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Crack Growth Analysis for F-111 Aircraft Nacelle Structure 1

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Crack Growth Analysis for F-111 Aircraft Nacelle Structure 1 ...

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									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 [1] 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 [4], 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 [9].
Analyses using spectrum loading with, and without, engine intake pressure loads were conducted.
2 Methodology

2.1 The cyclic plasticity model
METLIFE [10], 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 [11].

To account for notch plasticity, a model based on an Armstrong-Chaboche type constitutive
equation [9] 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 [11]. 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 [14]. 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 [15] 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
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      Results, FZS-12-5035.
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[3]   Ignjatovic, M. (2003) Investigation of the F111 FS496 Region Cracking Issues and Reviewed DADTA for
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[15] Chen, G., Wang, C. H. and Rose, L. R. F. (2002) A Perturbation Solution for a Crack in a Power-law
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