The Mechanical Characteristics of 2-D Braided Textile Composites Using Geometrical Representation

Abstract

*† A simple geometrical model to predict effective moduli of the 2-D braided textile composites is developed. To calculate homogenized material properties for 2-D braids, the concept of a Repeating Unit Cell (RUC) along with the iso-strain assumption and equivalence of strain energy of the RUC are used. The geometrical surface equations of the braid yarns, in terms of sinusoidal functions are introduced to describe three-dimensional braided yarn shapes. The micro-mechanical constitutive equations are employed to obtain appropriate elastic properties for the 2-D braided yarns. For a parametric study, various yarn sizes, yarn aspect ratios and braid angles are considered to investigate various characteristics of effective elastic moduli of the 2-D braided textile composites. Results from our analytical model for determining effective modulus for a 2-D braided textile composite were compared with available results in the existing literature. The comparison between our geometrical model and other models indicates excellent agreement, and the dependency of effective constitutive properties of a 2-D braided textile composite are established from a number of numerical examples. Nomenclature br θ + = the braid angle for the br θ + yarns br θ − = the braid angle for the br θ − yarns br c + θ = the crimp angle for the br θ + yarns br c − θ = the crimp angle for the br θ − yarns H = the total thickness for the 2-D braids’ RUC 1 u = the undulation length for the br θ + yarns in the x-y-z coordinate 2 u = the undulation length for the br θ − yarns in the x-y-z coordinate * 1 u = the undulation length for the br θ + yarns in the 1-2-3 coordinate * 2 u = the undulation length for the br θ − yarns in the 1-2-3 coordinate * 1 u u = the undulation arc-length for the br θ