Stress Distributions for a Quarter Plane Containing an Arbitrarily Oriented Crack

1983 ◽  
Vol 50 (1) ◽  
pp. 43-49 ◽  
Author(s):  
L. M. Keer ◽  
J. C. Lee ◽  
T. Mura
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Integral Transforms ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Quarter Plane ◽  
Dislocation Densities ◽  
Arbitrarily Oriented Crack

A solution for an elastic quarter plane containing an arbitrarily oriented crack is presented. The problem is formulated by means of Mellin integral transforms and reduced to a system of two coupled singular integral equations where the unknown quantities are the dislocation densities that characterize the crack. Numerical solutions are investigated for various orientations of the cracks. In each case the stress intensity factors are computed for the different parameters.

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.

A Semi-Infinite Elastic Strip Bonded to an Infinite Strip

1980 ◽  
Vol 47 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Shear Stress ◽  
Stress Intensity ◽  
Singular Integral ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Infinite Strip ◽  
Elastic Strip ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Concentrated Forces

The solution is obtained for the plane strain problem of a semi-infinite elastic strip whose end is bonded to and pressed against an infinite elastic strip. The infinite strip is supported by a pair of symmetrically located, concentrated forces. Using integral transform techniques, the solution is reduced to a set of singular integral equations of the second kind. The order of the singularity is determined and the equations are then solved numerically. The results show the normal and shear stress distributions as well as the stress-intensity factors for a range of support locations corresponding to various width ratios and material combinations.

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 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.

Determination of Stress Intensity Factors for Partial Penetration Axial Cracks in Thin-Walled Cylinders

1986 ◽  
Vol 108 (2) ◽  
pp. 83-86 ◽  
Author(s):  
Weili Cheng ◽  
Iain Finnie
Keyword(s):  
Stress Intensity ◽  
Hoop Stress ◽  
Numerical Solutions ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Axial Crack ◽  
Thin Walled ◽  
Walled Cylinder ◽  
Good Agreement

An approach based on the use of rotation and displacement solutions for a cracked element in plane strain is used to obtain the stress intensity factor for a long axial crack in a thin-walled cylinder. The hoop stress distribution in the cylinder prior to introduction of the crack is arbitrary. Results obtained with this approach are in good agreement with numerical solutions for several hoop stress distributions.

Mode-III Stress Intensity Factors of an Arbitrarily Oriented Crack Crossing Interface in a Layered Structure

2013 ◽  
Vol 29 (4) ◽  
pp. 643-651 ◽  
Author(s):  
C. K. Chao ◽  
L. M. Lu
Keyword(s):  
Stress Intensity ◽  
Layered Structure ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
Linear Interpolation ◽  
Plane Elasticity ◽  
Intensity Factors ◽  
Mode Iii ◽  
Line Segments ◽  
Arbitrarily Oriented Crack

ABSTRACTThe problem of a layered structure containing an arbitrarily oriented crack crossing the interface in anti-plane elasticity is considered in this paper. The fundamental solution of displacements and stresses is obtained in a series form via the method of analytical continuation in conjunction with the alternating technique. A dislocation distribution along the prospective site of a crack is used to model a crack crossing the interface and the singular integral equations with logarithmic singular kernels for a line crack are then established. The crack is approximated by several line segments and the linear interpolation equation with undetermined coefficients was applied for the dislocation function along line segments. Once the undetermined dislocation coefficients are solved, the mode-III stress intensity factors KIII at two crack tips can be obtained for various crack inclinations with different material property combinations. All the numerical results are checked to achieve a good approximation that demonstrates the accuracy and the efficiency of the proposed method.

Bonded Half-Planes Containing Two Arbitrarily Oriented Cracks: A Study of Containment of Hydraulically Induced Fractures

1985 ◽  
Vol 25 (01) ◽  
pp. 55-66 ◽  
Author(s):  
Chien-Ke Lu ◽  
Ching H. Yew
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plane Strain ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Strain Condition ◽  
Intensity Factors ◽  
Chebyshev Method

Abstract In the first part of this paper, the title subject is studied by introducing two modified singular integrals. The problem is reduced to a set of singular integral equations; and problem is reduced to a set of singular integral equations; and it is solved numerically by employing the Lobatto-Chebyshev method. The stress intensity factor at the fracture tips of a hydraulically induced fracture in a layered medium is calculated in the second part of the paper. The effect of the fluid pressure and the in-situ stress gradient as well as the effect of the relative layer material properties on the magnitude of the stress intensity factors are properties on the magnitude of the stress intensity factors are studied numerically. It has been shown that the relative magnitude of the stress intensity factor at the fracture tips can he used to indicate the direction of fracture movement. Introduction Extensive analyses of bonded half-planes containing cracks have been conducted by many authors. In general, there are two approaches to this problem. In the first approach, the Mellin transform is applied to the field equations. This leads to a set of integral equations, which, in turn, are solved numerically. Erdogan and Biricikoglu, Cook and Erdogan, Ashbaugh, and Erdogan and Aksogan have used this method in their analyses of stresses in the bonded planes containing straight cracks. In the other approach, the same problem is studied by employing the complex potential function of Kolosov and Muskhelishvili. For a general discussion of this method, see Refs. 5 through 9. By using this method, the general problem of a half-plane containing a system of curvilinear problem of a half-plane containing a system of curvilinear cracks is solved by Ioakimidis and Theocaris. The associated boundary value problem is deduced to a system of complex singular integral equations, which then are solved numerically by applying the Lobatto-Chebyshev method. In this paper, the problem is studied by using a method very similar to that developed in Ref. 10, However, since we are studying the propagation of a hydraulically induced fracture in a layered rock medium, the loading condition of our problem is different from that previously cited. In our formulation, the cracks are subject to different distributions of internal loadings. As demonstrated later, although our method is, in principle, similar to that reported in Refs. 10 and 11, it differs in many ways. Our method is suitable forsolving the problems of two cracks situated in two different half-planes and oriented at an arbitrary angle with respect to one another andstudying the problems pertaining to the environment of hydraulic fracturing. It also should be mentioned here that the method used in this study is an extension of the method developed by Lu in his study of a plane problem of many cracks and the problem of a partially bonded plate. In our analysis of the problem, the plane of the fracture is assumed to be in a condition of plane strain. In view of the order of magnitude differences between the fracture length, height, and width of a hydraulically induced fracture, we believe that this assumption is acceptable except, perhaps, at a very early stage of fracturing. The general problem of two bonded half-planes containing many cracks of arbitrary shapes is considered first. The problem then is reduced to a case of two arbitrarily oriented straight cracks. The solution is carried out in full. Numerical values of the stress intensity factor at the fracture tips pertaining to the containment of a hydraulically induced fracture are presented and discussed at the end of the paper. Formulation of the Problem In the following derivations, we follow the notations in Ref. 15; for completeness and clarity, some obvious results are listed without further referencing. Throughout the paper, we use the superscripts phi (x) and psi (x) for x epsilon X (along the interface); the subscripts phi (s) and psi (s) for s epsilon L (along cracks); and zeta epsilon L+X; x, xi epsilon X; and s, L in integrals. Consider an elastic plane (under either plane stress or plane strain condition) made by bonding together two plane strain condition) made by bonding together two planes of different materials, where k +, G+ and k -, planes of different materials, where k +, G+ and k -, G - are the material constants for the upper (Z + ) and the lower (Z-) plane, respectively. Let there be p nonintersecting smooth cracks. Lj =ajbj (j=1..... p) on both these half-planes. Let the intensity (force/unit length) of the external load applied on the surface of crack Lj be Xj (s) + i Yj (s), where s is the complex coordinate of a point on Lj. SPEJ P. 55

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.

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