Diffraction of a plane longitudinal wave by a penny-shaped crack

Robertson, Ian

doi:10.1017/s0305004100041116

Cited by 47 publications

(24 citation statements)

References 4 publications

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“…From this it follows that the crack faces would never make contact during vibration if we superpose on our solution the solution due to a static constant pressure pU) applied on the crack,, because this pressure gives rise to the following displacement at the crack faces [10]:…”

Section: Introductionmentioning

confidence: 99%

Diffraction of a plane shear elastic wave by a circular rigid disk and a penny-shaped crack

Jain¹,

Kanwal²

1972

Quart. Appl. Math.

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Introduction.Diffraction of P-waves by disk-shaped obstacles and cracks embedded in a homogeneous and isotropic elastic medium has recently been given considerable attention. A bibliography of this subject is given in [1]. The corresponding problems of diffraction of S-waves are also of considerable interest in seismology and geophysics. Knowledge of the modification of S-waves in the vicinity of a crack is helpful in predicting the nature of flaws in the material. The dynamic stress intensity factors in the vicinity of a crack also help in predicting the fracture and failure of the material. Furthermore, the observation of diffraction pattern of S-waves generated by earthquakes or explosions reveal the presence of inhomogeneities and structural discontinuities in the medium. However, this problem has not received much attention. The main difficulty is that diffraction of S-waves leads to an asymmetric boundary value problem which is rather difficult to solve.We present here the solution of the problem of diffraction of a plane S-wave for two cases. In the first case we discuss diffraction of S-waves by a rigid circular disk which is embedded in an infinite homogeneous and isotropic elastic medium. In the second case we analyze the corresponding problem of diffraction of a plane S-wave by a penny-shaped crack. It is assumed that the two faces of the crack are separated by a small distance so that they do not come into contact during vibration. The incident S-wave is assumed to be time-harmonic and is polarized in planes perpendicular to those of the disk and the crack. Furthermore, it is assumed to propagate along their axes of

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Section: Introductionmentioning

confidence: 99%

Diffraction of a plane shear elastic wave by a circular rigid disk and a penny-shaped crack

Jain¹,

Kanwal²

1972

Quart. Appl. Math.

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“…In recent years a number of such problems have been studied. Robertson [2], Mal [3,4,5,6,7], Sih and Leober [8] have studied the diffraction of longitudinal and torsional waves which are normally incident on the crack surface. All these attempts have been based on the assumption that the crack is sufficiently far away from the neighbouring boundaries, and hence the distribution of stresses in the solid is attributed to crack geometry or to the wave frequency of the elastic waves.…”

Section: Introductionmentioning

confidence: 99%

Interaction of elastic waves with a penny-shaped crack in an infinitely long cylinder

1982

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This paper contains an analysis of the interaction of longitudinal waves with a penny-shaped crack located in an infinitely long elastic cyclinder. The problem is reduced to a Fredholm integral equation of the second kind which is solved numerically for a range of values of the frequency of the incident waves and the radius of the cylinder. Numerical values of the dynamic stress intensity factor at the rim of the crack have been calculated.

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“…(4) can be simplified by using the techniques of contour integration [1,5,6]. The results after integration are written in the following form:…”

Section: Formal Solutionmentioning

confidence: 99%

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confidence: 99%

Interactive Diffraction of a Plane Longitudinal Wave by a Pair of Coplanar Central Cracks in an Elastic Solid

Tsai

1987

Review of Progress in Quantitative Nondestructive Evaluation

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The problem of the diffraction of a plane longitudinal wave by a penny-shaped crack has been solved using the techniques of Hankel transforms [1]. The interaction of elastic waves with a Griffith crack has been investigated for a range of values of the wave frequency [2]. More recently, approximate formulas have been derived for the problem of diffraction of elastic waves by two coplanar Griffith cracks in an infinite elastic medium [3].The scattering of a plane longitudinal wave at a pair of coplanar central cracks in an elastic solid is investigated in the present work. The wave is harmonic in time, impinging normally on the crack surfaces, which are assumed to remain separated dur ing small deformations of the solid. The interaction between the cracks affects not only the scattering of the wave, but also the severity of the cracks.

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Diffraction of a plane longitudinal wave by a penny-shaped crack

Cited by 47 publications

References 4 publications

Diffraction of a plane shear elastic wave by a circular rigid disk and a penny-shaped crack

Diffraction of a plane shear elastic wave by a circular rigid disk and a penny-shaped crack

Interaction of elastic waves with a penny-shaped crack in an infinitely long cylinder

Interactive Diffraction of a Plane Longitudinal Wave by a Pair of Coplanar Central Cracks in an Elastic Solid

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