Reversal in Failure Scaling Transition of Fibrous Composites
Publication: Journal of Engineering Mechanics
Volume 123, Issue 2
Abstract
A nonlinear fracture mechanics model is proposed for analysis of the flexural behavior of brittle-matrix composites with uniformly distributed secondary phases. In accordance with the Barenblatt-Dugdale model the bridging or cohesive zone of the material is replaced by a fictitious crack along which a closing traction distribution is applied. The dimensionless formulation brings out the parameters synthetically controlling the structural behavior and the size-scale effects. Different scaling transitions are predicted in the flexural behavior of the composite depending on different modeling of the toughening mechanisms. When a homogenized toughening mechanism for the whole composite is considered along with closing tractions as a linearly decreasing function of the crack opening displacement, a ductile to brittle transition is found as the beam depth increases. On the other hand, when the matrix toughness and the toughening mechanism of the reinforcements are separately modeled, and the closing tractions have a constant value until a critical crack opening displacement, a double brittle-ductile-brittle transition is found. Experimental tests on fiber-reinforced mortar beams in bending are successfully simulated.
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References
1.
Ballarini, R., Shah, S. P., and Keer, L. M.(1984). “Crack growth in cement-based composites.”Engrg. Fracture Mech., 20(3), 433–445.
2.
Barenblatt, G. I.(1959). “The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks.”J. Appl. Math. Mech., 23(3), 622–636.
3.
Barenblatt, G. I. (1962). “The mathematical theory of equilibrium cracks in brittle fracture.”Advances in applied mechanics, H. L. Dryden and T. von Karman, eds., Academic Press, Inc., New York, N.Y., 55–129.
4.
Bosco, C., Carpinteri, A., and Debernardi, P. G.(1990). “Minimum reinforcement in high-strength concrete.”J. Struct. Engrg., ASCE, 116(2), 427–437.
5.
Bosco, C., and Carpinteri, A.(1992). “Softening and snap-through behavior of reinforced elements.”J. Engrg. Mech., ASCE, 118(8), 1564–1577.
6.
Bosco, C., and Carpinteri, A.(1995). “Discontinuous constitutive response of brittle matrix fibrous composites.”J. Mech. Phys. Solids, 43(2), 261–274.
7.
Buckingham, E.(1915). “Model experiments and the form of empirical equations.”Trans. ASME, 37(1487), 263–296.
8.
Burakiewicz, A. (1978). “Testing of fibre bond strength in cement matrix.”Testing and test methods of fiber cement composites, R. N. Swamy, ed., The Construction Press, Ltd., Lancaster, U.K., 355–369.
9.
Carpinteri, A.(1981). “Static and energetic fracture parameters for rocks and concretes.”Mat. and Struct., 14(81), 151–162.
10.
Carpinteri, A.(1984). “Stability of fracturing process in r.c. beams.”J. Struct. Engrg., 110(3), 544–558.
11.
Carpinteri, A.(1989). “Cusp catastrophe interpretation of fracture instability.”J. Mech. Phys. Solids, 37(5), 567–582.
12.
Carpinteri, A., and Massabó, R. (1995). “Nonlinear fracture mechanics models for fibre reinforced materials.”Proc., Int. Symp. on Advanced Technol. for Des. and Fabrication of Composite Mat. and Struct., G. C. Sih, A. Carpinteri, and G. Surace, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 31–48.
13.
Cotterell, B., Paramasivam, P., and Lam, K. Y.(1992). “Modelling the fracture of cementitious materials.”Mat. and Struct., 25(145), 14–20.
14.
Cox, B. N., and Marshall, D. B.(1994). “Concepts for bridged cracks in fracture and fatigue.”Acta Metallurgica Materialia, 42(2), 341–363.
15.
Desayi, P., and Ganesan, N.(1986). “Fracture behavior of ferrocement beams.”J. Struct. Engrg., 112(7), 1509–1525.
16.
Dugdale, D. S.(1960). “Yielding of steel sheets containing slits.”J. Mech. Phys. Solids, 8(2), 100–104.
17.
Foote, R. M. L., Mai, Y.-W., and Cotterell, B.(1986). “Crack growth resistance curves in strain-softening materials.”J. Mech. Phys. Solids, 34(6), 593–607.
18.
Hillerborg, A., Mooder, M., and Petersson, P. E.(1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.”Cement and Concrete Res., 6(6), 773–782.
19.
Hillerborg, A. (1989). “Analysis of fracture by means of the fictitious crack model, particularly for fibre reinforced concrete.”Int. J. Cement Composites, 2(4) 177–184.
20.
Jamet, D., Gettu, R., Gopalaratnam, V. S., and Aguado, A. (1996). “Toughness of fiber-reinforced high-strength concrete from notched beam tests.” in Testing of fiber reinforced concrete, eds., D. J. Stevens et al., SP-155, ACI Detroit, 23–29.
21.
Jenq, Y. S., and Shah, S. P.(1985). “Two parameter fracture model for concrete.”J. Engrg. Mech., 111(10), 1227–1241.
22.
Jenq, Y. S., and Shah, S. P.(1986). “Crack propagation in fiber-reinforced concrete.”J. Struct. Engrg., 112(1), 19–34.
23.
Li, V. C., and Liang, E.(1986). “Fracture processes in concrete and fiber reinforced cementitious composites.”J. Engrg. Mech., 112(6), 566–586.
24.
Mai, Y. W. (1985). “Fracture measurements for cementitious composites.”Application of fracture mechanics to cementitious composites, S. P. Shah, ed., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 399–429.
25.
Ouyang, C., Pacios, A., and Shah, S. P.(1994). “Pullout of inclined fibers from cementitious matrix.”J. Engrg. Mech., 120(12), 2641–2659.
26.
Romualdi, J. P., and Batson, G. B. (1963). “Behavior of reinforced concrete beams with closely spaced reinforcements.”ACI J., 60(6), 775–789.
27.
Shah, S. P.(1988). “Fracture toughness of cement-based materials.”Mat. and Struct., 21(122), 145–150.
28.
Tada, H., Paris, P. C., and Irwin, G. (1985). The stress analysis of cracks handbook. Paris Productions Incorporated (and Del Research Corporation), St. Louis, Mo.
29.
Visalvanich, K., and Naaman, A. E.(1983). “Fracture model for fiber reinforced concrete.”ACI J., 80(2), 128–138.
30.
Wecharatana, M., and Shah, S. P.(1983). “A model predicting fracture resistance of fiber reinforced concrete.”Cement and Concrete Res., 13(6), 819–829.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 123 • Issue 2 • February 1997
Pages: 107 - 114
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Feb 1, 1997
Published in print: Feb 1997
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