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Scaling Theory of Elasticity and Fracture in Disordered Networks

Published online by Cambridge University Press:  21 February 2011

P. M. Duxbury  and
S. G. Kim
P. M. Duxbury
Affiliation:
Dept. of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University.
S. G. Kim
Affiliation:
Dept. of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University.
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Abstract

We discuss scaling theories for the elasticity and tensile fracture of random central force spring networks with bond dilution disorder. Effective medium theory works quite well for elasticity but needs very new ingredients to be even qualitatively correct for tensile fracture. A novel “extreme scaling theory” predicts a dilute limit singularity and a size effect in the tensile strength. These predictions are supported by numerical simulations.

We extend the above arguments to networks with distributions of bond disorder, and compare the central force network theories to models currently used in the study of rigid cellular materials.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 207: Symposium I – Mechanical Properties of Porous and Cellular Materials , 1990 , 179
Copyright
Copyright © Materials Research Society 1991

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References

1. Hashin, Z., “Analysis of Composite Materials - A Survey”, J. Appl. Mech. 50, 1983, pp. 481–505 Google Scholar
2. Feng, S., Thorpe, M.F. and Garboezi, E., “Effective-medium theory of percolation on central-force elastic networks”, Phys. Rev.Rev B31, 1985, pp. 276–280.Google Scholar
3. Feng, S., Halperin, B.I. and Sen, P.N., “Transport properties of continuum systems near the percolation threshold”, Phys. Rev. 35, 1987, pp. 197–214.CrossRefGoogle Scholar
4. Krajcinovic, D. and Silva, M.A.G., “Statistical Aspects of the Continuous Damage Theory”, Int. J. Solids Structures 18, 1982, pp. 551–562 CrossRefGoogle Scholar
5. Turcotte, D.L., Smalley, R.F. Jr. and Solla, Sara A., “Collapse of loaded fractal trees”, Nature 313, 1985, pp. 671–672; P. Ray and B.K. Chakrabarti, “A microscopic approach to the statistical fracture analysis of disordered brittle solids”, Solid St. Comm. 53, 1985, pp. 4 77–4 79.Google Scholar
6. Sahimi, M. and Goddard, J.D., “Elastic percolation models for cohesive failure in heterogeneous systems”, Phys. Rev. B33, 1986, pp. 7848–7851.Google Scholar
7. Sieradzki, K. and Li, R., “Fracture behavior of a solid with random porosity”, Phys. Rev. Letts. 56, 1986, pp. 2509–2511.CrossRefGoogle Scholar
8. Duxbury, P.M., Leath, P.L. and Beale, P.D., “Breakdown properties of quenched random systems-the random fuse network”, Phys. Rev. B36, 1987, pp. 367–380.CrossRefGoogle Scholar
9. Benguigui, L., Ron, P. and Bergman, D.J., “Strain and Stress at the fracture of percolative media”, J. de Phys. 48, 1987, pp. 1547–1551.Google Scholar
10. Guyon, E., Roux, S. and Bergman, D.J., “Critical Behavior of Elastic Failure Thresholds in Percolation”, J. de Phys. 148, 1987, pp. 903–904.Google Scholar
11. Beale, P.D. and Srolovitz, D.J., “Elastic fracture in random materials”, Phys. Rev. B37, 1988, pp. 5500–5507; G.N. Hassold and D.J. Srolovitz, “Brittle fracture in materials with random defects”, Phys. Rev. B 39, 1989, pp 9273–9281.Google Scholar
12. Roux, S., Hansen, A., Herrmann, H.J. and Guyon, E., “Rupture of Heterogeneous Media in the limit of infinite disorder”, J. Stat. Phys. 52, 1988, pp. 237–244; H.J. Herrmann, A. Hansen and S. Roux, “Fracture of disordered elastic lattices in two dimensions”, Phys. Rev. 39, 1989, pp. 637–648; A. Hansen, S. Roux and H.J. Herrmann, “Rupture of central-force lattices”, J. Phys. France 50, 1989, pp. 733–744; W.A. Curtin and H. Scher, “Brittle fracture of disordered materials”, J. Mater. Res. 5, 1990, pp. 535–553. S. Arbabi and M. Sahimi, “Test of universality for threedimensional models of mechanical breakdown of disorderd solids”, Phys. Rev. B 41, 1990, pp. 772–775.Google Scholar
13. Herrmann, H.J and Roux, S eds., “Statistical Models for the Fracture of Disordered Materials”, Elsevier Science Publishers, NY, 1990.Google Scholar
14. Thorpe, M.F., “Rigidty Percolation in Glassy Structures”, J. non-Cry. Sol. 76, 1987, pp. 109–116.Google Scholar
15. Gibson, L.J. and Ashby, M.F., ”Cellular Solids”, Pergamon Press, NY (1988).Google Scholar
16. David Clarke private communication.Google Scholar
17. see e.g. Castillo, E., “Extreme Value Theory in Engineering”, Academic Press, NY, 1988.Google Scholar
18. de Arcangelis, L., Redner, S. and Herrmann, H.J., “A random fuse model for breaking processes”, J. de Physique Lett. 46, 1985, L585–590.Google Scholar
19. Garboczi, E.J., “Effective froce constant for a central force random network”, Phys. Rev. B 37, 1988, pp. 318–320.Google Scholar
20. Gumbel, E.J., “Statistics of Extremes”, Columbia Univ. Press, NY 1958.Google Scholar
21. Kahng, B., Bartrouni, G.G., Redner, S., de Arcangelis, L. and Herrmann, H.J., “Electrical breakdown in a fuse network with continuously distributed breaking strengths”, Phys. Rev. B 37, 1988, pp. 7625–7637; K Sieradski private commumication; Y.S. Li and P.M. Duxbury, “Crack arrest by residual bonding in spring and resistor networks”, Phys. Rev. B 38, 1988, pp. 9257–9260;Google Scholar
22. Coppard, R.W., Dissado, L.A., Rowland, S.M. and Rakowski, R., “Dielectric breakdown of metal-loaded polyethylene”, J. Phys. CM. 1, 1989, pp. 3041–3045; P.M. Duxbury, P.D. Beale, H. Bak and P.A. Schroeder, “Capacitance and dielectric breakdown of metal loaded dielectrics”, J. Phys. D, 23, 1546 (1990).Google Scholar