ANALYTICAL METHODS FOR TEXTILE COMPOSITES
Equation (3.1) also holds if the waviness takes the form of a continuously varying,
normally distributed random misalignment angle,
ξ
, with variance
σ
ξ
= √2
π
d/
λ
[3.2].
For measured degrees of tow waviness, Eq. (3.1) yields knockdown factors of just
a few percent for nominally straight stuffers in well made 3D weaves [3.2]; and 2-10 % for
nominally straight axial tows in 2D triaxial braids [3.1]. For nominally straight fillers in 3D
weaves, the knockdowns are usually 10 - 30%. The knockdown is higher because fillers
are untensioned during weaving and therefore significantly less regular than stuffers [3.2].
For bias tows in triaxially braided glass-fiber composites, knockdowns are between 30%
and 50%, which are high values because the braid architecture demands that bias tows
follow wavy paths. Knockdowns for plain weaves would be similarly high for the same
reason. For a satin weave, knockdowns can be estimated by applying Eq. (3.1) just to the
exchange region, assuming no knockdown over the much straighter float, and taking a
weighted average. For typical satin weave, knockdowns of ~ 10% result.
Experimental measurements of elastic constants generally confirm the order of
magnitude predicted by Eq. (3.1). While stiffness measurements have not been reported for
equivalent tape laminates, stiffness knockdowns can be estimated by comparing
measurements for textiles with rule-of-mixtures estimates based on fiber and resin data or
data for unidirectional laminates. Knockdowns ≈ 5% are found in the warp direction for 3D
interlock weaves with reasonably straight stuffers [3.2,3.3] and for the axial direction in
triaxial braids [3.1,3.3]; and 10-40% in the weft direction of many 3D interlock weaves
(the fillers frequently being much more distorted by the through-thickness warp weavers)
or the bias direction of a triaxial braid [3.1-3.3]. Equation (3.1) is concluded to be a
reasonable guide to the stiffness of quasilaminar textile composites relative to equivalent
tape laminates, assuming that the latter have negligible stiffness knockdown due to
waviness.
Experimentally measured moduli for various 2D braids and equivalent tape
laminates are compared in Fig. 3-1. The braid and laminate specifications are given in Table
3.1. Fiber volume fractions were measured for all the panels used in these experiments and
the results normalized to 60% fiber volume fraction, assuming a proportional variation. The
longitudinal (0° direction) modulus for tension and compression agree closely. There is a
larger reduction in transverse tensile modulus, as would be expected from the greater
waviness of the braiding yarns. It is surprising that the transverse compressive stiffness of
all the braids is higher than their transverse tensile stiffness, even though the tape
equivalent modulus decreases in compression. This trend is not reported elsewhere.
