensity Factors ◽  
Isotropic Shell ◽  
Curvature Effects ◽  
In Series

A pressurized, shallow, elastically isotropic shell containing a crack is considered. The crack is assumed to lie along a line of curvature of the midsurface. The equations governing the essentially equivalent residual problem, in which the only external load is a uniform normal stress along the faces of the crack, are reduced via Fourier transforms to two coupled singular integral equations. The solutions of these equations depend on three parameters: λ, a dimensionless crack length, κ, the dimensionless Gaussian curvature of the midsurface at the center of the crack, and ν, Poisson’s ratio. Perturbation solutions for small values of λ are obtained by expanding the kernels of the integral equations in series. Explicit formulas for stretching and bending stress-intensity factors are obtained. These represent the first-order corrections due to curvature effects of the well-known flat plate results. The connection with the work of Copley and Sanders for cylindrical shells and Folias for spherical and cylindrical shells is indicated.

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