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

✍ Scribed by A.A. Al-Falou; R.C. Ball

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 245 KB
Volume: 37
Category: Article
ISSN: 0020-7683
DOI: 10.1016/s0020-7683(99)00061-x

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✦ Synopsis

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 satis®es the homogeneous equations of elasticity (except at the crack tip) and the boundary conditions on the crack face. Each Fourier mode diverges like r À1/2 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 sucient to determine the 3-D weight functions. In particular, the 3-D weight functions can be calculated without considering an explicit loading problem.

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