Abstract:The maximum strain experienced by the thinnest segment of a non-uniform fiber governs fiber breakage, yet this maximum strain can not be obtained from a normal single fiber test. Only the average strain of the whole fiber specimen can be obtained from a normal single fiber tensile test. This study has examined the relationship between the average strain, the maximum strain and the degree of fiber non-uniformity, expressed in coefficient of variation (CV) of fiber diameters along fiber length. The tensile strain of irregular fibers has been simulated using the finite element method (FEM). Using this method, average and maximum tensile strains of non-uniform fibers were calculated. The results indicate that for irregular fibers such as wool, there is an exponential relationship (i.e. ) and the alongfiber diameter variation (CV). The strain ratio decreases with the increase of the along-fiber diameter variation.

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The limiting irregularity of yarn is the minimum count variation expected from ideal yarn with a random fibre ends distribution. It can be calculated with the Martindale limiting irregularity model which takes into account the changes in the number of fibres in yarn crosssection and the variations in fibre cross-sectional areas. However, the variations in fibre cross-sectional areas are calculated from between-fibre diameter variations only, without considering the within-fibre diameter variations. Wool fibres exhibit diameter variations both between fibres and within fibres. Ignoring the within-fibre diameter variations may lead to an underestimation of yarn limiting irregularity. This paper reports an improved model for calculating the limiting irregularity of wool yarn, incorporating both between-fibre and within-fibre diameter variations of the constituent wool fibres. Experimental verification shows that this model can predict yarn limiting irregularity more accurately than the existing one. Based on this improved yarn limiting irregularity model, an improved effective fineness model which also incorporates both within-fibre and between-fibre diameter variations has been established.