Fatigue from Random LoadsFred KihmHBM nCode+33 1 30 18 20 20Fred.firstname.lastname@example.org
The Leading Solution for Durability Engineering• nCode products help:Test engineers maximize the value of measured data through rapidanalysis and collaborative data sharing.Design engineers make the right engineering decisions to deliveroptimized product performance.Operations and asset managers understand product usage to reducecosts and avoid unexpected failures.2
nCode Product Range• Complex analysis to report, simply done• Graphical, interactive & powerful analysis• World leading fatigue analysiscapabilities• Enables collaboration, manages data,and automates standardized analysis• Search, query and reporting throughsecure web access.• Data to information to decisions• Fatigue analysis technology for FEA• Process encapsulation• Fast, configurable, and scalableData Processing System for Durability Streamlining the CAE DurabilityProcessMaximizing ROI on Test andDurability
• The 5 Box Trick :GeometryMaterialPropertiesLoadingEnvironmentFatigueAnalysisFatigueResultsThe 5 Box Trick3 Main Approaches:• Stress-Life (SN Analysis)• Strain-Life (EN or Crack Initiation Analysis)• Crack Growth (LEFM)
Alternating StressCrystal surfaceSlip bands formalong planes ofmaximum sheargiving rise tosurface extrusionsand intrusionsStrainStressFailure mode 1:Failure when stressexceeds tensilestrength in a singlepass. This is notfatigue failure.Two failure modesTimeStressApply cyclicload at lowstress levelFailure mode 2:Failure occurs after a period of timeeven though stress is low. Thecomponent seems to get ‘tired’, hencethe name FATIGUE.
Transition from Stage I - IINot all stage I cracks develop to stage II.Most have insufficient energy to crossthe grain barriers. But it only takes one!Fast fractureBeacharks due tocrack propagation
Key Factors Affecting Fatigue• Stress or Strain range The bigger the range the faster the failure Fatigue life reduces exponentially with rangeStressRange• Mean Stress Tensile mean accelerates fatigue Compressive mean retards it Viewed conceptually, a tensile mean is actingto force open the crack while thecompressive mean is trying to keep it closed
The SN Curve• ‘Infinite life’ region doesn’t really exist• Aluminium doesn’t have an infinite life• Steel with variable amplitude loadingdoesn’t either• SN method uses linear stress as input butfatigue is driven by the release of plasticshear STRAIN energy.• Therefore SN is only valid when stress islinearly related to strain, I.e. below yield.PlasticregionTransitionb1b2ElasticregionInfiniteliferegion???Endurance
Dealing with Mean (Residual) StressesViewed conceptually, a tensilemean is acting to force open thecrack while the compressivemean is trying to keep it closed• Tensile mean accelerates fatigue• Compressive mean retards itGoodman CorrectionGerber CorrectionMean stress corrections are basedon modifications to the SN curve.The curve is lowered in thepresence of a tensile mean andraised in the presence of acompressive mean( )bfumf NSS -= 21`21 ss( )bfumfNSS -= 212`21ssS = Stress rangesm = Mean stressSu = Ultimate tensile strength
Signal statistics – Rainflow cycle analysis• Fatigue tests are conducted under constantamplitude sinusoidal loading• Real loading is usually fairly random• Rainflow Cycle Counting is a technique thatallows us to break down the real loads intoequivalent cycles ranges so we can do fatigueanalysis.SignalProcessing
Signal statistics – Rainflow cycle analysistime100300200400500Peak Valley Extractiontime100300200400500Reorder to startfrom ABS maxImagine the signal isfilled with watertime100300200400500Range Mean No.time100300200400500450225Drain water starting atlowest valley, measuretotal & mean depthdrained450 225 1time10030020040050015050Continue by draining nextlowest, etc.50 150 1100 300 2SignalProcessing
Signal statistics – Rainflow cycle analysisRange Mean No.450 225 1225Range12No.300100 300 215050 150 1• Take each cycle and create a 3Dhistogram showing range vs. meanvs. number of cycles counted...SignalProcessing
RangeN100 MPa60000Material Life CurveLifedamagedAccumulate %5.060000300==300 Cycles=i fiNNDamageDamage Counting with Mineretc...
Time History Peak ValleyExtractionRainflow CycleCountingN100 60000Damage CountingDamage HistogramLIFEFatigue Analysis RouteStressorStrainTimeStressorStrainTimesMean stressStrain Range
Statistical Nature of Fatigue (1/2)LoadhistoryGeometryFatiguePropertiesFatigueAnalysisFatigueResultsOptimizeScatter inmaterial dataVariableproductionqualityUnknown customer loadingResulting statistical distribution of life
Statistical Nature of Fatigue (2/2)Fatigue requires a well definedCycle distributionNormalized Rainflow histogramsRoad Load – 3 mnsRoad Load – 200 mnsLoad Historiesvariables 57%Material Properties24%Surface finish 16%Stress Concentrators 3%Fatigue is highlysensitive to loadsProbabilistic Sensitivity
What Do We Want From A Durability Test?• Durability test that’s suitablefor the item in question:a component,sub-assemblyor a whole vehicle• Test must replicate the same failuremechanisms as seen in the real world• Test should be representative of the realloading environment• Test should be accelerated where possible to reduce project time scalesand costs• Test specification can be used in FE based virtual test or real physicaltest (qualification tests)
30-Apr-13Page 22HBM– nCode KurtMunsonWhat Steps Are Involved?1. Duty or Mission Profiling Find out what’s expected of the vehicle / aircraft / component How long should it last? Determine the ordinary loads that it’s likely to see every day Determine the extraordinary loads it might see and be expectedto survive2. Test Synthesis Synthesise a test that exhibits the same damage as the MissionProfile
What is Mission Profiling?• The damage on most Automotive structuralcomponents is dominated by deterministic timeevents• Aerospace components are usually dominatedby continuous stochastic processesTake offCruiseAir combatInterceptCruiseDescentLand-10010203055.8 56 56.2 56.4Time (s)Acceleration(g)-0.200.20.4100 200 300Time (sec)Acceleration(g)DeterministicStochastic
24Vibration Test SynthesisTest Specification• Test can be expressed in the form of a PSD orSwept Sine signal• Test has same damage content as MissionProfile• Test accounts for statistical uncertainties• Test is accelerated to reduce test duration• Test is verified to ensure no unrealistically highloads are inducedMission Profilex 200 rptsx 200 hrsx 100 rpts++etc…
25Approach - ‘GAM EG-13’, ‘NATO AECTP-200’, ‘MILSTD 810-G’• Measured data is transformed into theFatigue Damage Domain• Mission (or Duty) profile is summed in theFatigue Damage Domain using Minor’srule and statistical safety factors applied• Target Mission damage is transformed back to aPSD, this is the accelerated test spectrum• PSD can be transformed to time signal or SineSweep if necessaryFatigue DamageDomainTime SignalPSDSine SweepPSDTime SignalSine SweepMeasured Input Accelerated Test OutputFatigueTransformInverseTransform
Review of Theory• Fatigue Damage Spectrum(FDS)– Damage vs. Frequency plot– FDS steadily builds throughexposure to vibration• Shock Response Spectrum(SRS)– Peak shock vs. Frequency plot– SRS sensitive to extremeamplitude peaksFlight load dataQualificationFlight load dataQualification
27Step 1Damage TransformationProcess FlowCalculateSRSCalculateFDSEventFDSEventSRSTime SignalPSDSine SweepStep 3Test SynthesisandValidationInvert FDSTestPSDTest TimeStep 2Mission ProfilingSum FDSMissionFDSEnvelopeSRSMissionSRSTest SpecificationCalculateSRSTestSRSValidateSRSFDS = Fatigue Damage Spectrum, represents fatigue damage content of input signalSRS = Shock Response Spectrum, represents maximum amplitude of input signal
Getting response PSD’s using the Harmonic Response Transfer Functions(f)L(f)=1gPSD of Input Load L1× =f1gf fG²/Hz MPa²/HzStress PSD at ElementFRF(f) = Complex transfertensor for unit Load Case L(f)Unitary Spectrum|FRF(f)|²
30PSD Rainflow CounterNumber of upwardzero crossings, E = 3Number of peaks, E[P] = 6= upward zero crossing= peakxtimeStress(MPa)1 secondTime HistoryxxxxxxStress2HzFrequency, HzGk(f)fk( ) = ffGfm nn nth Moment of area under PSD:Number of upwardzero crossings,Number of peaks,(Theory of SO Rice, 1954) 24020mmPEmmE==RMS RMS = m0
31The Cycle Range – The Narrow Band ApproachNarrow band PSD & time signal Probability of peaks givenby Rayleigh distribution(Theory of JS Bendat, 1964)Rainflow cycle PeakRange = -02804mSemSTPEN
32Limitation of Narrow Band ApproachtimetimeWide band time signal• The narrow band solutionassumes that all positive peaksare matched with correspondingtroughs of similar magnitude.Hence the red signal istransformed to the green signal.
33• Stress cycle range (rainflow) isweighted sum of values at 2, 4,and 6 RMS stressThe Cycle Range – Steinberg(Theory of Steinberg)N(S) = E[P]*T*0mRMS =0.683 at 2*RMS0.271 at 4*RMS0.043 at 6*RMS
34The Cycle Range – Dirlik (1985)( ) ( )4210 ,,, mmmmfSp D =• Stress cycle range (rainflow) isweighted sum of Rayleigh andExponential distributions developedfrom an extensive Monte Carlosimulationwhere; zSm=2 0 =mm m20 4xmmmmm = 1024( )Dxm12221= -DD DR21 1211=- - - D D D3 1 21= - -( )QD D RD= - - 1 25 3 21. Rx DD Dm=- -- - 121 121( )p SDQeD ZRe D Z emDZQZRZ= - --1 2223202222where; zSm=2 0 =mm m20 4xmmmmm = 1024( )Dxm12221= -DD DR21 1211=- - - D D D3 1 21= - -( )QD D RD= - - 1 25 3 21. Rx DD Dm=- -- - 121 121( )p SDQeD ZRe D Z emDZQZRZ= - --1 2223202222
35• Stress cycle range (rainflow) isweighted sum of Rayleigh andGaussian distributionsThe Cycle Range – Lalanne/Rice (2000)(Theory of Lalanne, 2000)
Validation – notched vibration specimen• Notched vibration specimen fixedto test rig at left hand end andvibrated vertically• Fatigue life estimated by FEanalysis and compared with testrig. Specimen Id Test Life (seconds)1 16202 10203 15604 15605 18006 18607 2100Average test life 1646Rice/Lalanne 1980Dirlik 1010Narrow band 1080Steinberg 5050
Conclusion Test Tayloring & Virtual Shaker Table• Create accelerated vibration shaker tests from multiple measured data sets withoutexceeding realistic shock levels.• Save time per test to reduce cost and increase throughput.• Improves confidence in results by more closely representing the real loadingenvironment.• Uses a fatigue damage spectrum approach and has many advantages over traditionalmethods of enveloping PSDs.• Simulate shaker tests up-front from FE results thus closing the loop for more efficient andright-first-time testing.