ANALYTICAL METHODS FOR TEXTILE COMPOSITES
are mutually exclusive. Thus, while woven fabrics are frequently the material of choice for
complex geometries, the designer must be aware that specified material directions may be
impossible to maintain on a doubly curved surface; and initially orthogonal yarns may not
remain orthogonal in the fabricated product.
Most 2D weaves involve two orthogonal directions of yarn, implying weak in-plane
shear resistance within a single ply. However, triaxial weaves, in which the yarns form 60°
angles to each other, have also been fabricated (Fig. 2-12, [2.5]). A single ply of triaxial
material would have approximately isotropic in-plane elasticity.
2.3.1.3 2D Braids
Figure 2-13(a) shows the interlacing pattern for a ±θ bias braid. Structurally, a 1x1
braid with yarns oriented at ±45° is indistinguishable from a plain weave rotated by 45°.
(In a 2D braid, the designation "nxn" refers to the number of bias yarns between crossover
points.)
Longitudinal or axial yarns can be introduced into the braiding process to create a
triaxial braid. The axial yarns are trapped within the crossovers of the bias yarns. In
principle, the axial yarns can remain straight, and therefore retain much of their
unidirectional properties. By controlling the relative size of the axial yarns and the angle of
the bias yarns, a wide range of final properties can be obtained. As with woven fabrics, the
pattern of crossovers can be controlled. Figures 2-13(b), (c), and (d) show three possible
patterns for triaxial brads. These figures show the braid patterns with gaps between the
yarns for clarity; the actual braid would normally have complete coverage.
Applications for braids can be limited by the size of the braiding machines available.
A large braider has 144 yarn carriers and a bed diameter of 2.25 m. Often, full coverage of
the mandrel by the bias yarns alone is required on each pass to minimize gaps and resin
pockets in the structure. Full coverage is obtained when [2.7]
w
b
/cos
θ
=P/2N (2.1)
where w
b
is the width of a bias yarn as it lies on the mandrel, P is the perimeter of the
mandrel, N is the number of bias yarn carriers in operation, and
θ
is the angle between the
bias yarns and the longitudinal axis of the structure. A less severe constraint is for full
coverage on a pass including the area covered by the axial yarns. In that case, full coverage
is obtained when
