Civil Engineering Reference
In-Depth Information
E
f
Loading
parallel
to fibers
Loading
perpendicular
to fibers
E
m
0
FIGURE 11.14
Modulus of elasticity of the
composite versus fiber volume fraction.
100
Volume fraction of fibers (%)
■
11.3.3
Randomly Oriented Fiber Composites
Unlike continuously aligned fiber composites, the mechanical properties of
randomly oriented fiber composites are isotropic. The modulus of elasticity of
randomly oriented fiber composites falls between the moduli of loading par-
allel to fibers and perpendicular to fibers. To estimate the modulus of elastic-
ity of randomly oriented fiber composites, Equation 11.6 can be rewritten as
E
c
= n
m
E
m
+
Kn
f
E
f
(11.20)
where
K
is a fiber efficiency parameter (Callister 1985). For fibers randomly and
uniformly distributed within three dimensions in space,
K
has a value of 0.2.
Sample Problem 11.2
A fiberglass composite consists of epoxy matrix reinforced with randomly oriented and
uniformly distributed E-glass fibers. The modulus of elasticity of the glass fibers and
the epoxy are 65 GPa and 7 GPa, respectively. If the volume percentage of fibers is
30%, and the fiber efficiency is 0.2, calculate the modulus of elasticity of the fiberglass.
Solution
From Equation 11.20, we have
E
c
=
0.67
*
7
+
0.2
*
0.33
*
65
=
9.0 GPa
■
11.3.4
Particle-Reinforced Composites
The analysis of loading a particle-reinforced composite depends on the specif-
ic nature of the dispersed and matrix phases. A rigorous analysis of loading a
particle-reinforced composite can become quite complex. Equations 11.6 and
11.18 serve as upper and lower bounds for the particle-reinforced properties.
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