Application of topological conservation to model key features of zero-torque multi-ply yarns

Abstract

During yarn formation by ring spinning, fibres are bent into approximately helical shapes and torque or twist-liveliness is created. The yarn torque causes yarn instability, manifested as snarling or entanglements, and this instability must be controlled during manufacturing processes. Generally, the torque depends on yarn geometric factors such as the yarn twist, linear density and the fibre properties. A practical solution to the problem of twist-liveliness is the formation of a two-fold yarn. This twisting or plying process produces a yarn structure where the energy of the system is determined by purely geometrical constraints of the plied structure and consequently when an energy minimum is reached the plied yarn obtained from the process is torsionally balanced and torque-free. In the present paper, the stability of plied textile yarns will be evaluated using the Topological Conservation law (Fuller, F. B., 1971, Proc.Nat. Acad. Sci. USA, 68, 815-819.) developed to study the post-buckling behaviour of twisted rods by Van der Heijden et al. (Int. J. Mech. Sci., 45, 161-196, 2003).The present work considers the equilibrium configuration of a series of multi-ply twisted yarns (2, 4, and 6 strands) of finite length.Several structural and mechanical properties are highlighted: (i) the influence of structural properties (the number of strands, the strand linear density and strand twist) and the ratio of the torsional and bending stiffnesses of the strands on the balance point in multi-ply yarns. The topological invariant of the twisted yarn (link) is used to calculate the ply and strand properties (writhe) and compared with experimental results obtained at CSIRO. The inter-strand pressure between strands of a multi-ply yarn, a feature of also known as D.

Electrically Stable Carbon Nanotube Yarn Under Tensile Strain

“…That would yield a higher tensile strength of the yarn which is approximately 20% stronger than that of the single twisted yarn. This is attributed to the elimination of both snarling and unbalance twisting phenomena which occur in single highly twisted yarn as discussed in [21].…”

Residual twist in a double-layer strand and its correlation with bending fatigue

“…(20) is useful to calculate the residual twist within the strand in a practical design. The manufacturing parameters, the primary and secondary twists Φ n m , can be related to the geometrical torsion τ and mechanical twist ω i as well as the topological conservation parameters (L k , T w , W r ) [18]. In the Appendix, we describe these relations and show that the topological conservation parameters can give the measures equivalent to those of the mechanical and geometrical twists.…”

“…By using the residual twists given by Eqs. (18) and (20), we now evaluate the fatigue life under cyclic bending by comparing the available testing results [6,17] for the (3+8)-glass strands with various combinations of the direction and magnitude of the twists. In Table 3, we indicate the directions of twisting moments in the inner and outer layers.…”

“…Tran et al [18] have considered that the application of topology conservation law to model the multi-ply yarns based on the works for a non-closed curve [12,16], extending the topology conservation law for a closed loop [5],…”

Improving the tensile strength of carbon nanotube spun yarns using a modified spinning process

“…Twisting can enhance stress transfer between CNT bundles under tensile forces [24,32]. However, the highly twisted CNT yarn tends to snarl or coil when unconstrained [33]. Figure 10 is a SEM image of a micro-snarling on a CNT yarn with 17000 TPM.…”