Because fibers are not isotropic, the fiber orientation thus has a determining effect on the system properties. In most twisted fibrous materials, fibers are oriented in a certain range of directions, and the system therefore has different properties at different directions.
It is considered common sense for textile scientists that when some fibers of modulus E
are oriented in a direction different from the yarn axis by an angle u, if ignoring the Poisson’s effect, then the contribution of these fibers toward yarn modulus E is the well-known law level, the fiber volume fraction of the yarn, the statistical variations, and the fragmentation process of yarn fracture behavior as discussed in next section.