Page 190 - Plastics Engineering

Mechanical Behaviour of Composites 173

Matrix. m

Fig. 3.3 Loading parallel to fibres

Stress-Strain Relationships

Combining equations (3.3) and (3.4)

and using equation (3.2)

If the fibres have a uniform cross-section, then the area fraction will equal
the volume fraction, so
E1 = EfVf + EmVm (3.5)
This is an important relationship. It states that the modulus of a unidirectional
fibre composite is proportional to the volume fractions of the materials in the
composite. This is known as the Rule of Mixtures. It may also be used to
determine the density of a composite as well as other properties such as the
Poisson’s Ratio, strength, thermal conductivity and electrical conductivity in
the fibre direction.
Example 3.1 The density of a composite made from unidirectional glass
fibres in an epoxy matrix is 1950 kg/m3. If the densities of the glass and epoxy