Abstract
Three-dimensional elasticity problems of plane tensile crack elongated along the plane curve are considered. The asymptotic solution of the problems is obtained by the method of outer and inner expansions applied directly to the two-dimensional integro-differential equation for the displacement of crack surface points. The formulae for crack opening and distribution of stress intensity factors are derived for various crack forms. Some estimates are found of the stress intensity factor in the small neighbourhoods of ends of the curve along which the crack extends and where the above mentioned asymptotic formulae don't hold. Comparison of obtained results with known analytical and numerical solutions demonstrates the high efficiency of our formulae.
Résumé
On considère les problèmes élastiques à trois dimensions caractérisant une fissure plane de traction s'étendant le long d'un plan. On obtient une solution asymptotiques en appliquant intégrodifférentielle à deux dimensions qui caractérise le déplacement des points de la surface de la fissure.
On déduit les formules d'ouvertures de la fissure et de distribution des facteurs d'intensité de contrainte, pour diverses formes de fissures. On établit une estimation du facteur d'intensité d'entaille dans le proche voisinage des extrémités de la courbe le long de laquelle s'étend la fissure, et où ne s'appliquent pas les formules asymptotiques décrites ci-dessus.
Une comparaison avec des résultats obtenus par des méthodes analytiques et numériques connues démontre que les formules proposées donnent entière satisfaction.
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References
V.V. Panasyuk, Limiting Equilibrium of Brittle Bodies with Cracks, Naukova Dumka, Kiev (1968).
R.V. Goldstein, Izvestiya AN SSSR, MTT, No. 3 (1979) 111–126.
R.V. Goldstein and V.M. Entov, Izvestiya AN SSSR, MTT, No. 3 (1975) 59–64.
V.S. Vladimirov, Generalized Functions in Mathematical Physics, Nauka, Moscow (1976).
J.R. Rice, in Fracture, Vol. 2, ed. by Liebowitz, Academic Press, New York and London (1968).
V.G. Maz'ya, S.A. Nazarov and V.A. Plamenevskiy, Asymptotic Solution of Elliptic Boundary Value Problems for Singular Perturbated Regions, Tbilisi University Press (1981).
J.J. Kalker, Journal of the Institute of Math. Applic. 19, No. 2 (1977) 127–144.
R.E. Johnson, Journal of Fluid Mechanics 99, Part 2 (1980) 411–431.
J.D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell Publishing Company, London (1968).
A.H. Nayfeh, Perturbation Methods, Wiley-Interscience, New York (1973).
B.I. Smetanin, PMM 32, No. 3 (1968) 458–462.
E.N. Mastrojannis and T.B. Vermandir, International Journal of Numerical Methods in Engineering 17, No 11 (1981) 1605–1611.
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Goldstein, R.V., Kaptsov, A.V. & Korelstein, L.B. Asymptotic solution of three-dimensional elasticity problems of elongated plane tensile cracks. Int J Fract 31, 83–104 (1986). https://doi.org/10.1007/BF00018916
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DOI: https://doi.org/10.1007/BF00018916