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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, R. C.. (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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Official URL: http://dx.doi.org/10.1016/S0020-7683(99)00061-X
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 |
| 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: | Abramovitz, M., Stegun, I.E., 1972. Handbook of Mathematical Functions. Dover. Al-Falou, A.A., Ball, R.C., 2000. Crack propagation in heterogeneous media. Int. J. Solids and Structures 37, 461±475. Ball, R.C., Larralde, H., 1995. Linear stability analysis of planar straight cracks propagating quasistatically under type I loading. Int. J. Fract. 71, 365±377. Bueckner, H.F., 1970. A novel principle for the computation of stress intensity factors. Zeitschrift f. Angewandte Mathematik u. Mechanik 50, 529±546. Bueckner, H.F., 1987. Weight functions and fundamental ®elds for the penny-shaped and the half-plane crack in three-space. Int. J. Solids and Structures 23 (1), 57±93. Ciarlet, P.G., 1993. Mathematical Elasticity, Three Dimensional Elasticity, vol. I. North±Holland. Freund, L.B., 1990. Dynamic Fracture Mechanics. Cambridge University Press. Lawn, B., 1993. Fracture of Brittle Solids. Cambridge University Press. Mushkelishvili, N.I., 1963. Some Basic Problems of the Mathematical Theory of Elasticity. Noordho�, Groningen. Rice, J.R., 1972. Some remarks on elastic crack-tip stress ®elds. Int. J. Solids Structures 8, 751±758. Sih, G.C., 1973. Handbook of Stress Intensity Factors. Lehigh University, Bethlehem Pennsylvania, 3.2.7±1. Willis, J.R., Movchan, A.B., 1995. Dynamic weight functions for a moving crack. I. Mode I loading. J. Mech. Phys. Solids 43 (3), 319±341. Wolfram Research, 1995. Mathematica, version 2.2.3 for Unix. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/13241 |
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