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

  • V. I. Räisänen (a1), M. J. Alava (a2), K. J. Niskanen (a3) and R. M. Nieminen (a4)

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.

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1.Cox, H. L., Br. J. Appl. Phys. 3, 72 (1952).
2. For shear-lag models for discontinuous fiber composites, see Robinson, I. M. and Robinson, J. M., J. Mater. Sci. 29, 4663 (1994).
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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.
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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.
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.
26.Duxbury, P. M., Guyer, R. A., and Machta, J., Phys. Rev. B 51, 6711 (1995).

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