Studies on the Japanese Paper Yarn (No. 33)

Observation of the Breaking Strength of a Yarn

Abstract

When a Japanese paper yarn is stretched and then cut, some fibers in the yarn are broken, and the rest slipped out.
If the breaking strength in the former case is to be expressed by ηP, and by (1-η) P_R in the latter, then the resultant breaking strength of yarn P is
P=P₀/1+6R₀ cot² β₀/t{1-1.43 cot² β₀ω₀/R₀ sin β₀(1+6R₀ cot² β₀/t)}(1)
P_R=P₀{(1+μl' cot² β₀/R₀)+0.25κtμl' cot² β₀/R₀ ω₀}
P=ηP+(1-η)P_R(3)
where, P₀ : Breaking strength of the cut materials.
P : Breaking strength of a yarn on the assumption that a yarn is cut due to breaking of all fibers.
P_R : Breaking strength of a yarn on the assumption that a yarn is cut due to slipping-out of all fibers.
β₀ : Pitch angle at the beginning of twist.
R₀ : Radius at the beginning of twist.
ω₀ : Width of the cut-materials.
t : Thickness of the cut-materials.
μ : Friction-coefficient.
l' : Average length of the fiber-element.
η : Ratio of broken fiber in %.
The significances of the above formula are tested and studied under various conditions.