Page 223 - Plastics Engineering

206 Mechanical Behaviour of Composites

3.10 Summary of Steps to Predict Stiffness of Symmetric Laminates

1. The Stiffness matrix [GI is obtained as earlier each individual ply in the
laminate.
2. The Stiffness matrix [A] for the laminate is determined by adding the
product of thickness and [GI for each ply.
3. The Compliance matrix [a] for the laminate is determined by inverting
[A] ie [a] = [AI-'.
4. The stresses and strains in the laminate are then determined from

:}h
{~}=~a~.{
YXY TXY
Example 3.11 A series of individual plies with the properties listed below
are laid in the following sequence to make a laminate

Determine the moduli for the laminate in the global X-Y directions and the
strains in the laminate when stresses of a, = 10 MN/m2, cy = - 14 MNlm2
and tXy = -5 MN/m2 are applied. The thickness of each is 1 mm.

E1 = 125000 MN/m2 E2 = 7800 MN/m2 G12 = 4400 MN/m2

~12 = 0.34
Solution The behaviour of each ply when subjected to loading at 13 degrees
off the fibre axis is determined using Matrix manipulation as follows:

Compliance Matrix StifSness Matrix

Stress Transformation Matrix Strain Transformation Matrix

c2 s2 -2sc ] sc
2sc
s2 c2
-sc sc (2 - s2)