Effects of atomic-scale structure on the

fracture properties of amorphous

carbon – carbon nanotube composites

Benjamin D. Jensen, Kristopher E. WiseNASA Langley Research Center

Gregory M. OdegardMichigan Technological University

13th U.S. National Congress on Computational Mechanics

July 26-30, 2015

https://ntrs.nasa.gov/search.jsp?R=20160006312 2020-06-30T13:27:04+00:00Z

Overview

Motivation• Carbon nanotubes (CNTs) have high specific stiffness and strength

• Composite design with CNTs will be different than for carbon fibers

• New reactive force field ReaxFF can be applied to model fracture

Objectives1. Estimate maximum CNT composite mechanical properties

2. Compare composite mechanical properties with:

a. Singlewall vs multiwall CNTs

b. Dispersed vs bundled CNT arrangements

c. CNT-matrix crosslinking

2

Bond breaking with ReaxFF

Molecular dynamics using ReaxFF:

– Allows bond breaking and formation to be modeled

– Multibody interactions via bond order function

0

20

40

60

80

100

120

140

1 1.5 2 2.5 3

Po

ten

tia

l E

nerg

y (

kca

l/m

ole

)

Distance (Å)

HarmonicReaxFF

−500

−250

0

250

500

750

1000

1 1.5 2 2.5 3

Fo

rce

(kca

l/m

ole

−Å

)

Distance (Å)

HarmonicReaxFF

3

Modeling Fracture with ReaxFF

New ReaxFFC-2013 parameterization fitted to:

– Diamond strained in the bulk and <001> direction

– Graphene strained in the bulk and axial directions

In-house analysis of ReaxFFC-2013* mechanical properties

of diamond, graphene, amorphous carbon, and CNTs:**

– Improved Poisson contraction response

– Elastic and fracture properties improved over previous

ReaxFFCHO parameterization

*Goverapet Srinivasan, S.; van Duin, A. C. T.; Ganesh, P., J. Phys. Chem. A 2015, 119 (4), 571-580.

**Jensen, B.D.; Wise, K.; Odegard, G.M., Submitted to J. Phys. Chem A

4

Simulation Setup

SWNT Array

SWNT Bundle MWNT Array5

Simulation Setup

1. Continuous/straight CNTs

2. Amorphous carbon (AC) matrix:– Relative simplicity

– High mechanical properties

3. Three CNT arrangements:– SWNT array, MWNT array, SWNT bundle

4. Five crosslinking fractions for each system:– 0%, 5%, 10%, 15%, 20%

6

Equilibration Procedure

−175

−170

−165

−160

−155

0 100 200 300 400 500 600

0

200

400

600

800

1000

1200

1400

E F G O P O P

Po

ten

tia

l E

ne

rgy (

kca

l/m

ol)

Te

mp

era

ture

(K

)

Time (ps)

Equilibration Step

Potential EnergyTemperature

7

Results

0

1

2

3

4

5

6

0 0.5 1 1.5 2

gc(r

)

r (nm)

all atomsCNT

AC

0

1

2

3

4

5

6

0 0.5 1 1.5 2

gc(r

)

r (nm)

0

1

2

3

4

5

6

0 0.5 1 1.5 2g

c(r

)

r (nm)

a) b) c)

Structuring of amorphous carbon at the CNT interface

Nanotube-centered cylindrical distribution functions, zeroed at the exterior nanotube wall

8

Results

9

Results

10

120

140

160

180

200

220

240

0 0.05 0.1 0.15 0.2 0.25

Axia

l S

pecific

Mod

ulu

s(G

Pa/(

g/c

m3)

Degree of Crosslinking

SWNT arrayMWNT array

SWNT bundle

Results

Axial Specific Moduli

11

• Templating of the matrix substantially increases

the axial modulus

• Dispersion of crosslink sites does not strongly

influence axial modulus

Results

Axial Specific Moduli

• Templating of the matrix substantially increases

the axial modulus

• Dispersion of crosslink sites does not strongly

influence axial modulus

120

140

160

180

200

220

240

0 0.05 0.1 0.15 0.2 0.25

Axia

l S

pecific

Mod

ulu

s(G

Pa/(

g/c

m3)

Absolute Degree of Crosslinking

SWNT arrayMWNT array

SWNT bundle

12

Results

Transverse Specific Moduli

• Multiwalled CNT resists CNT flattening, increasing

the transverse modulus

• Lack of crosslinks within the bundle limits

effectiveness of crosslinking for transverse stiffness

20

30

40

50

60

70

0 0.05 0.1 0.15 0.2 0.25

Tra

nsvers

e S

pe

cific

Mo

dulu

s (

GP

a/(

g/c

m3)

Degree of Crosslinking

SWNT arrayMWNT arraySWNT bundle

13

Results

Specific Shear Moduli

• SWNT bundle system has lowest specific shear

moduli in both directions

• Inner MWNT walls reinforce circular shape resulting

in higher out-of-plane specific shear modulus

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25

In−

Pla

ne

Sp

ecific

She

ar

Modu

lus (

GP

a/(

g/c

m3)

Degree of Crosslinking

SWNT arrayMWNT arraySWNT bundle

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25O

ut−

of−

Pla

ne

Sp

ecific

She

ar

Modu

lus (

GP

a/(

g/c

m3)

Degree of Crosslinking

14

0.4

0.5

0.6

0.7

0.8

0 0.05 0.1 0.15 0.2 0.25M

ino

r P

ois

son

’s R

atio

Degree of Crosslinking

SWNT arrayMWNT arraySWNT bundle

0.25

0.3

0.35

0.4

0.45

0 0.05 0.1 0.15 0.2 0.25

Ma

jor

Po

isson

’s R

atio

Degree of Crosslinking

Results

Poisson’s Ratios

• Major Poisson’s ratio largest around 7% crosslinking

• MWNT array resists deformation of the circular

cross-section resulting in lower minor ratios

15

SWNT array axial fracture (9% crosslinked)

16

MWNT array axial fracture (9% crosslinked)

17

SWNT bundle axial fracture (9% crosslinked)

18

Results

Specific Ultimate Stress

• Axial specific strength maximized around 4%

crosslinking

• Transverse strength continually improved through

crosslinking

24

26

28

30

32

34

36

0 0.05 0.1 0.15 0.2 0.25

Axia

l S

p. U

ltim

ate

Str

ess

(GP

a/(

g/c

m3)

Degree of Crosslinking

SWNT arrayMWNT array

SWNT bundle

4

6

8

10

12

14

16

18

0 0.05 0.1 0.15 0.2 0.25T

ran

s. S

p. U

ltim

ate

Str

ess

(GP

a/(

g/c

m3)

Degree of Crosslinking

19

Conclusions

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70

Axial

Trans.Sp

. M

od

ulu

s (

GP

a/(

g/c

m3))

Ultimate Sp. Strength (GPa/(g/cm3))

SWNT array

MWNT array

SWNT bundle

AC 2.37 g/cm3

AC 2.82 g/cm3

AC 3.35 g/cm3

Pure CNT array

Multiple data points for each system reflect impact of crosslinks to matrix

20

Summary

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70

Axial

Trans.Sp

. M

od

ulu

s (

GP

a/(

g/c

m3))

Ultimate Sp. Strength (GPa/(g/cm3))

SWNT array

MWNT array

SWNT bundle

AC 2.37 g/cm3

AC 2.82 g/cm3

AC 3.35 g/cm3

Pure CNT array

Increasing crosslinking

21

Multiple data points for each system reflect impact of crosslinks to matrix

Summary

SWNT vs MWNT– Interface templating has a substantial impact on the matrix properties,

and SWNTs maximize the surface area per CNT mass

– Inner MWNT walls reinforce the circular cross section

Arrays vs bundle– Very weak bonding within bundle reduces the properties that require

transferring load through the bundle

Crosslinking– Crosslinks decrease axial specific modulus, increase transverse

modulus

– Axial specific ultimate strength is maximized around 4% crosslinking

– Transverse specific ultimate strength is continually increased with crosslinking

– Crosslinking may inhibit void nucleation at the CNT/matrix interface

22

Acknowledgements

NASA Langley Research Center

- Mia Siochi

- LaRC Nano Incubator Team

Michigan Technological University

- Matthew Radue

- S. Gowtham

- Cameron Hadden

Pennsylvania State University

- Adri van Duin (Penn. State)

- Sriram Srinivasan (Penn. State)

NASA Langley Research CenterFunded in part by

Revolutionary Technological Challenges Program (GRANT NNX09AM50A )

SUPERIOR, a high-performance computing cluster at

Michigan Technological University, was used in

obtaining some of results

23

Questions

24

Supplemental Slides

25

Results

0

15

30

45

60

75

0 0.075 0.15 0.225 0.3 0.375

a)

Sp

. S

tre

ss (

GP

a/(

g/c

m3)

True Strain

Exterior CNTsInterior CNTs

Composite

0

15

30

45

60

75

0 0.075 0.15 0.225 0.3 0.375

b)

Sp

. S

tre

ss (

GP

a/(

g/c

m3)

True Strain

Individual CNT stress-strain responses

within the maximally crosslinked systemsMWNT array SWNT bundle

• Exterior/functionalized CNTs fracture earlier than

interior/unfunctionalized

26

Results

0

10

20

30

40

50

60

70

0 50 100 150 200 250

a)

Sp

. S

tre

ss (

GP

a/(

g/c

m3))

Time (ps)

CNTAC

CompositeUltimate

0 50 100 150 200 250

b)

Time (ps)

0

10

20

30

40

50

60

70c)

Sp

. S

tress (

GP

a/(

g/c

m3))

d)

0

10

20

30

40

50

60

70

0 0.075 0.15 0.225 0.3 0.375

e)

Sp

. S

tre

ss (

GP

a/(

g/c

m3))

True Strain

0 0.075 0.15 0.225 0.3 0.375

f)

True Strain

Axial stress-strain response

SWNT

array

MWNT

array

SWNT

bundle

Uncrosslinked Maximum crosslinking

27

Results

0

5

10

15

20

0 100 200 300 400 500

a)

Sp

. S

tress (

GP

a/(

g/c

m3))

Time (ps)

0 100 200 300 400 500

b)

Time (ps)

0

5

10

15

20c)

Sp

. S

tress (

GP

a/(

g/c

m3))

d)

CNTAC

CompositeUltimate

0

5

10

15

20

0 0.15 0.3 0.45 0.6 0.75

e)

Sp

. S

tre

ss (

GP

a/(

g/c

m3))

True Strain

0 0.15 0.3 0.45 0.6 0.75

f)

True Strain

Transverse specific stress-strain response

28