Analysis of a Crack Embedded in a Linear Elastic Half-Plane Solid

1995 ◽  
Vol 62 (1) ◽  
pp. 78-86 ◽  
Author(s):  
J. C. Sung ◽  
J. Y. Liou
Keyword(s):  
Stress Intensity ◽  
Half Plane ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Orthotropic Material ◽  
Singular Integral Equations ◽  
Kernel Functions ◽  
Intensity Factors ◽  
Material Parameters ◽  
Linear Elastic

A crack embedded in a half-plane solid traction-free on the infinite straight boundary is analyzed. The response of the material is linear elastic. A system of singular integral equations for the unknown dislocation densities defined on the crack faces is derived. These equations are then specialized to the problem of a crack located arbitrarily in an orthotropic material which are found to depend on two material parameters only. For a crack oriented either perpendicular or parallel to the infinite straight boundary, the kernel functions appearing in the singular integral equations are obtained in real form which are valid for arbitrary alignment of the orthotropic material. Furthermore, these kernel functions are found to be valid even for degenerate materials and can directly lead to those kernel functions for isotropic materials. Numerical results have been carried out for horizontal or vertical crack problems to elucidate the effect of material parameters on the stress intensity factors. The effect of the alignment of the material on the stress intensity factors is also presented for degenerate materials.

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 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 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.

The General Fracture Problem of a Functionally Graded Thermal Barrier Coating (TBC) Bonded to a Substrate

2004 ◽  
Author(s):  
F. Delale ◽  
X. Long
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Surface ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Thermal Barrier ◽  
Intensity Factors ◽  
Barrier Coating ◽  
Fgm Layer

In this paper we consider the general fracture problem of a functionally graded thermal barrier coating (TBC) bonded to a substrate. Functionally Graded Materials (FGMs) used in TBCs are usually made from ceramics and metals. Ceramics provide thermal and corrosion resistance while metals provide the necessary fracture toughness and heat conductivity. The volume fractions of the constituents will usually vary from 100% ceramic at the surface to 0% at the interface continuously providing seamless bonding with the metal substrate. To study the general fracture problem in the TBC we consider an arbitrarily oriented crack in an FGM layer bonded to a half plane. The elastic properties of the FGM layer are assumed to vary exponentially, while those of the half plane are homogeneous. The elastic properties are continuous at the interface. As shown in [1], then the governing elasticity equations become partial differential equations with constant coefficients. Using the transform technique, and defining the crack surface displacement derivatives as the unknown auxiliary functions, the mixed-mode crack problem is reduced to a system of Cauchy type singular integral equations. It is shown that at the crack tips the stresses still possess the regular square-root singularity, making it possible to use the classical definition of stress intensity factors. The singular integral equations are solved numerically using a Gaussian type quadrature and the mode I and mode II stress intensity factors are calculated for various crack lengths and crack orientations. Also the crack surface displacements are computed for different crack inclinations. It is observed that the crack orientation, crack length and the nonhomogeneity parameter affect the stress intensity factors significantly.

The Interaction of Collinear Arrays of Griffith Cracks on Two Radial Lines

1976 ◽  
Vol 98 (3) ◽  
pp. 1086-1091 ◽  
Author(s):  
O. Aksogan
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Mellin Transform ◽  
Singular Integral Equations ◽  
Graphical Form ◽  
Infinite Plane ◽  
Intensity Factors ◽  
Fundamental Function ◽  
Analytical Technique

The elastostatic plane problem of an isotropic homogeneous infinite plane with a number of Griffith cracks lying along two radial lines is considered. The analytical technique consists of the joint use of the Mellin transform and the Green’s function. The system of singular integral equations, thus obtained, is solved numerically taking advantage of the fact that the fundamental function is the weight function of the Chebyshev polynomials. The results for several cases are compared with those of previous authors. Stress intensity factors and probable directions of cleavage, which are important from the viewpoint of fracture mechanics, are studied in detail and illustrative numerical results for selected cases of geometry and loading are presented in graphical form.

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