Northwestern University Rod Ruoff Nanotechnology

Fracture Mechanics of One-Dimensional Nanostructures

Northwestern University Rod Ruoff Nanotechnology

Carbon Nanotube Source

SEM image of powdered cathode deposit core material with 30-40% MWCNT content from MER Corp.

SEM image of separated MWCNTs on a silicon wafer, after fractionation.

Arc-grown Multi-wall Carbon Nanotubes (MWCNTs) from MER Corp. AZ. were studied in this work. A simple fractionation process was used to remove some impurities and increase nanotube concentration.

Northwestern University Rod Ruoff Nanotechnology

Testing Tool: Nanomanipulator

A home-built nanomanipulator is used to perform mechanics study inside vacuum chamber of an scanning electron microscope (SEM).

X-Y stage

Piezo bimorph

Z stageCantilever Holder

Specimen/Cantilever Holder

X-Y Stage Z-stage

Piezoelectric Actuator

Nanomanipulator inside vacuum chamber of FEI Nova 600 SEM (Ruoff group)

Home-built nano-manipulator

Northwestern University Rod Ruoff Nanotechnology

Nanoscale Tensile Test

Experimental Setup

X-Y Stage

rigid cantilever

soft cantilever

Z Stage

Tensile Test Schematic

L

L+

s

Atomic force microscope (AFM) cantilevers are used as manipulation tools and force-sensing elements.

MWCNT

Northwestern University Rod Ruoff Nanotechnology

In situ Clamping - EBID

Electron beam induced deposition (EBID) is the process of using a high-intensity electron beam to deposit structures on a scanned surface. EBID is commonly used to make clamps in situ inside SEM.

A CNT in contact with an AFM tip, before and after EBID clamping

EBID principle

Hydrocarbon molecules

EBID clamp

Exposure area

Northwestern University Rod Ruoff Nanotechnology

“Sword-in-sheath” Fracture

Outer shellInner shells

Cross-sectional area: πDΔA

D

: inter-layer separation of graphite, 0.34 nm

Multi-wall carbon nanotubes fracture in a “sword-in sheath” manner during tensile test.

Northwestern University Rod Ruoff Nanotechnology

MWCNT Diameter Measurement

(a) AFM chip holder model

AFM cantilevers (c) Gatan TEM straining holder (model 654)

(d) SEM and TEM images of a MWCNT fragment attached to an AFM tip.

(b) An AFM chip in the AFM chip holder

Cantilever holders were designed to hold a shortened AFM chip for nanotube diameter measurement in TEM.

Northwestern University Rod Ruoff Nanotechnology

Stress & Strain Measurements

The whole tensile testing process was recorded by taking SEM images at each loading step.

Northwestern University Rod Ruoff Nanotechnology

MWCNT Tensile Testing Result

Fracture Strength Elastic Modulus

Average elastic modulus: ~ 910 GPa

Northwestern University Rod Ruoff Nanotechnology

Multiple Loading (Tube #6)

Test #

Gauge Length

(m)

Breaking Force

(nN)

Tensile Strength

(GPa)

Failure Strain

(%)

Elastic Modulus

(GPa)

1 4.08 220 21 1.4 1.8 0.3 1200 210

2 3.75 240 23 1.4 1.9 0.3 1250 210

3 3.46 420 41 2.6 3.0 0.2 1230 130

(1) (2) (3)

Northwestern University Rod Ruoff Nanotechnology

Nanoparticle Chain Aggregates

• Breaking Force: 42 25 nN

• Tensile Strength: 40 -100 MPa

• Elastic Modulus : 200 - 600 MPa

• Particle Contact Force: 8 4 nN

Tensile TestingStretching a chain

Contact Force MeasurementCarbon nanoparticle chain aggregates

• Nanoparticle diameter: 25-35 nm• Chain length: ~ 2 m

Northwestern University Rod Ruoff Nanotechnology

Nonlinearity: Large Deflection + Misalignment

)()( yFxLFMds

dEI yxxy

dF

EIL

dF

EIdy

dL

EIF

x

y

y

o

0

0

0

00

00

0

2

02

)sin()sin(

cos

2

)sin()sin(

sin

2

)sinsin

1(

2

where Fx=Fsin and Fy=Fcos

(Transformation; Converting to elliptic integrals)

LkFkF

k

kFkF

kEkE

LkFkF

k

kFkF

kEkE

kFkFL

EIF

x

y

cos),()(

cos2sin)

),()(

),()(21(1

sin),()(

cos2cos)

),()(

),()(21(

)),()((

1

1

1

1

1

1

1

1

212

F(k),F(,k) complete and incomplete elliptic integral of first kind. k and 1 are obtained from angle 0 with following relationships:

12sin 20 k

k2

2sin 1

L

F

x

y

y

0

x

s

Fy

Fx

(x,y)

Northwestern University Rod Ruoff Nanotechnology

Experimental Data Analysis

Slope

0

(degree)

Loading

Angle

(degree)

Applied Load Vertical Deflection y

Linear

(N)

Analytical

(N)

Error

(%)

Measured

(m)

Linear

(m)

Analytical

(m)

11.0 36.8 25.3 29.7 14.8 42.9 42.2 42.3

17.4 5.5 23.5 24.9 5.6 68.7 70.8 70.3

9.22 42.0 20.8 23.9 13.0 30.6 32.2 32.3

11.6 2.0 19.4 19.6 1.0 41.4 40.5 40.4

15.0 24.3 27.6 31.4 12.1 52.9 52.4 52.3

• AFM cantilevers were used as force-sensing elements in our nanoscale tensile testing experiments on templated carbon nanotubes inside SEM.

• Large deflection of the cantilever beam was encountered in the tests along with non-ideal alignment of the specimens.

• The linear analysis underestimated the applied load up to 15 %.

Northwestern University Rod Ruoff Nanotechnology

Error in Linear Estimation

L

L

EIKF

yL

yLL

0

20

3

2

cos2cos/

0

02

3

2

cos2

L

EI

LF

yL

L

212

2

02

)),()((

))sin()sin(

1(

2

0

kFkFL

EI

dL

EIF

o

LkFkF

k

kFkF

kEkE

dF

EIdyy

y

sin),()(

cos2cos)

),()(

),()(21(

)sin()sin(

sin

2

1

1

1

1

00

0

0

sin),()(

cos2cos)

),()(

),()(21(

)),()((

1

1

1

1

21

2

kFkF

k

kFkF

kEkE

L

kFkFEI

LF

yA

A

Normalization

Linear analysis

Analytical analysis