The Effect of the Bending Angle on the Particular Loop Tenacity of Fibers

The particular loop tenacity test when bending angle (180° in the ordinary test) is varied from 180° to 80° was carried out. 1. The theoretical equations expressing the relation between the bending angle and the loop tenacity are formulated on the following assumptions; a. A part of the linear region of a tested fiber is transfered into the bending region near the boundary between these two regions, and consequently the bending strain becomes smaller than the geometrical bending strain emo. b. The rupture of a fiber in the loop tenacity test takes place at the time when the sum of the bending strain and the stretching one has reached the breaking one in the simple stretching test of the same fiber. c. The change of this particular loop tenacity with the bending angle is dependent upon the degree of decrease of the above bending strain em, giving the following equations. : em=Cδand em= emo (1-2δ/ψ) where δ is quantity corresponding to the shear strain produced by the above transfer of the boundary; C is a constant; and ψ is the bending angle. 2. The theoretical equations are as follows;d1=1-emE1/fB (eyeB-em) whered1 and d2 are the ratio of the particular loop tenacity to the tenacity for simple stretching; E2 and E1 are the slope of the stress-strain curve respectively befor and after the yield point of the sample; fB and eB are respectively the ordinary breaking strength and strain; ey is the yield strain. 3. The experimental results for polyethylene terephthalate fibers are approximately explained by the above equations except in the case of the small bending angle. And the bending strain at the bending angle of 180° is estimated at about 15% against the breaking strain of 30% and 7% against the breaking strain of 10%.