Structural Analysis of a Two-dimensional Braided Fabric

Two-dimensional-braid geometry is analyzed. The cover factor of a fabric braided on a particular braider depends on three variables: braid angle, helical length, and braid diameter; however, only two of the three are independent because of an equation of constraint. The cover factor of an existing braid is a function of braid angle and diameter and maintains a constant helical length between its tensile and compressive jammed states. A stable jammed state with maximum crimp is found to exist when the braid angle is 45° and the helical length is a minimum. When the braid diameter is held constant by braiding on a constant-diameter mandrel, the cover factor is increased by decreasing the helical length or increasing the braid angle. The cover factor is directly related to the fabric width as a single independent variable. When the yarn cannot be considered as a flat strip but must instead be considered to have a circular cross-section, the maximum cover factor in the jammed state is shown to be 0.82.