Role of Atomic Scale Interfaces on the Thermal, Physical and Mechanical

Properties of Carbon Nanotube Based Devices

NAMAS CHANDRA Department of Mechanical EngineeringFlorida State/Florida A&M University

Tallahassee FL 32310

University of MarylandSeptember 7, 2005

DNA~2-1/2 nm diameter

Things Natural Things Manmade

MicroElectroMechanical devices10 -100 m wide

Red blood cellsPollen grain

Fly ash~ 10-20m

Atoms of siliconspacing ~tenths of nm

Head of a pin1-2 mm

Quantum corral of 48 iron atoms on copper surfacepositioned one at a time with an STM tip

Corral diameter 14 nm

Human hair~ 10-50m wide

Red blood cellswith white cell

~ 2-5 m

Ant~ 5 mm

The Scale of Things -- Nanometers and More

Dust mite

200 m

ATP synthase

~10 nm diameter Nanotube electrode

Carbon nanotube~2 nm diameter

Nanotube transistor

O O

O

OO

O OO O OO OO

O

S

O

S

O

S

O

S

O

S

O

S

O

S

O

S

PO

O

21st Century Challenge

Combine nanoscale building blocks to make novel functional devices, e.g., a photosynthetic reaction center with integral semiconductor storage

Th

e M

icro

wo

rld

0.1 nm

1 nanometer (nm)

0.01 m10 nm

0.1 m100 nm

1 micrometer (m)

0.01 mm10 m

0.1 mm100 m

1 millimeter (mm)

1 cm10 mm

10-2 m

10-3 m

10-4 m

10-5 m

10-6 m

10-7 m

10-8 m

10-9 m

10-10 m

Visi

ble

Th

e N

ano

wo

rld

1,000 nanometers = In

frar

edU

ltrav

iole

tM

icro

wav

eSo

ft x-

ray

1,000,000 nanometers =

Zone plate x-ray “lens”Outermost ring spacing

~35 nm

Office of Basic Energy SciencesOffice of Science, U.S. DOE

Version 03-05-02

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Note on Molecular DynamicsGiven for one instance an intelligence which would comprehend all forces by which nature is animated and the respective situation of beings who compose it ……… Nothing would be uncertain and the future , as the past, would be present to its eyes

Laplace, 1814

Given a geometric configuration of atoms, we can compute all the future configurations if we can compute the motion of each atom as a function of time if we know how the atoms will move under mutually interacting forces

Limitations Interacting forces given by

potential energy functions; Right function or series of functions critical

Space scale 1 μm3 of Al contains about 1010

atoms Time Scale 1 step= 1fs : For simulation of

1μs need 109 steps

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Carbon Nanotubes (CNTs)Carbon Nanotubes (CNTs)

CNTs can span 23,000 miles without failing due to its own weight.

CNTs are 100 times stronger than steel.

Many times stiffer than any known material

Conducts heat better than diamond

Can be a conductor or insulator without any doping.

Lighter than feather.

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Carbon Nanotubes (CNT)

Carbon Nanotubes: Graphite sheet rolled into a tube Single wall and Multiwall nanotubes Zigzag, armchair and chiral nanotubes Length ~ 100 nm to few m Diameter~ 1 nm

E ~ 1 TPa Strength ~150 GPaConductivity depends on chirality

ApplicationsC a rb o n n a n o t u b e s i nd if fe re n t o r i e n ta t io nV is c o -e la s ti c m e d iu m

High strengthcomposites

Functionalcomposites

Nano electronics

Energy storage

Nano sensorsMedical applications

Do these properties extend to CNT reinforced composites ?

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Do we realize the potentials of CNT in PMC?Researcher Matrix Vol% CNT

Exptl Calculation

SeriesParallel

Schaddler ‘98 Epoxy 2.85 (tension) 1.13 9.60 1.03

Epoxy 2.85 (comp) 1.4 9.60 1.03

Andrews ‘99 Petroleumpitch

0.33 1.20 9.09 1.003

1.62 2.29 12.46 1.016

Gong ‘00 Epoxy 0.57 1.12 4.98 1.0057

0.57 1.25 4.98 1.0057

Qian ‘00

(With surf actant)

Polystyrene 0.49 1.24 4.9151 1.0049

Ma’00 PET 3.6 1.4 4.564 1.037

Andrews’02 Polystyrene 2.5 1.22 14.86 1.035.0 1.28 28.73 1.0510.0 1.67 56.46 1.1115.0 2.06 84.18 1.1825.0 2.50 139.64 1.33

PPA 0.50 1.17 5.16 1.011.50 1.33 13.49 1.022.50 1.50 21.81 1.035.00 2.50 42.62 1.05

EC EM

EC EM

C f f m mE V E V E

Parallel modelUpper Bound

1 f m

C f m

V V

E E E

Series modelLower Bound

Answer is No-We do not

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Inte

rfac

e

Properties affected

Fatigue/Fracture Thermal/electronic/magnetic

Factors affecting interfacial properties

Trans. & long.Stiffness/strength

Interfacial chemistry Mechanical effects

Origin: Chemical reaction during thermal-mechanical Processing and service conditions, e.g. Aging, Coatings, Exposures at high temp..

Issues: Chemistry and architecture effects on mechanical properties.

Approach: Analyze the effect of size of reaction zone and chemical bond strength (e.g. SCS-6/Ti matrix and SCS-6/Ti matrix )

Residual stress

Origin: CTE mismatch between fiber and matrix.

Issues: Significantly affects the state of stress at interface and hence fracture process

Approach: Isolate the effects of residual stress state by plastic straining of specimen; and validate with numerical models.

Asperities

Origin: Surface irregularities inherent in the interfaceIssues: Affects interface fracture process through mechanical loading and frictionApproach: Incorporate roughness effects in the interface model; Study effect of generating surface roughness using: Sinusoidal functions and fractal approach; Use push-back test data and measured roughness profile of push-out fibers for the model.

Metal/ceramic/polymer

CNTs

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Critical Scientific Issues

• Critical issues in nanotube composites

– Alignment– Dispersion– Load Transfer

• Load transfer and to some extant Dispersion affected by interfaces

• Interface Bounding surface with physical / chemical / mechanical discontinuity

• CNT-matrix interfaces– Vanderwall’s forces– Mechanical interlocking– Chemical bonding

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Some issues in Elastic Modulii computation

• Energy based approach– Assumes existence of W. Then,– Validity of W based on potentials questionable under conditions such as

temperature, pressure– Value of E depends on selection of strain.

• Stress –Strain approach– Circumvents the above problems

– Evaluation of local modulus for defect regions possible

2

2YW

E

Averaging Volume

Total Volume

Atomic Volume

Stress Measures

Virial stress

1 1 1

2 2

N

ij i j j imv v r f

1 1 1

2 2

N N

ij i j i jm v v f r

BDT stress

1 1

1 1 1

2 2

N Nlutskoij i j j iLutsko

mv v r f

r

Lutsko stress

Averaging Volumefor Lutsko stress

ZY

X

Strain calculation in nanotubes

Defect free nanotube mesh of hexagons

Strain calculated using displacements and derivatives shape functions in a local coordinate system formed by tangential (X) and radial (y) direction of centroid and tube axis

Area weighted averages of surrounding hexagons considered for strain at each atom

Similar procedure for pentagons and heptagons

G

Y’X’

Z’ Z

X

Y

i

j

l

Updated Lagrangian scheme is used in MD simulations

Mechanical Properties ofNeat Defect-free CNTs

Elastic modulus of defect free CNT

Strain

Stress

(GPa)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

10

20

30

40

50

60

Bulk Stress (E=1.002 TPa)

Lutsko Stress (E= 0.997 TPa)

BDT Stress (E= 1.002 TPa)

-All stress and strain measures yield a Young’s modulus value of 1.002TPa

-Defect free (9,0) nanotube with periodic boundary conditions

-Strains applied using conjugate gradients energy minimization

-Values in literature range from 0.5 to 5.5 Tpa. Mostly around 1Tpa

Effect of Diameter

Strains

Str

ess

(GP

a)

0 0.01 0.02 0.03 0.04 0.05 0.060

10

20

30

40

50

(9,0) at defect

(10,0) at defect

(11,0) at defect

(13,0) at defect

(15,0) at defect

(9,0) no defect

(10,0) no defect

(11,0) no defect

(13,0) no defect

(15,0) no defect

stress strain curves for different (n,0)tubes with varying diameters.

stiffness values of defects for various tubes with different diameters do not change significantly

Stiffness in the range of 0.61TPa to 0.63TPa for different (n,0) tubes

Mechanical properties of defect not significantly affected by the curvature of nanotube

Residual stress at zero strain

Stress is present at zero strain values.

This corresponds to stress due to curvature

It is found to decrease with increasing diameter

Basis for stress calculation graphene sheet

Brenner et. al.1 observed similar variation in energy at zero strain

1 Robertson DH, Brenner DW and Mintmire 1992 1/Radius (A)

Sre

ss(G

PA

)

0.1 0.2 0.30

1

2

3

4

5

(8,0)

(9,0)

(10,0)

(11,0)

(12,0)

(15,0)

(17,0)

(20,0)(25,0)

(50,0)

N. Chandra et. al., Phys. Rev B 69, 09141 (2004)

Effect of Defects on theMechanical Properties

CNT with 5-7-7-5 defect

Lutsko stress profile for (9,0) tube with type I defect shown below

Stress amplification observed in the defected region

This effect reduces with increasing applied strains

In (n,n) type of tubes there is a decrease in stress at the defect region

z - position

Str

ess

(Gp

a)

-20 -10 0 10 2010

20

30

40

50

60

3 % Applied Strain

0 % Applied Strain

1 % Applied Strain

5 % Applied Strain

7 % Applied Strain

8 % Applied Strain

Shet and Chandra, J. Mat. Sci, 40, 27-36 (2005)Shet, Chandra, Namilae, Mech. Adv. Mat. Str,,55-65, (2005).

Evolution of stress and strain

Strain and stress evolution at 1,3,5 and 7 % applied strainsStress based on BDT stress

Local elastic moduli of CNT with defects

Strain

Str

ess

(GP

a)

0 0.025 0.05 0.075 0.10

10

20

30

40

50

60

(9,0) CNT no defect

Type I defect

Type II defect

(a)

(b)

(c)

-Reduction in stiffness in the presence of defect from 1 Tpa-Initial residual stress indicates additional forces at zero strain-Analogous to formation energy

-Type I defect E= 0.62 TPa

-Type II defect E=0.63 Tpa

Namilae and Chandra, Chem.. Phy. Letters 387, 4-6, 247-252, (2004)

Effect of Surface Modification(Functionalization)

Functionalized Nanotubes

Change in hybridization (SP2 to SP3)

Experimental reports of different chemical attachments

Application in composites, medicine, sensors

Functionalized CNT are possibly fibers in composites

108o120o

Graphite Diamond

How does functionalization affect the elastic and inelastic deformation behavior and fracture

Strain

Str

ess

(Gp

a)

0 0.01 0.02 0.03 0.04

5

10

15

20

25

30

35

(10,10) CNT 0.84 T Pa

(10,10) CNT with vinyl 0.92 T Pa

(10,10) CNT with butyl 1.03 T Pa

Functionalized nanotubes Increase in stiffness observed by functionalizing

Stiffness increase is more for higher number of chemical attachments

Stiffness increase higher for longer chemical attachments

Volume for Stress Calculation

Vinyl and ButylHydrocarbonsT=77K and 3000KLutsko stress

 

(8,0)

(10,10)

(10,10)

(10,10)

(10,10)

(10,10)

(12,0)

(15, 0)

(8,8)

(10,10)

(12,12)

(10,0)

3.13

3.91

6.78

6.78

6.78

6.78

6.78

4.69

5.87

5.42

6.78

8.13

21

21

21

21

21

31

-C2H3*

-C2H3

-C2H3

-C2H3

-C2H3

-C2H3

-C2H3

-C3H5

-C4H7

-C5H9*

-C2H3

-C2H3

21

21

21

21

21

50

0.862

0.854

0.859

0.849

0.721

0.837

0.784

0.837

0.837

0.837

0.837

0.837

1 .05

1 .04

0.977

0.951

0.889

0.932

0.906

0.940

1.03

0.95

1.02

1.11

Nanotube Radius Chemical # of E (TPa) w/o E (TPa)Group Attachments Attachments Attachments Stiffness

increase is more for higher number of chemical attachments

Stiffness increase higher for longer chemical attachments

Namilae and Chandra, Chem. Phy. Letters 387, 4-6, 247-252, (2004)

Local Stiffness of Functionalized CNTs Local Stiffness of Functionalized CNTs

Contour plots Higher stress atthe location ofattachment

Stress (GPa) Stress (GPa)

Stress (GPa)Stress (GPa) Stress (GPa)

(a) (b) (c)

(d) (e) (f)

Stress contours with one chemical attachment. Stress fluctuations are present

Radius variation

Atom Number

Ra

diu

s

100 200 300 400

6.6

6.7

6.8

6.9

7

7.1

7.2

7.3

with vinyl attachments

without attachments

Increased radius of curvature at the attachment because of change in hybridization

Radius of curvature lowered in adjoining area

Sp3 Hybridization here

Higher stress atthe location ofattachment

Stress (GPa) Stress (GPa)

Stress (GPa)Stress (GPa) Stress (GPa)

(a) (b) (c)

(d) (e) (f)

Defects Evolve at much lower strain of 6.5 % in CNT with chemical attachments

Onset of plastic deformation at lower strain. Reduced fracture strain

Evolution of defects in tensionEvolution of defects in tension

Defects EvolveEffect of functionalization

on defect evolution

Different Fracture Mechanisms ?

Fracture Behavior Different Fracture happens by

formation of defects, coalescence of defects and final separation of damaged region in defect free CNT

In Functionalized CNT it happens in a brittle manner by breaking of bonds

Namilae and Chandra, Chem. Phy. Letters 387, 4-6, 247-252, (2004)

Compressive Behavior(Weak and Strong bonding)

Displacement (A)S

tre

ss(G

Pa

)10 20 30 40

0

10

20

30

40

50

60

70

80

90

100

110

120

130

o

(a)

(b)

Compressive behavior of CNT in polymer matrix withWeak interface

Weak Interfaces

Compressive Behavior of CNT composites (weak) Compressive Behavior of CNT composites (weak)

Displacement (A)S

tre

ss(G

Pa

)10 20 30 40

0

20

40

60

80

100

120

140

160

(a)(b)

(c)(d)

(e)

(f)

(g)

o

Strong Interfaces

Compressive Behavior of CNT composites (strong)Compressive Behavior of CNT composites (strong)

•Deformation mechanism changes•Mechanical Response significantly altered

Strong Interfaces

Compressive response of (6,0)(15,0) nanotube with and without chemical bonding between the walls of nanotubes.

Tensile simulation with functionalization

Tensile simulation without functionalization

StrainS

tre

ss(G

Pa

)0.01 0.02 0.03 0.04 0.05 0.06

0

10

20

30

40

50

60

70(a)

(b)

(c)

(d)

(e)

Effect of interstitial on tensile behavior of MWNTs

Interstitial atoms increase the load transfer in tension, and both stiffness and strength increase

Paper under reviewInterstitial atoms in multiwall nanotubes

Hydrogen Absorption in CNTs(Nanosensors)

Hydrocarbon system:Brenner Bond-Order potential

Metallic material:Embedded Atom Potential

H-Metal: Customized Morse type Potential

Metal-C,C-C,H2-H2 long range interaction: Lennard Jones Potential

612

rr4)r(E

i ij

ijAijijRb rVBrVE )()(

i ij

jiitot ))R(2

1)(F(E

)e2e(DE)1

er

ijr(

2)1

er

ijr(

ij

Use of Multiple PE functions in Use of Multiple PE functions in Hydrogen SensorHydrogen Sensor

• Total: 832 atoms; 256 Pd and 576 H

• Periodic box: 60 x 60 x 60 A

T=300 K, P=20 atm

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140 160 180 200

Time (PS)

So

lub

ilit

y H

/Pd

Diffusion of Hydrogen in PalladiumDiffusion of Hydrogen in Palladium

Total: 1240 atoms; 320 C, 56 Pd

(4 FCC units) and 864 H

Periodic box: 100 x 100 x 20 A

T=300 K, P=20 atm

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100 120 140 160 180

Time (PS)

So

lub

ilit

y (H

/Pd

)

Hydrogen Diffusion in Pd Coated CNTsHydrogen Diffusion in Pd Coated CNTs

Diffusion of mixture of Hydrogen and Argon in Palladium coated CNT

Total: 827 atoms; 320 C, 56 Pd (4 FCC units), 38 H, 413 Argon

Periodic box: 100 x 100 x 20 A T=300 K

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 160 180Time (PS)

So

lub

ilit

y (H

/Pd

)

CNTs in Composites

Atomic simulation of CNT pullout test

Simulation conditions Corner atoms of hydrocarbon attachments fixed Displacement applied as shown 0.02A/1500 steps T=300K

Matrix

Fiber

Energy for debonding of chemical attachment = 3eV

Simulation of pull-out test Simulation of pull-out test

Interfacial shear

Displacement (A)

React

ion

(eV/A

)

5 10 15-1

0

1

2

3

4

5

6

7

8

Typical interface shear force pattern. Note zero force afterFailure (separation of chemical attachment)

After Failure

Max load

250,000 steps

Interfacial shear measured as reaction force of fixed atoms

Debonding and Rebonding of Interfaces

displacement (A)

Fo

rce

(eV

/A)

0 5 10 15-2

-1

0

1

2

3

4

5

6

7

8Rebonding

Debonding

Failure

Matrix

Debonding and Rebonding

Energy for debonding of chemical attachment 3eV

Strain energy in force-displacement plot 20 ± 4 eV

Energy increase due to debonding-rebonding

Matrix

displacement (A)

Fo

rce

(eV

/A)

0 5 10 15-2

-1

0

1

2

3

4

5

6

7

8

displacement (A)

Fo

rce

(eV

/A)

0 5 10 15-2

-1

0

1

2

3

4

5

6

7

8displacement (A)

Forc

e(e

V/A

)

0 5 10 15-2

-1

0

1

2

3

4

5

6

7

8

displacement (A)F

orc

e(e

V/A

)0 5 10 15

-2

-1

0

1

2

3

4

5

6

7

8

displacement (A)F

orc

e(e

V/A

)

0 5 10 15-2

-1

0

1

2

3

4

5

6

7

8

displacement (A)

Fo

rce

(eV

/A)

0 5 10 15-2

-1

0

1

2

3

4

5

6

7

8

Various types of Interface Behavior Various types of Interface Behavior

Increasing the length of attachment increases region ‘a’

Decreasing the number of attachments extends region ‘b’

Displacement (A)

For

ce(e

v/A

)

0 5 10 15-2

-1

0

1

2

3

4

5

6

7

8

(a)

(b)

(c)(d)

(e)

Peak force

failureab

c d

e

b

a

c

Behavior of different lengths of interfacesBehavior of different lengths of interfaces

Displacement (A)

Fo

rce

(eV

/A)

5 10 15

0

2

4

6

8

2

Temperature 50 K

Displacement (A)

Fo

rce

(eV

/A)

5 10 15

0

2

4

6

8

2

Temperature 1000 K

Displacement (A)

Fo

rce

(eV

/A)

5 10 15

0

2

4

6

8

2

Temperature 2000 K

Displacement (A)

Fo

rce

(eV

/A)

5 10 15

0

2

4

6

8

2

Temperature 300 K

Force to failure decreases with increasing temperature

Debonding-rebonding behavior at higher temperatures does not alter the energy dissipation

Temperature dependence of pullout tests

Multiscale Modeling Using Cohesive Zone Models

Assumptions Nanotubes deform in linear elastic manner Interface character completely determined by traction-displacement plot

D isplacement (d)

Typical t - d plot

M at r ix

F iber (N anot ube)

M at r ix

F iber (N anot ube)

W1

W2

W1

W2

(a)

(b)

(c )

(d )

u

Chandra et. a., IJSS, 39, 2827-2855, (2002)

Cohesive zone model for interfaces

Cohesive zone Models for nanoscale interfaces

Applied displacement (A)

Tra

ctio

n(G

Pa

)

5 10 15

0

0.1

0.2

0.3

0.4

0.5

0.6

Applied displacement (A)

Tra

ctio

n(G

Pa

)

5 10 15

0

1

2

3

4

5

Applied displacement (A)

Tra

ctio

n(G

Pa)

5 10 15 20 25

0

0.1

0.2

0.3

0.4

0.5

0.6

Applied displacement (A)

Tra

ctio

n(G

Pa)

5 10 15 20 25

0

1

2

3

4

5

(a)

(b)

Namilae and Chandra JEMT, 222-232,

(2005).

Finite element simulation

ABAQUS with user element for cohesive zone model

Linear elastic model for both matrix and CNT

About 1000 elements and 100 elements at interface

Parametric studies

Volume % CNT

Ela

stic

Mo

du

lus

(GP

a)

0 5 10 15 20

5

10

15

20

25

30

35

Interface Strength = 5 MPa

Interface Strength = 5 GPa

Interface Strength = 50 MPa

Interface Strength = 500 MPa

Perfect Interface

Variation of CNT content for different interface strengths

Parametric studies

Matrix Elastic Modulus (GPa)

Co

mp

osi

teE

last

icM

od

ulu

s(G

Pa

)

0 5 100

5

10

15

20

25

30

35

40

Interface strength= 50 MPa

Interface strength= 500 MPa

Interface strength= 5 GPa

Interface strength= 5 MPa

Perfect Interface

Pure Matrix

Variation of matrix stiffness for different interface strengths

Parametric studies

Fiber Elastic Modulus (GPa)

Co

mp

osi

teE

last

icM

od

ulu

s(G

Pa

)

200 400 600 800 1000

4

6

8

10

12

14

16

18

20SiCFiber

GlassFiber

CarbonFiber

CNT

Very low interface strength = 5 MPa

Interface strength = 50 MPa

Interface strength = 500 MPa

Interface strength = 5 GPa

Perfect Interface

Fiber Volume = 7.7%

Matrix E = 3.5 GPa

Variation of fiber stiffness for different interface strengths

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Summary

• Interfaces play a key role even at micro/nano scales.• Nanoscale effects can be effectively captured using

molecular dynamics model (using the right potentials).• MD results can be integrated in an heirarchical model

using CZM-Finite Element method• Using Atomistic scale we can determine atomic effect on

macro effects.• Understanding the effects of nanoscale interfaces, and

interface mechanics will be important in in a number of engineering applications.

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AcknowledgementAcknowledgement

Nanomechanics Group:Prof. A. Srinivasan, U. Chandra

Dr. S. Namilae, C. Shet

S. Guan, M. Naveen, Girish, Yanan, J. Kohle, Jason Montgomery

FuAlso contributed by AFOSR, ARO, NSF, FSURF

National Secrrity Agency, 2004-

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Further ReferencesFurther References(Nanotechnology(Nanotechnology

MD Papers:N. Chandra, S. Namilae, and C. Shet, Local elastic properties of carbon nanotubes in the presence of Stone -

Wales defects, Physical Review B, 69, 094101, (2004).S. Namilae, N. Chandra, and C. Shet, Mechanical behavior of functionalized nanotubes, Chemical Physics

Letters 387, 4-6, 247-252, (2004) N. Chandra and S. Namilae, Multi-scale modeling of nanocystalline materials, Materials Science Forum, 447-

448, 19-27, (2004)..C. Shet, N. Chandra, and S. Namilae, Defect-defect interaction in carbon nanotubes under mechanical loading,

Mechanics of Advanced Materials and Structures, (2004) (in print).C. Shet, N. Chandra, and S. Namilae, Defect annihilations in carbon nanotubes under thermo-mechanical

loading, Journal of Material Sciences , (in print).S. Namilae, C. Shet, N. Chandra and T.G. Nieh, Atomistic simulation of grain boundary sliding in pure and

magnesium doped aluminum bicrystals, Scripta Materialia 46, 49-54 (2002).S. Namilae, C. Shet, N. Chandra and T.G. Nieh, Atomistic simulation of the effect of trace elements on grain

boundary of aluminum, Materials Science Forum, 357-359, 387-392, (2001).C. Shet, H. Li and N. Chandra, Interface Models for grain boundary sliding and migration, Materials Science

Forum 357-359, 577-586, (2001).N. Chandra and P. Dang, Atomistic Simulation of Grain Boundary Sliding and Migration, Journal of

Materials Science, 34, 4, 656-666 (1998).N. Chandra, Mechanics of Superplastic Deformations at Atomic Scale, Materials Science Forum, 304, 3, 411-

419 (1998).

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Further ReferencesFurther References(Cohesive Zone Models)(Cohesive Zone Models)

C. Shet and N. Chandra, The effect of the shape of the cohesive zone curves on the fracture responses, Mechanics of Advanced Materials and Structures, 11(3), 249-276, (2004).

N. Chandra and C. Shet, A Micromechanistic Perspective of Cohesive Zone Approach in Modeling Fracture. Computer Modeling in Engineering & Sciences, CMES, Computer Modeling in Engineering and Sciences, 5(1), 21-34, (2004))

H. Li and N. Chandra, Analysis of Crack Growth and Crack-tip Plasticity in Ductile Material Using Cohesive Zone Models, International Journal of Plasticity, 19, 849-882, (2003).

N. Chandra, Constitutive behavior of Superplastic materials, International Journal for nonlinear mechanics, 37, 461-484, (2002).

N. Chandra, H. Li, C. Shet and H. Ghonem, Some Issues in the Application of Cohesive Zone Models for Metal-ceramic Interface. International Journal of Solids and Structures, 39, 2827-2855, (2002).

C. Shet and N. Chandra, Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Process, ASME Journal of Engineering Materials and Technology, 124, 440-450, (2002).

N. Chandra, Evaluation of Interfacial Fracture Toughness Using Cohesive Zone Models, Composites Part A: Applied Science and Manufacturing, 33, 1433-1447, (2002).

C. Shet, H. Li and N. Chandra, Interface Models for grain boundary sliding and migration, Materials Science Forum 357-359, 577-586, (2001).

AMML

Further ReferencesFurther References(Interface Mechanics)(Interface Mechanics)

Interface Mechanics:N. Chandra and H. Ghonem, Interfacial Mechanics of push-out tests: theory and experiments, Composites Part A: Applied Science and Manufacturing, 32, 3-4, 575-

584, (2001).D. Osborne, N. Chandra and, H. Ghonem, Interface Behavior of Ti Matrix Composites at elevated temperature, Composites Part A: Applied Science and

Manufacturing, 32, 3-4, 545-553, (2001).N. Chandra, S. C. Rama and Z. Chen, Process Modeling of Superplastic materials, Materials Transactions JIM, 40, 8, 723-726 (1999).S. R. Voleti, C. R. Ananth and N. Chandra, Effect of Fiber Fracture and Matrix Yielding on Load Sharing in Continuous Fiber Metal Matrix Composites, Journal of

Composites Technology and Research, 20, 4, 203-209, (1998).C.R. Ananth, S. R. Voleti and N. Chandra, Effect of Fiber Fracture and Interfacial Debonding on the Evolution of Damage in Metal Matrix Composites, Composites

Part A, 29A, 1203-1211, (1998) S. Mukherjee, C. R. Ananth and N. Chandra, Effect of Interface Chemistry on the Fracture Properties of Titanium Matrix Composites, Composites Part A, 29A, 1213-

1219, (1998) S. R. Voleti, C. R. Ananth and N. Chandra, Effect of Interfacial Properties on the Fiber Fragmentation Process in Polymer Matrix Composites, Journal of Composites

Technology and Research, 20, 1, 16-26, (1998). S. Mukherjee, C. R. Ananth and N. Chandra, Evaluation of Fracture Toughness of MMC Interfaces Using Thin-slice Push-out Tests, Scripta Materialia, 36, 1333-

1338 (1997). C. R. Ananth, S. Mukherjee, and N. Chandra, Effect of Time Dependent Matrix Behavior on the Evolution of Processing-Induced Residual Stresses in Metal Matrix

Composites, Journal of Composites Technology and Research 19, 3, 134-141, (1997). S. Mukherjee, C. R. Ananth and N. Chandra, Effect of Residual Stresses on the Interfacial Fracture Behavior of Metal Matrix Composites, Composite Science and

Technology, 57, 1501-112, (1997). C. R. Ananth and N. Chandra, Elevated temperature interfacial behavior of MMC: a computational study, Composites: Part A, 27A, 805-811 (1996). S. R. Voleti, N. Chandra and J R. Miller, Global-Local Analysis of Large-scale Composite Structures Using Finite Element Methods, Composites & Structures, 58, 3,

453-464, (1996). C. R. Ananth and N. Chandra, Evaluation of Interfacial Properties of Metal Matrix Composites from Fiber Push-out Tests, Mechanics of Composite Materials and

Structures, 2, 309-328 (1995).Xie, Z.Y. and N. Chandra, Application of GPS Tensors to Fiber Reinforced Composites, Journal of Composite Materials, 29, 1448-1514, (1995). S. Mukherjee, H. Garmestani and N. Chandra, Experimental Investigation of Thermally Induced Plastic Deformation of MMCs Using Backscattered Kikuchi Method,

Scripta Metallurgica et Materialia, 33, 1, 93-99 (1995). N. Chandra and C.R. Ananth, Analysis of Interfacial Behavior in MMCs and IMCs Using Thin Slice Push-out Tests', Composite Science and Technology, 54, 1 , 87-

100, (1995). C. R. Ananth and N. Chandra, Numerical Modeling of Fiber Push-Out Test in Metallic and Intermetallic Matrix Composites-Mechanics of the Failure Process', Journal

of Composite Materials, 29, 11, 1488-1514, (1995). N. Chandra., C.R. Ananth and H. Garmestani, Micromechanical Modeling of Process-Induced Residual Stresses in Ti-24Al-11Nb/SCS6 Composite', Journal of

Composite Technology and Research, 17, 37-46, (1994). Z. Xie and N. Chandra, Application of Equation Regulation Method to Multi-Phase Composites', International Journal of Non-linear Mechanics, 28, 6, 687-704,

(1993).

Buckling Behavior-Neat CNT

Buckling Behavior-Functionalized CNT

Compressive loading of carbon nanotubes

Using surface modified CNT in composites improves resistance to buckling

Thermal Stresses

Temperature (K)

Str

ess

(GP

a)

100 200 300 400 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

With AttachmentsWith AttachmentsNo AttachmentsNo Attachments

Thermal stress is higher for functionalized nanotube in polymer matrix

Strain

En

erg

yp

er

ato

m(e

V)

0.025 0.05 0.075 0.1

-7.165

-7.16

-7.155

-7.15

-7.145

-7.14

-7.135

-7.13

-7.125

Energy per atom experienced by the inner tube in (6,0) (15,0) double walled

Effect of capped and uncapped on the compressive behavior of MWNTs

Capped compressive simulation

Uncapped compressive simulation

Inner tube is loaded in compression, even with weak inter wall interaction