Page 254 - Plastics Engineering

Mechanical Behaviour of Composites 237
160 MN/m2 and txy = -100 MN/m2 are applied, determine whether or not
failure would be expected to occur according to (a) the Maximum Stress (b) the
Maximum Strain and (c) the Tsai-Hill criteria. The thickness of each ply is
0.2 mm.
El = 125 GN/m2, E2 = 9 GN/m2, G12 = 4.4 GN/m2, u12 = 0.34
=
61~ = 1.8 GN/m2, 32~ 0.08 GN/m2, 131~ = 1.57 GN/m2
62~ = 0.17 GN/m2, t12 = 0.1 GN/m2
Solution It is necessary to work out the global strains for the laminate (these
will be the same for each ply) and then get the local strains and stresses. Thus,
for the 30" ply

Using ho = -0.6, hl = -0.4, h2 = -0.2, h3 = 0, h4 = 0.2, h5 = 0.4 and
h6 = 0.6 (h = 1.2 mm) gives
[E;] = [ 7.51 10-~
2.94
Yxy -5.46
Thus

so = [z]
[ MN/m2

If this is repeated for each ply, then the data in Fig. 3.31 is obtained. It may be
seen that failure can be expected to occur in the +30" plies in the 2-direction
because the stress exceeds the boundary shown by the dotted line.
The Tsai-Hill criteria gives the following values
(i) 0" plies, 1.028
(ii) -30 plies, 0.776
(iii) 30 plies, 1.13
The failure in the 30" plies is thus confirmed. The Tsai-Hill criteria also
predicts failure in the 0" plies and it may be seen in Fig. 3.31 that this is