Page 281 - Aircraft Stuctures for Engineering Student

262 Airworthiness and airframe loads

would cause failure in Ni cycles the number of cycles nj required to cause total fatigue
failure is given by

(8.38)

Although S-N curves may be readily obtained for different materials by testing a
large number of small specimens (coupon tests), it is not practicable to adopt the
same approach for aircraft components since these are expensive to manufacture
and the test programme too expensive to run for long periods of time. However,
such a programme was initiated in the early 1950s to test the wings and tailplanes
of Meteor and Mustang fighters. These were subjected to constant amplitude loading
until failure with different specimens being tested at different load levels. Stresses were
measured at points where fatigue was expected (and actually occurred) and S-N
curves plotted for the complete structure. The curves had the usual appearance and
at low stress levels had such large endurances that fatigue did not occur; thus a fatigue
limit existed. It was found that the average S-N curve could be approximated to by
the equation

Sa = 10.3( 1 + lOOO/dZ) (8.39)
in which the mean stress was 90 N/mm2. In general terms, Eq. (8.39) may be written as
s, = S,(l+ C/dZ) (8.4)

in which S, is the fatigue limit and C is a constant. Thus Sa + S, as N + cy).
Equation (8.40) may be rearranged to give the endurance directly, i.e.

(8.41)

which shows clearly that as Sa + S,, N --+ cy).
It has been found experimentally that N is inversely proportional to the mean stress
as the latter varies in the region of 90N/mm2 while C is virtually constant. This
suggests a method of determining a ‘standard’ endurance curve (corresponding to a
mean stress level of 90N/mm2) from tests carried out on a few specimens at other
mean stress levels. Suppose S, is the mean stress level, not 90 N/mm2, in tests carried
out on a few specimens at an alternating stress level Sa:,, where failure occurs at a
mean number of cycles N,. Then assuming that the S-N curve has the same form
as Eq. (8.40)
(8.42)

in which C = 1000 and Smqm is the fatigue limit stress corresponding to the mean
stress S,. Rearranging Eq. (8.42) we have
(8.43)
The number of cycles to failure at a mean stress of 90 N/mm2 would have been, from
the above
Sm
N =-N,
90