AIAA-2009-2451 Finite Element Analysis for Advanced Repair Solutions: A Stress Analysis Study of...

American Institute of Aeronautics and Astronautics

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Finite Element Analysis for Advanced Repair Solutions: A Stress Analysis Study of Fastened and Bonded Fuselage Skin

Repairs

Domenico Furfari * and Nikolaus Ohrloff. Airbus, Hamburg, Germany

Gebhard Schmidt HIGH END Engineering GmbH, Hamburg, Germany

The advanced repair solutions investigated within this research programme, both mechanically fastened and adhesively bonded repairs, could extend their in-service life beyond the Design Service Goal (DSG) of the aircraft in which they are embodied. Beside the test activity (discussed in previous publications), calculation methods (based on Finite Element models) were developed to improve current methods to predict the fatigue behavior of repairs and to optimize the design principles of the advanced repair solutions. The use of internal doubler to reduce the secondary bending, different fastener type or additional fastener row, as well as, the influence of fastener installation (Hi-Lok interference fit) are reported. Other advanced repair solutions, such as bonded repair or the use of glare doubler to repair aluminum skin, were also investigated and reported in this work. In this paper different kind of Finite Element (FE) models used to simulate the tests are reported. The stresses resulted from the FE analysis were compared with the ones measured experimentally by strain gauges.

Nomenclature s = Static coefficient of friction k = Kinematic coefficient of friction r = Fastener radius rdepth = Fastener countersunk depth U0 = Initial GAP opening F0 = GAP preload Smax = Maximum stress Smin = Minimum stress Sm = Mean stress Sa = Stress amplitude = Strain = Stress E = Youngs Modulus S70E = Secant modulus at 0.7E slope n = Ramber-Osgood shape factor

I. Introduction

A. Background of the Research

* Research & Technologies, Structural Analysis Stress Methods, Kreetslag 10, 21129 Hamburg, Germany Senior Expert Fatigue, Structural Analysis, Kreetslag 10, 21129 Hamburg, Germany Stress Engineer, Stress and Methods, Georg-Heyken-Strae 4, 21147 Hamburg, Germany.

50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference17th4 - 7 May 2009, Palm Springs, California

AIAA 2009-2451

Copyright 2009 by Airbus. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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N the frame of the project IARCAS (Improve and Assess Repair Capability of Aircraft Structures) fatigue behavior of advanced repair solutions, both mechanically fastened and adhesively bonded, have been investigated.

As the time that the aircraft remains in service extends, the operational costs (such as maintenance inspections and related repair actions), vital to keep the aircraft in service with the required levels of safety, increases 1. Airlines operators repair their aircraft according to the repair solutions provided in the Structural Repair Manual (SRM). Existing repair solution, contemplated in the SRM of each in-service aircraft, should be improved and developed to extend the fatigue crack initiation and the crack growth lives (i.e. reduces the operation costs). In-service repairs on a primary structure of an aircraft are usually performed by the airlines according to the repair solutions provided in the Structural Repair Manual (SRM). Consequently, the aerospace industry has to enable a simple evaluation of damages and to provide repair procedures that are safe, less time consuming, simple to perform, inexpensive and durable as much as possible. As the reduction of downtimes is the highest priority of the operator, an increase of allowable damage size could be a big improvement for the airliner to reduce this time penalty or the Aircraft On Ground (AOG) situations that can also disturb the complete flight schedule and lead to even big delays in the air traffic.

B. Fuselage skin doubler repairs The standard fuselage skin repairs applied in the

aircraft, according to the SRM, require the use of the same material for the repair patches (hereafter called doublers) and the structural component to be repaired as well as common rivet diameter in all the fasteners of the repair, constant transverse and longitudinal fastener pitches and fixed doubler shape (standard rectangular shape with rounded corner of minimum 10 mm radius). An example of SRM fuselage skin repair is shown in Figure 1.

The influence of fastener diameter, variable transverse and longitudinal fastener pitches and optimized doubler shape (e.g. circular shape) have been investigated in this research program and the results of this activity are included in 2, 3. Many other factors can influence the fatigue life (inspection threshold) and inspection interval of repairs. The more important are: size of cut-out, doubler thickness, fastener type, edge margin (distance between fastener and doubler edge), number of fastener rows, countersunk depth. The impact on inspection threshold and inspection interval of these factors has been identified and assessed by Schmidt and Brandecker in previous work 4.

Beside such factors, which are manly related to design principles of repairs, it should be taken into account other ones that could be referred herein as human factors. The work environment, where the repair is embodied in the aircraft to keep it flying, is significantly different than the one during the manufacturing of the aircraft itself. The repairs are installed manually, that is holes are hand-drilled as well as fastener are hand-driven. In such conditions, reducing as much as possible the AOG time could lead to variation in the repair installation (in particular fastener installation) such as different rivet interference, unsymmetrically installed rivet, under driven rivet installation (lack of clamping force).

Recently, the Federal Aviation Administration (FAA) and Delta Airlines (DAL) jointly conducted a three years project on tear down inspection and extended fatigue tests of a retired Boeing 727 aircraft 5, 6. The tear down inspection of lap joints from the fuselage of the retired aircraft revealed evidence of variation in the rivet interference and

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Figure 1. Example of SRM fuselage skin repair.

(a) differences in rivet interference (b) unsymmetrically installed rivet Figure 2. Sections of rivets in lap joint 7, 8. Deformation of sealant showsvariation in rivet interference (a); in (b) evident unsymmetrically installed rivet.


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unsymmetrically installed rivet 9, 10, two examples are shown in Figure 2. Atre and Johnson investigated the influence of under-driven and over-driven rivets as well as the hole quality, on

the fatigue life of lap joints 11. The following conclusions can be drawn after this investigation: the fatigue life of the joints increased with increasing rivet interference; under-driven rivets in lap joint have significantly less fatigue life than over-driven rivets. On the other hand, Mller in his Ph.D. work demonstrated the importance of the squeeze force on the fatigue life of riveted joints 11.

II. Fastened Repair FE 3D Models

C. Software Tool FE 3D Model A software tool (named RE-JOINT: RivEted-JOINT), which consists of several MSC.Patran macros, was

developed to study the mechanical behavior of a flat lap/butt joint under static unidirectional loading and to create parametrically the FE models of the advanced fastened repair solutions investigated during this activity. RE-JOINT reads the input file (.txt file), builds the model (e.g. mesh, boundary conditions, load cases, etc. etc.) and writes an analysis file. In the input file the user defines the general structure of the joint by choosing sub-components from a library and positioning them as a sort of puzzle to build the final joint configuration. Figure 3 shows examples of sub-components from the library defined in the RE-JOINT tool. The user can define the specific sizes of each sub-component and the xy-coordinates of reference point to align the parts.

The results of the analysis are then imported and a post processing analysis performed. All macros were written with the PCL language (Patran Command Language). Two main macros (i.e. main1.pcl and main2.pcl) call subordinates macros specifically defined to build the FE model and for post processing analysis respectively. The main PCL macros itself are called by an UNIX shell script (i.e. run_job). This script creates a subfolder, copies the files in that folder and calls the macros. Once the FE model is created the Nastran analysis manager is called and the analysis job is submitted to MSC.Nastran for processing. After the analysis has finished, the *.f06 file is created and checked by Nastran. If errors occurre the script plots the relative errors information. The software tool has been developed for UNIX environment but it has been also adapted for Windows environment.

Particular attention has been paied to develop fastened joint FE models which include the complete rivet geometry (such as countersunk and formed head), contact definition (between skins and between fasteners and skins), elastic-plastic material behavior for full non-linear analysis. The input file (.txt) can enable GAP elements in all the contact regions of the components (i.e. between skins and between fasteners and skins). The macros called for this purpose create automatically the local coordinate systems used by the GAP element. The following paragraphs describe in more details the analysis models created by this tool.

D. Contact Definition with GAP Elements (Nastran FE-element) The non-linear GAP elements as contact definition between the components were used. The GAP element

provides point-to-point contact characterization setting with different stiffness value in both perpendicular and parallel direction of the contact. The GAP elements refer to a local coordinate system, which must be defined at the contact nodes with x-axis coincident to the direction between the point A and B of the element (A is the point of the GAP element connected to the first component and B is connected to the adjacent component).

The stiffness in the x-axis direction defines the open-close condition of the contact while the coefficient of friction (static or kinetic) defines the characteristic of the contact in the plane of the contact. The default value for the axial compression stiffness used in all the models was 1.000.000 N/mm. This value resulted convenient for all the models presented in this document. Very high values of the stiffness could cause non-convergence problems and low values of this parameter could cause inaccurate results as the components in contact could penetrate each other. For instance, if the GAP elements are not used for the joint geometry shown in Figure 4, the contact pairs penetrate each other causing inaccurate results. The GAP elements location is shown on the right side of the figure; in this example only GAP elements between the plates were used while the contact between the fasteners and the plates was simulated by merging the coincident nodes (equivalence). In general the closed GAP stiffness should not exceed the stiffness of the adjacent contact area by 1000 times. The axial tension stiffness (opening stiffness) was set to 0.001 N/mm.

Figure 3. Example of sub-components from library defined in RE-JOINT tool.


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When the GAP element is open (elongation of the element) there is no contact and then no friction. When the gap element is closed, there are three different conditions. The first case is when the gap is sliding (no friction, friction coefficient: s=k=0). The second case occurs when the gap element is sticking (s0). The third case occurs when the gap element is slipping (k0). The friction contact definition can be used to model the effect of the sealant in a joint or the effect of bonding if hybrid rivet-bond joint want to be modeled.

RE-JOINT gives also a possibility to merge the coincident nodes of adjacent components. In such way the cpu time is very much reduced but this choice is to the detriment of the accuracy of the stress distribution especially locally at the fastener connections.

Figure 5 shows an example of the maximum principal stress distribution of a 3 rivets lap joint. A strip of the joint (half rivet pitch, 11 mm) was modeled; this makes the model valid to analyze only solutions where the full transfer load condition is respected (such as, with the reference to 3 and 4, coupon specimens or the middle strip of large repair solution). Both coupon specimen geometry (2.0 mm skin thickness and 2.5 mm doubler thickness) and large/small flat panel geometry (1.6 mm skin thickness and 1.8 mm doubler thickness) were modeled. The material used for these models was Aluminum AA2024-T351 for all the components (skin, doubler and rivets) but is possible to select several different materials by the input file (a material database, included in a macro named matprop.pcl, has been included in the software tool). A geometric non-linear solution (elastic material behavior) was performed and the nodes at the contact region between the rivets and the plates were merged (equivalence). The location of the maximum stress and the value (256 MPa) is also shown in the figure.

In this case the local stress distribution is very much influenced by the contact characteristic both in terms of maximum stress location and value.

Figure 6 shows the maximum principal stress distribution of the base line solution after non linear analysis with linear material behavior. The results shown in the figure refer to MPa as units. The possible critical locations resulted from this analysis were the rivet hole at the doubler (skin run-out) and the rivet hole at the skin (doubler run-out) as shown in the figure a).

Comparing Figure 5 with Figure 6 it can be noted that the critical locations at the skin of the repair are positioned 90 degrees apart depending if contacts are modeled as merging common nodes or by means of GAP elements. The

Doubler-Skin

Skin-Support Doubler

Gap ElementsDoubler-Skin


Gap ElementsDoubler-Skin


Gap Elements

Figure 4. Gap elements location at surface contact (right). Jointsdeformation if GAP elements are not used (left).

256256

Figure 5. Maximum principal stress distribution 3D FE model of baseline solution with merging nodes (equivalence) at the contact areabetween rivets and plates.

Figure 6. Max principal stress distributions 3D FE model of base linesolution with GAP elements at the contact area between rivets andplates.


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more accurate model (with GAP elements at the contact surfaces) provides the correct critical location (which can led to the typical failure mode: net section failure). Moreover, the stress peak is also influenced by the local fastener model resulting in a complete wrong prediction (non conservative) of the local stress if the merge nodes technique is used (260MPa for the merged model against the 460MPa for the GAP elements model).

E. Fastener Modeling A 3D solid model of the rivet, including the countersunk and the formed head, is created automatically. The user

defines the radius r of the rivet in the input file and a macro, called by the main program, creates the complete geometry and a solid mesh (countersunk and form head included). The countersunk angle has a fixed value of 50. Figure 7 shows the geometry of the rivet countersunk used in the model.

The depth is calculated by the following formula:

rAFrdepth 2266.0180

)5090(tan 000

=

where, 0.266 is a basis correction factor; AF is an Adjustment Factor and 2r is the fastener diameter.

The formula is valid for a nominal diameter between 0.094 and 0.188 inch. All diameters bigger than 0.188 are multiplied by 0.286 (= Basis Correction Factor x Adjustment Factor).

This formula is optimized for NAS1097 and Hi-Lok fasteners. If other rivet types are used, rdepth should be re-calculated.

The value of rdepth was rounded to obtain a mesh compatible between adjacent components. The result depends on the parameter relemheigth (defined in the PCL-macros). A small value of relemheigth leads to closer values of rdepth.

Table I shows the rounded values of the rdepth correspondent to relemheight of 0.2. This value gives the best approximation of the real rdepth value of the rivet NAS1097.

GAP elements at the cylindrical and conical areas of countersunk rivets and between the formed head and the plate are created automatically (if the GAP option is enabled by the input file). At the conical part coordinate systems for each radial line of gap elements are created. The Patran commands creates the Cartesian GAP coordinate systems which are orientated perpendicular to the contact area with their x-axis.

Figure 8 shows the local coordinate systems of the GAP elements at the rivet contacts. Because the contact definitions by means of GAP elements imply a node-to-node connection it is required to have a high number of

Figure 7. Geometric features used to model thefastener head.

Table I. Depth of countersunk as function of fastenerdiameter for NAS1097 rivet. relemheight = 0,2

Inch mm Inch mm mm mm0,094 2,388 0,021 0,533 0,533 0,600,125 3,175 0,029 0,726 0,726 0,800,156 3,962 0,037 0,945 0,944 1,000,188 4,775 0,046 1,168 1,172 1,200,250 6,350 0,060 1,524 1,524 1,60

Rounded Re-joint

Value for rdepth

Nom DiameterD

B( = rdepth)

NAS1097 Real Re-joint

Value for rdepth

ZR x

z

x

z

Figure 8. Local coordinate systems for GAP element locations at the rivet contacts.The GAP elements are shown as red points in the pictures.


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coordinate systems at the countersunk surface contact (a coordinate system at each radial line of nodes). On the contrary a single cylindrical coordinate system was used to orient all the GAP elements at the cylindrical contact surface of the rivet.

F. Interference Fit and Friction The GAP elements are characterized by four parameters: s=coefficient of static friction, k=coefficient of

kinetic friction, U0=initial gap opening and F0=preload. It is possible to simulate the effect of the interference fit of the fasteners in the joint, setting an initial value of gap opening or a preload. For instance, because U0 is the separation of the gap element with the unit length, it can be used to simulate the interference fit. A negative U0 value can be used to simulate an interference fit between fasteners and holes. A positive initial gap is used to simulate a clearance fit of the fasteners in the holes. The gap nodes are separated (along the gap axis) by the initial gap value. About the preload F0, a positive axial force F0 indicates compression.

An example of application of the interference fit effects (for Hi-Lok fasteners) on the stress distribution for the 3 rivet rows lap joint model is reported in this paragraph. The interference conditions are modeled setting initial values of the gap displacement as described above. Five values of increasing interference were modeled: 10m, 20m, 30m, 40m and 50m. The load cases considered in the analysis were: I) interference fit (a fictitious external load of 1N was applied in the skin only to satisfy the boundary conditions) and II) external load (100 MPa based on the skin gross area) + interference fit. The effect of the interference fit on the stress distribution was assessed in terms of Smax, Smin, Sm (mean stress) and Sa (stress amplitude) changing.

The initial gap opening parameter was applied only for the gap elements at the cylindrical contact between the fastener and the sheets (skin and doubler). Figure 9 shows the gap elements with initial gap opening parameter U0 different than 0 to simulate the interference conditions (red nodes in the figure). Because only half of the joint was modeled (symmetry) to simulate 20m interference required an initial gap opening value of 10m in the model. Similarly 5m, 15m, 20m and 25m were used as initial gap opening values corresponding to interferences of 10m, 30m, 40m and 50m respectively.

The maximum principal stress distribution for the 3 rivet rows lap joint solution with no interference fit (initial GAP displacement 0 m) was already shown in Figure 6. At the reference location, corresponding to the element 19371 in the FE model, the maximum principal stress was 459 MPa.

Figure 10 shows the maximum principal stress distribution for the 3 rivet rows lap joint solution with 20m interference fit and no external load applied, only a fictitious load of 1N applied to the gross section of the skin. The very low external load applied was necessary to satisfy the boundary conditions. The stresses shown in the figure are in MPa. The maximum principal stress at the reference location (Elm 19371 of the FE model) resulted 181 MPa.

Figure 9. Location of GAP element for modeling the interference fitcondition.

Figure 10. Maximum principal stress distribution for the 3rivet rows lap joint solution with 20m interference fit. Noexternal load applied. All stresses are shown in MPa.


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Figure 11 shows the maximum principal stress distribution for the 3 rivet rows lap joint solution with 20m interference fit. The external load applied was 100 MPa based on the gross section of the skin. The stresses shown in the figure are in MPa. The maximum principal stress at the reference location (Elm 19371 of the FE model) resulted 370 MPa.

Comparing the maximum principal stress at the reference location for the solution without interference fit (initial GAP displacement 0 m) and with interference fit of 20 m resulted that the maximum stress for the solution without interference fit was reduced by approximately 20%. Moreover the minimum stress, when the external load is removed (0 MPa if no interference fit is considered), was increased if the interference fit is taken into account. The amplitude stress also decreased at values of interference fit considered.

Figure 12 shows the maximum principal stress distribution at the reference location of the 3 rivet rows lap joint solution model for increasing values of interference fit. The stresses shown in the plot are always the maximum principal stress at applied external load (Smax), with no external load applied (Smin) and the resulting amplitude stress

Sa=

2minmax SS and mean

stress

Sm=

+

2minmax SS .

The increasing value of the interference fit had as main consequence the reduction of the amplitude stress despite the increasing of the mean stress. For interference values greater than 25-30 m the effect on the amplitude stress is less relevant (horizontal asymptote in the plot).

In this case the fit line has shown a very good agreement with the FE results for interference value below 30m. At this interference value the corresponding stress was still elastic (270 MPa) but increasing the interference the Smin change following the non-linear trend as expected.

G. Advanced Fastened Repair Solution FE Models 1. Support Doubler Repair Solution

The design principle of this repair solution is described in details in 3. It consists of a single shear joint (3 fastener rows) with a support doubler located at the skin side of the upper and lower doubler run out. Even for this

Figure 11. Maximum principal stresses for the 3 rivet rows lapjoint with 20m interference fit and the external load.

y = 9.2029x - 0.9048R2 = 0.9989

y = -0.0035x3 + 0.4675x2 - 12.285x + 459.56R2 = 0.9995

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40 45 50

Interference Fit (micron)

Ref

eren

ce S

tres

s (E

lm 1

9371

) (M

Pa)

Smax (at Max Ext Load)Smin (at Min Ext Load)AmplitudeMean StressSmin - TrendlineSmax - Trendline

Figure 12. Maximum principal stress distribution at the referencelocation of the 3 rivet rows lap joint model for increasing values ofinterference fit. The stresses shown in the plot are always the maximumprincipal stress at applied external load (Smax), with no external loadapplied (Smin) and the resulting amplitude stress Sa and mean stress Sm.


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repair solution, a strip of the joint (half rivet pitch, 11 mm) of coupon specimen geometry and large/small flat panel was modeled (coupon specimen and large/small flat panel geometry are described in 3). Skin, doubler and support doubler were modeled using Aluminum AA2024-T351 while the fasteners (Hi-Loks) were modeled in Titanium (Ti-10Al-6V). Non-linear analysis was performed including both linear and non-linear material behavior.

Figure 13 shows the maximum stress distribution of this repair solution after performing non-linear solution with linear material behavior. The example reported in the following figures refers to the coupon specimen geometry (2.0 mm skin thickness, 2.5 mm doubler thickness and 4.0 mm support doubler thickness). The locations corresponding the peak stress (doubler and skin) are also shown in the figure. To make easier the location of the maximum stress the fasteners are not shown in the figure.

Figure 14 shows a close up view of the critical locations of support doubler repair solution. Stress values at the doubler location and skin location were 510 MPa and 450 MPa respectively. The highest stress resulted at the doubler location in the cylindrical surface contact with the remaining collar of the fastener (510MPa). This is the region where the countersunk geometrical discontinuity is more effective as stress concentrator.

In order to establish the most critical area suitable to fatigue crack initiation, it is important to evaluate the size of the area subjected to the maximum stress. Fatigue crack may initiate from material defects (porosities, inclusion or mechanical damages) in area with high stress concentrators. Hence the bigger the area subjected to high stress the more likely a fatigue crack may initiate. The material used for the skin and the doubler in this model was Al2024-T351, which has a yield stress of 335 MPa.

Figure 13. Maximum principal stress distribution (in MPa) for non-linear analysis with linear material behavior of coupon specimen geometry.Location corresponding to peak of stresses are also shown.

Figure 14. Maximum principal stresses at doubler and at skin position ofsupport doubler repair solution.

Figure 15. Von Mises stress distribution for coupon specimen geometry afterfull non-linear analysis including the non-linear material behavior.


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A full non linear analysis (including the non linear behavior of the material) was performed and the results (in terms of Von Mises stresses) are shown in Figure 15.

By limiting the maximum principal stress up to this value, it is possible to have an estimation of the area subjected to this stress, and therefore the location of the fatigue crack initiation, to be used for the fatigue life prediction.

At the critical location of the doubler, the region with highest stress (red region in Figure 15) was distributed to the half thickness of the doubler; in fact, at the critical location of the skin, the region with highest stress was covering the entire thickness of the skin.

The conclusion of this analysis is that, although the highest stress was found at the doubler position, the most critical location for fatigue crack initiation was assumed at the skin position. The fatigue life prediction was based on the maximum stress at this location. 2. Parametric Study

In order to optimize the design principle of this repair solution a parametric study was done. The main parameter under investigation was the support doubler thickness. The stress distribution, at the critical locations discussed in the previous paragraph, is effected by the stiffness of the joint. An increase of the support doubler thickness should correspond to an increase of the general stiffness of the joint, which leads to a reduced secondary bending effect with obvious reduction of the maximum stress. In fact, the increase of the doubler thickness causes a more pronounced eccentricity effect, which leads to an increase of the secondary bending. A compromise must be found and the results of this analysis are shown in the following paragraphs.

Figure 16 shows the effect of the increasing support doubler thickness on the maximum principal stress at the skin critical location of the support doubler repair solution with reference to the geometry of small/large flat panels (1.6 mm skin thickness and 1.8 mm doubler thickness).

An increasing of the support doubler thickness corresponds to a decreasing of the maximum stress. Values of the support doubler thickness greater than 3.2 mm does not lead to a significant reduction of the maximum stress. Figure 17 shows the maximum stress distribution at the critical skin location for the base line repair solution (figure a) and for the support doubler repair solution at increasing thickness of the support doubler (figure b,c and d). Increasing the support doubler thickness had, as main effect, the reduction of the maximum principal stress at the reference location. The absolute maximum stress location moved through the thickness towards the support doubler skin surface contact at increasing values of the support doubler thickness (as shown in Figure 17).

H. FE Model Validation To validate the FE models created by RE-JOINT tool, the results have been compared with strain gauge readings

of a coupon specimen containing a step, chemically milled radius at the doubler run-out area, with increased bending stress components in this region, where the strain gauges were installed

Figure 16. Effect of the support doubler thickness with respectto the maximum principal stress at the skin critical location.

Figure 17. Maximum principal stresses at increasingthickness of the support doubler.


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Figure 18 shows the coupon specimen geometry, details of the step chemically milled at the doubler run out are shown on the right side, including the maximum principle stresses at the doubler run out, where the strain gauges have been installed.

The coupon specimen with three rivet rows shown above has been tested with strain gauge readings applied near the radius (and at the opposite side of the coupon). Figure 19 shows the test rig and the strain gauge locations.

Details of the FE model at the rivet connection and at the step radius is shown in Figure 20 (top-left). A very fine mesh at stress concentration locations (such as rivet connections, chemically milled radius) was used. Figure 20 (bottom-left) shows the position and the length of the strain gauges with respect to the FE model.

The comparison between stresses calculated by FE analysis (FEA) and the ones measured by strain gauges revealed that the FE models are able to predict stress distribution around fastener connection of joints with maximum error of 7%.

Stress deviation between strain gauge readings (thick lines) and FEA (thin lines) demonstrated that a good estimation of the local stresses is possible. The stress field predicted by FE models has shown very good agreement with the one measured by strain gauges in coupon specimens as shown in Figure 20 (right).

Kt = 4.7 Kt = 3.9

Figure 18. Coupon geometry and maximum principle stresses at thedoubler run out.

Figure 19. Strain gauges positions. Strain gauges have been placed back to back (1-3 and 2-4).

Test and FEM Results - GAP Elements FE ModelStress vs. Nominal Stress

-120

-80

-40

0

40

80

120

160

200

240

0 10 20 30 40 50 60

Sigma Nominal N/mm

Stre

ss

MP

a

Test, SG1 Test, SG2Test, SG3 Test, SG4FEM, SG1 FEM, SG2FEM, SG3 FEM, SG4

1,5 mm

0,75 mm

Figure 20. Details of the FE model at the rivet connection and position and length ofthe SGs in the FE model.


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III. Curved Stiffened Fuselage Panel FE Model Two curved stiffened panels, representing a real fuselage structure, in which four repairs were introduced (SRM

repair to be used as reference and three advanced repair solutions including an hot bonded repair), were subjected to biaxial constant amplitude fatigue loading (Figure 21).

A software tool to study the mechanical behavior of a curved stiffened panel under biaxial loading (internal pressure and longitudinal load) was developed in this project. This tool consists of several macros written in MSC.PCL coordinated by a main macro which calls the other subordinated macros to create a Finite Element model and a MSC.Nastran input deck.

Figure 22 shows an example of a curved panel FE model (deformed shape after nonlinear analysis) created by this tool.

This model is a cutout of about 35 of the fuselage with a length and width of about 3200 x 1600 mm, including frames and stringers. All main measures like radius, frame sizes, pitches etc. can be adapted. Also a longitudinal lap joint with different configurations may be placed at the central stringer.

Figure 23 (right) shows the mesh size at the central area of the model which is 3-4 times finer than the outer part. Mesh details of the stiffener elements (frames and stringers) are also shown in Figure 23 (left). The outer part is meshed coarser to reduce analysis time. A stripe with unstructured mesh connects the finer and the coarser mesh. The most common used element type is the two dimensional CQUAD4 plate element (MSC.Nastran notation) with a rectangular shape. CTRIA3 triangle elements are used as gradual passage between coarse and finer mesh. A MPC connection (multipoint constraint) is used for applying the axial force.

Figure 21. Curved stiffened panel with four unlimited repair solutions.

Figure 22. Example of FE model of curved stiffened panel (right: deformed shape).

Figure 23. Mesh details of stiffener elements (left), refined mesh area at the center(right).


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The boundary conditions applied to the model are shown in Figure 24. Internal pressure and axial load were the loading conditions applied. The axial force is applied at a center node, which is connected to the panel with a MPC element (multipoint constraint of the type RBE2) in z-direction (axial direction).

The cutting edge is in between two stringers and frames. The FE model is fixed by symmetry boundary conditions. At the longitudinal sections, the degree of freedoms (DOF) 2,4,6 are fixed in the cylindrical coordinate system CS 3 - that is TT (tangential translation), RR (radial rotation), RZ (axial rotation) (as shown in Figure 24). At the cross section, the degrees of freedoms are 3,4,5 - that is TZ (axial translation), RR (radial rotation), RT (tangential rotation). The symmetry boundary conditions are conterminous to mirroring the model. This simplification ignores small unsymmetrical configurations like the stringer and frame orientation. The wide range of frames and stringers prevents local influence of the constraints at the model edges on the region under investigation in the middle. The structural behavior of the panel is the same as of a long, closed cylinder.

A geometric nonlinear static analysis was performed with MSC.Nastran (SOL 106). Within the scope of this analysis type, large deformations and follower forces are taken into account. Large deformations consideration means, that the stiffness matrix is updated according to the calculated deformation after every iteration step. This is important in case of large rotations which are induced by plate offset at repairs and lap joint (secondary bending). With the follower forces option on, the pressure applied at the plate elements remains perpendicular to them.

The material behavior is assumed as linear and isotropic. The main macro calls the other subordinated macros. With the !!input commands in the main macro, all

functions stored in the macro files are read and compiled. Now MSC.Patran can use the functions:

to read additional pcl functions and to open a new MSC.Patran database

to read the input files (two ASCII files containing all the geometric figures to create the panel and the loading conditions)

to create the FE model (geometry, mesh, loads and constrains)

to write an analysis file for the MSC.Nastran solver The user can control, which part of the program shall run

by setting switches in the main macro. Two ASCII input files contain the geometry of the panel

and all other information (lap-joint configurations) are required to create the FE model. These are the geometric parameters of the joint such as thickness and rivet pitches. An example of the parameters required to describe the stiffeners is shown in Figure 25. The MSC.Patran PCL macros read the required parameters from this text files and search for the parameters necessary to create the model.

Figure 26 shows how the stress distribution changes because of the presence of the four repairs (left). Both panels were equipped with a large numbers of strain gauges most of them installed back to back. The FE model of the panel containing repairs needs to be edited manually as repairs are not in the scope of the software tool.

Figure 24. Mesh details of stiffener elements (left), refined mesh area at the center (right).

Figure 25. Example of input parameter for a)Frame/Clip and b) Stringer geometry.


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All FE models have been validated comparing the stresses simulated by the analysis with the ones read by the strain gauges during the fatigue tests.

IV. Bonded Repair FE 3D Model

I. Introduction The FE 3D models to perform parametric studies of two flat bonded repair configurations are described in this

section. The models are created using StressCheck a FE program based on the p-level method (3.2). Two different bonded joint geometries have been modeled: butt-joints and small flat panels 4. Both joints were modeled with aluminum for the skin and doubler and combining aluminum for the skin and glare for the doubler. The adhesive layer was modeled too.

J. StressCheck FE Program StressCheck (developed by esrd) is based on the p-version of the finite element method. One of the

advantages of using p-method based program is the possibility to reduce the errors of approximation increasing the polynomial degree of the elements. Moreover, high aspect ratio elements for single ply modeling are feasible (prerequisite for thin solid layers like adhesive). Models can be created parametrically in such way the geometry and/or the properties of the model (e.g. element properties) can be changed easy for a full parametric study. One more important feature of StressCheck is the possibility to handle nonlinear analysis domains (nonlinear material behavior and geometric nonlinearities).

K. Models Description Figure 27 and Figure 28 show the technical drawings (left) and the corresponding FE mode made by

StressCheck (right) of coupon test specimen and small flat panel respectively. The skin was always modeled in aluminum while the doubler was modeled both in aluminum and glare. The models were created parametrically. Areas where high stresses are expected were meshed with smaller element size. Simple geometry entities (such as points and curves have been used in order to minimize meshing errors caused by re-meshing while changing the parameters. For instance, nodes and elements created at the corner of the doubler (small flat panel) must be located along an arc to make the element edge following the curvature. These nodes cannot be copied with an offset, because the curvature information gets lost (the elements created on base of these copied nodes will not have the same curvature). The possible solution for this inconvenience is to create arc lines for each curvature in the model. A FE 3D-model could be also created defining the model in 2D and then copying the plane model with an offset. The solid elements (eight nodes elements) can be created simply selecting the two planes containing the 2D models by StressCheck commands: Create Hexahedron Face to Face.

Figure 26. Example of FE model of curved stiffened panel containing four repairs (right).

Figure 27. Geometry (left) and StressCheck model (right) of coupontest specimen.


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L. Boundary Conditions Only a quarter of the real

specimen was modeled (symmetry constrains at the symmetry planes). The clamping area of the specimen was modeled as a small strip with fixed motion in the y-direction (direction out of the specimen plane). A tensile load corresponded to 100 MPa stress was applied at the gross section of the skin as external load. Figure 29 shows the boundary conditions of the butt-joint coupon test specimen.

Figure 30 shows details of the model (both coupon specimen and small flat panel). In left hand side of the figure the mesh size at the adhesive phase length is shown; the figure refers to the coupon specimen with aluminum/glare as material combination (the doubler was modeled in glare). In the right hand side of the figure details of the cutout and boundary conditions of the small flat panel model are shown.

M. Material Modelling 3. Aluminium Alloy AA2024-T351

Ramberg Osgood non-linear properties were used to model the plates (skin and doubler) and the outer layers of Glare in aluminum. A Ramberg Osgood material is defined by four parameters:

I) the modulus of elasticity (E); II) Poissons ratio (); III) the stress value (S70E) corresponding to the secant modulus of 0.7E slope; IV) n shape factor describing the shape of the stress-strain diagram in the yield region.

The Ramberg Osgood expression is: n

E

E

SES

E

+=

70

70

73

Typical values of n range between 4 and 90.

Figure 28. Technical drawings (left) and StressCheck model (right) ofsmall flat specimen.

Figure 29. Boundary conditions of butt-joint coupon test specimen.

Figure 30. Model details: mesh size at the adhesive phase length (couponspecimen); details of the cut-out and boundary conditions.


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The material coefficients used in this analysis are shown in Figure 31.

Figure 31. StressCheck material input and stress-strain Ramberg-Osgood plot for aluminum 2024.

4. Adhesive Modeling The adhesive was modeled as bilinear material (linear elastic and linear strain hardening). The plastic region was described by linear stress-strain relationship with lower slope than the elastic region. The stress-strain relationship are described by four parameters:

I) the elastic modulus (E); II) Poissons ratio (); III) the yield stress (Sy); IV) the tangent modulus to characterize strain hardening of the material (Et). The adhesive used in this analysis was FM-73M.06 and the material coefficients are shown in Figure 32.

Figure 32. StressCheck material input and stress-strain Ramberg-Osgood plot for adhesive FM-73M.06.

5. Glare

The Glare material was modeled using a sub-laminate definition available in Stress-Check program. A sublaminate is a homogenized stack of plies. Using this material definition presents several advantages such as decreasing the cpu time or allowing parametric models including Glare type as parameter to study (otherwise a new model must be created if the number of metal and prepreg layers is changed). The aluminum layers used in the sub-laminate were modeled as linear elastic.

For both models (coupon specimens and small flat panels) the type of Glare 3-4/3-0.3 were used. Three prepreg layers were modeled, the second and the third layer had the same orientation of fibers and they were only half of the real prepreg thickness. This way, these two layers act as a single layer, but the possibility to use different Glare as parameter to be changed is enhanced (for example Glare with three prepreg layers instead of two).


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Figure 33 shows how the Glare material was modeled. The outer layers were modeled in elastic-plastic aluminum, after which two prepreg layers were modeled, orienting the fibers at 0 and 90, respectively. The remaining inner layers were modeled using the sublaminate definition.

Figure 33. Glare model: aluminum layers, prepreg layers and sublaminate layer.

N. Parameters Definition Previous FE analyses have shown that the length of the adhesive phase and its thickness influenced very much

the local stress. Optimization study was performed and the above mentioned parameters were used as main parameters for the investigation. In addition to the small flat panel with bonded repair, a larger flat panel with bonded repair (corresponding to the large flat panel fully described in 3 and 4 was modeled. In the latter, the main differences in respect to the small flat panel are the panel size (longer and wider panel) and a larger size of the cut-out (and doubler).

All models were done in fully parametric way; this means that many parameters were enabled in order to have a flexible model for further parametric study. For each model (two for the coupon specimen geometry and two for the small flat panel configuration) 12 analysis were performed: at 0.1 mm adhesive thickness and increasing values of adhesive phase length; fixed value of adhesive thickness of 0.2 mm and increasing adhesive phase length values.

O. Analysis Parameters Full non linear analyses (both material and geometric nonlinearity) were performed for all the models. For each

model a linear analysis was performed with a p-level up to 8 (to reduce the cpu time maybe a lower p-level can be used but the convergence requirement should be satisfied). The energy convergence criterion was used with Newton-Rapson technique. The tolerance value for the convergence was 0.75%. The linear analysis resulted were used as reference for the non linear analysis.

P. Coupon Specimen FE-Model The results of the FE analysis of the coupon specimen geometry are described in this section. Both material

combinations Al/Al for skin and doubler and Al/glare combination (skin in aluminum and doubler in glare) results are included. The stress analysis was focused in the skin and the doubler at the adhesive line runout. The fatigue life prediction was based on the stresses obtained at these locations. The influence on the local stress distribution of both adhesive thickness and adhesive phase length was investigated.

6. Aluminum Skin Aluminum Doubler

Figure 34 shows the non linear analysis results in terms of maximum principal stress distribution for the coupon model. Both skin and doubler were modeled in aluminum. The adhesive thickness and the adhesive phase length were 0.1 mm and 0.3 mm respectively.


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Figure 34. Maximum principal stresses of coupon model with both skin and doubler in aluminum. Non linear analysis, adhesive thickness of 0.1 mm, adhesive phase length of 0.3 mm.

Figure 35 shows the maximum principal stress distribution at the doubler run out for the coupon model. Both

doubler and skin were modeled in aluminum. The non linear analysis was performed. The adhesive thickness and the adhesive phase length were 0.2 mm and 0.8 mm respectively.

a) Max principal stress at the doubler (b) Max principal stress at the skin

Figure 35. Maximum principal stresses at the doubler run out of coupon model for both skin and doubler (figure-a and b respectively).

7. Bondline Optimization

It was found that the adhesive thickness and the adhesive phase length are the main parameter that influence the stress distribution at the critical location (doubler run out). A detailed study was performed to determine the local stress at the skin for increasing values of the adhesive phase length. The coupon specimen was the model under investigation with both skin and doubler made in aluminum. Two values of adhesive thickness were selected for this analysis (0.1 mm and 0.2 mm).

Based on the experimental evidence that fatigue failure occurred at the skin (ref 4), the analysis was focused on the stress distribution at the skin. Figure 36 shows the maximum principal distribution at the skin of the bonded coupon specimen model plotted versus the adhesive phase length. The non linear analysis was performed for two values of adhesive thickness (0.1 mm and 0.2 mm). Both adhesive thickness models have shown a minimum local stress above a certain value of the adhesive phase length. The local stress is reducing considerably up a fixed value of the adhesive phase length and above this value there is not further reduction of the stress. This value resulted approximately 0.15 mm and 0.4 mm for the adhesive thickness of 0.1 mm and 0.2 mm respectively. The reduction of stress achievable with optimized adhesive phase length is up to 16% of the maximum stress for the 0.1 mm adhesive thickness model and up to 20% of the maximum stress for the 0.2 mm adhesive thickness model.


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Figure 36. Maximum principal stress distribution at the skin of bonded coupon specimen model for increasing values of adhesive phase length.

8. Aluminum skin Glare doubler

Figure 37 shows the non linear analysis results in terms of maximum principal stress distribution for the coupon model. Skin was modeled in aluminum and the doubler was modeled in glare. The adhesive thickness and the adhesive phase length were 0.2 mm and 0.9 mm respectively. Figure 38 shows the maximum principal stress distribution at the doubler run out for the coupon model. The doubler was modeled in glare and the skin was modeled in aluminum.

Figure 37. Maximum principal stresses of coupon model with skin made in aluminum and doubler in glare. Non linear analysis, adhesive thickness of 0.2 mm, adhesive phase length of 0.9 mm.

The non linear solution was performed under a far field stress applied of 100 MPa (based on the skin gross area).

The adhesive thickness and the adhesive phase length were 0.2 mm and 0.3 mm respectively. With this combination of material the maximum stress at the skin remain as the previous case (both components in aluminum) at approximately 230 MPa whilst the maximum stress at the doubler resulted 270 MPa. The maximum principal stress distribution at the doubler and at the skin is shown in Figure 38.


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Figure 38. Maximum principal stresses at the doubler run out of coupon model for skin made in aluminum and doubler in glare.

Q. Small Flat Panel FE Model The results of the small flat panel model are described in this section. For these models, both material

combinations Al/Al for skin and doubler respectively and skin in aluminum and doubler in glare results are included. The stress analysis was focused to the skin and the doubler at the adhesive line runout. 9. Aluminum Skin Aluminum Doubler

Figure 39 shows the maximum principal stress distribution of small flat panel model with both skin and doubler made in aluminum. A non linear analysis was performed. The adhesive layer had 0.1 mm thickness and 0.075 mm phase length. The results shown a maximum stress localized at the skin of 325 MPa approximately. Figure 39 (right) also shows a fatigue crack occurred at the critical location predicted by the analysis (from ref. 4). Several analysis were performed at increasing values of the adhesive phase length in order to investigate how the distribution of the stress at the critical location (doubler run-out) change. The effect of the adhesive thickness was investigated too, two values of the adhesive thickness were considered: 0.1 mm and 0.2 mm.

Figure 39. Maximum principal stress distribution of small flat panel model with both skin and doubler in aluminium. Test result (from ref. 4) is also shown with fatigue crack occurred at the stress critical location.

Figure 40 shows the maximum principal stress distribution at the skin of the doubler run-out for two values of

the adhesive phase lengths, 0.05 mm and 0.3 mm. The adhesive thickness chosen for this analysis was 0.1 mm. The maximum stress in both cases was approximately 325 MPa but increasing the adhesive phase length the area subjected to higher stresses resulted more localized within a region ahead the doubler run-out. Comparing the distribution of the stress shown in figure (a) and figure (b), leads to the following conclusion: the longer the adhesive phase length, the more localized the stress at the doubler run out.


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(a) adhesive phase length 0.05 mm (b) adhesive phase length 0.3 mm

Figure 40. Maximum principal stress distribution at the skin of the doubler run out in the absence of the adhesive phase length, figure (a) and with adhesive phase length of 0.3 mm, figure (b).

Acknowledgments The authors would like to thank a PhD student Goran Ivetic of University of Pisa, Italy for his contribution in

preparation of this paper.

References 1Armstrong, A., Future structures supportability strategy, Proceedings DSTL Structures Contextual Review, 2003.

Contextual Review, 2003. 2Furfari, D., Meyer, C., Lafly, A.L., Pramono, A., Advanced Repair Design Principles to Improve Fatigue and Damage

Tolerance Behavior of Fastened Repairs, Proceedings of 24th ICAF Symposium, Naples, Italy, 2007. 3Furfari, D., Woerden, H.J.M., Benedictus, R., Kwakernaak, A. (2009), Bonded Repair for Fuselage Damage: an Overall

Benefit to Commercial Aviation, Proceedings of 25th ICAF Symposium, to be published, Bos M. (Ed.), Rotterdam, The Netherlands.

4Brandecker B., Schmidt H.-J., In: Repair Assessment Program for Airbus A300 Aircraft, Proceedings of 19th ICAF Symposium, vol. I, p.619-637, Cook, R. and Poole P. (Eds.), Edinburgh, Scotland, 1997.

5Bakuckas, J. G., Carter, A., In: Destructive Evaluation and Extended Fatigue Testing of Retired Fuselage Structure: Project Update, Proceedings of the 7th DoD/FAA/NASA Conference on Aging Aircraft, p.1-12, New Orleans, Louisiana, 2003.

6Bakuckas, J. G., Bigelow, C. A., Carter, A., Steadman, D., In: Destructive Evaluation and Extended Fatigue Testing of Retired Aircraft Fuselage Structure, Proceedings of the 23rd ICAF Symposium, vol. I, p.229-240, Dalle Donne C. (Ed.), Hamburg, Germany, 2005.

7Radhakrishnan R., In: Damage Characterization, Joint FAA/Delta 8th Quarterly Meeting, Destructive Evaluation and Extended Fatigue Testing of a Retired Aircraft, Atlanta, GA, 2004.

8Radhakrishnan R., In: Damage Characterization, Joint FAA/Delta 10th Quarterly Meeting, Destructive Evaluation and Extended Fatigue Testing of a Retired Passenger Aircraft, Atlanta, GA, 2005.

9Atre A. P., Johnson W. S., In: Analysis of the Effect of Riveting Process Parameters on the Fatigue of Aircraft Fuselage Lap Joints, Proceedings of the 9th Joint FAA/DoD/NASA Aging Aircraft Conference, p.1-13, Atlanta, Georgia, 2006.

10Mller R. P. G., An experimental and analytical investigation on the fatigue behaviour of fuselage riveted joints, Ph.D. Thesis, Delft University of Technology, The Netherlands, 1995.

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