Page 149 - Plastics Engineering

132 Mechanical Behaviour of Plastics

are insensitive to notch condition, other thermoplastics will exhibit brittle failure
if they contain sharp cracks of significant dimensions.
Polycarbonate is perhaps the most notoriously notch-sensitive of all thermo-
plastics, although nylons are also susceptible to ductilehrittle transitions in
failure behaviour caused by notch sharpening. Other plastics such as acrylic,
polystyrene and thermosets are always brittle - whatever the crack condition.
For brittle failures we may use the fracture mechanics analysis introduced
in the previous sections. From equations (2.96) and (2.99) we may write
K% m2a
G --=- =constant (2.110)
c-
E E
From this therefore it is evident that the failure stress, af, is proportional to
u-'j2. This relationship is plotted as line B on Fig. 2.68. This diagram is now
very useful because it illustrates the type of ductilehrittle transitions which
may be observed in plastics. According to line B, as the flaw size decreases
the failure stress tends towards infinity. Clearly this is not the case and in
practice what happens is that at some defect size (w) the material fails by
yielding (line A) rather than brittle fracture.
This diagram also helps to illustrate why the inherent fracture toughness of
a material is not the whole story in relation to brittle fracture. For example,
Table 2.2 shows that polystyrene, which is known to be a brittle material,
has a K value of about 1 MN m-3/2. However, LDPE which has a very high
resistance to crack growth also has a K value of about 1 MN m-3/2. The
explanation is that polyethylene resists crack growth not because it is tough but
because it has a low yield strength. If a material has a low yield stress then its
yield locus (line A in Fig. 2.68) will be pulled down, possibly below the brittle
locus as happens for polyethylene. Fig. 2.69 illustrates some of the variations
which are possible in order to alter the ductilehrittle characteristics of plastics.
The brittle failure line can be shifted by changes in chemical structure, use of
alloying techniques, changes in processing conditions, etc. The yield locus line
can be shifted by the use of additives or changes in the ambient temperature
or straining rate.
It is apparent therefore that a materials resistance to crack growth is defined
not just by its inherent toughness but by its ratio of toughness to yield stress.
Some typical values of Kl,/a, are given in Table 2.2.
Another approach to the question of resistance to crack growth is to consider
the extent to which yielding occurs prior to fracture. In a ductile material it
has been found that yielding occurs at the crack tip and this has the effect of
blunting the crack. The extent of the plastic zone (see Fig. 2.70) is given by
2
1
rp = - (E) (2.111)
27t ar
for plane stress. The plane strain value is about one third of this.