Abstract
In a recent work (Roy and Saha, 2000) analytical expression for weight function has been deduced for an elliptic crack under normal loading. The integral equation method developed earlier was used in conjunction with Jacobi's polynomials in solving the problem. In the present work the same method is used to solve the title problem. New results of weight function have been given for the first time for the case of an elliptic crack under shear loading. The analytical expressions for mode II and mode III weight functions given, can be used to evaluate mode II and mode III stress intensity factors for an elliptic crack under polynomial as well as non-polynomial loadings. Some examples have been cited as illustrations.
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References
Banks-Sills, L. and Makevet, E. (1996). A numerical mode I weight function for calculating stress intensity factors of three-dimensional cracked bodies. International Journal of Fracture 76, 169–191.
Besuner, P.M. (1976). Residual life estimates for structures with partial thickness cracks. in Mechanics of Crack Growth, ASTM STP 590, 403–419.
Borodachev, A.N. (1990). A method of constructing weighting functions for a circular crack. PMM Journal of Applied Mathematics and Mechanics 54, 841–848.
Bueckner, H.F. (1970). A novel principle for the computation of stress intensity factors. Z. Angew. Math. Mech. 50, 529–546.
Bueckner, H.F. (1973). Field singularities and related integral representations. in Mechanics of Fracture-1(Edited by G.C. Sih), Noordhoff-Leyden, The Netherlands, 239–319.
Bueckner, H.F. (1977). The weight functions of mode I of the penny shaped and of the elliptic crack. in Fracture Mechanics and Technology(Edited by G.C. Sih and C.L. Chow), Vol II, Sijthoff and Noordhoff, Leyden, 1069–1107.
Chatterjee, M. (1991). Three-dimensional crack and punch problems. Ph.D. Thesis, Calcutta University.
Gradshteyn, I.S. and Ryzhik, I.M. (1980). Tables of Integrals, Series and Products[corrected and enlarged edition. English translation: A. Jeffery (Editor)]. Academic Press, Orlando, Fl.
Kaptsov, A.V. and Shifrin, E.I. (1996). Analytical solution of the problem for elliptical crack in elastic medium. II. Statical, shear, polynomial load. Preprint 559. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow (in Russian).
Kassir, M.K. and Sih, G.C. (1975). Three dimensional crack problems. Noordhoff, Leiden, The Netherlands.
Kostrov, B.V. and Das, S. (1984). Evaluation of stress and displacement fields due to an elliptical plane shear crack. Geophysical Journal of Royal Astronomical Society 78, 19–33.
Martin, P.A. (1986). Orthogonal polynomial solutions for elliptical cracks under shear loadings. Quarterly Journal of Mechanics and Applied Mathematics 39, 519–534.
Nishioka, T. and Atluri, S.N. (1983). Analytical solution for embedded elliptical cracks, and finite element alternating method for elliptical surface cracks, subjected to arbitrary loadings. Engineering Fracture Mechanics 17, 247–268.
Nishioka, T. and Atluri, S.N. (1990). The first-order variation of the displacement field due to geometrical changes in an elliptical crack. ASME Journal of Applied Mechanics 57, 639–646.
Orynyak, I.V. and Borodii, M.V. (1995). Point weight function method application for semi-elliptical mode I cracks. International Journal of Fracture 70, 117–124.
Orynyak, I.V. (1998a). Method of translations for a mode I elliptic crack in an infinite body. Part I: Polynomial loading. International Journal of Solids and Structures 35, 3029–3042.
Orynyak, I.V. (1998b). Method of translations for a mode I elliptic crack in an infinite body. Part II: Expansion of the fundamental solution into a series. International Journal of Solids and Structures 35, 3043–3052.
Rice, J.R. (1972). Some remarks on elastic crack-tip stress fields. International Journal of Solids and Structures 8, 751–758.
Rice, J.R. (1989). Weight function theory for three-dimensional elastic crack analysis. In Fracture Mechanics: Perspectives and directions (Twentieth Symposium), ASTM STP 1020, American Society for Testing and Materials, Philadelphia, 29–57.
Roy, A. and Chatterjee, M. (1992). An elliptic crack in an elastic half-space. International Journal of Engineering Science 30, 879–890.
Roy, A. and Chatterjee, M. (1994). Interaction between coplanar elliptic cracks-I. Normal Loading. International Journal of Solids and Structures 31, 127–144.
Roy, A. and Saha, T.K. (2000).Weight function for an elliptic crack in an infinite medium. Part I-Normal loading. International Journal of Fracture. 103, 227–241.
Sham, T.L. and Zhou, Y. (1989). Computation of three-dimensional weight functions for circular and elliptical cracks. International Journal of Fracture 41, 51–75.
Shen, G. and Glinka, G. (1991). Weight functions for a surface semi-elliptical crack in a finite thickness plate. Theoretical and Applied Fracture Mechanics 15, 247–255.
Smith, F.W. and Sorensen, D.R. (1974). The elliptical crack subjected to non-uniform shear loading. ASME Journal of Applied Mechanics 41, 502–506.
Torgov, S.V. (1992). 3-D mixed mode elliptical crack analysis by local weight functions. International Journal of Fracture 57, R65–R73.
Vainshtok, V.A. and Varfolomeyev, I.V. (1990). Stress intensity factor analysis for part-elliptical cracks in structures. International Journal of Fracture 46, 1–24.
Vainshtok, V.A. (1992). 3-D stress intensity factor analysis by local weight functions. International Journal of Fracture 54, R33–R40.
Vijayakumar, K. and Atluri, S.N. (1981). An embedded elliptical flaw in an infinite solid, subject to arbitrary crack-face tractions. ASME Journal of Applied Mechanics 48, 88–96.
Zhou, Y. and Sham, T.L. (1992). Computation of shear mode weight function for circular and elliptical cracks. International Journal of Fracture 56, 111–138.
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Saha, T., Roy, A. Weight function for an elliptic crack in an infinite medium-II. – Shear loading . International Journal of Fracture 112, 1–21 (2001). https://doi.org/10.1023/A:1013527528837
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DOI: https://doi.org/10.1023/A:1013527528837