Summary
Based on the transformation toughening theory an approximate solution is developed for predicting the stress intensity factor for a crack interacting with an inclusion of arbitrary shape and size under I/II mixed mode loading conditions. The transformation strains in the inclusion induced by the crack tip field and the remotely applied stresses are evaluated based on the Eshelby equivalent inclusion theory. As validated by detailed finite element analyses, the solution is applicable with good accuracy for the inclusion of arbitrary shape and large size under mixed mode loadings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Atkinson (1972) ArticleTitleThe interaction between a crack and an inclusion Int. J. Engng. Sci. 10 127–136 Occurrence Handle0224.73098 Occurrence Handle10.1016/0020-7225(72)90011-0
F. Erdogan G. D. Gupta M. Ratwani (1974) ArticleTitleInteraction between a circular inclusion and an arbitrary oriented crack J. Appl. Mech. 41 1007–1013 Occurrence Handle0294.73075
K. Y. Lam P. P. Ong N. Wude (1998) ArticleTitleInteraction between a circular inclusion and a symmetrically branched crack Theor. Appl. Fract. Mech. 28 197–21 Occurrence Handle10.1016/S0167-8442(98)00005-6
E. M. Patton M. H. Santare (1990) ArticleTitleThe effect of a rigid elliptical inclusion on a straight crack Int. J. Fracture 46 71–79
A. H. Chen (1997) ArticleTitleThe effect of an elliptical inclusion on a crack Int. J. Fracture 85 351–364 Occurrence Handle10.1023/A:1007420011592
P. Lipetzky S. Schmauder (1994) ArticleTitleCrack-particle interaction in two-phase composites, Part I: Particle shape effects Int. J. Fracture 65 345–358 Occurrence Handle10.1007/BF00012373
P. Lipetzky Z. Knesl (1995) ArticleTitleCrack-particle interaction in two-phase composites, Part II: Crack Deflection Int. J. Fracture 73 81–92 Occurrence Handle10.1007/BF00039853
G. T. M. Stam E. Giessen ParticleVan Der P. Meuers (1994) ArticleTitleEffect of transformation-induced shear strains on crack growth in zirconia-containing ceramics Int. J. Solids Struct. 31 1923–1948 Occurrence Handle0946.74543 Occurrence Handle10.1016/0020-7683(94)90200-3
S. B. Thomas M. J. Mhaiskar R. Sethuraman (2000) ArticleTitleStress intensity factors for circular hole and inclusion using finite element alternating method Theor. Appl. Fract. Mech. 33 73–81 Occurrence Handle10.1016/S0167-8442(00)00002-1
A. Portela M. H. Aliabadi D. P. Rooke (1993) ArticleTitleDual boundary element integral analysis of crack propagation Composites Struct. 46 237–247 Occurrence Handle0825.73888 Occurrence Handle10.1016/0045-7949(93)90189-K
M. B. Bush (1997) ArticleTitleThe Interaction between a crack and a particle cluster Int. J. Fracture 88 215–232 Occurrence Handle10.1023/A:1007469631883
C. Wang N. Libardi J. B. Baldo (1998) ArticleTitleAnalysis of crack extension paths and toughening in a two phase brittle particulate composites by the boundary element method Int. J. Fracture 94 177–188 Occurrence Handle10.1023/A:1007591216796
O. Tamate (1968) ArticleTitleThe effect of a circular inclusion on the stresses around a line crack in a sheet under tension Int. J. Fracture 4 257–266
J. Helsing (1999) ArticleTitleStress intensity factors for a crack in front of an inclusion Engng. Fract. Mech. 64 245–253 Occurrence Handle10.1016/S0013-7944(99)00061-2
Z. Li L. Yang (2004) ArticleTitleThe near-tip stress intensity factor partially penetrating an inclusion J. Appl. Mech. 71 465–470 Occurrence Handle10.1115/1.1651539
Z. Li Q. Chen (2002) ArticleTitleCrack-inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method Int. J. Fracture 118 29–40 Occurrence Handle10.1023/A:1022652725943
L. Yang Q. Chen Z. Li (2004) ArticleTitleCrack-inclusion interaction for mode II crack analyzed by Eshelby equivalent inclusion method Engng. Fract. Mech. 71 1421–1433 Occurrence Handle10.1016/S0013-7944(03)00162-0
J. D. Eshelby (1957) ArticleTitleThe determination of the elastic fields of an ellipsoidal inclusion and related problems Proc. Royal Soc. London, Series A, 241 376–396 Occurrence Handle0079.39606 Occurrence Handle87326
P. J. Withers W. M. Stobbs O. B. Pederson (1989) ArticleTitleThe application of the Eshelby method of internal stress determination to short fiber metal matrix composites Acta Metall. 37 3061–3084 Occurrence Handle10.1016/0001-6160(89)90341-6
Mura, T.: Micromechanics of defects in solids, 2nd rev. ed. Dordrecht 1987.
J. C. Lambropoulos (1986) ArticleTitleShear, shape and orientation effects in transformation toughening in ceramics Int. J. Solids Struct. 22 1083–1106 Occurrence Handle10.1016/0020-7683(86)90019-3
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, Z., Sheng, Q. & Sun, J. A generally applicable approximate solution for mixed mode crack-inclusion interaction. Acta Mechanica 187, 1–9 (2006). https://doi.org/10.1007/s00707-006-0375-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-006-0375-y