The Effect of the Bending Angle on the Loop Strength of Single Fibers

The modified loop strength test when the bending angle, which is 180° in ordinary tests, is varied from 180° to 80° was carried out, together with the following theoretical analysis and discussion. 1. The theoretical equations expressing the relation between the bending angle and the loop strength are obtained on the following assumptions: a. Some part of the linear region of a fiber is transfered by shear into the bending region, and the bending strain is reduced a little. b. The rupture of a fiber in the loop test takes place when the sum of the bending strain and the stretching strain has reached the breaking strain in the simple stretching test of the fiber. c. The change of the loop strength with the bending angle is dependent upon the degree of decrease of the above bending strain e, , giving the following equations: em; =Cδ., em; =emo; (1-2δ/φ), where δ is the quantity corresponding to the shear strain produced by the above transfer of the boundary; C a constant; and φ the bending angle. 2. The theoretical equations are as follows; α1; =1-em; E1; /fB; (ey; eB; -em; ), where α1; and α2; are the ratios of the loops strengths to the strengths for simple stretching; E2; and E1; the slopes of the stress-strain curves before and after the yield point of the sample; fB; and eB; the ordinary breaking strength and strain; ey; the yield strain. 3. The experimental results for polyethylene terephthalate filaments can be approximately explained by the above equations except the small bending angle. The bending strain at the bending angle of 180° is estimated roughly as 15%, for the breaking strain of 30%, and as 7% far the breaking strain of 11%.