Page 70 - Mechanics Analysis Composite Materials

Chapter 3

MECHANICS OF A UNIDIRECTIONAL PLY

Ply or lamina is the simplest element of a composite material, an elementary layer
of unidirectional fibers in a matrix (see Fig. 3.1) formed while a unidirectional tape
impregnated with resin is placed on the surface of the tool providing the shape of a
composite part.

3.1. Ply architecture

As the tape consists of tows (bundles of fibers), the ply thickness (whose minimum
value is about 0.1 mm for modern composites) is much higher than the fiber
diameter (about 0.01 mm). In an actual ply, the fibers are randomly distributed as in
Fig. 3.2. Because the actual distribution is not known and can hardly be predicted,
some typical idealized regular distributions, i.e., square (Fig. 3.3), hexagonal
(Fig. 3.4), and layer-wise (Fig. 3.5) are used for the analysis.
Composite ply consists of two constituents: fibers and matrix whose quantities in
the materials are specified by volume, v, and mass, m, fractions
6 Kll
Vf = - v, = - , (3.1)
K. > K!

(3.2)

Here, Vand Mare volume and mass, while subscripts “f’,“m”, and “c” correspond
to fibers, matrix, and composite material, respectively. Because K = V,+ V, and
M, = Mf + Mm,we have

There exist the following relationships between volume and mass fractions

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