THE CHOICE BETWEEN TEXTILES AND TAPE LAMINATES
found to be more easily draped over a cylinder. Draping characterictics over a doubly
curved surface (i.e., a surface that requires nondevelopable transformation strains for snug
coverage) also depend on in-plane extensibility and compressibility. This is difficult for
fabrics containing high volume fractions of more or less straight in-plane fibers, as required
for most airframe applications. For these textiles, only mild double curvature can be created
by draping without significant loss of fiber regularity. However, double curvature can be
achieved via net shape textile processes, such as braiding onto a mandrel (Section 2), thus
avoiding the problems of draping.
3.3 Stiffness
Compared to tape laminates, quasi-laminar textile composites with equal volume
fractions of in-plane fibers will usually have slightly lower in-plane stiffness because of
tow waviness. In a 2D textile, such as a plain weave or triaxial braid, waviness is
topologically inevitable: tows must be wavy to pass under and over one another. The
waviness can be reduced by selecting a satin weave rather than a plain weave, or using
tows with flat cross-sections; but not eliminated. In a 3D textile, such as an interlock
weave, in-plane tows are nominally straight. But even still, waviness is always greater in
practice than in an equivalent tape laminate, because of the disruptive effects of through-
thickness reinforcing tows.
Various more or less complicated models will be described in Sections 4 and 5 for
calculating the knockdown in composite stiffness due to tow waviness. Here a simple rule
is presented, which illuminates the essential trends and gives a fair estimate.
Suppose the waviness takes the form of sinusoidal oscillations in the path of an in-
plane tow, with wavelength
and amplitude
. If either the stress or the strain remains
uniform along the length of the tow, then under an aligned load its stiffness is knocked
down by the factor [3.2]
η
π
λ
ν
= +
− +
−
1 2 2 1
2
1
d E
G
x
xy
xy
( )
(3.1)
where E
x
and G
xy
are the axial and shear moduli of the tow and
ν
xy
is its axial Poisson's
ratio. For carbon/epoxy composites, the anisotropy factor in square brackets in Eq. (3.1)
takes a value near 40. The fractional loss of modulus, 1-
η
, rises approximately as (d/
λ
)
2
.
