Abstract
The interaction of a crack with perfectly bonded rigid isolated inclusions and clusters of inclusions in a brittle matrix is investigated using numerical simulations. Of particular interest is the role inclusions play on crack paths, stress intensity factors (SIFs) and the energy release rates with potential implications to the fracture behavior of particulate composites. The effects of particle size and eccentricity relative to the initial crack orientation are examined first as a precursor to the study of particle clusters. Simulations are accomplished using a new quasi-static crack-growth prediction tool based on the symmetric-Galerkin boundary element method, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating SIFs, and the maximum principal stress criterion for crack-growth direction prediction. The numerical simulations demonstrate a complex interplay of crack-tip shielding and amplification mechanisms leading to significant toughening of the material.
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References
Anderson TL (1995) Fracture Mechanics, Fundamentals and Applications. CRC Press
C Atkinson (1972) ArticleTitleThe interaction between a crack and an inclusion International Journal of Engineering Science 10 127–136 Occurrence Handle0224.73098 Occurrence Handle10.1016/0020-7225(72)90011-0
RS Barsoum (1976) ArticleTitleOn the use of isoparametric finite elements in linear fracture mechanics Int J Numer Meth Eng 10 25–37 Occurrence Handle0321.73067 Occurrence Handle10.1002/nme.1620100103
M Bonnet (1995) Boundary Integral Equation Methods for Solids and Fluids John Wiley & Sons England
M Bonnet G Maier C Polizzotto (1998) ArticleTitleSymmetric Galerkin boundary element method ASME Appl Mech Rev 51 669–704 Occurrence Handle10.1115/1.3098983
MB Bush (1997) ArticleTitleThe interaction between a crack and a particle cluster Int J Fract 88 215–232 Occurrence Handle10.1023/A:1007469631883
Erdogan C, Gupta GD, Ratwani M (1974) Interaction between a circular inclusion and an arbitrary oriented crack. J Appl Mech (Trans ASME) Dec:1007–1013
F Erdogan GC Sih (1963) ArticleTitleOn the crack extension in plates under plane loading and transverse shear J Basic Eng 86 519–527
KT Faber AG Evans (1983) ArticleTitleCrack deflection process - I Theory. Acta Mater 31 565–576 Occurrence Handle10.1016/0001-6160(83)90046-9
Ferber F, Hinz O, Herrmann K. (1993) Numerical and experimental modelling of crack systems in homogeneous and nonhomogeneous solids. In: C.A. Brebbia and G.M. Carlomagno (eds) Computational Methods and Experimental Measurements VI, Vol. 2: Stress Analysis. CMP, Southampton Boston/Elsevier, pp 259–276
LJ Gray (1991) ArticleTitleEvaluation of hypersingular integrals in the boundary element method Math Computer Model 15 165–174 Occurrence Handle0718.73095 Occurrence Handle10.1016/0895-7177(91)90062-C
LJ Gray GH Paulino (1998) ArticleTitleCrack tip interpolation, revisited SIAM J Appl Math 58 428–455 Occurrence Handle0949.74059 Occurrence Handle1617650 Occurrence Handle10.1137/S0036139996279166
LJ Gray A-V Phan GH Paulino T Kaplan (2003) ArticleTitleImproved quarter-point crack tip element Eng Fract Mech 70 269–283 Occurrence Handle10.1016/S0013-7944(02)00027-9
A Haddi D Weichert (1998) ArticleTitleThree-dimensional interaction between a crack front and particles Int J Numer Meth Eng 42 1463–1476 Occurrence Handle0904.73046 Occurrence Handle10.1002/(SICI)1097-0207(19980830)42:8<1463::AID-NME429>3.0.CO;2-1
MY He JW Hutchinson (1989) ArticleTitleCrack deflection at an interface between dissimilar elastic material Int J Solids Struct 25 IssueID9 1053–1067 Occurrence Handle10.1016/0020-7683(89)90021-8
RD Henshell KG Shaw (1975) ArticleTitleCrack tip finite elements are unnecessary Int J Numer Meth Eng 9 495–507 Occurrence Handle0306.73064 Occurrence Handle10.1002/nme.1620090302
C Hwu YK Liang WJ Yen (1995) ArticleTitleInteractions between inclusions and various types of cracks Int J Fract 73 301–323 Occurrence Handle10.1007/BF00027272
R Kitey HV Tippur (2005a) ArticleTitleRole of particle size and filler-matrix adhesion on dynamic fracture of glass-filled epoxy. I. Macromeasurements Acta Mater 53 1153–1165 Occurrence Handle10.1016/j.actamat.2004.11.012
R Kitey HV Tippur (2005b) ArticleTitleRole of particle size and filler–matrix adhesion on dynamic fracture of glass-filled epoxy. II. Linkage between macro- and micro-measurements Acta Materiala 53 1167–1178 Occurrence Handle10.1016/j.actamat.2004.11.011
MG Knight LC Wrobel JL Henshall LA Lacerda ParticleDe (2002) ArticleTitleA study of the interaction between a propagating crack and an uncoated/coated elastic inclusion using the BE technique Int J Fract 114 47–61 Occurrence Handle10.1023/A:1014837509347
J Lei Y-S Wang D Gross (2005) ArticleTitleAnalysis of dynamic interaction between an inclusion and a nearby moving crack by BEM Engineering Analysis with Boundary Elements 29 802–813 Occurrence Handle10.1016/j.enganabound.2005.04.002
R Li A Chudnovsky (1993) ArticleTitleVariation of the energy release rate as a crack approaches and passes through an elastic inclusion Int. J. of Frac. 59 R69–R74 Occurrence Handle1993IJFr...59...69L
R Li A Chudnovsky (1993) ArticleTitleEnergy analysis of crack interaction with an elastic inclusion Int J Fract 63 247–261 Occurrence Handle10.1007/BF00012471 Occurrence Handle1993IJFr...63..247L
P Lipetzky Z Knesl (1995) ArticleTitleCrack–particle interaction in two-phase composites part II: crack deflection Int J Fract 73 81–92 Occurrence Handle10.1007/BF00039853
P Lipetzky S Schmauder (1994) ArticleTitleCrack–particle interaction in two-phase composites part I: Particle shape effects Inter. J. of Frac. 65 345–358 Occurrence Handle10.1007/BF00012373
PA Martin FJ Rizzo (1996) ArticleTitleHypersingular integrals: how smooth must the density be? Int J Numer Meth Eng 39 687–704 Occurrence Handle0846.65070 Occurrence Handle1377122 Occurrence Handle10.1002/(SICI)1097-0207(19960229)39:4<687::AID-NME876>3.0.CO;2-S
AC Moloney HH Kausch T Kaiser HR Beer (1987) ArticleTitleReview—parameters determining the strength and toughness of particulate filled epoxide resins J. Mater. Sci. 22 381–393 Occurrence Handle10.1007/BF01160743 Occurrence Handle1987JMatS..22..381M
Y Nakamura M Yamaguchi (1992) ArticleTitleEffects of particle size on the fracture toughness of epoxy resin filled with spherical silica Polymer 33 IssueID16 3415–3426 Occurrence Handle10.1016/0032-3861(92)91099-N
Y Nakamura S Okabe T Iida (1999) ArticleTitleEffects of particle shape, size and interfacial adhesion on the fracture strength of silica-filled epoxy resin Polymers Polymer Composites 7 IssueID3 177–186
FJ Rizzo (1967) ArticleTitleAn integral equation approach to boundary value problems of classical elastostatics Quart Appl Math 25 83–95 Occurrence Handle0158.43406
GP Sendeckyj (1974) ArticleTitleInteraction of cracks with rigid inclusions in longitudinal shear deformation Int J Fract 10 45–52 Occurrence Handle10.1007/BF00955078
GC Sih (1974) ArticleTitleStrain energy density factor applied to mixed mode crack problems Int J Fract 10 305–321 Occurrence Handle10.1007/BF00035493
J Spanoudakis RJ Young (1984a) ArticleTitleCrack propagation in a glass particle-filled epoxy resin, Part 2 Effect of particle-matrix adhesion J. Mater. Sci. 19 487–496 Occurrence Handle10.1007/BF02403235 Occurrence Handle1984JMatS..19..487S
J Spanoudakis RJ Young (1984b) ArticleTitleCrack propagation in a glass particle-filled epoxy resin, Part 1 Effect of particle volume fraction and size J Mater Sci 19 473–486 Occurrence Handle10.1007/BF02403234 Occurrence Handle1984JMatS..19..473S
O Tamate (1968) ArticleTitleThe effect of a circular inclusion on the stresses around a line crack in a sheet under tension Int J Fract 4 257–265
C Wang W Libardi JB Baldo (1998) Analysis of crack extension paths and toughening in a two phase brittle particulate composite by the boundary element method: Int J Fract 94 177–188
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Kitey, R., Phan, AV., Tippur, H.V. et al. Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method. Int J Fract 141, 11–25 (2006). https://doi.org/10.1007/s10704-006-0047-x
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DOI: https://doi.org/10.1007/s10704-006-0047-x