Page 205 - Failure Analysis Case Studies II

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m, of 4.0. The crack growth rate is much faster than for subsequent aluminium alloys, but it is
unclear whether this is due to the alloy itself, the application, or the water environment of the test.
The consequences of the water environment of the tank test were addressed by Atkinson et al. [5]
at the time of the tests, and it was felt that a cabin skin would be cycled through wet and dry periods
during service (outside due to the weather and inside due to condensation), and this cycling may be
more damaging than the environment of a tank test. The degraded environmental performance in
aluminium alloys in aerospace applications has also been noted by Barter et al. [6].
The relation between AK, the applied stress range, Aa, and the crack length, a, can be written as

AK = F(a)Aa,/& (2)
where F(a) is a term (weight function) modifying the stress field in the presence of the bolthole, and
is a function of the crack length. The relationship in Eqn (2) can be substituted into Eqn (1) to
obtain
da
= A(Aafi)’”dN. (3)
[F(a) &Irn
The number of cycles to failure for particular initial and final crack sizes can be calculated by
integrating the above equation. The weight function for a crack emanating from a hole is a function
, of the crack length, and hence makes the analytical evaluation of the integral more difficult. However,
there are tabular and graphical forms of these weight functions [7] which can be incorporated into
the calculations. It may be assumed that there was only one crack emanating from the bolthole.
There was a second fatigue crack at the opposite side of the hole, but it had not grown to any great
extent before failure occurred. The value of ACT to be placed into Eqn (3) can be assumed to be the
maximum value of the stress for the appropriate crack length, as one pressure cycle of the aircraft
cabin always began at and returned to a pressure difference of zero, and hence the stresses in the
skin approached zero. The weight function used here is the case for a uniaxial tensile stress
perpendicular to the crack growth direction. This may not have been the case for the Comet skin,
and a biaxial tensile stress field may be closer to reality: however, the effect on the calculation of
initial crack sizes is small, and serves to increase the initial defect size required to cause failure after
1286 pressurization cycles.
Such a calculation gives an estimated initial defect size of around 100 pm, corresponding to the
total life of 1286 flights for Yoke Peter. As cracks many millimetres in length were seen during
construction, and located using a in. (1.6mm) drill, it is not surprising that a crack of the order
of lOOpm in size was not spotted during manufacture and subsequent inspections. It can also be
shown that, due to the accelerating nature of fatigue crack growth, the crack would have been
visible emanating from under the bolthead for very few flights. A compressive stress around the
bolthole, introduced during formation of the hole, would have reduced the fatigue crack growth
rate in the vicinity of the hole [8], and would thus require a larger initial defect size to cause failure
after 1286 pressurized flights than has been calculated above.
Using similar calculations for G-ALYU (the accelerated flight simulation Comet), which had
only 1.7 mm of fatigue crack growth before failure after 3057 “flights”, the size of the initial defect
would be predicted to be smaller, at less than IOpm.
At the time of the Court of Inquiry, much was made of the difference in the lives of Yoke Peter
(1 286 pressurizations), Yoke Yoke (903 pressurizations), and Yoke Uncle (3057 pressurizations).
The explanation at the time was that the expected spread in fatigue results from shortest to longest
was a ratio of 1:9, and the largest ratio here was 1:3.4. These results are not a surprise as the weakest
aircraft would always fail earlier than average, and Yoke Uncle, chosen at random from the Comet
fleet, was always statistically likely to have a longer fatigue life than those which had failed.
The difficulty in observing cracks during manufacture and subsequent inspection was highlighted
by the number of cracks monitored during the fatigue testing of Yoke Robert [5]. In this case, cracks
were first observed when they were around 6mm in length, even though the probable locations of
the cracks were known. Using the crack growth data, the approximate initial defect size was less
than 10 pm. This is much less than the 100 pm estimate for Yoke Peter, and no cracks were observed
in Yoke Robert around the ADF windows, even when the doubler plate had been removed for
inspection. It is probable that there was a larger than average production crack near the starboard