Cracks Interacting with Particles or Fibers in Composite Materials
Publication: Journal of Engineering Mechanics
Volume 117, Issue 7
Abstract
Micromechanics analysis of damage in heterogeneous media and composites cannot ignore the interactions among cracks as well as between cracks and inclusions or voids. Previous investigators can to this conclusion upon finding that states of distributed (diffuse) cracking (damage) cannot be mathematically represented merely as crack systems in a homogeneous medium, even though stable states with distributed damage have been experimentally observed in heterogeneous materials such as concrete. This paper presents a method for modeling interactions between a crack and many inclusions. Based on the Duhamel‐Neuman analogy, the effect of the inclusions is equivalent to unbalanced forces acting on the contour of each inclusion in an infinite homogeneous solid. The problem is solved by superposition; it is decomposed into several standard problems of elasticity for which well‐known solutions are available. The problem is finally reduced to a system of linear algebraic equations similar to those obtained by Kachanov for a system of interacting cracks without inclusions. The calculated estimates of the stress intensity factors differ from some known exact solutions by less than 10% provided the cracks or the inclusions are not very close to each other. Approximately, the problem can be treated as crack propagation in an equivalent homogeneous macroscopic continuum for which the apparent fracture toughness increases or decreases as a function of the crack length. Such variations are calculated for staggered inclusions. They are analogous to R‐curves in nonlinear fracture mechanics. They depend on the volume fraction of the inclusions, their spatial distribution and the difference between the elastic properties of the inclusions and the matrix. Large variations (of the order of 100%) are found depending on the location of the crack and its propagation direction with respect to the inclusions.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bažant, Z. P. (1987a). “Snapback instability at crack ligament tearing and its implication for fracture micromechanics.” Cem. Concr. Res., 17(6), 951–967.
2.
Bažant, Z. P. (1987b). “Why continuum damage is nonlocal: Justification by quasiperiodicmicrocrack array.” Mech. Res. Commun., 14(5/6), 407–419.
3.
Bažant, Z. P. (1989). “Stable states and paths of structures with plasticity or damage.” J. Engrg. Mech., ASCE, 114(12), 2013–2034.
4.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories. Oxford Univ. Press, New York, N.Y.
5.
Bažant, Z. P., and Tabbara, M. R. (1989). “Stability, bifurcation and localization in structures with propagating interacting cracks.” Report No. 89‐7/4.
6.
Bažant, Z. P., Tabbara, M. R., Kazemi, M. T., and Pijaudier‐Cabot, G. (1990). “Random particle model for fracture of aggregate or fiber composites.” J. Engrg. Mech., ASCE, 116(11), 2484–2504.
7.
Darwin, D., and Dewey, G. R. (1989). “Image analysis of microcracks.” Cracking and damage, J. Mazars and Z. P. Bažant, eds., Elsevier App. Sciences Pub., 65–77.
8.
Erdogan, F., Gupta, G. D., and Ratwani, M. (1974). “Interaction between a circular inclusion and an arbitrary oriented crack.” J. Appl. Mech., 41, 1007–1013.
9.
Evans, A. G., and Faber, K. T. (1983). “On the crack growth resistance of microcracking brittle materials.” Fracture in ceramic materials, A. G. Evans, ed., 109–136.
10.
Faber, K. T., Evans, A. G., and Drory, B. D. (1983). “A statistical analysis of crack deflection as a toughening mechanism in ceramic materials.” Fracture mechanics of ceramics, Vol. 6, C. Bradt et al., eds., 79–91.
11.
Furuhashi, R., Kinoshita, N., and Mura, T. (1981). “Periodic distribution of inclusions.” Int. J. Engrg. Sci., 19, 231–236.
12.
Gao, H., and Rice, J. R. (1988). A first order perturbation analysis of crack trapping by arrays of obstacles. Report Div. of Appl. Sci., Harvard Univ., Cambridge, Mass.
13.
Highsmith, A. L., and Reifsnider, K. L. (1982). “Stiffness reduction mechanisms in composite laminates.” Damage in composite materials, ASTM‐STP 115, K. L. Reifsnider, ed., American Society for Testing and Materials (ASTM), Philadelphia, Pa.
14.
Horii, H., and Nemat‐Nasser, S. (1985). “Elastic fields of interacting inhomogeneities.” Int. J. Solids and Struct., 21, 731–745.
15.
Horii, H., Zihai, S., and Gong, S. X. (1989). “Models of fracture process zone in concrete, rock, and ceramics.” Cracking and damage, J. Mazars and Z. P. Bažant, eds., Elsevier App. Sciences Pub., London, England, 104–115.
16.
Hu, X. Z., Cotterell, B., and Mai, Y. W. (1986). Computer simulation models of fracture in concrete. F. H. Wittmann, ed., Elsevier App. Sciences Pub., London, England, 91–100.
17.
Huang, J., and Li, V. C. (1989). “A meso‐mechanical model of the tensile behavior of concrete. Parts I and II.” Composites, 20(4), 361–378.
18.
Kachanov, M. (1987). “Elastic solids with many cracks‐simple method of analysis.” Int. J. Solids and Struct., 23, 23–43.
19.
Kunin, I., and Gommerstadt, B. (1985). “On elastic crack‐inclusion interaction.” Int. J. Solids and Struct., 21(7), 757–766.
20.
Legendre, D. (1984). “Prévision de la mine des structures en béton par une approache combinée: Mécanique de l'endommagement‐Mécanique de la rupture, Thèse de doctorat de 3ème cycle, Université Paris 6, France.
21.
Lin, T. H. (1968). Theory of inelastic structures. John Wiley and Sons, Inc., New York, N.Y.
22.
Maji, A. K., Ouyang, C., and Shah, S. P. (1990). “Fracture mechanics of quasibrittle aterials based on acoustic emission.” J. Mater. Res., 5(1), 206–217.
23.
Mori, T., Saito, K., and Mura, T. (1988). “An inclusion model for crack arrest in a composite reinforced by sliding fibers.” Mech. Mater., 7, 49–58.
24.
Mura, T. (1987). Micromechanics of defects in solids. 2nd Ed., Martinus Nijhoff Publishers, the Hague, the Netherlands.
25.
Muskhelishvili, N. I. (1953). Some basic problems of the mathematical theory of elasticity. Noordhoff, the Netherlands.
26.
Ortiz, M. (1988). “Microcrack coalescence and macroscopic crack growth initiation in brittle solids.” Int. J. Solids and Struct., 24, 231–250.
27.
Pijaudier‐Cabot, G., Bažant, Z. P., and Berthaud, Y. (1990). “Interacting crack systems in particulate or fiber reinforced composites.” Proc. Fifth Conf. on Numerical Methods in Fracture Mechanics, D. R. J. Owen et al., eds., Pineridge Publishers, Swansea, United Kingdom, 403–414.
28.
Pijaudier‐Cabot, G., and Berthaud, Y. (1990). Effets des interactions dans l'endommagement d'un milieu fragile—Formulation non‐locale. Comptes Rendus Acad. Sc., t. 310, Serie II, 1577–1582, (in French).
29.
Pijaudier‐Cabot, G., and Dvorak, G. J. (1990). “A variational approximation of stress intensity factors in cracked laminates.” European J. Mechanics, A/Solids, in press.
30.
Sih, G. C., and Chen, E. P. (1980). “Effect of material nonhomogeneity on crack propagation characteristics.” Engrg. Fract. Mech., 13, 431–438.
31.
Tada, H., Paris, P. C., and Irwin, J. K. (1985). The stress analysis of cracks handbook. 2nd Ed., Paris Productions Inc., St. Louis, Mo.
32.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity. 3rd Ed., McGraw Hill, New York, N.Y., 127.
33.
Zaitsev, Y. V. (1985). “Inelastic properties of solids with random cracks.” Mechanics of geomaterials, Z. P. Bažant, ed., John Wiley and Sons, Inc., New York, N.Y., 89–128.
34.
Zaitsev, Y. V., Kazatsky, M. B., and Saralidze, T. O. (1986). “Simulation of plain concrete behaviour and its experimental examination.” Fracture toughness and fracture energy of concrete, F. H. Wittman ed., Elsevier App. Sciences Pub., London, England, 201–205.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 117 • Issue 7 • July 1991
Pages: 1611 - 1630
Copyright
Copyright © 1991 ASCE.
History
Published online: Jul 1, 1991
Published in print: Jul 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.