When a crack is lodged in an inclusion, the difference between the elastic modulus of the inclusion and matrix material will cause the near-tip stress intensity factor to be greater or less than that prevailing in a homogeneous material. A method is derived for calculation of the near-tip stress intensity factor for the inclusion with arbitrary shape. The derivation of the fundamental formula is based on the transformation toughening theory. The equivalent transformation strain contributed from modulus difference between inclusion and matrix is calculated from Eshelby equivalent inclusion approach. As validated by numerical examples, the developed formula has excellent accuracy.
Issue Section:
Technical Papers
1.
Hutchinson
, J. C.
, 1987
, “Crack Tip Shielding by Micro-Cracking in Brittle Solids
,” Acta Metall.
, 35
, pp. 1605
–1619
.2.
Steif
, P. S.
, 1987
, “A Semi-Infinite Crack Partially Penetrating a Circular Inclusion
,” ASME J. Appl. Mech.
, 54
, pp. 87
–92
.3.
Erdogan
, F.
, and Gaupta
, G. D.
, 1975
, “The Inclusion Problem With a Crack Crossing the Boundary
,” Int. J. Fract.
, 11
, pp. 13
–27
.4.
Li
, R.
, and Chudnovsky
, A.
, 1993
, “Energy Analysis of Crack Interaction With an Elastic Inclusion
,” Int. J. Fract.
, 63
, pp. 247
–261
.5.
Evans
, A. G.
, and Faber
, K. T.
, 1981
, “Toughening of Ceramics by Circumferential Microcracking
,” J. Am. Ceram. Soc.
, 64
, pp. 394
–398
.6.
McMeeking
, R. M.
, and Evans
, A. G.
, 1982
, “Mechanics of Transformation Toughening in Bittle Materials
,” J. Am. Ceram. Soc.
, 65
, pp. 242
–246
.7.
Eshelby
, J. D.
, 1957
, “The Determination of the Elastic Fields of an Ellipsoidal Inclusion, and Related Problems
,” Proc. R. Soc. London, Ser. A
, 241
, pp. 376
–396
.8.
Withers
, D. J.
, Stobbs
, W. M.
, and Pedersen
, O. B.
, 1989
, “The Application of the Eshelby Method of Internal Stress Determination to Short Fibre Metal Matrix Composites
,” Acta Metall.
, 37
, pp. 3061
–3084
.9.
Moschobidis
, Z. A.
, and Mura
, T.
, 1975
, “Two Ellipsoidal Inhomegeneities by the Equivalent Inclusion Method
,” ASME J. Appl. Mech.
, 42
, pp. 847
–852
.10.
Taya
, M.
, and Chou
, T. W.
, 1981
, “On Two Kinds Ellipsoidal Inhomegeneities in an Infinite Elastic Body: An Application to a Hybrid Composites
,” Int. J. Solids Struct.
, 17
, pp. 553
–563
.11.
Johnson
, W. C.
, Earmme
, Y. Y.
, and Lee
, J. K.
, 1980
, “Approximation of the Strain Field Associated With an Inhomegeneous Pricipitate
,” ASME J. Appl. Mech.
, 47
, pp. 775
–780
.12.
Lambropoulos
, J. C.
, 1986
, “Shear, Shape and Orientation Effects in Transformation Toughening in Ceramics
,” Int. J. Solids Struct.
, 22
, pp. 1083
–1106
.13.
Budiansky
, B.
, Hutchinson
, J. W.
, and Lambropoulos
, J. C.
, 1983
, “Continuum Theory of Dilatant Transformation Toughening in Ceramics
,” Int. J. Solids Struct.
, 19
, pp. 337
–355
.14.
Mura, T., 1987, Micromechanics of Defects in Solids, Second Rev. Ed., Kluwer, Dordrecht, The Netherlands.
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