Yarn tenacity is the manifestation of fibre tenacity.

Yarn tenacity is, however, never equal to fibre tenacity, but is only a fraction of fibre tenacity. There are four reasons for this.

Further, of the fibres present at the place of break, only a fraction may break and contribute to yarn tenacity, while the rest may slip.

The fibres at the place of yarn break that break themselves and contribute to yarn tenacity, may not break at the ‘zero-gauge’, but at some finite gauge. In this context Lord’s concept (7) of a yarn-element that is subject to break in yarn testing is worth recalling. “Where a length of yarn is stressed the tension is not distributed uniformly along the length of each fibre. The yarn may be conceived as being composed of successive elements in the form of sections of fibre bundles. Not only will these bundles differ in fibre arrangement and linear density, giving tight and loose and also thick and thin places, but they will also differ in their length. The length of any given element is poorly defined, because the elements are not separate entities but each gradually merges into its neighbours at either end. Nevertheless, an average element length may be considered to exist. Amongst many other factors, the strength of the yarn will depend on the bundle strength of the elements, and in turn on the length of the elements. From this approach it is hardly surprising to find that, for carded yarns, the bundle strength measured at zero test length provides information less useful than measurements at 1/8-in. The increased regularity and parallelization of fibre arrangements in combed yarns suggests a decrease in effective length of yarn element, a feature which may also occur in doubling when fibres are brought into more intimate contact with each other. For such material the best test length for fibre-bundle strength determination may be one closer to zero than that found suitable for the looser, carded yarns.”

Thus according to Lord the differences between carded yarns on the one hand, and combed and doubled yarns on the other, make it preferential to use the 1/8-in.fibre-bundle tenacity for carded yarns, and the zero-gauge length tenacity for combed yarns in the respective predictive equations for yarn tenacity. There is an important corollary to this. The appropriate gauge-length of cotton tenacity to use in the prediction equations for yarn tenacity should decrease asymptotically with increasing levels of twist in the yarn. Now, as the test length is decreased, cotton fibre-bundle tenacity is known to increase asymptotically to the zero-gauge value. We have to incorporate this fact in the equation for the translation of fibre-bundle tenacity into yarn tenacity. We can achieve this by the use of fibre-bundle tenacity at zero-gauge in general, and at the same time by the inclusion in the equations of a fraction that would give the tenacity at the gauge-length appropriate for the level of twist in the yarn.

There is a subtle difference between the way fibres are broken in the determination of fibre-bundle strength and the way fibres are broken in the determination of tensile strength of yarn: all the fibres in the bundle under test, without exception, bridge the entire distance between the two clamps; as against this some fibres in the bundle that breaks in yarn testing may have one end lying within the break-zone, and will not, therefore, share the applied tensile load; the number of such fibres that do not share the applied load will, conceivably, depend on fibre-length distribution of the cotton. This has to be taken into account in the construction of the equation.

There is one more reason for the yarn tenacity falling short of the fibre-bundle tenacity. This is the obliquity of the fibres in the twisted yarn to the yarn-axis, which is the direction in which tensile stress is applied in the determination of the breaking load.

We have also provided for another important nuance in the situation. Instruments for yarn tenacity tests are calibrated by an external universal method; instruments for fire tenacity tests are calibrated with the help of ad hoc standards, that have no external validation.

Lastly, there is the contribution of the drafting system: two yarns from the same cotton, and of the same count and twist, but spun two drafting systems, may not be of same CSP. This is because the two yarns could differ in irregularity. In other words, over and above the count related contribution to irregularity, there is also a contribution of the drafting system. This has also to be accounted for by the model for yarn tenacity.