©Copyright, 2012 Eric Brannigan

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

Texas Tech University, Eric Brannigan, May 2012

i

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.


ii

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


iii

6.1 Present Work 46

6.2 Future Work 47

References 50


iv

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


v

List of Tables

Table 1.1 Material Properties ............................................................................................. 6 Table 4.1 List of all coating results .................................................................................... 43


vi

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


1

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.


2

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


3

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.


4

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)


5

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)


6

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.


7

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


8

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


9

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


10

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


11

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.


12

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


13

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.


14

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.


15

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)


16

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


17

(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)


18

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.


19

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)


20

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


21

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


22

(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


23

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)


24

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


25

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)


26

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.


27


28

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


29

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.


30

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.


31

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


32

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.


33

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


34

), 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


35

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


36

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


37

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)


38

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)


39

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.


40

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)


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).


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-


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


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


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.


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


47

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.


48

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


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


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 nanoscratch 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


51

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.


52

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