On the breaking of an embedded fibre in torsion

N. J. Freeman; L. M. Keer

doi:10.1016/0020-7225(71)90031-0

On the breaking of an embedded fibre in torsion

N. J. Freeman^*, L. M. Keer

^*Corresponding author for this work

Civil and Environmental Engineering

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The torsion of an infinite elastic circular cylindrical fibre, containing a penny-shaped crack, and embedded in an infinite elastic matrix, is considered. Using integral transform techniques the problem is reduced to the solution of a Fredholm integral equation of the second kind, provided the fibre remains unbroken. A solution to the Fredholm integral equation is obtained by iteration, and by direct numerical methods. Curves of the bond stress for various ratios of the crack radius to the radius of the fibre, and for different values of the elastic constants, are also given. Stress singularities of a fractional order are noted when the fibre is broken.

Original language	English (US)
Pages (from-to)	1007-1017
Number of pages	11
Journal	International Journal of Engineering Science
Volume	9
Issue number	10
DOIs	https://doi.org/10.1016/0020-7225(71)90031-0
State	Published - Oct 1971

ASJC Scopus subject areas

Materials Science(all)
Engineering(all)
Mechanics of Materials
Mechanical Engineering

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10.1016/0020-7225(71)90031-0

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abstract = "The torsion of an infinite elastic circular cylindrical fibre, containing a penny-shaped crack, and embedded in an infinite elastic matrix, is considered. Using integral transform techniques the problem is reduced to the solution of a Fredholm integral equation of the second kind, provided the fibre remains unbroken. A solution to the Fredholm integral equation is obtained by iteration, and by direct numerical methods. Curves of the bond stress for various ratios of the crack radius to the radius of the fibre, and for different values of the elastic constants, are also given. Stress singularities of a fractional order are noted when the fibre is broken.",

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year = "1971",

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AU - Freeman, N. J.

AU - Keer, L. M.

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N2 - The torsion of an infinite elastic circular cylindrical fibre, containing a penny-shaped crack, and embedded in an infinite elastic matrix, is considered. Using integral transform techniques the problem is reduced to the solution of a Fredholm integral equation of the second kind, provided the fibre remains unbroken. A solution to the Fredholm integral equation is obtained by iteration, and by direct numerical methods. Curves of the bond stress for various ratios of the crack radius to the radius of the fibre, and for different values of the elastic constants, are also given. Stress singularities of a fractional order are noted when the fibre is broken.

AB - The torsion of an infinite elastic circular cylindrical fibre, containing a penny-shaped crack, and embedded in an infinite elastic matrix, is considered. Using integral transform techniques the problem is reduced to the solution of a Fredholm integral equation of the second kind, provided the fibre remains unbroken. A solution to the Fredholm integral equation is obtained by iteration, and by direct numerical methods. Curves of the bond stress for various ratios of the crack radius to the radius of the fibre, and for different values of the elastic constants, are also given. Stress singularities of a fractional order are noted when the fibre is broken.

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ER -

On the breaking of an embedded fibre in torsion

Abstract

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