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Simulate///Finite Element Analysis aConduct FatigueAnalysis using FEACalculating structure fatigue and stresses through finite element analysis canhelp predict weak spots and other potential problems before manufacture.BY TONY ABBEY

Editor'sNote Tony Abbey eaches heN A F E M S FE A live FE Acassesn heUntedStates,EuropeandAsa hroughout heyear,and eacheseleamngcassesgobaly.Contac ony.abbey@nafemsorg or dealsFatigueis often cited as themost common formof fal-urein structures. I toccurs at reativey lowstresses,beow thecritica staticvaue But thestressesare cy-cling, tt picaly between tension and compression. Early re-search work was motivated by ralwayaxefaluressome170yearsago and is still bengundertaken to bringafulerunderstanding of fatigue

Cyclic loadingapplied on astructurewill resut incyclicloca stresses.A ralway axeseescompressiveloads in thetop and tensilein thebottom of theshaft. Rotating180reversestheloca stresses.A further 180 gvestheorignaloca stressstate

Thecyclic stress history becomes important whei itoccursat apotentia crack initiationsite This can beanymcroscopic leve defect or void inherent in themateria or

introduced by machiningor other environmenta effects.Damageis accumuated duringtheloadinghistory of thecomponent. I f thedamagegrows beyond acritica point, thecrackwill initiate

Fatigueanaysisdoesnot introduceacrack into thefi-niteeement mode. Instead, itassessesthestressstateto-gether with loadingand environmenta factors for potentiacrack initiation. A fatigue "falure" is an indication that acrack will start. No cacuation ismadeto exploresubsequent crackgrowth.

A finiteeementanaysis(FEA) is carried out to bnd locaregonsof highstressunder operatingconditions. Themaxi-mum and minimumstressesunder cyclic loadingarecon-sidered.

Fig. 1showsacyclic stressvariation. Thestressrangespansthemost positiveandnegativestresses. Stressampli-tudeoscillatesabout ameanstressleve. A stresscycle,then,occursbetween adjacentpeaks.

The number of stresscycles, together with thestressamplitude, dictates the fatigue life of the structure.

Stress K /\\j^ y y. AmplitudeTme (seconds)

FIG. 1: Typical local stress history.

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High-frequency loading is seen in a rotating machinetool. Wave loading on an offshore oil platform is lowfrequency. Fatigue life could be measured in terms ofhours oryears,respectivelywith both having a simlarcyclecount at falure.

Earlytest datashowed a distinct reationship among thestressamplitude (S), thecyclecount (N) and theexpectedfatigue life This led to theearlyadoption of the SN curve topredict fatigue (see Fig. 2).

Forastressamplitude (Si), the number of cyclesto falure(Ni)can becaculated.There is acutoff intheslopeat 106 or107cycles,described as theendurancelimt.This indicatesvery lowstressamplitudes couldachievean infinite fatiguelife. Steesexhibit this behavior. In practice, loading,geometrica and environmenta modifiers discussed later mayprevent this.Environmental and Loading ConsiderationsThere are quite a fewcaveatswith the SN curve, however.There is a wide scatter in test results, and the curve isdrawn so that 50% of test results lieequally aboveandbeow. For more conservative lifeestimates,a lower percentageline isused.

The test resultsare for a specific materia, condition.

environment and loadingt)q3e.A "raw" SN curve is abase-line on which to apply further factors to obtan arealisticlifeassessment.

Testspecimensareoftendefined as smooth polished. Thisstandard of finish is unlikely in any manufacturingprocess,so degradation factors are applied to the SN curve Castorforgedcomponentswill havemore degradation than high-quait)r machined parts.

Other factors haveto beassessedand applied. This isprobably one of thebiggestuncertanties in fatigue caculation: I t iseasyto enter inappropriatedatainto a friendlygraphica user interface (GUI)and overestimate the fatiguelife My recommendation is toseektraining oradvice,andobtana good textbook such as "Fundamentas of Meta Fatigue Anaysis" (Bannantine, et a. Prentice Hal 1990 ISBN0-0I3-340191-X).

Many manufacturers and certification organizationsgo further than material specimen tests, which are difficult to match to actua conditions. Component testsallow more specific understanding of factors affectingfatigue life. A full-scae fatigue test may beused on thecompleteassembly. Finite eement anaysis playsan important role in helping to correlate stresses(and hence,fatigue) at each level.

SimulatingSystems \FLOW- THERMAL - STRESS - EMAG - EL TROCHEMISTRY - CASTINGOPTIMIZATION f REACTING CHEMISTRY - \S \

CD-adapco

MULTIDISCIPLINARY CO-SIMULATION

info@cd-adapc1 www.cd-adapco.com

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Simulate l l l \n \ \e Element AnalysisHigh-cycle vs. Low-cycle FatigueI f loca stressesarelow enough andwithin theeastic regon, a component mayhavea long fatiguelifemeasuredinhundredsof thousandsofcycles.Thiswasthescenario intheearly fatigueworkwith ralway axes pressureboilersand thelikeThis is known as high cycle fatigue Theclassc SNcurveasdescribed earlier is theman tool. OnecautionhereAlthoughtheSN curveshowsastressat 1,000 cyclesthisissmply a lower datumpointon thecurveand shouldnever beused. I f astress leve is indicating a latiguelifebeow about 50,000cycles then theSN curveisnot beappropriateand weshould investigateusng the followingaternativemethod.

I n somecases, theloading is moresevereand locastresses at a crack initiation ste do go plastic for at leastpart of theloadingcycleAt thisleve of loading, thenumberof cyclesto falureismuch lower. It could beof theorder50,000cyclesorevenaslow as50cycles.

This isreerred to aslow cyclefatigue I t is morerecent technology? onlypossblewhen plastic influences werebetter underscood. Nowstressin a loadcycleischaracterized by?both itseasticand plastic responseThis producesa nonlinear stress-stran hysteressloop (see Fig. 3). Theamount of plastcity?isjudged by the"fatness" of thehy?stcressloop.Apurey?easticcy?ceissmply a"skinny?"linearstressstran curve

A stran-basedapproach isused tocharacterizetheloadcy?cleresponse Insdea component at theloca highstressregon, theloca materia seesa displacement or stran controlled loading fromsurrounding materia. Theeasticandplasticstran componentscan becaculated togvethetota

LogS

>1000Endurance Limit10^-lO^cycles

N1000 NiFIG,2:Stress amplitude vs. fatigue life in cycles.

stran rangeacrosstheloadingcy?cleA maxmum and mnimumstran replacesmaxmum and mnimumstress.

TheEN fatigue lifecurveis used, shown in Fig. 3. I tissmlar to theSN curve butusesstran amplitude Theintercept of thestran amplitudewith theEN curveestablishesthenumber of fatiguecyclesto falure Confusngy?,thetheory?andcurvesaredeveoped in termsof loadreversa,equating to Hafa loadcy?cleand stran rangewhich istwcethestran amplitude

Lowc?cefatigue(EN) caculations can predict fatiguelivesas low asa few hundred cy?clesUsng this approachwith lowstresslevesisfine asonly theeasticportionoftheeastic/plastic anay?ssisused and isequivaent to anSN solution.Mean Stress EffectsYov theSN approach, theleve of meanstresswithin astresscy?ceisimportant.I f bothmaxmum and mnimumstressesaretensle every?part of theloading cy?clehasatendency?to open and deveop acrack.Conversey?, if both arecompressve thecrack can't open. In other words: Compressvestressesarebeneicia, and acompressvemean stresswillextend thefatguelifeA tenslemean stresswill reducethefatguelife

Meanstressefectsareincorporated va an equivaent amplitudestresswith zero mean. ThebascSN cun?ecan thenbeusedhavng corrected for meanstress.

Correction methodsareasoused for thelowcy?cefatguecaculation usng theEN curve however, thesetend not tobeso important, astheinfluenceof mean stressisreduced inthepresenceofplastcity?

Notch EffectsPeak stress levescan beconcentrated at very loca featuressuch as a notch or hole Highcy?clefatigue can betoo conservativeusng thesestresses.Theloca fatiguemechanism isinfluenced by? factorsignored atthemacro leve, including notchszestressleve, stressgradient,etc. The stressconcentrationfactor (Kt) istheratio ofeasticpeak local stressto averageornomna stress.

Instead of usng this though,a term caled thenotch factor(Kf) isused. I ttendsto blunttheclasticstressresult andgvea longer life Calculating K f iscomplicated, and reies heavilyonempirica methodswith extra

LogN

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LogStrain Of'

dataon notchszestressgradient and other factors requiredfor estimation.

Low cycle fatigue withmoreextensiveloca plasticity tendstoblunttheeffectof anotch even further.Atypical correction methodology uses theNeuber re-lationship toestablish anenergy baancebetween thenonlinear stressstran curveof themateria and thelocaplasticit)' in thenotch.Unscrambling Load HistoryFig. 1showsaconstant amplitude loading. The am-plitudeand themean stressleve may in fact vary underloading. This mayoccurinnatura blocks of loading,orit may bearandomseriesofevents.

For block loading, eachblock isdeatwith separatey.Themean stresscorrectionismadeand thenumber of cycles(N) that can beenduredat thestress leve (S) isfound. Theratio of actua cyclesseen inthis block,n,compared to thetota that can beendured, isn /N . This fraction iscaled thedamageratio.I f n/ N equas0.5, then haf thefatiguelifeisusedup inthatsingleblock.

Thedamageratio fromeach of theblocksissummed.I f tota damageislessthan 1.0,there isadequate fatiguelife This accumulation processiscaled Miner's Law.

Miner's Law ignoressequencing effects, so asinglelargeloadcyclecan occur atthebeginning ortheend oftheloading history. In practice, early largelevesof loadoften bring beneficia compressiveresidua stresses,increasing thefatigue life

With amore random loading history, aprocessisrequired tosynthesize equivaent parsofpeaks. Onemethodisranflow counting.\V& imaginetheload historyturnedon itssideand water dripping down thepositiveandnegativefaces.Thepeak that juts out morewill capturearan drop. That peak istagged and removed fromtheload histont A seconddrip identifies thenext highestpeak,whichistaggedand removed. Thisprocesscontinues until al peaksareremoved and isdoneonboth faces.Corresponding peaks from each facearepared togiveequivaent cycles.

A similar process isused for low cyclefatigue, but is

Ae/2 =(a//E)(2N,)b+ e/(2N,)

Elastic

2Nt 2Nf;Log Reversals

FIG. 3: Low cycle fatigue EN curve showing plastic andelastic contributions.

morecomplicated becauseequivaent stabilizedhysteresisloopsaresynthesized.Going FurtherThisisajust abrief overview ofsomeof theessentia pointsof fatigue anaysisusing FEA.Fatigueanaysisgetsmorecomplicated if theloading history is not asimplelinearscaingof oneapplied load. Thisleadsus onto multi-axia fatigueanaysis,whichisverj' muchatthecuttingedgeof technology? Otherspeciaizationsnot described hereinclude fatigueof seamweds, spotwedsand bolted joints.Specia-purpose,FEA-based toolshavebeendeveoped todea with these

Finaly, toinvestigateaspecific crack andevauatehow itwill propagatefurther or stabilizeweturn toacomplementary?anay?ssmethodology?: fracturemechanics. ^OU.Tony Abbey s aconsultant anayswthhisown company,FETraining Heaso vorksas rainingmanager or N A -FEMS , responsbeor deveopngandhnpementing rainingcasses, ncudnga vde angeof e-learningcasses.Sende-mail about hisartice oDE-Editors@deske7tg.comliillillllini!illlllllllllllilllllj||||||||||||!illiillli||iiilillllllllllllll!ll!IIIIHIIIIIINFO^ FETraining: FETralnlng.com

NAFEMS: NAFEMS.org/e-learnInqFor more information on this topic, visit deskeng.com.

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