Page 249 - Plastics Engineering

232 Mechanical Behaviour of Composites

is complex. However, the stiffness of such systems may be predicted quite
accurately using the following simple empirical relationship.

Emdom = 3E1/8 + 5E2/8 (3.50)
Hull also proposed that the shear modulus and Poisson’s Ratio for a random
short fibre composite could be approximated by

Gmdm = gEi 4- $E2 (3.51)
I
-
Vmdom = - 1 (3.52)
2Gr
El and E2 refer to the longitudinal and transverse moduli for aligned fibre
composites of the type shown in (Fig. 3.29). These values can be determined
experimentally or using specifically formulated empirical equations. However,
if the fibres are relatively long then equation (3.5) and (3.13) may be used.
These give results which are sufficiently accurate for most practical purposes.

3.15 Creep Behaviour of Fibre Reinforced Plastics

The viscoelastic nature of the matrix in many fibre reinforced plastics causes
their properties to be time and temperature dependent. Under a constant stress
they exhibit creep which will be more pronounced as the temperature increases.
However, since fibres exhibit negligible creep, the time dependence of the prop-
erties of fibre reinforced plastics is very much less than that for the unreinforced
matrix.

3.16 Strength of Fibre Composites
Up to this stage we have considered the deformation behaviour of fibre compos-
ites. An equally important topic for the designer is avoidance of failure. If the
definition of ‘failure’ is the attainment of a specified deformation then the
earlier analysis may be used. However, if the Occurrence of yield or fracture
is to be predicted as an extra safeguard then it is necessary to use another
approach.
In an isotropic material subjected to a uniaxial stress, failure of the latter
type is straightforward to predict. The tensile strength of the material 6~ will
be known from materials data sheets and it is simply a question of ensuring
that the applied uniaxial stress does not exceed this.
If an isotropic material is subjected to multi-axial stresses then the situation is
slightly more complex but there are well established procedures for predicting
failure. If a, and ay are applied it is not simply a question of ensuring that
neither of these exceed 8~. At values of a, and ay below 3~ there can be
a plane within the material where the stress reaches 6~ and this will initiate
failure.