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TECHNICAL PAPERS

Transport in Stochastic Fibrous Networks

[+] Author and Article Information
X. Cheng, A. M. Sastry, B. E. Layton

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J. Eng. Mater. Technol 123(1), 12-19 (Jul 31, 2000) (8 pages) doi:10.1115/1.1322357 History: Received April 14, 1999; Revised July 31, 2000
Copyright © 2001 by ASME
Topics: Fibers , Networks
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References

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Figures

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Scanning electron micrograph of a nickel substrate (positive plate) used in the Ni/MH cell. The material pictured is comprised of nickel fibers, sinter bonded into a network of approximately 97% porosity (National Standard, Advanced Fiber Substrate material).
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Network generation approach (after Cheng et al. 5). A stochastic array of 1D fibers (a) is modified to enforce periodicity, then nonconductive ends are removed to assess the effective volume fraction utilized for unidirectional conductivity (b)
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(a) Utilized volume fraction versus original volume fraction, and (b) bond density, for various aspect ratios, for the case where the staple length is equal to the unit cell length. Twenty simulations were performed for each case; averaged data are shown.
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(a) Utilized volume fraction versus original volume fraction, and (b) number of bonds, for various aspect ratios, for the case where the staple length is 1.5 × unit cell length. Twenty simulations were performed for each case; averaged data are shown.
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Number of bonds versus volume fraction—simulations using the present network generation approach versus the theoretical prediction of Kallmes and Corte 8. Results are shown for three aspect ratios of fibers, (a) L/D=100; (b) L/D=50, and (c) L/D=10. In each case, 10 simulations were performed, and results shown are ±1σ.
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The resistor network approach (a), as in Fig. 4, are used to construct equivalent circuits (b)
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Comparison of effective conductivities from a classical, semi-empirical percolation approach (after Kirkpatrick 10 using t=1.3 per Stauffer 11 and Vc=4.2, per Balberg and Binenbaum 14) with simulation results, the theoretical upper bound (parallel model) and the degenerate result of classical micromechanics; aspect ratios are L/D=100 in all cases. Twenty simulations are shown in each case, with error bars denoting ±1σ. A large range is shown in (a), with the smaller range of volume fractions enlarged in (b).
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Simulation (±1σ) conductivities versus volume fraction, plofted versus the effective medium theory (Eq. (7b)) and the upper (parallel) bound (Eq. 9). Data shown are for L/Lu=1,L/D=100. Two techniques are shown, including (a) the resistor network approach and (b) the effective volume approach. Twenty simulations were run for each case.
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Simulation (±1σ) conductivities versus volume fraction, for L/Lu=1.5,L/D=100, for (a) the resistor network approach and (b) the effective volume approach. Twenty simulations were run for each case.
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Experimental data for resistivity versus simulation/model predictions. Two types of material, National Standard Fibrex (7% and 18% by volume) and AFS (3% and 5%) were studied. Each was comprised of a blend of fibers and particles. Simulations were performed for the aspect ratios and staple lengths reported by the manufacturer. Five simulations were run for each case.
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Evaluation of the effect of alignment in networks, for transverse conductivity. Networks with varying degrees of alignment in the x-direction were generated, as shown in (a) (here, for a volume fraction ∼20%, L/D=100,L/Lu=1, and average and standard deviation of orientation with respect to the x-axis of 0 and 10 deg, respectively). Effective conductivites versus orientation were then calculated via the resistor network approach (as measured by standard deviation of orientation of fibers following a normal distribution for orientation). Twenty simulations were run for each case, and ±1σ results are shown. (a) parallel; (b) transverse.

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