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. doi:10.1016/S0020-7683(99)00061-X

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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, Engineering and Medicine > 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
Dates:	Date Event September 2000 Published
Volume:	Vol.37
Number:	No.37
Number of Pages:	18
Page Range:	pp. 5079-5096
DOI:	10.1016/S0020-7683(99)00061-X
Status:	Peer Reviewed
Publication Status:	Published

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