Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

14.3 Fatigue Strength of Components 407

extremevaluedistributions,aremorerealisticandallowtheexistenceofminimumfatigueendurances
andfatiguelimits.
Thedamagingportionofafluctuatingloadcycleoccurswhenthestressistensile;thiscausescracks
toopenandgrow.Therefore,ifasteadytensilestressissuperimposedonacyclicstress,themaximum
tensilestressduringthecyclewillbeincreasedandthenumberofcyclestofailurewillbedecreased.
Conversely,ifthesteadystressiscompressive,themaximumtensilestressdecreasesandthenumber
ofcyclestofailureincreases.Anapproximatemethodofassessingtheeffectofasteadymeanvalueof
stressisprovidedbyaGoodmandiagram,asshowninFig.14.2.Thisshowsthecyclicstressamplitudes
whichcanbesuperimposedupondifferentmeanstresslevelstogiveaconstantfatiguelife.InFig.14.2,
Saistheallowablestressamplitude,Sa,0isthestressamplituderequiredtoproducefatiguefailureatN
cycleswithzeromeanstress,Smisthemeanstress,andSuistheultimatetensilestress.IfSm=Su,any
cyclicstresswillcausefailure,whileifSm=0,theallowablestressamplitudeisSa,0.Theequationof
thestraightlineportionofthediagramis

Sa

Sa,0

=

(

1 −

Sm

Su

)

(14.3)

Experimentalevidencesuggestsanonlinearrelationshipforparticularmaterials.Equation(14.3)then
becomes

Sa

Sa,0

=

[

1 −

(

Sm

Su

)m]

(14.4)

inwhichmliesbetween0.6and2.
Inpracticalsituations,fatigueisnotcausedbyalargenumberofidenticalstresscyclesbutbymany
differentstressamplitudecycles.Thepredictionofthenumberofcyclestofailurethereforebecomes
complex.MinerandPalmgrenhaveproposedalinearcumulativedamagelawasfollows.IfNcyclesof
stressamplitudeSacausefatiguefailure,then1cycleproduces1/Nofthetotaldamagetocausefailure.

Fig.14.2

Goodman diagram.