1 FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 AIRCRAFT - PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado 3 1 Diecção de Engenhaia e Pogamas da Foça Aéea Potuguesa, Estado Maio da Foça Aéea Av. Leite de Vasconcelos Amadoa 2 Áea Científica de Pojecto Mecânico e Mateiais Estutuais, Instituto Supeio Técnico Av. Rovisco Pais, Lisboa 3 Diecção de Engenhaia e Pogamas da Foça Aéea Potuguesa, Estado Maio da Foça Aéea Av. Leite de Vasconcelos Amadoa ABSTRACT The pediction of fatigue lifetime can be calculated by analyzing the accumulated damage of the aicaft stuctue though Mine's ule and vetical acceleation specta. Two diffeent cycle counting methods wee used to analyze the vetical acceleation signal which was ecoded duing 72 flight hous. The fist method was the ainflow counting method and the second one the level coss counting method, which is the method simila to the one used by the Potuguese Ai Foce (PoAF). The esults of these two counting methods wee compaed with the spectum used by Epsilon manufactue. Once the specta wee obtained, the damage was also calculated using two methods: the method that consides the influence of the mean stess and the method in which the damage is calculated accoding to the tapezoid ule. At the end all the specta wee used to calculate the damage though these two methods. The main conclusion was that the opeation of the PoAF Epsilon aicaft is moe sevee than the efeence used by the manufactue, and consequently the lifetime pedicted fo the aicaft should be 12 % lowe than the life defined by the manufactue. KEY WORDS: fatigue, spectum, damage, vetical acceleation, cycle counting methods 1. ITRODUCTIO In ode to pedict the fatigue lifetime of the aicaft, the manufactue of Epsilon caied out a eal scale fatigue test at the Cente d'essais Aeonautique de Toulouse (CEAT). Duing these tests the manufactue ealized that the aicaft lifetime is detemined by the factue of the second bulkhead beam, which occued afte simulated flight hous (FH) . In this test the manufactue used a spectum that was consideed chaacteistic of the typical aicaft opeation. In ode to define the secued fatigue lifetime of opeation fo the PoAF, one of the squadon's aicaft was peviously instumented to measue and ecod vetical acceleation and local stess in citical aeas. The objective of this study was analyse the collected data though two diffeent counting methods and two diffeent ways of assessing the damage. Finally, the objective is to compae the PoAF damage with the manufactue's damage in ode to pedict the lifetime of PoAF aicaft, because the spectum of vetical acceleation of the manufactue is diffeent fom the PoAF one. 2. FATIGUE COCEPTS Accoding to ASTM  the fatigue phenomenon is elated to dynamics solicitations, which stuctually and pemanently changes the mateial in a specific location whee cacks will appea. The pocess involves 4 phases: the nucleation of the cack, the micoscopic gowing of the cack, the popagation phase, and finally the uptue (factue) of the mateial.
2 2.1 Paametes that influence fatigue Thee ae seveal paametes that influence the fatigue behaviou of the mateial: The suface finishing of an aicaft component influences the fatigue behavio. Bette suface finishing inceases fatigue esistance of mateials and the cack initiation is moe difficult. The dimensions of the component ae impotant because bigge components mean bigge volume and aea, so moe suface impefections could occu, thus oiginating cacks. The mean stess inceases the ultimate fatigue stength in S- cuve. The Sodebeg and Goodman expession ae used to count the influence of the mean stess. In this pape it was used the Goodman law accoding to expession (1), . a f 0 m + 1 (1) Usually, fatigue cack begins in aeas with a high stess concentation facto, because the fatigue stength in these aeas is lowe. The envionment of opeations influences the fatigue behaviou in a significant way. If the component opeates in a wetland aea containing salt wate, besides the dynamics loadings the component will be attacked by a chemical pocess which degades the mateial (stess coosion) causing supeficial cacks. Anothe impotant envionment facto is the tempeatue, which can cause themal stess in the mateial. Figue 1 -Level coss counting method The second one is also quite commonly used in fatigue studies. The computational implementation of this method begins with the analyses of the signal, and then the highest o the lowest peak is chosen. The new signal will stat at this peak and then the distances between the 3 sequential points ae analyzed accoding to figue 2. In this pape this method is efeeed as Rainflow Counting (CRAIFLOW). If ΔS1 > ΔS2 the cycle is not count; If Δ S1 ΔS2 it is count one cycle. The maximum, minimum and mean values of the cycle ae calculated; 2.2 Aicaft dynamics solicitation The stuctue of an aicaft in his typical opeation has to esist to diffeent dynamics loadings that change duing the flight. Thee ae 4 phases in an aicaft flight with diffeent loadings: the taxiing, in which the aicaft is on the gound, the take-off, the mission and finally the landing. In this pape the infomation available is elated to 50 flights, which means appoximately 72 flight hous. Those numbes wee chosen because they can illustate the basic taining of a student pilot. 3. CYCLE COUTIG METHODS The counting methods ae used to count the numbe of cycles of vetical acceleation signals duing flights in ode to pedict the accumulated damage of the stuctue. Two diffeent kinds of cycle counting methods exists [4,5,6]: methods that use one single paamete and methods that use two paametes. In this pape the methods used wee the level coss counting method and the ainflow method. The fist one is a single paamete method that counts the numbe of times the signal cosses specific levels (see figue 1), the method is simila to the one used by the PoAF to count cycles in this aicaft so it is efeed as FAP Counting (CFAP). Figue 2 - Computational implementation of the ainflow method The esults of these two diffeent methods that wee implemented computationally wee compaed to the spectum that the manufactue used to pedict the lifetime of the Epsilon aicaft. Howeve, to make the compaison with the manufactue spectum possible, the specta that wee obtained with each method had to be eoganized. Afte that it was used a tansfe function detemined expeimentally by  to know the stess magnitude fo each cycle based. Befoe the implementation of both counting methods the signal of the vetical acceleation was analyzed by a ange facto to avoid noise o undesiable vaiations, . The influence of the ange facto means a diffeent numbe of cycles that could be counted. So it was necessay to study the influence of the ange facto in the detemination of the specta.
3 4. DAMAGE CALCULATIO The lifetime of a component is defined taking into account its cycles of opeation and the S- cuve that chaacteizes the mateial's esistance to fatigue, howeve in cases of vaiable amplitude loading the S- cuves can not be used diectly. Theefoe, thee ae seveal methods to associate the vaiable amplitude loadings to the component lifetime by calculating the accumulated damage. The main methods ae: the linea law of cumulative damage, the hypothesis of non-linea damage and the continuous mechanics damage . The simplest and most used is the fist method, the law of Palmgen and Mine. Once the numbe of cycles was calculated it was possible to detemine the damage that these cycles induced in the stuctue. In this pape the Mine's ule was used accoding to expession (2). Whee n is the numbe of cycles that wee counted at a specific stess and is the numbe of cycles which could be sustained by the mateial fo pevious stess until the mateial failed though fatigue. Consequently, in ode to know it was necessay to detemine de S- cuve of the mateial Alloy 2024-T351, and so axial tension tests and axial fatigue tests wee pefomed. The fist one was done to detemine the mateial popeties and to guess the fist stess to use in the fatigue tests. n FAP DAMAGE (DFAP) D (2) This methods was implemented accoding to  to the spectum that comes fom CRAIFLOW, CFAP and the manufactue. To implement this method the following steps wee followed: Detemination by the S- cuve the numbe of cycles that the mateial can withstand befoe a factue at maximum stess occus; With the expession (2) by making a vaiable change and using the tapezium ule the total damage can be calculated by the expession (3). D d i o i 0.25( i+ 1) 10 5 dy MEA STRESS DAMAGE (DTM) (3) This method was called Mean Stess Damage (DTM) and uses the specta povided by the manufactue, CRAIFLOW and CFAP in ode to make possible the compaison. The detemination of the accumulate damage it was done by using expession (4) which comes fom the Goodman expession but only depends on max (maximum stess), f0 (limit fatigue stess), R (stess atio) and (factue stess): a f 0 m + 1 max 1 R 1+ R f 0 2 (4) This new expession is vey useful because the counted cycles didn't have the same value of R that was used in the expeimental test so that it's necessay conside this diffeence. The value of R is calculated using max and m (mean stess) values. Afte the application of expessions (3) and using the S- cuve a new value of is calculated. ow the damage can be obtained using the Mine ule, whee the n takes the value of the numbe of cycles with the same magnitude. 5. EXPERIMETAL TESTS TO DETERMIE THE PROPERTIES OF ALLOY 2024 T-351 To detemine the popeties of Alloy 2024-T351 specific specimens wee ceated to use in the test machines accoding to ASTM . 5.1 Tension test The tension test was done in 2 specimens with the ISTRO machine model 3369 at Instituto Supeio Técnico (IST), whose maximum load capacity is 50 K. The esults obtained ae shown in table 1. Table 1- Tension tests data Specimen 1 2 Aveage E [GPa] [MPa] yield [MPa] UTS Accoding to FAA  the popeties obtained in this pape ae slightly bigge (fo the Young module thee is a discepancy of 7.5 % and fo the Yielding stess of 16 %). This test was impotant because, besides the detemination of the popeties of the mateials in the diection of lamination, it tells the aveage stess that should be used in fatigue tests. 5.2 Fatigue test To chaacteize the mateial behaviou due to fatigue loading 8 specimens wee used, 2 fo each stess magnitude. The tests wee pefomed in ISTRO machine model 1342 of the Instituto Politécnico de Setúbal whose capacity of load is 250 K. The esults ae shown in figue 3. These tests wee pefomed with stess ation of R0 and K t 0 (stess concentation facto).
4 Figue 3- S- cuve of the Alloy 2024-T351 (laminated diection) Figue 6 -CFAP and CRAIFLOW specta (ange0.5) 6. COMPUTATIOAL RESULTS 6.1 Results of the counting methods The counting methods wee implemented computationally using the MATLAB pogamme. As stated at the beginning, diffeent anges wee used to pepae the signal fo each counting method. The esults obtained with the CRAIFLOW and CFAP fo the ange values of 0, 0.3, 0.5, 0.7 and 1.2 ae shown in figue 4,5,6,7 and 8. Figue 7 -CFAP and CRAIFLOW specta (ange0.7) Figue 4 - CFAP and CRAIFLOW specta (ange0) Figue 8 -CFAP and CRAIFLOW specta (ange1.2) 7. AALYSES AD DISCUSSIO OF THE RESULTS 7.1 Counting methods Figue 5- CFAP and CRAIFLOW specta (ange0.3) 6.2 Results of the damage calculation Once the specta of the PoAF squadon wee obtained, the damage was calculated by 2 diffeent methods: the DFAP and DTM. Results ae shown in figues 9 and 10. By the analysis of figues 4 to 8 the values of ange used to obtain a easonable PoAF spectum ae: 0 and 0.3. Fo these values the esults obtained with the ainflow counting method (CRAIFLOW) ae vey simila to the esults that ae obtained with the level coss counting method (CFAP). When the ange value inceases, the CRAIFLOW method is moe affected than the CFAP. Accoding to figue 8 the cycles of lowest magnitude ae not accounted, so the occuences ae lowest fo vetical acceleation events smalle than 2, because when the highest values of ange ae being used the smallest values of vetical acceleation ae not taken in consideation.
5 Figue 9- Damage calculated with the DFAP Figue 10 - Damage calculated with the DTM Table 2-Final esults fo the TVF obtained fom the accumulated damage Method ange Specta TVF PoAF [FH] TVF PoAF Final [FH] 1 Diffeence [%] 2 DFAP 0 CFAP DFAP 0.3 CFAP DTM 0 CFAP DTM 0.3 CFAP DTM 0.5 CFAP DTM 0 CRAIFLOW Aveage In fact, if at the beginning a level of omission fo vetical acceleation values was defined, the small values of vetical acceleation could be ejected without any poblem. But in this pape an omission level was not used. On the analysis of seveity it was assumed the hypothesis that highe occuences of highe load factos can cause moe damage than a smalle numbe of occuences of lowe load factos. Accoding to this hypothesis the PoAF specta ae moe sevee than the manufactue, since the numbe of occuences fo highe values of load factos is slightly highe than the manufactue; this is clealy visible in figue 4 and Damage calculation Fom the esults obtained in the counting methods is expected that the damage of the PoAF spectum will be slightly highe than the manufactue. In ode to compae the damage value that was obtained with the diffeent methods, the esults wee epesented in figues 9 and 10. Fom the analysis of figue 9 it is fo the CFAP with ange values of 0 and 0.3 that the PoAF damage is highe than the manufactue damage. As was stated at the beginning of this chapte the PoAF damage will be slightly bigge that the manufactue's, so that the CRAIFLOW spectum cannot be used to calculate the fatigue lifetime of the aicaft because in all cases the value of the damage is not highe than the manufactue. When the damage is calculated with the DTM (figue 10) the spectum obtained with the CRAIFLOW method fo a ange of 0 can be used to analyse the fatigue lifetime of the aicaft. Because the damage in that case is slightly highe than the damage calculated with the spectum of the manufactue. The spectum obtained with the CFAP fo a ange of 0 to 0.5 can also be used to pedict the fatigue lifetime. Fo a ange values highe than 0.5 the CFAP and the CRAIFLOW cannot be used because the damage is smalle than the manufactue's. 7.3 Pediction of Epsilon aicaft lifetime The manufactue of the Epsilon aicaft due to a eal test done at the CEAT ealized that the fatigue life of the aicaft (TVF) was FH. Howeve it was use a safety facto (CS) of 3 that establish the FH fo the TVF . In this pape the TVF of the Epsilon aicaft was calculated based on the damage values of the methods that povided values of damage slightly bigge than the manufactue (figues 9 and 10). Fo example, in the CFAP spectum fo ange 0.3 was obtained a D PoAF x 10-4 and a D Manufactue x10-4. The calculation method used was the following: 4 D Manufactue 1000 FH TVF FH D D 89,458 Manufactue 89458FH Manufactue 1000 FH It was used a safety facto (CS) of 3 defined by the manufactue  2 Relative diffeence compaed to the damage given by the manufactue spectum
6 Fo the manufactue the uin of the stuctue does not happen when the damage is 1, as the Mine's law says, but when the accumulated damage is So it's assumed that the stuctue of the Potuguese aicaft will fail when the accumulated damage D PoAF \ TVF \ FH eaches the value of So assuming that the total accumulated damage fo the failue of the manufactue it's the same fo the Potuguese aicaft it's possible to pedict the fatigue life fo the Potuguese aicaft: D D PoAF 1000 FH TVF PoAF PoAFTVF FH TVF PoAF ?FH D PoAF1000 FH 4 TVF 1000 PoAF The manufactue to detemine the TVF, which should be taken as a efeence by the opeatos of Epsilon, was used a safety facto of 3. The final TVF consideed moe easonable, obtained with the method illustated above, ae shown in table 2. The TVF detemined by the manufactue was FH. Accoding to table 2 the fatigue life time of PoAF aicaft should be % less than the life time pedicted by the manufactue. Fo instance this fact it's in confomity with figue 4 whee the PoAF spectum ae sevee than the specta type used by the manufactue. 8. SUMMARY Afte this wok the main conclusions ae: Accoding to the counting methods the esults obtained with the ainflow counting method (CRAIFLOW) and the cossing level counting method (CFAP) ae vey simila; The best spectum to pedict the fatigue life of a stuctue ae the spectum obtained by CRAIFLOW and the CFAP methods fo smalle values of ange (0 o 0.3); The damage values obtained with the DTM method ae highe than the esults of the DFAP, consequence of the natue of the pocess; The load spectum of Potuguese Epsilon aicaft is moe sevee that the spectum adopted as a efeence by the manufactue. Theefoe the fatigue life time of the Potuguese Epsilon TB-30 should be FH, 12% less than the fatigue life time that was deteminate by the manufactue. 9. RECOMMEDATIOS In this wok the pediction of the fatigue life time was based on the damage accumulation and the Mine's ule. In the futue this study should be done assuming the popagation of the cack. This new study will give the adequate inspection peiodicity of the citical zone and it will also pedict the fatigue life using a diffeent method. ACKOWLEDGEMETS Finally the authos ae vey gateful to Potuguese Ai Foce Depatment of Engineeing, to Ai Foce Academy and Instituto Supeio Técnico. The views expessed in this pape ae those of the authos and do not necessaily eflect those of the Potuguese Ai Foce. REFERECES  CEAT, Epsilon - Documents de Synthese suite a la campagne D Essai de Fatigue. SOCATA, Goupe Aeoespatiale,  ASTM, Standad teminology - elating to fatigue and factue testing. ASTM E (Reappoved 2002),  Bannantine Julie A. Come Jess J., Handock James L. Fundamentals of Metal Fatigue Analysis. Pentice Hall, fist edition,  Pan Jwo Hathaway Richad B. Bakey Mak E Lee, Yung-Li, Fatigue Testing and Analysis. Elsevie,  J. B. de Jonge, Counting Methods fo the Analysis of Load Time Histoies. ational Aeospace Laboatoy (LR),.A.  ASTM, Standad pactices fo cycle counting in fatigue analysis. ASTM E ,  Maco Milhaadas, Relatóio do Tiocínio EngAe  W. J. Vink, LR Contact Repot CR L. ational Aeospace Laboatoy (LR),.A.  J. K. Sobczyk, B.F. Spence, Random Fatigue: Fom Data to Theoy.Academic Pess, IC,  João Pedo Silva, Relatóio do Tiocínio EngAe 2002/3. Abil  ASTM, Conducting foce contolled constant amplitude axial fatigue tests of metallic mateials. ASTM E ,  John Bakuckas Richad C. Rice, Jana L. Jackson and Steven Thompson, Metallic Mateials Popeties Development and Standadization (MMPDS). Fedeal Aviation Administation, Januay 2003.
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