BIE, FILE COPUYEPAIRS TO DAMAGE TOLERANT AIRCRAFT

"""jN24 1990r A by

Nf) T. SWIFT

NFEDERAL AVIATION ADMINISTRATION

presented to

INTERNATIONAL SYMPOSIUM ON STRUCTURAL

INTEGRITY OF AGING AIRPLANES

ATLANTA, GEORGIA

20 - 22 MARCH, 1990

\ DISTRI2jUTTON STAT'MENT A

Ap r-• !,r pub.ic reeOase;

90 (o, 4' l

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U:' T.' EREPAIRS TO DAMAGE TOLERANT AIRCRAFT f _

T. SWIFT

3229 E Spring Street d io rLong Beach, Calif. 90806-2425 cial

Summary - , ,.

The! esults of displacement compatibility analysis, representinga variety of repair doubler and lap splice configurations, arepresented with a view to illustratingýhow structural repairs candegrade the fatigue initiation life and damage tolerancecapability of primary transport aircraft structure. Examplesshow that fatigue initiation life is directly related to thepeak loads induced in the first fastener rows at the edges ofrepair doublers. Design of repairs to an equal or better staticstrength capability and the associated static strength analysiswill not normally highlight these peak loads which can resultin considerable degradation of structural fatigue life. Criticalfastener loads, based on displacement compatibility analysisaccounting for fastener flexibility, are parametricallypresented for a variety of skin and doubler thicknesses.Suggestions are made on how repair designs can be modified toimprove fatigue initiation life and subsequent fatigue crackdetectability particularly in the event of multiple-site damage.(MSD). The importance of riveting quality during repairs, oftennot up to initial manufacturing standards, is discussed withrespect to fatigue initiation life. A simplified butconservative method to generate crack growth curves isdiscussed with a view to easing the analytical burden for thesmall modifiers. It is hoped that this information, togetherwith conservative fatigue Sn data, will help the many smallrepair and modification stations gain an appreciation of thefatigue and damage tolerance quality of structural repairs.-Itis pointed out in the paper that the FAA regulations wereamended in December, 1978 for new transport category aircraftand in May, 1981 for aging transport aircraft to include adamage tolerance philosophy. This means that any repair to atransport category airframe, which may effect threshold,frequency and type of inspection of yprincipal structuralelements, must be evaluated for itV damage tolerancecapability.

Introduction

In December, 1978 the Federal Aviation Administration amendedtheir Fatigue Evaluation requirements for Transport CategoryAirplanes to include a damage tolerance philosophy. Prior tothis time FAR 25.571, Fatigue Evaluation of Flight Structure,included an option to design to either "Fail-Safe" or "Safe-Life" principles. The manufacturers had generally adopted theFail-Safe option with the exception of a few components such as

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engine mounts and landing gear. In satisfying the regulation tothe Fail-Safe option they had designed structure to be redundantso that catastrophic failure would not result after fatiguefailure or obvious partial failure of a single principalstructural element. However, the so-called Fail-Safe approachhad not included a disciplined engineering evaluation of crackgrowth and residual strength characteristics of each principalstructural element using fracture mechanics technology necessaryto specify inspection methods, threshold and frequency whichwould detect damage prior to catastrophic failure. There hadbeen a number of accidents in the mid seventies on aircraftdesigned to the Fail-Safe principle which may have beenprevented had such inspections been imposed. Thus, in December,1978 the FAA released amendment 45 to FAR 25.571 requiring thatnew structure be designed to "Damage Tolerant" principles unlessit could be shown that this approach would be impracticalwhereupon a "Safe-Life" option could be used. In May, 1981 anadvisory circular AC-91.56 was issued to provide guidancematerial for the issue of Supplemental Inspection Documents(SIDs) for existing Large Transport Category Airplanes. It wasexpected that advanced fracture mechanics principles would alsobe adopted to dcvelop these SIDs. Thus, for both new designs andexisting aircraft it is expected that engineering evaluation ofthe structure under typical load environmental spectra must showthat catastrophic failure due to fatigue, accidental damage orcorrosion will be avoided throughout the operational life of theaircraft. Over the last decade this process has been carriedout. Inspection programs for both new designs and existing olderaircraft have been based on a damage tolerance philosophy.However, up to the time of this writing, a system is not inplace to require that all repairs or modifications to principalstructural elements on these aircraft be evaluated to damagetolerance principles. Currently, the majority of these repairsare designed to an equal or better static strength requirement.Inspection procedures specified for the basic airplane are notbeing modified to reflect a change in design detail as a resultof the repair or modification. Although the repairs crmodifications may have equal or better static strengthcapability their effect on the fatigue quality andinspectability of the structure may be considerable. It isunderstood that a number of the major airframe manufacturers arecurrently working towards including damage tolerant evaluatedstandard repairs in their structural repair manuals. Others mayfollow this lead. This paper is intended to highlight thisproblem and perhaps outline some guidance to those occupied inaircraft modification and repair.

Degradation of Structure Due to Repair

In general, any repair to an airframe structure cansubstantially degrade fatigue life if extreme care in designdetail is not taken. In the past, engineering evaluation ofrepairs has been based on equal or better static strength onlywithout too much consideration for fatigue life. This philosophycan easily lead to static strength overdesign with consequentconsiderable loss in fatigue quality compared to the originalstructure. This phenomenon -an easil%, be demonstratedanp-ytic.-l!y by ccnsidering a very simple example case. Figure

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la shows a typical fuselage skin element 0.04 inches thickriveted to a typical stringer. This element is subjected tocyclic hoop (circumferential) stress due to internal cabinpressure ah. Assume for our example this stress is 15 KSI withstress ratio R = 0. The fatigue life of this element will bebased on the life at the row of rivet holes shown. These rivetholes are initially unloaded in the hoop direction. For ourexample case it will be assumed that the rivet holes have poorquality. This will be explained in detail later. The fatiguelife of this row of rivet holes can be obtained from Figure 2and as shown is about 160,000 cycles for 15 KSI with abr/aCr = 0.Suppose now we rivet a doubler to the skin as shown on figurelb. For our example we are not assuming any damage to theprimary skin and we are not assuming the skin is cut. In otherwords we are not depending on all load being transferred out ofthe skin into the doubler. We are merely considering a doublerfastened to a piece of undamaged skin. Following the usualconvention of increasing the doubler thickness one gauge, in thecase of damaged skin, we will assume the doubler thickness is0.05 inches. Whether we need it or not there will be loadtransfer out of the skin into the doubler due to straincompatibility between the two pieces. The two pieces arefastened together and will be attempting to strain together.The highest rivet loads, induced from the skin into the doubler,will be at the first row as shown in Figure lb. Figure Icillustrates the induced fastener load F in the skin reacted bythe load F applied to the doubler. The gross stress ah, alongline AB in Figure lc, will be unchanged in the presence of thedoubler but now we have induced a bearing stress in the hole abrwhich will degrade the fatigue life. This is illustrated by thevarious Sn curves of Figure 2. It can be seen that for constantamplitude stress the life is reduced with increasing abr/agrratio. The stress in the sheet will reduce to the bypass stressa and the stress in the doubler will increase to ad' In mostcases the critical location for fatigue will be at row 1 in thesheet where the gross stress is still 0 h and the bearing stressin the sheet is highest due to the highest fastener load. Inorder to determine the fatigue life at this location it isnecessary to determine the fastener loads in the first row. Thisis done through a displacement compatibility analysis of thejoint.

A typical strip, as indicated in Figure lb, is idealized asshown in Figure 3. Each rivet is simulated as an elastic springunder shear load and each portion of the skin and doubler stripis idealized as a bar. Bar displacements are obtained simply,from equation 1:

Bar displacement 6bar = PL/AE (1)

Where P = Bar loadL = Bar lengthA = Bar areaE = Bar modulus

Rivet shear displacements are given by empirical equation 2 [1]:

Rivet displacement riv = F[A+B(D/tD + D/ts)]/(ED) (2)

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Where F = Rivet shear loadD = Rivet diameterE = Sheet modulustd = Doubler Thicknessts = Skin thicknessA = 5.0 for aluminum rivets and 1.666 for steel

fastenersB = 0.8 for aluminum rivets and 0.86 for steel

fasteners

Displacements in the skin at each rivet are made compatible withthose in the doubler after accounting for rivet displacement.Load compatibility is merely assumed, for example as:

Ps - Ps2= F1, Ps2 - P = F2 etc.

and PD1 - PD2 F1 P, 2 - P03 F2 etc.

Where S and D denote skin and doubler.

The resulting load distribution in our example case is shown inFigure 4. It can be seen the highest loads are at the first rowand are 187.2 lbs per rivet. The skin bearing stress istherefore 187.2/(0.04 x .19) = 24632 psi. Bearing stress togross stress ratio abr/agr = 24362/15000 = 1.642. The calculatedlife is therefore 53800 cycles as indicated by Figure 2. Thus,the addition of the 0.05 inch thick doubler, even though for ourexample case is not transferring load across a damage area, hascaused a reduction in fatigue life from 160,000 cycles to 53,800cycles because of load transfer from the skin into the doublerdue to displacement compatibility. Figure 5 shows decreasingskin life with increasing doubler thickness obtained by similaranalysis. Further reductions in skin life are shown when steelfasteners are used due to higher first fastener load due toincreased stiffness.

It is shown in Figure 5 that the fatigue life of the skin isextremely sensitive to doubler thickness and that the life iscontrolled by the first fastener load. In order to provide someguidance to repairers and modifiers of airframe structure anumber of typical configurations have been analyzed.Displacement compatibility analysis was performed to givecritical fastener loads for a variety of skin doubler and lapsplice combinations. Figure 6 shows the idealization used forthe skin/doubler combinations. Sufficient rivets (5) wereconsidered so that rivet load away from the doubler edge wasinsignificant. The rivet load distribution is shown in Figure6 for a typical configuration assuming a unit 1 KSI appliedgross stress. Strip and rivet displacements were based onequations 1 and 2 respectively. Figure 7 shows first andcritical fastener load as a function of basic skin and doublerthickness for 1 KSI unit applied gross stress when 3/16 inchdiameter aluminum rivets were assumed for the skin/doublerconfiguration. Figirc 0 shows similar data when 3/16 inchdiameter steel fasteners are assumed. Figures 9, 10 and 11 showcritical fastener loads for 3, 4 and 5 rivet lap splices.Aluminum rivets, 3/16 inch diameter, were assumed for the lap

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splice configurations.

In the case of the lap splice configurations represented byFigures 9, 10 and 11 the following rules will be helpful.

1) When t 2 is thinner than t, the first attachment load is thehighest.

2) When t 2 is thicker than tI the last attachment load is thehighest.

3) When tI and t 2 are equal the first and last attachment loadsare equal.

Skin bearing stress abr can be calculated as a function ofapplied gross stress.agr from Figures 7 through 11. An estimateof conservative fatigue lives, not including local bendingstresses due to eccentricity, can be made using this informationalong with open hole fatigue data shown in Figures 12, 13 and14 for 2024-T3 material at stress ratios R = amir/mx of -0.2,0.0 and +0.2 respectively.

Figure 5 shows how overall fatigue life can be drasticallyreduced with increasing doubler thickness. Crack propagationlife is also influenced by fastener load induced by transfer ofload out of the skin into the doubler. However, the effect oncrack growth life is not so great as on overall fatigue life.The effect of fastener load is a very localized effect takingplace near the hole boundary. As the crack forms and starts topropagate the fastener bearing load becomes less significant init's influence on the crack tip stress intensity factor. Themajor difference in overall fatigue life is created in thenucleation portion of the life when the crack is extremelysmall. The effect of doubler thickness on crack growth life isillustrated by Figure 15. This figure shows the number ofconstant amplitude cycles, at a gross stress of 15.0 KSI withstress ratio R = 0, to propagate a crack in a 0.04 inch thickby 1.0 inch wide strip of 2024-T3 material. The initial cracksize is 0.02 inches on both sides of a 3/16 inch diameter holeand the final crack size is 0.35 inches on both sides of thehole. The table on Figure 15 shows some difference in crackgrowth life up to a doubler thickness of 0.05 inches but beyondthis doubler thickness there is little difference. Inducedfastener loads shown in Figure 15 assumed the configurationillustrated by Figure 7. It should be noted, however, that skinbending due to eccentricity of the load reaction due to doublerthickness is not accounted for. The curves on Figure 15 show thedifference in life between a configuration with no doubler andone with a 0.05 inch thick doubler. This analysis was performedusing the computer programs GEOFAC and LICAFF (2]. Forman'sequation was used to represent the crack growth rate as follows:

da/dN = (4.372 x 10"7 (AK)"z ... ]/((I-R)80 - AK] (3)

Repaired Structure Life Improvement

It has been illustrated by previous examples that repairs can

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drastically degrade fatigue life of basic structure. It wasanalytically demonstrated that this degradation is primarily dueto first fastener induced load caused by displacementcompatibility. This fastener load can be reduced and the fatiguelife improved by tapering the doubler. The objective in taperingis to reduce the doubler thickness between the first and secondfasteners. Merely tapering the doubler between the edge and thefirst fastener has no effect on reducing the first fastenerload.Figure 16 illustrates an example of how tapering can reduce thefirst fastener load. The fastener load distribution is comparedto the original example case of 0.04 inch thick skin with auniform 0.05 inch thick doubler. The reduced fastener load,resulting in a reduced bearing stress abr and therefore reducedabr/agr ratio, results in a life of 59,001 cycles at a grossstress agr of 15.0 KSI with R = 0. This is a life improvement ofnearly 10% compared to the life of 53,800 cycles obtained forthe uniform 0.05 inch thick doubler. It should be noted thatthese comparisons are being made with conservative open holefatigue data. Greater improvements could be shown using fatigueSn data representative of good quality riveting. However, thistype of riveting is rare in field repaired structure usually dueto space restrictions as will be discussed later.

Further reductions in first fastener load resulting in lifeimprovement can be achieved if the typical 0.05 inch thickdoubler is replaced by multiple doublers. This is usually easierto accomplish in field repairs anyway. As an example, a doublersystem involving standard gauges of 0.025 inches and 0.032inches were analyzed for comparison. The configuration is shownin Figure 17a. The 0.025 inch thick doubler is extended anotherfastener row. For this comparison strain compatibility analysisaccounting for fastener flexibility results in first fastenerload of 122.4 lbs resulting in skin bearing stress of 16.105 KSIand abr/a = 1.074. This results in a fatigue life of 70,500cycles aV a gross stress of 15.0 KSI. Thus, laminating thedoubler increases the fatigue life by 31% over the life obtainedfor the example case using a single 0.05 inch thick doubler.

Improvements in Inspectability

Any repair doubler applied externally to the fuselage structuresuch as that shown in Figure 1(b) will degrade the externaldetectability of the skin at the critical fastener row. Skincracking at the first fastener will be hidden externally by therepair doubler. Of course the skin will still be visuallyinspectable internally but then internal lining would have tobe removed. Also external inspectability of this type of repairis still possible with more sophisticated low frequency eddycurrent NDI. The inspectability of the repair can be improvedby placing the secondary doubler inside and the primary doubleroutside as shown in Figure 17b.

Further improvements in external inspectability can be made byremoving alternate fasteners at the first critical row toimprove residual strength capability and increase multi-site-damage (MSD) critical crack sizes. For example, Figure 18 showsour laminated doubler case but with alternate fasteners in the

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critical first row removed. This allows the net cross sectionalarea in the skin at the critical first fastener row to beincreased. In the case of MSD in 2024-T3 material the residualstrength is governed approximately by net section yield criteriabetween crack tips. Assuming net section yield governs theresidual strength capability then the critical MSD crack sizecan be expressed as:

acr = [ay(P-D) - uP]/[2(ay)] (4)

Where a= material yield strengthS= fastener spacingD = fastener diametera = applied gross stress

Assuming a B value of ay = 43.0 KSI for 2024-T3 unclad sheetmaterial in the LT direction from MIL-HDBK-5 the residualstrength diagram for the MSD case is shown on Figure 18 for P= 1.0 and 2.0 inches with rivet diameter 0.19 inches. It can beseen that the critical crack size is increased from 0.2306 with1.0 inch fastener spacing to 0.5566 inches with 2.0 inchfastener spacing. This provides for increased detectability andlonger crack growth life. However, the overall fatigue life willbe decreased with this configuration. Displacement compatibilityanalysis indicates that when alternate fasteners are removed theremaining fasteners in the critical first row try to load up awider strip of the secondary doubler thus increasing the firstfastener load. Analysis for our typical example at an appliedstress of 15 KSI indicates the first fastener load is increasedfrom 122.4 lbs to 184.2 lbs. This increases the bearing stressto 24.237 KSI resulting in a bearing to gross stress ratio abr/agr= 1.616. The resulting overall fatigue life becomes 54,500cycles. Therefore removing alternate fasteners in the criticalfirst row in the secondary doubler has degraded the overallfatigue life of the laminated configuration but considerablyimproved crack detectability.

The fatigue life can be improved by effectively tapering theinner doubler. This is done by fingering as illustrated byFigure 18. The fingers effectively reduce the inner doubler areabetween the first and second fastener rows thus relieving thefirst fastener load. This results in a lower skin bearing stressand improved crack initiation life. This configuration offersthe highest fatigue life coupled with the best externaldetectability.Remember, again the fatigue lives quoted are for open holequality.

Riveting Quality

The fatigue initiation life of the basic skin in the presenceof a repair doubler can be related to the quality of theriveting operation. If the rivets do not properly fill the holeafter "bucking" then poor fatigue quality can be expected asreflected in the open hole fatigue data of Figures 12 through14. Open hole fatigue data reflects a stress concentrationfactor, K,, of approximately 3.0 for wide thin sheet when Obr/Ogr= 0. This concentration factor results when the boundary of the

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rivet hole is allowed to deflect as illustrated in Figure 20(a).If the hole is filled with a pin capable of restraining the freeboundary displacement of the hole then the stress concentrationfactor is reduced to approximately 2.0 as illustrated by Figure20(b). This reduction in stress concentration factor at the holeboundary will result in improved fatigue life. Furtherreductions in effective stress concentration factor can beachieved if the rivet is bucked properly. Figure 20(d)illustrates that as the rivet is bucked it will swell in thehole and create the equivalent of an interference fit pinapplying a radial pressure to the hole boundary which in turncreates local radial and tangential stresses in the sheet aroundthe rivet. With little interference the material near the holeboundary becomes plastically deformed. It can easily be shownanalytically how this effect can reduce the effective stressconcentration factor at the hole boundary. Elastic-plasticstress analysis used in pressurized thick cylinders can be usedto illustrate this effect. Using this theory it is possible todevelop an equation relating the amount of interference to theradius of the plastic front as shown below:

2Ln(P/r)+(l+ )/(l-Vr) (Er/Es) (P/r) = IY3Er/(2rOy(l- vr)] (5)

This equation is solved by iteration for p/r. The value of P isthen used to calculate the resulting stress distribution asfollows:

Stresses in the CRP = aY/13[2Ln(R/P) - 1] (6)elastic region

I ap = ay/,3[2Ln(R/P) + 1] (7)

Stresses in the URE = ay/l3(P/R)2 (8)elastic region 1 = a//3(P/R) (9)

Where 0 RP = radial stress in plastic region

op = tangential stress in plastic region

aRE = radial stress in elastic region

a= tangential stress in elastic region

I = diametral interference

r hole radius

P = radius of plastic front

Er = modulus of rivet material

Es= modulus of sheet material

Vr= Poisson's ratio for rivet material

Vs = Poisson's ratio for sheet material

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R = radius at which stresses are required

Cy = material yield stress

Equation 5 was solved for diametral interference values, I, of0.003 and 0.004 inches respectively to illustrate how properrivet swelling can provide beneficial residual compressivestresses at the hole boundary. Rivet diameter was assumed to be0.19 inches in 2024-T3 sheet material with yield strength equalto 43 KSI. Poisson's ratio in the plastic range was assumed tobe 0.5. Figure 21 shows the resulting stress distribution inboth plastic and elastic regions. The compressive residualstresses would be subtractive from the applied tension stresseseffectively reducing the stress concentration at the holeboundary and subsequently improving the fatigue life. However,to obtain substantial interference the rivet must be buckedsquarely. Very often, especially in field repairs where spacemay be restrictive, the rivets are not bucked squarely resultingin a "clinched" installation. This situation often occurs whenthe working space is restrictive not allowing the bucking barto be held squarely. When clinching occurs the hole is notproperly filled and rivet swelling does not occur. Thus thebeneficial residual compressive stresses are not present. Infact, severe clinching can cause a situation where there may bea gap between the hole boundary and the rivet wall thus allowingsome free boundary displacement as shown in Figure 20(a). Whenthis occurs, reflective of poor quality riveting, the fatiguelife will be more representative of open hole Sn data shown inFigures 12 to 14. Figure 22 shows an example of rivet clinchingtaken from an actual failed field repair. The sketch on Figure22 illustrates the gap which can exist between the rivet and thehole boundary. This is graphically illustrated by Figure 23which shows a cross sectioned purposely clinched rivet. The gapbetween the hole boundary and the rivet wall is clearly visible.Figure 24 illustrates the variation in fatigue life which canbe expected with variations in riveting quality in 2024-T3 sheetat R = 0.

Figure 25 shows fatigue Sn data which may be reasonably expectedwith good quality 3/16 inch diameter rivets in 2024-T3 materialwhere the riveting is square and hole filling but with no loadtransfer. This data is a little difficult to use in the presenceof load transfer but this author has found the methods of LarsJarfall [3,4] to be useful in obtaining an effective stress aesswhich may be used with the Sn data of Figure 25 to approximatethe fatigue failure life. By reviewing the work of Jarfall itis possible to determine an effective stress as follows:

Ceff = [l' 3 Ktbr abr + Ktp a•]/Ktp (10)

Where aeff = effective stress

abr = bearing stress

a = bypass stress

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Ktbr stress concentration factor relating peakstress at edge of hole to abr

Kt = stress concentration factor -elating peakstress at edge of hole to ap

Of course the study of Jarfall's results should be used toobtain the proper parameters but this author has found thefollowing reduction of equation 10 to give reasonable resultswith Sn data of Figure 25 for good quality riveting. Again thisdata does not reflect possible bending in the joint due toeccentricities.

Ktb = 3.2, Ktbr = 1.4

Therefore aeff = 0. 5 6 9 abr + a(1)

Stresses in equations 10 and 11 are defined in Figures 12, 13and 14.

It should again be pointed out that field repairs are very oftennot of the fatigue quality represented by Figure 25. If advisecould be given it would be not to consider fatigue qualitybeyond that depicted by Figures 12, 13 and 14 for field repairs.Even then, a conservative scatter factor should be consideredto establish threshold for future detailed inspection of therepair. The reason for including Figure 25 was mainly toillustrate the differences in fatigue life between good qualityriveting and what may be expected in field repairs where accessmay not be as good as in the initial assembly of the airplane.

Degradation of Inspectability Due to Repairs

It has been shown how repairs can degrade the overall fatiguequality of the basic structure. It has also been shown that themost critical locations for future fatigue damage are in thebasic skin at the first attachment row in the doubler. Inaddition to degradation in overall fatigue life the repairitself can degrade the inspectability of the basic structureconsiderably. In order to illustrate this assume that a crackgrowing in a basic fuselage skin becomes visually detectablewith high reliability at say a half crack length of 0.5 inches.Assuming a constant amplitude cyclic stress of 15 KSI aithstress ratio R = 0 with crack growth rate represented byForman's equation 3, the crack growth life would be 29,600cycles as illustrated by Figure 26. Now consider a repairdoubler 9.0 inches long has been riveted to the basic skin. Themost critical location for future fatigue damage is in the skinat the first row of fasteners. Still assuming the visual halfcrack length of 0.5 inches the skin cr"ack would be able topropagate to a half crack length of 4.5 + 0.5 = 5.0 inchesbefore it could be detected visually externally. Thus the safeinspectable crack growth life has been reduced from 29600 cyclesto 1200 cycles. It can be seen that A eDubler length slightlylonger than 9.0 inches would leave no visually detectable lifefrom an external inspection standpoint. Of course, a lessdesirable internal visual inspection could be adopted but thiswould require internal lining removal. Also a more sophisticated

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low frequency eddy current inspection could be adopted. However,the more desirable external visual inspection capability couldbe completely degraded by this type of repair.

The external visual inspectability can be improved by includingan internal doubler as indicated by Figure 27. Thisconfiguration was addressed in Figure 17 and shown to haveimproved fatigue life of 31% for our example case over thedoubler type shown in Figure 26. The first fastener row in theinternal doubler is critical for fatigue cracking in the skin.A crack propagating in the skin at this row will he externallydetectable and so the crack growth life would be about 29600cycles as shown by Figure 26 for our example case. The residualstrength capability of this type of repair in the presence ofmulti-site damage can be improved by eliminating alternatefasteners in the critical row. This was indicated by Figure 18.Also the external visual detectability of this configurationwould be improved like the straight edged internal doubler alsos.,own on Figure 27. However there is a penalty on overallfatigue life by eliminating alternate fasteners. The purpose ofthe fingers, as previously explained, is to restore some of thisfatigue life by reducing the first fastener loads throughfingering or effectively tapering the internal doubler. Thefinger doubler repair is, in the opinion of the author, the bestcompromise for a permanent repair to basic fuselage structure.

Damage Tolerance Evaluation of Repairs

Current regulations mandate that repairs or modifications tocommercial transport category airplanes which have beencertified to the damage tolerance regulations FAR 25.571, or areoperating under a Supplemental Inspection Document (SID), mustbe evaluated for damage tolerance. The reason for this is thatthe in-service structural safety of these aircraft is beingmanaged through inspection programs based on a damage tolerancephilosophy. Inspections for principal structural elements aredeveloped through an engineering evaluation of crack growth andresidual strength, both of which are extremely sensitive togeometry. Any change in the geometry of principal structuralelements such as repairs or modifications can drastically changethe threshold, frequency and method of inspection and can alsoeffect the residual strength capability of the structure.Obviously the original manufacturers of the airplanes are in thebest position to Jo this evaluation. They usually have the know-how and are in possession of all the structural loads and stressdata necessary for such an evaluation. However, the currentsystem is such tnat there are hundreds of repair stations, smallmodification companies, operators and private DERs who areinvolved in the repair and modification of airplane structures.In order to support the aging fleet over the next decade thenumber of these repair stations and small modification companiesmust increase. Information contained in a recent GeneralAccounting Office (GAO) report on aging aircraft states that bythe year 2000 there will be 4474 commercial transport airplanes,manufactured by Boeing, Douglas and Lockheed, world wide, which

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will be operating beyond the initial 20 year life goal. Themanufacturers of these airplanes will need considerableassistance to keep them operating safely and repaired. The smallrepairers and modifiers, currently performing repair analysisbased on equal or better static strength only, will need todevelop capability to perform damage tolerance evaluations.Conservative, simplified methods need to be developed to assistthese small modifiers and repairers in performing crack growthand residual strength analysis in order to ease the burden onthe major manufacturers. These manufacturers need to concentrateon producing new aircraft to replace the aging fleet. Thesestatements are obviously over simplified. Exact damage toleranceevaluation is an extremely sophisticated process requiringexperts in fracture mechanics who must also be experts in basicairframe stress analysis. The number of these experts in theindustry is small and the job over the next decade will beoverwhelming unless we do something about it now. As a firststep, then, simplified methods need to be developed that willenable hundreds of modifiers and repairers to performconservative analysis to support inspection programs for repairsand modifications. It is the opinion of the author that allrepairs receive 100% continual inspection beyond a conservativethreshold. Because of operational schedules and the economicneed to keep airplanes flying the repair system may have to bein two stages. Immediate temporary repairs good for a limitedtime followed by permanent repairs supported by a damagetolerance evaluation. The greatest problem to the small modifierin performing damage tolerance evaluations is crack growthanalysis. This generally needs original manufacturers load andstress data. Residual strength evaluation is not necessarily aconsiderable problem to a good fracture mechanics analyst sincethis falls into the same category as equal or better staticstrength analysis. ie the residual strength can usually beassessed from a knowledge of the airframe geometry. The firststep then is to develop simplified, conservative, crack growthanalysis methods. This of course has been done to some extentby a number of researchers. The most appealing method, at leastto this author, is the method developed by Boeing's DamageTolerance Technology group. Sufficient information exists in theliterature [5, 6, 7, 8, 9] to provide an outline of the method.Some of the necessary data needed to complete this method doesnot exist in the open literature but this data can be readilydeveloped with some effort.

Development of a simplified crack growth method

In general a crack growth analysis requires the solution of thefollowing equation:

N = da/[F(amx,R,a,M,G,oy)]a i

Where ox = maximum applied stressR = stress ratio omin/aaxai = initial crack lengthaf = final crack lengthM = material influence

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G = geometric influenceay = material yield strength

The majority of large airplane manufacturers have developedsophisticated numerical integration crack growth computerprograms to solve this equation for a variety of materials andgeometries and load spectra variations. These programs are beingused to design new aircraft to meet the damage toleranceregulations and in some cases to develop SIDs for agingaircraft. Some manufacturers are using these methods to assessstandard repairs with a view to updating their structural repairmanuals. The crack growth method developed by Boeing allowsrapid development of crack growth curves. Boeing has addedsophistication to this method by considering load sequenceeffects under spectrum loading. It is the opinion of this authorthat for a conservative analysis of repairs additionalsophistication needs to be left to the large manufacturers atthis stage. The following is an outline of the development ofthe Boeing method but with parameters altered to fit in withfamiliar fracture mechanics methodology. The development hereneglects the sophistication of load sequence effects includedin the Boeing approach and which generally produce more accurateand less conservative results. In other words crack growthretardation is not included in the following approach. Theapproach is made possible through the following basicassumptions:

"• Walker type simulation of crack growth rate data

"* Separation of geometrical effects from stress and material sothat integration of geometrical effects can be performedseparately

"* Standardization of complex randomized load spectra into asingle repeatable flight

"* Simulation of this single flight by a single constantamplitude cycle with zero stress ratio

"• Subsequent constant amplitude crack growth analysis to producea crack growth versus flights curve.

The Walker crack growth equation is expressed as:

da/dN = C{(l-R)q K"')p (12)

The parameters for this equation are defined on Figure 28. Theequation is basically a straight line equation when plotted onLog-Log paper. When da/dN is plotted against the effectivestress intensity factor range, Keff = (l-R)q x,, a single lineis produced as shown to the left of Figure 28. Plotting da/dNas a function of the true stress intensity factor range, AK,allows several lines at different stress ratio, R, to be drawnas shown to the right of Figure 28. The width of the band oflines is controlled by the exponent q on the (l-R) term. Thisenables a better fit to be made of the test data points. Thevalue of P is the slope of the lines as indicated.

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Inverting equation 12 gives:

dN/da = 1/C( (I-R)q Kax)"P

af q -N = fa. l/C((1-R) IKax) da

N = I/C( (I-R)q}P f af(Km,) daa,

Substituting for K.,:

N = l/C(1/[aa,(l-R)q])P fafSda/(d-w-&8 )a,

load and material terms geometry terms

let GSP = af da/[( ,/r-) P]Ja,

Then N = i/C{Omx(l-R)}'1 P G-p

Or N = 1/C(1/(Gaax(l-R)q])P (13)

Where G = ( f da/[( .(A7 ) P] 1}/P (14)

Equation 13 gives the number of cycles N to propagate a crackfrom an initial size a. to a final size af with the effects ofgeometry defined by equation 14.

The term G will depend on the geometrical configuration. Theresults of equation 14 for all possible geometries is notincluded in the literature given by references [5, 6, 7, 8, 9,].However, this term can easily be obtained by numericalintegration for each specific geometry. There are manyreferences in the literature providing the term . or the effectof geometry on the stress intensity factor K. For example, oneof the most comprehensive of these is reference [10]. All otherterms in equation 14 are defined.

Only in the simplest of cases can equation 14 be analyticallyintegrated, for example, in the case of an infinitely wideunstiffened panel, where = 1.0.

= (f a)"P da = -P/2 a)-P/2

ai 1ai

15-P/2 [ alP/._.2 a

Therefore G'P = (Or) lP/2 [_a a

f r~at)1~P/2 - a1P/2]a

G 11(7r) -P/ a2 l-IP2( it

Figure 29 shows a plot of this equation for two values of af.There is a need to develop figures such as Figure 29, based onequation 14, for a variety of typical geometries by numericaiintegration.

For the benefit of those not familiar with this approachconsider the case of a through crack in a panel of finite width20.0 inches. The value of P for this case is generally acceptedto be (Sec(ra/W)]1/2 reference (11). From equation 14

"P= af )P da

f ai

Therefore for our example case

afG-P= Jff (aE[Sec(ira/W)j/2) -P da (15)

ai

Now we need to plot the term {].ra[Sec(ra/W) 11/2 )p as a functionof a. Figure 30 shows this plot for ai = 1.0 to af = 4.0 for our20 inch wide panel example. In this case the slope of the da/dNcurve, P, for aluminum alloy has been assumed 3.7. This valuewill vary from alloy to alloy but a value of 3.7 is a reasonableaverage value to use for aluminum. We now need a plot of Gversus initial crack size a,. Assume for a start a, = 1.0. Thevalue of GP will be the area under the curve ABCDEFGH shown inFigure 30. This can be obtained either by the mid-ordinate orSimpson's rule. For our case this value is approximately0.09345. Therefore G = [0.09345]31/3.7 = 1.89767. Similarly for a.= 2.0 the value of G"P will be the area under the curve BCDEFG.

For our case this is approximately 0.02948. Therefore G =[0.02948]"1/3.7 = 2.59204. Using this simple approach a curve ofG versus a1 can be plotted. The result for our case of a 20 inchwide panel is shown on Figure 31. This procedure to obtain aplot of G can be used for any complex geometry provided the termP, as a function of crack size a, is known. As mentionedpreviously# can be found for many geometries in the literature.

A useful tip to consider is that the term (/r P )_P can beintegrated in pieces. Therefore, for example:

(af J•f a 2 P' = - )P da =P da + (,/i1 )' da +G fafi fa a a

16

f afr(4 ) P da etca,

This is illustrated by Figure 32.

Therefore G"P = [GI"P + G2 "P + G3 "P] or G = [GI"P + G2 "P + G3 "P]"-/P

In this case Gi"P is the area under the curve ABGH, G2"P is thearea under curve BCFG and G3 P is the area under curve CDEF. Theusefulness of being able to integrate the geometrical term G-in pieces is best illustrated if one considers that theobjective of a crack growth analysis is to produce a crackgrowth versus cycles curve. In this case it is an advantage toplot a G curve for the maximum value of af expected. This singlecurve can then be used to obtain G for lower values of af. Thisconcept is illustrated by Figure 33. For example if we have acurve of G having been developed for af = 8.0 as shown to theleft of Figure 33 but we want to consider crack growth from a,= 1.0 to af = 6.0 we can say:

G(6.0 - 1.0] = ((G[8.0 - 1.0])"p - (G[8.0 - 6.0])'-P}"P (16)

Terms similar to G(6.0 - 1.0] mean G obtained between the limits1.0 to 6.0. We can obtain the respective values of G[8.0 - 1.0]and G[8.0 - 6.0] from the curve to the left of Figure 33 and usethese values in equation 16 to obtain G[6.0 - 1.0]. This ispossible since (G[8.0 - 1.0])}p is the integral of (,/i fl )'Pbetween the limits 1.0 and 8.0 which is the area of the curveshown to the right of Figure 33 represented as ABCDEF. Similarly(G(6.0 - 1.0])- is the integral of (.i48)-P between the limits1.0 to 6.0. Since the curve to the left of Figure 33 is basedon the upper limit of 8.0 only then we use this to obtain G[6.0- 1.0) by subtracting area BCDE from area ABCDEF and this isequivalent to area ABEF representing {G[6.0 -1.0]) P. We thenraise this area to the power -1/P and this represents G[6.0 -1.0].

Expanding the concept illustrated by Figure 33 we can calculatemore points on the crack growth curve if we only have one curveof G versus af by the same procedure. Figure 34 illustrates theprocedure for 4 points on a typical crack growth curve. The term(G[8.0 -1 .0])P represents the entire area under the curve of(.Ira 4)-p from 1.0 to 8.0 shown to the right of Figure 33. Thenumber of cycles to propagate the crack from 1.0 to other cracklengths are obtained by subtracting the remaining area of thecurve of (,/7- 4P8 )'P beyond the crack length required asillustrated in Figure 34. The values of G again are obtainedfrom the G versus a, curve as illustrated by the curve to theleft of Figure 33.

To simplify the crack growth analysis under spectrum loading thefirst assumption is to assume all flights are similar. That isthe crack is propagating under a single repeatable flight. Thisassumption is more reasonable for commercial transport aircraftthan it would be for say a military fighter. This singlerepeatable flight is then simulated to a single cycle having thesame crack growth as the repeatable flight.

17

From equation 13 N = I/C(i/[Gam,(l-R)q])P

Or N = I/(CGP) (i/[( x(l-R)q])p

Crack growth per cycle

1/N = CGP(a 0 x(l-R)q)p (17)

Consider a single repeatable flight as shown in Figure 35. Thetotal crack growth for this flight can be calculated usingequation 17 by summing the growth for each cycle. It is usualpractice to truncate the negative stresses so the cyclesconsidered are those represented by the heavy lines between dotson Figure 35. However, some prefer to leave in the negativestresses, take the full range of stress from negative topositive, and then use the appropriate crack growth ratecorresponding to the negative R ratio. There is usually verylittle difference between the two results. The total crackgrowth for the single flight is therefore:

i=nT = CGP Z (aimx(l-Ri)q)p (18)

i=1

The stress level S is then obtained, at a stress ratio R = 0,which will give the same crack growth as the single flight. Thiscan be obtained by substituting R = 0 and amx • S into equation17. Therefore the growth for the single cycle is:

C(GS)P (19)

We can equate equations 18 and 19 to obtain the value of S:

i=nCGp Z (i,,x(l-Ri)q)P = CGP (S)p

i=l

i=nTherefore S = [ E (aix(l-Ri)q)P I1 /P

i=l

S = [(alm,(l-R1)q)p + (02ma(l-R2)q)p + etc.]I/ (20)

This value of S, at a stress ratio R = 0, is substituted intoequation 13 to obtain the number of cycles to propagate thecrack from a, to af with G determined for a, to af.

Therefore N = I/C(I/[GS])P

Or N = 1/C(GS)"P (21)

Crack Growth Evaluation of Specific Repair

Simplified methods to allow small repairers and modifiers todevelop crack growth curves have been discussed. However, evento perform this simplified analysis it is necessary to have a

18

knowledge of stress levels in the basic structure. Without thisknowledge it is impossible to perform even a simple damagetolerance evaluation. If, however, a crack growth curve for aparticular element, prior to repair, were available then it maybe possible to use this information to obtain a crack growthcurve for the modified structure. Consider the very simpleexample of an original structural element as shown in Figure 36awhich may be the vertical web of a wing spar cap. This elementmay have been repaired by adding a reinforcement strap as shownby Figure 36b perhaps to replace corroded material. If theoriginal element had been classified as a principal structuralelement in the initial damage tolerance evaluation, performedto either certify the airplane or to develop the SID, then acrack growth curve must have been developed by the manufacturer.This curve may have been generated using a more sophisticatedcycle-by-cycle crack growth analysis method including theeffects of retardation and using a particular equation tosimulate da/dN. What is needed is to determine the constantamplitude stress level S at a R ratio of zero which will matchthe crack growth curve for the original element. This would bedone by calculating G for the original configuration usingequation 14 and then varying S in equation 21 to match theoverall crack growth life covered by the original crack growthcurve. There are some minor problems associated with thisapproach. A very simple example will help illustrate theseproblems. Suppose the original stress spectrum for the elementshown in Figure 36a was as illustrated in Figure 37. This hasbeen simplified to illustrate a point. Suppose the existingcrack growth curve were based on an initial 0.05 inch crack atone side of a hole as shown on Figure 36a. Suppose the originalcrack growth curve was based on Forman's equation given byequation 3. Crack growth retardation may have been accounted forusing the Willenborg model [12]. The resulting crack growthcurve, produced by RECYCL [2], would be as shown on Figure 38curve A. Now if equation 21 were used to match the overall lifefor this curve, using equation 14 for G, and varying the stresslevel S in equation 21, then a life match would be establishedat a stress S of 19.45 KSI using a Walker equation with C =3.88xi010I. The value of C is not important since the same valuewould be used to generate a crack growth curve for the modifiedstructure. The resulting curve is illustrated by curve B onFigure 38. Even though the overall life has been exactly matchedthe shape of this curve is not the same. The primary reason forthis is that retardation was considered to develop curve A andthe peak stress of 17 KSI in the spectrum created a plastic zoneat the crack tip which effected the growth of subsequent cyclesand reduced the slope of the crack growth curve when the crackwas small. Since retardation was not considered for curve B theslope at the start of the curve was greater. If the originalcurve had been generated neglecting retardation effects butusing the same Forman's equation 3 then the result would be asshown by curve C, developed by LICAFF [2], on Figure 38. Againusing the value of G developed from equation 14 and varying thestress level S in equation 21, the overall crack growth lifewould be matched at a stress of 22.43 KSI using the Walkerconstant C = 3.88xi0"I. The resulting curve is shown as curve Don Figure 38. Now it can be seen that the shape of this curveis a closer fit to the curve developed under spectrum loading

19

without the effects of retardation. The slight difference inshape is due to the differences in the crack growth equationused. The Forman equation, used to generate curve C, is not astraight line equation as is the Walker equation. The spectrumanalysis without retardation was repeated using the Walkerequation with C = 3.88x10 10 , q = 0.6 and P = 3.7. The resultsare shown on Figure 39. Equation 21 was then used to match thiscurve and a perfect match was achieved at a constant amplitudestress of 19.95 KSI. This match is illustrated by the points onthe curve. The purpose of determining the constant amplitudestress level S which matches the original curve is to use thisstress in equation 21 to develop a crack growth curve for themodified element. This would be done by calculating G for themodified element accounting for load transfer at the first rivetand the loss in visual detectability when the crack is under thedoubler. Equation 14 would be used to develop the new G valuebased on standard stress intensity expressions found in theliterature. This procedure would allow a crack growth curve forthe modified structure to be developed without a knowledge ofthe original stresses but with a knowledge of the original crackgrowth curve. The purpose of Figure 38 was to illustrate thatsome caution must be exercised when using this procedure becauseof the possible mismatched shape illustrated by Figure 38 curvesA and D. For example the matching curve B reflects a longercrack growth life from a detectable crack to critical if thedetectable size is larger than the initial crack size used toproduce the curve. For example, if the detectable size wasconsidered to be 0.15 inches (say) the safe crack growth lifefrom the original curve is 19000 flights but is 35000 flightsusing the matched curve. Because of this it is better todetermine S in equation 21 to fit the curve from the detectablesize to the critical size.

Future Possibilities

A method to generate crack growth curves for the modified orrepaired structure was discussed using a very simple examplecase. The approach required a knowledge of the original crackgrowth curve. Without this curve or a knowledge of the originalstress spectrum it is impossible to obtain the requiredinformation. One possibility requiring some limited research maybe to divide the airplane structure into a numaber of zones,perhaps six or eight zones for the fuselage, the lower wingsurface and the horizontal stabilizer tension surface. Standardconservative stress spectra could be developed, perhaps usingthe standard TWIST spectrum, for the most critical points ineach zone. This could be done using the most conservative ig and1P stresses to be found anywhere in the industry. These standardspectra would then be used along with the simplified methodsdiscussed to produce conservative crack growth curves andinspection intervals. The only alternative to this is topersuade the original manufacturer, with all his knowledge ofthe original stress spectra and loads, to perform the analysis.

Conclusions

Any repair to an airframe structure has the potential todrastically degrade fatigue life and damage tolerance

20

capability.

"* In most cases the critical location for future fatigueinitiation is in the basic skin at the first fastener row in

the repair doubler.

"* Curves are presented illustrating degradation in fatigue lifeof the basic structure as a function of repair doubler

thickness.

" Fatigue life of the basic structure can be calculated as afunction of applied gross stress and bearing stress in theskin at the first fastener row.

" Curves are presented, based on displacement compatibilityanalysis accounting for fastener flexibility, which willenable the critical fastener loads to be determined as afunction of skin and doubler thickness for five common repairconfigurations.

"* Data from these curves, together with conservative Sn curvesprovided, will allow a repairer or modifier to assess thefatigue quality of the repair.

" Some ideas are provided which will enable improved fatiguelife and inspectability by laminating the repair doubler.

" Simplified methods which may enable a small modifier orrepairer to develop crack growth curves for the basicstructure after repair are discussed.

Bottom Line

All repairs to principal structural elements on aircraftcertified to FAR 25.571 amendment 45 or on aircraft assessedto AC 91-56, where a SID document exists for the airplane,must be evaluated for damage tolerance.

New inspection methods/thresholds/frequencies must beestablished for the repaired structure.

The repaired airplane should be inspected at the determinedfrequencies after the established threshold.

Note

The opinions expressed in this paper are those of the author andnot necessarily those of the FAA. The author is an advisor toThe Aircraft Certification Service who have final authority.

21

References

(1]. Swift, T., "Damage Tolerance Analysis of RedundantStructures," Fracture Mechanics Design Methodology, AGARD-LS-97, North Atlantic Treaty Organization, London, England,Jan. 1979, pp. 5-1.

[2] Computer programs LICAFF, GEOFAC and RECYCL, FractuREsearchInc. 9049 Cupstone Drive, Galena, Ohio 43021, USA.

(3] Jarfall, Lars., "Optimum Design of Joints: The StressSeverity Factor Concept," Aircraft Fatigue Proceedings ofthe 5th ICAF Symposium, Melbourne, Australia, 22-24 May,1979.

(4] Jarfall, Lars., "Fatigue Cycling of Riveted or BoltedJoints," FFA report HF-1239. The Aeronautical ResearchInstitute of Sweden, June 1969.

(5] Craig, L., and Goranson, U.G., "Airworthiness Assessmentof Boeing Jet Transport Structures." Presented at the 10thICAF Symposium, Brussels, Belgium, May 16-18, 1979.

[6] Goranson, U.G., and Hall, J., "Airworthiness of Long-LifeJet Transport Structures." Presented to the RoyalAeronautical Society Spring Convention on Long-LifeAircraft Structures, London, England, May 14-15, 1980.

(7] Craig,L., et al "Airworthiness o2 Long-Life Jet TransportStructures." Presented at the Air Transport Associationof America Forum, Miami, Florida, October 1-3, 1980.

[8] Goranson,U.G., et al "Long-Life Damage Tolerant JetTransport Structures." Presented at ASTM Symposium "Designof Fatigue and Fracture Resistant Structures," Bal Harbor,Florida, Nov. 10-11, 1980.

(9] Gunther, C.K., and Goranson, U.G., "Spectrum LoadingEffects on Crack Growth in Major Components of CommercialTransport Aircraft." Presented to the InternationalConference on Application of Fracture Mechanics toMaterials and Structures, Freiburg, Germany, June, 1983.

[10] Rooke, D., and Cartwright, D., "Compendium of StressIntensity Factors." Printed in England for Her Majesty'sStationary Office by The Hillingdon Press, Uxbridge, Middx.England, Sept 1974.

[11] Feddersen, C.E., "Evaluation and Prediction of the ResidualStrength of Center Cracked Tension Panels." Published in"Damage Tolerance in Aircraft Structures," ASTM STP 486,May 1971.

[12] Willenborg, J., Engle, R.M. and Wood, H.A., "A Crack GrowthRetardation Model Using An Effective Stress Concept." USAir Force Tech. Memo. 71-I-FBR. Jan. 1971.

22

ah O6KS h is KII

0.04Z-4. 4.. 0.06

2

CRTIA LOCATION a A 4

ROW OF RIE RIVLTS

A d.

Fig. 1. Exampl of Doule Eleen

23

50

30 -b BEARING STRESS

SSTRESS RATIO R -0 GROSS STRESS20 -

16 K6I _______

010

2024-T3 CLAD SHEETI .I , ..... I I i i ui ,,,, a , a i~Iaami iii I Il,,,I

10 10 104 o0s 106

LIFE (CYCLES)

Fig. 2. Open Hole Sn Data 2024-T3

DOUBLERELEMENTS

Ps Ps2 PS2 Ps3 PS3 PS4 Ps4

je- jRIVETS

~II 2T 3II 4 H5 h1ý1 Pi2 PD2 P03 D03 PD4 D4 PDS /

SKIN APPLIED LOAD-'ELEMENTS

Fig. 3. Idealization of Strip

24

0. 04 SKIN

0.05 DOUBLER

+J

•..4,- .+.-t

+

•+ 4. .- .t

20 40 60 so 100 120 140 160 180 200

15 KSI LOAD IN EACH RIVET (LBS)

Fig. 4. Rivet Load Distribution For Example Case

CRITICAL IN SKIN AT FIRST ROW

140 .- . . .+ . . .• .

S++ + + +15 KSI

r-4 DOUBLERS100

0.04 INCH THICK SKIN

U S~ RIVETS

S40 \-0 0STEEL FASTENERS

to

a I a l

0.01 0.04 0.0o 0.0o 0.10DOUBLER THICKNESS (INCHES)

Fig. 5. Skin Fatigue Life At First Fastener

25

0.04 INCH THICK3/16 ALUM. RIVETS-- UBLR\

0.04 INCH THICKSKIN

1.0 INCH TYPICAL 1.0 INCH

r1 KSI

4 + GROSSI 235STRESS

FIRST RIVETi

12

10

8

6

1 2 3 4 1Fig. 6. Rivet Load Distribution in a Example Idealized Strip

26

40 BASIC SKIN THICKNESS (INCHES)- 9I40-----------------------------------------0.190

0.160

35___

0.125

30_ /____1ý 1-, 0.100

0.090

U) 0.080

~25 & /00.071.

U) 0.063

S20 1____ __0.050

0.04

0.042

04

0.4 00Z.2 01 0.202

DOUBLLRR 1HCNS KINHES

Fig. 7. First Fastener Load Per 1 KSI Gross Stress - 3/16Inch Diameter Aluminum Rivets

27

BASIC SKIN THICKNESS (INCHES)-50------------------------------0.190

45 0.160

40 0.125

0.100

7Zý 0.090

00

E-4

0 0.050

el2O 0.4

0.0632

215

0.0250

w 0.0320

CA 10

FIRST ATTACHMENT-

DOUBLER 1 KSI

BASIC SKIN

0.04 0.08 0.12 0.16 0.20DOUBLER THICKNESS (INCHES)

Fig. 8. First Fastener Load Per i KSI Gross Stress -3/16 InchDiameter Steel Fasteners

28

70 SKIN THICKNESS t1 (INCHES)

+ + 0.190

60

FIRSTATTACMENT0.160

(255

*50

0.125

~45

~40 0.100

/A "11000.090S35

'a' 0.080

0.063

0.050

Oc0 0.040

E-__ 15__ _ __ _ _ _ _ 0.032

cn ____0.025

10 0.020

5

0.04 0.08 0.12 0.16 0.20SKIN THICKNESS t2 (INCHES)

Fig. 9. First Fastener Load Per 1 1(SI Gross Stress. 3 AttachmentLap Splice - 3/16 Inch Diameter Aluminum Rivets

29

55 SKIN THICKNESS t1 (INCHES)

0.190

50_ __ 0.160

45

40 -012

CO) 35 0.100

0.9

X) 30_ A 0.080

25

0.050

z 200.040

~15 0.032

E-4 0.025

~1o ____0.020

0.04 0.08 0.12 0.16 0.20SKIN THICKNESS t2 (INCHES)

Fig. 10. First Fastener Load Per 1 1(51 Gross Stress. 4Attachment Lap Splice - 3/16 Inch DiameterAluminum Rivets

30

SKIN THICKNESS t1 (INCHES)50 - !

0.190

45____ _ 0. 160

C4)

M 35 OOlO0.100

C,)o

H •00 0. 09030

V-4 0.080

0.071

S0.063

E-4 0.050

///• • - ---- 0.040

015025

10 0.020

5_ _________FIRST ATTACHMENT -7

4 . 4t . 4

__~~-4 ., i i i _ 1. KSI

0.04 0.08 0.12 0.16 0.20

SKIN THICKNESS t 2 (INCHES)

Fig. 11. First Fastener Load Per 1 KSI Gross Stress. 5Attachment Lap Splice - 3/16 Inch Diameter AluminumRivets

31

'I ýT-r- T IL-T-FEB 7

440

fII

__- A_ _ i T JT1-

(0J

E4~4J

0010

7-L-'-U)0U~-Y 0V00

L9*0,

CUT).B S3ISSO~WlIV

32

4444i

7 z2

C'4 Pi__

A A_

00*U)0 0ý 00

('4i

(I001V3~L SO flIY

33

'C1

00*0

L9.0

4.i

l<0

E-4

02" 'd

(I~ 0X 4.)S3dl SH KLIV

34

CYCLES REQUIRED TO GROW CRACKFROM 0.02 INCHES TO 0.35 INCHESAT 15.0 KSI R = 0

DOUBLER INDUCED CYCLESTHICKNESS FASTENER LOAD

(INCHES) (LBS)0 0 27508

0.050 187.2 255240.063 203.4 254560.071 211.2 254230.100 232.2 25337

15 KSI

DOUBLER SKIN Ile 15 KSI Ile

THICKNESS

0.4.04

S0.3 BEARING LOAD INDUCEDo BY DOUBLERz

N 0.2 0.05 INCH THICK DOUBLER

g0.1 NO DOUBLER

5 10 15 20 25 30CYCLES X 10.3

Fig. 15. Effect of Doubler Thickness on Crack Growth Life

35

DOUBLER--

0 .05 0. 0 20.05

o.0A ,- 15 KsI

SKIN

i ,BASIC 0.05 DOUBLER-

TAPERED DOUBLER

150-+

'~100 +

z AT FIRST FASTENER

E4 br = 21.632 KSI"50 Obr/O or = 1.442

LIFE =59000 CYCLES

Fig. 16. Effect of Doubler Tapering on First Fastener Load AndFatigue Life

36

• ~0.04 -

0.025

SKIN.4.. 0.032 4-+

"- ..•..-* SECONDARY DOUBLER ÷ * 4INSIDE . . I ÷

IMPROVED EXTERNAL.. -. "DETECTABILITY AT CRITICAL

FIRST FASTENER ROW

• ..4-. "PRIMARY DOUBLER

"SECONDARY DOUBLEREXTENDED ONE FASTENER ROW

15 KSI

ADVANTAGES OF THIS REPAIR DESIGN

"• FIRST FASTENER LOADS IN SKIN REDUCED FROM 187.2 TO 122.4 LBS

"• SKIN BEARING STRESS oa 4 REDUCED FROM 24.632 KSI TO 16.105 KSI

"* BEARING STRESS TO GROSS STRESS RATIO a•/lar REDUCED FROM1.642 TO 1.074

"• FATIGUE LIFE INCREASED FROM 53,800 CYCLES TO 70,500 CYCLES

Fig. 17. Improved Fatigue Life by Doubler Lamination

37

15 KSI

"SKIN+- FIRST FASTENER LOAD IN SKIN

+~ + 184.2 LBS

S4. 4- + BEARING STRESS IN SKIN 24.237 KSI

S O D4- -b/aoo - 1.616

SECONDARY + + FATIGUE LIFE 54,500 CYCLESDOUBLER + - -÷

4-4-4- 4. -PRIMARY DOUBLER

+ +4-

4- ALTERNATE FASTENERS REMOVED

2" D P

P"1.0 2.0~25

S20+ a

S15

io j _y [P - D]- aP

10 c = 2 (ay]

cn ~01 0n

BASED ON a 43 KSID= 0.19

SII I , 1 i I I i

0.5 1.0

CRITICAL CRACK SIZE ac, (INCHES)

Fig. 18. Improved Crack Detectability By Removing AlternateFasteners In Critical Row

38

ANY SKIN CRACKING AT CRITICAL FASTENER ROWIS EXTERNALLY VISIBLE

~15 KSI •- SKIN

FIRST FASTENER ROW

FINGER TO REDUCEFIRST FASTENER LOAD

INNER SECONDARY DOUBLER(0.025 INCHES THICK)

INSIDE

OUTER PRIMARY DOUBLER(0.032 INCHES THICK)

0 FIRST FASTENER LAD IN SKIN 174 LBS

* BEARING STRESS IN SKIN 22.895 KSI

• obr/ogr = 1.526

0 FATIGUE LIFE 57,000 CYCLES

Fig. 19. Finger Doubler Configuration To Reduce First FastenerLoad, Improve Fatigue Initiation Life And Skin CrackDetectability

39

HOLE BOUNDARY ALLOWED TO HOLE BOUNDARY HELDDISTORT RIGID

a bOPEN HOLE FILLED HOLE

Kt APPROX. 3.0 NO INTERFERENCE

Kt APPROX. 2.0

lI BUCKED RIVET

PRESSURE INDUCED BY RIVETSWELLING

EFFECTIVE Xt CAN BE LESS THAN2.0 DEPENDING ON AMOUNT OFINTERFERENCE DUE TO RIVETSWELLING

Fig. 20. Effect Of Riveting On Stress Concentration Factor

40

PLASTIC ZONE

PLASTIC FRONT R RP

STRESSES WITHIN

ELASTIC ZONE

P 0.004 INCHESINTERFERENCE STRESSES WITHIN

30 - PLASTIC ZONE

P 0.003 INCHES

INTERFERENCE

S20 -0.004 INCHES

> • INTERFERENCE

b2m z

S10 0

E 0.003 INCHES

0b 0 INTERFERENCE

S0.2 0.4z

THESE STRESSES AT THE HOLEBOUNDARY WOULD BE SUBTRACTIVE

-10 FROM APPLIED TENSION STRESSESRESULTING IN IMPROVED LIFE

-20

Fig. 21. Elastic-Plastic Stress Distribution Around a 0.19 InchDiameter Rivet In 2024-T3 Sheet With Varying DegreesOf Equivalent Interference

41

EXAMPLE OF RIVET CLINCHINGFROM AN ACTUAL FIELD REPAIR

2 3$

RIVETS REMOVED FROM THE

REPAIR

GA ALLWIN HOL BOUNDARYKIN

DISPLACEMENT

Fig. 22. Examples Of Rivet Clinching

42

Fig. 23. Lack Of Rivet Hole Filling Due To clinching

40

30 ~- +

-FILLED HOLE WITH ZERO -

20 E-4 -INTERFERENC ---- )' � _ .- .

---- OPEN HOLE-. - -

_ _ _ H #4'AT

i:::}::LIFE (CYLS + .. R 0

103 10'4 10 106

Fig. 24. Effect Of Riveting Quality On Fatigue Life

43

0 0 e4U1

T -z-l 1Ml 1-107-44- 444

i 4=6 _----------

E-'0

0 ý

0 4)

4 N

4-)

-af'

(ism) ssaHiIS ssoH

44

CRACK IN PARENT SKIN SKIN IS CRITICAL AT(NO REPAIR) FIRST RIVET ROW

REPAIR DOUBLER

CRACK AT CRITICALRIVET ROW IN SKIN

IS VISUALLY UNDETECTABLEA AcJ , UNDER REPAI/R

BECOMES DETECTABLE1/2 INCH BEYOND

CREPAIR~DOUBLER

Sk k15 KSI, R =0

20

NO REPAIR CRACK GROWTH LIFEDETECTABLE TO CRITICAL

29600 CYCLES

15

zH 2024-T3 MATERIAL

10 E-0 CRACK GROWTH PERIODz DETECTABLE TO CRITICAL I

1200 CYCLES

5 DETECTABLE CRACK LENGTH BEYOND DOUBLER

EDGE OF DOUBLER

INITIAL DETECTABLE CRACK

5 10 15 20 25 30

CYCLES X 10'3

Fig. 26. Example Of Impaired Crack Growth Detectability WithRepair Doubler

45

EXTERNAL DOUBLER

ArArA, t.- INTERNAL DOUBLER

CRITICAL FASTENERROW

CRACK EXTERNALLY DETECTABLE

\ \ INTERNAL FINGEREXTERN DOUBLER

f % %-

CRACK EXTERNALLYDETECTABLE

THIS CONFIGURATION HASIMPROVED RESIDUAL STRENGTH IN PRESENCE OF MSD

Fig. 27. Improved Doubler Design For External Detectability AndResidual Strength Improvement

46

.4 .20 , STRESS

RATIOR = amil/Jmax

p p

da/dN da/dN

/

C C

1 10 100 1 10 100

Keff = (l-R)qKm, A K

da/dN = C{ ((-R)q K.x)P

where C = Intercept with K = 1.0 ordinate

R = Stress Ratio ami.l/Cx

q = Exponent to control width of R ratioband of lines

rx = Maximum stress intensity factor a.oYwa

aWX = Maximum applied gross stress

8 = Geometry effect

P = Slope of da/dN line

Fig. 28. Walker Crack Growth Rate Equation

47

FINAL5.0 - FNA af = 2. 0CRACK SIZE

4.0

af = 4.0

3.0G

2.0

1.0

1.0 2.0 3.0

INITIAL CRACK SIZE a1 (INCHES)

Fig. 29. Example Of The Geometric Term G For AnInfinitely Wide Panel

0.12 A

, 0.10N

j 0.08

O 0.06

U')

0.04 B

0.02 I CED

'H 'G , F , E

1.0 2.0 3.0 4.0

CRACK SIZE a (INCHES)

Fig. 30. Curve Of (,"aj)"P For Finite Width Panel

48

4.0 -

FINAL CRACK SIZE af 4.0

3.0 -

W 20.0 INCHES

2.0 -

G

1.0 - a

'T'T-1.0 2.0 3.0

INITIAL CRACK SIZE a, (INCHES)'

Fig. 31. Example Plot Of G For 20.0 Inch Wide Panel

A

B

DH G E

a, af

a da

Fig. 32. Step Integration of (,/-ra -P

49

G

af= 8.0

G[8.0-6.0]

G(8.0-1.0)

I ICI I

I I ,__ _ _ _D1.0 6.0 1.0 6.0 8.0

CPACK SIZE CRACK SIZE

Fig. 33. Integration of G"p In Pieces

G[2.0-1.0] = ([G(8.0-1.0)]'p - [G(8.0-2.0)]'p}'I/p

G[3.0-1.0] = ([G(8.0-1.0)]'p - [G(8.0-3.0)]-p)-/p

G[4.0-1.0] = ([G(8.0-1.0)]'p - [G(8.0-4.0)]-p)-/P

G[5.0-1.0] = ([G(8.0-1.0)]"p - [G(8.0-5.0)] f" I/P

N1 = N[2.0-1.0) = 1/C([G(2.0-1.0)]S)"p

N2 = N[3.0-1.0] = 1/C([G(3.0-1.0)]S)'p

N3 = N[4.0-1.0] = 1/C([G(4.0-1.0)]S)"e

N4 = N[5.0-1.0] = 1/C((G(5.0-1.0))S)"p

a5.0

~a 4 .0 -. _

Sa3.0

u a 2.0 -

at) a. 0

j aLIFE (CYCLES)

Ng3 .o N 2 O n N 1 N

Fig. 34. G For various Points On Crack Growth Curve

50

SINGLE REPEATABLE FLIGHT

-CRACK GROWTH ASSUMED ONINCREASING LOAD ONLY

I# SINGLE CYCLE PRODUCINGSAME CRACK GROWTH ASREPEATABLE FLIGHT

Fig. 35. Simulation Of Repeatable Flight To A Single Cycle

ORIGINAL CRACK GROWTH CURVEBASED ON A CRACK AT ONESIDE OF A HOLE

3.0-1 , -

j 0.19 INCH DIA. REPAIR REINFORCING STRAP

0.16" a b

Fig. 36. Example Of Repaired Element

51

20

1 16 17 16 16

17 1717STRESSES

S10 10 1 0 S9 9 9 9

Fig. 37. Simple Example Spectrum For Repeatable Flight

1.6

CONSTANT AMPLITUDE'

SPECTRUM

U, (d) C.AMP.S-1.2- 22.43 KSIS1.2•

. WALKERz(c) SPECTRUM

"NO RETARDATIONFORMAN (b) C. AMP.

0.8 / 19.45 KSIH WALKER

S0.4(a) SPECTRUM

RETARDATI ONFORMAN

10 20 30 40 50

FLIGHTS X 10.3

Fig. 38 Crack Growth Comparison Spectrum/Constant Amplitude

52

1.6

u 1.2SPECTRUM"NO RETARDATIONWALKER

N 0.8

0 0.4 C .19.95 KSI

S~WALKER

10 20 30 40 50

FLIGHTS X 10.3

Fig. 39. Crack Growth Comparison Spectrum/Constant AmplitudeUsing Same Crack Growth Equation