northwestern university rod ruoff nanotechnology fracture mechanics of one- dimensional...
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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