A New Orientation Density Function of Ideally Migrating Fibers to Predict Yarn Mechanical Behavior

An orientation density function of migrating fibers is newly defined to predict the mechanical behavior of yam. Applying the new function to yam with a helical structure produces the same results as the existing theories, and the function is applicable to even more general cases. Ideal migration behavior is mathematically analyzed by introducing two parameters that describe the migration behavior of fibers in the directions of the yarn axis and the yam's radial axis. The relative initial tensile modulus of the migrating yarn is calculated by applying two parameters to the orientation density function. The relative initial modulus depends strongly on both the migration period in the direction of the yarn axis and the degree of migration in the direction of the yam's radial axis.