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TECHNICAL PAPERS

Micromechanics of a Compressed Fiber Mass

[+] Author and Article Information
Mårten Alkhagen

Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden and School of Textiles, University College of Borås, SE-50190 Borås, Sweden

Staffan Toll

Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden and School of Textiles, University College of Borås, SE-50190 Borås, Swedenstaffan.toll@me.chalmers.se

J. Appl. Mech 74(4), 723-731 (Oct 23, 2006) (9 pages) doi:10.1115/1.2711223 History: Received May 31, 2005; Revised October 23, 2006

A theory is presented for the rate modeling of flexible granular solids based on affine average motion of interparticle contacts. We allow contacts to form and break continually but assume the existence of a finite friction coefficient rendering contacts force free as they form or break. The resulting constitutive equations are of the hypoelastic type. A specific model for the deformation of a fiber mass is then developed. The model improves on previous theories for fiber masses in at least two respects: First, it is more general in that it is not restricted to uniaxial compression, although it is restricted to predominantly compressive deformations histories, due to neglect of frictional dissipation. Second, by allowing torsion as well as bending of fibers, this theory covers a larger deformation range. Compression experiments are performed on carded slivers of PA6 fibers under various conditions. The measured response is found to be in close agreement with that predicted by the model.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

SEM micrograph of carded polyamide-6 fibers with a diameter of 50μm

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Figure 2

Segmentation of a fiber where 2b is the crimp spacing

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Figure 3

Schematic of a contact point with the local basis vectors e, n, and θ indicated. The primed basis vectors refer to the contacting fiber.

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Figure 4

Evolution of some structural parameters for an initially 3D random fiber mass during uniaxial compression

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Figure 5

Uniaxial compressive stress P=−Σ33 versus volume fraction Φ. The dotted line is the van Wyk equation with k=0.01.

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Figure 6

Schematic of sample deformation and the resulting stress distribution Σ33∕Σ33∞ in compression. The objective is to measure the asymptotic stress, Σ33∞, far from the edge.

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Figure 7

The RH dependence of the elastic modulus, e, for PA-6 monofilaments. The dotted line is an arbitrary curve fit.

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Figure 8

Tensile data for PA6 monofilament at 24% RH. The straight line indicates the initial elastic modulus, e.

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Figure 9

Compression data for a fiber mass consisting of fibers with d=35μm

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Figure 10

Compression data for a fiber mass consisting of fibers with d=50μm

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