Civil Engineering Reference
In-Depth Information
FIGURE 11.13
Patterns of loading continuously
aligned fiber-reinforced composites: (a) loading parallel
to fibers and (b) loading perpendicular to fibers.
(a)
(b)
where
e =
total
strain
e
c
=
composite
e
m
=
matrix
strain
strain
e
f
=
fiber
Also, the force applied to the composite
F
c
is the sum of the force carried by
the matrix
F
m
and the force carried by the fibers
F
f
:
F
c
=
F
m
+
F
f
(11.2)
Thus,
s
c
A
c
= s
m
A
m
+ s
f
A
f
(11.3)
where
s
i
=
stress
of component
i
of component
i
A
i
=
area
Replacing
s
with
Ee
for each material, we can write Equation 11.3 as
E
c
eA
c
=
E
m
eA
m
+
E
f
eA
f
(11.4)
where
E
is the modulus of elasticity. Canceling
e
and dividing by
A
c
,
we have
E
f
A
f
A
c
E
m
A
m
A
c
E
c
=
+
(11.5)
or
E
c
= n
m
E
m
+ n
f
E
f
(11.6)
where is the volume fraction of each component and
Equation 11.6 shows that the composite's modulus of elasticity is the
weighted average of the component moduli.
The share of the load carried by the fibers can be determined as follows:
n
n
m
+ n
f
=
1.
F
f
F
c
s
f
A
f
s
c
A
c
E
f
eA
f
E
c
eA
c
E
f
E
c
n
f
=
=
=
(11.7)
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