Individual aircraft life monitoring:An engineering approach for fatigue damage evaluation

Rui JIAO,Xiofn HE,*,Yuhi LI

aSchool of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

bAviation Industry Corporation of China,Beijng 100022,China

1.Introduction

When an aircraft fleet is put into service,realistic loads experienced by each aircraft vary significantly with different operational environment such as weather conditions,runway quality and skill of pilots.Different operational load histories lead to variations in fatigue damage accumulated in each aircraft structure.1If the difference between realistic load history and that previously stated is neglected,two problems may arise:

(1)Structural safety may be adversely affected.If the realistic load spectrum is more severe than the designed one,cracks may occur earlier than the repair point of critical locations,thus leading to structural fatigue failure.

(2)The economy of aircraft may also be compromised.If the realistic load spectrum is mild and the management of fleet still follows an average damage estimation,the aircraft may be retired prior to its life span.

To ensure the safety and economy of aircraft,it is thus necessary to implement individual aircraft monitoring when a fleet is put into service.With operational data collected,fatigue life expended and remaining life of aircraft structures can be estimated.2

Fatigue monitoring of individual aircraft involves operational data collection,load spectrum development,damage estimation,fatigue life prediction and management.3The existing literature on it is extensive2,4,5and plenty of methods have thus far been developed for operational data collection and fatigue life management.6–10Generally realistic load history can be accurately monitored using flight parameter-based method or strain gauges at critical points,complemented by fatigue test calibration and data processing.11,12Pertinent approaches regarding fatigue damage analysis fall into two categories:fatigue analysis-based method and crack growth analysis-based method;13however,there are limitations in application of both methods.For fatigue analysis-based method,14–16empirical parameters are often used to determine the fatigue quality of structure details,which may result in low accuracy since those parameters fail to reflect real structural status.Although crack growth analysis-based methods can improve accuracy,this method is complex to be applied and the analysis results remain to be validated by fatigue tests as those models cannot appropriately account for load interaction.17–19

Accurate fatigue damage evaluation for critical structures in service is the core of fatigue monitoring.To solve the existing problems,a strain-based fatigue crack initiation model is proposed in Ref.20to calculate fatigue damage accumulated on wing root under individual spectra.Test-analysis correlations show that this model is suitable for tension dominated load spectra,but the case with significant compressive loading remains to be refined.Besides,the strip-yield model was applied to calculate the total life in Ref.20,with pertinent parameters obtained from test results.However,in the implementation of this model,empirical adjustments are needed when different long spectrum histories are considered.Although the flight-by-flight approach proposed in Ref.21incorporates load sequence and load interaction effects,further development and evaluation are required to assess its applicability in predicting fatigue crack growth under untested spectra for different materials.Therefore,an accurate,efficient and practical approach is required for damage estimation and fatigue life prediction in fatigue monitoring.In this paper,firstly the fatigue analysis model is developed using full-scale fatigue test data.Then,fatigue test and data analysis are conducted to verify the applicability of this approach.Finally,an application of the proposed approach is illustrated.

2.Requirements for fatigue monitoring of individual aircraft

Several requirements are needed to conduct fatigue monitoring for individual aircraft:

(1)Mechanical properties of related materials are obtained,including the elasticity modulus,yield strength,tensile strength,S-Ncurve,etc.

(2)The load spectra for full-scale fatigue tests are definitely determined.During the aircraft structural development stage,the load spectra for full-scale fatigue tests are compiled based on relevant theories and experience,and the load spectrum for each critical structure can therefore be obtained.

(3)Regarding the fatigue life of aircraft structures,full-scale fatigue test data are complete and comprehensive.During the final stage of aircraft structural design,full-scale fatigue tests are conducted under the predetermined load spectrum to identify critical locations and obtain pertinent crack growth information.

(4)Realistic load spectra for individual aircraft can be developed based on the operational data.

3.Engineering approach for fatigue damage evaluation

Since reliable load spectra of critical structures can be obtained through fatigue monitoring,a stress-based fatigue analysis model is developed for damage estimation and fatigue life prediction.

3.1.Issues in traditional nominal stress method

3.1.1.Analysis procedure

For the traditional nominal stress method,nominal stress traces are rain flow cycle counted,in which peaks and valleys are paired into cycles.For cycles with non-zero mean stresses,equivalent fully-reversed stress amplitudes are then determined using the constant life curve.The damage for each cycle is calculated with materialS-Ncurve,and the total fatigue damage is accumulated with Miner’s rule.In addition,safe life can be calculated by the quotient of fatigue life and fatigue scatter factor.The analysis procedures22are shown in Fig.1.

3.1.2.Issues in traditional method

Factors significantly affecting the accuracy of damage estimation are as follows:

(1)S-Ncurve parameters of structural details.Based on a series of materialS-Ncurve,the interpolating method is used to obtain theS-Ncurve for realistic structural details,considering material status,loading condition and surface quality as correction factors.However,those factors are generally acquired from experience,which may fail to reasonably reflect the real fatigue properties of structural details.

(2)Limitation of current cumulative damage theories.

Fig.1 Analysis procedure for traditional nominal stress method.

Plenty of theories and experimental researches23,24show that linear cumulative damage theory fails to account for the load interaction in random load spectra,resulting in inaccurate damage estimation.Besides,current nonlinear cumulative damage theories25,26remain to be improved.

(3)Fatigue scatter factor.A scatter factor of 4 is usually adopted for a fleet accounting for the variation in load spectra and structural properties.When the aircraft in a fleet is monitored individually,a scatter factor less than 4 may be adopted,as the load-time histories of the aircraft in service are clear.

3.2.Stress-based fatigue analysis model

As discussed,the determination ofS-Ncurve parameters for realistic structural details is significant to improve the accuracy of life prediction approach.To achieve this purpose,we first obtain the fatigue life of critical locations via full-scale fatigue tests under the reference load spectrum.Next,the nominal stress method is applied to back calculate theS-Ncurve parameters for realistic structural details using fatigue test data.Finally,fatigue life of critical locations under individual load spectra is predicted using the determinedS-Ncurve.

Procedures of the engineering approach are brief l y described in Fig.2,with details below:

(1)By using the reference load spectrum,full-scale fatigue tests are conducted to obtain fatigue life of critical structures.

(2)The nominal stress-based method is adopted to back calculate theS-Ncurve parameters to reflect fatigue properties of realistic structural details.

(3)The determinedS-Ncurve and stress-based method are used to evaluate fatigue damage and predict the fatigue life for critical locations under individual load spectrum.

(4)Given the variation of the structural fatigue property,scatter factors need to be determined to obtain the fatigue damage with certain reliability.

(5)Fatigue life expended index is calculated and remaining life is estimated.

3.3.Determination of S-N curve

TheS-Ncurve22can be represented by

whereCis the fatigue limit,and α andAare shape parameters.

There are three parameters inS-Ncurve,i.e.C,α andA.More samples will be required if more parameters need to be determined,which is often accompanied by less robust computation results.Therefore,theS-Ncurve parameters should be appropriately restrained according to the influence of each single parameter in fatigue life calculation.However,it is difficult to theoretically discuss the influence since the relationship between those parameters and fatigue life is nonlinear.We therefore intend to numerically analyze the influence by assuming each parameter inS-Ncurve respectively varies±5%and calculating corresponding variation of fatigue life.As greater change of fatigue life indicates more sensitivity of fatigue life to the parameter,the most sensitive parameter can be determined.

3.3.1.Sensitivity analysis of 7B04-T74 aluminum alloy

The fatigue life prediction for 7B04-T74 aluminum alloy specimens under Spectrum 1 with a lower stress level in Section 4.1 will be illustrated as an instance,with sensitivity of each parameter analyzed.

(1)Sensitivity analysis of α

Calculate the fatigue life withAandCfixed and α varying±5%,and the results are shown in Table 1.

(2)Sensitivity analysis ofA

Calculate the fatigue life with α andCfixed andAvarying±5%,and the results are shown in Table 2.

(3)Sensitivity analysis ofC

Calculate the fatigue life with α andAfixed andCvarying±5%,and the results are shown in Table 3.

3.3.2.Sensitivity analysis of TA15M titanium alloy

The sensitivity analysis of TA15M titanium alloy is the same as that of 7B04-T74 aluminum alloy in Section 3.3.1,and the results are shown in Tables 4–6.

3.3.3.Determination of S-N curve

As can be seen from Tables 1–6,the most sensitive parameter is α,followed byCandA.From Eq.(1),we find that α indicates the variation rate of fatigue life with the changes of stress level,the rate generally being the same under different stress levels.Besides,Cis the fatigue limit of details,andAis the intercept ofS-Ncurve whenCis determined.The main difference between realistic details and material lies in fatigue property,which is related withCandAdirectly.Compared withA,Cis more sensitive and should be determined to reflect the realistic structural status.

Fig.2 Procedure of fatigue damage evaluation.

Table 1 Analysis results of α of 7B04-T74 aluminum alloy.

Table 2 Analysis results of A of 7B04-T74 aluminum alloy.

Table 3 Analysis results of C of 7B04-T74 aluminum alloy.

Table 4 Analysis results of α of TA15M titanium alloy.

Table 5 Analysis results of A of TA15M titanium alloy.

Table 6 Analysis results of C of TA15M titanium alloy.

To determine the parameters inS-Ncurve,α andAare first surveyed.Typical values27of α andAof different materials are shown in Table 7.

As shown in Table 7,the values of α andAare somewhat robust,indicating that stress ratio has insignificant influence under a certain stress concentration factorKt.In addition,based on the information of previous fatigue tests,the values of α andAare basically constant for similar materials with different surface qualities.As a result,α andAof realistic structures are taken the same as that of corresponding materials with the similarKt.

To determine the value ofC,back-calculation method is implemented.We select an initial value ofC,change it with a certain interval,and calculate corresponding fatigue life of critical structures under the reference load spectrum.The valueofCis determined once the calculated life is equal to the life experimentally obtained.The analysis details are shown in Fig.3.In this case,theS-Ncurve not only reflects fatigue property of realistic structures,but also eliminates the calculation error of Miner’s rule.

Table 7 Typical values27of α and A.

3.4.Fatigue scatter factor

Fatigue scatter factors1are used to determine the structural safe life and ensure the predefined reliability of the aircraft.The fatigue scatter factor1can be defined as

Fig.3 Procedure of determination of C.

wheretPis the service life with a certain reliability level.

In fleet management28,variations of load spectra and structural properties are considered when the fatigue life scatter factor is determined.But in fatigue monitoring,only the variation of structural properties will be considered since the load-time history of each aircraft can be obtained,which will lead to a lower scatter factor.

Assuming that fatigue life follows the lognormal distribution,we have the following relationship:28

whereupis thepth percentile of the standard normal distribution and σ0the standard deviation of logarithmic life.

The reliability level in Eq.(3)corresponds to a survival ratepequal to 99.9%and confidence level equal to 0.5,with the influence of specimen number neglected.Regarding the standard deviation for logarithmic life σ0,the US navy28suggested 0.1 based on statistical analysis of fatigue test data,from which we can obtain a scatter factor of 2.

3.5.Fatigue analysis procedure

The fatigue analysis procedure22adopted in this paper can be brief l y described as follows:

(1)Obtain corresponding stress spectra for critical locations,based on the load spectrum of an individual aircraft

(2)Determine fatigue property for realistic structures

The three-parameter formula shown in Eq.(1)is used to describe theS-Ncurve.

The constant life curve is described as

where σais the stress amplitude,σa0the peak value of fluctuating stress, σmthe mean stress,and σsthe yield stress of material.

(3)Cycle-by-cycle fatigue life calculation

Each stress cycle can be expressed as （σai，σmi）or （σmaxi，Ri）,where σmaxiis the peak stress,andRithe stress ratio,and the latter is usually used in engineering.There in after,σmaxiwill be referred to σi.

According to Eq.(4),upon converting （σi，Ri）into

whereR*is the stress ratio with the same fatigue life of（σi，Ri）,andthe corresponding peak stress.

Substituting Eq.(5)into Eq.(1),we have the fatigue life as

(4)Fatigue damage evaluation

According to Miner’s rule,fatigue damage for a load spectrum block can be given by

wherekrepresents the loading series,nithe number of Loadiin one block,andNithe corresponding mean fatigue life,which can be obtained by Eq.(6).

(5)Fatigue life calculation

Mean fatigue life can be obtained using the following expression:

wheret0is the flight hour corresponding to one spectrum block(per base life period).

(6)Safe life calculation

With the scatter factor of SF,we have structural safe life as

(7)Remaining fatigue life estimation

Fatigue Life Expended Index(FLEI)can be used to illustrate the fatigue life consumption at any timete,which is denoted as FLEI(te)and can be obtained by

whereD(te)is the total damage accumulated in service.

The remaining fatigue life can be calculated by

whered(F)is the predicted mean damage rate in subsequent service for critical structures,which is determined by predicted individual spectrum.

4.Verification of proposed approach

4.1.Fatigue tests

4.1.1.Specimens

Specimens are designed and fabricated to simulate structural details in a critical location of the wing in terms of material,geometry and processing quality.The specimens are made of 7B04-T74 aluminum alloy and TA15M titanium alloy,with material properties listed in Tables 8–11.The specimen geometry is shown in Fig.4.

4.1.2.Load spectra

Two individual load spectra(Spectrum 1 and Spectrum 2)are used in the fatigue tests.Fig.5 shows corresponding acceleration exceedance curves and Fig.6 shows a fraction of each load spectrum.

Table 8 Chemical composition and mass fraction of 7B04-T74 aluminum alloy.

Table 9 Mechanical properties of 7B04-T74 aluminum alloy.

Table 10 Chemical composition and mass fraction of TA15M titanium alloy.

Table 11 Mechanical properties of TA15M titanium alloy.

Fig.4 Geometry of specimen.

Fig.5 Cumulative number of exceedance vs acceleration for two load spectra.

4.1.3.Test results

Fatigue tests are conducted on a closed-loop servo-hydraulic controlled testing machine(MTS 880)at room temperature.Axial loads in the form of sinusoidal wave are applied to specimens with a frequency of 8 Hz.The fatigue tests are conducted under two individual load spectra with different stress levels,and further details can be found in Table 12.

Fig.7 shows the typical fracture surfaces with clear marker bands.An optical microscope with a grating scale is used to measure the position of each marker band,with the error controlled within 0.01 mm.The number of load cycles corresponding to each marker band is back-extrapolated from that of the last marker band.When cracks appear on both sides of the hole,the earlier initiated one is taken as the lead crack,29corresponding to a longer critical crack size.Therefore,the crack growth data along the radical direction are obtained for the lead crack in each specimen and plotted in the semi-log coordinate(see Fig.8).

Fig.6 Fractions of load spectra.

Table 12 Details of fatigue tests.

Three-point Lagrange interpolation is adopted to estimate the fatigue life respectively corresponding to specif i ed crack depth 0.2,0.4,0.6,0.8 and 1.0 mm.Assuming that crack initiation life follows the lognormal distribution,ln(μ,σ2),we can estimate the median life and the standard deviation as follows:

Fig.7 Typical fracture surfaces.

Fig.8 Crack growth(a,t)data for lead cracks.

wheretis the fatigue life,nthe number of specimen,μ the estimated log-mean life used to determine the median lifet50,and σ the standard deviation of lg(t).

The distribution parameters estimated using Eq.(12)are shown in Table 13,where also shows the mean fatigue life corresponding to the specific crack depth.

4.2.Validation of proposed approach

The stress concentration factorKtof test specimen is 2.682 derived via finite element analysis.Then the materialS-Ncurve withKtbeing 3 is selected,with relevant parameters27beingA=98.739,α=0.404(stress ratioR=0.06)for 7B04-T74 test specimens andA=2700.868,α=0.834(R=0.06)for TA15M test specimens.

When fatigue life corresponds to a specif i ed crack length under Spectrum 1 with 53 MPa for 7B04-T74 and 118 MPa for TA15M,we can respectively obtain the value ofCusing back-calculation method.The pertinent parameters are listed in Table 14.Analysis results are shown in Tables15 and 16,indicating a good fit between the experimental results and the analysis ones,with all errors being less than 15% for7B04-T74and TA15M test specimens.

Table 13 Statistic results of test life.

Table 14 Value of pertinent parameters.

Table 15 Analysis results of fatigue life for 7B04-T74.

Table 16 Analysis results of fatigue life for TA15M.

Table 17 Crack growth(a,t)data for lead cracks of critical structure.

5.Application for monitoring a critical structure

After full-scale fatigue test,a teardown inspection of aluminum alloy structural details simulated above is performed.Then,crack length in the locations can be determined using quantitative fractography.The crack growth data are listed in Table 17,with corresponding stress spectrum(reference stress spectrum)shown in Fig.9(a).The individual aircraft stress spectrum of this structural detail is compiled based on operational data and finite element modeling(Fig.9(b)).

Fig.10 Status of fatigue life expended.

The approach presented in this paper enables the calculation of FLEI and crack size in critical structures to be conducted at any specif i ed time.Calculation results are shown in Figs.10 and 11.Fig.10 also shows the FLEI of this location from the full-scale fatigue test,in which scattered points located beyond the reference line are proofs of severe realistic usage,suggesting that missions with benign damage should be assigned to ensure flight safety.On the other hand,those scattered points located below the reference line show mild realistic usage,thus allowing assignment of missions with severe dam-age,which is aimed at improving the fleet economy.Besides,the estimated crack length at specif i ed time can provide a reference for repair.

Fig.9 Relative stress spectrum.

Fig.11 Crack length vs time history.

6.Conclusions

This paper proposes an engineering approach for fatigue damage evaluation and fatigue life prediction of critical structures based on traditional nominal stress method.With the fatigue property of realistic structural details and the calculation error of Miner’s rule taken into account,the full-scale fatigue test data are used to determine theS-Ncurve parameters.Then,theS-Ncurve and Miner’s rule are used in fatigue life prediction of the same critical locations under individual load spectra.Fatigue tests are conducted for 7B04-T74 aluminum alloy specimens and TA15M titanium alloy specimens under two load spectra,and the analysis results well correlate with the experimental ones.Besides,the relationship between crack length and fatigue life can also be obtained with this approach.The proposed approach has been proved to have high accuracy,justifying its applicability in fatigue monitoring of individual aircraft.

Acknowledgements

The authors gratefully acknowledge the support from National Natural Science Foundation of China (No.11772027),National Key Research and Development Program of China(No.2017YFB1104003)and Aeronautical Science Foundation of China(No.28163701002).

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