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Cohesive Solutions for Structural Integrity and Fatigue Life Prediction
University of Bristol, 12 March 2019
Carlos G. Dávila
Durability, Damage Tolerance, and Reliability BranchNASA Langley Research CenterHampton VAUSA
NASA Advanced Composites Program
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Advanced Composites Project (ACP)Postbuckled Panel with BVID, Strength and Life
2
The NASA ACP seeks to reduce the
timeline required for development
and certification of new aircraft.
High fidelity analysis methods can
reduce the testing requirements of
primary aircraft structures.
A compression-loaded skin-stringer
panel was selected as the basis of
method validation.
Technical Challenge 1:
Accurate Strength and Life Prediction
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Building Block: Compression-Loaded Skin-Stringer Panel
3
Material properties
Characterization of material properties based on “first principles”
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Seven Point Bend Test Results
UT scan Analysis
• Can skin/stiffener be modeled with a single interface?
4
Shell/cohesive model
• Quasi-static• Fatigue
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Simplified Shell Model of 3PB Specimen
Predicted
Test
Interface law w/ bridge
Interface law – nominal tape/tape
Bridge
d
s
Shell Model
Crack initiation
Propagation
Peak load
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Simplified Shell Model of 3PB Specimen
Interface law w/ bridge
Interface law – nominal tape/tape
Bridge
d
s
Shell Model
Base Bridge
Gic = 0.24 0.600 N/mm
GIIc = 0.739 3.500 N/mm
Sigc = 90 3.45 Mpa
Tauc = 93 10.34 Mpa
KI = 5E+05 1.8E+04 N/mm3
Ksh = 1.6E+05 3.0E+04 N/mm3
BK = 2.07 3
Computed (Turon’s constraint)
Standard (initiation) Calibrated (propagation)
x3.5
Gc_ss/Gc_init
x 5.7
Bridging strengths
Bridging toughness
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Global-Local Analysis of Large Structures
Example: design of hat-stiffened panel
Approach
Use Abaqus SUBMODELING approach to drive local model from global displacements
Investigate effects of flange termination on stiffener debonding of postbuckled panel
Square flange
terminationTapered flange
termination
Global
modelLocal models
Cohesive
layer
Skin Skin
Tapered flangeAbrupt flange termination
Issue:Design Options
7
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Global-Local Analysis of Large Structures
Critical disbond location identified by performing axial sweep of flange.
Local model out-of-plane deformation Local model disbond
Global model out-of-plane
deformation
Left flange of
stringer examined
with local models
Critical location identified
by local model
8
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Fatigue
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Fatigue Propagation Rate Using the Paris Law
10
Murri, NASA/TM–2013-217966
( )max
d
d
maC G
N=
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Turon Fatigue Cohesive Model
11
( )( )2
1d 1 d
d d
f c
f c
pz
d dd a
N l N
− + =
Turon Fatigue Damage Law
( )max
d
d
maC G
N=
• Both Gmax and lpz are global quantities that are difficult to extract from the integration points.
• The damage rate is “non-local,” and its implementation is difficult.• The Paris law does not apply to short cracks
However:
(Composites A, 2006)
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S-N or Paris Law?
12
S-N Curve Paris Law
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S-N or Paris Law?
13
S-N Curve Paris Law
S-N Curve and Paris law are related
Can we develop a cohesive model based on S-N that can predict crack propagation?
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Cohesive Fatigue Damage Model
14
Consider case of bar subjected to cyclic load
Assume cohesive law is envelope of fatigue damage
What damage law?
F
Time
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Cohesive Fatigue Damage Model
15
( )*
d
d
DD
N
= +
* c
f cD
− =
−
( )max
0
1d
FDf c
DN D
D
−−
= +
Number of cycles to failure obtained by integrating dN from A to B
A B
S-N curve
Consider damage law:
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S-N Curve Corresponding to Damage Model
16
( )max
0
1d
FDf c
DN D
D
−−
= +
Damage model entirely defined by parameters and
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S-N Diagram for Delamination
17
• A single line appears to fit the S-N curve from N = 1 to 107
• The parameters and of the damage model can be obtained by fitting experimental results
R = min/ max = 0.1
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Endurance limit vs. tensile strength (R = -1)
18
[Chart generated with CES Edupack, GrantaDesign, S. Gorsse]
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Goodman Diagram (GD)
19
e
c
mean
amp
0
R = −1
R = 1
R = 0.5R = 0 1
meanamp
e
c
= −
1
2
eR
c R
=
−
The GD is design tool that represents the locus of stress states corresponding to a runout stress or a given number of cycles to failure
R = min/ max
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S-N curves for Different R Ratios
20
2
ceR
R
=
−2 cycles
Test data for R = 0.1
S-N curves are “anchored” at two points
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Determination of Model Coefficients and
21
Experimental S-N data desirable but not needed to determine and
( )*
d
d
DD
N
= +
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Flowchart of UMAT
22
Fatigue model was implemented as a UMAT user-written material subroutine for Abaqus cohesive elements
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Analysis of Double Cantilever Beam Specimen (DCB)
23
Applied load remains constant
Detail of propagation zone
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Propagation Rates for DCB Specimen
24
Test: Murri, NASA/TM–2013-217966
Analyses of DCB were conducted with 4 different applied loads (displacement control)
R = 0.1
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R-Curve Effect on DCB Specimen
25
Test: Murri, NASA/TM–2013-217966
R-curve
Quasi-static response of DCB using superposition of bridging laws
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Delamination Propagation Rates for DCB with R-Curve
26
Predicted delamination growth rates in a DCB specimen for several values of applied displacement (red) and applied force (green).
R = 0.1
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Delamination Propagation Rates for DCB with R-Curve
27
Predicted delamination growth rates in a DCB specimen for several values of applied displacement (red) and applied force (green).
R = 0.1
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Delamination Propagation Rates for DCB with R-Curve
28
Predicted delamination growth rates in a DCB specimen for several values of applied displacement (red) and applied force (green).
R = 0.1
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Delamination Propagation Rates for DCB with R-Curve
29
Comparison of predicted delamination growth rates with R-curve bridging included with experimental results
R = 0.1
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MMB – Delamination Propagation Rate
30
Test: Ratcliffe, 2014
MMB tests and analyses conducted under force control
Mode ratio = 0.5
R = 0.1
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Effect of Stress Ratio R on Propagation Rates
31
( )* 1
d
d
m R
R
a GC
N G
−
=
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Effect of Stress Ratio R on Propagation Rates
32
( )* 1
d
d
m R
R
a GC
N G
−
=
( )* 1m m R
= −
( )*
d
d
DD
N
= +
Present model
Allegri Model (2012)
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Comparison with Allegri Model
33
( )*
d
d
DD
N
= +
Damage Model Allegri Model (2012)
S-N law
( )( )( )
1max
1
0
1d
1
FDf
c
N D
D D
−
=
− +
( )
( )
maxd
d 1 c
DD
N D
+ =
−
or,
( )1
b
R
=−
Paris Law
2m
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Fatigue: Three Point Bend (3PB) Specimen
Skin/stiffener separation
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3PB: Delamination Length vs. Cycle Count
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Progression of cracks and delaminations in a 3PB specimen
Increasing load
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Simplified Model of 3PB Specimen
37
Symmetric model Sigc = 90 MPaMesh: 0.072 mm
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Concluding Remarks
38
Fatigue Cohesive Constitutive Model:• Based on S-N curve rather than Paris law.• Relies on relationships between S-N and Paris.• Simplified loading procedure keeps load constant during analysis.• Fatigue Model Parameters Obtained Without Test Data.
R-Curve Effects Modeled Using Cohesive Superposition• R-curve effect explains differences between load control and
displacement control.• R-curve is intended to capture effect of blunting, delving,
bridging, and migrations.
Initial Evaluation Conducted on 3PB Specimens• Extreme nonlinearity in results highlights the difficulty in
predicting fatigue.
• Additional work needed to confirm that the model can predict the propagation rates for different materials and loading conditions.