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Thelowest diameter distribution and strength variation of Australiansuperfine Merino wool and Inner Mongolia cashmere within diameter andlength groups

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Thelowest diameter distribution and strength variation of Australiansuperfine Merino wool and Inner Mongolia cashmere within diameter andlength groups

Differentfactors are important in the determination of price, product qualityand processing performance of wool fibre. Some of these factorsinclude the fibre diameter, strength, diameter and theirdistribution. Studies have indicated that the wool diametercorresponds to the log-normal distribution [6]. The variability inwool diameter makes the wool fibres different from the syntheticfibres. The fibre bundle test is usually employed commercially forthe determination of fibre strength since the single fibre tensiletest is tedious and time-consuming as one will have to work with anindividual fibre over time. However, the resultant force when usingan individual fibre is usually lower than the average fibre strengthobtained in a fibre bundle because of the different power of everysingle fibre in the fibre bundle. The incongruity is mainlydetermined by the disparity of single fibre strength. Little changesin the diameter of a single thread significantly affect the breakingforce of the fibre. However, the influence of differences in fibrediameter on the variation in fibre strength is still undetermined. Asindicated by the existing rectilinear association between thebreaking potency of the fibre and the fibre’s square diameter, thedistribution of the breaking force must also obey the log-normaldistribution as well.

Furthermore,there exists a relationship between the fibre’s Coefficient ofVariation’s breaking force and the fibre diameter which havestatistically been established. The diameter of the thread clearlyaffects the breaking force of the fibre being tested and this hasalso been supported by some studies conducted on the same. For asmall sample size, therefore, the Constant of Variation in minimumfibre cross sectional thickness should be employed instead of thecoefficient of variation of the maximum diameter. In the equationsavailable for the calculation of the coefficients, the secondequation of Coefficient of Variance fits the observed data betterthan the first equation especially for the small samples of scouredwool. Two assumptions are however made in the establishment of theserelationships. The first assumption is the linear relationshipbetween the fibre breaking strength and the minimum fibre diameter’ssquare. The second assumption states that there should exist alog-normal distribution of the minimum diameters of the fibres. Withthe initial hypothesis, there is a simple relationship between theCoefficient of Variance of breaking force and the Coefficient ofVariance of the least diameter and this has been derived empiricallyand verified using the scoured wool. The breaking strength isaffected by some factors but the diameter has a greater significancein the determination of the breaking force of the fibre.

Upto this period, a minimal number of studies have established thespreading of sole ASFW and IMC fibre forte within diameter groups.This paper focuses on the correlation that exists between variationsin the diameter of the fibre and the strength variations. Thesechanges can also be applied to the unprocessed ASFW and IMC fibres inthe groups of the different diameters (1-micron interval). Thechanges in the breaking force of the different fibres lead to aresultant indication of the strength of the particular fibres.

TheLinear Dependency of breaking force on the square of least diameter

Aclear rectilinear association exists amid the breaking energy and thesquare mean fibre thickness as stipulated by the different methodsemployed by some researchers. From various studies, it has been foundthat approximately eighty-five percent of soft wool and seventypercent of a significant wool break at the point where the diameteris minimal. The correlations of the breaking force and the square ofminimum diameter exist at several experimental diameters for the ASFWand IMC as indicated by various studies. There exists a high linearcorrelation with the breaking force of the ASFW and the IMC fibresand this has a relationship with the square of minimum fibre diameterirrespective of the fibre length.

Correlationsbetween the differences in minimal fibre diameters and single fibrebreaking force

Thebreaking strength of the ASFW and the IMC fibres are predictable asthe minimum diameters of fibres in the different diameter groups fitthe log-normal distribution. Also, a linear correlation existsbetween the breaking potency and the square of the least fibrediameters. The second and third equations can be applied to all thediameter groups in ASFW and IMC. The Coefficients of Variance of thebreaking force of both the measured and predicted single fibre, aswell as the relative errors of the ASFW and IMC fibres, are listed intable two.

Thetable indicates that a large number of the predicted values have aslightly lesser than the measured values. The values indicated in thetable are not true for the scoured wool as reported in the past work.It is, therefore, true that some errors exist between predicted andmeasured CV values in the table. Prediction of CV values shown by thesecond equation is closer to the experimental results that thoseindicated by the third equation. The results of this are morereasonable since the third equation used an approximation to simplifythe relationship.

Adecrease in the diameter groups has shown a resultant increase in thedifferences between the predicted and the measured values. Themeasured value is, however, much lesser in the coarser diameters thanthose found in the groups with finer diameters. The findings,therefore, give an indication that as the diameters get finer,factors different from the fibre diameters may impact on the breakingforce. For the coarser diameter groups, the findings may indicatethat the fibres have a likelihood of breaking at their thinnestpoint. In the finer fibre groups, there exists uniformity andtherefore, the fibres may break at a different point where defects orflaws in structure exist. Results from past studies suggest that thebreaking force of gnarled or handled wool is typically by thedifferences in the fibre thickness and that the other factors such asinternal structural defects have little impact on the breaking force,especially along the length of the fibre. However, the differences inthe predicted and measured values might be caused by other factors.It should be agreed that the ASFW and IMC do not have a clearcircular cross-sectional area. The tensile strength of the fibrecould also be affected by the fibre crimps and the resultanttorsional stress in the fibre during stretching. However, the resultsobtained in this paper indicate that the combined impact of thesefactors is insignificantly minimal.

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