Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-29T08:12:56.419Z Has data issue: false hasContentIssue false

Disorder and Scaling in Regular and Hierarchical Composites

Published online by Cambridge University Press:  21 February 2011

P. M. Duxbury*
Affiliation:
Dept. of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University.
Get access

Abstract

We first summarize the scaling behavior of breakdown strengths and transport and elastic moduli of random two phase composites. We then consider the effect of disorder on two hierarchical structures. The first, a tree-like structure illustrates the fact that disordered trees, such as occur in many natural circulatory systems, show large fluctuations in their conductance and current flow. The second, a continuous fiber composite (CFC), leads us to suggest that, due to its greater flaw tolerance, a hierarchical microstructural design may improve the longitudinal and transverse toughness of CFC's.

Type
Research Article
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Hale, D.K., “The Physical Properties of Composite Materials”, J. Mat. Sci. 11, 1976, pp. 21052141; G.W. Milton, ”Bounds on the Elastic and Transport Properties of Two-Component Composites”, J. Mech. and Phys. Solids 30, 1982, pp. 177–191.Google Scholar
2. Hashin, Z., “Analysis of Composite Materials - A Survey”, J. Appl. Mech. 50, 1983, pp. 481505; R. Landauer, ”Electrical Conductivity in Inhomogeneous Media”, in Electrical, Transport and Optical Properties of Inhomogeneous Media”, American Institute of Physics, 1978, pp. 2–43; S. Feng, M.F. Thorpe and E. Garboczi, “Effective-medium Theory of Percolation on Central-force Elastic Networks”, Phys. Rev B31, 1985, pp. 276–280.Google Scholar
3. Zabolitzky, J.G., Bergman, D.J. and Stauffer, D., “Precision Calculation of Elasticity for Percolation”, J. Stat. Phys. 44, 1986, pp. 211223; See D. Stauffer in Ref. 4.Google Scholar
4. Stauffer, D., “Introduction to Percolation Theory”, Taylor and Francis (London, 1985); S. Feng, B.I. Halperin and P.N. Sen, “Transport Properties of Continuum Systems Near the Percolation Threshold”, Phys. Rev. 35, 1987, pp. 197–214; P.M. Duxbury, P.L. Leath and P.D. Beale, “Breakdown Properties of Quenched Random Systems-the Random Fuse Network”, Phys. Rev. B36, 1987, pp. 367–380; E. Guyon, S. Roux and D.J. Bergman, ”Critical Behavior of Elastic Failure Thresholds in Percolation”, J. de Phys. 48, 1987, pp. 903–904.Google Scholar
5. Duxbury, P.M. and Kim, S.G., “Scaling Theory of Elasticity and Fracture of Disordered Networks”, Mat. Res. Soc. Symp. 207, 1991, pp. 179195.Google Scholar
6. Weibel, E.R. and Gomez, D.M., “Architecture of the Human Lung”, Science 137, 1962 pp. 577585.Google Scholar
7. Stinchcombe, R.B., “Conductivity and Spin-Wave Stiffness in Disordered Systems-An Exactly Soluble Model”, J. Phys. C7, 1974 pp. 179203; J.P. Straley, “Critical Phenomena in Resistor Networks”, J. Phys. C9, 1976 pp. 783–795.Google Scholar
8. Hull, Derek “An Introduction to Composite Materials”, Cambridge Univ. Press, 1981.Google Scholar
9. Turcotte, D.L., Smalley, R.F. Jr. and Solla, Sara A., “Collapse of Loaded Fractal Trees”, Nature 313, 1985, pp. 671672; W.I. Newman and A.M. Gabrielov, “Failure of Hierarchical Distributions of Fiber Bundles I and II”, UCLA preprints.Google Scholar
10. Harlow, D.G. and Pheonix, S.L., “Probability Distributions for the Strength of Fibrous Materials Under Local Load Sharing I: Two Level Failure and Edge Effects”, Adv. Appl. Prob. 14, 1982 pp. 6894; S.L. Pheonix and R.L. Smith, “The Strength Distribution and Size Effect in a Prototypical Model for Percolation Breakdown in Materials”, Cornell preprint.Google Scholar