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The effect of yarn torsional rigidity was verified on the Cooper model for fabric bending rigidity in any direction. We made five cotton fabrics with different weft densities and prepared three commercial fabrics as experimental samples. The torsional rigidity of yarn from the bobbin and that of yarn directly extracted from fabric were measured with a yarn torsional tester. The bending rigidity of yarn from the bobbin was measured using the same pure bending tester as used in fabric bending testing. The bending rigidity of thin fabric was calculated using torsional rigidities of yarns extracted from the fabric and showed better agreement with the experimental values than that calculated using the torsional rigidity of yarn from the bobbin. Indeed, measurements showed that the torsional rigidity of yarn from the bobbin was appreciably higher than the torsional rigidity of yarn from the fabric. This is due to the crimp in the yarn. The fabric bending rigidity can be predicted using the Cooper model with torsional rigidities of yarns extracted from the fabric., Article, TEXTILE RESEARCH JOURNAL. 87(4):424-432 (2017)

An approximate torsional rigidity constant and a torsional shape factor for fibers with a generalized elliptical cross-section were obtained in the closed form. The Galerkin method was used to solve the torsion problem and Saint-Venant’s approximation formula for torsional rigidity constant was also obtained.

Closed form solutions for torsional rigidity and the torsional shape factor for fibers whose cross section is a generalized cardioid are obtained. Complex variable techniques are used to solve the torsional problem, and a conformal mapping function is derived using the method of successive approximation. Closed form solutions for bending rigidity and bending shape factor are also obtained with Green's theorem. The expression for the perimeter for a generalized cardioid is found. Expressions derived here for torsional and bending behavior should have wide applications in the optimal design of fiber cross sections.

The effect of polyester fibers with nonround cross sections on the rotor spinning of 100% polyester and 50% polyester/50% cotton yarns is determined. The polyester cross sections are hollow with a 5% void and trilobal, oval, ribbon, peanut, and scalloped oval shapes. The polyester fibers (oval, ribbon, peanut, scalloped oval shapes) with aspect ratios greater than one have fewer yarn breaks than the stiffer polyester fibers (round, hollow, trilobal shapes) with an aspect ratio of one. The peanut and scalloped oval fibers, which combine a multilobal character with an aspect ratio greater than one, have the fewest yarn breaks. The superior rotor spinning of these nonround fibers is believed to be the result of enhanced twist propagation due to lower torsional rigidity and lower fiber-to-surface contact.

Literature pertinent to fiber properties and handle of fine Merino lamb's and fleece wool is critically discussed. The softness of handle of fine Merino wool varies inversely with loose fiber resistance to compression. This complex raw wool parameter has geo metric and mechanical attributes. Fiber bending and torsional rigidity are important mechanical factors that depend on mean fiber diameter, cross-sectional shape, and Young's modulus. Crimp frequency, amplitude, and form are equally important geo metric factors. Those characteristics that distinguish lamb's and adult wool and appear to account for the relative softness of hand of lamb's compared with fleece wool are presented in Part II.

Torsional rigidity is one of the most important mechanical properties of fibers and yarns and has considerable effects on the performance of fabrics made therefrom. A new instrument called a Torsional Rigidity Analyzer has been developed by TORAY Industries, Inc., a synthetic fiber manufacturer in Japan, for the measurement of torsional rigidity, torsional hysteresis, and residual torque of all fibers ranging from fine fiber to heavy yarn such as tire cord or carpet yarn. This analyzer utilizes a new torque balance method which is a modification of the rotary viscometer. By this analyzer the twist-torque diagram of the sample is obtained automatically in the X-Y recorder. This paper describes the analyzer and some applications to fine fibers and multifilament yarns.

The variation of the coefficient of shear modulus for blended yarns deviates slightly from a linear relationship, based upon the relative amounts of the components present in the yarn, being more nearly linear as the twist decreases. For yarns having lower twist factors there is a good correlation between experimental and calculated data. In the case of yarns with higher twist, calculated values may be higher than those observed experimentally. Reasons for this difference are given. Equations are presented that will permit rapid calculation of approximate results; other equations presented will give more accurate results but will require painstaking calculation.

This paper reports on the transient behavior of the texturing threadline in single heater operation. Twist response and threadline-tension response are shown for disturbances in spindle speed, overfeed, outlet velocity, and entry pretension. The twist response in the texturing zone is exponential in form, with local twist levels shifting without overshoot to new levels consistent with new steady-state values of process parameters. Transient twist response in the post-spindle zone involves a rise, then falling off to zero real twist. Transient-tension behavior is seen as a dual response both to new steady-state process parameter levels and also to threadline contractive effects of changing twists. Twist changes are observed to initiate in the heater entry zone of the threadline and then sweep across to the spindle. This observation suggests the existence of significant differences in torsional rigidity along the threadline and requires modification of analytical models for predicting transient texturing behavior.

The measurement of the torsion constant of cotton fibers is usually determined by the single-fiber method. The bundle method proves to be faster, and the determination of this physical property by the bundle method is analyzed and the experimental results are discussed.

An apparatus is described for determination of the torsional rigidity and rigidity modulus of textile fibers. The apparatus is a modification of the torsion pendulum and is especially suitable for determination of changes in torsional moduli, e.g., after some treatment. Tests have been made on wool fibers subjected to treatments with either potassium hydroxide in ethanol or sodium hydroxide in butanol kerosene. In the first case the rigidity modulus decreased about 10% on account of the treatment, while no change occurred in the second case. The rigidity modulus is a much more sensitive indicator of changes in the outer parts of the fiber than is Young's modulus.

A method for measurement of the torsional rigidity of fibers immersed in liquids is described. The procedure employs a torsion double pendulum which permits measure ments to be made dynamically without interfering with the condition of the fiber for successive tests. The theory of the double pendulum is discussed.

When a wool fiber is extended in water, the concomitant values of the torsional modulus of the fiber remain relatively constant up to around 30% extension. Beyond this 30% longitudinal extension the torsional modulus of the wet wool fiber progressively increases with extension. This latter behavior, together with the observed relationship between the torsional modulus of the unextended wool fiber and the slope of the post-yield region of its longitudinal stress-strain curve, have been explained in terms of the series-zone model for keratin libers.