computational fracture mechanics for compositesoutline • delamination sources at geometric and...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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