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Crack Growth Analysis for F-111 Aircraft Nacelle Structure 1 ...
Crack Growth Analysis for F-111 Aircraft Nacelle Structure G. Chen, R. Boykett, and K. Walker Air Vehicles Division, Defence Science and Technology Organisation, Melbourne, Australia Abstract: In order to understand the effect of local aerodynamic intake loads in addition to the regular primary flight loads on fatigue cracking in the F-111 aircraft nacelle former and surrounding intake structure, a numerical procedure has been developed. The cracking is characterised by local cyclic notch plasticity resulting in residual stresses. Previous analysis ignored the effect of the intake loads, and its result did not correlate well with service reported cracking. The stress distribution in the vicinity of the notch was calculated using a nonlinear kinematic hardening cyclic plasticity model and a generalised form of Neuber’s rule. The stress intensity factors were calculated using the Green’s function approach. Numerical results show that the intake loads have two effects; they change the magnitude of the stress, and they cause the mean spectrum stress to be reduced. The overall effect retards the fatigue crack growth. The resulting crack growth prediction including the intake loads and an improved cyclic plasticity model correlates significantly better with in-service data than the previous analysis. Keywords: cyclic plasticity model, plasticity-induced crack closure model, crack growth model, F-111, fuselage 1 Introduction Cracking of the Fuselage Station 496 (FS 496) nacelle formers on the F-111 aircraft has been a problem for both the Royal Australian Air Force (RAAF) and the United States Air Force (USAF), representing an ongoing maintenance burden and a risk to flight safety. The FS 496 nacelle former is primary structure and hence its failure may result in catastrophic loss of the aircraft. Currently the RAAF manage these issues by the installation of a repair doubler, and by using routine inspection at intervals (525 hours) which are significantly more conservative than those generated by analytical results. Those analytical crack growth results  obtained by the manufacturer (Lockheed Martin) gave an unfactored durability life (growth of a crack from 0.127 mm to critical) of 50,000 hours, thus supporting a 25,000 hour inspection interval. Despite the fact that significant efforts have been made by the manufacturer and others [2, 3], no better results than 50,000 hour life prediction have been obtained because of the complexity of the problem. Most importantly, continuing cracking has been found in the forward flange of aircraft in the RAAF fleet, even after a repair doubler installation. This places significant doubt on the accuracy of the analysis. Being a high strength D6ac welded steel forging situated near the entrance to each inlet, the FS 496 nacelle former: (a) redistributes body loads from the wing carry-through box (WCTB) to the fuselage, (b) provides stabilisation of surrounding longerons and structural panels, (c) provides a support for the forward inlet structure and stabilisation of surrounding longerons and structural panels, (d) translates air pressure loads to the surrounding structure. The loading actions (a) and a easy part of (b) were addressed in the Finite Element (FE) Internal Loads Model (ILM) created by Lockheed Martin. Issue (c) and the complicated but critical structural panels of (b) were ignored in the ILM because of the complex structure details. The issue (d) was ignored because of the difficuties of modelling the air pressure loads along the intake. The effect of intake loads may come from two aspects: they change (i) the magnitude of the local stress, which was validated in a primary investigation , and (ii) the subsequent load spectrum. The overall effects of (i) and (ii) have a significant impact on fatigue crack growth. Considering issues (b), (c), and (d) above, extensive studies [4-8] were carried out in DSTO, ranging from inlet structure investigation, analytical fluid analysis, computational fluid analysis, propulsion analysis, stress analysis, regression analysis and finally crack growth analysis. New methods were developed to deal with the complex natures of the problem. This paper summarises the crack growth analysis part of the work. Crack growth analysis of the FS 496 former is a sophisticated problem, due to the combination of aero dynamic intake loading and structural details causing notch plasticity. In this work, fatigue crack growth analysis for the former was conducted using a plasticity-induced analytical crack closure model. The notch plasticity aspects were addressed by the Armstrong-Chaboche method . Analyses using spectrum loading with, and without, engine intake pressure loads were conducted. 2 Methodology 2.1 The cyclic plasticity model METLIFE , is crack growth analysis software first developed for use on the F-111 aircraft by the Lockheed Martin company. This software has deficiencies in the cyclic plasticity module, leading to the development of the Crack Growth Analysis Program (CGAP) by DSTO . To account for notch plasticity, a model based on an Armstrong-Chaboche type constitutive equation  is used in CGAP. The main equations are briefly presented here. If f represents the yield surface, it can be expressed as: f J 2 ( S ij X ij ) R ( p ) y 0 (1) X ij k 1 ij k 2 X ij p p Where J 2 3 2 ( S ij X ij )( S ji X ji ) y is the uniaxial (cyclic) yield stress of the material. X ij is the back stress tensor that represents the shift of the yield surface in the stress space. p is the equivalent plastic strain. K1 and k2 are material parameters. S ij is the deviatoric stress tensor, S ij ij kk /3 (2) Where kk 11 22 33 . In Equation (1), R , representing the effect of isotropic hardening, is a function of the equivalent plastic strain p: p R R (1 e ) (3) 2.2 Plasticity-induced crack closure model The fatigue crack growth model implemented in CGAP is based on the analytical crack closure model [12, 13]. The principle is that the crack grows when the crack tip is open, and otherwise remains closed during part of the subsequent tensile loading due to the residual plastic deformation left in the wake of a growing crack. The stress Intensity factor K is given by: C K w ( x ) ( x ) dx (4) 0 Where w(x) is the Green’s function for the specific crack configuration, ( x ) is the normal stress distribution on the crack plane and c is the current crack length measured. 3 Model and Material The location of service cracking in the FS 496 nacelle former can be idealized as a finite width and thickness plate with a single edge crack as depicted in Figure 1(c). A fleet crack at the critical location yy Critical Location a FS 496 yy (a) (b) (c) Figure 1. (a) F-111 Aircraft, (b) Nacelle Former & Intake Structure, and (c) Crack Growth Model. CGAP model inputs and assumptions: Flaw model 2-D hole with corner flaw, elastic-plastic analysis Load application: Apply Cold-Proof Load Test (CPLT) stress prior to spectrum cycling and after every 2000 flight hours. Cold Proof Load Testing (CPLT) is a periodic proof o load testing program, in which the aircraft is cooled to –40 F to embrittle the D6ac steel structure, and then loads appropriate to (g is an acceleration) –2.4g o o and +7.33g at 56 wing sweep angle and –3.0g and +7.33g at 26 wing sweep angle are applied. Thickness = 2.794 mm Width = 63.5 mm Initial flaw size = 0.127 mm Notes: F-111 C model configuration without repair doubler Material and properties: = D6ac steel, 1516.9 -1654 MPa Heat Treat Elastic modulus: = 200 Gpa Poisson’s ratio: = 0.32 Yield strength: = 1310 MPa Ultimate strength: = 1520 MPa The crack growth rate curve is given by: dc / dN C ( K eff ) G/H n (5) Where C and n are two material constants, e.g. c = 1.6335e-0.09, n=3.7979 . H is a function of the maximum stress-intensity factor and the cyclic fracture toughness and G is a function of the threshold stress-intensity factor range and the effective stress-intensity factor range. Here G and H are set to 1. 4. Spectrum Loading The crack growth analyses were performed under two different load conditions: (1) under only normal aerodynamic loads, without considering the intake nacelle loads and (2) under both normal aerodynamic loads and the intake nacelle loads. Flight condition data were processed with DSTO developed Fluid Dynamic Model [5, 8] and Finite Element Model [4, 6] to derive the stress spectra. The FDM was developed to allow for both the absence and presence of intake loads. The spectra without, and with, the intake loads as shown in part in Figure 2 are compression-dominated. In both figures, the first five turning points represent the ground-based CPLT sequence, which has two overload and underload spikes. The first 45 turning points in the spectra are shown after that. The level of both overload and underload is severe, and they would be expected to have a significant effect on the crack growth behaviour 1500 1500 1000 1000 500 500 Stress (MPa) Stress (MPa) 0 0 -500 -500 -1000 -1000 -1500 -1500 -2000 -2000 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Turning Points Turing Points (a) (b) Figure 2: Spectra for the service crack location in part: (a) without intake loads and (b) with intake loads. 5. Near Notch Stress Distribution For the analysis of crack growth, the stress intensity factor is computed for each loading cycle. When the stress distribution ahead of the notch root is determined, the stress intensity factor at maximum stress can be calculated using the Green’s function method and Bueckner’s principle, which states that the crack tip stress intensity factor for a traction free crack in an externally loaded body is equal to the stress intensity factor for a crack loaded with distributed traction on the crack faces, where the distributed traction is determined by applying the external load to the un-cracked body. For a given remote load, a different notch configuration leads to a different stress distribution, and different crack geometries require different Green’s functions. The details of the stress analysis work are detailed in [4-6]. 6. Crack Growth Analysis The numerical procedures outlined above were implemented in CGAP, which involves the modelling of notch plasticity using a nonlinear kinematic hardening constitutive equation and Green’s function for Stress Intensity Factor (SIF) calculation. The crack growth analysis under the spectrum loading was carried out with and without the intake loads. The spectra used are shown in part in Figure 2. The crack growth results are presented in Figure 3. When the intake loads are ignored, the predicted unfactored durability life is 700 hours, and when they are included the durability life is 2,356 hours. 4 G ro w th vs H o u rs 3 .5 3 Without intake loads C ra c k L e n g th (m m ) 2 .5 2 With intake loads 1 .5 1 0 .5 0 0 500 1000 1500 2000 2500 F lig h t H o u rs Figure 3: Crack Growth Analysis Results: solid line represents the results with intake loads, while the broken line represents the spectrum without intake loads. 7. Discussion From Figure 3, a clear difference between the crack growth curves with, and without, intake loads can be seen. The predicted flight hours for the case ignoring the intake loads is 700 hours, and for the case with the intake loads, it is 2,356 hours. The in-service average failure result for this location is about 4,500 hours . The consideration of the intake loads results in longer flight hours for the same crack length, which is also close to in-service crack measurements. The effect of intake loads comes from two aspects; the intake loads change the magnitude of the local stress, and also shift the subsequent load spectrum down. The overall effect retards the fatigue crack growth. Using half of the predicted fatigue life as a fleet inspection interval, the comparison for the inspection interval of this location based on this report, Lockheed Martin’s work, the in-service failure result, and the current RAAF fleet interval are shown in the following table: Table .1 Inspection intervals for in-service crack location. Basis Lockheed The results from In-service RAAF fleet Martin result this work failure result Inspection Interval 25, 000 1178 2250 <1000 (flight hours) The CPLT sequence, because of the overloading in both tension and compression, can produce plastic deformation at the notch root. Without considering notch plasticity, a much higher stress can be present at the crack tip, resulting in faster crack growth. The plastic deformation can produce a tensile residual stress field in the vicinity of the notch, i.e. the residual stress can shift the spectrum mean load, thus changing the crack growth rate. Accepting the validity of K as the correlating parameter, the effect of notch plasticity on crack growth is a combination of limiting the local stress by the flow stress and the generation of a residual stress field due to the plastic deformation. Depending on the level and the sequence of the overload and underload, the net effect may be acceleration or retardation of the crack growth. In CGAP, K eff is used, which takes into account the effects of crack closure, but is strictly appropriate only for small-scale yielding. To better deal with notch plasticity for large-scale yielding, it is necessary  to use cyclic crack opening displacement as correlation parameter that is significantly different from what would be obtained from long-crack tests. This introduces a desirable element of empiricism in the predictive capability. 8. Conclusions and recommendations. A fatigue life analysis for FS 496 fuselage nacelle structure was conducted using the DSTO- developed code CGAP. Numerical results show that the additional effect of intake loads may come from two aspects. The intake loads not only have impact on the magnitude of the local stress but may shift the mean load of the subsequent combined load spectrum down. The overall effect retards the fatigue crack growth. A fatigue life prediction for the most severely loaded location was produced, which correlated well with the in-service failure data and showed that the existing management strategy is conservative. References  Lockheed Martin Corporation (LMC) (1998) RAAF F-111 C Durability and Damage Tolerance Analysis Results, FZS-12-5035.  Lockheed Martin Corporation (LMC) (2000) RAAF F-111 C/A/G FS 496 Nacelle Former: Historical Summary of Structural Integrity Issus, Analysis, and Current Status, FZS-12-380006.  Ignjatovic, M. (2003) Investigation of the F111 FS496 Region Cracking Issues and Reviewed DADTA for Relevant DADTA Items, Aero Structures Letter Report. Part 1.  Chen, G., Walker, K., Swanton G. and Hill, S. D. (2004) Stress Analysis of Aerodynamically Loaded Structure under Supersonic Conditions. Proceedings of SIF 2004, Australia, September.  Chen, G., Walker, K., Swanton G. and Hill, S. D. (2004) An Envelope Method for Stress Analysis of Aerodynamically Loaded Structure under Subsonic Conditions. Proceedings of SIF 2004, Australia, September, p.32.  Chen, G., Boykett, R. and Walker, K. (2007) Development and Validation of a Simple Approach to Model Aerodynamic Loads on a Military Jet Intake Structure. Innovations in Structural Engineering & Construction.  Chen, G., Walker, K., Swanton G. and Hill, S. D. (2005) Modelling the F-111 Fighter Bomber Aircraft Engine Intake Loads. Proceedings of ACAM, Australia.  Chen, G. and Walker, K. (2005) Computational Fluid Dynamics Analysis for the F-111 Fighter Bomber Aircraft Engine Intake. Proceedings of AIAC 2005, Australia.  Chaboche, J. L. (1986) Time Independent Constitutive Theories For Cyclic Plasticity. International Journal of Plasticity, 2, 149-188.  Ball, D. L. (2000) METLIFE v1.3 Technical Approach (DRAFT), MR(FF)-1022, Lockheed Martin Tactical Aircraft Systems.  Hu W. and Walker K. (2006) Fatigue Crack Growth from a Notch under Severe Overload and Underload. The International Conference on Structural Integrity and Fracture, Sydney, Australia.  Führing, H. and Seeger, T. (1979) Dugdale Crack Closure Analysis Of Fatigue Crack Under Constant Amplitude Loading. Engineer Fracture Mechanics, 11, 99-172.  Newman, J. C. Jr. (1992) FASTRAN II - a Fatigue Crack Growth Structural Analysis Program, NASA, NASA TM-104159.  Everard, P. and Goldsmith, N. (2001) FS496 Nacelle Former Fractography Report. F-111 Testing & Tear Down Fractography Report. No: 2001/004. AMRL File No: B2/228. DSTO.  Chen, G., Wang, C. H. and Rose, L. R. F. (2002) A Perturbation Solution for a Crack in a Power-law Material Under Gross Yielding, Fatigue Fract Engng Mater Struct 25, pp231-242.
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