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Does the shear-lag model apply to random fiber networks?

Published online by Cambridge University Press:  31 January 2011

V. I. Räisänen ,
M. J. Alava ,
K. J. Niskanen  and
R. M. Nieminen
V. I. Räisänen
Affiliation:
CSC–Center for Scientific Computing, P.O. Box 405, FIN-02101 Espoo, Finland
M. J. Alava
Affiliation:
Helsinki University of Technology, Laboratory of Physics, FIN-02150 Espoo, Finland
K. J. Niskanen
Affiliation:
KCL Paper Science Centre, P.O. Box 70, FIN-02151 Espoo, Finland
R. M. Nieminen
Affiliation:
CSC–Center for Scientific Computing, P.O. Box 405, FIN-02101 Espoo, Finland and Helsinki University of Technology, Laboratory of Physics, FIN-02150 Espoo, Finland
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Abstract

The shear-lag type model due to Cox (Br. J. Appl. Phys. 3, 72 (1952) is widely used to calculate the deformation properties of fibrous materials such as short fiber composites and random fiber networks. We compare the shear-lag stress transfer mechanism with numerical simulations at small, linearly elastic strains and conclude that the model does not apply to random fiber networks. Most of the axial stress is transferred directly from fiber to fiber rather than through intermediate shear-loaded segments as assumed in the Cox model. The implications for the elastic modulus and strength of random fiber networks are discussed.

Type
Articles
Information
Journal of Materials Research , Volume 12 , Issue 10 , October 1997 , pp. 2725 - 2732
Copyright
Copyright © Materials Research Society 1997

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References

REFERENCES

1.Cox, H. L., Br. J. Appl. Phys. 3, 72 (1952).CrossRefGoogle Scholar
2. For shear-lag models for discontinuous fiber composites, see Robinson, I. M. and Robinson, J. M., J. Mater. Sci. 29, 4663 (1994).CrossRefGoogle Scholar
3.Page, D. H. and Seth, R. S., Tappi J. 63, 113 (1980).Google Scholar
4.Perkins, R. W., in Materials Interactions Relevant to the Pulp Paper and Wood Industries, edited by Caulfield, D. F., Passaretti, J. D., and Sobczynski, S. F. (Materials Research Society, Pittsburgh, PA, 1990), Vol. 197, p. 99, and references therein.Google Scholar
5. See, e.g., Galiolis, C., Composite Sci. Technol. 48, 15 (1994) and references therein.CrossRefGoogle Scholar
6.Andrews, M. C., Day, R. J., Hu, X., and Young, R. J., J. Mater. Sci. Lett. 11, 124 (1992).CrossRefGoogle Scholar
7.Murat, M., Anholt, M., and Wagner, H. D., J. Mater. Res. 7, 3120 (1992).CrossRefGoogle Scholar
8.Monette, L., Anderson, M. P., and Grest, G. S., J. Appl. Phys. 75, 1155 (1994).CrossRefGoogle Scholar
9.Duxbury, P. M., Beale, P. D., and Moukarzel, C., Phys. Rev. B 51 (6), 3476–3488; C. Moukarzel and P. M. Duxbury, J. Appl. Phys. 76, 4086 (1994).CrossRefGoogle Scholar
10.Blumentritt, B. F., Vu, B. T., and Cooper, S. L., Polym. Eng. Sci. 15, 428 (1975).Google Scholar
11.Karbhari, M. and Wilkins, D. M., Scripta Metall. Mater. 25, 707 (1991).CrossRefGoogle Scholar
12.Åström, J., Saarinen, S., Niskanen, K., and Kurkijärvi, J., J. Appl. Phys. 75, 2383 (1994).CrossRefGoogle Scholar
13. Cf, e.g., Sahimi, M., Physica A 186, 160 (1992).CrossRefGoogle Scholar
14.Hansen, A., in Statistical models for the fracture of disordered media, edited by Herrmann, H. J. and Roux, S. (North-Holland, Amsterdam, 1990), p. 115 ff.Google Scholar
15. Version 4.9, Hibbitt, Karlsson & Sorensen Inc., 1080 Main St., Pawtucket, RI 02860.Google Scholar
16. We note here in passing that strictly speaking in our simulations the elastic modulus is not equal to Young's modulus, because the Poisson contraction is prohibited. The relation between the two in 2D is given by [see, e.g., Landau, L. D. and Lifshitz, E. M., Theory of Elasticity (Pergamon Press Ltd., London, 1959), p. 52] where E 0 is the elastic modulus of a network with fixed y-coordinate of the edges perpendicular to external stress, E is the elastic modulus of a network with Poisson contraction, and ν − 0.33 is the Poisson contraction coefficient that can be obtained from the Cox model.Google Scholar
17.Corte, H. and Kallmes, O. J. in The Formation and Structure of Paper, Transactions of the Symposium held at Oxford, edited by Bolam, J. (William Clowes and Sons, Ltd., London, 1962), pp. 13–52.Google Scholar
18.Pike, G. E. and Seager, C. H., Phys. Rev. B 10, 1421 (1974).Google Scholar
19.Jangmalm, A. and Östlund, S., Nordic Pulp and Paper Res. J. 10, 156 (1995).CrossRefGoogle Scholar
20.Heyden, S. and Gustafsson, P. J., A network model for application to cellulose fiber materials, conference paper in 7th Int. Conference on Mechanical Behavior of Materials, May 1995, The Netherlands.Google Scholar
21.Hansen, A., in Statistical models for the fracture of disordered media, edited by Herrmann, H. J. and Roux, S. (Elsevier Science Publishers, North-Holland, 1990), p. 134.Google Scholar
22.Hashin, Z. and Shtrikman, S., J. Mech. Phys. Solids 11, 335 (1963); see also Z. Hashin, J. Appl. Mech. 50, 481 (1983) and references therein and M. Deng and C. T. J. Dodson, Paper: An Engineered Stochastic Structure (Tappi Press, 1994), pp. 204–206 for an application to fiber networks.CrossRefGoogle Scholar
23.Grubb, D. T., Li, Z-F., and Phoenix, S. L., Comp. Sci. Technol. 59, 237 (1995).Google Scholar
24. See, e.g., Niskanen, , in Products of Papermaking—Transactions of the Tenth Fundamental Research Symposium held at Oxford: September 1993, p. 685, Fig. 32.Google Scholar
25.Hansen, A., in Statistical models for the fracture of disordered media, edited by Herrmann, H. J. and Roux, S. (Elsevier Science Publishers, North-Holland, 1990), p. 149 ff.Google Scholar
26.Duxbury, P. M., Guyer, R. A., and Machta, J., Phys. Rev. B 51, 6711 (1995).Google Scholar