Page 282 - Aircraft Stuctures for Engineering Student

8.7 Fatigue 263

The corresponding fatigue limit stress would then have been, from a comparison with
Eq. (8.43)

sL,m = saqm/(l + c/@) (8.45)

Tie standard endurance curve for the component at a mean stress of 90N/mm2 is
from Eq. (8.40)

sa = s;,m(l + C/fi) (8.46)
Substituting in Eq. (8.46) for Sk,m from Eq. (8.45) we have
s- sa:m (1 + C/fi) (8.47)
a - (1 + c/m)
in which N' is given by Eq. (8.44).
Equation (8.47) will be based on a few test results so that a 'safe' fatigue strength is
mually taken to be three standard deviations below the mean fatigue strength. Hence
we introduce a scatter factor K,, (>1) to allow for this; Eq. (8.47) then becomes
s- Sa,m (1 + C/a) (8.48)
a - Kn(l + C/m)
K, varies with the number of test results available and for a coefficient of variation of
0.1, K,, = 1.45 for six specimens, K,, = 1.445 for 10 specimens, K,, = 1.44 for 20 speci-
mens and for 100 specimens or more K,, = 1.43. For typical S-N curves a scatter
factor of 1.43 is equivalent to a life factor of 3 to 4.

We have seen that an aircraft suffers fatigue damage during all phases of the ground-
air-ground cycle. The various contributions to this damage may be calculated
separately and hence the safe life of the aircraft in terms of the number of flights
calculated.
In the ground-air-ground cycle the maximum vertical acceleration during take-off
is 1.2g for a take-off from a runway or 1.5g for a take-off from grass. It is assumed
that these accelerations occur at zero lift and therefore produce compressive
(negative) stresses, -STo, in critical components such as the undersurface of wings.
The maximum positive stress for the same component occurs in level fight (at lg)
and is +S1,. The ground-air-ground cycle produces, on the undersurface of the
wing, a fluctuating stress SGAG = (SI, + ST0)/2 about a mean stress SGAG(~~~~) =
(S1, - STo)/2. Suppose that tests show that for this stress cycle and mean stress,
failure occurs after NG cycles. For a life factor of 3 the safe life is NG/3 so that the
damage done during one cycle is 3/NG. This damage is multiplied by a factor of
1.5 to allow for the variability of loading between different aircraft of the same
type so that the damage per flight DGAG from the ground-air-ground cycle is
given by

DGAG = 4.5/N~ (8.49)