4—THE FINITE-DEFORMATION THEORY OF PLAIN-WEAVE FABRICS. PART II: THE UNIAXIAL-DEFORMATION THEORY

TLDR

The biaxial deformation theory from Part I can be applied to uniaxial loading because no transverse tension is present, but a transverse resistance force must still be considered. This paper introduces a transverse resistance function Fc, represented by constants C₀ and C₁, to analyze uniaxial tensile deformation of plain‑weave fabrics. The authors employ the Part I structural model, derive C₀ and C₁ from yarn bending rigidity and fibre friction, and present an experimental procedure to determine these constants, comparing theoretical and measured Fc functions. Experimental load‑extension curves for several fabrics closely match the theoretically predicted curves, validating the uniaxial deformation theory.

Abstract

The uniaxial tensile deformation of a fabric is analysed as a special case of the biaxial theory presented in Part I, and the bending rigidity of the yarn at right angles to the tensile direction is introduced. The structural model presented in Part I is used again to solve the uniaxial case. The biaxial-deformation theory introduced in Part I can, however, be applied directly to solve the uniaxial case because no tension is applied to the yam in the transverse direction, that is, there is no resistance force preventing the straightening of the yarn in the transverse direction. There must, though, be some kind of force, and this resistance force. F c, is introduced in this paper and represented by two constants C 0 and C 1. Theoretical considerations for introducing these constants are presented whereby the bending rigidity and the coefficient of friction of the fibre are used. An experimental method for obtaining the constants is also introduced, and the F c functions obtained by theoretical and experimental methods are compared. Finally, the uniaxial load-extension curves of some fabrics are measured and compared with the theoretically calculated curves.