Materials for engineering, 3rd Edition - (Malestrom)

Composite materials 199
400
Composite modulus (GN m –2 )
300
200
100
Tungsten
wires
Tungsten
particles
0
0 0.2 0.4 0.6 0.8 1.0
V f
6.7 Modulus versus volume fraction for W–Cu composites.
to be less than 1 or 2%, and this acceptability of the approximation is evident
in the experimental data shown above.
The value predicted by the law of mixtures must be regarded as an upper
bound, because the strain in the reinforcement and the matrix are not identical
in practice. We have seen, however, that this approach predicts reasonably
well the longitudinal properties of unidirectional continuous filament
composites, and law of mixtures predictions provide upper limit goals that
may be aimed at by those who design and develop composite materials.
Assuming uniform stress within the composite:
Continuous fibres or lamellae
If a composite is loaded along an axis perpendicular to that of the fibres or
lamellae (Fig. 6.9), it is reasonable to assume that the stresses in the two
components are equal. In the case of fibres, which are more commonly
encountered, the total strain of the composite ε c is the weighted mean of the
individual strains in the fibre ε f and matrix ε m , i.e.