29—THE MECHANICS OF TWISTED YARNS: THE INFLUENCE OF TRANSVERSE FORCES ON TENSILE BEHAVIOUR

Abstract

An idealized theoretical model of a yarn is assumed, and, after considering the stresses acting on a small element of the yarn, the conditions for radial equilibrium in the yarn are worked out. This leads to expressions for the tensile and transverse stresses in the fibres as functions of (i) the position in the yarn, (ii) the stress which would be present in fibres under the same extension as the yarn, (iii) the twist angle of the yarn, and (iv) the Poisson's ratio of the fibres. Integration of the components of these stresses parallel to the yarn axis gives an expression for yarn tension. Finally, the behaviour when fibres start to break is considered.