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Research Papers

The Effect of Fiber Diameter Distribution on the Elasticity of a Fiber Mass

[+] Author and Article Information
Mårten Alkhagen1

Department of Applied Mechanics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden; School of Textiles, University College of Borås, SE-50190 Borås, Sweden

Staffan Toll

Department of Applied Mechanics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden; School of Textiles, University College of Borås, SE-50190 Borås, Sweden

1

Present address: SCA Hygiene Products AB, R&D Personal Care, SE-40503 Gothenburg, Sweden.

J. Appl. Mech 76(4), 041014 (Apr 27, 2009) (6 pages) doi:10.1115/1.2966178 History: Received December 10, 2007; Revised May 30, 2008; Published April 27, 2009

A random mass of loose fibers interacting by fiber-fiber contact is considered. As proposed in a previous paper, the elastic response is modeled based on the statistical mechanics of bending and torsion of fiber segments between fiber-fiber contact points. Presently we show how the statistical approach can be used to account for a distribution of fiber diameters rather than just a single diameter. The resulting expression has the same form and the same set of parameters as its single-diameter counterpart, except for two dimensionless reduction factors, which depend on the fiber diameter distribution only and reduce to unity for monodisperse fibers. Uniaxial compressibility experiments are performed on several materials with different bimodal fiber diameter distributions and are compared to model predictions. Even though no additional parameters were introduced to model the effect of mixed fiber diameters, the behavior is accurately predicted. Notably, the effect of the nonuniform fiber diameter is strong: A mixture of two fiber diameters differing by a factor of 2 can reduce the response by an order of magnitude, compared to the case of uniform diameter.

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Copyright © 2009 by American Society of Mechanical Engineers
Topics: Fibers
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References

Figures

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Figure 1

Segmentation of a fiber, where 2b is the fiber crimp spacing

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Figure 2

Schematic of a contact point with the fiber diameters and the local basis vectors indicated. The primes refer to the contacting fiber.

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Figure 3

The stiffness reduction versus the fiber radius ratio for various mixing proportions, according to Eq. 33

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Figure 4

The stiffness reduction versus the fiber radius ratio for various mixing proportions, according to Eq. 43

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Figure 5

Experimental data for fiber masses where d1=27μm and d2=50μm and the 1-fraction Φ1 are 0.25, 0.50, and 0.75, respectively. The solid lines are model fits to determine the experimental reduction factors Γbexpt and Γtexpt.

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Figure 6

Γb according to Eq. 33 (solid lines) compared to experimental data (the squares correspond to Φ1=0.25, the triangles to Φ1=0.5, and the circles to Φ1=0.75)

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Figure 7

Γt according to Eq. 43 (solid line) compared to experimental data (the squares correspond to Φ1=0.25, the triangles to Φ1=0.5, and the circles to Φ1=0.75)

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