Structural analysis of wool yarns

In this report the behaviour of textile yarns under tensile loading is studied with the aid of finite-element techniques, with particular emphasis on wool yarns. Both continuous filament- and staple fibre- yarn models are developed and evaluated. The continuous-filament yarn model is based on an earlier model developed by Carnaby, which is adapted to comply with the rigorous rules of finite-element theory. Because of the large displacements and strains which occur and the non-linear material V properties the analysis utilises non-linear continuum mechanics to describe the governing equations, which are based on the principle of virtual work. An alternative analysis is also developed in which the governing equations are directly derived from the equilibrium conditions for the internal stresses. Both analyses yield results which compare favourably with those obtained by Carnaby, but use only a fraction of the previously required computing time which inhibited extensive evaluation of his model. In order to model the long-gauge behaviour of wool yarns a staple-fibre yarn model is presented, based on earlier work by Hearle, which incorporates fibre migration and slippage. Extensive changes have been made to Hearle's original model, reflecting the advances made in the continuous-filament yarn analyses. Major additional features are the incorporation of changes in yarn configuration due to slippage, non-linear material behaviour, and a more realistic modelling of the lateral contraction of a yarn. The alternative finite-element analysis is used because it simplifies the application to non-conservative problems. A number of specially spun yarns were used to evaluate both the continuous filament- and the staple fibre- yarn analyses.