Carbon Fiber Mechanical Properties: Reconciling … Fiber Mechanical...Carbon Fiber Mechanical...
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Carbon Fiber Mechanical Properties: Reconciling Models and Experiments Carlos A. León y León and Xinzhang Zhou 2 nd Innovative International Composites Summit Paris, France March 29-31, 2011
Transcript of Carbon Fiber Mechanical Properties: Reconciling … Fiber Mechanical...Carbon Fiber Mechanical...
Carbon Fiber Mechanical Properties:
Reconciling Models and Experiments
Carlos A. León y León and Xinzhang Zhou
2nd Innovative International Composites Summit Paris, France March 29-31, 2011
Outline
Carbon Fiber Mechanical Properties: Models vs. Experiments
A: Where we are (A)
B: Where we could be (B)
C: How best to bridge A and B
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Mechanical Properties of
Commercially Available Carbon Fibers
4
5
6
7
8
Ten
sile
Str
en
gth
[G
Pa
]
10% 3% 2% 1%
0.5%
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0
1
2
3
0 100 200 300 400 500 600 700 800
Ten
sile
Str
en
gth
[G
Pa
]
Modulus [GPa]
Hexcel
Others
Scale of Models and Experiments
• Carbon structures span over 1010 in length scale
• Theoretical models predict extremely high mechanical
properties at small length scales
• Recent experiments support theoretical predictions
• Need to transfer gains to larger scales
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Mechanical Properties of Solid Carbon Forms
100
1000
10000
Ma
gn
itu
de
[G
Pa
]Strength
Modulus
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1
10
100
Atoms Graphene Nanotubes Whiskers Single
Filaments
Dry
Bundles
Impregnated
Tows
Structural
Composites
Ma
gn
itu
de
[G
Pa
]
Maximum Theoretical and Practical Limits
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C-C Bonds Under StrainAb Initio, Molecular Dynamics and Finite Element Analyses
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Atomistic Approach to Brittle Failure
• Transition from nano-scale (atomic bonds) to micro-scale
� thermodynamic energy balance (Griffith)
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Mechanical Property Variation with ScaleGeometric Link � Fractal Dimension (Mandelbrot)
2
4
6
8
10
ln {
Str
en
gth
or
Mo
du
lus
[GP
a]}
C - ModulusSlope ~ -0.13
C - StrengthSlope ~ -0.24
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-6
-4
-2
0
-5 0 5 10 15 20
ln {
Str
en
gth
or
Mo
du
lus
[GP
a]}
ln {Scale [nm]}
Al - StrengthSlope ~ -0.37
Glass - Strength (Griffith)Slope ~ -0.31
Carbon Fiber Tensile StrengthComparison of Test Methods
0.4
0.6
0.8
1.0
log
(Te
nsi
le S
tre
ng
th [
GP
a])
Critical Length for
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-0.2
0.0
0.2
0.4
0.0 0.5 1.0 1.5 2.0 2.5
log
(Te
nsi
le S
tre
ng
th [
GP
a])
log (Gauge Length [mm])
Critical Length for
Shear Failure (δ)
Modulus Measurement and Modeling
300
400
500
600
Mo
du
lus
[GP
a]
Measured (PAN)
Corrected (PAN)
Ideal (Graphite)
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0
100
200
300
0.30 0.35 0.40 0.45 0.50 0.55 0.60
Mo
du
lus
[GP
a]
Degree of Graphitization {Calc. from d-spacing; 1 = Graphite}
Strength Measurement and Modeling
y = -1.0526x - 5.7571
y = -0.1439x + 0.2401
1.1
1.2
1.3
1.4
1.5
1.6
ln (S
tren
gth
[G
Pa]
)
15 mm
30 mm
40 mm
6.63 um
6.75 um
6.90 um
7.10 um
7.23 um
7.35 um
7.53 um
7.65 um
• Average Load vs. Volume scatter � Filament Diameter Variability
• Decoupling strength contributions shows filament strength is more sensitive to
changes in transverse (diameter) than axial (length) dimensions
• Differences impact data interpretation from gauge-dependent (e.g., Weibull)
vs. gauge-Independent tests
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1.0
1.1
-8.0 -7.5 -7.0 -6.5 -6.0 -5.5
ln (Volume [mm3/filament])
Statistical Flaw DistributionsExcluding Clustering/Orientation/Other Effects � Molecular Dynamics
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0
100
200
300
400
500
600
700
800
300 400 500 600 700 800 900 1000
Nu
mb
er
Of
Fla
ws
De
tect
ed
pe
r M
ete
r
Tensile Strength[ksi]
Old
New
Average Population
Strength = 609 ksi
Average Population
Strength = 798 ksi
Summary and Conclusions
• Models and experiments show key scale transitions for carbon fiber structure and
mechanical properties in composites.
• Below 100 nm, experimentally measured properties approaching theoretical upper
limits are already being reported.
• Above 1 mm, carbon fibers are tested and modeled with statistical approaches.
• Improving carbon fiber mechanical properties demands careful consideration of
experimental and theoretical details over wide length scales.
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