Mechanics of Elastic Performance of Textile Materials

Abstract

Theoretical analyses are given of the effects of fiber properties and yarn structure on singles yarn bending rigidity, assuming the fibers to be elastically isotropic and to exhibit linear stress—strain behavior. The two extreme cases of complete freedom and no freedom of relative fiber motion are analyzed. The effects on yarn rigidity of fiber dimensions, fiber stiffness, torsional to bending rigidity ratio, yarn density, size, twist, fiber clustering, and prior relaxation treatments are analytically investigated. 1. Where freedom of fiber motion prevails, yarn rigidity is equal to the sum of fiber bending rigidities geometrically modified by yarn twist in a manner such that twist increases produce decreases in yarn rigidity. 2. For most practical yarns, residual torsional stresses produce only a minor influence (increase) in yarn rigidity. 3. Relaxation of twisting stresses prior to yarn bending alters very slightly the effects of yarn twist on rigidity. Conaequently only changes in fiber modulus produced by relaxation are of significance. 4. Fiber clustering, i.e., the aggregate action of groups of fibers, produces marked increases in yarn rigidity, roughly proportional to the number of fibers per cluster. 5. The extreme case of fiber clustering, i.e., no freedom of relative fiber motion, results in rigidity of the order of the number of fibers in the yarn divided by the yarn packing factor times the rigidity obtained when freedom of motion prevails. The rigidity of blended yarns is discussed, and the interaction of gross yarn structure, properties of the fibers being blended, and their spatial distributions qualitatively analyzed. 1. For a uniform blend distribution, total rigidity is determined from the summative rigidities of the fibers, modified by yarn twist to the same proportionate extent as is a self-fiber yarn. 2. Location of fibers in a nonuniform blend determines not only the yarn rigidity but also its variation with twist. Generally, when stiffer fibers predominate in the core of the yarn, less rapid decreases in rigidity with twist increases take place than in a uniform blend ; the converse is true when the stiffer fibers are present in the yarn sheath. 3. Changes in fiber location resulting from twist or blend changes can significantly affect yarn rigidity.