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A mathematical model for natural fiber crimp is proposed which assumes that the analogy with Timoshenko's theory of bimetal thermostats is valid. Formulas for crimp parameters are derived accordingly. They correctly account for the inverse relation ship between crimp and denier which has been shown to exist for wool fibers. Experi mental data obtained with fibers related to "Orlon Sayelle" 2 Type 21 fibers support the validity of the assumed model. The crimp model hypothesis leads logically to a helical coil spring model for the spatial configuration of natural crimp of fibers. The actual spatial path of crimp is shown to depend in part on fiber bending and torsion rigidities and environmental constraints. The equations derived by Holdaway, based on the helical coil model, for the force-extension characteristic of natural crimp are shown to be valid for the elastic behavior of crimped fibers in the unerimping regions of the load-elongation curve. A technique is described for direct measurement of the ratio of bending to torsion rigidity of naturally crimped fibers. For a number of fibers, of the type that includes Orlon Sayelle Type 21, the ratio has been measured and found to vary between about 1.0 and 3.5.
Brand et al. (Mon,) studied this question.