A small deflection model for yarn bending in a plain weave fabric

Purpose The purpose of this paper is to establish a simple and practical elastica model for the deflection of weft (warp) in a plain wave fabric. Design/methodology/approach The weft yarn is considered as an elastic beam fixed supported at the ends and deflected in the middle by a vertical load. An analytical model, based on the elastic theory and small deflection case is adopted to study the factors affecting the deflection of the yarn. To investigate the model, yarns with different rigidities are used. A total of five different yarn counts are produced in the same ring spinning system and then used as weft yarn in a plain weave fabric. All other parameters of the yarns and the fabrics are kept identical. Fresh fabrics are analyzed and the maximum deflection of the weft is measured using the microscope. The actual curves of the deflected weft are then compared with the theoretical curves. Findings The experimental curves show to agree well with the theoretical model. The results also show that as yarn linear density decreases, the deflection increases. Originality/value The paper shows that while the large deformation “elastica” theory is typically used for woven fabric modeling, the small deflection theory can be useful for rapid computation.