Design Criteria for Pseudoductile Fiber-Reinforced Composites
Publication: Journal of Engineering Mechanics
Volume 122, Issue 1
Abstract
The toughness of brittle materials can be significantly improved by the incorporation of fibers. Moreover, both theoretical and experimental investigations have shown that properly designed fiber composites can exhibit pseudoductile tensile behavior with multiple cracking rather than brittle failure with the formation of one single crack. To attain pseudoductile behavior, two criteria have to be satisfied: (1) the steady-state cracking criterion; and (2) the further cracking criterion. In the literature, criteria for steady-state cracking are usually obtained numerically or derived approximately with assumed profiles of the bridged crack. In this paper, a general analytical approach for the determination of an exact condition for steady-state cracking is presented. The steady-state cracking criteria for several important cases are then derived and compared with available numerical or approximate solutions. Then, an approximate but conservative criterion for further cracking is also developed. Since the two criteria involve the microparameters of the composite (such as properties of fiber, matrix, interface, fiber size, and volume fraction), they can be used as guidelines for the choice of microparameters in composite design.
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References
1.
Atkinson, C., Avila, J., Betz, E., and Smelser, R. E.(1982). “The rod pull-out problem, theory and experiment.”J. Mech. Phys. Solids, 30(3), 97–120.
2.
Aveston, J., Cooper, G. A., and Kelly, A. (1971). “Single and multiple fracture.”The properties of fiber composites. Science and Technology Press, Ltd., Guildford, Sweden, 15–24.
3.
Bower, A. F., and Ortiz, M.(1991). “A three-dimensional analysis of crack trapping and bridging by toughening particles.”J. Mech. Phys. Solids, 39(6), 815–858.
4.
Bowling, J., and Groves, B. W.(1979). “The debonding and pull-out of ductile wires from a brittle matrix.”J. Mat. Sci., 14(2), 431–442.
5.
Budiansky, B., Hutchinson, J. W., and Evans, A. G.(1986). “Matrix fracture in fiber-reinforced ceramics.”J. Mech. Phys. Solids, 34(2), 167–189.
6.
Fares, N.(1989). “Crack fronts trapped by arrays of obstacles: numerical solutions based on surface integral representation.”J. Appl. Mech., 56(12), 837–843.
7.
Gao, Y., Mai, Y. W., and Cotterell, B.(1988). “Fracture of fiber-reinforced materials.”J. Appl. Math. & Phys. (ZAMP), 39(4), 550–572.
8.
Gopalaratnam, V. S., and Shah, S. P.(1987). “Tensile fracture of steel fiber reinforced concrete.”J. Engrg. Mech., ASCE, 113(5), 635–653.
9.
Gurney, C., and Hunt, J. (1967). “Quasi-static crack propagation.” Proc., Royal Soc. London, A299, 508–524.
10.
Lawrence, P.(1972). “Some theoretical considerations of fiber pull-out from an elastic matrix.”J. Mat. Sci., 7(1), 1–6.
11.
Leung, C. K. Y.(1992). “Fracture-based two-way debonding model for discontinuous fibers in elastic matrix.”J. Engrg. Mech., ASCE, 118(11), 2298–2318.
12.
Leung, C. K. Y., and Li, V. C. (1989). “First cracking strength of short fiber reinforced ceramics.”Ceramics Engrg. Sci. Proc., 10(9–10), 1164–1178.
13.
Leung, C. K. Y., and Li, V. C.(1991). “A new strength-based theory for the debonding of discontinuous fibers in an elastic matrix.”J. Mat. Sci., 26, 5996–6010.
14.
Li, V. C.(1993). “From micromechanics to structural engineering—the design of cementitious composites for civil engineering applications.”J. Struct. Engrg. and Earthquake Engrg., 10(2), 37–48.
15.
Li, V. C., and Leung, C. K. Y.(1992). “Tensile failure modes of random discontinuous fiber reinforced brittle matrix composites.”J. Engrg. Mech., ASCE, 118(11), 2246–2264.
16.
Li, V. C., Wang, Y., and Backer, S.(1990). “Effect of inclining angle, bundling and surface treatment on synthetic fiber pull-out from a cement matrix.”Composites, 21(2), 132–140.
17.
Li, V. C., Wang, Y., and Backer, S.(1991). “A micromechanical model of tension-softening and bridging toughening of short fiber reinforced brittle matrix composites.”J. Mech. Phys. Solids, 39(5), 607–625.
18.
Marshall, D. B., and Cox, B. N.(1987). “Tensile failure of brittle matrix composites: influence of fiber strength.”Acta Metallurgica, 35(11), 2607–2611.
19.
Marshall, D. B., and Cox, B. N.(1988). “A J-integral method for calculating steady-state matrix cracking stresses in composites.”Mech. of Mat., 7, 127–133.
20.
Marshall, D. B., Cox, B. N., and Evans, A. G.(1985). “The mechanics of matrix cracking in brittle-matrix fiber composites.”Acta Metallurgica, 33(11), 2013–2021.
21.
Naaman, A. E., Namur, G. C., Alwan, J. N., and Najm, H. S.(1991). “Fiber pull-out and bond slip. I: analytical study.”J. Struct. Engrg., ASCE, 117(9), 2769–2790.
22.
Shah, S. P., and Ouyang, C. (1991). “Mechanical behavior of fiber-reinforced cement-based composites.”J. Am. Ceramics Soc., 74(11), 2727–2738, 2947–2953.
23.
Stang, H., Li, Z., and Shah, S. P.(1990). “The pull-out problem—the stress versus fracture mechanical approach.”J. Engrg. Mech., ASCE, 116(10), 2136–2150.
24.
Stang, H., and Shah, S. P.(1986). “Failure of fiber reinforced composites by pull-out fracture.”J. Mat. Sci., 21(3), 953–958.
25.
Takaku, A., and Arridge, R. G. C.(1973). “The effect of interfacial radial and shear stress on fiber pull-out in composite materials.”J. Phys. D: Appl. Phys., 6, 2038–2047.
26.
Thoulass, M. D., and Evans, A. G.(1988). “Effect of pull-out on the mechanical properties of brittle matrix composites.”Acta Metallurgica, 26(3), 517–522.
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Published In
Journal of Engineering Mechanics
Volume 122 • Issue 1 • January 1996
Pages: 10 - 18
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jan 1, 1996
Published in print: Jan 1996
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