Page 194 - Plastics Engineering

Mechanical Behaviour of Composites 177
value VI. From Fig. 3.5 the value of VI is obtained from

In practice the maximum volume fraction, V,, which can be achieved in
unidirectional fibre composites is about 0.8. Designers must therefore arrange
for volume fractions to be in the range V1 + V,. It should also be noted that
in commercial production it is not always possible to achieve the high standards
of manufacture necessary to obtain full benefit from the fibres. It is generally
found that although the stiffness is predicted quite accurabzly by equation (3.5),
the strength is usually only about 65% of the value calculated by the rule of
mixtures. For fibre reinfonxmeint systems other than unidirectional fibres, these
values can be reduced even more. To allow for this a constant ‘k’ is sometimes
included in the fibre contribution to equation (3.6).
Example 3.4 Far the PEEWcarbon fibre composite referred to in
Example 3.2 calculate the values of V1 and Vht if it is known that the ultimate
tensile strength of PEEK is 62 MN/m2.

Solution From equation (3.7)

a,, - a; 0.062 - 0.058
-
Vent = - = 0.19%
f Ornu - 0; 2.1 + 0.062 - 0.058
and from equation (2.46)
u,, - U& - 0.062 - 0.058
v1 = - = 0.2%
ofu - 0; 2.1 - 0.058

(ii) Properties Perpendicular to Longitudinal Axis
The properties of a unidirectional fibre will not be nearly so good in the
transverse direction compared with the longitudinal direction. As a material
in service is likely to be subjected to stresses and strains in all directions it
is important to be aware of the properties in all directions. The transverse
direction will, of course, be the weakest direction and so it is necessary to pay
particular attention to this.
The transverse modulus, Ec~, may be determined in a manner similar to that
described earlier for the longitudinal modulus. Consider a unidirectional fibre
composite subjected to a transverse force, Fc~, in the direction perpendicular
to the fibre axis.