Theoretical Analysis of the Large Deflection of the Elastic Yarn with Inter-Fiber Friction

Abstract

In this paper, the large deflection of a thin elastic rod having internal friction is analysed.
The analyses have been made for the two processes, the one is the increasing bending process and another is the recovering process where the forces are applied at the two free-ends of the rod.
The obtained results shows following properties.At the increasing process, the effect of thct internal friction on the force-deflection property is small except in the very small deflection region, in which there is small rising of the force caused by internal friction.
At the recovering process, the internal friction causes remarkable hysteresis phenomena, and it was found that the hysteresis behavior depends on a parameter a where,
a=2H_B/Bl₀
B Slope of the bending property (torque-curvature property) of the rod. 2H_B;hysteresis-width in the bending property.l₀;length of the rod.
An experiment was carried out for the purpose to examine the calculated results using a ring shape specimen of spun yarn, and it was confirmed that the prediction by the theoretical calculation has good accuracy for both increasing and recovering processes of actual spun yarn.