Chemistry Reference
In-Depth Information
of the fibers should be at least about 100 for the full benefits of reinforcement.
This is why particulates like carbon black are reinforcements only for hydrocar-
bon elastomers but not for plastics generally.
To estimate the degree of reinforcement from parallel continuous fibers
assume that the deformations of the fibers and matrix polymer will be identical
and equal to that of the specimen when the composite material is stretched in a
direction parallel to that of the fibers. The applied stress is shared by the fibers
and polymer according to:
σ
C
A
C
5
σ
F
A
F
1
σ
P
A
P
(5-36)
where
is the stress (force/cross-sectional area), A is the area normal to the fiber
axis and the subscripts C, F, and P refer to the composite material, fiber, and
polymer, respectively. Since
σ
σ
is given by
σ
5
Y
(5-37)
[this is Eq. (4-36)] where Y is the tensile modulus (with the same units as stress)
and e is the nominal strain (increase in length/original length), then
Eq. (5-36)
is
equivalent to:
Y
C
A
C
5
Y
F
A
F
1
Y
P
A
P
(5-38)
(because
A
C
5
A
F
5
A
P
in this case). The weight fraction of fiber, w
F
, in the
composite is:
A
F
ρ
F
A
F
ρ
F
1
w
F
5
(5-39)
A
P
ρ
P
(since the lengths of the specimen, fibers, and polymer component are all equal).
Here
ρ
P
are the respective densities of the fiber and polymer. The ratio of
the load carried by the polymer to that carried by the fiber is:
ρ
F
and
σ
P
A
P
σ
F
A
F
5
Y
P
A
P
Y
F
A
F
5
Y
P
Y
F
U
ρ
F
1
ω
F
2
1
(5-40)
ρ
P
To take a specific example, consider a glass-reinforced polyester laminate,
where the chemical reactions involved in polyester technology are sketched in
Fig. 5.5
. A mixture of saturated and unsaturated acids is mixed with polyhydric
alcohols (here shown as a diol) to form an unsaturated polyester. The unsaturated
acid (maleic anhydride) provides sites for cross-linkages during subsequent sty-
rene polymerization [shown in reaction (ii)]. Some of the diacid needed to pro-
vide sufficient polyester molecular weight
2000) is a saturated species
(isophthalic acid in this example) because the cross-linked polymer would be
excessively brittle if the cross-links were too close together. The unsaturated poly-
ester produced in step (i) is mixed with a reactive monomer, usually styrene.
Glass reinforcement in the proper form is impregnated with the styrene
polyester
mixture and “cured” by free-radical polymerization of the styrene across the
(
B
