Carbon Composite Strengthening: Effects of Strain Rate Sensitivity and Feature Size
by
Eric Brannigan, B.S.
A Thesis
In
MECHANICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE IN
MECHANICAL ENGINEERING
Approved
Alan F. Jankowski, PhD. Chair of Committee
Iris Rivero, PhD.
Alexander Idesman, PhD
Peggy Gordon Miller Dean of the Graduate School
May, 2012
©Copyright, 2012 Eric Brannigan
Texas Tech University, Eric Brannigan, May 2012
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Acknowledgements
I would like to thank everyone who helped me get to where I am today, because without
them, none of this would have been possible. First I would like to thank Dr. Alan Jankowski for
help with everything, from obtaining the samples to the editing of the thesis. With his guidance I
learned about life, school, and more than I thought I could ever learn about materials of all
kinds. I would also like to thank Dr. H.S. Tanvir Ahmed who taught me how to use the all the
tools in the lab, gave me advice on being a teaching and research assistant, and told me what to
expect from graduate school. I would like to thank Dr. Hermann and the Bruker/CETR staff for
their help calibrating the Universal NanoMaterial Tester and running the experiments. I would
like to thank my thesis committee Dr. Alexander Idesman and Dr. Iris Rivero as well for their
expertise and advice when it came to my degree. I would also like to thank everyone in the
Mechanical Engineering Department and the Texas Tech University Graduate School for
supporting my research and making everything possible. I would last like to thank my family and
friends, because it was only with all their support that I was able to stay focused on my goals
and graduate.
Texas Tech University, Eric Brannigan, May 2012
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Table of Contents
Acknowledgements i
Abstract iv
List of Tables v
List of Figures vi
Chapter 1 1
Introduction 1
1.1 Nanomaterials 1
1.2 Carbon Composites 3
1.3 Forged Turbostratic Carbon Fiber Composite 4
1.4 Nano class composites 9
Chapter 2 12
Experimental Methods 12
2.1 Three Point Bending 12
2.2 Characterization Methods 15
2.3 Carbon Imaging 18
Chapter 3 19
Analytic Models 19
3.1 Three Point Bending 19
3.2 Nanoanalyzer 22
3.3 X-Ray Diffraction 24
Chapter 4 27
Results 27
4.1 Bending Test 27
4.2 X-Ray Diffraction 31
4.3 Universal Nano Materials Tester 34
Chapter 5 44
Discussion 44
5.1 Turbostratic Carbon Fiber Composite 44
5.2 Nanocomposites 45
Chapter 5 46
Conclusion 46
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6.1 Present Work 46
6.2 Future Work 47
References 50
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Abstract
Strain rate sensitivity of strength is analyzed for a bulk, turbostratic carbon reinforced epoxy
resin composite. The strength of the composite was measured using a rate-modified version of
the standard, 3-point bending test. Rate sensitivity of stress was calculated by varying the strain
rate of stress on the samples, and measuring the increase in yield strength. Metal reinforced
carbon matrix composite coatings were also examined, with CuC, NiC, and CuNiC samples
analyzed using nano-indentation and tapping mode AFM hardness and modulus measurements.
The carbon structures within the coatings are nanoscale, and characterization of the carbon
features in the coatings and the bulk fiber composite allow for conclusions to be drawn
regarding the structured relationship within metallic and non-metallic carbon composites. For
the fibers, we find that bending strength is rate sensitive as attributed to the turbostratic
carbon-fiber component. The material has a strength to weight ratio comparable to Ti-6Al-4V
alloy.
For the coatings, we find that the hardness and elastic modulus are dependent on whether
the morphology is layered versus particulate, with the nanodisperse morphology having the
highest hardness and elastic modulus.
Keywords: turbostratic carbon; strain rate sensitivity; nanomaterials; 3 point bending; tapping
mode; nanoindentation; Cu(Ni)/C; thin film; nanostructured coatings
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List of Tables
Table 1.1 Material Properties ............................................................................................. 6 Table 4.1 List of all coating results .................................................................................... 43
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List of Figures
Figure 1.1 Grain size and activation volume 2 Figure 1.2 Stress strain curve showing regions where strain rate sensitivity (m) and
stain hardening (n) occur 7 Figure 1.3 SEM images of FTCFC with epoxy etched away to reveal fiber size. 8 Figure 2.1 Three 3 point bend test is realized for strength measurement of the
FTCFC material 14 Figure 2.2 High resolution bright-field TEM images representing cross sections of –
(a) Cu/C (b) Cu(Ni)/C and (c) Ni/C nanostructured materials 18 Figure 3.1 Approximation of beam bending path using 4th order approximation 21 Figure 3.2 The Miniflex II is a compact tabletop x-ray diffractometer that scans in
the θ/2θ mode 25 Figure 3.3 Detail of the internals of the Miniflex II: the sample (at center) rotates
counter-clockwise along with the detector (at right) as exposed to an incident collimated x-ray beam from the emitter (at left) 25
Figure 3.4- XRD scan of turbostratic carbon with an epoxy superimposed Peaks indicate amorphous carbon behavior. 26
Figure 4.1 Typical loading/displacement curve for turbostratic carbon composite 28 Figure 4.2 Three FTFC samples loaded at varying strain rates 29 Figure 4.3 Strain rate sensitivity of stress 30 Figure 4.4 Bragg reflections as recorded in the θ/2θ mode for CuKα radiation for
the Cu(Ni)/C coatings 32 Figure 4.5 Ni/C: λNi/C = 4.49 nm; 4 nm C-top/bottom layer; ΓNi = 0.40; N = 24;
unpolarized; E = 8.04 KeV (Cu kα radiation) 33 Figure 4.6 Cu/C: λCu/C = 3.0 nm; 4 nm C-top/bottom layer; ΓCu = 0.347; N = 75;
unpolarized; E = 8.04 KeV; σrms = 1.26 nm (best fit) is >hCu 33 Figure 4.7 Cu(Ni)/C: λCu(Ni)/C = 3.34 nm; 4 nm C-top/bottom layer; ΓCu(Ni) = 0.35; c =
Cu.66Ni.34; N = 30; unpolarized; E = 8.04 KeV; σrms = 0.53 nm 34 Figure 4.8 Approach curve for Cu/C 36 Figure 4.9 Cu(Ni)/C approach curve 37 Figure 4.10 Ni/C approach curve 37 Figure 4.11 Cyclic load-displacement curves for Cu/C (left), Cu(Ni)/C (middle), and
Ni/C (right) as determined with the NI module 39 Figure 4.12 Variation of hardness with contact depth shows the nanodisperse
Cu(Ni)/C laminate has the highest surface hardness 40 Figure 4.13 The variation of elastic modulus with contact depth shows a slightly
higher stiffness for the nanodisperse Cu(Ni)/C laminate 42
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Chapter 1
Introduction
1.1 Nanomaterials
Hall-Petch strengthening has been well documented1,2 and established for polycrystalline
nanostructures. Feature size, such as grain size, affects the strength of these materials on the
bulk scale. Strengthening can be defined as inversely proportional to the square-root of a
dimensional feature (h), such as grain size. For example, the tensile strength can be expressed3
as a function of grain size as seen in equation (1.1) as
(0.1)
where σo is the intrinsic strength, and ks is a material constant. M. Dao et. al.4 describe this
phenomenon experimentally with quantification of the mechanical behaviors for several
nanocrystalline metals. There is a critical grain size for increasing strength, and at this critical
point there is an increase of grain boundary effects that reduce strength, offsetting the
reduction of dislocation-based strengthening mechanisms. This reduction in strength is
dependent on atomic size and spacing5, and can be seen in Figure 0.1 Grain size and activation
volume, representative of the Ni-W system. The minimum activation volumes shown
correspond with the maximum strength in relation to grain size, and for all metals this minimum
grain size is on the order of nanometers.
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Figure 0.1 Grain size and activation volume
In general, at some degree of grain refinement to the nanoscale, the enhancement of strength
becomes saturated and then softens as the constituent nanocrystalline (nc) phase eventually
transitions to an amorphous structure. This is evidenced in nc Au-Cu at grain sizes below which
Hall-Petch strengthening ceases. The activation volume rapidly increases, and strain-rate
sensitivity m decreases below 6-7 nm grain size.
The anticipated loss of strength for nanocrystalline materials with grain sizes below some
critical value coincides with the absence of conventional dislocation-based mechanisms6,7,8, and
is generally described as the devolution from perfect dislocation slip along grain boundaries into
partial dislocation assisted twinning and stacking faults9. This behavior is followed by grain
boundary migration and triple-junction motion10,11,12 as in the case of high strain rate plasticity.
For nanoscale deformation on such a small scale, softening can be modeled using grain
boundary sliding molecular dynamics simulations.
An alternative physical concept that can be used to achieve such a generalization is to view
nanocrystalline and ultrafine grain polycrystalline structures as a mixture of bulk and grain
0
5
10
15
20
25
30
35
40
45
1 10 100 Ac
tiva
tio
n V
olu
me
(v/b
3)
Grain Size (nm)
Activation Volume/Grain Size
Ni
Ni-W
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boundary phases. The two phases can interact mechanically by exchanging mass and
momentum, but the overall ‘‘composite’’ should obey the standard balance laws of continuum
mechanics with each phase obeying its own constitutive equations.
1.2 Carbon Composites
The objective of this research is to compare several carbon composites that are very different
in structure in order to determine the varying effects of deformation mechanisms on strength.
When a component needs light weight and high strength, many modern designers look to
Carbon composites. Some of the strongest carbon composites are made with carbon that is sp3
bonded: nanotubes, buckyballs, or graphene sheets. While being superior to all other forms of
carbon in terms of strength to weight ratio, mass production of mainstream consumer goods
featuring these products remains too expensive, so other variations of carbon strengthening
mechanisms currently dominate the industry. One such example of a carbon composite is the
forged turbostratic carbon fiber composite (FTCFC) developed by Lamborghini and Callaway at
the University of Washington13 used in both high end golf clubs and sports cars. The FTCFC is
intended for use in structural components such as automobile fenders and the crown of golf
club drivers where lightweight materials with a superior strength to weight ratio are
advantageous for design use. Turbostratic carbon14 has properties similar to both amorphous
and Diamond-Like Carbon (DLC), as its structure contains bonds representative of both.
Turbostratic carbon fibers have high tensile strength, unlike heat-treated mesophase-pitch-
derived carbon fibers which have high Young's modulus and low elasticity.
Turbostratic carbon is generally regarded as a variant of hexagonal graphite15; both consist of
vertically aligned graphene layers with a regular spacing but differ in stacking ordering.
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Hexagonal graphite is an ordered A-B stacking structure, while layers of turbostratic carbon may
randomly translate to each other and rotate while remaining parallel. Since hexagonal graphite
is a stable structure, the translation and rotation of graphene layers changes the interlayer
spacing and the shape of atomic layers. Turbostratic carbon fibers are rolled and crumpled
sheets of these hexagonal sheets that are micron scale diameter. This random orientation of
bonds within the fibers allows for some contribution to strengthening normal to the fiber axis,
but structurally it allows for the concentration of load bearing properties of graphite sheets to
be oriented along the fiber axis.
1.3 Forged Turbostratic Carbon Fiber Composite
The FTCFC is claimed to have a strength-to-weight ratio superior to that of Ti-6A-4V alloy
which has35 a failure strength of 930 MPa and a density of 4.43 gm/cc. The preparation of ASTM
standard tensile bars is awkward due to the high contact between the epoxy resin matrix and
the high strength carbon fiber. As a suitable alternative to ease constraints that damage from
conventional grab mounts would incur, a three point bend test is selected. This method is
accessible to the high loading rates that can simulate impact strain rates encountered when the
FTCFC is loaded, i.e. as when a golf club crown or car fender would be loaded upon impact.
This investigation explores the effect of varying strain rate in bending tests to determine the
extent to which strength is changed and how the strength behavior compares to metal alloy,
carbon fiber, and epoxy resin materials. Strain rate is a measure of the effect of strain ε per
second, and is denoted by έ as seen below.
(0.2)
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For a bend test, it’s determined as the variation of displacement velocity with respect to the
midspan deflection. To determine strain rate sensitivity, the standard bending test procedure
must accommodate changes in displacement velocity. The effect of stress on this parameter is
determined by comparing the logarithmic change in flow stress of the material to the logarithm
change in rate at which the strain was applied. The Dorn equation states that stress is
proportional to the exponential change in the strain rate as a power-law relationship shown
below in equation (0.3) as
(0.3)
This equation assumes that m is given by equation (1.4) as
(0.4)
In the Dorn equation, C is a material constant, and the strain rate sensitivity exponent (m) is
the slope of the logs of the stress versus strain rate. It has been widely reported16,17,18,19,20,21 that
an increase in strain rate sensitivity exponent is seen as the feature size decreases for metals
and polymers.
The effect of strain rate sensitivity is not the same as the effect of strain hardening, which has
a power-law relationship for strength with plastic strain beyond the elastic limit, i.e. the yield
point, as seen in the following equation (1.5) as
(0.5)
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Where n is strain hardening exponent, K is a material constant and ε is the strain. The strain
hardening exponent (n) differs from the strain rate sensitivity exponent (m) as the hardening
exponent comes into effect during plastic deformation, and is associated with cyclic loading,
while the strain rate sensitivity exponent changes extends the onset of plastic deformation, and
its effect can be seen in a single load on a material.
The density (ρ), yield strength (σy), and strain rate sensitivity exponents (m) characteristic of
the epoxy resin, turbostratic carbon fiber, and Ti-6Al-4V alloy are listed in table 1.1 for reference
in approximating the stress-strain response of the FTCFC. The m-values are reported for έ ranges
where deformation behavior is mitigated by solution effects (έ < 10-1 sec-1) and dislocation
behavior (έ < 10-3 sec-1).
Table 0.1 Material Properties
Material ρ (gm/cc) σy (MPa) m
Epoxy resin 1-2 50 0.1
Turbostratic carbon 1.3 10000 0.05
Ti-6Al-4V 4.33 930 0.05
To demonstrate the difference between the strain rate sensitivity exponent (m) and strain
hardening factor (n), Figure Figure 0.2 Stress strain curve showing regions where strain rate
sensitivity (m) and stain hardening (n) occur is a stress/strain curve from a turbostratic carbon
bending test that is labeled to show the difference between the elastic (red) and plastic (blue)
regions. Strain hardening occurs in the plastic region as governed by equation (0.5) whereas the
strain rate sensitivity marks the onset of plasticity at the yield point that varies with the strain
rate.
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Figure 0.2 Stress strain curve showing regions where strain rate sensitivity (m) and stain hardening (n) occur
Strain rate sensitivity is, simply put, the measure of change in yield stress related to the
change in load rate. The samples were loaded in 3-point bending at a fixed rate, with several
samples being tested at each midspan displacement rate between 0.1 mm/s and 5 mm/s.
Samples of similar strain rates are expected to have somewhat identical results, but several
variables might influence the results. Manufacturer quality control could result in variation in
sample curvature and thickness, while fiber density variation and surface flaws may influence
the measured properties of the bulk material.
Forged Composite comes mixed together in a paste of fibers and epoxy that can be squeezed
into any shape desired. The material tested is removed from the crown of a Callaway Diablo
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OctaneTM driver; the first golf club manufactured using this carbon fiber composite. Callaway
claims the substitution of the forged composite for Titanium causes a 33% reduction in weight
while at the same time causing an increase in flexural strength. The purpose of the crown in a
clubhead is to absorb energy generated in the initial high speed impact with a golf ball and
release it as the ball leaves the clubface, increasing the ball’s velocity and creating backspin. To
gain a better understanding of the scale of the fibers, some SEM images were taken of the
etched composite for viewing of the individual fibers. The fibers can be seen below in Figure
Figure 0.3 SEM images of FTCFC with epoxy etched away to reveal fiber size. where a fiber
bundle is visible after etching.
Figure 0.3 SEM images of FTCFC with epoxy etched away to reveal fiber size.
The images of the fibers indicate there may have been nanoscale features before the etchant
roughed the surface. In Figure 1.3b-c it is possible to see features that traverse the length of the
a b
c d
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fiber surface that are on the order of nanometers. These features may be due to the forging
process of the fibers or due to nanoscale carbon structures that are bundled to create these
fibers, but higher resolution imaging will be required to validate these claims.
To estimate the properties of the composite, we can compute the material’s fiber/epoxy ratio
and assume that the fiber has values are that are similar to ideal Diamond Like Carbon (DLC).
The SEM images show fibers with an average radius of ~3 μm, which allows us to determine the
volume of a single fiber viewed in cross section. With the manufacturer’s claim of 500,000 fibers
per in2, we can calculate the total area fibers occupy is approximately 2.2% of the cross section.
Using the rule of mixtures it is possible to estimate the strength of the composite using the
values from table 1.1 and equation (0.6) as
(0.6)
Assuming the fibers have the strength of DLC, or 10 GPa, their tensile strength would
contribute 220 MPa to the composite using the law of mixtures. A standard epoxy has a yield
strength of 50 MPa22, and with 97.8% of the cross section comprised of epoxy, the total yield
strength would be 268 MPa according to the rule of mixtures for composite materials along the
fiber axis.
1.4 Nano class composites
By scaling the composite to the nanoscale, the relationship between carbon and metals as
used in thin film coatings is investigated further. Coatings made up of nickel, carbon, and copper
were created using sputter deposition as a material for reflective x-ray optics, and featured
various atomic configurations. Copper and nickel were chosen because of their unique
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properties when combined with carbon. Nickel favors strong bonds and therefore tends to form
stable layers, while copper will tend to form spheres to minimize carbon contact area, as it does
not readily chemically bond with carbon. In combination, Cu and Ni form a continuous solid
solution so that alloy composition can be readily changed and assess layer formation. When all
three materials are combined, there is a tendency for nickel addition to stabilize copper layer
growth with carbon. The result of this bonding is high-Z/low-Z corrugated metal layers within a
carbon matrix. The typical hardness values for nanoscale nickel and copper are 7 and 2 GPa
respectively, which should be comparable to ~3 times the strength of their composites.
Morphology change and 3D structuring could have an effect on hardness and elastic modulus
values, increasing both values with the increase of vertical structuring relative to the surface.
Isolated nickel-copper clusters may then evenly distribute throughout the matrix. These
carbon regions could affect the overall elastic modulus measurement of the material because of
morphology effects. Quantitative values will be measured through tapping mode hardness
testing and nano-indentation techniques. The elastic modulus and hardness will be measured by
nanoindentation (NI) and tapping-mode Atomic Force Microscopy (AFM).
The materials were made using sputter deposition using planar magnetrons operated in the
dc mode. The nanocomposite films were deposited23 onto Si(111) wafers, creating Cu(Ni)-C
coatings that were 0.15-0.25 μm thick. For the sample preparation, the exposure of the
substrate was alternately cycled between 0.05-0.2 nm·s-1 fluxes from the C and Cu(Ni) sources.
The Argon working gas was kept constant at 0.66 Pa pressure with a flow rate of 26 cm3/min.
The carbon was sputtered under the conditions of 450-550 W and 415-525 V, the nickel was
kept at 50 W with 300 V, and the copper at 35 W and 250 V. In all the samples, the working
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distance was kept at 10 cm to keep the energetic sputtered neutrals completely thermalized, i.e.
reducing the kinetic energy to zero. This deposition condition should eliminate all intermixing
between component layers and interfaces attributed to energetic bombardment effects during
the deposition process, but the chemical gradients and strain energy contributions can still also
affect the shape of the forming composite structure.
Verification of these results is possible using the Universal NanoMaterials Tester (UMNT) with
the Nanoindenter attachment (NI). This nanoscale measurement tool makes it possible to
measure the elastic modulus in addition to the hardness of these thin coatings. The
nanoindenter uses a Berkovich tip with a radius of 0.5 μm that is mounted vertically on a Linear
Variable Displacement Transducer (LVDT). Unlike the cantilever mount in the nanoanalyzer, this
unit is designed to plastically deform the surface of the material with a given load, resulting in a
strain applied over a small area and depth.
The effect of high strain rates on the deformation mechanisms of composites was predicted to
be the result of several factors, most importantly the translation and rotation of grain structures
as the result of stress at elevated strain rate. Deformation rates are dependent on the rate of
loading, where deformation mechanisms such as grain rotation only occur during faster
deformation rates. Dislocation motion allows for additional relaxation, and since dislocations are
smaller than grains, dislocation motion is more prevalent at slower deformation rates.
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Chapter 2
Experimental Methods
Three Point Bending
Tensile tests and bending tests are the two most common means of measuring bulk material
properties, applying a Linear Variable Displacement Transducer (LVDT) and a load cell to
accurately measure load and displacement. The stress and strain in a material can be derived
from these measurements using equations that are dependent on the measurement technique.
Tensile tests are well suited to materials that can be formed into wires or foils and thin straight
segments that can be machined into an acceptable shape. “Dog bone” shaped samples have a
thin section of a known cross section that will bear the stress of loading, and wider end pieces
that ensure a firm grip for the test setup.
Beam bending tests are designed for materials that can be shaped into thin strips, and consist
of three and four point loading setups. The four point loading setup uses two bases, separated
by two evenly spaced deflectors. This setup is best for long specimens, and focuses on beam
deflection over a small area between the deflectors. The three point bending test uses one
moving deflector evenly separating two bases, and measures the stress over the length of the
beam held between the bases. Bending tests are preferred for the FTCFC samples because of
the natural curvature of the club head. The curvature of the strips of the composite would make
it very difficult to mount strips in the grips of a tensile tester without straightening the sample
and creating any surface stresses. The straightening of a sample as grips secure its position
creates preloading along its shortest side. This preloading might be enough to permanently yield
the sample along the concave side. Another reason bending tests were chosen is that they allow
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for more accurate measurements, because only the bottom of the beam is actually put into
tension, meaning that defects play a smaller role. This can be more accurate than a tensile test
that measures stress over a cross sectional area, because there can be more voids within the
tensile sample.
To test the rate sensitivity of the yield strength of the turbostratic carbon composite, a
modified version of the standard bending test procedure is used to accommodate the high
flexibility of the FTCFC versus metals and alloys. Mechanical testing was carried out on a Test
ResourcesTM table-top universal tester with the 3 Point Flexure Bend Fixture - G238-10-290
attachment. Three point bending test procedure calls24 for samples whose curvature to
thickness ratio is greater than 500. When the minimum specimen strip thickness is 0.51 mm, the
total length should be 165 times this value. The span length should be 100 times longer than the
nominal thickness when that thickness is less than 0.51 mm. It is also recommended that the
sample be at least 12.7 mm in width. The test setup is shown in Figure 2.1 with one of the FTCFC
samples placed on a 50.8 mm span length.
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Figure 0.1 Three 3 point bend test is realized for strength measurement of the FTCFC material
To calculate the elastic modulus and bending strength, both the load and deflection must be
recorded during testing. Data was recorded with sampling rates between 5 and 50 Hz to ensure
the total number of data points taken during the experiment would not be greater than 10,000.
To run the experiment, several deflection scripts were written and applied to each specimen at
a constant rate. A preload of 2 N was first applied to each sample to settle the sample between
the bend point mounts that provide a uniform test starting point for each experiment. The first
deflection and retraction traveled 2 mm, and this motion minimized friction at the supports. The
next deflection step straightened the sample, traveled 2 mm past the horizontal, and then
returned the sample to its preloaded state. To determine the ultimate stress, fracture stress and
yield stress, another deflection was performed where the load was increased at a constant
deflection rate until failure of the sample. All tests performed on a single specimen were
performed at a constant velocity and strain rate, and samples experienced strain rates from
0.000032 to 0.01834 sec-1 were induced with deflector velocities of 0.02 to 5 mm/s at midspan.
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The samples for the 3 point bending tests were prepared using a rotary Dremel© tool,
equipped with an SiC cutting wheel to dry cut strips out of FTCFC that were 10 cm long by 1.3
cm wide, from Callaway golf club heads. The natural curvature to the crown causes the test
strips to not be perfectly flat or perfectly straight. The extent of out of plane curvature varied
between samples, but preloading made this insignificant by removing all curvature before
loading the samples to yield.
1.5 Characterization Methods
The x-ray diffraction (XRD) measurements of long and short-range order were carried out on a
Rigaku Miniflex tabletop diffractometer, as used in the θ/2θ mode. X-ray diffraction provides
the measurement of interplanar spacing from which lattice defects, layer pair spacing,
composition profile, even crystal structure and grain size can be determined with
monochromatic Cu Kα radiation. When grain size (hg) is to be determined, the width of the
crystalline peaks for the θ/2θ scan can be assessed by means of the Scherrer equation (0.1) as
(0.1)
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where the full-width at half-maximum (FWHM) intensity at the Bragg reflection is β, the Bragg
angle is θ, the x-ray wavelength λ equals 0.15412 nm (for Cu Kα), and the shape factor is K. The
measured broadening factor βm is corrected by an instrument broadening factor βi as based on
machine calibrations to material standards. For single crystals the corrected broadening factor
βc can be determined by equation (2.2) for the Bragg reflection of interest as
(0.2)
This method is applicable25 for most crystalline materials with feature sizes between 5 and 250
nm. In addition, x-ray diffraction can be used for determining the residual stresses that
accompany combinations of varying atom sizes and displacements within the material.
Hardness and elastic modulus will be measured using loading and displacement curves
generated during testing cycles on the nanoindenter. The Oliver-Pharr method26 of analysis that
will be used for this study strictly works for materials which are polycrystalline and somewhat
homogenous in nature. The Oliver-Pharr method uses the elastic unloading regime to determine
stiffness (S) at the max displacement (hmax) in equation (0.3) as
(0.3)
Using the stiffness, the contact depth (hc) can be determined from the maximum load and
displacement using equation (0.4) as
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(0.4)
here e is a tip coefficient calibrated for the geometry of the tip. The hardness (H) and reduced
elastic modulus (E*) are determined using the contact area Ac and tip-shape coefficients (cb, b,
e). The contact area is determined by a parabolic curve fit of the loading curve as shown in
equation (0.5) as
(0.5)
The coefficient cb is determined as a function of indentation depth h by calibration to a known
material such as fused silica. With the contact area determined, the hardness can be solved by
dividing the maximum load by the contact area as in equation (0.6) as
(0.6)
E* can then be found as a function of stiffness and contact area, as well as tip constant b as in equation (0.7) as
(0.7)
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1.6 Carbon Imaging
To measure the overlap of the components, high resolution TEM images of the Cu(Ni)-C
nanostructures as shown in Figure Figure 0.2 High resolution bright-field TEM images
representing cross sections of –(a) Cu/C (b) Cu(Ni)/C and (c) Ni/C nanostructured materials were
taken23 by Jankowski, et al.
Figure 0.2 High resolution bright-field TEM images representing cross sections of –(a) Cu/C (b) Cu(Ni)/C and (c) Ni/C nanostructured materials
In the images above it is possible to see that the immiscibility of carbon in copper lead to the
formation of particles within a matrix. The limited solubility (<3%) of carbon with nickel tend
towards a stable layered growth. In Figure Figure 0.2 High resolution bright-field TEM images
representing cross sections of –(a) Cu/C (b) Cu(Ni)/C and (c) Ni/C nanostructured materialsb it is
apparent that the addition of Ni to the Cu particles presents an intermediate transition state,
with the apparent structuring of 3D objects superimposed within layered positions.
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Chapter 3
Analytic Models
2.1 Three Point Bending
The elastic modulus in bending for a beam of varying thickness is determined by the following
leaf spring equation (0.1) for three point bending27 as
(0.1)
Where L is the span length, b is the width of the beam, and h is the maximum thickness of the
sample, load is represented as P and deflection is z. The span length was set at either 76.2 or
50.8 mm (3 or 2 inches), depending on which condition best fit the length of the sample to
produce a midspan deflection at failure that is 1-2% of the span length below a horizontal. The
thickness of the samples varied from 1.2 mm to 1.65 mm, dependent upon both the individual
clubhead as well as the position in the clubhead crown. The yield strength is determined for a
beam in bending from the maximum load by the following equation (0.2) as
(0.2)
This equation is derived from equation 3.3 below for bending stress in a beam(0.3) as
(0.3)
Texas Tech University, Eric Brannigan, May 2012
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Where M is the bending moment, c is the perpendicular distance from the outermost surface to
the neutral axis, and I is the area moment of inertia. This solution to the bending equation (0.2)
requires the yield load Py to determine the maximum strength at the center of a beam, in a
loading system identical to the leaf spring of a car. A leaf spring can be approximated as two
cantilevers28 of varying thickness joined at the point of loading, i.e. the same loading setup as
the three point bend test. The yield stress and elastic modulus equations (0.1) and (0.2) only
apply to constant thickness beams that are loaded at the center, and does not account for
variance in beam dimension. This can lead to some problems for the samples that have a
variation in thickness where the thickest section is not directly underneath the contact point of
loading. In order to increase accuracy in results, this equation will be modified to include the
thickness at the point of failure, as some samples did not yield at the point of loading.
For beam segments that evidenced failure at a position offset from the load, a modified
version of these equations will allow for the measurement of the stress and load at the point of
failure. For proof stress, which is a function of bending moment in the direction of beam length,
meaning the stress varies linearly between the maximum value and zero as a function of
distance from the center, and the bending proof can therefore be calculated from the following
equation (0.4) as
(0.4)
Where x is absolute value of position of the failure point along the beam as measured from the
center, and α represents the location of the load, which will be equal to ½ for all three point
bending tests. The deflection of the beam at any point along its length (L) can be determined by
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assuming the ends are constrained and the deflection is roughly parabolic, which leads to the
creation of the following equation (0.5), which generates a deflection as shown in Figure Figure
0.1 Approximation of beam bending path using 4th order as a 4th order displacement where
(0.5)
Figure 0.1 Approximation of beam bending path using 4th order approximation
Equation (0.4) uses the same values for x, α, and L as the previous equation, and uses δmax as
the position of the indenter during the test. Figure Figure 0.1 Approximation of beam bending
path using 4th order shows the deflection of a beam in the direction of loading, with deflection
calculated in terms of maximum deflection and length in terms of the maximum distance from
center. The strain is calculated below in equation (0.6) as
y = -1x4 + 2x2--1 -1
-0.5
0
-1 -0.5 0 0.5 1
No
rma
lized
Defl
ecti
on
Normalized Length
Deflected Beam Shape
Texas Tech University, Eric Brannigan, May 2012
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(0.6)
In equation (0.6), L and δx represent the same values as previous equations, and h is the
thickness of the beam at the point of interest. In equation (0.7), the strain rate έ is found to be
the derivative of equation (0.6) as a function of time, where the deflection is time dependent
and replaced with velocity v as
(0.7)
2.2 Nanoanalyzer
Traditional penetrating measurements of hardness successfully measure bulk materials29, but
are often unable to measure thin films due to the aspect ratio between the penetration depth
and the film thickness. Nano-indentation and tapping mode Atomic Force Microscopy (AFM) are
two characterization methods that implement submicron scale surface interaction to find the
elastic properties of thin films. Nano-indentation was carried out using Bruker-Center for
Tribology Research’s (CETR) Universal Nano-Materials Tester (UNMT or UMT), utilizing a
Berkovich anvil diamond tip with a 500 nm tip radius. To measure the elastic modulus and
hardness, nine load cycles with ramped loads between 0.1 mN and 5 mN were applied to a
single point on the surface of the material, and this process was repeated at 9 different points
on the surface, making for a total of 81 data curves being generated for each sample. The
relationship between penetration depth and applied load allows the user to compute the elastic
modulus and the hardness of the material at each given depth. For thin films, it is well known
from the application of Meyer plots30 that at 10% of the film thickness there is a significant
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contribution from the substrate that increases with increased indent depth. All of the thin film
coatings measured in this paper were deposited on Si (111) wafers with a known elastic
modulus of 180 GPa and hardness of 10 GPa, which is significantly harder than copper and
nickel.
The tapping-mode AFM measurements were made using the same CETR unit, but with the
Nanoanalyzer (NA) tool, which uses a Berkovich tip mounted on an oscillating fork that can
produce images, tapping mode measurements, and perform scratch tests. The NA tapping mode
technique was used for confirmation of the measurement of the elastic modulus of the thin
films. The tapping mode measurement allowed for the determination of the reduced elastic
modulus, and therefore the material’s elastic modulus using known values of Poisson’s ratio for
the diamond tip and the material. The change of vibration frequency (Δf) is measured as the tip
approaches the surface, which is caused by van der Waals forces changing the tip vibrating
frequency as the tip to surface separation approaches zero. When the changing frequency is
measured, the next equation (0.8) can be used to calculate the reduced elastic modulus as
(0.8)
Where E* is the reduced elastic modulus for the material being measured and the tip, C is a
machine constant, and α is given by the following equation (0.9) as
(0.9)
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In this equation, the change in ΔF2 is compared to the change in tip displacement z (in arbitrary
units). Laser interferometry is used to directly calibrate the arbitrary tip displacement units with
the actual elevation in nanometers.
2.3 X-Ray Diffraction
In addition to these tests which characterize material strength and hardness, x-ray diffraction
was carried out on the nanoscale coatings to determine surface morphology and laminate layer
behavior. A Rigaku Miniflex-II was used to bombard surfaces of the samples with x-ray radiation
as they rotated through a range of 1° to 70° 2θ with respect to the x-ray source. This means
while the x-ray source does not move, the sample rotates θ degrees and the detector rotates 2θ
around the sample, effectively keeping the angle between the surface and the emitter (θ) equal
and opposite of the angle between the surface and the detector (θ). The resulting intensity
measurements of x-rays diffracted from a surface allows for the determination of interatomic
spacing as well as laminate layer-pair spacing. Local maxima in the intensity correspond to the
interplanar spacing of the elements present, while the widths of these peaks correspond to the
domain (i.e. grain) size. The metals analyzed here are face centered cubic (FCC) structures,
meaning the most easily visible diffracted planes will be those that are close packed in the [111]
direction. The distance (d-spacing) between atomic planes of one composition can be measured
using Bragg’s law, seen in equation (3.10) as
(0.10)
where n is the order of the reflection (1st, 2nd, 3rd, etc.), λxray is the wavelength of the x-ray
radiation emitted, θ is the angle between the surface and the incoming beam, and d is the
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interplanar spacing. Figures Figure 0.2 The Miniflex II is a compact tabletop x-ray diffractometer
that scans in the θ/2θ modeand Figure 0.3 Detail of the internals of the Miniflex II: the sample
(at center) rotates counter-clockwise along with the detector (at right) as exposed to an incident
collimated x-ray beam from the emitter (at left) show the Rigaku Miniflex II and its rotating
components.
Figure 0.2 The Miniflex II is a compact tabletop x-ray diffractometer that scans in the θ/2θ mode
Figure 0.3 Detail of the internals of the Miniflex II: the sample (at center) rotates counter-clockwise along with the detector (at right) as exposed to an incident collimated x-ray beam from the emitter (at left)
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A successful test will record and output a graph plotting x-ray intensity versus angle 2θ. Figure
3.4 shows two superimposed scans (in red) for turbostratic carbon and one independent scan (in
green) for an epoxy resin.
Figure 0.4- XRD scan of turbostratic carbon with an epoxy superimposed Peaks indicate amorphous carbon behavior.
The FTCFC (red curve) has peaks similar to amorphous and diamond like carbon as well as the
epoxy resin (green curve). The positions of peaks for turbostratic carbon (t-C) and hexagonal
carbon (h-C) are labeled. It can be seen in the results that there is evidence of these carbon
forms within the FTCFC. The epoxy resin scan was taken from a sample of a Fibreglast, Inc.
product as made with bisphenol-A-based 2000 epoxy and 2120 hardener components.
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Texas Tech University, Eric Brannigan, May 2012
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Chapter 4
Results
3.1 Bending Test
After all of the bending tests were performed, loading curves from the maximum deflection
tests were analyzed to determine the strength of the FTCFC. A sample curve is shown below in
Figure 4.1 that displays the raw data from one test. The sign of the loading is negative for
tension where the deflection is negative for beam surface expansion. It is possible to see the (I)
preloading of the sample to a flat horizontal position, and the elastic region of interest (II) as
highlighted in red.
-120
-100
-80
-60
-40
-20
0
20
-15 -10 -5 0 5 10
Lo
ad
(N
)
Displacement (mm)
I
II V
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Figure 0.1 Typical loading/displacement curve for turbostratic carbon composite
In Figure 4.1, we see a loading curve from a three point bending tests representative of all
loading curves, with several regions highlighted. Region I shows the deflection to reduce
curvature to zero, region II shows the loading of the beam in the elastic regime, region III is the
onset of failure at yield, region IV is the region of plastic deformation where the linear σ-ε
relationship no longer applies, and region V is where widespread visible fracture occurs. The test
started out at an elevation of 6 mm and straightened out fully at a position around -4 mm (I and
II) for a 10 mm displacement. It then yielded at a -7 mm elevation (III) before snapping at a -10
mm elevation. The result was a 16 mm total deflection from the start to finish of the
experiment. For this experiment, it can be seen that the onset of 3 pt beam bending behavior
for analysis occurred at a load of -26 N (I and II), the yield load was at -70 N (III), and the
ultimate load was -96 N.
With this information available for each sample, conversion of load to stress and deflection to
strain were performed using equations (3.1) and (3.2). The result produced stress-strain curves
as seen in Figure 4.2 that showed strain rate sensitivity causing an increase in yield stress due to
increasing strain rate. In Figure 4.2, there are three of these bending test results arranged
alongside each other for clarity. The fastest rate showing a higher yield stress and therefore,
larger elastic section than at the lower strain rates. The curves have been inverted through the
origin so that the values for stress and strain are now positive to ease use when viewing. The
preloading data (I) and the post-fracture data (V) are not shown as it was not required for the
strength calculations.
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Figure 0.2 Three FTFC samples loaded at varying strain rates
The strain rate sensitivity is determined from the results of experimental yield strength as a
function of strain rate for each bending test, and then plotting the results in Figure 4.3 through
the relationship of equation (1.1). Almost all of the results fall within an 8% error associated
with the yield strength measurement.
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Figure 0.3 Strain rate sensitivity of stress
From the curve fit of the data in Figure 4.3, it can be determined that the strain rate sensitivity
exponent (m) of the carbon-fiber reinforced epoxy matrix composite was found to be 0.056 ±
0.016. The turbostratic carbon fiber composite had a yield strength that increased from 230.3 to
362.4 MPa corresponding to the increasing strain rate of the experiments. In comparison, strain
rate sensitivity exponents between 0.03 and 0.1 are typical31 for ceramics loaded within this
strain rate range.
To assess the manufacturer ascertain of an improvement in the yield strength to volume ratio
versus Ti-6Al-4V, it is necessary to compare the density of the composite to that of titanium. The
mass and volume of the composite were measured using a microbalance and micrometer
respectively, and the density of specimen was determined to be 1.3 g/cm3, which falls inside a
y = 418.65x0.0561 R² = 0.7117
100
1000
0.00001 0.0001 0.001 0.01 0.1
yie
ld s
tren
gth
σy (
MP
a)
strain rate έ (s-1)
Strain Rate Sensitivity
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density range typical for many epoxy composites32. Taking the calculated yield stress range, the
maximum strength to volume ratio can be directly compared to the strength to density ratio
seen in equation (0.1) as
(0.1)
Where R is the stress to density ratio, σy is the yield stress and ρ is the material density. This
ratio makes it possible to calculate the maximum and minimum values for a computed strength
to density ratio, which ranges between 174.9 to 275.2 MPa cm3/gm as a function of strain rate.
Using the properties of a 60% α phase titanium alloy33,34,35,36,37, typically used in the sporting
and aerospace industry, we can directly compare our measured results to a bulk titanium that
will be very similar to the titanium used in the clubhead. With a density of 4.43 g/cm3 and a yield
strength of 930 MPa, the titanium alloy has a strength to density ratio which is 209.9 MPa
cm3/gm. It can therefore be said that based on the results of the experiments, the maximum
strength to density ratio of the carbon composite is 1.3 times that of Ti-6Al-4V.
3.2 X-Ray Diffraction
X-ray diffraction scans were taken of the copper/carbon Cu/C, nickel/carbon Ni/C, and
copper(nickel)/carbon Cu(Ni)/C nanostructured samples covering the 2θ angles ranging from 0
to 80° to determine crystalline structure, with the results shown below in Figure 4.4 below.
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Figure 0.4 Bragg reflections as recorded in the θ/2θ mode for CuKα radiation for the Cu(Ni)/C coatings
Bragg reflections from these θ/2θ scans of all the composite coatings at high angle are used
to determine the Long Range Order (LRO) of the structure. These scans indicate by the large
peak widths that the carbon-based coatings are nanocrystalline. A single grain would reflect all
the x-rays back at one angle creating a narrow reflection range, while a mosaic of smaller grains
can be aligned differently producing a wide range where the peak is reflected. The lack of a
distinct carbon peak indicates that the carbon present is likely to be amorphous as is found for
sputter deposited carbon, i.e. a disordered structure. To determine the Short Range Order
(SRO), higher resolution scans must be completed, this time focusing on the grazing angles
(θ<12°). To determine the surface roughness (σrm), the x-ray reflectivity is simulated38 at grazing
incidence through use of the Fresnel equations and Kohn’s analytic formulae. A computer
program is available through the Lawrence Berkeley National Laboratory website as based on
the Henke simulation program code39 where the interface roughness for each sample was
computed as based on the presence of multiple peaks and their intensity profile. The simulation
used input parameters of composition, multilayer period (λ), the ratio of the bottom layer
Texas Tech University, Eric Brannigan, May 2012
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), the
number of layer pairs (N), substrate material, x-ray polarization, and the x-ray source energy.
Simulations derived from this method were compared to the experimental grazing angle scans,
and the results for unpolarized, 8.04 KeV (Cu k) x-rays are shown below in Figures 4.5-4.7.
Figure 0.5 Ni/C: λNi/C = 4.49 nm; 4 nm C-top/bottom layer; ΓNi = 0.40; N = 24; unpolarized; E = 8.04 KeV (Cu kα radiation)
Figure 0.6 Cu/C: λCu/C = 3.0 nm; 4 nm C-top/bottom layer; ΓCu = 0.347; N = 75; unpolarized; E = 8.04 KeV; σrms = 1.26 nm (best fit) is >hCu
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Figure 0.7 Cu(Ni)/C: λCu(Ni)/C = 3.34 nm; 4 nm C-top/bottom layer; ΓCu(Ni) = 0.35; c = Cu.66Ni.34; N = 30; unpolarized; E = 8.04 KeV; σrms = 0.53 nm
The surface roughnes
nanolaminate has the smoothest transitions, its roughness value of 0.28 nm was much less than
the observable layer thickness from TEM cross sections, i.e. confirming the presence of a
layering effect. Roughness values in Figure 4.6 for Cu/C where λCu/C = 3.0 nm showed an
estimated roughness greater than the component metal layer thickness (hCu), i.e. evidencing the
lack of true layering. The result for the Cu(Ni)/C sample in Figure 4.7 where λCCu(Ni)/C = 3.34 nm is
in between where a 0.53 nm roughness is fit to a Cu(Ni) layer that is 1.17 nm thick. The TEM
images taken in cross section as seen in Figure 2.2 confirm this result, with some evidence of
layering effects discernible between metallic structures within the carbon matrix.
3.3 Universal Nano Materials Tester
With images and x-ray diffraction scans confirming the presence of nanoscale morphologies,
physical property tests were needed to evaluate the change of hardness and elastic modulus in
these coatings. The Universal Nano Materials Tester (UNMT) uses several different test modules
interchangeably to measure the properties of coatings and bulk materials, allowing for multiple
Texas Tech University, Eric Brannigan, May 2012
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property measurements on each material system with a single tool. The Nanoindenter (NI) and
Nanoanalyzer (NA) modules allow for Young’s modulus (E) measurements of coatings to be
taken using different techniques on the same tool platform. In addition, the NI allows for
hardness measurements to be taken at depths within nanoscale coatings that are not influenced
by substrate properties. Calibration measurements were carried out with well established
reference values provided for Young’s modulus. These reference materials include:
polycarbonate (3.5 GPa), fused silica (71.7 GPa), Si(100) (130 GPa), Si(111) (188 GPa), Ni(111)
(305 GPa) and W(110) (410 GPa).
The first method undertaken to measure elastic modulus was the tapping mode of an Atomic
Force Microscopy (AFM). The tapping mode allows direct measurement of elastic deformation
at displacements40 of only 5-20 nm, making it the best technique for characterizing submicron
scale coatings. The elastic regime is found as the cantilever probe is brought into contact with
the surface and the amplitude (Am) of vibrations is suppressed to less than 1 nm. To determine
the reduced elastic modulus (E*), linear variation between the square of the change in resonant
frequency shift (Δfr)2 with displacement of the tip position (z) is set equal to α2. The square root
of this measured α value is then plotted versus the reduced elastic modulus (E*) using a power
law relationship defined previously in equation (0.8).
A summary of the tapping mode test results is shown in Figures 4.8-4.10 for Cu/C, Cu(Ni)/C,
and Ni/C, respectively. The top panel of each Figure shows the squared frequency of all nine
approach curves, with an average curve shown in red. The middle graphs display the amplitude
of the tip vibrations of the approach curves. The blue lines establish the boundaries of the
region of interest wherein the amplitude decreases from one to zero nanometers. The bottom
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panel compares the actual tip height z, measured by laser interferometry to the displacement
transducer in the NA as measured in arbitrary units. Module results are shown below for
frequency shifts (Δf2) (top row), amplitude (A), (middle row), and tip to surface separation (z),
(bottom row) with verification with tip displacement (z) in arbitrary units. Figures 4.8-4.10 show
the results for all experiments.
Figure 0.8 Approach curve for Cu/C
Δf2 (Hz2)
A (nm)
Z (nm)
a (au)
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Figure 0.9 Cu(Ni)/C approach curve
Figure 0.10 Ni/C approach curve
Δf2 (Hz2)
A (nm)
Z (nm)
a (au)
Δf2 (Hz2)
A (nm)
Z (nm)
a (au)
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Using the calibration acquired from tests on fused silica, the reduced elastic modulus E*
values are determined for this particular Berkovich-indenter cantilever probe and shown below
in the equation below (0.2) as
(0.2)
To verify these NA modulus measurement results, indentation tests were carried out on the
same samples in the UNMT using the NI module. For the NI tests, 81 individual loading and
unloading curves were generated from each sample. The ramped loads for each test iteration
varying from 0.1 mN to 5 mN, with cycled unloading to 10% of the previous maximum value.
These steps were repeated 9 times at 9 different points per sample in a grid pattern evenly
spaced that measured 60 μm by 60 μm. These loading and unloading steps provide for the
measurement of the hardness, elastic modulus, width, and depth sensitivity. With thin coatings
it is well documented that there is no substrate hardness contribution within the first 10% of the
coating. The increased variation with depth will allow for measurement of the increase in the
substrate contribution, which can then be assessed in analysis of the data. The data is shown
below in Figure Figure 0.11 Cyclic load-displacement curves for Cu/C (left), Cu(Ni)/C (middle),
and Ni/C (right) as determined with the NI module with cyclic load-displacement curves for Cu/C
(left), Cu(Ni)/C (middle), and Ni/C (right) as determined with the NI module.
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Figure 0.11 Cyclic load-displacement curves for Cu/C (left), Cu(Ni)/C (middle), and Ni/C (right) as determined with the NI module
From the Figure Figure 0.11 Cyclic load-displacement curves for Cu/C (left), Cu(Ni)/C (middle),
and Ni/C (right) as determined with the NI module results, it can be seen that there are
hysteresis effects, i.e. the buildup of internal stresses from past loads, which is evidenced by the
small area between the corresponding loading and unloading curves. In a material that
experienced no hysteresis, the force generated against the indenter tip would be the same
during loading and unloading at each depth in the sample. This means that each loading line
should follow the unloading line before it until it passes the previous maximum load. Hysteresis
indicates the presence of strain hardening with progressive plastic deformation that
accompanies an increase in indentation depth. Results of the unloading curves shows that
hardness (H) and reduced elastic modulus (E*) vary with indentation depth.
The coatings also experienced some viscoelastic behavior that was detected in the
nanoindentation tests. The NI is able to detect nonlinear behavior of materials during the 9
ramped-indent testing procedure, and for some materials, hysteresis effects are prominent and
can be seen in the Figure 4.11 data. The coatings all exhibited some level of hysteresis and one
Loa
d (
mN
)
Depth (μm) Depth (μm) Depth (μm)
Texas Tech University, Eric Brannigan, May 2012
41
reason for this may be interfaces between the carbon and metal features of the material.
Temperature dependent effects of relaxation cannot be the cause because the tests were
performed at constant temperature. Therefore, there are only two41 active sources of grain
motion within these structures under these conditions that are the strain applied during
indentation, and the viscoelastic hysteresis effects.
Processing the data found in Figure Figure 0.11 Cyclic load-displacement curves for Cu/C (left),
Cu(Ni)/C (middle), and Ni/C (right) as determined with the NI module allows us to calculate
hardness and elastic modulus for each of the 81 indents and loads for each material. The Ni/C
and the Cu/C hardness values correspond with the hardness values of the pure metals3 at a
nanocrystalline grain size, while the Cu(Ni)/C displayed a significant increase in hardness at the
surface in comparison. The values that are shown below in Figure Figure 0.12 Variation of
hardness with contact depth shows the nanodisperse Cu(Ni)/C laminate has the highest surface
hardness where a variation of hardness with contact depth is measured shows that the
nanodisperse Cu(Ni)/C laminate has the highest surface hardness (GPa) of each material at
different contact depths (μm).
Texas Tech University, Eric Brannigan, May 2012
42
Figure 0.12 Variation of hardness with contact depth shows the nanodisperse Cu(Ni)/C laminate has the highest surface hardness
The indent tests that show the nanodisperse Cu(Ni)/C laminate has the highest surface
hardness is an indication of a morphological effect on the plastic deformation of these
composite nanostructures. The hardness of the Ni/C and the Cu/C are comparable to the values
of nanocrystalline metal components, which is indicative of pure metallic structures controlling
the hardness measurement. There is a divergence of values within the Ni/C indent tests, the
harder of which resembled the trend of the Cu(Ni)/C. This two phase behavior in the results can
be explained by a morphological change present at some indent sites that only affected the
group of harder indents. The TEM images in FigureFigure 0.2 High resolution bright-field TEM
images representing cross sections of –(a) Cu/C (b) Cu(Ni)/C and (c) Ni/C nanostructured
materialsshow that while layering is the dominant behavior, the Ni layer thickness varies in
some places enough to be similar to nanoparticles, and these sites would have similar properties
and behavior to the Cu(Ni)/C structure.
The nanocrystalline Cu(Ni)/C was considerably harder than either of the two pure elements,
signifying an increase in coating hardness that is often associated with high hardness and high
stiffness coatings which are used for hard surface applications such as cutting tools. Diamond-
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43
like carbon (dlc) coatings have hardness values of 15-20 GPa, whereas TiN nanolaminate-based
superlattice coatings have hardness values >40 GPa approaching the value for pure crystalline
diamond at 50 GPa. A high hardness is usually associated with a high elastic modulus, i.e. a
brittle coating. Reduced elastic modulus values (E*) measured from each indent are displayed in
Figure Figure 0.13 The variation of elastic modulus with contact depth shows a slightly higher
stiffness for the nanodisperse Cu(Ni)/C laminate below.
Figure 0.13 The variation of elastic modulus with contact depth shows a slightly higher stiffness for the nanodisperse Cu(Ni)/C laminate
A morphological effect is seen on the Cu(Ni)/C nanodisperse laminate, as it has higher elasticity
than either of its components, which is consistent with the Figure Figure 0.12 Variation of
hardness with contact depth shows the nanodisperse Cu(Ni)/C laminate has the highest surface
hardness trends for hardness. With increasing indentation depth, the E* values tend towards
the Si(111) E* substrate value of 175 GPa, which corrected gives an E value of 188 GPa that falls
within an acceptable range42.
Values from both the NI and NA tests are compiled below in table 4.1 with a list of computed
elastic moduli as determined from measurements of the reduced values. It is important to note
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44
that a Poisson ratio (v) of 0.25 is assumed in the calculations for the nanostructured carbon
composites. The elastic modulus (E) was determined using the Hertz equation and calibration
measurement assumption that for a diamond tip that (1-νi2)/Ei = 0.0008 in the following
equation (0.3) as
(0.3)
In Table Table 0.1 List of all coating results, the elastic modulus values (E) and the reduced
values (E*) for both measurement techniques are shown in bold, along with the material
constant α used to calculate them for tapping mode AFM.
Table 0.1 List of all coating results
Material H
(GPa) ENI*
(GPa) ENI
(GPa) α
(Hz/√nm) ENA*
(GPa) ENA (GPa)
Cu/C 1.7 ±0.3 43 ±4 42 37.2 59.5 58.4
Cu(Ni)/C 25 ±1 138 ±5 144 58.4 138 145
Ni/C 7.5 : 12 84 ±3 84 44.9 84.5 84.6
fused silica 9.0 69 71 35.0 70 72
Si(100) - - - 55.9 127 130
The elastic modulus results are very similar when compared between the two NI and NA
measurement techniques. Results for the fused silica, Ni/C and the Cu(Ni)/C were all within 1
GPa of each other. Tapping mode measurements were consistently higher than the
nanoindentation measurements. This means there was a slight difference between the
Texas Tech University, Eric Brannigan, May 2012
45
calibrations of the two techniques. The Cu/C result was the most diverse between the methods,
with tapping mode measurements 16.4 GPa higher than those of the nanoindentation.
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46
Chapter 5
Discussion
4.1 Turbostratic Carbon Fiber Composite
In the FTCFC, it was apparent that material response to loading varied due to strain rate, and a
standard rate bending test would not generate sufficient data to completely characterize the
behavior of the material under all conditions. In addition to strain rate sensitivity, most
composites also have a temperature sensitivity factor that influences strength and hysteresis.
Polymers also have several dislocation mechanisms42 that are strongly affected by thermal
conditions and previous loading conditions. Though the samples in this experiment were studied
at room temperature, many of the principles discussed involving thermal shifts are relevant to
this study. The ability of polymer materials to deform is determined by molecular mobility,
which is characterized by and relaxation mechanisms that are accelerated by stress and
temperature.
In the case of the turbostratic carbon-fiber composite, we saw the load was primarily carried
by fiber, which made up 2.2% of the volume. Bending test results give yield strength values
similar to those predicted using the rule of mixtures. From these assumptions, we can say that
turbostratic carbon has similar strength properties to the ceramic DLC. Ceramics are strain rate
sensitive, and in the region of strain rates between 10-1 to 100 sec-1, m values have been
reportedError! Bookmark not defined. as high as 0.30 for coatings. For strain rate sensitivities
greater than 100 s-1, strain rate sensitivity can vary greatly, even becoming slightly negative,
which would result in a loss of strength. This means a ceramic might not behave in the same
way as metals, with positive m values under high strain-rate loading conditions. Car wrecks can
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have components experiencing strain rates of 102 sec-1, indicating that additional research at
higher strain rates than were achievable in these experiments might be necessary to completely
assess the behavior of the composite wherein the ceramic fiber carries most of the load bearing
capacity.
4.2 Nanocomposites
The Cu(Ni)/C nanocomposites show a transition from a well-defined nanolaminate growth to a
dispersion of nanoparticles within a DLC matrix occurs as the Cu to Ni ratio is reduced. A
morphology effect on the nanoindentation hardness (H) and Young’s modulus (E) is measurable,
with increases observable for a layered distribution of nanoparticles. Within the Cu.23(Ni).12/C.65,
a 25 GPa hardness is measured, which is several times larger than the 8 GPa nanocrystalline Ni
and 2-4 GPa nanocrystalline Cu components, whereas the 145 GPa elastic modulus remains
relatively low in comparison to a 180 GPa value43 for polycrystalline Cu-Ni.
The ratio of elastic modulus to hardness is important in the realm of high strength coatings, as
a high E value may lead to delamination when a soft substrate deforms independently of the
surface layer. The ratio of 5.8 is several times smaller than reported for super hard coatings as
those used in the coating tool industry that typically have ratios of 10-20 or more. Some
superhard coatings such as CBN have ratios as high as 41.744 or other novel materials such as
TiO2 , which has a ratio of 28.445. A 1D to 3D transition in nano morphology has lead to a high
hardness, yet compliant composite ceramic-metallic (cermet) material.
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Chapter 5
Conclusion
5.1 Present Work
The forged, carbon fiber composite is reported by the manufacturer to have one-third the
density of titanium, yet features a greater load carrying capacity per unit mass in bending. The
entire Callaway Diablo Octane crown, which is approximately 20 in2 in surface area, contains 10
million of the turbostratic carbon fibers at the area density of 500,000 fibers/in2. The fabrication
process uses six tons of force to mold the shape of the part, which constitutes up to 33% of the
club head. These ultra-light components are claimed to result in lower total head weight and a
center of gravity lowered by 26%.
Turbostratic carbon fibers are found dominate both the strength and the rate sensitivity of the
epoxy-matrix composite behavior. Testing of the FTCFC in bending evidences strength to density
ratio that was 1.3 times higher than the Ti-6Al-4V it replaced structurally. This ratio is not quite
within measured experimental error of the 1.5 ratio that would provide for a 33% reduction in
weight while maintaining the same elastic and strength behavior. However, these current
experiments do not account fully for the exact composition of the Ti-Al-V alloy. For comparison,
the titanium alloy was assumed to have a yield stress of 936 MPa, and if, for example, a softer
titanium with a yield stress of 815 MPa had been used, it would have provided a ratio of 1.5 that
meets these specifications exactly. Titanium alloys can vary in σy based on processing techniques
as well as composition. An annealed titanium alloy, for example, will be much more flexible than
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49
one that is subject to rapid quenching. Therefore, it can be assumed that the manufacturer’s
claim of a 33% weight reduction is possible and plausible for these two materials.
For the nanodisperse carbon-matrix coatings, it is found that the hardness and elastic modulus
are dependent on whether the metallic component morphology is layered versus particulate.
The layered nanodisperse morphology for Cu(Ni)/C has the highest hardness – well above its
constituents, yet an elastic modulus closer to a rule-of-mixtures values thereby providing for a
greater H:E ratio. That is, the hardness of the Cu(Ni)/C and Ni/C thin films indicates a 3D
laminate structuring that is significantly harder than the nanocrystalline constituents alone,
while remaining relatively compliant.
5.2 Future Work
The research performed in this body of work leaves several opportunities for continuation in
the future. The FTCFC work answered some questions but left some to be answered about the
behavior of the composite under a variety of loading conditions, but perhaps did not provide a
complete understanding of the differences between the FTCFC and the titanium replacing may
be accomplished in future work. For example, tests at strain rates >10-1 sec-1 will increase the
understanding of strain rate sensitivity beyond the scope of work of this study. The strain rate
equation (0.7) shows that a decrease in sample length will most affect an increase in strain rate,
allowing for more bending tests to be performed at higher strain rates while keeping the
velocity of the tool constant at its maximum value.
High strain rate measurements can also be taken on the UMNT using the NA tool in the
nanoscratch test mode. The nanoscratch test uses the same Berkovich tip from the tapping
mode test to indent the material under an applied load while traversing its surface, which plows
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50
material out of the scratch indent as it moves. The scratch width can then be measured using
the same nanoprobe tip to perform an imaging scan of the surface. This scratch width and the
scratch indent velocity can be used to determine strain rate within the deformed material. This
technique allows for strain rates that are much greater than those achievable in bending or
tension. Strain rates of 102 sec-1 have been achieved46 using micro- and nano- scratch test
modes. Scratch testing can be done on the FTCFC as well as the titanium it replaces, and
comparisons can be made between the two materials at strain rates on the order of 102 sec-1.
The measurement of the titanium alloy in bending will allow for a reliable comparison
between the two materials and verify the claims of the manufacturer. Titanium alloy segments
can be sampled from the sole plate of the same club heads that the FTCFC samples were
removed from, even though they will be somewhat shorter due to the geometry of the club
head. Ti-6Al-4V alloys often have a hard hexagonal close packed (hcp) α-phase and a ductile
body centered cubic (bcc) β-phase. Testing the titanium alloy used will allow for determination
of the combination of the α and β phases and verification that the properties coincide with the
data. Nanoscratch tests can also be performed on the titanium alloy to determine strain rates
beyond the range measureable by the three point bending tests, and tests at these high rates
would prove that the FTCFC retains its superior strength to weight ratio at strain rates
associated with high impact conditions.
The nanoscratch testing technique could also be carried out on the nanoscale metallic
composite coatings. These tests could allow for measurements to be taken of individual
nanoscale layers for comparison of the surface scratch hardness values with those values
measured by nanoindentation. The nanoindentation method only provides measurement of the
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hardness of the layers of material in the vertical direction, where scratch testing allows for
measurement of the properties as the indenter moves along the surface. One scratch test can
provide an average hardness through scratch width measurements along its path. Nanoscale
carbon, copper, and nickel should also be tested as individual components to verify the data
collected about their bulk nanoscale properties.
Nanodisperse layered composites should also be created using alternative metals, such as
titanium or aluminum, to determine the effect of morphological variations on the increase in
hardness and yield strength. The Cu(Ni)/C samples that were tested in this study were originally
assessed for the stability of layer growth as is critical to high-performance optical use. However,
a significant morphological effect on the hardness was found. The sputter deposition of carbon
with high hardness in different morphologies will reveal if the higher hardness to elastic
modulus ratio is retained with higher hardness constituent materials, and if the structure is
optimal for mass production. A robust and economic composite nanostructure with a hardness
to elastic modulus ratio less than 1 in 10-20 would revolutionize the hard coatings industry, and
would lead to materials that are ductile in application as the substrate they are layered on,
resulting in coatings that may never delaminate or separate.
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52
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