Oct 2008Slide 1

4TH INTERNATIONAL CONFERENCE OF COMPOSITES TESTING & MODEL IDENTIFICATION

Dayton, Ohio, USA October 20, 2008

Gerald E. MabsonTechnical Fellow

The Boeing Company

FRACTURE ANALYSIS FOR BONDLINES AND INTERFACES OF COMPOSITE STRUCTURES

Oct 2008Slide 2

Presentation Format

• Introduction• Static 2D interface element• Static 3D interface element• Interlaminar fatigue element• Calibration testing• Summary

Oct 2008Slide 3

Problem Statement

• To reduce the cost of laminated composite structures, large integrated bonded structures are being considered– In primary structures, bondlines and

interfaces between plies are required to carry interlaminar loads

– Damage tolerance requirements dictate that bondlines and interfaces carry required loads with damage

Oct 2008Slide 4

Solution Path

• Apply Linear Elastic Fracture Mechanics (LEFM) to bondlines and interfaces– 2D and 3D delaminations– Propagation– Mode separation– Multiple cracks– Non-linear behavior (e.g. postbuckling)– Composite structure– Practical (CPU time, minimum set of models)– Static and dynamic solution applicability

Oct 2008Slide 5 11/6/2008

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Boeing 787Composites Serve as Primary Structural Material

Composites50%

Aluminum20%

Titanium15%

Steel10%

Other5%

Carbon laminateCarbon sandwichOther compositesAluminumTitaniumTitanium/steel/aluminum

Boeing 787

Oct 2008Slide 6

787 Section 41

Oct 2008Slide 7

787 Section 43

Completing Drill & Trim

Oct 2008Slide 8

787 Sections 47/48

Oct 2008Slide 9

787 Section 41

Fatigue Test Airplane Component

Oct 2008Slide 10

787 Final Assembly

Oct 2008Slide 11 11/6/2008

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Wing

Oct 2008Slide 12 11/6/2008

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Wing-to-Body Join

Oct 2008Slide 13

Structural Analysis and Certification ApproachCertified by analysis, supported by test evidence

Oct 2008Slide 14

Advances in Analysis Methods Applied to 787

Extensive use of bonded structures in applications with out of plane loading (pressure, postbuckling)– Direct use of interlaminar

fracture mechanics for bond lines and interfaces

• Extensive use of non linear finite element analysis in preliminary and detailed design

Oct 2008Slide 15

Structural TestSkin and Stringer Elements

Post Buckling

Visible Impact Damage

Compression

Large Damage

Tension

Compression

Shear

Freeze-Thaw

Large Notch Y-Factor

Tension

Oct 2008Slide 16

Presentation Format

• Introduction• Static 2D interface element• Static 3D interface element• Interlaminar fatigue element• Calibration testing• Summary

Oct 2008Slide 17

2D Interface Element Usage

Patent pending

Fracture mechanics interface elements control growth of delamination into new material

Interface elements located along plane of delamination

By using a series of overlapping interface elements, delaminations can be propagated along a path in either direction.

Direction of propagation is not pre specified.

Oct 2008Slide 18

Interface Element for Mixed Mode Fracture Analysis

δ=0

6 5 4

1 2 3

dL dR

Element node numbers are shown

x,u

y,v

Patent pending

• Nodes 2 and 5 are initially bound together (stiffness is virtually infinite)

• Stiffness between all other nodes is zero

• Antennae node pairs 1,6 and 3,4 sense approaching crack, provide displacement and area in VCCT calculation.

• Constrained node pair 2,5 provide force inVCCT calculation, initiate release and follow strain softening law based on fracture energy calculation.

Oct 2008Slide 19

Modified Virtual Crack Closure (VCCT) Implementation

2,5 3,46

v1,6

1

x,u

y,vElement node numbers are shown

6 and 1 nodesbetween nt displaceme Vertical5 and 2 nodesbetween force Vertical

widthrate releaseenergy I mode Critical

rate releaseenergy I mode where21

: whenrelease start to will5 and 2 Nodes

6,1

5,2,

25,2,6,1

=

====

≥=

vFbGG

GGbd

dFv

v

IC

I

ICIL

Rv

Fv,2,5

Fv,2,5 crit

V2,5 crit

V2,5

bdGArea RIC=

Mode II treated similarly

For Pure Mode I

Patent pending

Oct 2008Slide 20

2D Interlaminar Fracture Elements - Propagation

By using a series of interface elements, delaminations can be propagated along a plane in either direction.

Patent pending

Oct 2008Slide 21

Mixed Mode Fracture Criteria

IIICIICIC

p

IIIC

III

n

IIC

II

m

IC

I

G,G,Gp,m, n,

GG

GG

GG

:parameters specifieduser

npropagatiocrack for ,1≥⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

Other mode mix equation forms have been easily incorporated

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1

Mode Mix, (GII+GIII)/GT

GTC

Oct 2008Slide 22

Fracture Interface Element Advantages

• Initiation of node release based on fracture– Unlike cohesive failure models

• Relatively mesh size independent– Unlike direct techniques based on local displacement or

stress fields

• Intermediate crack tip location– Typically not available when VCCT applied manually

• Mode separation• Remeshing not necessary

– Assumed crack interface, not crack direction

Oct 2008Slide 23

Double Cantilever Beam (DCB) Analysis Comparison

Oct 2008Slide 24

Non-Symmetric Multi-Delamination Analysis

10 layers

12 layers2 layers

Interface elementsInitial cracks

a1

a2

a2

L

From Alfano and Crisfield 2001

E11 = 115.0 GPaE22 = 8.5 GPaE33 = 8.5 GPaG12 = 4.5 Gpaν12 = 0.29ν13 = 0.29ν23 = 0.3

Gc1 = 0.33 N/mmGc2 = 0.80 N/mm

L = 100 mma1 = 40 mma2 = 40 mmwidth = 20 mmLayer thickness=0.1325 mm

Oct 2008Slide 25

Multi-Delamination Analysis Results

Oct 2008Slide 26

Non-Symmetric Multi-Delamination- Comparison with Test and Analyses

0. 5. 10. 15. 20. 25.

60.

50.

40.

30.

20.

10.

0.

Force (N)

Displacement (mm)

Data from Alfano and Crisfield 2001

Fracture Interface Element Model Prediction

Oct 2008Slide 27

Presentation Format

• Introduction• Static 2D interface element• Static 3D interface element• Interlaminar fatigue element• Calibration testing• Summary

Oct 2008Slide 28

18-noded 3D Interface Element for Composite Delamination Modeling

Practical application of VCCTNo remeshing of FE model

• Finite size delaminations• Unreinforced interface fracture

Patent pending

Oct 2008Slide 29

Crack Front with 3D FractureInterface Elements

A. Manual Crack FrontInterrogation

B. Interface Element Automatic Crack Front Interrogation

Connected Nodes

Disconnected NodesZero residual force

Connected Nodes

Disconnected NodesZero residual force

Disconnected NodesResidual force

Fv,2,5

Fv,2,5 crit

V2,5 crit

V2,5

bdGArea RIC=

Displacement

Load

Release force calculated bymixed-mode modified VCCT (Not stress based!)

Patent pending

Oct 2008Slide 30

Finite Width DCB Analysis – Straight Initial Crack Front

Oct 2008Slide 31

Full Width Disbond 1/2” Square Finite Sized Disbond

PPFull widthnoodle radiusdisbond

1/2” squarenoodle radiusdisbond

• Light gauged bonded stiffener design• Narrow span Tpull test to interrogate noodle region• Complex progression of failure observed in test• Comparison of test and analysis results• Modeled using 3D fracture interface element• Full width disbond case modeled using 2D interface element

Noodle Radius Disbond Analysis

Oct 2008Slide 32

Noodle Radius Disbond Analysis½” Square Disbond Animation

Oct 2008Slide 33

Noodle Radius Disbond AnalysisOnset of Disbond Growth from ½” Square

Disbond

CriticalLocation

CriticalLocation

Oct 2008Slide 34

Delamination Analysis of Bonded Stiffener Termination

Load-path eccentricity causes delamination

Oct 2008Slide 35

Bonded Stiffener Separation CausedBy Approaching Through Penetration

Heavy Gauge Stiffeners

Oct 2008Slide 36

Presentation Format

• Introduction• Static 2D interface element• Static 3D interface element• Interlaminar fatigue element• Calibration testing• Summary

Oct 2008Slide 37

Interlaminar Fatigue Problem

Oct 2008Slide 38

Interlaminar Fatigue Element

• VCCT-based interface element contains functionality necessary for a progressive interlaminar fatigue element.

• Three fatigue analysis approaches– Short growth based on Paris Law Growth and total G– Short growth based on mixed-mode Paris Law– Onset of growth based on measured 5% growth in

DCBs and a crack tip Energy Release Rate, G.

Oct 2008Slide 39

Paris Law Fatigue Growth

thresholdfatigue at the rate openingCrack

regime Paris theof end

upper at the )( rate openingCrack

rate releaseenergy thresholdFatigue

limit”) “Paris torefers :(Note regime Paris theoflimit upper defining

II and I modein rates releaseEnergy ,

=

=

=

=

thresh

pl

thresh

IIplIpl

da/dN

G

pl

GG

λ

λ

( )

Cthreshold GGGG

GcdNdaGc

dNda

<>

Δ⋅=⋅=

and where

or maxββ

or

for

Oct 2008Slide 40

Simplified 2D Interlaminar Fatigue Element

Implemented as ABAQUS UEL

)( jMIN dnMINN =

( )j

ijaccumjj dn

dadaxdn ⎟⎠⎞

⎜⎝⎛−Δ= −1

_

Gj for all activeinterface elements Δa/ΔN vs. (Gmax)tot

When Gth < Gj < GParis Limit

Cycles to failure each element

Find minimum cycles to fail

Next ABAQUS increment

“Master Element” does bookkeeping for all elements

At least one element release per increment

( )βjoj

GCdnda

=⎟⎠⎞

⎜⎝⎛

at element k

( )j

MINi

jaccumi

jaccum dndaNdada ⎟

⎠⎞

⎜⎝⎛⋅+= −1

__

Accumulate damage

iMIN

iTotal

iTotal NNN += −1

Release element kCount cycles

j = element indexi = increment number

( )βGCdnda

o Δ=⎟⎠⎞

⎜⎝⎛

( )βMaxo GCdnda

=⎟⎠⎞

⎜⎝⎛

or

Δx

Oct 2008Slide 41

2D Fatigue in DCBUser Defined Load Step History

Load = Pmax = constantAssume Linearity, R = Pmin/Pmax

Fatigue growth step1 inc. = 1 node release

Pmax

Oct 2008Slide 42

Interlaminar Fatigue Analysis

Fine Mesh DCB

Coarse Mesh DCB

FE Models Used in Development

Oct 2008Slide 43

2D Fatigue Element in DCB ModelParis Law Growth

Given Paris Law and for a DCB, ( )βGcdNda

Δ⋅= ( )EIBPaG

2

≈

( ) ( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅

−⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ=

−

121

21

2

ββ

β o

o

o aa

ca

PaEIBNthen

Oct 2008Slide 44

Single Leg Bend Model andMixed Mode Paris Law

5% Compliance Change = 0.24” of growth

160 lbf

Pfatigue = 160 lbf Pcrit(static) = 237 lbfN5% ~ 380,000 cyclesPcrit / Pfatigue = 1.48

Oct 2008Slide 45

Presentation Format

• Introduction• Static 2D interface element• Static 3D interface element• Interlaminar fatigue element• Calibration testing• Summary

Oct 2008Slide 46

Structural Analysis and Certification ApproachCertified by analysis, supported by test evidence

Oct 2008Slide 47

Fracture Mechanics - Crack Loading Modes

•Crack propagation modes

Oct 2008Slide 48

Mixed Mode Fracture Criteria

IIICIICIC

p

IIIC

III

n

IIC

II

m

IC

I

G,G,Gp,m, n,

GG

GG

GG

:parameters specifieduser

1

:npropagatiocrack For

≥⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1

Mode Mix, (GII+GIII)/GT

GTC

IIICIICIC

n

T

IIIII

T

II

T

IIIIC

T

IIIIC

T

IIIIIICICTC

TCT

GGGn

GGG

GG

GGG

GGG

GGGGG

GG

,,,:parameters defineduser

where,n propagatiocrack For 1−

⎟⎟⎠

⎞⎜⎜⎝

⎛ +⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+−++=

≥

Traditional Interaction BKR Interaction

Oct 2008Slide 49

Fracture Calibration Tests Material Property Test Standards

ASTM Standards- existing

D5528 Static DCB (also ISO standard)

D6115 Fatigue Onset DCBD6671 Static Mixed mode

-in workMode II static (3ENF)Mode III staticMode I fatigue propagationMode II fatigue onsetMode III fatigue onset

Double Cantilever Beam(DCB) Coupon, Mode I

End Notch Flexure(ENF) Coupon, Mode II

GIC

GIIC

Oct 2008Slide 50

Double Cantilever Beam Test

Oct 2008Slide 51

Functionality Check FEM vs Theory Unreinforced DCB Coupon

Oct 2008Slide 52

End Notch Flexure Test

Oct 2008Slide 53

Functionality Check FEM vs TheoryENF Coupon

Including Unstable to Stable Transition

Oct 2008Slide 54

Delamination Length Effects on Apparent GC

G1c

GIC_ss

GIC

Delamination Length, a

Ply Bridging (R-curve)

Tow bridging in 0-degree fabric layup creates steady-state “process zone”

No significant process zone

GIC_ss = GIC

GIC and GIC_ss Defined (Mode I)

Similar definitions for Mode IIGIIC and GIIC_ss Defined

Oct 2008Slide 55

Presentation Format

• Introduction• Static 2D interface element• Static 3D interface element• Interlaminar fatigue element• Calibration testing• Summary

Oct 2008Slide 56

Summary - Static

• 2D and 3D static fracture interface elements have been developed

• Multiple crack tips/fronts can be modeled simultaneously

• Strength based initiation capability is available for 2D and 3D fracture interface elements

• This technology is available in Abaqus Standard.

Oct 2008Slide 57

Summary - Fatigue

• VCCT-based elements provide excellent platform to implement automatic interlaminar fatigue analysis based on Paris Law

• 2D Progressive crack growth in FE models is numerically stable

• Better results for fine mesh due to energy release rate calculated at beginning of node release.

• Error if mode mix not considered

Oct 2008Slide 58

Future Enhancements - Analysis

• Crack branching• Improve efficiency and stability• Application to explicit finite element

formulation

• Routine analysis of multiple delaminations (barely visible impact damage)

Oct 2008Slide 59

Future Enhancements - Testing

• Need industry standard methods for both static and fatigue– Mode II, mode III, mixed mode

• Practical in service NDI for delaminations

Oct 2008Slide 60

Acknowledgements

• Composite Affordability Initiative Program• 787 Program

• Lyle Deobald• Bernhard Dopker• NSE Composites• Al Miller

Oct 2008Slide 61 11/6/2008

Filename.ppt | 61

Thank you