Materials for engineering, 3rd Edition - (Malestrom)

Organic polymeric materials 171
materials, it originates from defects which have a stress concentrating effect.
Such defects can arise from the processing of the material, service damage
or from poor design.
Because of their non-linear elastic response and the possibility of localized
crack-tip plasticity, it may not be appropriate to apply linear elastic fracture
mechanics methods to the testing of polymers. Crack-opening displacement
(COD) measurement (see Chapter 2) is important in relation to plastics.
Values of K Ic are obtained under plane strain conditions using thick samples
and there is a problem with plastics in fabricating good quality and
representative thick samples.
A further problem with polymer fracture toughness assessment is that
crack growth may not be unstable, but may be time-dependent and occur
where K is less than K Ic . A simple model which may be applied to plastics
describes the crack growth rate, da/dt in terms of material constants C and
m, i.e.:
d a/d t = CK m
I
Impact tests
When plastics are deformed under impact loads, the molecular structure may
be unable to relax at the high applied rate of strain and so the material may
fracture in a brittle manner due to breakage of the molecular chain. Various
empirical tests have been devised to measure the susceptibility of polymers
to impact loads: these include machines in which the potential energy of a
pendulum is used to fracture the sample. These are simple and quick to
perform, and the test-piece contains a sharp notch which produces a triaxial
state of stress. Many plastics show a transition from ductile to brittle behaviour
when tested over a range of temperature, the exact temperature depending on
the loading-rate and the notch sharpness. Such tests are thus essentially
qualitative in character and are of limited value in their ability to predict the
impact resistance of particular products.
Product impact tests are often written into standards for polymer products.
Thus, samples of PVC pipes or other extruded products may be subjected to
a falling-weight type of test in order to assess their energy of fracture.
A deformation map for PMMA, shown in Fig. 5.8, characterizes the
regions where particular deformation mechanisms are dominant. The diagram
is thought to typify the behaviour of linear polymers and shows deformation
regions as a function of normalised stress (with respect to Young’s modulus)
versus normalized temperature (with respect to the glass transition temperature).
In the brittle field of Fig. 5.8, the strength is calculated by linear-elastic
fracture mechanics. In the crazing field, the stresses are too low to make a
single crack propagate unstably, but they can cause the slow growth of the
cavities within the crazes. As the temperature increases, crazing is replaced