Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 101 (2015) 26 – 33
3rd International Conference on Material and Component Performance under Variable Amplitude Loading, VAL2015
Simulation of Operational Loading Spectrum and its Effect on Fatigue Crack Growth Jiří Běhala,*, Petr Homolaa a
VZLÚ, Beranových 130, Prague 199 05, Czech Republic
Abstract The paper presents analyses of crack growth rates for two different types of load sequences. The first one was the measured natural sequence of operational loads and the second one was evaluated as a blocked sequence with the same loading spectrum. Specimens from 2124-T851 aluminum alloy were made and tested. Numerical simulations of the performed tests were made using the FASTRAN retardation model implemented in the AFGROW software and the effect of the type of loading sequence was identified. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility the Czech for Mechanics. Peer-review under responsibility of theof Czech SocietySociety for Mechanics
Keywords: Operational loading; block sequence; load spectrum; crack growth; computational analysis
1. Introduction Fatigue crack growth evaluation is an important part of DAMAGE TOLERANT analyses. According to the Airworthiness requirements [1] it can be done by experiments or calculations supported by experiments. A loading sequence as the representative of the real aircraft in service missions has to be designed for the structural certification. The most realistic method for loads ordering is a random application of load peaks in particular flights but the ordered loading blocks can be applied as well, if the loads are ordered from low-to-high-to-low load amplitudes in particular flights [2].
* Corresponding author. Tel.: +420 225 115 193; fax: +420 283 920 018. E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Czech Society for Mechanics
doi:10.1016/j.proeng.2015.02.005
Jiří Běhal and Petr Homola / Procedia Engineering 101 (2015) 26 – 33
The fatigue crack growth is significantly affected by load peak successions. Standard airplane spectra are presented as cumulative exceedances for each maximum and minimum value of load factors in the loading time series encountered. Thus two significant facts can be stated: ‚ No information about any subsequent load peaks is for disposal to simulate the load consequence effect on material behavior. ‚ All load ranges in generated sequence are maximized based on the same occurrence of the upper and lower peaks. The first problem is sometime solved by randomization of the spectrum load ranges despite that a new problem arises – what is the right random ordering. The second problem consists in the fact, that most of the load ranges are really smaller than it is encountered in the one-parametric sequence – a transition on the given upper level is from different lower levels, as can be seen from Fig.1. In order to study the problem, a real operational sequence was used to eliminate a discussion if the other randomly generated sequence is credible. Of course, it is only one realization on one airplane, the spectrum is not representative for whole fleet of the given airplanes, but the main goal of this study regarding to the load range consequence can be studied very well. Nomenclature ny Fny Ncycle Nflight Fa da/dN R FK FKeff c" u1g W B
airplane load factor airplane load factor range number of load cycles number of simulated flights crack length increment fatigue crack growth rate stress ratio stress intensity factor range effective value of stress intensity factor range stress state coefficient stress level at horizontal flight width of specimen thickness of specimen"
2. Description of the loading sequences 2.1. Naturally random ordered sequence A few sequences with random ordering of loads were developed and standardized, for example TWIST [3] and FALSTAF [4] for transport airplanes or military fighters, both implemented in AFGROW program [5], HELIX and FELIX [6] for rotorcraft. And more random sequences were developed using in-house generators. Each of the mentioned sequences can be discussed how perfectly the operational loads are simulated. To exclude these doubts, a real operational load measurement was used as an unique load sequence realization. The MUL1 registration accelerometer was used to measure 2D load spectra. An advantage of the instrument is its possibility to record all load peaks time series from which the 2D spectra are evaluated. The time data are presented on the Fig.1a for all 187 registered flights, on the Fig.1b is a detail of the time series. Very important is the fact, that the load peaks are naturally ordered what is primary control variable for the mechanism of a crack growth increments formation. Even if the sequence represents less than 200 flights, it can be used for 2D spectrum evaluation, see Fig.2.
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a
b
Fig.1. (a) Whole registered load sequence, (b) detail of the load sequence.
Fig.2. 2D load factor spectrum evaluated from the measured real operational loading.
Jiří Běhal and Petr Homola / Procedia Engineering 101 (2015) 26 – 33
The standard spectrum can be evaluated using the peak values of the measured load factors as well, see Fig.3. No amplitude filter is used because the filter on Fny = 0.1 level was applied in the MUL1 load factor registration device. The device arrangement allowed to register the flight data only.
Fig.3. Standard 1-parametric load factor spectrum of the measured load factor sequence and its approximation by 10 levels for a block sequence generation.
2.2. Block ordered sequence According to [2] the other acceptable type of a sequence is the sequence with the loads ordered in blocks with the same 1-parametric loading spectrum. The information about a natural load peaks ordering is lost if the 2D load factor spectrum is reduced to 1-parametric spectrum. To minimize an effect of the loss of the loads real ordering the loads can be ordered in a form of short blocks with the loads ordered from low to high to low load amplitudes in particular flights [2]. The CESAR loading sequence generator was developed in the frame of the homonymic European project [7] for this purpose. The sequence consists from particular flights, each flight can consists from flight phases, landing impact, braking, turns and taxiing. The used sequence contained flight loads only, which were split into 3 flight phases to generate short blocks and particular flights were separated by ny = 0. Loading levels and its occurrence are evaluated to approximate the real spectrum, Fig.4. According to the Airworthiness Standards [2] loads in each phase are ordered from low-to-high-tolow load amplitudes, see Fig.5
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Fig.4. 2D load factor spectrum evaluated from the block loading sequence.
Fig.5 Segment of the block loading sequence.
3. Experiment 3.1. Specimen geometry For testing under variable amplitude, two middle tension, M(T), specimens of dimensions of 350x100x4 mm (height, width, thickness) were made of the 2124-T851 aluminum alloy plate of 50 mm in thickness. The specimens were cut in L-T direction and an initial double-sided notch of the total length of 5 mm was sparked out symmetrically in the specimens. The test specimen geometry is shown in Fig.6.
Jiří Běhal and Petr Homola / Procedia Engineering 101 (2015) 26 – 33
Fig.6 M(T) specimen dimensions.
3.2. Crack growth measurements Two major stages, fatigue pre-cracking and fatigue crack growth under variable loading amplitude, were applied during the fatigue crack propagation tests. The first stage is represented by cyclic loading with a sinusoidal form and constant amplitude up to crack increment Fa = 1.3 mm, the second one was performed under the real random sequence or the blocked sequence, both transformed at u1g = 70 MPa. The tests were conducted in laboratory environment at room temperature. Visual method using index lines with Fa = 1 mm spacing was used for crack propagation monitoring. All four surface crack traces were measured. 4. Crack growth evaluations The FASTRAN retardation model implemented in the AFGROW computational program was used to predict the crack growth under variable amplitude loading. Fatigue crack growth rates of the 2124-T851 aluminum alloy on three levels of the stress ratios were measured in the VZLU material test lab [8] according to relevant ASTM standards. A specific feature of the FASTRAN retardation model is an approach to the effective stress intensity factor evaluation [9] which is different from the ASTM standard recommendation. To keep a consistency in stress intensity transformation from FK(R) to FKeff at measured crack growth data evaluation and FKeff to FK(R) decomposition internally in the FASTRAN code for actually applied loading peak, the measured data has to be re-evaluate according to the same approach [10]. The evaluated data were approximated by the PARIS equation; see the regression line in the Fig. 7.
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Fig. 7 Fatigue crack growth rates of the 2124-T851 aluminum alloy approximated by the PARIS equation.
The main advantage of the FASTRAN retardation model is a possibility to evaluate all parameters for the crack growth analysis from the M(T) specimen standard tests [11] including the stress state factors c. The tested specimens were relatively thin, its rate W/B = 25, and the crack growth was started from a through cracks, the constant value of the stress state coefficient c = 1.73 can be used to get a good description of the stress state in that specimens in comparison with the measured crack growth curves, see Fig. 8.
Fig. 8 Measured crack growth curves in comparison with the results of the AFGROW simulations using the FASTRAN retardation model.
Jiří Běhal and Petr Homola / Procedia Engineering 101 (2015) 26 – 33
5. Conclusions The real operational sequence was used to evaluate loss or gains, when one-parametric spectrum is used for test load sequence generation. The tests confirmed the block loading is about twice severe than the real operational loading, even if the load exceedance spectrum is the same. DAMAGE TOLERANT analyses using FASTRAN retardation model implemented in AFGROW computing program provided practically the same results, but it is necessary to add, that the input data have to be evaluated according to the algorithm on which the FASTRAN retardation model was developed. Acknowledgements The paper was funded with the support for research organisation development provided by the Ministry of Industry and Trade of the Czech Republic. References [1] FAR Part 23 Airworthiness Standards, Normal, Utility, Acrobatic, And Commuter Category Airplanes, Sec_ 23_573 effective as of 04-11-2008 [2] FAA Advisory Circular, Fatigue, Fail-Safe, and Damage Tolerance Evaluation of Metallic Structure for Normal, Utility, Acrobatic, and Commuter Category Airplanes, AC 23-13A, 2005 [3] H. Lowak et al, MINITWIST - A shortened version of TWIST, Report No. TB-146, Laboratorium fur betriebsfestigkeit, Darmstadt, 1979 [4] J.B. De Jonge, Additional information about FALSTAFF, NLR-TR 79056 U, 1979 [5] J.A. Harter, AFGROW Users Guide and Technical Manual, Version 2.02.01.18, LexTech ,2014 [6] P.R.Edwards, J. Darts, Standardized Fatigue loading sequences for helicopter rotors (HELIX and FELIX), Part 2: Final definition of HELIX and FELIX, RAE Technical Report 84085, 1984 [7] J. Běhal, Load sequence evaluator for fatigue test, Report CE-VZLU-T2.1-D2.1.4-2, VZLÚ, 2009 [8] R. Růžek et al, Materiál properties of 50 mm plate made of 2124-T851 in L-T direction, in Czech, Report MOSTA.0409.V.U.PD, VZLÚ, 2011 [9] J.C. Newman, jr., FASTRAN-II – A fatigue crack growth structural analysis program, NASA TM-104159, 1992 [10] J. Běhal, Computational fatigue crack growth characteristics of 50 mm plate made of 2124-T851 aluminum alloy to be used by the FASTRAN retardation model implemented in AFGROW code, in Czech, Report MOSTA.0425.V.U.PD, VZLÚ, 2012 [11] J. Běhal, L. Nováková, Stress state factor evaluation based on a fractographic analysis for use in the crack growth FASTRAN retardation model of the AFGROW computing code, Engineering Failure Analysis, Volume 35, 2013, Pages 645–651
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