The order of stress singularity near the vertex in three-dimensional joints

International Journal of Solids and Structures

Volumn 37, Issue 35, 2000, Pages 4737-4762

  Koguchi, Hideo ^a   Muramoto, Takashi ^a  

^a NAGAOKA UNIVERSITY OF TECHNOLOGY   (Japan)

Author keywords

Dundurs' parameters; Eigenequation; FEM; Stress singularity; Three dimensional joints

Indexed keywords

EID: 0012248049     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(99)00159-6     Document Type: Article

References (33)

1. Barsoum, R.S., 1988. Theoretical basis of the finite element iterative method for the eigenvalue problem in stationary cracks. Int. J. Numer. Methods Eng. 26, 531-539.
2. Bazant, Z.P., 1974. Three-dimensional harmonic functions near termination or intesection of gradient singularity lines: a general numerical method. Int. J. Engng Sci. 12, 221-243.
3. Bazant, Z.P., Estenssoro, L.F., 1979. Surface singularity and crack propagation. Int. J. Solid Structures 15, 405-426.
4. Bazant, Z.P., Kerr, L.M., 1974. Singularities of elastic stresses and of harmonic functions at conical notches and inclusions. Int. J. Solids Struct. 10, 957-964.
5. Benthem, J.P., 1977. State of stress at the vertex of a quarter-infinite crack in a half-space. Int. J. Solid Structures 13, 479-491.
6. Benthem, J.P., 1980. The quarter-infinite crack in a half space; alternative and additional solutions. Int. J. Solid Structures 16, 119-130.
7. Bogy, D.B., 1968. Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. 35, 460-466.
8. Bogy, D.B., 1970. On the problem of edge-bonded elastic quarter-planes at the boundary. Int. J. Solids and Struct. 6, 1287-1313.
9. Bogy, D.B., 1971a. Two-edge bonded elastic wedges of different materials and wedge angles under surface tractions-2. J. Appl. Mech. 38 (2), 377-386.
10. Bogy, D.B., 1971b. On the plane elastostatic problem of a loaded crack terminating at a material interface. J. Appl. Mech. 38, 911-918.
11. Cook, T.S., Erdogan, F., 1972. Stresses in bonded materials with a crack perpendicular to the interface. Int. J. Engng Sci. 10, 677-697.
12. Dempsey, J.P., Sinclair, G.B., 1979. On the stress singularities in the plane elasticity of the composite wedge. J. Elasticity 9 (4), 373-391.
13. Dundurs, J., 1969. Discussion of edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. 36, 650-652.
14. Fenner, D.N., 1976. Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface. Int. J. Fracture 12 (5), 705-721.
15. Ghahremani, F., Hutchinson, J.W., Tvergaard, V., 1990. Three-dimensional effects in microcrack nucleation in brittle polycrystals. J. Am. Ceram. Soc. 73 (6), 1548-1554.
16. Ghahremani, F., 1991. Numerical variational method for extracting 3D singularities. Int. J. Solids and Structures 27, 1371-1386.
17. Ghahremani, F., Shih, C.F., 1992. Corner singularity of three-dimensional planar interface cracks. J. Appl. Mech. 59, 61-68.
18. Hein, V.L., Erdogan, F., 1971. Stress singularities in a two-material wedge. Int. J. Fracture Mechanics 7 (3), 317-330.
19. Kerr, L.M., Parihar, K.S., 1977. Singularity at the vertex of pyramidal notches with three equal angles. Q. J. Appl. Math. 35, 401-405.
20. Kerr, L.M., Parihar, K.S., 1978. Elastic stress singularities at conical inclusions. Int. J. Solids Struct. 14, 261-263.
21. Koguchi, H., Hino, T., Kikuchi, Y., Yada, T., 1994. Residual stress analysis of joints of ceramics and metals. Experimental Mechanics 34, 116-124.
22. Koguchi, H., Inoue, T., Yada, T., 1995. Stress singularity in three-phase bonded structure. J. Appl. Mech. 63, 252-258.
23. Li, Y., Koguchi, H., Yada, T., 1992. Investigation of method of stress relaxation around the apex of ceramics-metal bonded structure (consideration of shape effect of apex in three dimensional dissimilar materials). Trans. Jpn. Soc. Mech. Eng. 58, 1417-1423.
24. Koguchi, H., 1997. Singularity analysis in three-dimensional bonded structure. Int. J. Solids Structures 34 (4), 461-480.
25. Nakamura, T., Parks, D.M., 1988. Three-dimensional stress field near the crack front of a thin elastic plate. J. Appl. Mech. 55, 805-813.
26. Pageau, S.S., Joseph, P.F., Biggers, S.B., 1994. The order of stress singularities for bonded and disbonded three-material junctions. Int. J. Solids and Struct. 31, 2979-2997.
27. Pageau, S.S., Biggers Jr, S.B., 1995. Finite element evaluation of free-edge singular stress fields in anisotropic materials. Int. J. Num. Method in Engineering 38, 2225-2239.
28. Picu, C.R., Gupta, V., 1997. Three-dimensional stress singularities at the tip of a grain triple junction line intersecting the free surface. J. Mech. Phys. Solids 45 (9), 1495-1520.
29. Rongved, L., 1955. Force interior to one of two joined semi-infinite solids. Second midwestern conference on solid mechanics. 1-13.
30. Somaratna, N., Ting, T.C., 1986. Three-dimensional stress singularities in anisotropic materials and composites. Int. J. Eng. Science 24, 1115-1134.
31. Theocaris, P.S., 1974. The order of singularity at a multi-wedge corner of a composite plate. Int. J. Eng. Science 12, 107-120.
32. Yamada, Y., Okumura, H., 1981. Analysis of local stress in composite materials by the 3-D finite element. In: Proceedings of the Japan-U.S. Conference, Tokyo, pp. 55-64.
33. Yang, Y.Y., Munz, D., 1994. Determination of the regular stress term in a dissimilar materials joint under thermal loading by the Mellin transform. J. Thermal Stresses 17, 321-336.