Closed form solutions for a finite length crack moving in an orthotropic layer of finite thickness

Danyluk, H. T.; Singh, Brij Mohan

doi:10.1016/0020-7225(84)90069-7

Cited by 7 publications

(9 citation statements)

References 4 publications

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“…Assuming w3 = -cr, x2) and introducing the transformation Applying the same method as in [1,2], the problem (3.1) reduces to a half-plane boundary value problem, solved by the Keldish-Sedov technique [3] For an orthotropic material, Eqs. (4.4) and (4.5) are in agreement with those obtained in [5], apart from the additional constant term in (4.4). This disagreement probably arises from the fact that the superposition principle was not applied in [5], The isotropic case is recovered as in [4] with the same comment.…”

Section: Qesupporting

confidence: 88%

“…(4.4) and (4.5) are in agreement with those obtained in [5], apart from the additional constant term in (4.4). This disagreement probably arises from the fact that the superposition principle was not applied in [5], The isotropic case is recovered as in [4] with the same comment.…”

Section: Qesupporting

confidence: 87%

“…After transformation of the basic equations, the complex variable approach is used to obtain closed-form expressions for the stress field as well as the stress intensity factors at the crack tip. The results obtained in [4,5] are recovered as particular cases.…”

mentioning

confidence: 92%

“…Both problems have been reduced to half-plane boundary value problems, solved by the Keldysh-Sedov method as explained in [3]. This kind of problem has also been studied in [4] by an integral transform technique and recently extended in [5] to an orthotropic layer. …”

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confidence: 99%

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Elastodynamic crack problems in an anisotropic medium through a complex variable approach

Piva¹

1986

Quart. Appl. Math.

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Abstract. The complex variable approach is used to obtain closed-form solutions to elastodynamic crack problems in a strip of anisotropic elastic medium, with one plane of symmetry, under antiplane shear stress. The two problems examined involve a finite-length crack propagating in an infinitely long strip of finite width when the edges are subjected either to constant displacements or shearing stresses. The special cases corresponding to either an orthotropic medium or an isotropic medium are recovered.1. Introduction. In recent papers [1, 2], the complex variable approach has been used to obtain closed-form solutions to elastodynamic crack problems in a homogeneous and isotropic elastic strip under antiplane shear stress.The problems analyzed are the classical ones of a finite-length crack moving at constant velocity in an infinitely long strip of finite width with the lateral boundaries subjected to either displacements or shearing stresses. Both problems have been reduced to half-plane boundary value problems, solved by the Keldysh-Sedov method as explained in [3]. This kind of problem has also been studied in [4] by an integral transform technique and recently extended in [5] to an orthotropic layer.

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Section: Qesupporting

confidence: 88%

Section: Qesupporting

confidence: 87%

mentioning

confidence: 92%

mentioning

confidence: 99%

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Elastodynamic crack problems in an anisotropic medium through a complex variable approach

Piva¹

1986

Quart. Appl. Math.

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“…Kassir and Tse [14] used an integral transform method to solve the plane problem of a steadily moving Griffith crack in an orthotropic medium. Danyluk and Singh [15] applied the same technique to obtain closed-form solutions to antiplane problems of a crack moving in an orthotropic layer.…”

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confidence: 99%

An alternative approach to elastodynamic crack problems in an orthotropic medium

Piva¹

1987

Quart. Appl. Math.

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Abstract. A similarity transformation is used to reduce the system of second-order equations, governing elastodynamic plane problems in an orthotropic medium, to a first-order elliptic system of the Cauchy-Riemann type. A complex variable notation is then introduced to derive in a straightforward way the solution of two noticeable elastodynamic crack problems.1. Introduction. The problem of determining the stress field induced by a steadily propagating crack in a two-dimensional elastic medium is of primary interest in fracture mechanics. A great many results have been obtained for isotropic materials, and dutiful mention is made to the more significant analytical studies.Yoffe [1] discussed the plane problem of a crack of constant length moving with constant speed in an isotropic medium stressed at infinity. The same problem was solved later by Radok [2] who used a complex variable method.Craggs [3] considered the shape of a semi-infinite crack loaded over a segment of its edges. In solving the related boundary value problem, he used Cauchy's integral representation which, however, does not permit one to determine analytically the singular terms of the solution.

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On a moving Griffith crack in anisotropic piezoelectric solids

Soh

Liu²,

Lee

et al. 2002

Archive of Applied Mechanics (Ingenieur Archiv)

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The generalized plane problem of a finite Griffith crack moving with constant velocity in an anisotropic piezoelectric material is investigated. The combined mechanical and electrical loads are applied at infinity. Based on the extended Stroh formalism, the closed-form expressions for the electroelastic fields are obtained in a concise way. Numerical results for PZT-4 piezoelectric ceramic are given graphically. The effects on the hoop stress of the velocity of the crack and the electrical to mechanical load ratios are analyzed. The propagation orientation of a moving crack is also predicted in terms of the criterion of the maximum tensile stress. When the crack speed vanishes, the results of the present paper are in good agreement with those given previously in the literature.

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Closed form solutions for a finite length crack moving in an orthotropic layer of finite thickness

Cited by 7 publications

References 4 publications

Elastodynamic crack problems in an anisotropic medium through a complex variable approach

Elastodynamic crack problems in an anisotropic medium through a complex variable approach

An alternative approach to elastodynamic crack problems in an orthotropic medium

On a moving Griffith crack in anisotropic piezoelectric solids

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