Page 162 - Plastics Engineering

Mechanical Behaviour of Plastics 145

Then using equation (2.116)
a, =uf (1 - 2)

So applying the fatigue strength reduction factor and the factor of safety
2.5 x 4 x 100 - 13 - 4 x 50 x 2.5)
nd2 1.5 nd2 x 40
This may be solved to give d = 6.4 mm.

2.21.5 Effect of Stress System
In the previous sections the stress system has been assumed to be cyclic
uniaxial loading since this is the simplest to analyse. If, however, the material
is subjected to bending, then this will alter the stress system and hence the
fatigue behaviour. In general it is found that a sample subjected to fluctuating
bending stresses will have a longer fatigue endurance than a sample of the
same material subjected to a cyclic uniaxial stress. This is because of the stress
gradient across the material in the bending situation. Fatigue cracks are initiated
by the high stress at the surface but the rate of crack propagation is reduced
due to the lower stresses in the bulk of the material. In addition, the crack
initiation phase may have to be lengthened. This is because mouldings have
a characteristic skin which appears to resist the formation of fatigue cracks.
Under uniaxial loading the whole cross-section is subjected to the same stress
and cracks will be initiated at the weakest region.
The stress gradient also means that the occurrence of thermal softening fail-
ures is delayed. At any particular frequency of stressing, thermal softening
failures will not occur until higher stresses if the stress system is bending
rather than uniaxial.

2.21.6 Fracture Mechanics Approach to Fatigue
During fatigue the stress amplitude usually remains constant and brittle failure
occurs as a result of crack growth from a sub-critical to a critical size. Clearly
the rate at which these cracks grow is the determining factor in the life of the
component. It has been shown quite conclusively for many polymeric materials
that the rate at which cracks grow is related to the stress intensity factor by a
relation of the form
da
-
_- Cz(AK)" (2.1 17)
dN
da
where - the crack growth rate
is
dN
AK is the alternating stress intensity factor corresponding to the stress range
Au (Le. AK = K,, - Kmin) and C2 and n are constants.