Page 242 - Plastics Engineering

Mechanical Behaviour of Composites 225

In this case [B] # 0 and so [a] and [d] cannot be obtained by inverting the [A]
and [D] matrices respectively. They must be obtained from
[; :] ;]-l
[;
=
The in-plane strains and the moments and curvatures are all linked in this
non-symmetrical lamina and are obtained from

all a12 a16 bll b12 b16
a21 a22 a26 b21 b22 b26
a61 a62 a66 b61 b62 b66
811 812 816 dll d12 d16
821 822 86 d21 d22 d26
861 862 866 d61 d62 d66
where
N = 0. h(Nx = 50 N/mm)
which gives the strains and curvatures as
ex = 3.326 x cy = -2.868 x yxy = -3.405 x IOv5

Kx = 0.012 IlUl-', Ky = -0.01 mm-', K~~ = 0.019 mm-'
The important point to note from this Example is that in a non-symmetrical
laminate the behaviour is very complex. It can be seen that the effect of a simple
uniaxial stress, ax, is to produce strains and curvatures in all directions. This
has relevance in a number of polymer processing situations because unbalanced
cooling (for example) can result in layers which have different properties, across
a moulding wall thickness. This is effectively a composite laminate structure
which is likely to be non-symmetrical and complex behaviour can be expected
when loading is applied.
The reader may wish to check the matrices in this Example:
14.37: io4 1.41 io4
A = 1.41 x lo4 1.27 x 104
0 1.40 x 104
6.65 10-~ -5.73 10-~ -6.81 0-7
0-5]
-6.81 x -2.05 x 1.02 x 0-4
B= [ -1.46 x io3 604.5 -1.67 x io3 1
-792
258.2
604.5
-16.7 x lo3 -792 604.4
2.30 10-~ -2.09 10-~ 3.77 10-~
-2.24 x 1.49 x 5.34 x
9.55 10-~ 2.01 10-~ -2.03 x 10-~