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4.2.4 Unit Cell Models for Textile Composites

As described in Chapter 2, textile composites, including two-dimensional woven and
braided composites, are manufactured with advanced machinery following specifically
designed parameters. Such manufacturing processes result in textile composites
possessing geometric periodic patterns, i.e., there exists a piece of minimum sized
sample of composite which can be copied with translational increments only repetitively
to map out the whole composite structures. For a fibre reinforced textile composite
material, the minimum sized periodic sample is chosen as the unit cell of the material
because it is small and also contains all individual constituents and microstructural
features. Unit cell approach has been widely used in almost all available
micromechanics models developed for fibre reinforced textile composites (Chou and KO
1989; Tan et al., 1997a; Mouritz et al., 1999; Tan, 1999).
Prediction of the effective properties for a unit cell to a fibre reinforced composite
material proved and remains to be a great challenge. Presentation of all
micromechanics models available is a daunting task. To present some of the basic
concepts and ideas, we choose to divide all models into two categories, i.e., analytical or
semi-analytical approach and numerical approach based on finite element methods
(FEM). In analytical models, simple formulas may be obtained for the effective
properties based primarily on a large number of assumptions. In the numerical based
models, effective properties can be evaluated numerically only by taking into account
more detailed features of the microstructure, such as fibre tow architectures, using the
finite element method.

4.3 UNIT CELL MODELS FOR 2D WOVEN COMPOSITES

Two-dimensional woven composites are produced on a loom that interlaces two sets of
fibre yarns at right angle to each other. The lengthwise yarns are referred to as warps,
while the yarns perpendicular to the warps are called fills or wefts. Each yarn is a
bundle, and its size is related to the number of fibres in the yarn, the diameter of the
fibres, and the packing density of fibres. Figure 4.1 depicts schematically the top views
of some commonly used 2D woven composites and the cross-sectional views of the
weaves. The various types of woven composites can be readily identified by the
patterns of repeats in both warp and weft directions, defined by two geometrical
quantities n," and nB/ . The number of n," means that a weft (fill) yarn is interspersed
with every n,"-th warp yarn, while the number of nB/ indicates that a warp yarn is
interlaced with every n,f-th weft (fill) yarn. For all weaves in Figure 4.1, the two
geometrical quantities are identical, i.e. n," = nxf = nd . The plain weave has a tighter
interlacing, while the twill and satin weaves have a looser interlacing. The interlacing
of the yarn causes the yam undulation or yarn crimp.
There has been extensive research on the prediction of effective properties for 2D
fibre reinforced woven composite materials. It is not the intent of this book to include
all published models; instead, we chose to present some of the widely known models by
classifying them into one-, two- and three-dimensional models as well as the
applications of finite element method.