Page 224 - Plastics Engineering

Mechanical Behaviour of Composites 207
Overall Stiffness Matrix Overall Compliance Matrix

-
Q(0) = T,' . Q. T, S(e) = Q(e)-I
6.27 io4 2.71 io4 3.66 io4
2.71 x IO4 2.21 x IO4 1.87 x IO4
3.66 x io4 1.87 io4 2.88 io4
Hence, the Extension Stiffness matrix is given by
A = 2.Q(O) + 4.e(35) + 4.Q(-35)
[7:530, 105 2.22 105
A = 2 22 x 105 1.93 x 105 ]Nmm
0 2.39 x IO5
The compliance matrix is obtained by inverting [A]

a =A- I
[ 2.0 ;IOp6 -2.31 x lop6
u = -2.31 x lop6 7.84 x lop6 0 ] (Nmm-I)
0 4.17 x lop6
The stiffness terms in the global directions may be obtained from:
1
E, = E, = 49.7 GN/m2
all x IO'
1 1
E, = E, = 12.8 GN/m2 and G,, = = 24 GN/III~
a22 x 10' a66 x 10

(note the high value of Poisson's Ratio which can be obtained in composite
laminates)
a12
uyx = - vyx = 0.295
a22
[;J =a. [

I
;
and the strains may be obtained as
E,

E, = 5.24 sy = 1.33 x yxy = -2.08 lop4
E, = 0.052%, E, = -0.133%, rry = -0.021%
It may be seen from the above analysis that for cross-ply (0/90), and symmetric
angle ply [-O/O], laminates, A16 = ,461 = 0 and A26 = A62 = 0 (also a16 =
a61 = a62 = 0). For other types of laminates this will not be the case.