Simulating the stress-strain properties of woollen yarns

Abstract

This thesis describes a new model of the behaviour of staple fibre yarns under longitudinal extension. Within this new model, several of the most important yarn structural features are described by arbitrary distribution functions. These include mass and twist variation along a yarn, fibre length, fibre diameter, and fibre strength. The initial packing of fibres over any cross-section is considered to be a function of both the local linear density and twist level.

In the model a yarn is treated as a series of discrete segments, each of which may have a different linear density and twist. As this hypothetical structure is extended, constraints of torque and tensile equilibrium result in non-uniform segment strain, and twist movement between segments.

The stress-strain properties of a yarn segment are determined from the behaviour of all the fibres that pass through its central cross-section. Each of these fibres is considered individually, and may have different physical dimensions and material properties. Each fibre is considered to consist of a large number of fibre segments, each of which may have a unique breaking stress.

As a segment extends, fibres contract laterally towards the yarn axis. Individual fibres will partially or completely slip relative to the rest of the structure. Fibres may also break, and such broken fibres may still contribute to yarn tension.

This model is applied to woollen yarns. The breaking stress distribution of wool fibres is examined. Models are developed to predict the 'core-extent' length distribution of fibres within a woollen yarn, the radial fibre packing density in woollen yarns, and the relationship between Uster evenness and the mass and twist variation in short yarn segments.

The predictions of the model are compared with the experimentally measured stress-strain curves of 36 different woollen yarns. These yarns vary in twist, and the fibres they are made from vary in mean diameter, mean length, core bulk, and fibre type. Limited evaluation of the full model results in predicted tenacity and breaking strain distributions that can not be differentiated from the measured distributions by the Kolmogorov-Smirnov two-sample test. A more comprehensive validation of a simplified model shows that the model can predict the tenacity of woollen yarns which are made from fibres with a wide range of properties and which contain a wide range of twist levels.