The Tangent Compliance of Staple-fibre Bundles in Tension

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Abstract
The mechanical properties of an untwisted oriented assembly or “bundle” of fibres differ from those of the constituent fibres and are most conveniently described by a tangent-compliance matrix whose non-zero entries can be readily related to various uniaxial tests. The most interesting and distinguishing characteristic of a staple-fibre bundle is its compliance when stretched in the direction of preferential fibre orientation. The resistance to deformation is highly dependent on the lateral pressure, which determines the amount of relative fibre slippage. A theoretical connexion between the properties of the individual fibres in the bundle and the behaviour of the bundle is established in this paper. The key fibre properties are shown to be the length distribution, the average tensile properties, and the single-fibre withdrawal (i.e., frictional) properties. A reasonable agreement with experimental data is found, although evaluation of the model is difficult. It is suggested that the theory will find application in finite-element models used to predict yarn mechanics.

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