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Abstract

The fatigue life of critical structural locations inthe wing of the Finnish Air Force (FAF) Hawkjet trainer was estimated. This was done byusing calibration coefficients determined bymeans of a virtual fatigue test.

The load distribution and load history ofthe manufacturer’s Full Scale Fatigue Test(FSFT) was first reproduced by using an FE-model. The peak through histories of thestresses in the critical structural locations weredetermined. The calculated histories were thenused as an input in the virtual fatigue testcalculations.

A fatigue life calibration coefficient basedon the ratio of virtual fatigue test estimatesversus FSFT results was calculated. It wasdetermined separately to each selected criticallocation. On the basis of flight measurementdata, aerodynamic loads calculation and FE-models were calibrated and the stress historiesof critical items in average usage by the FAFwere determined.

By correcting the results of the fatigue lifeanalyses using the calibration coefficientsproduced by the virtual fatigue test, moreaccurate fatigue life estimates in FAF usagecould be made. The calibration of resultsagainst in reality detected structural damagesimproves the accuracy of analytical methodsallowing the correction of differences betweenthe actual structure and the idealized FE-model.Since new fatigue tests are not required, it ispossible to make reasonable fatigue lifeestimates at lower costs compared withtraditional methods that require fatigue tests.

1. Introduction

Most operational aircraft have been tested forfatigue by means of a full scale fatigue test. Theload arrangement of the test specimen is asimplification of the reality and the loadspectrum in the test is based on assumptions ofthe aircraft type’s future use. Due to lack ofadequate knowledge of loadings in the designphase, surprises can be expected during theactual use of aircraft – the fatigue life of astructure may prove to be considerably shorterthan expected. Besides, in the course of thefatigue test or after it the aircraft can besubjected to a number of modifications, whichmay change stress concentrations in thestructure or even the mission-specific mass ofthe entire aircraft.

Conducting a full scale fatigue test is avery expensive process. This is why it isnormally made once only and the fatigue life ofthe aircraft in each operator’s use is assessed,where appropriate, using fairly simplecalculation methods. These have traditionallybeen, for example, flight hours, the number oflandings or a computational quantity based ong-level exceedances. As concerns later aircrafttypes, the monitoring of elapsed aircraft life istypically based on strain gauge or flightparameter analysis. Because large scatter istypical in fatigue life predictions, a ratherconservative approach has to be taken todetermine the aircraft type’s safe-life criteria. Ifmore accurate prediction of the actual servicelife of an aircraft in the use of each operator waspossible, the aircraft operational life could beextended closer to it’s real limits. Furthermore,more precise results of analyses decrease the

FATIGUE LIFE EVALUATION OF CRITICALLOCATIONS IN AIRCRAFT STRUCTURES USING

VIRTUAL FATIGUE TEST

Jarkko TikkaPatria

Keywords: fatigue life, finite element method, operational loads measurement

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risk of structural failure. The method, presentedherein, which is based on the virtual fatigue test,is an attempt to achieve higher accuracy incomparison with conventional analytical lifepredictions.

2. Hawk Mk 51 aircraft wing fatigue lifedetermination

This presentation describes a research projectcarried out for the Finnish Air Force todetermine the fatigue life for the wing structureof the Hawk jet trainer. Calculations are donefor the FAF average usage spectrum. Becausethe project was about estimating the fatigue lifeof a ‘safe-life’ structure in operational use, andnot the actual structural certification, it wasreasonable to conduct the fatigue life evaluationby numerical analyses without resorting toexpensive fatigue tests. The accuracy of theanalyses has been improved by utilizing theexisting knowledge of structural damages.

The research was initiated partly becauseof the difference discovered between the actualload spectrum and the manufacturer’s fatiguetest spectrum, as shown in Figure 1. The actualmass of operational aircraft differs from the4400 kg used in the fatigue testing. In themajority of the most consuming flights asregards the wing life, the aircraft mass isslightly above 4700 kilos. Besides, alreadyduring the manufacturer’s fatigue test a lot ofcracking was discovered in the wing mainstructure. On these grounds new fatigue lifeanalyses were well justified. [1,2]

The fatigue life analysis focuses onpotentially critical areas, which, when damaged,may risk flight safety and result in the wingretirement or costly repairs. The fatigue life hasbeen determined against the FAF average usage,because the circulation of aircraft in differenttasks compensates for pilot and mission relateddifferences in the aircraft usage. For eachparticular aircraft cumulative g-level targetshave also been set to control the fleet lifeconsumption and especially the retirementschedule. In addition to the fatigue life,estimates have been made of crack growth rates

and, where appropriate, the critical cracklengths.

Figure 1 Vertical loading spectra of the operator and thefatigue test. ’FSFT(EFH)’ is the spectrum tested in the

fatigue test. ’FSFT(SFH)’ is the same spectrum with thedesign scatter factor of 5. ‘FAF’ is the actual spectrum of

the Finnish Air Force.

3. Fatigue life calculation

The fatigue life calculation is implementedanalytically without new fatigue tests.Information on structural behavior accumulatedin the course of FSFT has been utilizedwhenever possible. The most central parameterfor the fatigue life of the wing is the FatigueIndex (FI). It is a non-dimensional quantity usedwhen defining the wing operational lifeaccording to the ‘safe life’ principle. Thecumulative FI value is calculated after eachflight on the basis of g-counter exceedancelevels.

3.1 Full scale fatigue test results

The most important source data used in thepresentation are the results of themanufacturer’s full scale fatigue test.

The results led to the selection of sixstructural locations critical to the wing life. Foreach item, the crack observation moment anddata on its exact location and size were recordedduring the FSFT. In operational use, crackinghas been found in one of these critical locationsonly.

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FATIGUE LIFE ANALYSIS OF AIRCRAFT CRITICAL STRUCTURALITEMS BY MEANS OF THE VIRTUAL FATIGUE TEST

3.2 Other source data

3.2.1 Contents of the training programThe Finnish Air Force has defined the principalcontents of the Hawk training program. Itcontains a categorization into different types ofmissions and describes, among others, theaverage duration of flight depending on themission type, the number of missions per 1000flight hours and the mission-specific FIconsumption per 1000 flight hours. On the basisof the description, it was possible to generatethe FAF average usage spectrum measured bymeans of strain gauges in the course of a smallnumber of flights.

3.2.2 Flight measurement dataThe Finnish Air Force has instrumented someaircraft with strain gauges. During so calledMini-OLM flights strain gauges were installedin certain areas only, such as the tailplane or thecentre fuselage. The instrumentation of two so-called “full-OLM” aircraft is more extensiveand they are in normal flying service at thesquadrons. Figure 2 shows the strain gaugesinstalled in an OLM aircraft. This study utilizesthe flight measurement data received from OLMaircraft during a small number of flights whichrepresented typical flying. Also data from oneMini-OLM installation was used. The Mini-OLM installation consisted of three axiallymeasuring strain gauges [3], fixed on the mostcritical locations on the wing. The strain gaugesinstalled in the OLM aircraft were of full bridgetype [4].

Both aircraft instrumented with straingauges performed certain calibration flightmanoeuvres, which typically included constant-g turns. On the basis of these manoeuvres it waspossible, with certain limitations, to comparethe results received from the above mentionedtypes of instrumentation.

Figure 2 OLM strain gauges shown circulated

3.2.3 Aerodynamic modelAn aerodynamic model of the Hawk aircraft forthe FINFLO Navier – Stokes flow solver hasbeen developed by the Helsinki University ofTechnology. Figure 3 shows the grid of themodel on the aircraft surface. The grid of thehalf model is comprised of 3.7 million cells.With this model both symmetrical andunsymmetrical stationary flight conditions werecalculated [5].

Figure 3 The grid of the aerodynamic model on aircraftsurface [5]

Thanks to this advanced aerodynamiccalculation method a realistic load distributioncould be produced. Furthermore, it was possibleto examine how realistic the manufacturer’sfatigue test loading was. It was found out to befairly representative especially at higher g-

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levels. Figure 4 shows the wing shear forcedistribution at 7.5 g normal acceleration underFSFT and FINFLO loads.

Figure 4 Wing shear force at 7.5 g normal acceleration.The black line indicates FINFLO and the red line FSFT

[2] loads.

3.2.4 Finite element modelsA global FE-model (Finite Element model) ofthe complete aircraft has been constructed(Figure 5). The global model is comprised ofapprox. 55.000 elements. The accuracy of themodel does not yet suffice for actual fatigue lifeestimates, but it can be used to determine

realistic translational boundary condition formore accurate sub models. A sub modelfacilitates the determination of transferfunctions from the nearest applicable straingauge to the critical structural detail. The globalmodel can be used to assess the stress levels ofstructural locations defined as critical by fatiguetests and make assumptions on whether severestresses exist in that area in reality as well.

The sub-models have been used in anattempt to describe the stress concentration inthe critical item with adequate accuracy as to thefatigue life analysis. One of the sub models usedis shown in Figure 6. Sub models are calibratedto correspond with strains measured duringMini-OLM calibration manoeuvres. The Mini-OLM strain gauges have been used because theymeasure only one strain component as opposedto OLM instrumentation with full bridge straingauges. In that case, the transverse straincomponent does not complicate theinterpretation of the results. The differencebetween sub-model strains and flight test resultswas in this study between –13 percent and +5percent.

Figure 5 The global FE-model for the Hawk Mk 51

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FATIGUE LIFE ANALYSIS OF AIRCRAFT CRITICAL STRUCTURALITEMS BY MEANS OF THE VIRTUAL FATIGUE TEST

Figure 6 An example of a sub-model(hole diameter 8 mm).

3.3 Virtual fatigue test

The load history of the original full scale fatiguetest at the wing critical locations wasreconstructed as the so-called virtual fatiguetest. The FSFT load history comprised a blockof 25 equivalent flight hours (EFH), which wasrepeated. The block consisted of 27 flights,

representing 19 different missions. Each flightinvolved individual flight manoeuvres or gustloads, each of them starting and ending at levelflight. The flights were started from “ground”and ended as well. The time history of aparticular flight by manoeuvres is shown inFigure 7. The flight manoeuvre loads wereapplied to the aircraft by hydraulic cylinders andfuel tank pressure.

The FSFT loading arrangement wasreconstructed on the finite element model. Toachieve an enough realistic boundary conditionthe fixed points were located at the fuselage.The whiffletrees of the original test betweenhydraulic jacks and pads attached to the wingwere statically determined. Since the hydraulicjacks were force-controlled, the FE modelloading could be implemented with point forces.Figure 8 shows a part of the original loadingarrangement and Figure 9 of its reconstructionon the FE model.

Figure 7 Loading history by flight manoeuvres during one flight [2]

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Figure 8 Loading arrangement of FSFT. ® Bae Systems

Figure 9 FSFT arrangements reconstructed onan FE-model

The wing structure behaves linearly at loadsbelow design limit loads thus enabling the useof the superposition principle and linear staticsolutions. When reconstructing the FSFT loadspectrum, a unit load was separately applied toeach hydraulic jack position, and by using sub-models the stress state generated by the loadwas determined at the critical locations. Theloads applied by the hydraulic jacks during eachflight manoeuvre were established and bysuperimposing the results of the unit loadapplication the stress state by flight manoeuvrewas calculated for the critical items.

By locating the stress states generated byflight manoeuvres into a 25-flight-hour block,the peak through history of each critical itemcould be simulated in the fatigue test. Figure 10shows the peak through history of one criticalitem in the 25 EFH block.

On the basis of the generated peak throughhistories, a calculated fatigue life wasdetermined for each critical structural itemduring the virtual fatigue test. In each location,the calculated fatigue life was determined by thetotal life (S-N) and crack initiation (ε-N)methods. The calculations were based, whereappropriate, on various material data. Crackgrowth rates were also estimated.

Figure 10 The FSFT peak through history of one critical item in 25 EFH block

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FATIGUE LIFE ANALYSIS OF AIRCRAFT CRITICAL STRUCTURALITEMS BY MEANS OF THE VIRTUAL FATIGUE TEST

By comparing the actual fatigue lives of criticalstructural items with calculated results, thecalibration coefficient K for each critical itemwas determined using the following formula:

LifeFatigueFSFTCalculatedLifeFatigueFSFTMeasured

K______

= (1)

In calculations with crack initiation method thecrack growth time from initial crack length(normally 1 mm) to the crack size measured inFSFT was taken into account. Depending on thematerial data used, the calibration coefficientswere typically between 0.5 and 2.

3.4 Air Force usageOn the basis of the training program contentdefinition by FAF, a block of flightsrepresenting various mission types wasdetermined for an aircraft instrumented withOLM strain gauges. Each of the mostconsuming mission type was represented at leastby one flight. The rainflow data representingFAF average usage was produced for thenecessary strain gauges of the OLM installation.The FI-consumption per mission type was set tocorrespond with the actual usage.

Owing to the fact that the strain gauges ofthe OLM installation were not located in thecritical structural locations, their stress state hadto be determined as a function of the straingauge measurement results. However, thistransfer function is dependent on the aircraftflight condition, and since the applied straingauge data was in rainflow format, flightparameters corresponding to the strain gaugestress values could not be known.

To define the transfer function and itsflight condition dependent content, i.e. thetransfer function’s range of variation, the FE-model was used to simulate a variety of flightconditions. Transfer functions were determinedfor each flight condition from the strain gaugesimulated by the FE model to the peak stress ofthe critical location. The flight conditionsinvolved are presented in Table 1.

Table 1 Flight conditions used to determine transferfunctions

Condition nz Note

symm. pull up -2 symm. pull up 2 symm. pull up 5 symm. pull up 5 zero fuel pressure roll start 1 aileron design case roll 1 50 deg / s roll 1 100 deg / s roll 1 150 deg / s landing -1 undercarriage design case refueling -1 81 kPa fuel pressure

Because several of the critical items werelocated in the integral fuel tank area, the effectsof the tank pressurization and refueling on thestresses were checked. They were found to beinsignificant. Rolling maneuvres and the ailerondesign case were used to determine theasymmetric loading content. Based on theundercarriage design case, the effects of theground–air–ground cycle (GAG) were studied.Figure 11 shows the stresses encountered by onecritical detail and the nearest strain gauge in thesimulated OLM installation. Figure 12 presentsthe transfer function values for the same itemunder different load conditions.

Figure 11 The maximum stress on one critical item (red)and the stress in the nearest OLM strain gauge simulatedon the FE model (blue) under different flight conditions.

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Figure 12 A transfer function derived from the neareststrain gage to the critical location under different flight

conditions

As shown in Figure 12, the transfer function isnot constant but depends on the flyingcondition. Because the flight parameters werenot included in the flight measurement data, aconstant value was determined for each transferfunction. If the flight parameter data had beenincluded, the transfer function could also havebeen determined as depending on it. Transferfunctions were selected within the most lifeconsuming flight envelope area of 4 to 5 g.Should the transfer function values besignificantly higher in other areas, a slightlyhigher transfer function was selected tomaintain conservatism. The biggest differencesin transfer function values compared with thesymmetrical 4 - 5 g pull-ups were caused by lowstress flight conditions. Consequently, an errorin the transfer function regarded as constantdoes not create major difference in the results ofthe fatigue life analysis.

As regards FAF usage, the fatigue lifecalculations were made using the same materialvalues and calculation methods as in the FSFTanalysis. The critical location stress dataconsisted of the strain gauge rainflow resultsmultiplied by the transfer function. As a result,calculated fatigue lives and crack growth ratesin FAF average usage were established.

3.5 Calibrated fatigue life in FAF usageThe calculated fatigue lives of the criticalstructural items in FAF usage were corrected bythe results from the virtual fatigue test. Owingto the well-known loading history and loadlevels in the virtual fatigue test, it can beassumed that the differences between the fatiguelife calculations and those measured in FSFTcan be primarily contributed to an error in thematerial data and the FE-model

Since the calculated fatigue lives in FAFusage were determined using the same materialdata and FE-model as in the virtual FSFT, it isreasonable to assume that the relative error inthe calculated fatigue life estimates is congruentwith the virtual fatigue test. Consequently, thecalibrated fatigue life for critical items in FAFusage can be calculated using the followingformula:

LifeFatigueFAFCalculatedKLifeFatigueCalibrated _____ ⋅= (2)

where K has been determined by means of thevirtual fatigue test.

Table 2 gives an example of the calculation ofthe calibrated fatigue life of one criticalstructural item using the S-N analysis.

Table 2 An example of the calibration of the fatigue lifeanalysis

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FATIGUE LIFE ANALYSIS OF AIRCRAFT CRITICAL STRUCTURALITEMS BY MEANS OF THE VIRTUAL FATIGUE TEST

4. Results from the fatigue life calculation

As a result of the fatigue life calculation, fatiguelife estimates for critical structural items wereestablished using S-N and ε-N methods.Furthermore, estimates were made of the crackgrowth rates and critical crack lengths. Asummary of the results from the fatigue lifecalculation is presented in Figure 13. As shownin the figure, the scatter of results usingmaterials from different sources, is moderateeven with calibrated calculation. According tothe results, the achievement of the certified 68FI life is not excluded, but it is possible thatsome cracking will occur before that.

Figure 13 A summary of fatigue life calculation; the solidline represents S-N analysis results and the broken line

the combined results from ε-N analysis and crack growthrate calculation. The red dot indicates the only damage onthe bottom skin panel detected so far. The vertical line at

68 FI is the certified safe life for wing.

Figure 14 shows the results of the crack growthcalculation for one critical item. Since there isnot much information about initial crackdimensions or growth rates in FSFT, the crackgrowth rate calculations were made based oninitial cracks of different depth per length ratios.

Figure 14 An example of the crack growth analysisresults, where ‘a’ is the depth of a semi-elliptic crack and

‘2c’ the crack length. The black color represents theresults calculated with the material data used by

AFGROW [6] and the red by VTT [7] accordingly.

4.1 Analysis of resultsThe order of magnitude of the results receivedfrom the fatigue life calculation is reasonable incomparison with the 68 FI design life. Theresults shown in Figure 12 do not involvescatter factors, and therefore the achievement ofthe design life can not be fully ascertained. As awhole, the results from S-N analyses are slightlymore pessimistic in comparison with the ε-Ncalculations. The trend is expected, since thecalculated life expectations fall between thelow-cycle and high-cycle areas. Compared withthe S-N analysis, the local strain method givessmaller damage at certain very high load cycles.

As concerns in-service experience, the onlyobservation of calculated critical locations ismade on the machined radius of the bottom skinpanel. It is within the scatter of ε-N results andsupports the calculations. At that location, theS-N analysis seems to give pessimistic results.

5. Summary

This presentation determines the fatigue livesfor the critical structural locations on the wingof the Hawk jet trainer in the Finnish Air Force(FAF) average usage.

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The manufacturer’s full scale fatigue test(FSFT) was simulated by means of an FE-model. On that basis, the calculated fatigue livesfor the critical structural items were determinedin FSFT. By comparing the resulting calculatedfatigue lives with the damage observationmoments recorded during FSFT, a correctioncoefficient was determined for each criticallocation. Using aircraft instrumented with straingauges, the wing loading spectrum in FAFusage was determined and fatigue life estimateswere calculated in the average usage. The FSFTcorrection coefficient was used to correctcalculated fatigue lives in FAF usage. As theoutcome of the work presented herein are thecalibrated fatigue lives in FAF usage.

With the procedure used in thispresentation it is possible to achieveconsiderably higher accuracy than in fatigue lifeestimates based solely on the results of the finiteelement method and computational fluiddynamics. The increased accuracy is contributedto the use of experience from the FSFT and thecorrection of the idealized structural model tocorrespond to the actual structure. Because thewhole procedure can be carried out without newfatigue tests, the costs from the analysis willremain at a reasonable level.

Owing to the fact that the test results didnot fully ascertain the achievement of theoriginal wing design life, the most criticallocations will have to be subjected tocomponent level fatigue tests. With increasingflight measurement data from the OLMinstallation, it would be worth repeating thefatigue life analysis of the most criticalstructural items by utilizing the measured totalusage instead of the average usage defined bythe training program.

References:[1] Cotton J. Hawk T.Mk.1. Fatigue Test Loadings,

HSA-KST-N-HAW-661, Hawker Siddeley AviationLtd., 1975

[2] Henley K. Hawk Fatigue Test Loadings, Bae-KGT-D-HAW-01114, British Aerospace, 1982

[3] Liukkonen S., Teittinen T. ja Siljander A.Komposiittivuoratun HW-keskirungon lennonaikaisetmittaukset, VAL33- 012358, VTT, Espoo 2001 (inFinnish).

[4] Liukkonen S., Teittinen T. ja Laakso R. HW-348:OLM-lentojen erillinen analyysi, VAL37-012012,VTT, Espoo 2001 (in Finnish)

[5] Salminen E. ja Siikonen T. Hawkin siivenaerodynaamiset kuormat III, Raportti T-13, Espoo2000 (in Finnish).

[6] AFGROW: The crack growth life predictionprogram. Version 4.0001.11.8. (http://fibec.flight.wpafb.af.mil/fibec/)

[7] Koski K., Bäckström M., Siljander A., Wallin M.Lentokonerakenteiden särönkasvulaskentaohjelmientestaus yksinkertaistetun ja todellisen case-tapaustenavulla, VAL37-992177, VTT, Espoo 1999 (inFinnish).