Page 73 - Mechanics Analysis Composite Materials

58 Mechanics and analysis of composite materials
For the carbon-epoxy composite material considered above as an example, assume
that the foregoing procedure results in rnf = 0.72. Then, Eqs. (3.4), (3.9, and (3.7)
give uf = 0.63, pc = 1.58 g/cm3, and up = 0.013.
For real composite materials, we normally have uf = 0.5W.65. Lower fiber
volume content results in lower ply strength and stiffness under tension along the
fibers, while higher fiber content, close to the ultimate value, leads to reduction of
the ply strength under longitudinal compression and in-plane shear due to poor
bonding of the fibers.
Since the fibers have circular cross-sections, there exists the ultimate fiber volume
fraction, uy which is less than unity and depends on the fiber arrangement. For
typical arrangements shown in Figs. 3.3-3.5, ultimate arrays are presented in
Fig. 3.6, and the corresponding ultimate fiber volume fractions are

1 rcd2 IT
square array u;! = (7) = - = 0.785,
4
2 nd2 rc
hexagonal array vu - ~ - 0.907,
=
‘-d26( 4)=26
~
layer-wise array u;! = dz c2) - =:=0.785 .

5.2. Fiber-matrix interaction

f.2.1. Theoretical and actual strength
The most important property of advanced composite materials is associated with
rery high strength of a unidirectional ply accompanied with relatively low density.
rhis advantage of the material is provided mainly by fibers. Correspondingly a
iatural question arises as to how such traditional lightweight materials like glass
)r graphite that were never applied as primary load-bearing structural materials can

Fig. 3.6. Ultimate fiber arrays for square (a), hexagonal (b), and layer-wise (c) fiber distributions.