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The 3-D weight functions for a quasi-static planar crack

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Al-Falou, A. A. and Ball, Robin. (2000) The 3-D weight functions for a quasi-static planar crack. International Journal of Solids and Structures, Vol.37 (No.37). pp. 5079-5096. ISSN 0020-7683

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Abstract

We explicitly evaluate the 3-D weight functions for a planar crack in an isotropic, homogeneous material; these give the full stress intensity factors induced by a static point force applied at an arbitrary position. If we Fourier decompose the 3-D weight functions with respect to the z variable then each Fourier mode satisfies the homogeneous equations of elasticity (except at the crack tip) and the boundary conditions on the crack face. Each Fourier mode diverges like r(-1/2) near the crack tip and decays exponentially for non-zero k(z). It is proved that these necessary conditions, which hold everywhere in the elastic material excluding the crack tip, are also sufficient to determine the 3-D weight functions. In particular, the 3-D weight functions can be calculated without considering an explicit loading problem. (C) 2000 Elsevier Science Ltd. All rights reserved.

Item Type: Journal Article
Subjects: Q Science > QC Physics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Faculty of Science > Physics
Library of Congress Subject Headings (LCSH): Fracture mechanics
Journal or Publication Title: International Journal of Solids and Structures
Publisher: Pergamon
ISSN: 0020-7683
Official Date: September 2000
Volume: Vol.37
Number: No.37
Number of Pages: 18
Page Range: pp. 5079-5096
Identification Number: 10.1016/S0020-7683(99)00061-X
Status: Peer Reviewed
Publication Status: Published
References:

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URI: http://wrap.warwick.ac.uk/id/eprint/13241

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