Summary
The elastic T-stress and stress intensity factor K for embedded elliptical cracks have been investigated in elastic plates by detailed three-dimensional finite element calculations. The distributions of normalized K and T-stress have been obtained along the crack front with aspect ratios (a/c) of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0, and far-field tension and the effect of Poisson's ratio have also been considered. The normalized K increases and the normalized T-stress decreases with the increase of Poisson's ratio ν. For ν=0.3, the normalized K gradually increases in the range of crack face angle ϕ≥22.5° and decreases in the range of ϕ≤22.5° with increasing a/c. When ϕ rises to 90°, the K values tend to maximum for various a/c. The normalized T-stress increases in the beginning and then decreases with the increase of ϕ except for a/c = 1.0. By fitting the numerical results with the least squares method, empirical formulae have been given for the convenience of engineering applications. Combining with the corresponding out-of-plane constraint factor T z , the three-parameter K-T-T z approach has been provided, which can accurately describe the stress field around the crack front.
Similar content being viewed by others
References
Irwin, G. R.: Fracture dynamics. In: Fracturing of metals, pp. 147–166 ASM Publications 1948.
G. R. Irwin (1958) Fracture Flűgge (Eds) Handbuch der Physik, vol. VI Springer Berlin 551–590
M. L. Williams (1957) ArticleTitleOn the stress distribution at the base of a stationary crack J. Appl. Mech. 24 109–114 Occurrence Handle0077.37902 Occurrence Handle84273
Bilby, B. A., Cardew, G. E., Goldthorpe, M. R., Howard, I. C.: A finite element investigation of the effect of specimen geometry on the fields of stress and strain at the tips of stationary cracks. In: Size effects in fracture, pp. 37–46. London: Mechanical Engineering Publications 1986.
S. G. Larsson A. J. Carlsson (1973) ArticleTitleInfluence of non-singular stress terms and specimen geometry on small-scale yielding at crack-tips in elastic-plastic materials J. Mech. Phys. Solids 21 447–473 Occurrence Handle10.1016/0022-5096(73)90012-4
X. Wang (2003) ArticleTitleElastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates Engng. Fract. Mech. 70 731–756 Occurrence Handle10.1016/S0013-7944(02)00081-4
J. W. Hutchinson (1968) ArticleTitleSingular behaviour at the end of a tensile crack in a hardening material J. Mech. Phys. Solids 16 13–31 Occurrence Handle0166.20704 Occurrence Handle10.1016/0022-5096(68)90014-8
J. R. Rice G. F. Rosengren (1968) ArticleTitlePlane strain deformation near near a crack tip in a power-law hardening material J. Mech. Phys. Solids 16 1–12 Occurrence Handle0166.20703 Occurrence Handle10.1016/0022-5096(68)90013-6
S. M. Sharma N. Aravas (1991) ArticleTitleDetermination of higher-order terms in asymptotic elastoplastic crack tip solutions J. Mech. Phys. Solids 39 1043–1072 Occurrence Handle0761.73090 Occurrence Handle10.1016/0022-5096(91)90051-O
N. P. O'Dowd C. F. Shih (1991) ArticleTitleFamily of crack-tip fields characterized by a triaxiality parameter-I. Structure of fields J. Mech. Phys. Solids 39 989–1015 Occurrence Handle10.1016/0022-5096(91)90049-T
L. Xia T. C. Wang C. F. Shih (1993) ArticleTitleHigher-order analysis of crack tip fields in elastic power-law hardening materials J. Mech. Phys. Solids 41 665–687 Occurrence Handle0780.73061 Occurrence Handle10.1016/0022-5096(93)90022-8
S. Yang Y. J. Chao M. A. Sutton (1993) ArticleTitleHigher-order asymptotic crack tip fields in a power-law hardening material Engng. Fract. Mech. 45 1–20 Occurrence Handle10.1016/0013-7944(93)90002-A
Z. P. Bazant L. F. Estenssoro (1979) ArticleTitleSurface singularity and crack propagation Int. J. Solids Struct. 15 405–426 Occurrence Handle0424.73086 Occurrence Handle10.1016/0020-7683(79)90062-3 Occurrence Handle529190
W. Yang L. B. Freund (1985) ArticleTitleTransverse shear effects for through-cracks in an elastic plate J. Mech. Phys. Solids 21 977–994 Occurrence Handle0579.73103 Occurrence Handle802876
E. Mahgoub X. M. Deng M. A. Sutton (2003) ArticleTitleThree-dimensional stress and deformation fields around flat and slant cracks under remote Mode I loading conditions Engng. Fract. Mech. 70 2527–2542 Occurrence Handle10.1016/S0013-7944(03)00082-1
X. M. Kong N. Schluter W. Dahl (1995) ArticleTitleEffect of triaxial stress on mixed-mode fracture Engng. Fract. Mech. 52 379–385 Occurrence Handle10.1016/0013-7944(94)00228-A
H. Yuan W. Brocks (1998) ArticleTitleQuantification of constraint effects in elastic-plastic crack front fields J. Mech. Phys. Solids 46 219–241 Occurrence Handle0939.74584 Occurrence Handle10.1016/S0022-5096(97)00068-9
W. L. Guo (1993) ArticleTitleElastoplastic three dimensional crack border field-I Engng. Fract. Mech. 46 93–104 Occurrence Handle10.1016/0013-7944(93)90306-D
W. L. Guo (1993) ArticleTitleElastoplastic three dimensional crack border field-II Engng. Fract. Mech. 46 105–113 Occurrence Handle10.1016/0013-7944(93)90307-E
W. L. Guo (1995) ArticleTitleElastoplastic three dimensional crack border field-III Engng. Fract. Mech. 51 51–71 Occurrence Handle10.1016/0013-7944(94)00215-4
W. L. Guo (1999) ArticleTitleThree-dimensional analysis of plastic constraint for through-thickness cracked bodies Engng. Fract. Mech. 62 383–407 Occurrence Handle10.1016/S0013-7944(98)00102-7
T. M. Nakamura D. M. Parks (1992) ArticleTitleDetermination of elastic T-stress along three-dimensional crack fronts using an interaction integral Int. J. Solids Struct. 29 1597–1611 Occurrence Handle0825.73558 Occurrence Handle10.1016/0020-7683(92)90011-H
L. G. Zhao J. Tong J. Byrne (2001) ArticleTitleStress intensity factor K and the elastic T-stress for corner cracks Int. J. Fracture 109 209–225 Occurrence Handle10.1023/A:1011016720630
Q. H. Zuo F. L. Addessio J. K. Dienes M. W. Lewis (2006) ArticleTitleA rate-dependent damage model for brittle materials based on the dominant crack Int. J. Solids Struct. 43 3350–3380 Occurrence Handle10.1016/j.ijsolstr.2005.06.083 Occurrence Handle1121.74447
D. N. Fang Z. K. Zhang A. K. Soh K. L. Lee (2004) ArticleTitleFracture criteria of piezoelectric ceramics with defects Mech. Mater. 36 917–928 Occurrence Handle10.1016/j.mechmat.2003.08.011
R. O. Ritchie C. J. Gilbert J. M. McNaney (2000) ArticleTitleMechanics and mechanisms of fatigue damage and crack growth in advanced materials Int. J. Solids Struct. 37 311–329 Occurrence Handle1075.74072 Occurrence Handle10.1016/S0020-7683(99)00096-7
C. Seife (2003) ArticleTitleColumbia disaster underscores the risky nature of risk analysis Science 299 1001 Occurrence Handle10.1126/science.299.5609.1001
J. H. Zhao W. L. Guo C. M. She B. Meng (2006) ArticleTitleThree dimensional K-T z stress fields around the central embedded elliptical crack front in elastic plates Acta Mech. Sinica 22 148–155 Occurrence Handle10.1007/s10409-006-0095-5
A. P. Kfouri (1986) ArticleTitleSome evaluation of the elastic T-term using Eshelby's method Int. J. Fracture 30 301–315 Occurrence Handle10.1007/BF00019710
R. S. Barsoum (1976) ArticleTitleOn the use of isoparametric FEs in linear fracture mechanics Int. J. Numer. Meth. Engng. 10 25–37 Occurrence Handle0321.73067 Occurrence Handle10.1002/nme.1620100103
R. C. Shah A. S. Kobayashi (1971) ArticleTitleStress intensity factor for an elliptical crack under arbitrary normal loading Engng. Fract. Mech. 3 71–96 Occurrence Handle10.1016/0013-7944(71)90052-X
W. L. Guo (2000) ArticleTitleRecent advances in three-dimensional fracture mechanics Key Engng. Mater. 183 193–198 Occurrence Handle10.4028/www.scientific.net/KEM.183-187.193
Guo, W. L., Pitt, S. D., Jones, R.: Three-dimensional strength assessment for damage tolerant structures. In: Proceedings of the International Conference on Strength Theory (Yu, M., ed.). Xian, 1998.
W. L. Guo H. Dong M. Lu X. Zhao (2002) ArticleTitleThe coupled effects of thickness and delamination on cracking resistance of X70 pipeline steel Int. J. Pres. Ves. Pip. 79 403–412 Occurrence Handle10.1016/S0308-0161(02)00039-X
B. Zhang W. L. Guo (2005) ArticleTitle T z constraints of semi-elliptical surface cracks in elastic plates subjected to uniform tension loading Int. J. Fracture 131 173–187 Occurrence Handle10.1007/s10704-004-5105-7
T. Chang W. L. Guo (1999) ArticleTitleEffects of strain hardening and stress state on fatigue crack closure Int. J. Fatigue 21 881–888 Occurrence Handle10.1016/S0142-1123(99)00085-7
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, J., Guo, W. & She, C. Three-parameter description of the stress field near the border of an embedded elliptical crack. Acta Mechanica 190, 29–44 (2007). https://doi.org/10.1007/s00707-006-0409-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-006-0409-5