The two elastica methods (long column and loop) to measure the flexural rigidity of the fiber and yarn are devised.
In the long column method, a sample of length
l is standed perpendicularly and a load larger than its critical one of the buckling is applied to the top (free) end. In measuring the vertical deflection
xα ie the interval between a horizontal line and loaded end is measured experimentaly, the flexural rigidity is obtained by the folloing equation:
Where;
F(α,
k) denominator of perfect elliptical integration of the 1st kind,
k=sinα/2 where α is tangent of loaded end of the distorted sample, this α is obtained by the graph (Fig. 3) indicating the relations between
xα/
l-
k-
F(α,
k). When the sample's own weight is negligible small, this formula is available to the cantilever method loaded at its free end. In this case, it is convenient to obtain α using a graph of
yα/
l-
k (Fig. 2), where
yα is the vertical deflection from its initial coordinate and
Pcos α
sin α is used replaing
P. These long column method is applicable only for large deniers of above 20 denier and yields incorrect results at lower deniers.
The loop method is a development from the above method, applicable to more fine filaments. This principle is reported by D. Sinclare in 1950 (ref. cited No.10). As shown in Fig. 4 & 5, looped sample is extended verticaley between torsion balance and cathetometer. If the height
a from the vertical line between two clamped ends where distance is large enough to neglect the end moment, and loop apex, and tension
T are measured experimentally,
EI is obtained from the equation:
It is more convenient to make fiber into a bundle to measure finer samples.
In order to measure
EI of the fiber bundle, stable ply twist yarn is used, when twisted yarn composed of
m filaments is folded, expected stable ply is obtained (Fig. 7). In this case, there are relations denoted in eqs. 1-3 between apparent flexural rigidity of twisted sample
Bn and
EI of a filament, especialy when the twisted angle with fiber axis (π/2-θ) is very small, i.e. θ=90,
The results of
EI of a filament from this method is larger than that from the other single yarn method, its value increases as θ is increased.
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