A. H. Wilkins

Movement of fibers in assemblies

Abstract Previous studies of the mechanics of fiber assemblies have neglected fiber movements that are due to perturbations of the assembly. Axial movements, which are treated in the paper, are important in pilling, bagging, felting, and incremental drafting of yarns in weaving, but lateral movements may also occur. A dynamical model is analogous to molecular statistical mechanics. Both a diffusion model and a driven model are presented. The resistance to movement is due to gripping forces, which may be externally imposed or caused by structural features, such as twist; both are easy to take into account. The geometric forms of entanglements and the way in which they add to frictional resistance are discussed in more detail.

Fibre slippage in cyclically perturbed fibrous assemblies

The dynamics of fibre slippage within general non-bonded fibrous assemblies is studied in the situation where the assembly is subjected to general small cyclic loads. Two models are proposed. The first is applicable when the general cyclic loading is complemented by an occasional tugging force on one end of a fibre, which causes it to gradually withdraw from the assembly, such as might occur during the pilling of a textile. The second considers the situation in which the cyclic perturbations act around a constant background load applied to the assembly. The dynamics is reminiscent of self-organized critical behaviour. This model is applied to predict the progressive elongation of a single yarn during weaving.

Mechanistic modelling of pilling. Part I: Detailing of mechanisms

Abstract Mechanistic models of pilling are discussed in general terms, and a framework for pilling simulations is thereby created. A fundamental flaw in earlier models of pilling is revealed. A more comprehensive model of fibre diffusion and withdrawal from the fabric is proposed, and this is solved in general terms to find the rate of fuzz growth. Fuzz wear-off and entanglement into pills are discussed. Fibre fatigue is introduced, and it is demonstrated that this potentially increases the rate of withdrawal of anchor fibres.

Mechanistic modelling of pilling. Part II: Individual-fibre computational model

Abstract A one-dimensional computational model of pilling of a fibre assembly has been created. The model follows a set of individual fibres, as free ends and loops appear as fuzz and are progressively withdrawn from the body of the assembly, and entangle to form pills, which eventually break off or are pulled out. The time dependence of the computation is given by ticks, which correspond to cycles of a wear and laundering process. The movement of the fibres is treated as a reptation process. A set of standard values is used as inputs to the computation. Predictions are given of the change with a number of cycles of mass of fuzz, mass of pills, and mass removed from the assembly. Changes in the standard values allow sensitivity studies to be carried out.