Page 248 - Plastics Engineering

Mechanical Behaviour of Composites 23 1

Also, as before, the average fibre stress may be obtained from
- [(af)max~(~ - e,) + [(af>max~+e, = [(af>max~ (1 - i)
fff = e
So from (3.6)

(3.49)

Note that in order to get the average fibre stress as close as possible to the
maximum fibre stress, the fibres need to be considerably longer than the critical
length. At the critical length the average fibre stress is only half of the value
achieved in continuous fibres.
Experiments show that equations such as (3.49) give satisfactory agreement
with the measured values of strength and modulus for polyester sheets re-
inforced with chopped strands of glass fibre. Of course these strengths and
modulus values are only about 20-25% of those achieved with continuous
fibre reinforcement. This is because with randomly oriented short fibres only
a small percentage of the fibres are aligned along the line of action of the
applied stress. Also the packing efficiency is low and the generally accepted
maximum value for Vf of about 0.4 is only half of that which can be achieved
with continuous filaments.
In order to get the best out of fibre reinforcement it is not uncommon to try
to control within close limits the fibre content which will provide maximum
stiffness for a fixed weight of matrix and fibres. In flexure it has been found
that optimum stiffness is achieved when the volume fraction is 0.2 for chopped
strand mat (CSM) and 0.37 for continuous fibre reinforcement.
Example 3.18 Calculate the maximum and average fibre stresses for glass
fibres which have a diameter of 15 pm and a length of 2.5 mm. The interfacial
shear strength is 4 MN/m2 and L,/L = 0.3.
Solution Since L > L, then
(gf )max = - -A)= x 0.3
2tyC, - 2tyL e,
2 x 4 x 2.5 x
-
d
15
x
(af),,, = 400 MN/m2
- fff = (af)max - 2) = 400 (1 - y)
Also (1

5f = 340 MN/m2
In practice it should be remembered that short fibres are more likely to be
randomly oriented rather than aligned as illustrated in Fig. 2.35. The problem
of analysing and predicting the performance of randomly oriented short fibres