Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

414 CHAPTER 14 Fatigue

It can be seen from Eq. (14.26) that gust damage increases in proportion toVe5.26so that increasing
forwardspeedhasadramaticeffectongustdamage.
Thetotalfatiguedamagesufferedbyanaircraftperflightisthesumofthedamagecausedbythe
ground–air–groundcycle,thedamageproducedbygusts,andthedamageduetoothercausessuchas
pilot-inducedmaneuvers,groundturningandbraking,andlandingandtake-offloadfluctuations.The
damage produced by these other causes can be determined from load exceedance data. Thus, if this
extradamageperflightisDextra,thetotalfractionalfatiguedamageperflightis

Dtotal=DGAG+DgRav+Dextra

or

Dtotal=4.5/NG+DgRav+Dextra (14.27)

andthelifeoftheaircraftintermsofflightsis

Nflight= 1 /Dtotal (14.28)

14.5 CrackPropagation...................................................................................

Wehaveseenthattheconceptoffail-safestructuresinaircraftconstructionreliesonadamagedstructure
being able to retain sufficient load-carrying capacity to prevent catastrophic failure, at least until the
damageisdetected.Itisthereforeessentialthatthedesignerbeabletopredicthowandatwhatrate
a fatigue crack will grow. The ESDU data sheets provide a useful introduction to the study of crack
propagation;someoftheresultsarepresentedhere.
Theanalysisofstressesclosetoacracktipusingelasticstressconcentrationfactorsbreaksdown,
sincetheassumptionthatthecracktipradiusapproacheszeroresultsinthestressconcentrationfactor
tendingtoinfinity.Instead,linearelasticfracturemechanicsanalyzesthestressfieldaroundthecrack
tipandidentifiesfeaturesofthefieldcommontoallcrackedelasticbodies.

14.5.1 Stress Concentration Factor

Therearethreebasicmodesofcrackgrowth,asshowninFig.14.4.Generally,thestressfieldinthe
regionofthecracktipisdescribedbyatwo-dimensionalmodelwhichmaybeusedasanapproximation
formanypracticalthree-dimensionalloadingcases.Thus,thestresssystematadistancer(r≤a)from
thetipofacrackoflength2a,showninFig.14.5,canbeexpressedintheform

Sr,Sθ,Sr,θ=

K

( 2 πr)

1

2

f(θ ) (see[Ref.2]) (14.29)

inwhichf(θ)isadifferentfunctionforeachofthethreestressesandKisthestressintensityfactor;
Kisafunctionofthenatureandmagnitudeoftheappliedstresslevelsandalsoofthecracksize.The

terms(2πr)

1

(^2) andf(θ)mapthestressfieldinthevicinityofthecrackandarethesameforallcracks
underexternalloadsthatcausecrackopeningsofthesametype.