PREDICTION OF ELASTIC CONSTANTS AND THERMAL EXPANSION
In reality, the tows in textile composites do usually have more complicated
internal structure than unidirectional composites. Fibers within single tows follow
tortuous, tangled paths, rather than being perfectly aligned. Large filament count tows
are formed by combining several smaller tows, which usually leaves resin rich
internal boundary layers. The smaller tows may also be twisted separately and the
larger tow they form may be twisted as a whole, either deliberately or inadvertently.
The tow will then not strictly be transversely isotropic. Yet these complications will
not violate overall symmetry significantly. Minor deviations from transverse isotropy
in individual tows will not alter the symmetry of the tow architecture on the scale of
the textile. Local biases cancel one another out over larger scales. The effects of twist
and other fiber irregularities within tows on macroscopic elasticity are never more
than a modest reduction in the effective axial stiffness of a tow; perhaps ~ 1%. They
are generally insignificant compared to the effects of tow waviness (Section 3).
5.1.3 Fiber Packing and Resin Pockets
Because textile composites are manufactured with relatively large fiber tows
which curve around one another in complex patterns, they contain significant volumes of
resin pockets. The density of fibers, V
t
, within tows is therefore higher (typically 0.65 ≤
V
t
≤ 0.7) than the fiber density, V, averaged over representative volumes of the composite
(typically 0.5 ≤ V ≤ 0.6). It is the latter density that is measured by standard tests of fiber
volume fraction, e.g. measuring the areal weight of preforms; or measuring the fiber
content of composites by matrix dissolution [5.9].
Direct measurement of the volume of resin held in resin pockets requires
painstaking sectioning of specimens. In engineering design situations, it will probably
always be the case that resin pockets will be incompletely characterized. The volume
fraction of fibers within tows will therefore not be known exactly.
Nevertheless, in textile composites designed for high stiffness, this uncertainty
will always have a negligible effect on computed macroscopic properties. In high
stiffness applications, a good fiber architecture is one in which all critical elastic moduli
are fiber dominated; in other words, nearly straight fibers are so oriented that any
extensional or shear strain is opposed by the axial extension or compression of fibers.
Now the axial stiffness of a tow is very nearly proportional to the fiber volume fraction,
V
t
, assumed to exist within it; while the fraction of the whole composite constituted by
the tow is inversely proportional to V
t
for fixed fiber counts. Therefore, the contribution
