Page 247 - Plastics Engineering

230 Mechanical Behaviour of Composites

(a) Fibre lengths less than Ct
In this case the peak value of stress occurs at x = 0, so from equation (3.45)

2Tyf
Of = -
d
The average fibre stress, Ff, is obtained by dividing the area under the
stresdfibre length graph by the fibre length.

- ;e(?)
Uf =
e
Now from (3.6)
. I
a, = (2) + ak(1 - Vf) (3.46)
Vf

(b) Fibre length equal to Ct
In this case the peak stress is equal to the maximum fibre stress.
So at x = 0
2ryft
Uf = (af = - (3.47)
)-
d

Average fibre stress = Ff =
4

So from (3.6)
.~
a, = (F) Vf +ak(l- Vf) (3.48)

(c) Fibre length greater than Ct
(i) For > x > - et)

CT~ = constant = (af),,,=

2ryet
af = -
d