Three-dimensional stress singularities at the tip of a grain triple junction line intersecting the free surface

Journal of the Mechanics and Physics of Solids

Volumn 45, Issue 9, 1997, Pages 1495-1520

  Picu, Catalin R ^a,b   Gupta, Vijay ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Brown University   (United States)

Author keywords

A. Crack nucleation; A. Microstructures; A. Stress concentration; C. Finite elements

Indexed keywords

CRACK PROPAGATION; CRYSTAL ORIENTATION; FINITE ELEMENT METHOD; MICROSTRUCTURE; POLYCRYSTALS; STRAIN RATE; STRESS ANALYSIS;

GRAIN TRIPLE JUNCTION LINE; STRESS SINGULARITIES;

STRESS CONCENTRATION;

EID: 0031233422     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(97)00014-8     Document Type: Article

References (24)

1. Bazant, Z. P. (1973) Termination of intersection of gradient singularity lines: a general numerical method. Int. J. Eng. Sci. 12, 221-243.
2. Bazant, Z. P. and Estenssoro, L. F. (1979) Surface singularity and crack propagation. Int. J. Solids Struct. 15, 405-426.
3. Bazant, Z. P. and Keer, L. M. (1974) Singularities of elastic stresses and of harmonic functions at conical notches and inclusions. Int. J. Solids Struct. 10, 957-964.
4. Benthem, J. P. (1977) State of stress at the vertex of a quarter-infinite crack in a half-space. Int. J. Sol. Struct. 13, 479-492.
5. Chiu, Y. P. (1977) On the stress field due to initial strains in a cuboid surrounded by an infinite elastic space. J. Appl. Mech. 44, 597-590.
6. Evans, A. G. (1978) Microfracture from thermal expansion anisotropy - single phase systems. Acta Metall. 26, 1845-1853.
7. Ghahremani, F. (1991) A numerical variational method for extracting 3D singularities. Int. J. Solids Struct. 27, 1371-1386.
8. Ghahremani, F. and Shih, C. F. (1992) Corner singularities of three-dimensional planar interface cracks. J. Appl. Mech. 59, 61-68.
9. Ghahremani, F., Hutchinson, J. W. and Tvergaard, V. (1990) Three-dimensional effects in microcrack nucleation in brittle polycrystals. J. Am. Ceram. Soc. 73, 1548-1554.
10. Gudmundson, P. and Ostlund, S. (1990) Stress singularities at the free surface of a dynamically growing crack. J. Appl. Mech. 57, 112-116.
11. He, M. Y and Hutchinson, J. W. (1989) Crack deflection at an interface between dissimilar elastic materials. Int. J. Solids Struct. 25, 1053-1067.
12. Keer, L. M. and Parihar, K. S. (1977) Singularity at the vertex of pyramidal notches with three equal angles. Q. J. Appl. Math. 35, 401-405.
13. Keer, L. M. and Parihar, K. S. (1978) Elastic stress singularities at conical inclusions. Int. J. Solids Struct. 14, 261-263.
14. Nakamura, T. and Parks, D. M. (1988) Three-dimensional stress field near the crack front of a thin elastic plate. J. Appl. Mech. 55, 805-813.
15. Parihar, K. S. and Keer, L. M. (1978) Stress singularity at the corner of a wedged-shaped crack or inclusion. J. Appl. Mech. 45, 791-796.
16. Picu, R. C. (1996) Singularities of an interface crack impinging on a triple grain junction. Int. J. Solids Struct. 33, 1563-1573.
17. Picu, R. C. and Gupta, V. (1995a) Observations of crack nucleation in columnar ice due to grain boundary sliding. Acta Metall. Mater. 43, 3791-3798.
18. Picu, R. C. and Gupta, V. (1995b) Crack nucleation in polycrystalline ice due to elastic anisotropy and grain boundary sliding. Acta Metall. Mater. 43, 3783-3790.
19. Picu, R. C. and Gupta, V. (1996a) Singularities at grain triple junctions in two dimensional polycrystals with cubic and orthotropic grains. J. Appl. Mech. 63, 296-300.
20. Picu, R. C. and Gupta, V. (1996b) Stress singularities at grain triple junctions with freely sliding grains. Int. J. Sol. Struct. 33(11), 1535-1541.
21. Simmons, G. and Wang, H. (1985) Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook. The MIT Press, Cambridge, MA.
22. Somaratna, N. and Ting, T. C. T. (1986a) Three dimensional stress singularities at conical notches and inclusions in transversely isotropic materials. J. Appl. Mech. 53, 89-96.
23. Somaratna, N. and Ting, T. C. T. (1986b) Three dimensional stress singularities in anisotropic materials and composites. Int. J. Engng Sci. 24, 1115-1134.
24. Tvergaard, V. and Hutchinson, J. W. (1988) Microcracking in ceramics induced by thermal expansion or elastic anisotropy. J. Am. Ceram. Soc. 71, 157-166.