Stresses in bonded materials with a crack perpendicular to the interface

Cook, T. S.; Erdoğan, F.

doi:10.1016/0020-7225(72)90063-8

Cited by 513 publications

(222 citation statements)

References 21 publications

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“…Zak and Williams (1963) used the eigenfunction expansion method to analyze the stress singularity at the tip of a crack, perpendicular to and terminating at the interface. Cook and Erdogan (1972) used the Mellin transform method to derive the governing equation of finite cracks perpendicular to an interface and obtained the stress intensity factors. Erdogan and Biricikoglu (1973) solved the problem of two International Journal of Solids and Structures 40 (2003) www.elsevier.com/locate/ijsolstr bounded half planes with a crack going through the interface.…”

Section: Introductionmentioning

confidence: 99%

A crack perpendicular to the bimaterial interface in finite solid

Chen

Wang

Kao-Walter

2003

International Journal of Solids and Structures

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The dislocation simulation method is used in this paper to derive the basic equations for a crack perpendicular to the bimaterial interface in a finite solid. The complete solutions to the problem, including the T stress and the stress intensity factors are obtained. The stress field characteristics are investigated in detail. It is found that when the crack is within a weaker material, the stress intensity factor is smaller than that in a homogeneous material and it decreases when the distance between the crack tip and interface decreases. When the crack is within a stiffer material, the stress intensity factor is larger than that in a homogeneous material and it increases when the distance between the crack tip and interface decreases. In both cases, the stress intensity factor will increase when the ratio of the size of a sample to the crack length decreases. A comparison of stress intensity factors between a finite problem and an infinite problem has been given also. The stress distribution ahead of the crack tip, which is near the interface, is shown in details and the T stress effect is considered.

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Section: Introductionmentioning

confidence: 99%

A crack perpendicular to the bimaterial interface in finite solid

Chen

Wang

Kao-Walter

2003

International Journal of Solids and Structures

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“…Formulation of this problem is straightforward. For example, referring to (28] where and coupling will be through Fredholm type kernels only.…”

Section: Integral Equations With Generalized Cauchy Kernelsmentioning

confidence: 99%

“…Description of such techniques also falls outside the scope of this article. Among thesê a one may mention the methods usedto evaluate such physical quantities as the stress intensity factors, the strain energy release rate, and the crack 91 opening displacement directly in terms of the (calculated) density functions of the integral equations (see, for example, [28] , [29] , [311- [34]). …”

Section: The Fundamental Functions Mmentioning

confidence: 99%

Mixed Boundary-value Problems in Mechanics

1978

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“…The integrals in (5) and (8) are to be interpreted in Cauchy principal value and Hadamard sense, respectively [5]. The integral equation can also be obtained by using w(t) rather than ip(t) as the unknown function and, for example, following the procedure outlined in [6], It may be noted that in terms of w some of the stress components of physical interest may be expressed aŝ…”

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confidence: 99%

“…Once the integral equation is solved, in this problem too all the desired field quantities may be expressed in terms of v(t) and the corresponding kernels. For example, the cleavage stresses along the planes 0 = 0,# = it/2, and 6 = tt may be written as [8] <W'.° )-^r ( …”

mentioning

confidence: 99%

On the solution of integral equations with a generalized Cauchy kernel

Kaya

1987

Quart. Appl. Math.

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Abstract. In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t -x)~2, x"~2(t + x)" (n > 2,0 < x, t < b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

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Stresses in bonded materials with a crack perpendicular to the interface

Cited by 513 publications

References 21 publications

A crack perpendicular to the bimaterial interface in finite solid

A crack perpendicular to the bimaterial interface in finite solid

Mixed Boundary-value Problems in Mechanics

On the solution of integral equations with a generalized Cauchy kernel

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