Page 252 - Plastics Engineering

Mechanical Behaviour of Composites 235
(ii) Maximum Strain Criterion
Once again, let a, = 1 MN/m2. The limiting strains are given by

&IC
- 3.04 x 10- 3
=
E1

212
i/12 - 0.031
G
[:;I
The strains in the local directions are obtained from

[ :; ] = s.
Y12 TI2
El = 1.144 E2 = 1.128 io? y12 = -1.688 x 10-~
;IT
- = 1659, i2T ~583, -- - 188
?I2
-
El E2 Y12
Thus once again, an applied stress of 188 MN/m2 would cause shear failure in
the local 1-2 direction.
(iii) Tsai-Hill Criterion
For an applied stress of 1 MN/m2 and letting X be the multiplier on this
stress, we can determine the value of X to make the Tsai-Hill equation become
equal to 1.

2
x .a1 x2 ' ala2 x . a2 x . TI2
(TI2-( )+(F)2+(r)
=*
Solving this gives X = 169. Hence a stress of a, = 169 MN/m2 would cause
failure. It is more difficult with the Tsai-Hill criterion to identify the nature
of the failure ie tensile, compression or shear. Also, it is generally found that
for fibre angles in the regions 5"-15" and 40"-90", the Tsai-Hill criterion
predictions are very close to the other predictions. For angles between 15" and
40" the Tsai-Hill tends to predict more conservative (lower) stresses to cause
failure.
Example 3.20 The single ply in the previous Example is subjected to the
stress system

a, = 80 MN/m2, ay = -40 MN/m2, rxy = -20 MN/m2
Determine whether failure would be expected to occur according to (a) the
Maximum Stress (b) the Maximum Strain and (c) the Tsai-Hill criteria.