Abstract
A geometrical model is proposed to explain the conformational change of fibres in a single yarn during extension in the low-stress region, assuming that fibre slippage and fibre elongation do not occur. The key parameters affecting the yarn low-stress extension are the yarn twist factor and the yarn packing fraction. On extension, a yarn is compressed diametrally and a limit of low-stress extension is attained when the yarn packing fraction reaches an assumed maximum value of 0.76. Using the Van Wyk theory of compression of fibre assemblies, a relationship between the tensile stress and the yarn extension is derived and the load-extension curve of a single yarn in the region of low-stress extension is defined. Equations are also derived enabling calculation of the yarn packing fraction from the low-stress load-extension curve of a yarn. This work establishes a first step towards the more complex models to characterise the low-stress extension of twofold yarns and woven fabric.
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