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Electronic Theses, Treatises and Dissertations The Graduate School
2012
Through-Thickness Thermal ConductivityImprovement of Carbon Fiber ReinforcedComposites by Using a HeterogeneouslyStructured Resin MatrixDaniel Peter Gallagher
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THE FLORIDA STATE UNIVERSITY
THE GRADUATE SCHOOL
THROUGH-THICKNESS THERMAL CONDUCTIVITY IMPROVEMENT OF CARBON FIBER
REINFORCED COMPOSITES BY USING A HETEROGENEOUSLY STRUCTURED RESIN MATRIX
By
DANIEL PETER GALLAGHER
A Thesis submitted to the
Program in Materials Science
in partial fulfillment of the
requirements for the degree of
Master of Science
Degree Awarded:
Summer Semester, 2012
ii
Daniel Peter Gallagher defended this thesis on April 20, 2012.
The members of the supervisory committee were:
Zhiyong Liang
Professor Directing Thesis
Tao Liu
Committee Member
James Brooks
Committee Member
The Graduate School has verified and approved the above-named committee members,
and certifies that the thesis has been approved in accordance with university
requirements.
iii
ACKNOWLEDGEMENTS
A number of people were invaluable to the completion of this research.
I would like to thank the following people:
The Air Force for providing funding for this research
Harold Brown and Dr. Michael Zimmer for giving training on the LFA457 Microflash machine
which enabled the measurement of the thermal conductivity
Chip Young for his advice on composite construction and tab composition
Jerry Horne for his advice and tutelage on composite contruction
Dr. Shaokai Wang for all his help with the composites
Vanessa Lopez for running C-Scan tests on the samples studied in this research
Dr. Richard Liang for advising
My family for all of their support
Everyone else at HPMI for believing in me and helping me with various minor issues
iv
TABLE OF CONTENTS
List of Figures ................................................................................................................................ vi
Abstract .......................................................................................................................................... ix
1. Introduction ............................................................................................................................. 1
2. Motivation ............................................................................................................................... 2
3. Problem Statement .................................................................................................................. 3
4. Objective ................................................................................................................................. 4
5. Literature Review.................................................................................................................... 5
5.1 Thermal Conductivity ...................................................................................................... 5
5.2 Thermal Conductivity in Carbon Fiber Reinforced Composites ..................................... 6
5.3 3-D Woven Composites ................................................................................................... 9
5.4 Efforts to Improve Through-Thickness Thermal Conductivity at HPMI ...................... 11
5.6 Metallic Filler ................................................................................................................. 12
5.6.1 Copper Filler ........................................................................................................... 13
5.6.2 Silver Filler ............................................................................................................. 14
5.7 Carbon Nanotubes .......................................................................................................... 17
5.7.1 Percolation Threshold ............................................................................................. 19
5.7.2 Effects of Straightness and Aspect Ratio of Carbon Nanotubes on Thermal
Conductivity .......................................................................................................................... 22
5.8 Heterogeneously Structured Resin Matrix with Conductive Fillers .............................. 23
5.9 Laser Flash Apparatus for Thermal Conductivity Measurement ................................... 26
6. Research Uniqueness ................................................................................................................ 29
7. Patterned Resin Deposition Method ..................................................................................... 30
7.1 Materials Selection and Cost Analysis ............................................................................... 33
7.2 Proof of Concept Case Study ......................................................................................... 33
v
7.2.1 Thermal Diffusivity/Conductivity Measurement ......................................................... 34
7.2.2 Mechanical Property Tests ........................................................................................... 34
7.2.3 Microstructure Observation ......................................................................................... 34
7.3 Technical Challenges ..................................................................................................... 35
7.3.1 Resin Spreading ........................................................................................................... 35
7.3.2 Pattern Deposition and Creation .................................................................................. 35
7.4 Method Viability ................................................................................................................. 35
8. Experimentation ....................................................................................................................... 36
9. Results and Discussion ............................................................................................................ 38
9.1 Thermal Results .................................................................................................................. 38
9.2 Mechanical Results ............................................................................................................. 42
9.2.1 Tensile Results ............................................................................................................. 42
9.2.2 3-Point Bend Results.................................................................................................... 50
9.3 Morphological Analysis ...................................................................................................... 53
9.3.1 C-Scan Tests ................................................................................................................ 53
9.3.2 SEM Analysis .................................................................................................................. 59
10. Conclusions ............................................................................................................................ 63
11. Future Work ........................................................................................................................... 64
12. Bibliography .......................................................................................................................... 65
13. Biographical Sketch ................................................................................................................ 69
vi
LIST OF FIGURES
Figure 1: Temperature Gradient Heat flows from Hot (dark) to Cold (light) ................................. 6
Figure 2: Graphitic Crystals in the Core of Carbon Fibers ............................................................. 7
Figure 3: Arrangement of Carbon Atoms in Graphitic structure .................................................... 7
Figure 4: Thermal Conductivities of Select Carbon Fiber .............................................................. 8
Figure 5: Three-Dimensional Molecular Structure of Solid Epoxy................................................ 8
Figure 6: Schematic for 3D Weaving Process ................................................................................ 9
Figure 7: Previous Research Efforts to Increase Through-Thickness Thermal Conductivity of
Carbon Fiber Composites at HPMI............................................................................................... 11
Figure 8: Thermal Diffusivity of a Resin/Copper composite vs. Volume Fraction ...................... 13
Figure 9: SEM of Silver Flakes 90% <20 micron ........................................................................ 15
Figure 10: Thermal Conductivity of a Silver Flake/Resin Composite with different sized flakes.
Flake A: 3.2 Microns, Flake C: 9.9 Microns ................................................................................ 16
Figure 11: Temperature Dependence of an individual Carbon Nanotube .................................... 17
Figure 12: Thermal Conductivity of MWCNT, Graphene sheets and Graphite ........................... 18
Figure 13: Heat Transfer between Carbon Nanotubes .................................................................. 19
Figure 14: Cross-linked Carbon Nanotube Model ........................................................................ 19
Figure 15: FEM Model of Carbon Nanotube Interface ................................................................ 20
Figure 16: Effects of Interface on Thermal Conductivity ............................................................. 21
Figure 17: Effect of the aspect ratio on the H factor of a CNT's Thermal Conductivity (a) and
demonstration on how a non-straight CNT can have the same average length as a straight one (b)
....................................................................................................................................................... 23
Figure 18: Effects of Straightness and Aspect Ratio on Thermal Conductivity of a CNT ........... 24
Figure 19: SEM images of Homogeneous Silver Filler (left) and Heterogeneous Silver filler
(right) ............................................................................................................................................ 25
Figure 20: Thermal Conductivity Comparison of Filler Volume fraction in Heterogeneous and
Homogeneous Composites............................................................................................................ 26
Figure 21: Cutaway of Netzsch LFA 457 ..................................................................................... 27
vii
Figure 22: Change in Temperature vs. Time graph used to determine t1/2 ................................... 28
Figure 23: Resin pattern for Pattern Deposition Technique ....................................................... 30
Figure 24: Fisnar SL101N Resin Dispenser ................................................................................. 31
Figure 25: Pattern Deposition ....................................................................................................... 32
Figure 26: Uncured Pattern Sample .............................................................................................. 32
Figure 27: Production Setup for Automatic Resin Deposition ..................................................... 33
Figure 28: LFA 457 Microflash .................................................................................................... 36
Figure 29: Thermal Results at Room Temperature....................................................................... 38
Figure 30: Average Thermal Diffusivity ...................................................................................... 39
Figure 31: Average Specific Heat ................................................................................................. 39
Figure 32: Average Thermal Conductivity ................................................................................... 40
Figure 33: Tensile Failure Modes ................................................................................................. 42
Figure 34: Young’s Modulus of the first set of samples ............................................................... 44
Figure 35: Tensile Strength of the first set of samples ................................................................. 44
Figure 36: Mechanical Data .......................................................................................................... 45
Figure 37: Tensile test stress-strain curves of the neat samples to the 5 wt% silver samples ...... 46
Figure 38: Tensile test stress-strain curves of the 7.5 wt% silver samples to the 9 wt% silver
samples .......................................................................................................................................... 46
Figure 39: Average Young's modulus of the second set of samples ............................................ 47
Figure 40: Average tensile strength of the second set of samples ................................................ 47
Figure 41 DGM Failure (2.5 wt% Heterogeneous Sample) ......................................................... 48
Figure 42: AGM Failure (2.5 wt% Homogeneous Sample) ......................................................... 48
Figure 43: SGM Failure (5 wt% Heterogeneous Sample) ............................................................ 48
Figure 44: Flexural Test Stress-Strain Curves 2.5 wt% silver samples to 5 wt% silver samples . 50
Figure 45: Flexural Test Stress-Strain Curves of 7.5 wt% samples to 9 wt% samples ................ 51
viii
Figure 46: Max Force Applied ...................................................................................................... 51
Figure 47: Max Stress ................................................................................................................... 52
Figure 48: Max Strain ................................................................................................................... 52
Figure 49: Homogeneous 5 wt% Silver Composite C-Scan ......................................................... 54
Figure 50: Heterogeneous 5 wt% silver Composite C-Scan ........................................................ 54
Figure 51: Heterogeneous 2.5 wt% Silver Composite C-Scan ..................................................... 55
Figure 52: Homogeneous 2.5 wt% Silver Composite C-Scan ...................................................... 55
Figure 53: Heterogeneous 5 wt% Silver Composite C-Scan ........................................................ 56
Figure 54: Homogeneous 5 wt% Silver Composite C-Scan ......................................................... 56
Figure 55: Heterogeneous 7.5 wt% Silver Composite C-Scan ..................................................... 57
Figure 56: Homogeneous 7.5 wt% Silver Composite C-Scan ...................................................... 57
Figure 57: Heterogeneous 9 wt% Silver Composite C-scan ......................................................... 58
Figure 58: Homogeneous 9 w% Silver Composite C-Scan .......................................................... 58
Figure 59: SEM image of 9 wt% pattern sample .......................................................................... 59
Figure 60: AGM Failure (2.5 wt% Silver Homogeneous Composite) ......................................... 60
Figure 61: DGM Failure (2.5 wt% silver Heterogeneous composite) .......................................... 61
Figure 62: SGM Failure (5 wt% heterogeneous composite) ........................................................ 61
ix
ABSTRACT
In order to obtain an increased through-thickness thermal conductivity in carbon fiber reinforced
composites, a novel method using heterogeneously structured resin with conductive filler was
studied. Samples were produced using an alternating line pattern deposition of a highly
concentrated silver-resin mixture and the neat resin. Microstructures and properties of the
resulting composites were compared to those of a homogeneously dispersed filler matrix
composite of similar loadings.
Two different sets of pattern sample composites were produced using similar methods, but one
used a manually deposited pattern method of depositing the resin, and the other used a dispenser.
Both produced repeatable results which were comparable to each other, but the dispenser
allowed for more uniform line deposition. The thermal diffusivity and conductivity of the
resultant composites were measured by use of the LFA 457 Microflash device, and tensile and
flexural tests were also conducted to obtain their mechanical properties.
The results show that using a heterogeneously structured resin matrix with conductive filler on
the composite leads to a significant increase in thermal conductivity over the homogeneous
counterpart of the same loading, and an even greater increase over the neat carbon fiber/epon 862
composite. Through-thickness thermal conductivity in excess of 5 W/m K was obtained by
using a 9 wt% silver loading heterogeneous composite. Also the mechanical properties of higher
filler loading composites were comparable between the heterogeneously structured matrix and
the homogeneously structured matrix composites.
1
1. INTRODUCTION
Composite materials are important for many modern engineering applications. They are used in
a variety of functions that vary from the aerospace industry to automotive, sports or even medical
functions. Many different reinforcement materials can be used in composites, from chopped
glass fibers to continuous carbon fibers, from polymer-based fibers to metallic fibers.
Depending on the composite properties desired, a specific fiber type is chosen in combination
with a matrix to produce the desired composite properties.
Carbon fiber is most commonly used in aerospace applications for strong, light materials that
replace parts that were once made of metal. For example carbon fiber reinforced composites
have a tensile modulus that is comparable to steel along with a much higher tensile strength.
The density of carbon fiber reinforced composites tends to be only about 25% of steel, which is
why it is desirable to use as a replacement for metal parts on airplanes and space shuttles.
The thermal conductivity of a carbon fiber reinforced composite is anisotropic depending on
whether the measurement is along the fiber length or if it is at an angle to the longitudinal
direction of the fiber. Carbon fiber’s longitudinal thermal conductivity is comparable in
magnitude to that of graphene, but its radial thermal conductivity is lower. [1] As a result, their
composites show a much lower through-thickness or out-of-plane thermal conductivity, which is
considered a major drawback for composite materials.
2
2. MOTIVATION
2D woven carbon fiber reinforced composites display a thermal conductivity of approximately
0.3 W/m K in their through-thickness direction, and their in-plane thermal conductivity is
significantly higher, on the order of as high as 700 W/m K, depending on the type of carbon fiber
used. [1] The United States Air Force has expressed a desire for an increased through-thickness
thermal conductivity for 2D woven carbon fiber reinforced composites, thus research into
methods of increasing the through thickness thermal conductivity in affordable, efficient
methods have been researched. It is possible that the applications of such a composite would be
used to further decrease the weight of a plane or shuttle to reduce fuel consumption.
Previous research efforts to increase the through-thickness thermal conductivity have displayed
some success, but it is necessary to further study the microstructure and improve the
performance of composites.
3
3. PROBLEM STATEMENT
Current 2D woven carbon fiber reinforced composites display a through-thickness thermal
conductivity that is an order of magnitude lower than their in-plane thermal conductivity. There
are multiple reasons for this. Carbon fiber is a highly anisotropic material; its thermal
conductivity is dramatically different when measured longitudinally than when it is measured
radially. While there are some measurements taken for carbon fiber’s radial thermal
conductivity, this is not necessarily fully accurate and if such measurements are used to estimate
the thermal conductivity of a composite in the transverse direction, the estimated values are not
reliable.
Another aspect of the composite that causes low through-thickness thermal conductivity is the
fact that the through-thickness direction’s thermal conductivity is dominated by the thermal
conductivity of the resin. The matrix that transfers the load to the fibers does not conduct heat
easily due to its microstructure. While there are ways of increasing thermal conductivity of the
matrix that exist currently, the methods that exist already do not display enough of an increase to
be significant for the targeted increase. [2]
Therefore a novel method and technique must be studied and explored. For example, recently
the LORD Corporation developed a resin matrix that had the filler heterogeneously dispersed
within it. [3, 4] The reported results for through-thickness thermal conductivity were
remarkably higher than their homogeneously structured resin counterparts. By studying and
applying similar heterogeneous structures in composites, it is hoped that the dramatic
improvement of through-thickness thermal conductivity can be attained in this research.
4
4. OBJECTIVE
The objective of this research is to use heterogeneously structured matrices with conductive
fillers to increase the through-thickness thermal conductivity of carbon fiber reinforced
composites. This will be accomplished by using a method outlined later in this proposal, and if
the new technique is successful, it will be optimized such that the thermal conductivity is
maximized along with the limited impact on the mechanical properties in the resultant
composites. Detailed objectives include:
1. Select and evaluate different conductive fillers
2. Study techniques to produce heterogeneous resin matrices and composites
3. Characterize the heterogeneously structured matrix composites including:
a. Mechanical properties
b. Thermal properties
c. Microstructure
4. Explore the structure-thermal property relationships
5
5. LITERATURE REVIEW
5.1 Thermal Conductivity
Before delving further into how thermal conductivity can be increased in the through-thickness
direction of a composite, it must be fully understood as a thermal transport mechanism and how
thermal conductivity behaves in a solid, let alone inside a composite.
Thermal conduction is one of the many ways that heat can transfer within a material. It can be
characterized by the following equation:
(1)
In Equation 1, is the thermal conductivity of the material, which is multiplied by the
temperature gradient ( ) to get the acceleration of the heat transfer (q”) through the material as
shown in Figure 1. Heat moves from hotter areas to cooler areas using heat carriers such as
phonons or electrons. In an anisotropic material, such as carbon fiber, the thermal conductivity
varies depending on the direction at which it is measured.
Thermal conductivity in metals is dominated by the electrons for heat transport. The thermal
conductivity is proportional to the amount of electrons moving, their speed and what their mean
free path of transport is [1]. The longer the mean free path is for the electrons, the greater speed
at which the electrons can transfer heat, thus the higher the thermal conductivity due to a lack of
collisions to impede the transport.
6
In the case of non-metal materials, such as graphene or carbon fiber, which lack free electrons,
lattice waves, also known as phonons, dominate heat transport. Similarly to metals, the thermal
conductivity does depend on the mean free path that exists for the phonons to travel along. Due
to the fact that the amount of phonons changes based on the temperature, the mean free path for
the phonons to travel along also varies based on temperature. In order to calculate the mean free
path for phonons, one must look at two different kinds of scattering that the phonons can
encounter: phonon-phonon scattering ( ), and phonon-defect scattering ( ). The
mean free path for phonons ( ) in a material can be expressed using the following equation:
(2)
This allows the calculation of thermal conductivity in a solid material. In the case of composites,
between each layer of the composite a mean free path must exist for the heat to transfer through
for the thermal conductivity to be of any significance. [5]
5.2 Thermal Conductivity in Carbon Fiber Reinforced Composites
Carbon fiber reinforced composites are made up of at least two constituent materials: the
reinforcement (carbon fiber) and the matrix (typically epoxy resin). Both have individual
properties that when combined together produce a strong composite. Individual carbon fibers
come in one of two forms: Pitch Carbon fiber or PAN carbon fiber. The thermal conductivity of
each varies from 20-1000 W/m K and 10-100 W/m K respectively. [2] These individual thermal
conductivities are measured in the longitudinal direction of the carbon fiber due to the difficulty
Figure 1: Temperature Gradient
Heat flows from Hot (dark) to Cold (light)
7
of measuring the axial thermal conductivity of an individual fiber that is only a few microns in
diameter.
Carbon fiber is made up of a graphitic crystal structure that can be arranged in the core of the
fiber as seen in Figure 2. [6] An example of the graphitic structure can be seen in Figure 3. It is
due to this graphitic structure arranged in such a fashion that the properties of the carbon fiber
are anisotropic. The crystalline structure of the carbon fiber allows heat to have a mean free
path along its length, creating a conduction path for the phonons to travel along. Figure 4
displays the difference between the axial thermal conductivity and the radial thermal
conductivity for several types of carbon fiber and compares it to an epoxy resin.
Figure 3: Arrangement of Carbon Atoms in Graphitic structure
Figure 2: Graphitic Crystals in the Core of Carbon Fibers
8
Material Base Axial Tc
(W/m K)
Radial Tc
(W/m K)
CN80-Fiber Pitch 320 11
YS80-Fiber Pitch 320 11
T300-Fiber PAN 100 11
T700-Fiber PAN 100 11
SC-15 Resin Epoxy 0.19 0.19
Figure 4: Thermal Conductivities of Select Carbon Fiber
The most common resin used in aerospace applications is epoxy resin. Epoxy resins are
thermoset resins which display a crosslinking behavior during the curing process. It is due to
this that the mechanical properties of the thermoset resins dramatically increase after curing,
allowing better, more efficient load transfer to the reinforcement. Unfortunately the
microstructure of a thermoset resin is amorphous, as seen in Figure 5, which causes problems in
the creating of long mean free paths in resins and also between the layers of carbon fiber used in
the composite. The amorphous crosslinking that is desirable for the increase of mechanical
properties actually causes a low thermal conductivity between the layers, thus decreasing the
through-thickness thermal conductivity of the composite.[6]
Figure 5: Three-Dimensional Molecular Structure of Solid
Epoxy
9
5.3 3-D Woven Composites
Due to the anisotropy of carbon fibers and the amorphous nature of epoxy resin, it would seem
that the most logical step to create a high through-thickness thermal conductivity carbon fiber
reinforced composite would be to create a composite made from three-dimensional woven fibers
instead of simply layering two-dimensional woven fibers. This would create a mean free path
in the z-direction due to having fibers that are in the direction that the thermal conductivity is
needed. This takes advantage of the high thermal conductivity of the carbon fibers themselves
by weaving them in such a fashion that there are z-direction fibers as shown in Figure 6.
Theoretically this would also cause an increase in mechanical properties in the z-direction due to
the fibers being used to reinforce that direction under both tension and pressure. [1, 7, 8]
While it would seem logical to give thought to three-dimensionally woven composites, the
implementation of such composites is very challenging. In the case of two-dimensionally
Figure 6: Schematic for 3D Weaving Process
10
woven fabrics used for composites, there are mass-produced sheets of the fabric commercially
available, and it is simple to produce parts using the two-dimensionally woven fabric.
To even produce a three-dimensionally woven part, a special machine just for 3D weaving must
be used, and the machine is costly. Unlike with 2D weaving, individual parts have to be custom
woven for each part and production speed is very limited when using 3-D weaving, whereas they
can be formed by simply cutting the ply lamina in the case of 2D parts.[7]
11
5.4 Efforts to Improve Through-Thickness Thermal Conductivity at HPMI
The problem of increasing the through-thickness thermal conductivity of carbon-fiber reinforced
composites is one that has been extensively studied at the High-Performance Materials Institute
(HPMI) at Florida State University. Dr. Zimmer’s research looks at a number of techniques
used to increase the through-thickness thermal conductivity.[2] Figure 7 shows a collection of
data obtained from his dissertation using the various techniques he tried to increase the through
thickness thermal conductivity with. All measurements are at room temperature, and the data
gathered between 10 -11 volume percent or weight percent for the fillers used.
Figure 7: Previous Research Efforts to Increase Through-Thickness Thermal Conductivity of Carbon Fiber Composites
at HPMI
The techniques used include the use of conductive resin, the inclusion of long multiwall carbon
nanotubes between the layers, stitching nanotube yarn or copper wire, and the inclusion of
buckypaper between the layers. These met with varying success on the increase of the thermal
conductivity.
CFRC, 0.6
Conductive Resin
MWNT (10 v%),
1.2
Stitch Method
(10.99% Vf), 2.25
Long MWNT (10
wt %), 1.05 Buckypaper, 0.8
0
0.5
1
1.5
2
2.5
Th
erm
al
Co
nd
uct
ivit
y
(W/m
K)
Technique
Thermal Conductivity(W/mK)
Thermal
Conductivity(W/mK)
12
Conductive resins were made by introducing a conductive filler, in this case multiwall
nanotubes, into the resin and allowing it to disperse evenly throughout. As seen in the graph, the
introduction of a 10 volume % of multiwall nanotubes into the resin doubled the thermal
conductivity off the carbon fiber reinforced composite, from 0.6 W/m K to 1.2 W/m K. But
unfortunately it is still far below the targeted value of 20 W/m K or higher.[2]
The best technique shown above was the stitching method. It quadrupled the carbon fiber
reinforced composite through-thickness thermal conductivity, at the same loading of filler or
filler equivalent as the conductive resin method, but this leads to a complicated manufacturing
process.
However, conductive resin approach is still attractive since the potential for mass production and
low cost exists. Metallic fillers are often seen as the best for increasing the thermal conductivity
of a resin, such as copper nanoparticles or silver nanoparticles.[9-11] Another potential filler for
use inside the conductive filler is a multiwall carbon nanotube. However, if a specific filler is to
be used, there are several other factors that must be taken into account to determine if it is the
best for use as thermally conductive filler, such as a filler’s percolation threshold, its own
thermal conductivity, and how easy it is to disperse inside the resin to make the composite. [2]
5.6 Metallic Filler
The mean free path for phonons is constrained to contact between structured and ordered lattice
sites. An epoxy resin matrix does not contain an ordered structure for their atoms, thus phonon
transport within it is very difficult. However, in the case of metals, heat conduction is
dominated by electron transport, which is not constrained by a lattice. Electrons move freer
when moving along a lattice path, and they can jump gaps from one conduction area to another
which is called electron hopping. [5] This makes metals ideal for use as thermally conductive
filler as when they are mixed into a resin, there are almost guaranteed to be gaps in the interface
13
between the metallic particles, thus phonon transport will not work through direct conduction.
The transport shifts to radiation or induction in that case which is a slower form of heat transfer
through a material thus causing a lower form of thermal conductivity.
5.6.1 Copper Filler
One potential type of metallic filler is copper in nanoparticle form. Bulk copper has a thermal
conductivity of 399 W/m K, and this is due at least in part to the face centered cubic lattice
formed by bulk copper. [9, 12, 13] Copper nanoparticles are commonly included as a filler in
thermally conductive resin as a method for improving the conductivity.
There are several factors when including nanoparticle filler that affect the thermal conductivity
of the resin. The first is the nanoparticle size. This affects the interface between each particle
and the resin in which it is included. Another is the amount of nanoparticles included in the
resin. Higher volume fractions of nanoparticles, as seen in Figure 8, can cause an increase in
Figure 8: Thermal Diffusivity of a Resin/Copper composite vs. Volume Fraction
14
thermal conductivity or diffusivity as described by the Rule of Mixtures, and at some critical
volume fraction, the thermal conductivity will dramatically increase due to the percolation factor
of metallic particles in a composite.[14]
Unfortunately, there are disadvantages to including such particles into a resin. The more
nanoparticles included in the resin, the higher the resin’s viscosity when handling it, thus making
the resin harder to use for composite fabrication. Higher volume fractions also usually reduce
mechanical performance, taking away from desired tensile strength or desired compressive
strength in lieu of increasing the thermal or electrical conductivity. These disadvantages must be
considered when incorporating a filler of any sort into a resin for composite applications.[9, 12,
13, 15, 16]
5.6.2 Silver Filler
Another potential metallic filler that can be used to improve the thermal conductivity of a resin is
silver. Silver’s bulk thermal conductivity is 400 W/m K, and when included in a resin
composite, it can cause significant improvement of thermal conductivity. Similarly to copper,
various kinds of nanoparticles can be used for the incorporation of silver as thermally conductive
filler in resin matrices
The most common form of silver filler is silver flakes. There are numerous models for how the
irregularly sized and shaped silver flakes affect the thermal conductivity of the resin due to their
interfaces with each other.[11] These models agree with experimental results for low filler
loadings of the resin, but they diverge from experimental result when the filler content rises
above a critical amount. Meanwhile the rule of mixtures model greatly exaggerates the thermal
conductivity of the composite of the silver and resin as it makes several assumptions about how
heat transport works within the composite. [9] The first assumption it makes is that both the
resin and the metals are given equal probability of use in heat transfer. This assumption is a
fallacy due to the way the interface between the silver and the resin works. For most filler
15
loadings, the filler will be significantly less than that of the resin, which does not allow the silver
to be fully in contact with each other, but instead each flake is suspended in resin, with the heat
having to transfer through an amorphous insulator to get back to a conductor. The second
assumption the rule of mixtures model makes is that the silver and the resin are perfectly
interfacing with each other. This is feasibly possible, but it is also extremely unlikely when
particle size becomes very small because they have a large surface area.
There are three factors that affect thermal conductivity when using silver flakes as filler to
improve said conductivity.[10, 11] The first factor is the size of the silver flakes. Flake size
affects the volume percentage of silver flakes able to be put in and how it is dispersed inside the
resin. Commonly used sizes are within the one to twenty micron range, as seen in the SEM
image of Figure 9. Another factor that affects the thermal conductivity is the volume fraction of
the silver flakes, as seen in Figure 10. At low filler volume fractions, it behaves according to
established models, but when higher volume fractions come into play, another factor affects the
thermal conductivity greatly. This factor is the percolation threshold,[14] a critical point at
which the thermal conductivity dramatically increases over the predicted values. Yet another
factor that affects the thermal conductivity is how the silver flakes are dispersed in the resin. If
they are well dispersed over the entire area of the resin, they affect the thermal, mechanical, and
electrical properties of the entirety of the composite rather than just specific areas. Fillers are
commonly dispersed in the resin matrix through use of hand mixing, sonication, or using a
vacuum to ensure that no air gets mixed in as well.[11, 17]
Figure 9: SEM of Silver Flakes 90% <20 micron
16
Figure 10: Thermal Conductivity of a Silver Flake/Resin Composite
with different sized flakes. Flake A: 3.2 Microns, Flake C: 9.9 Microns
17
5.7 Carbon Nanotubes
The properties of carbon nanotubes have been studied extensively. The thermal conductivity of
an individual carbon nanotube is quite high between room temperature and the measurement
range of the experiment, as shown in Figure 11. Figure 11 displays a graph of the temperature
dependence of the thermal conductivity of an individual multiwall carbon nanotube, and it can be
seen that at room temperature (300 K), an individual carbon nanotube displays a thermal
conductivity of around 5000 W/m K. [18]
Carbon nanotubes may display high thermal conductivity when looking at the individual carbon
nanotube, but when they aggregate, their conductivity tends to decrease. A similar effect can be
seen when comparing a monolayer graphene sheet to graphite. A monolayer sheet displays
uniformity without discontinuity that allows heat to transfer swiftly along the layer. Graphite is
a series of such layers that do not display lattice uniformity between them, causing a reduction in
the thermal conductivity. Now were the aggregated carbon nanotubes aligned, there would be a
different story here, as aligned carbon nanotubes behave like the monolayer graphene sheet.
Figure 12 displays the graphene and graphite examples given compared with MWCNT at the
same temperatures. [18]
Figure 11: Temperature Dependence of an
individual Carbon Nanotube
18
In order to better understand why a randomly aligned aggregate of carbon nanotubes does not
conduct as well as an aggregate that contains aligned carbon nanotubes, one needs to understand
how heat transfers between carbon nanotubes. If the carbon nanotubes are connected end-to-
end, ballistic heat transfer dominates their thermal conductivity, and their thermal conductivity
remains similar to that of an individual carbon nanotube.[19] However, if the carbon nanotubes
are connected wall to wall, the heat transfer behaves as shown in Figure 13. Heat travels
quickly along the edge of the wall of the multiwall carbon nanotube and transfers from outer wall
to outer wall quickly. However, the inward radial motion of the heat transfer is far slower than
the outer wall length-wise and circumferential motion of the heat transfer. This happens
because carbon nanotubes have the basic structure of a rolled up sheet of graphene. This
structure is a 2-D structure wound into a tube which makes phonon transfer easier, but the
inward radial conductivity is hampered by the lack of interface between the walls of the tubes
due to the van der Waal’s force.[10, 20-24]
Figure 12: Thermal Conductivity of MWCNT, Graphene
sheets and Graphite
19
Figure 13: Cross-linked Carbon Nanotube Model
Figure 14: Heat Transfer between Carbon Nanotubes
20
5.7.1 Percolation Threshold
When introducing a nanoparticle into a resin, there is a theory that at a critical amount of the
filler in the resin there is a sharp increase in the conductive properties of the resin/particle
composite. Above but near this critical threshold, the resin displays steep increases in the
electrical conductivity of the composite. This increase in electrical conductivity obeys the
universal power scaling law near the threshold:
(3)
In Equation 3, p is the volume fraction of the filler in the composite, and pc is the volume
fraction of the filler at the percolation threshold. The conductivity exponent is equal to two in a
three-dimensional field. This swift increase in the electrical conductivity is associated with the
formation of clusters of the percolating filler along with more clusters of the filler being attached
to the already existing clusters. Carbon nanotubes have been shown to display an electrical
percolation threshold at very low volume percents, around 0.1 vol%. Compared to metallic
nanoparticles with spherical fillers, this is a significantly lower amount; spherical fillers tend to
hit percolation threshold at around 20-30% by volume.
Figure 15: FEM Model of Carbon Nanotube Interface
21
This same threshold exists for thermal conductivity with metallic fillers, but carbon nanotube
composites and carbon nanotube suspensions do not display a percolation threshold for thermal
conductivity. [14] This is likely due to the fact that nanotubes do not tend to come in direct
contact with each other between the two end-to-end interfaces. As shown in the previous Figure
13, heat is transported more easily along the length of the tube than through the tubes. When the
tubes are randomly aligned within the resin, this does not allow for a significant increase of heat
transmission around the electrical percolation threshold, and in fact will tend to cause a more
continuous increase in thermal conductivity. Unlike metals, the thermal conductivity of carbon
nanotubes is dominated by phonon transport. Phonons, unlike electrons cannot hop between
structures without an ordered structure between them. Thus the nanotubes in resin are unable to
attain the high thermal conductivity at the percolation point unlike metals.4
Figure 15 displays an FEM model of two carbon nanotubes that are interfaced at their ends. As
seen in the model, there is a slight spacing between the nanotubes due to the van der Waal’s
force between them. This FEM analysis was used with a model that depended on the spacing
between the carbon nanotubes to calculate the thermal conductivity of such a composite. [14]
Figure 16: Effects of Interface on Thermal Conductivity
22
The results of which are displayed in Figure 16. The interface between the two nanotubes is
modeled using an interfacial resistance as well. An increase in the spacing between the two
nanotubes significantly decreased the thermal conductivity between them.[14]
5.7.2 Effects of Straightness and Aspect Ratio of Carbon Nanotubes on Thermal
Conductivity
Despite the fact that carbon nanotubes do not display a percolation threshold point for thermal
conductivity when introduced into a polymer composite or a nanofluid, they still display a high
thermal conductivity for individual nanotubes, and as shown by Zimmer’s research,[2] they can
lead to an increase in the thermal conductivity of a composite. There are also other factors that
affect the thermal conductivity displayed by a nanotube/resin composite.
Like carbon fiber, carbon nanotubes are anisotropic. Their thermal conductivity along the
longitudinal direction is well documented as discussed in previous sections. Unfortunately, due
to the incredibly small diameter of carbon nanotubes, measuring their radial thermal conductivity
is bordering on the impossible with current measurement techniques.
Carbon nanotubes tend to fold over on themselves when allowed to freely move and rotate in a
liquid. [25] The more complex the twists and turns are, the less straight the mean free path is for
the heat carriers to travel along, which creates a lower thermal conductivity. Figure 17 (b)
shows two equivalent length nanotubes, one completely straight, and one that isn’t straight at all,
and it displays what the heat transfer behaves like in each of them with the q vector. In Figure
17 (a), a dimensionless factor known as H which is the influence of the aspect ratio on the
thermal conductivity as shown in the following equation:
[ ] (4)
In Equation 4, f is the volume fraction of CNTs, the kc33 and k
c11 are the axial and transverse
thermal conductivities of the CNTs, and km is the thermal conductivity of the isotropic matrix in
23
which the carbon nanotubes are in. This model was used to produce the thermal conductivities
displayed in Figure 18, which varies based upon both the straightness and the aspect ratio. As
seen in the figure, the straighter a carbon nanotube is the higher its thermal conductivity, and the
higher its aspect ratio, the higher its thermal conductivity. Ideally, in a composite, one would
want to have high aspect ratio carbon nanotubes along with extremely straight carbon nanotubes.
Also, due to the anisotropy of the carbon nanotubes, ideally they would be aligned in the
direction that the thermal conduction path is needed.[25, 26]
Figure 17: Effect of the aspect ratio on the H factor of a
CNT's Thermal Conductivity (a) and demonstration on how
a non-straight CNT can have the same average length as a
straight one (b)
24
5.8 Heterogeneously Structured Resin Matrix with Conductive Fillers
Currently, a research group from the LORD Corporation has developed a novel technique using
a heterogeneously structured resin matrix of conductive fillers to attempt to increase the through-
thickness thermal conductivity of a carbon fiber composite.
The idea behind using heterogeneous fillers is that the fillers gather at points between the layers
of the composite to produce conduction paths for the heat carriers to travel along. They
produced a B-staged thin film of a conductive resin, and partially cured it such that it displayed
the amount of tack necessary for it to adhere to the carbon fiber prepreg used in the experiment.
It was then prepared using a vacuum bag method to reduce the voids in the composite. A side-
by-side comparison of cured epoxy that was prepared using this method for an SEM imaging is
displayed in Figure 19. The silver particles are white in the images, and the resin is the alternate
color. The reported thermal conductivity of such a resin is as high as 20 W/m K, as shown in
Figure 20. [3, 4]
Figure 18: Effects of Straightness and Aspect
Ratio on Thermal Conductivity of a CNT
25
Figure 19: SEM images of Homogeneous Silver Filler (left) and Heterogeneous Silver filler (right)
26
The specific preparation of the B-Staged thin film is how the heterogeneous structure was
produced within the resin. Prior to introduction into the resin, the LORD Corporation coated the
silver flakes with a non-polar acidic coating. They then mixed the coated silver flakes into the
resin so that they were homogeneously dispersed. During the curing to the B-Stage, the polar
resin and the non-polar coatings on the silver filler repelled one another causing the silver flakes
to aggregate in the resin matrix as seen in Figure 19 (right). Next, a curing temperature was
selected such that the resin would cure and the silver flakes would sinter together at the same
time. The sintered silver is what produced the improved mean free path for the thermal and
electrical conductivity in the resultant composite.[27]
Figure 20: Thermal Conductivity Comparison of Filler Volume fraction in
Heterogeneous and Homogeneous Composites
27
5.9 Laser Flash Apparatus for Thermal Conductivity Measurement
Several thermal conductivity measuring techniques exist, but we will focus on the laser flash
technique for determining thermal diffusivity in this research.
The laser flash technique is a way of measuring thermal diffusivity. It works by uniformly
flashing a laser on a sample of thickness L, heat diffusing upwards through the sample to cause
the back side of the sample to heat up. Infrared radiation emits from the sample which is then
measured by an infrared detector and the signal is plotted versus time. Figure 21 shows the
device that is used by HPMI.
Once the signal has been plotted, half the time required to reach the maximum signal is taken.
This is called the half time. This is plugged into Equation 5 as t1/2, L is the sample thickness,
and is the thermal diffusivity. (5)
(6)
Figure 21: Cutaway of Netzsch LFA 457
28
Equation 6 displays the relationship between the thermal diffusivity and the thermal
conductivity. Multiplying the thermal diffusivity, the specific heat, and the density of the
sample gives its thermal conductivity in Watts/m K..[28]
This complies with ASTM Standard E-1461 for testing thermal diffusivity with a flash method.
The LFA 457 Microflash allows control of the test environment’s temperature with a furnace or
cryostat, and measurements are done in a vacuum or inert gas environment in the chamber. The
laser also uniformly strikes the sample.
Figure 22: Change in Temperature vs. Time graph used to
determine t1/2
29
6. RESEARCH UNIQUENESS
As of right now, the only reported group working on heterogeneously structured resin matrix
composites is the LORD Corporation. [3, 4, 27] Their results demonstrated very promising
areas of thermal conductivity improvement. This case study focused on a method of directly
controlling the conduction path by manually designing where the filler would be when the resin
cured. The method used in this case study is the Patterned Resin Deposition (PRD) Method.
30
7. PATTERNED RESIN DEPOSITION METHOD
This particular case study focused on a novel method of producing heterogeneous composites
that has been called the Patterned Resin Deposition Method (PRD). This is a method which
combines hand-layup with a precise preordained pattern of resin and filler as seen in Figure 23.
Samples were prepared using the pattern deposition method on carbon fiber fabrics. Six layers
of 15.24 cm x 15.24 cm squares of IM7 carbon fiber fabric were cut for each sample prepared.
For each sample set, 50 ml of Epon 862 Epoxy resin was mixed with 13.7 ml of Epikure Curing
Agent "W." One neat carbon fiber/epoxy sample was prepared as the control with
approximately fifty weight percent of resin.
In order to prepare the first set of pattern samples and the homogeneous samples, resin was
weighed on a scale while in a syringe first. Then the amount of Alfa Aesar 99.9% <20 micron
silver flakes necessary to get twice the goal weight percent was added to the resin, and a second
syringe was filled with neat resin. The total resin weight percentages, just in the resin were as
follows for the silver: 5 wt%, 10 wt%, 15 wt%, and 18 wt%. Production of silvered resin
beyond a 36 wt% loading is difficult as the resin will not mix with the silver flakes beyond that
Figure 23: Resin pattern for Pattern Deposition Technique
31
point. Lines of high silver resin were deposited on the carbon fiber fabric next to neat resin
using the pattern in Figure 23.
After depositing the pattern on the fabric, another piece of fabric was laid on top and then the
pattern was deposited again. This was repeated five times and a final layer of fabric was laid on
top. The composite was cured under a hot press at about 200 degrees Celsius and under
approximately 1.72 MPa of pressure for three hours. A second set of pattern samples was
produced using the Fisnar SL101N automatic resin dispenser (Figure 24) to place the pattern
onto the fabrics. This has the benefit of having a constant flow rate exiting the syringe along
with an easier to control line size. The pressure the resin was under was 0.5 bar, and the line
width was 1.39 mm. To ensure that the appropriate loading of silver was prepared for the silver
lines, resin was poured into one syringe first which was then ejected into a container for
weighing. After the resin was weighed, silver flakes were mixed into the resin until the resin
and silver flakes were at the appropriate weight percent ratio. The silvered resin was then
placed into another syringe for deposition. A second syringe of equal size was filled with neat
resin to prepare the pattern. Carbon fiber fabric cut into 12.7 x 19.05 cm sheets was arranged in
a row of five sheets. First the silvered resin part of the pattern was applied to the top of each of
the five sheets, and then the neat resin, as seen in Figure 23, and demonstrated in Figure 25.
After the pattern was deposited, the sheets were stacked on top of each other, leaving the fifth
Figure 24: Fisnar SL101N Resin Dispenser
32
sheet with an exposed pattern. (Figure 26) A sixth sheet, with no resin deposited on it was then
placed on top to be the outer layer. The remaining resin, neat and silvered, was mixed together
to provide the resin for the homogeneous samples. A picture of the full setup can be seen in
Figure 27
.
Figure 25: Pattern Deposition
Figure 26: Uncured Pattern Sample
33
Figure 27: Production Setup for Automatic Resin Deposition
The second sets of both the homogeneous and heterogeneous samples were cured in a similar
fashion to the first set of samples. They were cured at approximately 200 degrees Celsius under
1.72 MPa of pressure using the hot press for three hours.
7.1 Materials Selection and Cost Analysis
For this study, three materials were necessary for the production of the heterogeneous
composites. The fibers selected were an IM7 carbon fiber woven fabric, a PAN-based carbon
fiber for the ease of manufacturing. This was selected due to its relatively low cost as well. The
resin selected was Epikure Epon 862 epoxy resin, which is commonly used for aerospace
applications. The conductive filler selected, as seen in the previous section, was silver flakes,
99.9% <20 micron silver flakes from Alfa-Aesar. The cost of the silver per ten grams ranged
from 40-60 USD. At this cost, it is cost-effective to attempt to use the minimum amount of
silver to get the greatest possible increase in properties.
7.2 Proof of Concept Case Study
After the proof of concept samples were created, they were tested for both thermal and
mechanical properties, and their morphological structure was also observed.
34
7.2.1 Thermal Diffusivity/Conductivity Measurement
The LFA 457 Microflash was used to determine the through-thickness thermal diffusivity of the
composite samples in accordance with the ASTM E-1461 standard. The samples were made
into 8 x 8 mm squares with a thickness of between 1 and 1.5 mm for use in the LFA. Once the
thermal diffusivity was obtained, the specific heat was calculated using the LFA’s comparison
calculation which calculates the specific heat based upon the diffusivity of the tested sample and
that of a standard sample as a reference. After the density was obtained, these three results were
multiplied to obtain the thermal conductivity.
7.2.2 Mechanical Property Tests
Samples were prepared in compliance with ASTM Standards D638 and D7264 for tensile and
flexural testing respectively. Samples were cut to half of the requirements for the ASTM D638
tensile test in order to conserve resources, but the standard was consulted for tab size and for test
parameters. The samples were prepared as 12.7 cm by 6.35 cm strips and tabs were cut into
2.54 cm x 1.27 cm strips and adhered to the ends of the samples for testing. Tensile tests were
performed by using the MTS 858 tabletop universal testing machine.
Flexural test samples were strips cut to a width of approximately 12.7 mm and tested over a 40
mm gage length in accordance with the ASTM D7264 standard for three point bend tests. The
machine used to do the 3 point bend was also the MTS machine.
7.2.3 Microstructure Observation
The samples were studied under both the C-Scan and the Scanning Electron Microscope (SEM)
to determine their morphological properties. The C-Scan parameters were a resolution of 200
micrometers, and the sample rate was 250 Megahertz.
35
7.3 Technical Challenges
7.3.1 Resin Spreading
Like all new manufacturing methods, this was not without challenges. The first encountered
challenge was that the resin would spread during curing. The pattern itself had to be spaced
such that there was space for the lines to spread out and wet the fabrics so the composite could
fully cure and not leave any areas of the composite that did not have resin. It was found that a
spacing of approximately 6.35 mm between each line of the pattern allowed for the wetting of all
the fabric fibers and allowed for the full curing of the composite.
7.3.2 Pattern Deposition and Creation
The next encountered challenge was the deposition of the pattern itself. Initially, the samples
were prepared using manually depressed syringes in order to deposit the pattern. This created
problems with controlling the straightness of the conduction path lines, and with obtaining a
precise pattern which was desired. The second set did not have this challenge as the use of the
Fisnar SL101N allowed for a more precise control of line straightness in the pattern along with
speed of resin deposition.
7.4 Method Viability
The Resin Pattern Deposition method has had the least amount of actual challenges to producing
a sample. It has proven to be relatively swift, easy to reproduce, and it allows the tailoring of
the conduction path based upon the pattern used. The pattern itself can be used to control the
amount of silver in the entire composite with ease. It is for this reason that the Resin Pattern
Deposition Method had been chosen for production and study within the context of this research.
36
8. EXPERIMENTATION
Thermal diffusivity tests were performed according to the ASTM E-1461 standard by use of the
Netzsch LFA 457 Microflash. (Figure 28) Samples 8 mm x 8 mm in size had their thermal
diffusivities measured at 30, 50, 75, 100, 125, 150, and 175 degrees Celsius. Two from each set
of silver loadings of either the pattern samples or the homogeneous samples were tested at a time
along with a reference sample of either graphite or Pyrex. After diffusivity results were
obtained, the specific heat of each sample was calculated by using the LFA software. This is
done by using the comparative method of comparing the change in temperature curves used to
calculate the thermal diffusivity of the test sample with that of the reference sample. The
reference samples have a known specific heat, while the test samples have an unknown specific
heat.
Figure 28: LFA 457 Microflash
37
After the specific heat was calculated, the densities of the test samples were obtained by using a
comparative weight scale that measured the weight out of water and in water. After the
densities were obtained, the thermal conductivity was calculated by use of Equation 7.
(7)
Tensile tests were performed on the samples according to the ASTM D3039 test. Samples were
prepared as described in the previous section and were tested individually to obtain the modulus
and the ultimate tensile strength of each sample. Three to four samples were tested to get an
average that would give a more universal result. The pattern samples were tested along the
pattern and at the normal to the pattern in order to determine if the pattern had any real effect on
the tensile properties of the composite. A three point bending test is also planned for the
composites.
The morphologies of the samples were first analyzed using a nondestructive sonic test known as
the C-Scan. Then later, the samples were studied under an SEM to obtain an image of their
morphology.
38
9. RESULTS AND DISCUSSION
9.1 Thermal Results
The thermal results are displayed in Figures 29-32. Figure 29 is a table that displays the
numerical thermal data at room temperature. Figure 30 is the average thermal diffusivity of the
samples at different filler loadings. Figure 31 is the average specific heat at different filler
loadings. Figure 32 is the average thermal conductivity at different filler loadings.
Diffusivity (mm^2/s) Specific Heat (J/g/K) Density (g/cm^3) Thermal Conductivity (W/m K)
Average Std Dev Average Std Dev Average Std Dev Average Std Dev
Neat 0.42 0.05 3.90 0.14 1.44 0.02 2.37 0.28
2.5 wt %
Heterogeneous 0.65 0.26 1.75 0.66 1.49 0.03 1.60 0.53
5 wt%
Heterogeneous 0.63 0.04 3.33 0.18 1.54 0.09 3.21 0.18
7.5 wt%
Heterogeneous 0.62 0.10 3.45 0.11 1.59 0.09 3.41 0.80
9 wt%
Heterogeneous 0.74 0.05 4.17 0.26 1.68 0.02 5.19 0.49
2.5 wt %
Homogeneous 0.58 0.04 3.66 0.35 1.43 0.03 3.01 0.19
5 wt%
Homogeneous 0.74 0.04 3.20 0.03 1.51 0.03 3.55 0.24
7.5 wt%
Homogeneous 0.71 0.04 3.42 0.18 1.51 0.05 3.42 0.30
9 wt%
Homogeneous 0.55 0.03 3.53 0.53 1.56 0.04 3.01 0.60
Figure 29: Thermal Results at Room Temperature
39
Figure 31: Average Specific Heat
Figure 30: Average Thermal Diffusivity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
25 75 125 175
Th
erm
al
Dif
fusi
vit
y m
m^
2/s
Temperature (Degrees Celsius)
Average Thermal Diffusivity
Neat CF/Epoxy
Pattern Sample 2.5 wt% Silver
Homogeneous 2.5 wt% Silver
Pattern 5 wt% Silver
Homogeneous 5 wt% Silver
Pattern Sample 7.5 wt % Silver
Homogeneous 7.5 wt% Silver
Pattern Sample 9 wt% Silver
Homogeneous 9 wt% Silver
Pattern Sample 9 wt% infused
0
1
2
3
4
5
6
7
8
0 50 100 150 200
CP
J/g
/K
Temperature
Average Specific Heat
Neat CF/Epoxy
Pattern Sample 2.5 wt%
Homogeneous 2.5 wt%
Pattern Sample 5 wt%
Homogeneous 5 wt%
Pattern Sample 7.5 wt%
Homogeneous 7.5 wt%
Pattern Sample 9 wt%
Homogeneous 9 wt%
Pattern Sample 9 wt%
40
The results obtained for the thermal conductivity and thermal diffusivity seem consistent with
what was expected considering the loading and whether the samples were pattern based or not.
The best results were obtained by the highest loading of silver's pattern sample. This was 9 wt%
in the entire composite, but 18 wt% in the resin part of the composite alone. It displayed a
maximum thermal conductivity of approximately 6.85 W/m K at 175 degrees Celsius. The
room temperature (30 degrees Celsius) thermal conductivity of this composite was 5.35 W/m K.
The 9 wt% pattern sample which was infused with the neat resin after the pattern had been
allowed to partially cure for a few days displayed a lower thermal conductivity yet was still
higher than the neat and other samples of similar loadings. This is likely due to the fact that
when the resin was allowed to flow through, under heat, the pattern may have been partially
destroyed by the flowing resin.
The increased thermal conductivity displayed by a higher filler loading is in agreement with the
literature. However, the use of a concentrated pattern caused a higher increase than displayed in
the homogeneous sample of the same loading. While it is possible that the particular section
Figure 32: Average Thermal Conductivity
0
1
2
3
4
5
6
7
0 50 100 150 200
W/m
K
Temperature
Average Thermal Conductivity
Neat CF/Epoxy
Pattern Sample 2.5 wt%
Homogeneous 2.5 wt%
Pattern Sample 5 wt%
Homogeneous 5 wt%
Pattern Sample 7.5 wt%
Homogeneous 7.5 wt%
Pattern Sample 9 wt%
Homogeneous 9 wt%
Pattern Sample 9 wt% Infusion
41
taken to be measured was a coincidence, the samples were taken from random points in the
composite and then averaged together. There is very little deviation in their thermal
conductivities, so it is possible that by concentrating the silver in these points, a conduction path
was formed. This is also shown in the SEM results later (Figure 59) which displayed that the
silver had gone between the layers, creating conduction paths. A proper conduction path means
a longer mean free path, which would mean higher thermal conductivity.
Two interesting observations displayed themselves in the thermal results. The neat sample,
which had the lowest thermal diffusivity, displayed a higher-than-expected thermal conductivity.
The lowest loading pattern sample also displayed a thermal conductivity and specific heat that
was lower than that of the neat sample. This may be due to inaccuracies in the measurement of
the specific heat or due to sampling issues. Ways to obtain better results would be to obtain the
specific heat via the use of the DSC or repeating the experiment on a similarly designed second
sample set.
As expected, though, the thermal diffusivity and thermal conductivity increased as the
concentration of silver in the composite increased. An even more dramatic increase was shown
with the pattern sample results when the silver loading reached 9 wt% in the composite. In the
concentrated areas of the pattern, the silver loading was locally much higher and likely closer to
36 wt% in that area. This is around the percolation threshold of silver flakes in resin, which
could account for the sharp increase in thermal properties.
42
9.2 Mechanical Results
9.2.1 Tensile Results
According to the ASTM D3039 standard, tensile test failure modes can be described using the
terms in Figure 33 which is accompanied by some example failure modes.
Figure 33: Tensile Failure Modes
43
9.2.1.1 First Set Samples
The modulus and tensile strengths obtained from the mechanical tests are displayed in Figures 34
and 35. These are graphed according to weight percent of silver in the entire composite, and
they use the average for each weight percent. They also separate the results out into
heterogeneous and homogeneous data. The heterogeneous samples are the pattern samples,
while the homogeneous samples are not.
For the first sample set, the mechanical test results did not turn out entirely as expected. Failure
modes displayed by the samples tested initially had the samples failing either on the tabs
themselves or at the tabs. This produced the likely inaccurate test results displayed in Figures
34 and 35. The displayed modulus and tensile strength were significantly lower than expected
due to increased stress at the grips and tab failure. It is due to this failure that a second set of
measurements was needed.
44
Figure 34: Young’s Modulus of the first set of samples
0
5000
10000
15000
20000
25000
30000
35000
40000
0 2 4 6 8 10
MP
a
Weight percent
Young's Modulus
Heterogeneous
Homogeneous
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7
MP
a
Weight %
Tensile Strength
Heterogeneous
Homogeneous
Figure 35: Tensile Strength of the first set of samples
45
9.2.1.2 Second SetSamples
The results from the second set are displayed in Figures 36-43. The failure modes described in
Figure 36 are from ASTM D3039 as described by Figure 33. The stress-strain curves are
presented in Figure 37 and Figure 38.
Sample Modulus (GPa) Std Dev Yield Stress
(MPa)
Std. Dev Typical Failure Mode
Neat 35.8 N/A 342.31
77.15
2.5 wt% Het (Along
Pattern)
45.0 N/A 379.81 68.93 DGM
2.5 wt% Het (Against
Pattern)
31.6 N/A 441.10 108.40 DGM
5 wt% Het (Along
Pattern)
64.1 N/A 230.82 14.18 SGM
5 wt% Het (Against
Pattern)
36.22 N/A 228.16 5.92 AGM
7.5 wt% Het (Along
Pattern)
41.7 N/A 523.61 71.42 LGM
7.5 wt% Het (Against
Pattern)
54.9 N/A 523.61 71.42 LAV
9 wt% Het (Along
Pattern)
63.0 N/A 337.36 45.08 LGM
9 wt% Het (Against
Pattern)
63.0 N/A 337.36 45.08 LGM
2.5 wt% Homogeneous 42.13 N/A 605.92 61.33 JGM
5 wt% Homogeneous 14.5 N/A 422.84 46.86 AGM
7.5 wt% Homogeneous 33.2 N/A 286.36 86.81 LAT
9 wt% Homogeneous 31.6 N/A 428.67 133.19 LGM
Figure 36: Mechanical Data
46
Figure 37: Tensile test stress-strain curves of the neat samples to the 5 wt% silver samples
Figure 38: Tensile test stress-strain curves of the 7.5 wt% silver samples to the 9 wt% silver samples
0
200
400
600
800
1000
1200
0 1 2 3 4 5 6 7
Str
ess
(M
Pa
)
Strain (%)
Stress-Strain Neat - 5 wt%
Neat Sample 1
Neat Sample 2
Neat Sample 3
2.5 wt% with Pattern 1
2.5 wt% with Pattern 2
2.5 wt% with Pattern 3
2.5 wt% Against Pattern 1
2.5 wt% Against Pattern 2
2.5 wt% Against Pattern 3
2.5 wt% Homogeneous 1
2.5 wt% Homogeneous 2
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6
Str
ess
(M
Pa
)
Strain (%)
Stress-Strain 7.5 to 9 wt%
7.5 wt% Pattern 1
7.5 wt% Pattern 2
7.5 wt% Pattern 3
7.5 wt% Homogeneous 1
7.5 wt% Homogeneous 2
9 wt% Pattern 1
9 wt% Pattern 2
9 wt% Pattern 3
9 wt% Homogeneous 1
9 wt% Homogeneous 2
9 wt% Homogeneous 3
47
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
0 2 4 6 8 10
MP
a
Weight Percent Silver
Average Young’s Modulus
Heterogeneous
Homogeneoujs
0
100
200
300
400
500
600
700
0 2 4 6 8 10
MP
a
Weight Percent Silver
Average Strength
Heterogeneous
Homogeneous
Figure 39: Average tensile strength of the second set of samples
Figure 40: Average Young's modulus of the second set of samples
48
9.2.1.2.1 Failure modes
The following figures display typical failure modes for the mechanical tests done on this set of
composites
Figure 42: AGM Failure (2.5 wt% Homogeneous Sample)
Figure 43: SGM Failure (5 wt% Heterogeneous Sample)
The second set of tensile test results was taken using the same MTS machine as the first set, but
the tabs were made out of a G10 material and were bonded to the samples using JB-Qwik, a
quick-setting epoxy resin. The results obtained from this set of measurements are displayed in
Figures 36-40. The stress-strain curves show that the samples had linear elastic deformation up
to the elastic limits and beyond that, they began to weaken and break down.
While some samples had similar problems as the first set, namely tab failure and breaking at the
grips, the tests proved to be valid as most of the failure modes were not failure within the tab or
Figure 41 DGM Failure (2.5 wt% Heterogeneous Sample)
49
at the tab. At low filler concentrations, homogeneous distributions tended to display higher
yield stresses, whereas at higher filler concentrations there seemed to be less of a difference
between the two. The modulus tended to be higher on the heterogeneous samples overall, and in
both the homogeneous and heterogeneous samples, the modulus increased with the introduction
of more filler. .
The failure modes displayed by the lower concentration samples seems to suggest that their
results are more accurate. The 2.5 wt% heterogeneous sample failed due to delamination, the
2.5 wt% homogeneous sample failed in an AGM. Both kinds of 5 wt% samples had similar
failure modes to the 2.5 wt% samples. These suggest that a low concentration of filler does not
have a high effect on failure mode type.
The concentration of silver flakes in the resin of the samples has a direct impact on the
mechanical properties. However, the heterogeneous samples are arranged in such a way that
the silver is in distinct areas of the composite. This creates areas of localized stress rather than
uniformly distributing the stress throughout the entire composite. In lower concentrations, the
areas taking the stress in the heterogeneous composite are forced to support more of the stress
than the homogeneous composite of the same filler loading can support; the homogeneous
composite’s stress is expected to be spread throughout the composite because the silver is
uniformly spread throughout. At lower filler loadings, the homogeneous samples are expected to
have better mechanical properties.
However, when there is higher filler loading, the effect of the silver on the homogeneous
composite’s mechanical properties is stronger. In the heterogeneous composite, there is also a
greater effect from the silver due to a higher stress concentration on the areas without silver, but
in the higher loadings the effects of this stress concentration are not as high as the effects of the
silver itself on the mechanical properties, causing the difference in mechanical properties for
homogeneous and heterogeneous samples at such loadings to be negligible.
50
9.2.2 3-Point Bend Results
Figures 44-48 display the results for the 3-Point Bend results. Figures 44 and 45 show the
stress-strain curves for these results. The samples are represented by letters which show their
weight percent in the first letter (A is 2.5 wt%, B is 5 wt%, C is 7.5 wt%, D is 9 wt%), and
whether they are heterogeneous (A) or homogeneous (B) in the second letter.
Figure 44: Flexural Test Stress-Strain Curves 2.5 wt% silver samples to 5 wt% silver samples
0
200
400
600
800
1000
1200
0 0.005 0.01 0.015 0.02 0.025 0.03
Str
ess
(M
Pa
)
Strain (%)
Stress-Strain Curves 2.5 wt% and 5 wt%
AA1
AA2
AA3
AB
BA1
BA2
BA3
BB1
BB2
51
Figure 45: Flexural Test Stress-Strain Curves of 7.5 wt% samples to 9 wt% samples
Figure 46: Max Force Applied
0
100
200
300
400
500
600
700
800
900
0 0.005 0.01 0.015 0.02 0.025 0.03
Str
ess
(M
Pa
)
Strain (%)
Stress-Strain Curves 7.5 wt% and 9 wt%
CA1
CA2
CA3
CB1
CB2
CB3
DA1
DA2
DA3
DB1
DB2
0.00
50.00
100.00
150.00
200.00
250.00
300.00
0 1 2 3 4 5
Ne
wto
ns
wt% Silver
Max Force Applied
Heterogeneous
Homogeneous
52
Figure 47: Max Stress
Figure 48: Max Strain
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
900.00
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
N/m
m^
2
wt% Silver
Max Stress
Heterogeneous
Homogeneous
0.00
0.50
1.00
1.50
2.00
2.50
0 1 2 3 4 5
Pe
rce
nta
ge
Wt %
Max Strain
Heterogeneous
Homogeneous
53
The 3-Point Bend results clearly demonstrate something which has already been demonstrated
with the tensile test results; at lower filler concentrations, the mechanical properties of the
homogeneous samples are significantly higher than that of heterogeneous samples while at
higher concentrations this difference is negligible. At the lower filler loadings, the homogeneous
samples clearly have better mechanical properties, such as being able to withstand both a higher
stress and a higher strain, yet when the filler loading increases beyond 7.5 wt%, the
homogeneous and heterogeneous composite flexural properties are within a close margin of error
to each other.
9.3 Morphological Analysis
9.3.1 C-Scan Tests
9.3.1.1 First Set
Figures 49 and 50 show the C-scan data of both a homogeneous and one of the pattern samples at
7.5 wt%. These samples were prepared from the bulk sample prior to cutting it. This is a
nondestructive test to view the microstructure. In Figure 50, the red spots are the silver. In
Figure 50, the red spots and the accompanying light blue and green in lines are the silver.
54
Figure 49: Homogeneous 5 wt% Silver Composite C-Scan
Figure 50: Heterogeneous 5 wt% silver Composite C-Scan
55
9.3.1.2 Second Set
Figure 51: Heterogeneous 2.5 wt% Silver Composite C-Scan
Figure 52: Homogeneous 2.5 wt% Silver Composite C-Scan
56
Figure 53: Heterogeneous 5 wt% Silver Composite C-Scan
Figure 54: Homogeneous 5 wt% Silver Composite C-Scan
57
Figure 55: Heterogeneous 7.5 wt% Silver Composite C-Scan
Figure 56: Homogeneous 7.5 wt% Silver Composite C-Scan
58
Figure 57: Heterogeneous 9 wt% Silver Composite C-scan
Figure 58: Homogeneous 9 w% Silver Composite C-Scan
59
The C-Scan images of the composites, shown in Figures 49-58, show the differences between the
homogeneous and heterogeneous samples clearly. Figure 49 displays a homogeneous composite
that clearly has silver flakes throughout the sample. The flakes are represented by the red areas
in the composite, and Figure 50 clearly displays the pattern in the heterogeneous composite. In
a higher loading, there is a greater response to the acoustic waves that the C-scan uses due to a
higher presence of silver in the composite. This is shown in Figures 51-58, which are taken from
the second set of samples. The C-Scan shows that the pattern is relatively uniform throughout
the sample, with the lines being distinctively visible, thus the silver is only in the designated
areas in the heterogeneous composites.
9.3.2 SEM Analysis
9.3.2.1 First Set Morphological Data
Figure 59 shows an SEM image of the 9wt% Silver pattern sample composite.
Figure 59: SEM image of 9 wt% pattern sample
60
The hypothesis that explains why heterogeneous composites display a high thermal conductivity
is that the silver flakes have started to sinter together. This theory is suggested to be accurate
from the SEM image displayed in Figure 59. The flakes displayed in the pattern there have
started to sinter together, creating a more solid conduction path. While the flakes haven’t
completely sintered together, this suggests that it may be possible to obtain a truly sintered
heterogeneous composite if the process can be refined to allow it. The flakes also display a
connectivity between the layers of carbon fiber which indicates that there is a conduction path.
9.3.2.2 Second Set Failure Mode SEM
The folllowing figures are SEM images of the failure modes displayed in the previous section.
Figure 60: AGM Failure (2.5 wt% Silver Homogeneous Composite)
61
Figure 61: DGM Failure (2.5 wt% silver Heterogeneous composite)
Figure 62: SGM Failure (5 wt% heterogeneous composite)
62
As discussed previously, the content of silver and its design have an impact on the failure modes
of the composite. The heterogeneous composites both had aspects of delamination in their
failure mode, and this is likely due to the arrangement of the pattern as they were tested. The
samples were tested against the pattern, and they delaminated. The homogeneous sample had
silver spread throughout it and it failed in a jagged failure, much in the same way a well-made
neat sample would fail.
63
10. CONCLUSIONS
In this study, heterogeneous composites using silver filler in an alternating line pattern were
manufactured and tested for their thermal and mechanical properties. They were compared
against homogeneous composites of similar silver concentrations. It was observed that on
average, the thermal diffusivity and the thermal conductivity of the heterogeneous composites
was higher than their homogeneous counterparts. The highest displayed thermal conductivity
was in excess of 5 W/m K on the 9 wt% pattern sample. The conductivity increase shown is a
200% increase from the measured thermal conductivity of the neat CF/Epon 862 composite
(control), and an over 600% increase from the value in the literature for a neat CF/Epon 862
composite. It was observed that the tensile and flexural properties of high loading composites
did not significantly differ between the homogeneous and heterogeneous composites. This
suggests that a higher thermal conductivity can be obtained without sacrificing much mechanical
properties compared to homogeneous composites of a similar loading. Furthermore, the density
of the heterogeneous and homogeneous composites is comparable due to the weight percent of
silver included within the composite as a whole, thus allowing a lighter composite with a higher
thermal conductivity for heterogeneous composites.
64
11. FUTURE WORK
The current study was limited in that it only covered one sort of filler, silver, and only one sort of
resin. Further study into this subject matter could attempt new methods of producing
heterogeneous composites, use of new metals such as alluminum or copper, or potentially
graphite flakes instead of metals. The silver flakes did not penetrate the carbon fiber fabric as
well, so further study could include the use of smaller silver particles that can penetrate the
fabric, thus creating a full conduction path. Another suggestion is the use of a different pattern,
such as a checkerboard or cocentric square pattern.
65
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13. BIOGRAPHICAL SKETCH
Daniel Peter Gallagher, II was born in Roanoke, VA on July 29, 1987. He earned his Bachelor’s
in Physics from Florida State University in 2009, and is currently a MS candidate for the
Materials Science program at Florida State University. He has been on the thermal analysis team
at the High Performance Materials Institute since August 2009, and has worked on both thermal
conductivity measurement and improvement of composites.