ANALYTICAL METHODS FOR TEXTILE COMPOSITES
Neither is it especially critical to determine the packing density of fibers within
tows. Composite elastic constants depend only slightly on the volume that is assigned to
tows (the remainder being interstitial resin) provided the overall fiber count is correct.
Recall Section 5.1.3. For carbon tows in well compacted composites with overall fiber
volume fractions of 50-60%, the packing density has consistently fallen in the range 65-
70%. Any value in this range will return consistent results.
5.4.2 Matrix Dominated Elastic Constants
Only a few elastic constants in most textile composites could be regarded as
matrix dominated. They include the through-thickness modulus in 2D and quasi-laminar
3D textiles; and the in-plane shear modulus in a weave consisting of orthogonal warp and
weft yarns. Accurate prescription of fiber orientations and tow irregularities are not
especially important in predicting these constants. They change relatively slowly with
fiber orientation, because the stiffness of a unidirectional composite (i.e. a tow segment)
is very insensitive to the orientation of the load when the load is nearly transverse (e.g.,
[5.2]). The only essential geometrical characteristic is the average fiber volume fraction.
5.4.3 Calibrating the Fiber Volume Fraction
Thus being certain of fiber volume fraction is a critical issue in running predictive
codes. Because there is no single method of describing the geometry of a textile
composite and because reality so often differs from the idealizations of geometrical
models, particular care must be taken. Some of the factors distinguishing real composites
from popular geometrical models include the ability of tows to deform and fill space
more efficiently than possible if they are constrained to have a particular cross-section;
inconsistency in the spacing of tows, especially if a fabric is draped; and unpredictability
in the crimp factor (ratio of arc length to projected length) of tows, especially if they are
woven or braided. Generally, the best guide to fiber volume fraction is an experimental
measurement. Volume fractions predicted a priori from the manufacturer's specifications
for a textile preform are vulnerable to error.
It is therefore necessary to adjust the input for any analytical code to match the
experimentally measured fiber volume fraction. In TEXCAD, fiber volume fraction is an
input quantity. The unit cell geometry is adjusted internally to accommodate the specified
value. CCMTEX attempts to calculate fiber volume fraction based on process
parameters. This is a useful feature in the early design of a textile, but is not preferred
once the actual material has been made and better information is available. Finite element
