COMPUTATIONAL FRACTURE MECHANICS FOR COMPOSITES

STATE OF THE ART AND CHALLENGES

Ronald KruegerNIA - Senior Staff Scientist

CAA/FAA Workshop on Adhesive Bonding, Gatwick, UK, October 2004

ACKNOWLEDGEMENTS

T. Kevin O’Brien, ARL/VTD at NASA LaRCJames Reeder, NASA LaRCIsabelle Paris, Composites Innovations Inc. - MontrealJames Ratcliffe, NRC at NASA LaRCPierre Minguet, The Boeing Company - PhiladelphiaD.M. Hoyt, NSE Composite, SeattleGerald Mabson, The Boeing Company - SeattleJeff Schaff, Sikorsky AircraftCatherine Ferrie, Bell Helicopter Textron Inc. - Fort WorthLarry Ilcewicz, FAA - SeattleCurtis Davies, FAA - Atlantic City

OUTLINE

• Delamination sources at geometric and material discontinuities• History of skin-stiffener debonding testing and analysis

• Fracture mechanics methodology for delamination onset prediction• Experiments to determine fracture toughness• Finite element analysis to compute mixed-mode energy release rate

• Past studies on skin/stringer debonding• A shell/3D modeling technique• Application of Fracture Mechanics Methodology

• Summary

• Outlook

• Summary of FAA/ASTM D30 Workshop

• Remaining challenges

DELAMINATION SOURCES AT GEOMETRIC AND MATERIAL DISCONTINUITIES

Skin stiffener interaction

Corner

Solid-sandwich transition

Internal ply drop

Straight free edgeExternal ply drop

InterlaminarStresses

τxz

σzz

HISTORY OF SKIN/STIFFENER DEBONDING PRESSURIZED COMPOSITE FUSELAGE

• Composite Fuselage Technology Development*

Crown panelframe bonded onto skin to

reduce manufacturing costs

Out-of-plane loading dueto pressurization

deformed shape

*L.B. Ilcewicz, Composite Technology Development for Commercial Airframe Structures

HISTORY OF SKIN/STIFFENER DEBONDING POST-BUCKLED THIN-SKIN ROTORCRAFT FUSELAGE

Post-buckling behavior drives weight in thin-skin rotorcraft fuselage

Buckling generates severe stresses on the bondline between skin and stiffeners

Composite fuselage stiffened skin*

V-22 Osprey Tiltrotor aircraft

*Pierre Minguet, Boeing

HISTORY OF SKIN/STIFFENER DEBONDING POST-BUCKLED THIN-SKIN ROTORCRAFT FUSELAGE

Testing of Stiffened Shear Panel Debonding MechanismBoeing, Philadelphia*

Qxy

Mxx

N xx

Failure initiation

SkinFlange

Bondline

Frame or stiffener

Tip of flange

Simplified Specimen

Skin

Stiffener flange

*Pierre Minguet, Boeing

CURRENTLY USED FAILURE METHODOLOGIES

• Stress-Based Failure Criteria• Damage Mechanics

– Decohesion element (interface elements) Carlos Davila, Pedro Camanho, to be implemented in ABAQUS 6.5 released in December 2004

• Linear Elastic Fracture Mechanics– Captures discontinuity of interlaminar disbonds or delaminations– Stress singularities not an issue– Characteristic material data can be generated using simple specimens

and tests

FRACTURE MECHANICS METHODOLOGY

Energy Release Rate

crack opening in plane shear tearingmode I mode II mode III

Failure occurs if local mixed mode energy release rate exceeds a critical value !

G=GI+GII+GIII

G =

dWdA

−dUdA

EXPERIMENTS TO DETERMINE FRACTURE TOUGHNESS

Mode I - DCB Specimen

• ASTM D5528 - static• ASTM D6615 - fatigue

crack openingmode I

Mode II - 4ENF Specimen*

• Standard in development

in plane shear mode II

*Rod Martin, MERL - Barry Davidson, Syracuse University

EXPERIMENTS TO DETERMINE FRACTURE TOUGHNESS - continued

Mixed Mode I/II - MMB Specimen*

+

crack opening + in plane shear mode I mode II

• ASTM D6671

*James Reeder, NASA Langley Research Center

2D MIXED MODE FRACTURE CRITERION IS STATE OF THE ART

0 0.2 0.4 0.6 0.8 1Mixed Mode Ratio GII/GT

GC,

J/m2

DCB, Mode I 4ENF, Mode IIMMB, Mode I and II

curve fit

3D MIXED MODE FRACTURE CRITERION IS MISSING TODAY

0

GIII/GT

GIIIc

1.0

GII/GT

GIIc

1.0

GIc

GT

Mode III - ECT Specimen* Failure surface Gc =Gc(GIc, GIIc, GIIIc)**

tearingmode III

• Standard in development*James Ratcliffe,NRC at NASA Langley Research Center **James Reeder, NASA Langley Research Center

STATUS OF FRACTURE TOUGHNESS TESTINGFATIGUE ONSET VALUES

0

50

100

150

200

250

300

350

400

100 101 102 103 104 105 106 107

GImax, J/m2

N, cycles to delamination onset

DCB fatigue datacurve fit to datacurve fit ± one standard deviation

Fatigue Delamination Onset in S2/E7T1 DCB Specimens

GImax=cNd

ASTM Standard D6115

Isabelle Paris, Composites Innovations Inc. - Montreal

Kevin O’Brien, ARL/VTD at NASA LaRC

STATUS OF FRACTURE TOUGHNESS TESTINGFATIGUE PROPAGATION VALUES

Proposed Fatigue Delamination Growth Characterization: Normalizing by the Static R-Curve*

GR a

aStatic delamination R-curve

N

da/dN

dadN

= AGmax a( )GR a( )

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

n

Gmax/GR*Isabelle Paris, Kevin O’Brien, Rod Martin

ANALYSIS TOOLSOVERVIEW

Analytical Closed Form Solutions for Simple ConfigurationsEdge delamination - Kevin O’Brien

SUBLAM– Georgia Tech, Erian Armanios

– Developed by Material Science Corporation under SBIR contract with the FAA for use with General Aviation bonded joints - Gerald Flanagan

– Can be used to calculate SERR as a function of disbond length

Single-Step SERR Calculation

Bonded Joint Crack Propagation

Co-Cured Structural Elements Curved Beam

Shear Loading Tapered Elements

Closed-form solutions for complex geometries

z

Concentrated lineforce T3

Distributedtractions p(y)

w+

w-

1

2

y, n

ANALYSIS TOOLSOVERVIEW - continued

“Crack Tip Element” - Barry Davidson – Closed-form linear-elastic solution aimed at overcoming computational

difficulties in determining strain energy release rate and mode mix.– Obviates need for locally detailed 2D and 3D FEMs– Limited to linear analysis

Post-buckled delaminations

ANALYSIS TOOLSVIRTUAL CRACK CLOSURE TECHNIQUE (VCCT)

Virtual Crack Closure Technique (VCCT)– Two and three-dimensional analysis

– Nonlinear analysis

– Arbitrarily shaped delamination front

GI = 12∆a

⋅ ′ Y ⋅ ∆ ′ v

GII = 12∆a

⋅ ′ X ⋅ ∆ ′ u

GT = GI + GII

∆a∆a

∆v’∆u’

Y’

X’

y’ ,v’,Y’

x’ ,u’,X’

undeformed outline

deformed elements

ANALYSIS TOOLSBoeing 2D VCCT Interface Element - Formulation

• Interface Element for Mixed Mode Fracture Analysis*

Fv,2,5 crit

Node numbers are shown

t=0

6 5 4

1 2 3

dL dR

x,u

y,v

• Node pair 2,5 are initially bound together• Node pairs 1,6 and 3,4 are unconstrained

and act to sense approaching crack

Nodes 2 and 5 will start to release when:12

v1,6Fv,2,5bdL

= GI ≥ GIC

GI = mode I energy release rateGIC = Critical mode I energy release rate

Mode II treatedsimilarly

Fv,2,5

LoadPure Mode I

V2,5 crit

V2,5

Area = GICdRbModified VCCT

2,5 3,46

v1,6

1 Displacement

x,u

y,vNode numbersare shown

* G. Mabson, Boeing, Patent Pending

ANALYSIS TOOLSBoeing 2D VCCT Interface Element - Propagation

• Fracture Interface Elements Along Crack Plane*

• By using a series of overlapping interface elements, delaminations can be propagated along a predefined path.

• Direction of propagation is not pre-specified.

• Propagation is integral part of the analysis.

• 3D VCCT interface element for delamination available.

• ABAQUS implementation expected for December 2004.

Fracture mechanics interfaceelements control growth ofdelamination into new material

Interface Elements locatedalong plane of delamination

* G. Mabson, Boeing, Patent Pending