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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