Bundle strength of polyester fibers determined using a series-parallel combination model

Abstract

This paper describes the bundle strengths of PET filaments from a statistical point of view. A bundle is an arrangement of a number of filaments. We applied the weakest-link theory and probabilistic load-sharing rules to estimate the bundle strength from the breaking strength data of PET filaments. We analyzed the breaking behavior of 12 filament bundles according to their length and number of filaments and compared the breaking behavior of a prepared specimen yarn with that of a commercial PET filament yarn. The breaking strength of the PET filaments, which we tested using a MANTIS® tester, was compared with that of the actual yarn. We compared the actual tested values obtained by INSTRON® with the expected values, which we calculated from the MANTIS® data by using Peirce's theory and Knox's hazard function. The key effects that determine the actual random breakage behavior of a bundle include not only the load-sharing rules in the constituent filaments but also the slippage and friction between adjacent filaments, the appearance of which we distinguished especially in the bundle consisting of a large number of filaments and in small-denier filaments. The PET filaments were better approximated when using the Peirce's weakest-link theory than they were by Knox's hazard function. In a series-parallel model, we found that the number of parallel filaments and their load-sharing behavior had larger effects on the bundle strength than did the weakest-link effects of continuous elements.