Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

14.4 Prediction of Aircraft Fatigue Life 409

Thecorrespondingfatiguelimitstresswouldthenhavebeen,fromacomparisonwithEq.(14.10),

S′∞,m=Sa,m/( 1 +C/

√

N′) (14.12)

Thestandardendurancecurveforthecomponentatameanstressof90N/mm^2 isfromEq.(14.7)

Sa=S′∞,m/( 1 +C/

√

N) (14.13)

SubstitutinginEq.(14.13)forS′∞,mfromEq.(14.12),wehave

Sa=

Sa,m

( 1 +C/

√

N′)

( 1 +C/

√

N) (14.14)

inwhichN′isgivenbyEq.(14.11).
Equation(14.14)willbebasedonafewtestresultssothata“safe”fatiguestrengthisusuallytaken
tobethreestandarddeviationsbelowthemeanfatiguestrength.Hence,weintroduceascatterfactor
Kn(>1)toallowforthis;Eq.(14.14)thenbecomes

Sa

Sa,m

Kn( 1 +C/

√

N′)

( 1 +C/

√

N) (14.15)

Knvarieswiththenumberoftestresultsavailable,andforacoefficientofvariationof0.1,Kn=1.45
for6specimens,Kn=1.445for10specimens,Kn=1.44for20specimens,andfor100specimensor
moreKn=1.43.FortypicalS–Ncurves,ascatterfactorof1.43isequivalenttoalifefactorof3to4.

14.4 PredictionofAircraftFatigueLife.................................................................

Wehaveseenthatanaircraftsuffersfatiguedamageduringallphasesoftheground–air–groundcycle.
The various contributions to this damage may be calculated separately and hence the safe life of the
aircraftintermsofthenumberofflightscalculated.
In the ground–air–ground cycle, the maximum vertical acceleration during take-off is 1.2gfor a
take-offfromarunwayor1.5gforatake-offfromgrass.Itisassumedthattheseaccelerationsoccur
atzeroliftandthereforeproducecompressive(negative)stresses,−STO,incriticalcomponentssuch
as the undersurface of wings. The maximum positive stress for the same component occurs in level
flight(at1g)andis+S 1 g.Theground–air–groundcycleproduces,ontheundersurfaceofthewing,a
fluctuatingstressSGAG=(S 1 g+STO)/2aboutameanstressSGAG(mean)=(S 1 g−STO)/2.Supposethat
testsshowthatforthisstresscycleandmeanstress,failureoccursafterNGcycles.Foralifefactorof
3,thesafelifeisNG/3sothatthedamagedoneduringonecycleis3/NG.Thisdamageismultipliedby
afactorof1.5toallowforthevariabilityofloadingbetweendifferentaircraftofthesametypesothat
thedamageperflightDGAGfromtheground–air–groundcycleisgivenby

DGAG=4.5/NG (14.16)

Fatiguedamageisalsocausedbygustsencounteredinflight,particularlyduringtheclimbanddescent.
SupposethatagustofvelocityuecausesastressSuaboutameanstresscorrespondingtolevelflight,
andsupposealsothatthenumberofstresscyclesofthismagnituderequiredtocausefailureisN(Su);