Page 195 - Plastics Engineering

178 Mechanical Behaviour of Composites

Equilibrium Condition
Referring to Fig. 3.6. The force in the fibres will be the same as the force
in the matrix:
F2 = Ff = F,
I' 'L

1

Fig. 3.6 Loading perpendicular to fibres

Assuming that the width and thickness (into the page) is the same for both the
matrix and the fibres, then
a2 = af = 0, (3.9)

Geometry of Deformation Equation
The total transverse deformation will be the sum of the deformations in the
matrix and the fibres

62 = 6f + 6,
~2hc = Efhf + Emhm (3.10)
where h is the thickness of the relevant component.

Stress-Strain Relations

Then, from (3.10) and (3.1 1) we may write

afhf + amhm
- - -_
-
a2
E2 Ef he Em he