Materials for engineering, 3rd Edition - (Malestrom)

Composite materials 201
E m
E f
σ
E f
E c
Voigt
Rule of mixtures
Reuss
E m
E m E f
σ
0 1
f f
6.10 Moduli of composites versus volume fraction, according to
equations [6.3] and [6.4].
perpendicular to the grain. The degree of anisotropy (κ) of a material may be
expressed as
E
κ = ||
– 1
E ⊥
in terms of the moduli parallel to and perpendicular to a principal axis.
Discontinuous, non-aligned fibres
In a composite with discontinuous fibres, or one in which the fibres are
aligned over a range of directions, equation [6.3] cannot predict the composite
modulus in the nominal fibre direction. The fibre orientation distribution is
difficult to assess and the effect of such misalignment may be incorporated
into the rule of mixtures (equation [6.3]) by including an efficiency factor, B,
so that the equation becomes:
E c = BE 1 f matrix + E 2 f f
where B is unity for complete alignment, is 1 / 2 if the fibres are aligned in
two directions at right-angles, stressed in one of these directions, is 3 / 8 if
the fibres are randomly distributed in a plane and the composite is
stressed in the plane, and is 0.2 if the fibres are randomly distributed in three
dimensions.