A method for evaluation of in-service fatigue cracks

Transcription

1 Engineering Failure Analysis 12 (2005) A method for evaluation of in-service fatigue cracks L. Molent a, *, R. Singh b, J. Woolsey c a Air Vehicles Division, Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend, Vic. 3207, Australia b Royal Australian Air Force, Aircraft Structural Integrity Section, RAAF Williams, Vic. 3027, Australia c Institute for Defense Analyses, Mark Center Drive, Alexandra, VA, USA Received 28 June 2004; accepted 29 June 2004 Available online 2 September 2004 Abstract This paper examines the case of unexpected fatigue crack detection in a fleet of military aircraft and proposes a technique to determine the mean life of the failures and/or appropriate inspection intervals. Use is made of the Frost and Dugdale relation, that suggest that as a first approximation a linear relationship exists between the natural log of the crack length or depth and the service history (number of cycles) for a large number of practical cases. Crown Copyright Ó 2004 Published by Elsevier Ltd. All rights reserved. Keywords: Crack growth laws; Load Spectra; Fatigue prediction; Flaw size; Aircraft failures; Damage assessment 1. Introduction In a typical scenario, the aircraft fleet manager has just learned for the third time in the last eighteen months, that a component has been found cracked on one of the 500 military aircraft under their charge. After the first case of cracking, the manufacturer assured the manager that the component had been thoroughly tested, and that this cracking had to be an anomaly. A maintenance error, or an unusual in-flight load could have been at fault, but not the basic design. After the second occurrence, the manufacturerõs assurances were less emphatic, but essentially unchanged. After three instances of cracking, it was clear that the part would have to be redesigned and replaced. The managerõs dilemma was that redesigning the part, manufacturing the new design, and installing it in the fleet would take at least two years. The cracking had not yet caused an accident, but the safety experts have told the manager that had this item failed, an accident was possible. The manager must decide how to manage risk for the next two years. * Corresponding author. Tel.: ; fax: address: lorrie.molent@defence.gov.au (L. Molent) /$ - see front matter. Crown Copyright Ó 2004 Published by Elsevier Ltd. All rights reserved. doi: /j.engfailanal

2 14 L. Molent et al. / Engineering Failure Analysis 12 (2005) The alternatives include doing nothing and accepting the risk of continued cracking and the possibility of an accident. An inspection program is usually instigated, which should reduce the risk of failure, but due to uncertainties in aircraft loading histories, provides no direct measurement of the criticality of the detected cracks. Generally, such a program would lead to some aircraft being grounded, eliminating risk for those aircraft and reducing overall risk, but reducing operational capability. This would leave precious few aircraft to spare before the serviceõs ability to accomplish its mission became impaired. In such a scenario, the decision process involves a complex probability problem concerning the likelihood of additional failures and acceptable risk. To compound the difficulty little guidance is provided in aircraft design specifications for this situation. Traditionally, a scatter factor is applied to either the mean lives of the detected cracks, or even the lowest life of those detected, to set a safe-life. The situation presented is not uncommon, and this paper proposes a methodology that demonstrates that the traditional lifing approach may be very conservative and thus, unnecessarily expensive in terms of loss of capability and logistics. The Australian Defence Science and Technology Organisation (DSTO) has evaluated a wealth of data (see for example [1],[2]) that confirms the methodology proposed by Frost Dugdale [3,4] that as a first approximation a linear relationship exists between the log of the crack length or depth and the service history (number of cycles): lnðaþ ¼bN þ lnða 0 Þ or a ¼ a 0 e bn ; ð1þ where N is the fatigue life, b is a parameter that is geometry, material and load dependent, a is the crack depth and time N, a 0 is the initial crack-like flaw size (depth of the crack at the start of loading) and where the far field stress and crack geometry remain constant then: b ¼ f ðrþ: ð2þ Frost Dugdale [3,4] also proposed that b could be expressed as: b ¼ kðdrþ 3 : ð3þ The above relationships have been shown to hold for a wide range of typical materials and geometries and for both constant amplitude and variable (i.e., in-service) loading [1]. This p ffiffiffi relationship in Eq. (1) appears to be valid whenever the stress intensity factor is a linear function of a (i.e., in the absence of load shedding and residual stress gradients). Ongoing investigations at DSTO are aimed at reconciling this observation with that implied by more conventional LEFM models. While this relationship appears to be a reasonable approximation over most of the life of many typical cracks [1,2], growth rate acceleration towards the end of life can cause an upward trend in the crack growth acceleration rate. From fractographic observation of many cracks this appears to be caused, in part by the onset of static fracture [5] modes as well as ductile fatigue crack growth, such as inclusion fracture and ultimately tearing and changes in geometry pffiffi and the coalescence of other cracks growing nearby to form a larger crack i.e., a linear function of a no longer applies. This deviation from exponential growth only accounts for a small fraction of the total crack life where load shedding is not involved. This paper briefly summarises the salient aspects of the Frost Dugdale relationship and shows how it can be applied to estimate the mean life of in-service detected failures and set appropriate inspection intervals. 2. Frost Dugdale relationship In order to demonstrate the Frost Dugdale relationship we can consider Fig.1 (from [6]) and Fig.2 (from [7]) as presented by Barter et al. [1]. These data represent the quantitative fractography (QF) measurements

3 L. Molent et al. / Engineering Failure Analysis 12 (2005) Fig. 1. Graph of QF crack depth against flight hours for cracks in aluminium alloy 7050-T7451 test coupons loaded with two F/A-18 usage spectra, from [6]. of cracks and the resulting slopes of these measurements. The results were from fatigue coupon tests on 7050 aluminium alloy tested under two complex, variable amplitude (250 flight) spectra derived from service usage of a fighter aircraft. From Fig. 1 it is seen that a reasonably straight line existed between ln(a) and test simulated flight hours as described by Eq. (1). Further, the line intersects the ln(a) axis at zero hours at what is considered to be the initial crack-like size of the discontinuity initiating cracking. Importantly, it has been seen for many in-service loading spectra (particularly those of agile aircraft like fighters) that the nucleation period for crack initiation is short and crack-like growth is observed virtually from the commencement of loading (see [1,2]). The exceptions in-service may be crack initiation due to corrosion or fretting, so some investigation of discovered service cracking must be carried out to eliminate the possibility of these. The concept of cracks initiating in the first few per centõs of a fatigue specimenõs life has been observed for decades by many investigators (see for example [8]). Thus, for the purposes of this work it will be assumed that cracks in agile service aircraft commence growing as per Eq. (1) from the date of induction (and corrosion and fretting damage have been discounted). Also for the purposes of this discussion an initial Equivalent Pre-crack like Size (EPS) is known, and that this size, for the current discussion is typical of the sizes found through quantitative fractography for typical aircraft metallic materials, which is approximately between 0.02 and 0.05 mm (see [1,2,7 11]). An indication of the critical crack size is also required and for the high stress levels typical of agile aircraft will be similar to those seen in Fig. 1 i.e., 5 10 mm. Fig. 2 demonstrates that the crack growth rate conforms to the relation described by Eqs. (2) and (3). However, the use of these relationships is not required for this current work. 3. Typical service defects It is usual that after the report of one or two detected cracks in a fleet, that a manager will call for the remaining (available and accessible) aircraft to be inspected.

4 16 L. Molent et al. / Engineering Failure Analysis 12 (2005) Fig. 2. Crack growth slopes versus notch stress for two spectra, from [7]. Typical data generated from such an in-service inspection program (from [12]) is presented at Table 1 for the location shown in Fig. 3. In this case the inspection results were conducted prior to the planned second modification of this area. These data demonstrates several points, namely: 1. There is considerable variation (as would be expected) in the operational hours of the fleet aircraft (as well as those with detected cracking). Table 1 also demonstrates that in addition to monitoring aircraft usage hours, many fleet managers have access to more robust means (e.g., direct loads monitoring) of determining Fatigue Life Expended (FLE see [13]). 2. Not all aircraft inspected return positive results (i.e., crack indications). This may be the case because the Non-Destructive Inspection (NDI) techniques used will have a lower crack detectability threshold (affected by accessibility and environment) or that the usage severity of these aircraft is below those experiencing cracking. 3. The detected crack lengths values are generally from the same population (i.e., 0.76, 1.02, 1.52 mm, etc.). This is a reflection of the accuracy and sensitivity of the selected NDI technique. 4. There seems no direct relationship between usage and detected crack length. The results of fleet inspection normally prompt further action. The fleet manager may instigate a modification program to address the fleet cracking or in the extreme case may ground aircraft. Traditionally the inspection results are used to set a safe-life at which point the necessary actions are implemented. In many cases the average crack life is further factored by a fatigue scatter factor to arrive at this life (see [12] for example). Generally no account is taken of the null results. In other cases the lowest life detected is used to set the safe-life (see [14] for example). However these approaches are likely to be very conservative as in most cases the inspection results do not indicate imminent failure of the component. The method proposed herein directly addresses this deficiency and is an extension of the full-scale fatigue test interpretation techniques proposed in [15 17]. Clark et al. [11] also used a similar process to recover

5 L. Molent et al. / Engineering Failure Analysis 12 (2005) Table 1 Typical data from fleet inspection program (adapted from [12]) Aircraft Mod a 1 FLE b Mod 1 EFH c Mod 2 FLE Mod 2 EFH Side Crack Dimension (mm) d No crack No crack RH 2.03-I, > 2.03-O No crack RH 0.51-O No crack No crack No crack No crack RH 1.52-I No crack LH/RH 1.02 = I/RH + LH max No crack No crack LH,RH 1.02-O/LH,7.24-O/RH RH 0.76-O No crack No crack No crack No crack No crack No crack No crack No crack No crack LH 0.76-O RH 1.02-I No crack No crack LH 0.76-O No crack No crack No crack No crack No crack No crack No crack LH 1.02-I RH 1.02-I LH 1.02-I RH > 1.52-I a Mod, modification program; b FLE, Fatigue Life Expended Index; c EFH, equivalent flight hours; d O, outboard hole; I, inboard hole. the useful life of a fleet of trainer aircraft after the unexpected in-flight fatigue failure of one aircraft. For illustration purposes the fictitious inspection results presented in Table 2 and Fig. 4 will be used. Here a fleet of ten aircraft have all been inspected.

6 18 L. Molent et al. / Engineering Failure Analysis 12 (2005) Crack growth extrapolation Fig. 3. Location of cracking on the F/A-18 Y497 upper outboard longeron. For any component exhibiting cracking it will be assumed that a knowledge of the stress state at the critical location will be known such that conventional linear elastic fracture mechanics techniques can be used to estimate the critical crack size. If component failure has actually occurred then this value may be known with more certainty, given that the corresponding failure load is also known. For the purposes of the fol- Table 2 Example inspection results A/C Hours Crack depth (mm) Mean 1670

7 L. Molent et al. / Engineering Failure Analysis 12 (2005) Carck Depth (mm) (1000,1) (1500,1.5) (2000,2) (3000,1) (1500,0.8) 0.50 (2300,0.5) (800,0) (1100,0) (1300,0) (2200,0) Hours Fig. 4. Example fleet inspection results. lowing illustration a critical crack size of 10 mm will be assumed for a residual strength criteria. It is also assumed that cracks start growing from the time the aircraft entered service. Using the Frost Dugdale relationship the (example) inspection results can be extrapolated from the expected initial crack size EPS, to the time when the critical crack depth is exceeded, through the detected crack size, as shown in Fig. 5 and presented in Table 3. Thus, a crack growth curve is produced for each subject aircraft. It has assumed that the detected cracking have resulted from the upper bound (worst or largest) of the initial discontinuity distribution typically expected. Thus, the scatter in fatigue lives is due to usage severity differences. For the example presented this initial discontinuity size was assumed to be 0.02 mm for all components. If the initial discontinuity size for individual components can be established by other means, then these individual values should be used. Further in this example it was decided (conservatively) to assume that the null NDI results represented the case were the minimum threshold crack depth (assumed to be 1 mm) was just failed to be detected. In this way the entire fleet population is considered. The benefits of this approach can been seen in Table 3 where the mean life increases from 1670 to 2666 h. Thus, the level of conservatism is significantly reduced. The same crack growth curves can be used to estimate the useful life beyond the minimum detectible crack threshold for the setting of inspection intervals. The above analyses have also been repeated for an initial discontinuity size of 0.05 mm in Fig. 6 and Table 4. Here, it can be seen that the mean life to failure increases to 3004 h. Thus, choosing a typical value for initial discontinuity state (e.g., 0.02) is more conservative than choosing an extreme value (e.g., 0.05 mm). This implies that if the lead cracks can be attributed to unusually large initiating discontinuities then the available life increases. The advantage of using the Frost Dugdale method, over more conventional LEFM crack growth models, can be best illustrated by considering Fig. 7 [7]. Here an input set for AFGROW [19] was chosen to best predict the coupon crack growth results as derived by Pell et al. [7]. Several problems are noted from the AFGROW results:

8 20 L. Molent et al. / Engineering Failure Analysis 12 (2005) Critical crack depth NDI threshold 1.00 Crack depth (mm) 0.10 A/C 9 A/C 1 A/C 6 A/C 7 A/C 2 A/C 3 A/C 4 A/C 8 A/C 10 A/C mm Hours Fig. 5. Extrapolated (example) fleet inspection results from a 0.02 mm initial discontinuity. Table 3 Extrapolated (example) fleet inspection results for 0.02 mm initial discontinuity A/C Hours Detected crack depth (mm) Critical crack depth (mm) Coefficient b Predicted hours to a critical 9 a a a a a Assuming crack depth of NDI threshold (1.00 mm). 1. An EPS of 0.05 was used in these predictions. For smaller EPS (more typical of those determined from QF, see Figs. 1 and 7) AFGROW predicted no crack growth. 2. Conventional LEFM models do not produce log-linear crack growth. This is particularly significant for late-life crack growth. If the crack depth beyond the NDI detectable threshold is considered in Fig. 7, the LEFM model does not indicate significant remaining life. However, it is clear from the QF data that significant crack growth life remains and could be utilised. 3. The LEFM is not always conservative.

9 L. Molent et al. / Engineering Failure Analysis 12 (2005) Critical crack depth NDI threshold 1.00 Crack depth (mm) m A/C 9 A/C 1 A/C 6 A/C 7 A/C 2 A/C 3 A/C 4 A/C 8 A/C 10 A/C Hours Fig. 6. Extrapolated (example) fleet inspection results from a 0.05 mm initial discontinuity. Table 4 Extrapolated (example) fleet inspection results for 0.05 mm initial discontinuity A/C Hours Detected crack depth (mm) Critical crack depth (mm) Coefficient b Predicted hours to a critical 9 a a a a Mean a Assuming crack depth of NDI threshold (1.00 mm). 5. Discussion The analyses above demonstrate the advantages of using the Frost Dugdale relationship (Eq. (1)) to estimate the mean life to failure of an inspected population, since Eq. (1) has been shown to apply to a wide

10 22 L. Molent et al. / Engineering Failure Analysis 12 (2005) Crack Depth (mm) MPa Ref. Stress MPa Ref. Stress MPa Ref. Stress MPa Ref. Stress AFGROW for each Ref. Stress Flight Hours Fig. 7. F/A-18 Spec 1, Phase I, II, III and IV coupon QF data versus AFGROW predictions made using the AFGROW in-built Al7050 material database Harter T-Method (EPS: A = 0.05 mm, C = 0.05 mm), from [7]. range of problems (see [1]). Similarly, this methodology should have wide application in the lifing of fatigue cracking in agile p ffiffiffi aircraft. That is in cases where the stress intensity factor at the critical location is a linear function of a, residual stress fields are not present, the spectra are of the same type for the population members (e.g., all tension dominated fighter aircraft spectra for example) and load shedding is unlikely (although the later will tend to increase the available life). In addition to the inspection results, an accurate estimate of the candidate materialõs initial discontinuity state (a 0 ) is desirable. It has been shown that an over-estimate of a 0 can reduce the conservatism of the analyses (compare Figs. 6 and 5). A program of accelerated fatigue testing and teardown of ex-service components, coupled with quantitative fractographic analyses of the detected cracks, may provide such an estimate (see [18] for example). Another source of data is from coupon fatigue tests of the candidate material, preferably with a discontinuity state similar to that expected in service components (see for example [7,9]). However, in the latter cases the effects of service induced defects (e.g., corrosion and mechanical damage) may not be considered. The analyses also focus attention on the accuracy of the NDI inspection results. Improvements in this science would have wide ranging benefits, in addition to improving the accuracy of the methodology proposed here. Alternatively, the fleet manager should consider, where possible, to excise the detected cracks for fractographic examination and careful measurement, rather than, for instance, blending away those cracks. Finally, the methodology proposed here might have other uses. One other application is for the interpretation of the results of full-scale fatigue tests (for example see [16]). As it is rare to be able to determine the critical crack size of all cracks in a test under the application of residual strength loads, the Frost Dugdale relationship can be used to estimate the critical crack depths. All cracks would be excised to provide accurate initial discontinuity states.

11 L. Molent et al. / Engineering Failure Analysis 12 (2005) Also, more in-depth statistical analysis may provide an alternative to the calculation of mean lives as illustrated in this paper. For instance, the predicted life to the critical crack depth shown in Table 3 may be fitted to a specific (e.g., lognormal) distribution so that life limits/inspection thresholds may be determined to suit the risk levels mandated by the governing design standard for the aircraft. Further, most Aircraft Structural Integrity Programs (ASIP) (e.g., MIL-STD-1530B) require evaluation of fleet data against promulgated life limits (or inspection programs). The maintenance of aircraft structural integrity is essential for the continued airworthiness of an aircraft. Close monitoring and management of inservice degradation must be achieved throughout the life of the aircraft to reduce risk of failure. Therefore, a requirement exists that regular in-service damage assessments are conducted to confirm the promulgated life limits or that safety-by-inspection programs still provide the required level of risk mitigation. The process of evaluating fleet defects as outlined in this paper may be useful in performing these assessments. 6. Conclusion The log-linear relationship between crack depth and service life first proposed by Frost and Dugdale has been exploited here to extend the usefulness of the results of in-service inspection for cracking in aircraft metallic components. After assuming a representative material initial discontinuity crack-like size, the relationship allows for a simple extrapolation of the detected crack sizes to critical size that accounts for the variability of fleet loading history. In this way a more accurate estimate of the mean safe-life of the population or inspection intervals set is estimated. Acknowledgements The authors acknowledge the useful discussions held with Mr. P. White and Mr. S. Barter of DSTO. Also to Mr. Vui Tung Mau for his assistance in producing some of the figures used herein. References [1] Goldsmith NT, Clark G. Analysis and interpretation of aircraft component defects using quantitative fractography. In: Strauss BM, Putatunda SK, editors. Quantitative methods in fractography, ASTM STP Philadelphia: American Society for Testing and Materials; p [2] Barter S, Molent L, Goldsmith N, Jones R. An experimental evaluation of fatigue crack growth. Journal Engineering Failure Analysis (accepted April 2004). [3] Frost NE, Dugdale DS. The propagation of fatigue cracks in test specimens. J Mech Phys Solids 1958;6: [4] Frost NE, Marsh KJ, Pook LP. Metal fatigue. Oxford: Clarendon Press; [5] Ritchie RO, Knott JF. Mechanisms of fatigue crack growth in low alloy steel. Acta Metall 1973;21: [6] Pell RA, Mazeika PJ, Molent L. The comparison of complex load sequences tested at several stress levels by fractographic examination. (2003). In Proc. of International Committee on Aeronautical Fatigue Symposium, Lucerne, Switzerland, May [7] Pell RA, Molent L, Green AJ. The fractographical comparison of F/A-18 aluminium alloy 7050-T7451 bulkhead representative coupons tested under two fatigue load spectra at several stress levels. DSTO-TR Melbourne: February [8] Forsyth PJE, Ryder DA. Some results of the examination of aluminium alloy specimen fracture surfaces. Metallurgia 1961(Mar). [9] Barter SA. Fatigue crack growth in 7050T7451 aluminium alloy thick section plate with a surface condition simulating some regions of F/A-18 structure. DSTO-TR Melbourne: July [10] Head AK. The growth of fatigue cracks. Philos Mag 1953;44(7): [11] Clark G, Jost GS, Young GD. Recovery of the RAAF Macchi MB326H A tale of an ageing trainer fleet. In: Cook R, editor. Proceedings of 19th ICAF symposium. UK: EMAS publications; 1997.

12 24 L. Molent et al. / Engineering Failure Analysis 12 (2005) [12] Structural engineering modification stress report, SRP1 NRE DIL CB049: Y497 former outboard top flange, DWG K RAS Basic. Bombardier Aerospace Defence Services. Canada: 7 February [13] Molent L, Aktepe B. Review of fatigue monitoring of agile military aircraft. J Fatigue Fracture Eng Mater Struct 2000;23(Sept.): [14] Molent L, Stimson M, Dickinson T, Inan S, Whiteroad I, Anderson I. F/A-18 structural refurbishment project assessment activity vol. 1. DSTO-TR- 1238, March [15] Molent L. Aft fuselage maintenance critical structure crack growth data. DSTO minute file no. BM2/121. Melbourne: July [16] White P, Barter S, Molent L. Probabilistic fracture prediction based on aircraft specific fatigue test data, In: Proceedings of the th Joint FAA/DoD/NASA Aging Aircraft Conference San Diego: September 16 19, [17] Moews J, Trezise S. Application of Def Stan 970 to the F/A-18 aft fuselage/empennage. Aerostuctures report ER-F ASM343. Melbourne, Australia: December [18] Dixon B, Molent L. Ex-Service F/A-18 centre barrel fatigue flaw identification test plan. DSTO-TR-1426, May [19] Harter JA. AFGROW: users guide and technical manual. Air Vehicles Directorate, Air Force Research Laboratory OH, AFRL- VA-WP-TR-2003, June [available for download at