1
Carlos G. DávilaDurability, Damage Tolerance, and Reliability Branch
NASA Langley Research CenterHampton, VA
The Long Road to Virtual Testing of Composite Structures
– Are we there yet? –
University of Bristol, UK
March 11, 2019
Analysis
Test
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Virtual Testing of Composite Structures
– Why? –
Mathematical Methods and Models in Composites V. Mantic (Ed.)
3
Wing Trouble: Skin/Stiffener Delamination (2009)
Delamination
Compression
TensionWing box
Rib
Wing loading
Wing loads cause high shear stresses and delamination at the upper stiffener termination.
Citing a “manageable” structural
issue, Boeing postponed the first
flight of the 787, saying it will be
several weeks before a new
schedule is released. This is the
fifth delay of Boeing’s fast-
selling, mostly composite
Dreamliner, which already is
nearly two years behind schedule.
Boeing shares plummeted in early
trading, dropping 8.6 percent just
before 8 a.m., PST.
www.heraldnet.com/news/boeing-postpones...
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Rolls-Royce RB211 Hyfil Blade Failure (1970)
5
NASA X-33 - Matrix Cracking and Delamination (1999)
Tank failed during testing. X-33 Program cancelled by NASA
X-33
RLV
Cryopumping in sandwich core
Internal pressure, P
Gas expands
Facesheet Delamination
Matrix cracks provide
primary leakage path
in composite tanks
Transverse matrix crack
Leakage pathP
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New Paradigm Shift in Materials and Structures
New technologies have blurred the boundary between what is considered a material and what is a structure.
Materials are not necessarily “homogeneous continua”.
• Engineer better materials
• Utilize advanced materials more effectivelyGoals:
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Three Pillars of Mechanics of Materials
“Advanced materials are essential to economic security and human well being…”
Materials Genome Initiative
• Revolutionary manufacturing capabilities
• New technologies for experimental observation
• Computational tools for nonlinear analysis
Enabling Technologies:
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Nonlinear Computational Tools for the Analysis of Damage
Nonlinear fracture mechanics in finite element analysis
Extended finite elements (X-FEM)
Low velocity impact (C.Lopes, 2015)
Carbon nanotube (V. Yamakov, 2015)
Compact Tension Specimen (C. Dávila, 2015)
Molecular dynamics simulations (MD)
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Scales of Damage in Composites
“Physics” of failure:• At each scale, damage is described by different physical observations
Matrixcrack
Delamination
Matrixcrack
Fiberkink
-45
0
Structure Microstructure
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Issues of Scale
1. Structural complexity and Building Block Approach
2. Level of physics (selected idealization)
3. Size effect (change in strength w/ specimen dimensions)
“Scaling is the most important aspect of every physical theory”
(Z. Bažant)
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1. Structural Complexity and Building Block Approach
Building Block Integration
Verification of Design
Data and Methodology
Development of Design
Data
Number of Specimens
Chro
no
logic
al S
equ
en
ce
Sp
ecim
en
Co
mp
lexity
Certification Methodology (CMH-17)
Levels of Structural Testing & Analysis
Static/
Fatigue
Material Selection and Qualifications Coupons
Design Allowables Coupons
Structural Elements
Sub-components
Full Scale
Article
• More accurate design tools reduced recurring costs
• Reduced reliance on testing
• Faster design processreduced non-recurring costs
An
alys
is
•High-fidelity Progressive Damage Analysis
Components
Coupon
Full Scale
Sub-component
Component
Sub-element
Element
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2. Idealization of Damage – Level of Physics
Structural Mesoscale (CDM)
Mesoscale (CDM+Discrete)
Micro-Mechanical
Molecular Dynamics
Increasing Material “Predictability”
Increasing Complexity of Material Characterization
Increasing Numerical Complexity
Decreasing Scale of Idealization
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3. Scaling Laws for Strength
Galileo, 1638
da Vinci, 1505
• Strength of Materials
• Material strength
• Cross-section
• Length (?)
The strength of a rope depends on:
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Cracks
Aloha airlines accident (1988)
Liberty Ship accidents (1943): cold brittleness of welded joint
Multi-site damage (MSD)
Broken wheel rim (1876)
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Scaling Laws for Cracks
• Fracture Mechanics (Griffith, 1921; Irwin, 1946) • Weakness is due to the presence of flaws
a
GE cu
=
“a flaw becomes unstable when the strain
energy change that results from an increment
of crack growth is sufficient to overcome the
surface energy of the material”
• Energy Criterion (LEFM)
• Energy Release Rate
dA
dG
−=
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3. Scaling: the Effect of Structure Size on Strength
(Galileo, 1638)(da Vinci, 1505)
Strength of Materials
Fracture Mechanics (Griffith, 1921)
“weakness is due to the
presence of flaws”
a
GE cu
=
(da Vinci, 1505; Mariotte, 1686; Weibull, 1939)Statistical Theory of Size Effect
“weakest-link hypothesis”md
u L /−
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Scaling: the Effect of Structure Size on Strength
Strength or Fracture?
Testing strength of granite block
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Scaling: the Effect of Structure Size on Strength
Scaling from test coupon to structure
Structural size, in.
Yield or Strength Criteria
Linear Elastic
Fracture
Mechanics
log n
log D
(Z. Bažant)
Scaling Laws
Normal testing
a
GE cn
=
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Influence of on My Understanding of Composites
• Wisnom, M. R. (1991). The effect of specimen size on the bending strength
of unidirectional carbon fibre-epoxy. Composite Structures, 18(1), 47-63.
• Wisnom, M. R. (1992). On the increase in fracture energy with thickness in
delamination of unidirectional glass fibre-epoxy with cut central plies. Journal
of reinforced plastics and composites, 11(8), 897-909.
• Wisnom, M. R. (1991, April). Delamination in tapered unidirectional glass
fibre-epoxy under static tension loading. In 32nd Structures, Structural
Dynamics, and Materials Conference (p. 1142).
• Hallett, S. R., Jiang, W.-G., Khan, B., and Wisnom, M. R., "Modelling the
Interaction between Matrix Cracks and Delamination Damage in Scaled
Quasi-Isotropic Specimens," Composites Science and Technology, Vol. 68,
No. 1, 2008, pp. 80-89.
• Hallett, S. R., Green, B. G., Jiang, W. G., and Wisnom, M. R., "An
Experimental and Numerical Investigation into the Damage Mechanisms in
Notched Composites," Composites Part A: Applied Science and
Manufacturing, Vol. 40, No. 5, 2009, pp. 613-624.
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Damage Length Scales in Structural Materials
Strength versus toughness:• Strength and toughness are the result of the interplay between a number of individual
mechanisms originating at different length scales.
• Some damage mechanisms inhibit crack propagation.
Idealization of fracture processes
R. Ritchie, 2011
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Cohesive Laws: Strength AND Toughness
Bilinear Traction-Displacement Law
cc Gd =
0 )(
Two material properties:
• Gc Fracture toughness
• c Strength
2c
cc
GEl
=
Characteristic Length:
t0 Yield or Strength Criteria
log n
log D
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2c
cp
GEl
=
a0
F, D
Crack Length and Process Zone
As the strength c decreases,
1. the length lp of the process
zone increases
2. the error of the Linear
Elastic Fracture Mechanics
solution increases.
a0
a0+lp
Force, F
Applied displacement, D
LEFM error
Gc=constant
Decreasing c
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Crack Length and Process Zone
0
0
0
5
5100
100
al
lal
la
p
pp
p
Brittle:
Quasi-brittle:
Ductile:Long crack Brittle
Quasi-
brittle
ShortcrackDuctile
LEFM error
Force, F
Applied displacement, D
LEFM error
LEFM error
2c
cp
GEl
=
a0
F, D
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Length of the Process Zone (Elastic Bulk Material)
mm.7.4=pl
A
B
C
D
E
F
Symmetry
Sym
me
tryh/ao=1
Maximum Load
ao
h
mm.7.4=pl
CT Sun,
Purdue U2ao
Short Tensile TestLexan Polycarbonate
2h
Cohesive
elementsmm.4.36.0
2=
c
cc
GEl
(CT Sun, Purdue)
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• The use of cohesive laws to predict the
fracture in complex stress fields is explored
• The bulk material is modeled as either
elastic or elastic-plastic.
h/a=0.25 (long process zone)
Observations:
• LEFM overpredicts tests for h/a<1
Lexan Plexiglass tensile specimens (CT Sun)
h/a=0.25h/a=0. 5h/a=1h/a=2h/a=4
2h
2a
h/a=1 (short process zone)
mm.7.4=pl
Width=pl
Near-uniform stress (ligament)
0
1000
2000
3000
4000
5000
6000
0 1 2 3 4
Force, N
h/a
Test (CT Sun)
LEFM
Cohesive
Cohesive Laws - Prediction of Scale Effects
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Continuum Idealization of Crack Through Finite Element
Under shear, smeared orientations cause load transfer across
cracks, and spurious secondary failure modes.
Physical idealization Strain-based idealizationCrack nucleation
Fiber rotation
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CompDam: Deformation Gradient Decomposition (DGD)
𝑿R(1)
𝑿R(2)
𝜹
1
2𝒙B(2)
𝒙(1)
𝒙(2)
1
2𝒙B(2)
ො𝒆N
ො𝒆F
, 𝒙B(1)
Concept:Use deformation gradient (DG) 𝑭instead of strains e to describe the
deformation of the continuum.
The continuum deformation is decomposed
into its crack and bulk material components
along each reference direction, e.g.:
𝑭B1= 𝑭 1 𝑭B
2= 𝑭 2 −
1
𝑙2𝑹cr𝜹
𝝉 = 𝑘 1 − d 𝜹
The DG accounts for the orientation of
the cracks and the orientation of the
fibers (trellising).
Equilibrium is imposed
to solve for 𝑭B and 𝜹(DGD)
F. Leone, NASA, 2015
CompDam_DGD GitHub repository: https://github.com/nasa/CompDam_DGD
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Boeing 787 composite fuselage
New composite airframe designs
consist of thin skins that are
stiffened longitudinally by stringers
and circumferentially by frames
For structural efficiency, the
strength reserves within the
postbuckling range must be
exploited
Next-Generation Composite Airframe
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, 40
Teflon insert
Single Stringer Compression Specimen
Single Stringer Compression Specimen(SSCS)
SSCS is designed to have response and damage tolerance characteristics similar to those of a multi-stringer panel
(Dimensions in mm)
Flight direction
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Interpretation of Digital Image Correlation (DIC)
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Typical modes of failure that result
from postbuckling deformations:
Delamination
Crippling (collapse due to crushing)
Stringer crippling
Delamination
SSCS Modes of Failure: Delamination and Crippling
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Collapse Sequence
Flange debonding
and tunnelingStringer crippling
58 mm
Delamination inside skin
A B C
Infrared camera
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Predicted SSCS Response
Residual thermal deformation
First buckling
Initiation of
matrix damage
Initiation of
delamination
Collapse
4X Magnification
B.C. for potting applied Stringer crippling
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Seven Point Bend (7PB) Test
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Examining Skin/Stiffener Separation with the 7PB Test
• How to model “real” delaminations?• Can the detail features of the interface damage be ignored?• What material properties should we use?
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Benefits of the 7PB Test
7PB test fixture
Analysis
Test
In the 7PB, skin/stiffener separation can be introduced in a controlled manner.
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7PB Load Frame and Advanced Instrumentation
Load frame
Control station
Data acquisition
Acoustic Emission microphones
Test specimen
Infrared camera 7PB fixture Digital image correlation (not shown)
Strain gages
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Monitoring Damage in the 7PB Test
Real-time NDE techniques monitor the progression of damage
Delamination
Passive Thermography(Infrared camera, IR)
Digital Image Correlation (DIC)
Cracks
Acoustic Emission (AE)
Propagation
Time
Aco
ust
ic E
ven
ts
SkinSkin
Flange
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Nondestructive Evaluation (NDE) Techniques
Ultrasonic scanning (UT)
X-Ray Computed Tomography (CT)
Skin
Flange Delaminations
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Propagation of Interface Damage
Pristine – Specimen 7PB-010
3477 N 3497 N 3931 N 4204 N
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Seven Point Bend Test Results
UT scan Analysis
• Can skin/stiffener be modeled with simple shell models?
Shell/cohesive model
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Characterization of Fracture Properties
Mode IDirect Cantilever Beam (DCB)
Mixed Mode Bending (MMB)
GIc, GIIc,h
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Applied Load
Delamination
FabricTape
Complexities of Interfacial Damage
1. R-curve effects
2. Complexities of interfaces between dissimilar materials
3. Migration of delamination
Causes:• Bridging• Delving• Other damage modes
GIc, J/m2
Crack Propagation, mm.
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MMB Skin/stiffener separation
Wagner, W., and Balzani, C., Computers and Structures, 2008
Standard Tests and Structural Interfaces
4 times!
Gc_interface ≈ 4 X Gc_tape
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0/0 interface(standard test)
Typical structural interface
Is Gc the same?
Interface Surface Roughness
Top
Bottom
Top
Bottom
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R-Curve Effect in Mode I
Delamination resistance curves for DCB Test
Gc - initiation
Gc - steady-state
Forc
e
Displacement
Fiber bridging
P. Davidson, A. Waas, 2012
G. Murri, NASA/TM–2013-217966
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Pereira, A.B., and de Morais, A.B., "Mode I Interlaminar Fracture of Carbon/Epoxy Multidirectional Laminates,"
Composites Science and Technology, Vol. 64, No. 13–14, 2004, pp. 2261-2270.
R-Curves for Multidirectional Laminates
300
4 times !
GIc
, J/m
2
Crack Propagation, mm.
Initiation
Steady-state (laminate)
Steady-state (standard test)
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Properties that Depend on Sub-ply Effects
Test
Analysis w/ tape/tapeproperties
Analysis w/ tape/fabricproperties
Model of MMB specimen
Fabric
Tape
MMB in fabric-side-up orientation
Mixed Mode Bending (MMB)
[0f]/[0t]7/[0f]
[0t]/[0f]/[0t]5/[0f]/[0t]
Tape/fabric interface
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Modeling the R-Curve Effect
Gc - initiation
Gc - steady-stateBilinear
Trilinear
Forc
e
Displacement
Trilinear cohesive law
Bilinear cohesive law
Superposed cohesive laws
Gc - initiation
GR
Crack increment, Da
Gc – steady-state
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Migration of Delamination
Simple migration pattern
Complex migration patterns
Emile Greenhalgh, Imp. Coll., 2006
F. Leone, LaRC, 2016
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Three Point Bend (3PB) Doubler Specimen
Skin/stiffener separation
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3PB Specimen - Detailed “3D Models”
Interlaminar delamination
−45° matrix cracks
Skin/stiffener delamination
• Flange Layup – [+45/0/−45/+45/−45/0]S fabric• Skin Layup - [−45/+45/0/90/−45/+45]S tape
45/0 -45/45 Fabric/-45
1) CompDam_DGD
2) Floating Node Method (FNM)Fabric/-45 -45/45
45/0
• Delamination predicted in different interfaces.
• Delamination migration and bridging occurs via matrix cracks.
Failure Process:
N. Carvalho, 2016
F. Leone, 2016
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Comparison with X-Ray/CT Data
Load: 53.9 lb Load: 60. lbs
Front -
A
Interface 0
+45 Ply and Interface 1
Leone, 2017
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3PB Specimen: Predicted Response
Detailed
CDM model
• Predicted morphology of damage is excellent, but response is too brittle
• It appears that “standard” material properties are not satisfactory for
damage propagation
Too much error!
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Simplified Shell Model of 3PB Specimen
Interface law w/ bridge
Interface law – nominal tape/tape
Bridge
Shell Model
Cohesive law captures the effects of all damage
mechanisms contributing to the energy release rate
Skin Cohesive Doubler
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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
3D detailed model
57
Global-Local Analysis of Large Structures w/ Submodelling57
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
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Are We There Yet?
…and how about Fatigue?
UT scan Analysis
Shell/cohesive model
Yes! (kinda...)
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Progress has been accomplished!
Better Understanding of Scale Issues
• Composites: structure within a structure
• Effect of structural size on strength and toughness
• Role of process zone, model and mesh requirements
TapeFabric
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Modeling Skin/stiffener Separation
• The collapse of postbuckled structures is usually the result of skin/stringer separation
• Interfacial damage is not well understood
• Models must account for
• R-curve effects
• Complexities of interfaces between dissimilar materials
• Migration of delamination
• The level of fidelity required to model typical delaminations has not yet been established.
• Even the best analysis tools available may not account for all of the energy dissipation mechanisms that are required.
