The critical length, the number of slipping fibers and the breaking strength of staple yarn of fibers of equal length are theoretically studied. Then, the critical length at which the applied pressure is just sufficient to cause the fiber to break is gained from the following equation where, μ; the coefficient of friction between the fibers r0; the mean radius of curvature of helix C; thickness of the fiber θ; twist angle in the surface layer R; the radius of the thread θ0; mean twist angle (=2θ/3) g (t); length of fiber lc; the critical length Hence, the number of slipping fibers is: where, b; number of fibers at the cross section of the thread and, the breaking strength of yarn is where, T0; breaking strength of fiber σ; number of projecting fibers at cross section of the thread
In experiments with viscose staple fibers, the experimental values of the critical length and the breaking strength of spun yarn fitted well to the calculations.