Why clothes don't fall apart: tension transmission in staple yarns

TL;DR

This paper models tension transmission in staple yarns using abstract LP models with friction laws, revealing a percolation transition that explains yarn strength and failure modes.

Contribution

It introduces a percolation transition framework for understanding tension transmission and yarn strength, linking mechanical behavior to a phase transition.

Findings

Existence of a percolation threshold for tension transmission

Identification of mean slack as an order parameter

Switch from ductile to brittle failure mode

Abstract

The problem of how staple yarns transmit tension is addressed within abstract models in which the Amontons-Coulomb friction laws yield a linear programming (LP) problem for the tensions in the fiber elements. We find there is a percolation transition such that above the percolation threshold the transmitted tension is in principle unbounded, We determine that the mean slack in the LP constraints is a suitable order parameter to characterize this supercritical state. We argue the mechanism is generic, and in practical terms corresponds to a switch from a ductile to a brittle failure mode accompanied by a significant increase in mechanical strength.