On the Extended Theory of Mechanics of Twisted Yarns

The theory of mechanics of twisted homogeneous filament yarns is extended in terms of fibre angles to the yarn axis. Firstly, the axial strain of an element in a yarn is generally considered in the three dimensional analysis. The axial stress of the element is then examined in terms of each element angle to the axis. From these analyses on, the yarn stress can be discussed as a function of the filament angles to the yarn axis as well as the distribution function for the angles and the filament stress according to the strain. Secondly, in order to confirm the possibility that a yarn stress-strain curve can be computed by knowing the distribution for the angles, some simple mathematical models are applied as general distribution functions for the filament angles in a yarn. Practical yarns are then discussed. As a case study, the prediction of the stress-strain curve of a randomly interlaced yarn, with a filament angle served by the Normal Distribution, is carried out. The theory and computer programs developed here can be used not only to compute but also to predict the stress-strain curve of each particular structure of homogeneous filamest yarns such as the single, the ply, or even the cabled yarn. Numerical and graphical outputs of estimated yarn stresses will be obtained by the input of some experimental data and assumed values.