Fatigue Analysis at Filled Hole Locations White Paper[1]

7/28/2019 Fatigue Analysis at Filled Hole Locations White Paper[1]

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Fatigue Analysis at Filled HoleLocations An AnalyticalApproach

2013, QuEST Global Services


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Contents

Abstract 1

Water Industry - Outlook 1

Growth Drivers 1

Impact of Water on Industries & Mankind 1

Risks Associated with Water 2

Global Water and Water Treatment Equipment Market 2010 to 2015 2

Global Water Market 2

Water Infrastructure Critical Needs 3

Global Water Industry Design and Consulting Market Outlook 4

Water Treatment Solutions Technologies in Use and Emerging in Select Markets 2020 5

Water Treatment and Process, Design, and Consulting Outsourcing 5

Outsourcing Design Engineering Process 6

Advantages 6

Conclusion 7

Author Profile 8

About QuEST 9

Contents

Abstract 1

Introduction 1

Fatigue Scenarios 2

Fatigue Spectrum 3

Analysis Procedure 5

SN Curves for Composites 5

The Ordinate 5

R Ratio 6

Normalization of Applied Spectrum 6

Illustrative Example 8

Limitations 10

Scope for Future Work 11

Conclusion 11

Author Profile 12

About QuEST 13

White Paper Fatigue Analysis at Filled Hole Locations An Analytical Approach


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2013, QuEST Global Services1


Abstract

Over the recent past, material scientists andengineers have started developing custom made

structures from composite materials in order toobtain desired mechanical, electrical, magnetic,thermal, optical, and environmental properties.Because of the above advantages, compositeshave, over the recent past, been used inprogressively greater quantities in the aerospaceindustry. Boeings 787 Dreamliner and Airbus

A350 are among the new generation of commercial aircrafts that use composite materialsextensively.

The weight of aircraft components made of composite materials is reduced by approximately

Introduction

As with all other materials, composites are alsoprone to failure. The failure analysis of compositesis quite a challenge as they are anisotropic andheterogeneous in nature.

Great strides have been made in the developmentof analytical and empirical models to substantiatecomposite materials for static loading conditions.This has largely reduced the need to testcomposites under static loading.

Also, the general belief is that composite materialsare not prone to fatigue failure. However, inaerospace applications, composites are seldom

20%, such as in the case of the 787 Dreamliner [1]. Although bonded joints of composite materials

have been shown to have very high theoreticalefficiency in literature, the preferred method of

joining structures in aircrafts is by using bolted or riveted joints. The number of fasteners in anaircraft runs into millions. For example, there are afew hundred thousand rivets or bolts in a pair of

A350 wings.

This white paper seeks to address the issues andchallenges faced by the aerospace industry inquantifying these composite fastened joints for fatigue conditions.

without stress concentrations, and stressconcentrations would inherently act as nuclei for crack initiation.

A thorough knowledge of the fatigue behavior of composites is very important for proper design andoptimization of structures for use in the aerospaceindustry. The prevalent practice is to certify acomposite structure based on evidence fromstructural testing.

However, experimental prediction of the fatiguebehavior of various composites under differentfailure modes is prohibitively expensive, as there

Materials used in 787 body Total materials usedBy weight

Fiberglass

Aluminium

Carbon laminate composite

Carbon sandwich composite

Aluminium/steel/titanium

Aluminium 20%

Titanium 15%

Other 5%

Steel 10%Composites50%

Figure 1: Materials Used in Boeing 787 Body [1]


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are unlimited combinations of matrix type, fiber type, and stacking sequences possible.

In this paper, an approach is presented todetermine the fatigue life of composites used inaircraft structures with filled holes acting as stressconcentrations.

In order to use the approach, while it is recognizedthat some coupon testing may be necessary, theadvantage of the approach is that it utilizescommonly available analytical/empirical rulesprevalent in generic F&DT analyses to determinethe RFs at any filled hole location. Also, this simplemethodology can be automated in a tool and canbe easily used to determine the fatigue criticality of a composite structure at fastener locations.

Fatigue Scenarios

Most primary structures in an aircraft, which arenowadays being manufactured using compositelaminates, have unavoidable geometricdiscontinuities that lead to stress concentrations.



Figure 2: Building-Block Approach Showing the Pyramid of Tests Used for Structural Substantiation [2]

COMPONENTS

S T R

U C T

URAL F E AT

URE

S

SUB-COMPONENTS

DETAILS

ELEMENTS

COUPONS

G E N E R I C S P E C I M E N S

N O N - G

E N E R I C S P E C I M E N

S

DAT ABA

S E

These stress concentrations act as cracknucleation sites.

Listed below are some of the common stressconcentrations:

1) Fil led Holes (fastener locations) Theselocations are subjected to bearing/bypassstresses

2) Corners (in C-sections spars, etc.) Thecorners are subjected to inter-laminar tensionand shear stresses

3) Open Holes (window cut-outs in the fuselageskins, etc.) These locations are subjected tofield stresses

This paper mainly focuses on the substantiation of filled holes for composite fatigue. It is generally

believed that in composite materials, after crackinitiation, there is a rapid propagation resulting incatastrophic failure. Furthermore, the varioustemperature changes that aircraft structures aresubjected to causes them to be subjected tothermal fatigue.


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Table 1: Mission Mix of Commercial Aircrafts

Table 2: GAG Segments for Various Missions

Figure 3: Schematic Representation of a GAG Cycle

TROPICAL POLAR STANDARD DAY

Short Range Mission (SRM)

Medium Range Mission (MRM)

Long Range Mission (LRM)

It has to be noted that the structure should be designed in such a way that there is no crack initiation duringthe entire Design Service Objective (DSO).

Fatigue Spectrum

Commercial aircrafts are designed to operate in the following nine missions:

The GAG cycle for each of the missions can be broadly broken down as shown below:

Ground

Departure

Climb

Landing Post-flight

Ground

Pre-flight Take-off Unloaded and controls checkPushback towTaxi Maneuvers (turns,breaking, etc.)

Engine run-upTake-off rollRotation lift-off

Gear retractionFlaps down

- Gusts- Maneuvers

Flaps retraction

GustsManeuvers

Descent

Approach

Initial descent- Gusts- Maneuvers

Spoiler deploymentFinal descent

- Gusts- Maneuvers

Flap extensionFlaps extended

- Gusts- Maneuvers

Gear extension

Touchdown- Spin up/down

- DriftSpoiler deployment

Landing roll-out- Thrust reverse

- Idle thrustTaxi maneuvers(turns, braking, etc.)

CruiseGusts

Maneuvers

Ground Ground Ground

Climb 1

Cruise 1 Cruise 1

Climb 1

Climb 2

Cruise 2 Cruise 2

Climb 2

Take-off Take-off Take-off

Climb

Cruise

Descent

Approach

Landing

Descent

Approach

Landing

Descent

Approach

Landing

SRM (75 to 100 Min) MRM (270 to 330 Min) LRM (660 to 750 Min)



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Table 3: Incremental Loads and Temperature Conditions at Various GAG Segments

Figure 4: Example Flight Stress History [3]

Thermal Condition (@ fuselage as an

example) (assembly temperature 23 degrees C)GAGFlightSegment

Ground

Take-off

Climb

Cruise

Landing

Approach/Descent

Cold

Cold

Cold Cold Cold

Cold Hot to Cold

Hot Hot

Cold Hot Hot

Towing

Pushback/Spring-back

Pre-flight Braking

Bump during taxi-out

Bump During Take-off runRotation

Vertical gust

Lateral Gust

Coordinated Turn

Vertical gust

Lateral Gust

Rotation

Vertical gust Cold

Cold Hot Hot

Cold Cold to Hot

Lateral Gust

MLG Touch Down

Bump after touch down

Post Flight braking

Bump during taxi-out

Turn (slow/medium speed andhigh speed)

Turn (slow/medium speed andhigh speed)

Mechanical Incremental Cases Polar Standard Tropical

In each of the above segments, there will be incremental cases. Some typical incremental loads are listedin Table 3.

SS mf

S mf 1.5

0.5

0.5

GAGTRANSITION

TAXI LOADS

MEAN FLIGHTSTRESS

GUST LOADS

MEAN GROUND STRESS

TIME

(a)

0

These mechanical 1g and incremental cases, combined with the thermal loads at various segments of theGAG, result in a Thermo-Mechanical spectrum of fatigue stresses.


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Figure 5: Schematic Representation of a Composite Joint

Figure 6: Stress State at a Fastener Location

Analysis Procedure

Consider a composite to composite joint, as shown below:

Each bolt in this joint is subjected to the in-plane bearing/bypass stresses as shown below:

PyPx

xy

xy

y +

y

y

y

x x +

x

x

x

In order to analyze the bolt for fatigue, a thermo-mechanical mix spectrum of all these stresses has to bedetermined, i.e., the bearing and bypass stresses for the various 1g and incremental load casescorresponding to the various missions has to be determined.

However, the coupon test-based S-N curve will generally be based on field stresses. In order to comparewith the test based S-N curve, we have to generate a spectrum of field stresses.

SN Curves for Composites

SN curves can be used for composite material analysis, with certain salient features as explained below.

The Ordinate

Since infinite number of laminates can be developed using any given lamina, the SN curves for compositesare normalized by expressing the ordinate as a percentage of mean static strength. By doing so, the SNcurves for any particular lamina can be used for most laminates developed from that lamina material. Themean static strength can be determined from standard coupon testing, based on the prevalent ASTM

standards (ex: ASTM D 6742/D 6742 M 07 for filled hole tension and compression testing)

Figure 7 shows an example of normalized SN curves of the field stresses for three sample laminae, whichhas to be developed through a coupon test program.




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Figure 7: Example Normalized SN Curve of the Field Stresses for Three Sample Lamina Materials

Figure 8: Conversion of Bearing to Equivalent Bypass

Material 1

Material 3 Material 2

DOS

mean (IXDSO)

Number of Cycles (N)

S %

o f S t a t i c S t r e n g

t h

R Ratio

In general, the testing for composite fatigue is done at an R ratio (ratio of minimum stress to maximumstress) of -1. This is because unlike in metallics, compressive stresses adversely affect fatigue life of composites.

Normalization of Applied Spectrum

Since each cycle of the local stress spectrum is compared to a normalized SN curve, the local stressspectrum shall be normalized too. Thus the local stress spectrum is divided by the mean static strengthand multiplied by 100.

In order to determine a spectrum of field stresses, the bearing stresses need to be converted into anequivalent far-field stress, so that it can be added to any existing bypass stress, as shown below.

Bearing Bearing

Bypass

Bypass + (Conv. Factor* Bearing)

Bypass(a) (b)

(c)

(d)




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Any finite element software can be used todetermine the conversion factor to convertbearing stresses into an equivalent far-fieldstress, using relevant stress concentrationfactors.

Figure 8 (a) shows a composite filled hole locationsubjected to bearing and bypass stresses. InFigure 8 (b), the stress concentration due tobypass is schematically shown (at the 3 O Clockand 6 O Clock positions). Under bearing stresses,the stress concentration at the 12 O Clockposition is shown in Figure 8 (c). However, usingany finite element software, the stressconcentration due to bearing at the 3 O Clock and6 O Clock positions can be determined, and anequivalent bypass can be determined for theapplied bearing stress. Figure 8 (d) shows the

equivalent field stress, i.e., the applied bypassand the equivalent bypass due to the appliedbearing stress.

Once the spectrum of field stresses (as shown inFigure 8 (d)) is generated, an equivalent strainbased resolved stress is determined as explainedbelow:

Determination of resolved stress from the 2Dstress state

Once the stresses state shown in Figure 6 isconverted to a state containing only bypassstresses (shown in adjacent sketch), the threestresses x , y and xy can be resolved by thetransformation equations into stresses on a planeat (+90) degrees from x-axis.

y

x

xy

x

xy

y

Eq. (1) can be further transformed to give thebiaxial stresses on an element at angle .

'

(1)

(2)

(3)

(4)

Note that unless and are principal stresses,there will still be a shear stress present on the

element. However shear stresses do not (for smalldeformations) contribute to direct strain and soare ignored.

The direct strain in the direction of is

where = Poissons ratio

(5)




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(7)

(6)

This is the strain due to the biaxial system of stresses. Consider the same strain in a uniaxial stress field. A strain equivalent stress is given by

Substituting from eq. (3) and (4)

The fatigue RF is determined by following the below process.

Figure 9: Flowchart to Determine Fatigue RF

RAINFLOW COUNTING OF NORMALIZED SPECTRUM

MINERS RULE TO DETERMINE THE N

DETERMINE S% FROM SN CURVECORRESPONDING TO N

mean (1* DSO )S% N DETERMINE RF =

mean (1* DSO)COMPARE WITH AS SHOWN IN FIGUREE 7

FOR EACH , DETERMINE SPECTRUM OF AND NORMALIZE THESPECTRUM AS EXPLAINED EARLIER

REPEAT THEPROCEDURE FOR

= 0O

TO 180O

RF = Min (RF1, RF2, RF3,).Max Damage Angle = corresponding to RF

Illustrative Example

For example, consider a composite joint under astress state shown in the adjacent sketch.

Let us assume a composite to be made bystacking layers of lamina with a normalized curvefor field stresses as shown below in Figure 10.

For the given stress state, a strain equivalentstress can be determined for various values,for various 1g and incremental cases, so that a

spectrum of - for each is obtained.

y

x

xy




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Table 4:Illustration of the Process in Figure 9

* - All data presented in the table is for illustration purposes only In Table 4

Figure 10: Example Normalized SN Curve for the Material (mean(1*DSO) = 42%)

42%

Number of Cycles (N)

S ( %


t h )

1 0 0 0 0 0 0 C y c l e s ( D S O )

Post-processing the spectrum using the rainflow counting technique, the N can be determined correspondingto each - spectrum. Using the results of the rainflow counting and the normalized SN curves, the RF canbe determined for various values, as shown in Table 4 and Figure 11.

17000000 35.5 1.18

200000000 30 42 1.40

1000000000 27.7 1.52

N fromMiners Rule

EQ (S% fromSN Curve)

mean(1*DSO) (%)

RF Raw Data Post Processed UsingRainflow Counting Algorithm

-0-1 N0-1

N0-2

N0-3

N0-n

-0-2

-0-3

-0-n

-45-1

-45-2

-45-5

-45-n

-90-1

N45-n

N90-1

-90-2 N90-2

-90-3 N90-3

-90-n N90-n

N45-1

N45-2

N45-5

0

45

90

-

-

-

-

--

--

-

-

-

-




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Figure 10: Example Normalized SN Curve for the Material (mean(1*DSO) = 42%)

--n is the strain equivalent stress (eq. (7)) and N-n is the number of cycles at the corresponding stresslevel. This data is obtained by applying the Rainflow Counting algorithm to the normalized spectrum of thestrain equivalent stress corresponding to an angle of resolution .

N can be obtained after rainflow counting using the relation:

(8)

EQ for each value can be obtained from the SN Curve, as shown in Figure 11.

mean(1*DSO) = 42%, as shown in Figure 11

Number of Cycle (N)

S ( %


t h )

42%

35.5%

30%27.7%

1 0 0 0 0 0 0 C y c l e s ( D S O )

1 7 0 0 0 0 0 0 C y c l e s

2 0 0 0 0 0 0 0 0 C y c l e s

1 0 0 0 0 0 0 0 0 0 C y c l e s

As can be seen from Table 4, RF is minimum for = 0.Hence,Maximum damage angle = 0RF = 1.18

Limitations

This approach can only be applied in the presence of material specific normalized SN curves correspondingto the failure mode. It is imperative that a coupon test program is undertaken to develop the curves. The testprogram needs to be adequately extensive, and needs to include parametric studies to study the effects of laminate thickness, hole diameter, environmental conditioning etc., so that appropriate knockdown factorscould be used as and when applicable.

Certain assumptions are necessary if this approach has to be used for filled hole locations, such asdetermination of an equivalent bypass flow corresponding to a given bearing load. A complete understandingof the time history is a pre-requisite before the application of this methodology. Automation is necessary to

perform repetitive, time consuming calculations such as rainflow counting. This approach is applicable only for laminated composites, and cannot be used for sandwich structures.




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Scope for Future Work

A set of normalized SN curves can be developedfor the most commonly used laminae in aircrafts

for future references. Also, parametric studies canbe performed and knockdown factors can bedeveloped by generating SN curves usingcoupons of different diameters, and at variousenvironmental conditions.Similar methodologies can be developed for other commonly occurring failure modes in compositeaircraft structures, such as corner unfolding,buckling etc.

Another closely related topic to the fatiguebehavior of composite laminates is the residualstrength analysis of laminates, which has not beendiscussed in this paper. Further studies that will beable to relate the effect of mean static strength, thepredicted life from normalized SN curves and theresidual strength of laminates will be able toprovide a thorough understanding.

Conclusion

The high use of fastener joints, combined with theshift towards more composite structures in modernaircrafts demands an efficient way to quantify the

fastener locations for fatigue failure. Themethodology presented in this paper can be used

to determine fatigue reserve factors at fastener locations with minimum need for testing. Theapproach can also be suitably used for open holelocations such as penetrations and cut outs. Themaximum damage angle can also be determinedfrom this approach, and is a useful input during

joint design.

References:

1) http://www.appropedia.org/Composites_in_the Aircraft_Industry2) Laminate Statistical Allowable Generation for Fiber-Reinforced Composite Materials: LaminaVariability Method, U.S D.O.T, Jan 2009, TomblinJ., Seneviratne, W.3) European Approaches in Standard SpectrumDevelopment, Aalt A. ten Have, Development of Fatigue Loading Spectra, 1989




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Author Profile

Satya Iyengar is Chief Engineer, Airbus Wing andPylon Design Center at QuEST and is responsiblefor technical and quality standards of work done inthe Airbus ODC. He also provides technicalsupport to the planning and management of projects and work packages and ensuresimplementation of procedures within the QualityManagement System at the ODC.

Satya is also responsible for identifying andinitiating training on relevant subjects includingknowledge of Airbus tools, methods, andprocedures. He has worked extensively on avariety of GKN projects such as the A350 spar corner bending, rib post analysis, EA2, EA3, andEA4 projects, A400M inlet ducts, A400M detailedFEM, A380 FTE, and Concessions on A380, SA,LR aircrafts. Satya holds a B. S. degree in

Mechanical Engineering from BangaloreUniversity and an M. S. degree in MechanicalEngineering from the University Of Cincinnati

Email: [email protected]

Author Profile

Vinay Rao has been with QuEST for over twoyears now and works as a Lead Engineer at theGKN GDC India Center. He has spent his entirecareer in the Aerospace industry, mostly workingon composite materials and structures and hasadequate experience in structural stress analysisas well as coupon and sub-component levelcomposite material testing and qualification.

Vinay is a Mechanical Engineer by qualification,with a Bachelors degree from VTU, and aMasters degree (specializing in laminatedcomposites) from Wichita State University. Email: [email protected]




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Documents

Fatigue Analysis at Filled Hole Locations White Paper[1]