64 2 Material Behaviour and Failure
occur after which the crack extends a finite amount. This can be seen by examining
the failure surfaces of fatigued components, which show a series of lines represent-
ing the intermediate positions of the crack tip during the process. These lines are
sometimes referred to as beach marks.
Failure by yielding or brittle fracture will occur as soon as a sufficiently large
load is applied, but fatigue failure requires that the load be applied and removed
a large number of times and hence generally only occurs after several months or
even years in service. During this time, large numbers of components may have been
manufactured and sold, so design errors resulting in fatigue failures can be very
expensive in terms of warranty claims, recalls and loss of customer confidence.
Many of the characteristics of fatigue failure can be traced to the fact that the
process starts from a microscopic initial defect in the material or the surface. These
defects are randomly distributed and oriented and hence apparently identical com-
ponents may exhibit significantly different fatigue behaviour. Even under idealized
laboratory conditions, where the specimen characteristics are controlled within tight
limits, the number of cycles of loading at a given stress level required to produce
failure may differ between specimens by as much as a factor of 100.
If the company for which you work has sold 1,000,000 components to your de-
sign and 5 of them failed in fatigue after 6 months, you should immediately look
for another job before it is too late! The reason is that the first few failures lie in the
tail of the statistical distribution curve which will usually be approximately Gaussian
when plotted against the logarithm of the number of cycles to failure. In this region,
the curve climbs steeply, so 5 failures after 6 months will probably translate into
200,000 failures in the first 3 years.
In view of these considerations, it is surprising that design against fatigue is a
fairly recently developed science. In fact, widespread interest in fatigue can be traced
to the 1950s, following a series of dramatic aircraft crashes featuring the DeHaviland
Comet — one of the earliest passenger jets. The debris from these crashes was col-
lected and meticulously reassembled to reveal that the fracture started in each case
from the same small hole towards the rear of the fuselage. A full scale aircraft was
then tested on the ground to simulate the cyclic effects of cabin pressurization and de-
pressurization and a similar fatigue failure was thereby produced under experimental
conditions. Previous to this, design against structural failure was largely based on
static yield stress or ultimate strength, using a large factor of safety. Of course, if
the safety factor is large enough, this procedure gives a design that is safe in fatigue
as well, but it is then a matter of experience or guesswork just how large is large
enough. It is characteristic that difficulties with this procedure first appeared in the
aircraft industry, where the payoff from weight reduction makes it advantageous to
pare safety factors as far as current knowledge permits.
2.3.1 Experimental data
As with static yield and brittle fracture, design against fatigue requires (i) some basic
experimental data obtained under idealized conditions and (ii) some kind of ‘failure
theory’ to reduce the vast range of possible service stress fields and histories to a