Cotton thread is made of many tiny fibres, each just 2-3 cm long, yet when spun together the fibres are capable of transmitting tension over indefinitely long distances. From a physics perspective, how threads and yarns transmit tensionmaking them strong enough to keep clothes from falling apartis a long-standing puzzle that is not completely understood. In a new paper published in Physical Review Letters entitled “Why Clothes Don’t Fall Apart: Tension Transmission in Staple Yarns,” physicists Patrick Warren at Unilever R&D Port Sunlight, Robin Ball at the University of Warwick, and Ray Goldstein at the University of Cambridge have investigated yarn tension in the framework of statistical physics. Using techniques from linear programming, they show that the collective friction among fibres creates a locking mechanism, and as long as there is sufficient friction, a random assembly of fibres can in principle transmit an indefinitely large tension. Their results provide a quantitative basis for the heuristic explanation proposed by Galileo in 1638, who was puzzling over the problem of how a rope can be so strong when it is made of such small fibres. “The very act of twisting causes the threads to bind one another in such a way that when the rope is stretched the fibres break rather than separate from each other,” he wrote. In modern terms, Galileo was describing friction. In the new study, the researchers modelled the yarn as a group of randomly overlapping fibres. The results showed that, as the friction increases, a percolation transition emerges. As the researchers explain, this transition corresponds to “a switch from a ‘ductile’ failure model where the yarn fails by fibre slippage to a ‘brittle’ failure mode where the failure mechanism is fibre breakage.” Above this threshold, the tensile strength becomes roughly 100 times stronger than before. “We now understand better at a fundamental level how friction stops fibrous materials from falling apart,” Goldstein told Phys.org. “From an applied perspective, we can use the insights to underpin the design of fabric conditioners, for example.” In the future, the model could also be used to optimise the properties of sewing threads made of various fibre blends. When extended from fibres to granular media, the results may also have applications for better understanding the stress transmission in sand piles and grain silos. In addition, the researchers plan to investigate the threshold in greater depth. “We plan to write a longer paper exploring the nature of the ‘supercritical’ state, above the percolation transition,” Goldstein said.
Phys.org, 23 April 2018 ; http://phys.org