Radial distribution functions (RDFs) for random, hard-core model patterns and actual composite material microstructures have been determined. The environs of the typical fiber in the random pattern have a higher fiber areal density nearer to the fiber than farther away. These differences increase with volume fraction. The RDFs for random patterns show good agreement with theory. The RDFs for Nicalon/zirconia titanate composites appear similar to the random case, but also display an angular dependence on near-neighbor distribution. The proximity of near-neighbors has important ramifications for modeling the micromechanics of tow-based fiber composite mateials.
Get full access to this article
View all access options for this article.
References
1.
1. Everett, R. K. and J. H. Chu. 1993. "Modeling of Nonuniform Composite Microstructures,"J. Comp. Mat., 27(11):1128-1144.
2.
2. Everett, R. K.1994. "Estimating Nearest-Neighbor Distance in Random Distributions," submitted to Acta Metall.
3.
3. Pysher, D. J.et al.1989. "Strengths of Ceramic Fibers at Elevated Temperatures,"J. Am. Ceram. Soc., 72(2):284-288.
4.
4. Bender, B. A.et al.1992. "Optimization of the Mechanical Properties of Silicon Carbide-Fiber-Reinforced Zirconia Titanate Matrix Composites through Controlled Processing,"J. Am. Ceram. Soc., 75(6):1628-1635.
5.
5. Kirkwood, J. G. and E. M. Boggs. 1942. "The Radial Distribution Function in Liquids,"J. Chem. Phys., 10:394-402.
6.
6. Hansen, J. P. and I. R. McDonald. 1986. Theory of Simple Liquids, Second Edition. London: Academic Press.
7.
7. Wertheim, M. S.1964. "Analytic Solution of the Percus-Yevick Equation,"J. Math. Phys., 5(5):643-651.
8.
8. Smith, W. R. and D. Henderson. 1970. "Analytical Representation of the Percus-Yevick Hard-Sphere Radial Distribution Function,"Mol. Phys., 19(3):411-415.
9.
9. Yuste, S. B. and A. Santos. 1993. "A Heuristic Radial Distribution Function for Hard Disks,"J. Chem. Phys., 99(3):2020-2023.
10.
10. Verlet, L. and J.-J. Weis. 1972. "Equilibrium Theory of Simple Liquids,"Phys. Rev. A, 5(2):939-952.
11.
11. Berryman, J. G. and G. W. Milton. 1988. "Microgeometry of Random Composites and Porous Media,"J. Phys. D, Appl. Phys., 21:87-94.
12.
12. Milton, G. W.1981. "Bounds on the Electromagnetic, Elastic, and Other Properties of Two-Component Composites,"Phys. Rev. Lett., 46(8):542-545.
13.
13. Beran, M. and J. Molyneux. 1966. "Use of Classical Variational Principles to Determine Bounds for the Effective Bulk Modulus in Heterogeneous Media,"Q. Appl. Math., 24:107-118.
14.
14. Torquato, S. and G. Stell. 1982. "Microstructure of Two-Phase Random Media. I. The n-Point Probability Functions,"J. Chem. Phys., 77(4):2071-2073.
15.
15. Ju, J. W. and T. M. Chen. 1994. "Effective Elastic Moduli of Two-Phase Composites Containing Randomly Dispersed Spherical Inhomogeneities,"Acta Mech., 103:123-144.
