Page 193 - Plastics Engineering

176 Mechanical Behaviour of Composites

This is because, with brittle fibres, failure of the composite will occur when
the fibres reach their fracture strain. At this point the matrix is subjected to the
full applied load, which it is unable to sustain,
Thus, as shown earlier, the ultimate strength of the composite may be
predicted by the rule of mixtures.
= OfuVf + UkVm (3.6)

However, as shown in Fig. 3.5, this equation only applies when the volume
fraction is greater than a certain critical value, V~t. From Fig. 3.5. this will be
defined by
amu(1 - Vcrit) = UfuVcrit - Vcrit)

Vf -

0 1

Fig. 3.5 Effect of volume fraction on strength

In addition it may be seen that the strengthening effect of the fibres is only
observed (i.e. a,, > amu) when the volume fraction is greater than a certain