Page 192 - Plastics Engineering

Mechanical Behaviour of Composites 175

It may be seen that a very large percentage of the applied force is carried by
the fibres. Note also that the ratio of stresses in the fibre may be determined
in a similar way.
From the rule of mixtures, the stresses are related as follows.

~1 = UfVf + amVm
urn
a1
- = Vf + -(1- Vf)
Of Of
am Em
As the strains are the same in the matrix and fibres - = -
Of Ef
3.8
Em
01
-
- - Vf + -(1 - Vf) = 0.3 + -(0.7) = 0.307
Of Ef 400
Thus,
-
Uf = 3.26
01
As shown in Fig. 3.4 stress-strain tests on uniaxially aligned fibre compos-
ites show that their behaviour lies somewhere between that of the fibres and
that of the matrix. In regard to the strength of the composite, acur the rule of
mixtures has to be modified to relate to the matrix stress, a; at the fracture
strain of the fibres rather than the ultimate tensile strength, a,, for the matrix.

-

uni- -- 6i-- - - - randoF
directional directional

0 Strain

Fig. 3.4 Stress-strain behaviour for several types of fibre reinforcement