ANALYTICAL METHODS FOR TEXTILE COMPOSITES
the warp direction. In practice, c
w
is difficult to predict a priori, because the paths of warp
weavers in the finished product vary greatly with process parameters. Experimentally
determined values are typically between 1.1 and 1.3 for layer-to-layer angle interlock
weaves, near 1.5 for through-the-thickness angle interlock weaves, and between 2 and 5
for orthogonal interlock weaves [2.15].
2.3.2.4 3D Braids
Various process models have been derived to describe the complex unit cells of 3D
braids (see [2.16-2.20]). The following simple expressions were given in [2.18] for the 4-
step, 1x1 braid (without inlaid axial yarns).
The 4-step, 1x1 braiding pattern produces the 3D unit cell shown in Fig. 2-17. The
yarns in the unit cell are inclined in 4 directions; 2 parallel to surface ABDC, and 2 parallel
to surface CDEF, as shown in the accompanying diagram. These surfaces are cut at 45°
angles to the surface of the fabric.
Consider a rectangular array of yarn carriers, with m columns and n rows in the
array. The total number of required yarns, N, is
N = (m+1)(n+1)-1 (2.11)
The number of machine cycles required for all the yarn carriers to return to the original
positions is given by N/G, where
G = m n/R
mn
(2.12)
with R
mn
the least common multiple of m and n. The normalized cycle length, h
d
, is
defined as the fabric length produced in one cycle, divided by the diameter of the yarn,
which is assumed to remain circular. The cycle length cannot be easily predicted, because it
is a function of the beat-up.
The angle formed by internal yarns,
γ
, is given by
γ
= arctan(4/h
d
) . (2.13)
Equation (2.12) is valid up to an angle of 55° (h
d
= 2.8), beyond which jamming is
predicted. A plot of the fiber inclination angle versus h
d
is shown in Fig. 2-18.
