OVERVIEW OF TEXTILES
simple geometric models have been presented in Refs. [2.10] through [2.13]. The
following illustrative formulae for a plain weave are reproduced from Ref. [2.10].
Consider a 2D plain weave composite. Assume that the fabric has full coverage,
i.e., there are no gaps between the yarns; and that the yarn spacing and fiber counts are
equal in the fill and warp directions. The yarn cross-sectional area, A, can be determined
from
A =
πd
f
2
(2.3)
where d
f
is the filament diameter, n is the yarn filament count, and p
d
is the yarn packing
density. The yarn packing density can be measured using photomicrographs of sections.
Typical values are in the range 0.7 - 0.8.
Alternatively, if one knows the linear density of the dry yarn, D
y
, then
A =
(2.4)
where D
y
is in denier (g/9000 m), and
ρ
f
is the fiber density (g/cm
3
).
The overall fiber volume fraction for the unit cell shown in Fig. 2-16 is
V
f
=
(2.5)
where a is the yarn spacing, controlled during fabrication by fixing the number of yarn
carriers over the fabric width; and H is the cell height, usually equated to the cured layer
thickness specified by the manufacturer. Often, the areal weight of the dry fabric, w
a
, is
specified in g/m
2
, and in this case
w
a
=
. (2.6)
The yarn thickness, t, is related to H by t = H/2. For full coverage, the yarn width, w,
must equal the yarn spacing.
The path taken by each of the four yarns in the unit cell consists of two straight
portions and three curved portions (Fig. 2-16). The curves are commonly assumed to be
sinusoidal, with the z-coordinate of the yarn centerline expressed as
