Load-Deformation Behavior of Three-Dimensional Crimped Filaments: Theoretical Analysis and Experimental Verification

Abstract

A theoretical analysis of the load-contraction behavior of a crimped filament, whose axes lie in a three-dimensional space, is presented. Three first order nonlinear si multaneous differential equations describe the deformed shape of the filament in space. These equations are solved numerically using suitable crimp boundary con ditions to analyze the load-contraction behavior and the deformed shape of a false- twist crimped filament. A bicomponent fiber model is considered as a special case of false-twist crimp with an original helix angle of 90° in the helically set filament. To verify the theory developed, polyester and nylon 6 monofilaments were heat- set in helical shapes of different radii and helix angles to produce false-twist and bicomponent models. Experimental results show an excellent correlation with the predicted values.