Page 253 - Plastics Engineering

236 Mechanical Behaviour of Composites
Solution

(a) Maximum Stress Criterion
[::]=.[:I
The stresses in the 1-2 directions are

T12 TXY
a1 = 61.9 MN/m2, 02 = -21.9 MN/m2, ~12 = -47.3 MN/m2

There are thus no problems in the tensile or compressive directions but the
shear ratio has dropped below 1 and so failure is possible.

(b) Maximum Strain Criterion
The limiting strains are as calculated in the previous Example.
[::I =s. [ :q
The local strains are obtained from

Y12 r12
~1 = 9.04 x ~2 = -5.69 x yl2 = -0.032

Once again failure is just possible in the shear direction.
(c) Tsai-Hill Criterion
The Tsai-Hill equation gives

(:)2- IT (q2+ (z)2+(E)2=1.08
IT
02c
As these terms equate to >1, failure is likely to occur.
3.16.2 Strength of Laminates
When a composite is made up of many plies, it is unlikely that all plies will
fail simultaneously. Therefore we should expect that failure will occur in one
ply before it occurs in the others. To determine which ply will fail first it is
simply a question of applying the above method to each ply in turn. Thus it is
necessary to determine the stresses or strains in the local (1 -2) directions for
each ply and then check for the possibility of failure using any or all of the
above criteria. This is illustrated in the following Example.
Example 3.21 A carbon-epoxy composite has the properties listed below.
If the stacking sequence is [O/-30/30], and stresses of ax = 400 MN/m2, ay =