Improved High Volume Instrument Elongation Measurements

Cotton fiber elongation (extensibility, elongation at breaking load) is one of the least utilized measurements from the high volume instrument (HVI). This may be due, in part, to the large standard deviation of this HVI measurement. In addition, the correlation of fiber elongation with yarn elongation is not as high as the physical theory of yarn strength suggests. Thus, an improved method for deriving elongation from HVI stress-strain data was needed. The response of the HVI breaker system was characterized by clamping an index card in the jaws and measuring the tensional force applied to the nonrupturing card. This measured response was then used to correct the raw HVI stress-strain curves. A modified analysis of this corrected stress-strain curve resulted in improved measurements of fiber elongation and crimp. A set of 18 cottons was broken at 10 different break amounts to test the validity of the curve correction and modified analysis. Comparisons of these modified measurements with bundle stress-strain curves generated from Mantis® single-fiber data showed similar levels of elongation (approximately 5% higher than traditional stelometer values). Measurements were also made on samples from the 1990 through 1994 crops in order to investigate the correlations of the modified elongation data with stelometer data and to determine the utility of the modified elongation measurements as predictors in yarn strength and elongation models. M including cotton fibers, change shape or deform when external stress (force per unit area) is applied. This deformation normally occurs almost instantaneously and is quantified as strain (the ratio of the change in size to the initial size). Deformational strain in response to stress may be extensional (e.g. a change in length of a column) or shear (e.g. as in the bending of a beam) (Mintzer et al., 1957; Preston, 1974). The ratio of stress to strain is referred to as a modulus – the bulk modulus for compressive stress, Young's modulus for tensile stress, and shear modulus for shearing stress. As long as the elastic limit of the stressed material is not exceeded, the mechanical system returns to the original form when the stress load is removed. In C.R. Riley, Jr., Zellweger Uster, Inc.; 456 Troy Circle; Knoxville, TN 37919. Received 25 August 1997. *Corresponding author. Abbreviations: HVI, high volume instrument; ICC, International Calibration Cotton. 62 RILEY: IMPROVED HVI ELONGATION MEASUREMENTS Fig. 1. HVI breaker mechanism diagram. such ideally elastic materials, the modulus is constant. This is referred to as Hooke's law, and materials obeying Hooke’s law are referred to as Hookean solids [Reiner, 1966]. However, the strains for which Hooke’s law holds are quite small, and the elastic limit of cotton fiber cell walls is exceeded after only very small strains [Preston, 1974]. Moreover, the value of Young’s modulus is time-dependent in that the precise value depends on the rate of application of stress and is historydependent in that repeated stretching, even within the elastic limit, changes fiber structure and, hence, the modulus [Preston, 1974]. In addition to the natural deviations of cotton fibers from the Hooke’s law ideal [Preston, 1974], deformations within the mechanical system used to produce strength and corresponding elongation measurements also create errors in measurements of the elongation of the fiber beard as the beard is broken [Taylor, 1986; 1995]. The basic mechanism for breaking a fiber beard in a Spinlab high volume instrument (HVI) is shown in Figure 1. When a fiber beard is analyzed, the comb first moves to the right, measuring the fiber length by Fibrograph [ASTM D 4605-86, 1993, ASTM D 1447-89, 1994; Taylor, 1995]. The comb is then moved to the left so that the desired ‘break amount’ of fiber is positioned over the leading edge of the rear jaw. The jaws clamp the beard; and the breaker step motor rotates, causing the rear jaws to move to the right at constant velocity. Force and displacement voltage signals are recorded at every second step of the breaker step motor [ASTM 4605-86, 1993]. The force exerted on the jaws by the fiber beard causes the breaker system to deform. As load is applied to the jaws by the fiber beard, the jaws deflect, the force transducer and mounting brass screws stretch, and the main beam coupling the motor to the force transducer at the rear deflects. Since the traditional method for measuring stress or displacement is the rotation of the motor, these deformations in the mechanical system create errors in measurements of the stress-strain curve for the fiber beard. When considering the deflection of the breaker system, it is important to consider the relative magnitude of the distances involved in fiber elongation and the breaking of the fiber beard. If the elongation is 10% and the break gage is 3.175 mm, the total travel to the peak of the stress-strain curve is only 0.3175 mm. Thus, even small deflections are important in measuring elongation. A total deflection of only 0.0381 mm represents a 20% error in a 6% elongation measurement. Displacement transducers mounted near the jaws have been used to measure the motion of jaws directly. However, the mechanical design of the HVI prevents direct attachment of transducers to the jaws at the clamp point without compromising the mechanical integrity of the breaker system. This limitation, the small displacements involved in elongation measurements, and the signal-to-noise ratio of the transducers have limited the success of this approach [Riley, 1996]. Further, the pitch of the screw coupled with the step angle of the step motor produces 25.4 mm of travel for the ball-nut assembly with every 800 steps [Riley, 1996]. As the step motor rotates, a reading of the force transducer is made at every two steps, which is equivalent to 0.0635 mm of travel of the ball-nut assembly on the breaker motor. The lever arm ratio is 3:1, which corresponds to a reading after every 0.0212 mm of travel of the rear jaw, assuming that there is no deformation deflection in the system. Since the break gage is 3.175 mm, this travel increment for each increment in the index corresponds to an elongation increment of 0.67%. As a graphic example, a force and displacement curve for a strong cotton plotted against this index is shown in Figure 2. If there were no deflection, the displacement curve would have been a straight line. 63 JOURNAL OF COTTON SCIENCE, Volume 1, Issue 1, 1997 Fig. 2. Force and jaw displacement vs. motion of step motor. Fig. 3. Raw and corrected force on HVI for staple 37. Deviations from a straight line represent the deformation within the system. As the load on the system increases, the curve deflection becomes greater. At the peak of the curve for a strong cotton, the deflection represents about 30% of the total travel. (In offered example, the fibers used were from a D-6 cotton, one of the strongest cottons tested with a strength of about 34 g tex on the International Calibration Cotton (ICC) scale.) The maximum deflections of the HVI breaker system depend on both the strength of the cotton and the selected break mass [Taylor, 1995]. The range of deflections encountered in cotton fiber force/displacement curves is from approximately 6% to 35% [Riley, 1996]. The most successful stress-strain curves plot the force for the motion of the rear jaw at equidistant points. Since the curves in Figure 2 can be represented by a pair of parametric equations with a common variable of index, the index variable can be eliminated from the two equations and a composite ’corrected’ curve plotted. An example of the raw curve measured by the HVI and the same curve corrected for deflection is shown for staple type 37 in Figure 3. In this way, the mechanical displacement error problem may be resolved by obtaining the curve representing the travel distance of the rear jaw as a function of the index variable for each sample. In addition to the correction calculations described above, a direct measurement of HVI jaw deformation and the resulting stress-strain curve deflection was needed. Such direct measurements were made, using a 3x5 inch paper index card. This report describes the applicability of correction factors obtained with this inexpensive, simple, nearHookean material, which does not elongate significantly under loads typical of the HVI, and which can be clamped between the HVI jaws without damage to the jaws. MATERIALS AND METHODS Fiber Samples Tested Verification of the HVI elongation correction involved 18 cotton samples, including the current 8x8 cotton standards used to evaluate new high volume instruments, six USDA-Clemson test cotton standards used with the Universal Strength Tester, and four International Calibration Cottons (ICC) in Table 1. An independent study of the elongation measurement correction was obtained by testing 119 USDA crop samples from 1990 through 1994.