A New Decrimping Equation

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Abstract
The solution obtained by Olofsson of the differential equation governing the shape of a yarn with some set-weave crimp under loading is applied to decrimping. A new "decrimping equation" is devised, which accounts for both longitudinal extensibility and unbending. The new equation is found to fit the decrimping of a Corriedale fiber at both 65% RH and when wet, with errors less than the fiber diameter (40 microns) in six centimeters. However, estimates for Young's modulus in bending obtained from the application of the theory are approximately two times the estimates of Young's modulus in extension. The decrimping of a wool yarn with set-weave crimp has also been fitted with a root mean square (rms) error of 120 microns in 10 centimeters. The variation of the fitting error with load is similar for both fiber and yarn. By introducing a nonlinearity in the linear extensibility of the yarn, its decrimping curve can be fitted to rms error of 30 microns. KEYWORDS

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