Page 230 - Plastics Engineering

Mechanical Behaviour of Composites 213

where d = D-' since [B] = 0.

K~ = 0.435 m-', K~ = -0.457 m-', K~~ = -0.147 m-l
uXy = 1.052 uYx = 0.95

When the bending moment is applied the global stresses and strains in each
ply may be obtained as follows:

E, = Kx . z, Ey = Ky . z, yxy = Kxy . z

At the top surface, Z = -5 mm

= -2.17 x = 2.28 yxy = -7.34 x 10-~
and the stresses are given by

So that
a, = -47 MN/m2, uy = 5.7 MN/m2, rxy = 15.4 MN/m2.

The local stresses and strains are then obtained from the stress and strain
transformations
= T,, [ "1 and [ ] = T,, [ "1

[ 5'2 TXY Y12 YXY
u1 = -44.1 MN/m2, u2 = 2.8 MN/m2, ti2 = -19.5 MN/m2
= -3.6 E2 = 4.7 x y12 = -4.44 x 10-~

For the next interface, z = -4 mm, the new values of E~, and yxy can be
calculated and hence the stresses in the global and local co-ordinates. f = 1
and f = 2 need to be analysed for this interface but there will be continuity
across the interface because the orientation of the plies is the same in both
cases. However, at z = -3 mm there will be a discontinuity of stresses in the
global direction and discontinuity of stresses and strains in the local directions
due to the difference in fibre orientation in plies 2 and 3.
The overall distribution of stresses and strains in the local and global direc-
tions is shown in Fig. 3.23. If both the normal stress and the bending are applied
together then it is necessary to add the effects of each separate condition. That
is, direct superposition can be used to determine the overall stresses.