CHARACTERIZATION OF TENSILE AND COMPRESSIVE PROPERTIES OF SINGLE FIBER FILAMENT OF TOHO HTS 40 CARBON FIBER
A Thesis by
Vaidehi Panchal
Bachelor of Science, IIAEIT, India 2012
Submitted to the Department of Aerospace Engineering and the faculty of the Graduate School of
Wichita State University in partial fulfillment of
the requirements for the degree of Master of Science
December 2017
© Copyright 2017 by Vaidehi Panchal
All Rights Reserved
iii
CHARACTERIZATION OF TENSILE AND COMPRESSIVE PROPERTIES OF SINGLE FIBER FILAMENT OF TOHO HTS 40 CARBON FIBER
The following faculty members have examined the final copy of this thesis for form and content, and recommend that it be accepted in partial fulfillment of the requirement for the degree of Master of Science, with a major in Aerospace Engineering. Suresh Keshavanarayana Raju, Committee Chair Nicholas Smith, Committee Member Ramazan Asmatulu, Committee Member
iv
DEDICATION
To late Mr. Krishnachandra Panchal and late Mrs. Kumkum Panchal.
To my parents, Mr. Anil Panchal & Mrs. Amita Panchal, family and friends.
v
ACKNOWLEDGEMENT
I express my sincere thanks to my advisor and committee chair, Dr. Suresh
Keshavanarayana Raju, for providing me an opportunity to work with him. I deeply appreciate
his continued guidance and support during the tenure of my research. I would also like to thank
Dr. Nicholas Smith and Dr. Ramazan Asmatulu for accepting to be members of my thesis
defence committee. I am grateful to Wichita State University for allowing me access to well-
equipped laboratories and all the facilities for fulfilment of this research. I am grateful to my
family and friends for their constant motivation and guidance, which led the way to the
successful fulfilment of this research and helped me during the research work.
vi
ABSTRACT
In this work, the longitudinal tensile and compressive properties of TOHO HTS 40
carbon fiber filaments was characterized experimentally. The tensile strength and modulus
were measured using a single filament tension tests using gage lengths ranging between 0.5
inches to 3 inches. The compression strength was measured using a loop test. The measured
tensile modulus had an average value of 192 GPa across gage lengths and did not exhibit
significant dependence on the gage length. The average tensile strengths at each gage length
exhibited the well-known length effects, with the strength decreasing from an average value of
4 GPa at a gage length of 0.5 inches to 2.52 GPa at a gage length of 3 inches. The average
compression strengths from the loop tests was found to be 3.86 GPa.
vii
TABLE OF CONTENTS
Chapter Page
1. INTRODUCTION……………………………………………………………………..1
2. LITERATURE REVIEW………………………………………………………...........4
2.1 Fiber geometry………………………………………………………………...4
2.2 Tensile Testing………………………………………………………………...5
2.3 Compression Testing………………………………………………………..…8
2.3.1 Tensile recoil test method…………………………………………...…8
2.3.2 Elastic loop test method………………………………………………12
2.3.3 Bending beam test method……………………………………………15
2.3.4 Bending beam test method with Laser Raman microscope………..…18
2.3.5 Direct axial compression test method………………………………...21
2.3.6 Direct measurement with bending beam test method…………………22
2.3.7 Direct measurement method…………………………….....................23
3. RESEARCH OBJECTIVE…………………………………………………………...26
4. EXPERIMENTAL PROGRAM……………………………………...........................27
4.1 Diameter measurement ………………………………………………………27
4.2 Tensile Testing…………………………………………………….................28
4.2.1 Elastic modulus measurement………………………………………..31
4.2.2 Failure strain % measurement………………………………………..33
4.2.3 Tensile strength measurement……………………………………..…33
4.3 Compression testing by elastic loop method………………………………....34
5. RESULTS AND CONCLUSION…………………………………………………….37
6. FUTURE WORK…………………………………………………………………….39
viii
TABLE OF CONTENTS (continued)
Chapter Page
REFERENCES……………………………………………………………………………….40
APPENDIXES……………………………………………………………………….……….44
ix
LIST OF TABLES
Tables Page
4.1 Observations of the diameter of fiber filaments………………………………………27
4.2 Values of Length and diameter of a loop at critical point……………………………..36
5.1 Comparison for Pan-based Carbon fibers with experimental results
of Carbon fiber TOHO-HTS 40………………………………………………………38
x
LIST OF FIGURES
Figure Page
1.1 Elastic modulus range for different fiber types…………..……………………………1
1.2 Tensile strength range for different fiber types…………………………………..……2
2.1 PAN and Pitch-based Carbon fiber diameters……………………………………..…..5
2.2 Preparation of single fibre specimen for axial tensile testing..………………………..6
2.3 Load displacement curve showing pre-load, yield point, full scale load and elongation……………………………………………………….....6
2.4 Tensile elastic modulus of some PAN and Pitch-based carbon fibers………..…...…..7
2.5 Tensile strength of some PAN and Pitch-based carbon fibers……..…………………..7
2.6 Tensile Recoil test method………….………………………………….……………....9
2.7 Probability of failure versus mid recoil stress with logistic model fit……………..…10
2.8 Probability of survival and failure versus mid recoil stress..........................................10
2.9 Compressive strength of carbon fibers obtained from tensile recoil method………...11
2.10 Elastic loop method experimental set up………………………………………………12
2.11 Picture of kink band on a fiber………………………………………………………...13
2.12 Compressive strength of carbon fibers obtained from elastic loop method……………15
2.13 Schematic diagram of bending beam test apparatus………………………………….16
2.14 Tensile and compressive load distribution on the beam...……………………………17
2.15 Schematic diagram of experimental set up of bending beam test…………….………18
xi
LIST OF FIGURES (continued)
Figure Page
2.16 Raman frequency shift as a function of compressive strain for a Kevlar 29 fiber, represents On-set of visible kink ban formation………………………………..…....20
2.17 Compressive strength of carbon fibers obtained from bending beam method.………20
2.18 Experimental set up of direct axial compression test……………………………........21
2.19 Schematic diagram of Direct Method………………………………………………...22
2.20 Resultant graph plotted with longitudinal compressive strength with respect to different gage lengths…………………………………………………23
2.21 Schematic diagram of experimental set up of direct measurement method…………...24
2.22 Kink band formation and post kink splitting of fiber filament under direct compression………………………………………………….………….24
2.23 Compressive strength of carbon fibers obtained from direct method…………………25
4.1 Fiber diameter images taken from optical microscope………………………………..27
4.2 Tensile testing experimental set up………………………………………...…………29
4.3 Schematic diagram of tensile testing experimental set up…………………………….29
4.4 Schematic diagram of test sample for tensile testing………………………………….30
4.5 Force-extension graph obtained from tensile testing……………………………..…..30
4.6 Stress-Strain graph plotted with 0.5 inches gage length………………………………31
4.7 Stress-strain graphs plotted for different gage lengths……………….…..………...…32
4.8 Elastic modulus measured using different gage lengths………………………..…….32
4.9 Failure strains measured using different gage lengths……………………………...…33
xii
LIST OF FIGURES (continued)
Figure Page
4.10 Tensile strengths measured using different gage lengths……………………………..34
4.11 Schematic diagram of elastic loop test set up………………………….........................34
4.12 Fiber loop images with dimensions…………………………………………………...35
4.13 L/D - Length graph from loop test method…………………………………………….35
1
CHAPTER 1
INTRODUCTION
In continuous fiber reinforced composites, fibers are the primary load carrying
constituents and occupy a larger portion of the total material volume. ‘Fiber’ is a common term
used for a single filament as well as various assemblages of filaments such as strand, tow, end,
roving, and yarn [25]. Many of the most recent advancements in composite have been in the
field of aerospace, where highly specialized fibers such as carbon/graphite fiber, glass fiber,
kevlar aramid fibers are used to create incredibly strong and lightweight components. Each
fiber type has some unique characteristics which are used in combination with the matrix, based
on the desired application.
Carbon/graphite fiber is high strength and high modulus fibers with a low coefficient
of thermal expansion. Whereas, kevlar aramid fibers are low strength and low modulus fiber.
Kevlar fibers are comparatively lighter than carbon fibers. However, kevlar fibers have good
resistance to impact abrasion, cuts etc. Lastly, glass fiber has high strength and low modulus.
Glass fibers have good chemical, temperature and impact resistance. Comparison of fiber
strengths and modulus of different fibers are shown in figure (1.1) and figure (1.2).
Figure (1.1) Elastic modulus range for different fiber types [28]
0
100
200
300
400
500
600
700
800
900
Glass Aramid Carbon Fiber
Elas
tic
Mo
du
lus
(GP
a)
Fiber
2
Figure (1.2) Tensile strength range for different fiber types [28]
Due to their superior specific strength, specific stiffness, and fatigue resistance, carbon fibers
are preferred for aerospace applications, in spite of the cost penalty. Some applications of
carbon fiber are in the primary and secondary structures of aircraft, mid-fuselage structures,
automobile, marine and sports industries.
Carbon fibers are made from PAN precursor material, pyrolyzed at 2400̊ F and contains
93-95% carbon [25]. TOHO HTS-40 is a high strength carbon fiber manufactured in Japan and
Germany [24]. This fiber is made using a poly-acrylonitrile (PAN) precursor. Some of the
common characteristics [24] of TOHO HTS-40 carbon fiber are-
• High strength and high modulus
• Low density
• Low fatigue
• Chemically Inert
• Non-corrosive
• High resistance against acid and alkalis
• Low thermal Expansion
• Low thermal conductivity
2500
3000
3500
4000
4500
5000
Glass Aramid Carbon Fiber
Ten
sile
Str
engt
h (
MP
a)
Fiber
3
• Low X-Ray absorption
Over the years, the structural analysis of continuous fiber reinforced composites has been
increasing in refinement and the level of detail study. Due to the advances in micromechanics
and computational methods, the stress analysis extends all the way done to the fiber matrix and
interphase region. This level of details is required to accurately predict the initiation of damage
in the composite under various loading scenarios. The inputs to models at the microscale
include the fiber and matrix properties (e.g., modulus, strength, thermal expansion, etc) as well
as the spatial arrangement of the fibers.
The measurement of fiber properties poses several challenges owing to its geometry
and the distribution of flaws along the length. The fiber properties have been measured using
direct methods for longitudinal tension where the geometry of the filaments is suitable for such
loading. On the other hand, the compression responses are much more difficult to measure due
to the extremely slender geometry of the filaments.
In the present study, the different methods of measuring longitudinal (axial) tensile and
compressive strength and moduli of single filaments are summarized based on publications in
the open literature. The advantages, limitations, equipment, and sensors required for each test
are discussed. While one may find the average (nominal) values for strength and modulus from
the data published by the manufacturer, the information of the scatter in the data and other
material artifacts such as dependence on length, etc., is not easily available in open literature.
Such information is required in micromechanics models, which predict the homogenized
composite properties while taking into account the statistical nature of the filament properties.
In this study, the axial tensile and compressive properties of a PAN-based carbon fiber, TOHO
HTS-40, have been measured experimentally. The details of the experiments, results, and
observations are presented in this document.
4
CHAPTER 2
LITERATURE REVIEW
The measurement of filament mechanical properties such as moduli and strength poses
several challenges experimentally due to their geometry. Even though the fibers have relatively
high strength and modulus, due to their small diameters, the measurements require careful
handling of the filaments, low range load cells, non-contact strain measurement equipment,
etc. In this chapter, the test methods, observations, and results reported by previous
investigators are presented. This chapter focusses mainly on the longitudinal tension and
compression properties of fibers.
2.1 Fiber geometry
One of the key geometric quantities required for generation of fiber properties is the
cross-section area. This requires a reliable measurement of the fiber diameter. The fiber
diameter, owing to the size of the fibers, can only be measured using optical methods. To
measure the diameter of a fiber, fibers are chopped into very small pieces and mixed with
methanol in such a way that fibers get separated into single filaments [22]. The mixture is then
poured on the microscope slide and the slide is left undisturbed to allow the methanol to
evaporate. The slide is then kept on an optical microscope base and magnification of 200x is
used to take direct images of fiber filaments on the slide [22]. The range of diameter of carbon
fibers is 2-20 m [25]. Some PAN and Pitch-based carbon fiber diameters obtained by
microscopy method are shown in figure (2.1).
5
Figure (2.1) PAN and Pitch-based Carbon fiber diameters [7,20,16]
2.2 Tensile Testing
The tensile properties of fibers are measured using a simple tension test on a filament.
The tests are performed as per the ASTM test standard D3379-75 [22]. This method has been
widely used by various researchers [1,11,13,16,22] to measure the properties of different fiber
materials. Owing to the small fiber diameters, the filaments can be easily damaged due to
handling prior to the actual tensile loading. To prevent this, the filament is mounted on a slotted
sheet of paper as shown in figure (2.2).
The slot length is equal to the desired gage length and fiber filament is glued at both
ends of the slot as shown in figure (2.2). The slotted paper with the bonded filament is then
mounted in the grips of an electromechanical testing machine. The tension testing is typically
conducted under displacement control and the measurement of force requires a sensitive low
range load cell. For instance, a filament with a typical diameter of 8m and tensile strength of
6 GPa, will require about 0.3N of force to break it.
7.01 6.75
4.97 5 5.21 5.19 5.07
6.96.5 6.4
109.5 9.4
0
2
4
6
8
10
12
Dia
met
er (
µm
)
Carbon Fibers
6
Figure (2.2) Preparation of single fibre specimen for axial tensile testing [22]
Before starting the tensile testing, the paper is cut from the middle of the slot. The tensile
loading is increased monotonously until the filament fails. The typical force-displacement
diagram for a filament as reported by Ilankeeran et.al., is shown in figure (2.3). The crosshead
displacement is often the only measure of filament elongation as contact based strain
measurement methods are not practical for measuring filament deformation. The crosshead
displacement is converted into filament elongation by accounting for the machine compliance.
The machine compliance is estimated by using the data from testing of filaments with different
gage lengths [22].
Figure (2.3) Load-displacement curve showing pre-load, yield point, full scale load and elongation [22]
7
The typical elastic moduli and tensile strength of some carbon fibers are reported by various
researchers are presented in figure (2.4) and figure (2.5) [16,7,20]. The gage lengths are not
often reported with these values.
Figure (2.4) Tensile elastic modulus of some PAN and Pitch-based carbon fibers [7,16,20]
Figure (2.5) Tensile strength of some PAN and Pitch-based carbon fibers [7,16,20]
0
100
200
300
400
500
600
700
Tens
ile E
last
ic M
odul
us (G
Pa)
Fibers
012345678
Tens
ile st
reng
th (G
Pa)
Fibers
8
2.3 Compression Testing
The compression testing of fibers is much more challenging than tension testing due to
the very low stability of slender fibers. The compression strength of filaments has been
measured by various investigators using different methods which induce compression loading
in fiber either directly or indirectly. These methods include the tensile recoil method
[1,2,7,20,21], the elastic loop method [3,5,18,20], the bending beam method [5,10], and direct
compression loading method [4,7,8,9,16,19]. The details of the individual test methods, their
advantages and limitations are discussed in the following paragraphs.
2.3.1 Tensile recoil test method
Tensile recoil method was proposed by Allen in 1987 [21]. In this technique, a
predetermined axial tensile load is applied to the fiber filament, which induces strain energy in
the filament. The filament is then cut by an electric charge or sharp scissor, exactly in the
middle of the gage length, as shown in figure (2.6). This results in the initiation of recoil effect
in the filament. When the fiber is cut, the tensile stress reduces to zero and strain energy is
converted into kinetic energy. The stress wave-fronts move along the fiber towards the clamped
ends and by the time these waves touches the rigid end, strain energy completely takes the form
of kinetic energy.
Once kinetic waves hit the rigid end, kinetic energy is converted back to strain energy.
During this snapback phenomenon, some amount of stress is induced in the fiber which is equal
to the applied tensile stress. If this resultant stress crosses the compressive limit, fiber
undergoes failure.
9
Figure (2.6) Tensile Recoil test method [1]
There are two ways to calculate the compressive strength from the recoil test. Firstly, a number
of observations are taken with increasing values of tensile loads. Then, mean of the values of
stress under which last nonfailure and first failure are observed, is considered as the
compressive strength of the filament.
The second method of compression strength calculation is based on the probability
distribution [1]. It is assumed that the recoil failure at either end is an independent process. A
curve is plotted between the probability of failure and the recoil stress level as shown in figure
(2.7) [1]. When the fiber has the same probability of survival and failure, the mid recoil stress
corresponds to 50% probability of failure, which signifies the compressive strength. The
second method shows much fewer variations when wide stress range data are being tested as
fitted curve gives better accuracy.
10
Figure(2.7) Probability of failure versus mid recoil stress with logistic model fit [1]
Based on the concept of the probability distribution, there is another way of calculation [2]. In
this approach, stress ranges are selected, and the average of highest and lowest values of stress
ranges are taken into consideration for testing fiber filaments. Then, a graph of percentage
survival of fiber halves and applied stresses are plotted as shown in figure (2.8). The stress
value which corresponds to 50% of fiber halves survival is assumed as compressive strength.
Figure (2.8) Probability of survival and failure versus mid recoil stress [2]
11
Tensile recoil test method is based on some assumptions [2],
• It is considered that fiber obeys Hook’s law.
• Fiber is rigidly clamped at each end of gage length, and the fiber has zero initial
velocity.
• Fiber has uniform tensile stress along its length at failure with the exception that the
stress is zero at the location of breaking.
This method is acceptable to a great extent due to procedural simplicity and ability to produce
repeatable results. On the contrary, there are some disadvantages of this method, such as an
indirect interpretation of compressive property and artificially derived failure of fiber.
Since dynamic impact and buckling takes place in the filament, this method underestimates
compressive strength [7]. The tensile compressive strength of some PAN and Pitch-based
carbon fibers obtained from tensile recoil method is shown in figure (2.9).
Figure (2.9) Compressive strength of carbon fibers obtained from tensile recoil method [2,7,20,21]
0
0.5
1
1.5
2
2.5
Com
pres
sive
Stre
ngth
(GPa
)
Fibers
12
2.3.2 Elastic loop test method
Elastic loop method was first used by David Sinclair, in 1950, to measure the tensile
strength of glass fiber. In the elastic loop method, the fiber is bent into a loop and the size of
the loop is gradually reduced by pulling both the ends to observe first kink band at the bottom
of the loop, as shown in figure (2.10). In 1980, M. G. Dobb and others concluded that kink
bands form just before the elastic instability of the fiber and critical bending stresses are
developed at the bottom of the loop when the size of the loop is reduced [5]. The radius of
curvature is measured by the circle drawn inside the loop.
Figure (2.10) Elastic Loop Method experimental set up [5]
When the fiber is bent in a loop and stretched to a smaller size, fiber experience compression
on the inner side of the loop and tension on the outer side. Compression on the inner side of
loop breaks the lateral bond between the molecules and results in micro-buckling and shear
slip in molecular chains [3]. This buckled material cave into an angled kink band. An image of
a kink band is shown in figure (2.11). Hence, the load at which first kink band is observed is
considered as the compressive load that the filament can withstand.
13
Figure (2.11) Picture of Kink Band on a fiber [3]
This method states that for elastically deformed fibers in a loop, the ratio of major (vertical-
axis) to the minor (horizontal-axis) is 1.34, irrespective of any modulus anisotropy that can
occur between the tension and compression side of the looped fiber [3]. When the fiber enters
the plastic region, the ratio of major to minor axis increases rapidly. The point at which fiber
leaves elasticity is termed as the critical point. At this point, failure takes place on the
compression side of the fiber, at the location of minimum radius of curvature. Size of the loop
and fiber deformation is recorded by micrographs taken by the microscope.
For small size loops, fiber filament is looped and trapped in oil between a coverslip and
the microscope slide. Light oil must be used to avoid friction because the fiber filament is very
delicate. Now, the loop size is reduced gradually by pulling the ends of the loop with the help
of fixtures, as shown in figure (2.10). This process is continued until first kink band is observed
at the bottom of the loop. During this process, micrographs are taken at various stages using an
optical microscope. Strain in fiber is calculated with the help of loop geometry at the critical
point and equation (2.6).
14
𝒆𝒄𝒓 =𝒓
𝑹𝒎 (2.6)
𝑒𝑐𝑟 = critical compressive strain
𝑟 = fiber radius.
𝑅𝑚 = minimum radius of curvature at the location where last kink band is observed in the
loop.
Scanning electron microscopy method is conducted by Sukru Fidan [5] to observe very small
fiber deformation that cannot be conducted by optical microscope method. Fibers are bent in
different sizes of loops and placed on the specimen holder. Sizes of the loops are intentionally
kept nearly the same as the size of the loop in which first kink band is observed in optical
microscopy method. Now the loops are coated with 10 nm layer of Au/Pd, to avoid charging
in the electron beam. Then observations are taken using scanning electron microscope at 20KV.
Kink band is observed at the bottom of the loop and then only one arm of the loop is traced till
the last kink band is observed on the fiber surface. Now micrographs of the loop are taken at
the location where the last kink band was observed. At the same time, a circle is drawn into the
loop and radius is measured as minimum radius, and critical compressive strain is derived by
equation (2.6).
Elastic loop test is an inexpensive method and measurements are easily calibrated.
Compressive deformation is observed on the compressed side of the fiber, so there are no issues
with surface irregularity. A tensile compressive strength of some pan and Pitch-based carbon
fibers obtained from elastic loop method is shown in figure (2.12).
15
Figure (2.12) Compressive strength of carbon fibers obtained from elastic loop method
[3,5,18,20]
2.3.3 Bending beam test method
In 1985, De Teresa [5] used bending beam test to study compressive failure
mechanism of polymer fibers. In this method, the measured compressive load is applied to
initiate kink band in the fiber. With this attempt, the researchers tried to explain compressive
failure mechanism in the extended chain polymers due to elastic micro-buckling instabilities.
In this method, fiber is bonded to the surface of an elastic rectangular plexiglass beam
and the beam is bent as shown in figure (2.13). Considering that the fiber is perfectly bonded
to the beam, strain observed at the surface of the beam would be equal to the strain in the fiber
at the same location. By keeping the beam in the same position, kink band formation is
observed with the help of an optical microscope. The last kink band formed is known as the
critical kink band. At this point, the strain is called critical compressive strain which is then
multiplied by tensile elastic modulus to calculate the compressive strength of the fiber.
3.7 3.7
2.32.6
21.8
0.50.67
1.24
0.47 0.43 0.390.17
00.5
11.5
22.5
33.5
4C
ompr
essi
ve st
reng
th (G
Pa)
Fiber
16
Figure 2.13 Schematic diagram of bending beam test apparatus [5]
A single fiber is mounted onto the surface of the beam. Several layers of urethane are coated
on the beam and allowed to dry for at least a day. Shrinkage of the coating film is not expected
because the thickness of the coating is very small as compared to the thickness of the beam. As
a measure of precaution, each fiber is measured with an optical microscope, for any possible
unwanted fiber deformation due to bonding and handling, before each test is conducted.
Now, the beam is clamped in the fixture. A circular wedge is placed between the beam
and the base plate of the fixture to deflect the beam, and it is gradually moved closer to the
clamped end of the beam. At any point, the diameter of the wedge is considered as the
deflection of the beam. It is considered that deflecting rate of the beam is very important in
terms of strain growth rate in fiber. Therefore, the beam is loaded slowly to make sure that fiber
beam bonding and the coating is less affected. By holding the beam in the bent position, fibers
are examined with an optical microscope. Ultimately, the strain is calculated by linear beam
theory formula, as shown in equation (2.7).
17
𝑒(𝑥) =3𝑡𝑑
3𝐿2 (1 −𝑥
𝐿) (2.7)
t = thickness of the beam
d = wedge diameter or deflection of the beam
x = the distance from the clamped edge to the location where the strain is calculated
L = the distance from the clamped edge of the
beam to the wedge centre
The critical compressive strain is calculated by using the distance ‘L’ in place of ‘x’ in the
equation (2.7). Tension and compression load distribution on the beam, when load ‘P’ is
applied is shown in figure (2.14).
Figure (2.14) Tensile and compressive load distribution on the beam [10]
This method has several advantages such as, along with the simplicity of procedure and eases
to measure, this method gives precise results. Axial stress gradient along the fiber is very useful
to measure strain at different stress values. Moreover, this gradient can be easily varied by
changing wedge size or placing the wedge near the clamped end. However, if there is any
surface irregularity exists in the fiber, this method may give results that are near to accurate
and not exact.
18
2.3.4 Bending beam test method with Laser Raman microscope
A modified version of bending beam theory was introduced by C. Vlattas and C.
Galiotist to make it more accurate [10]. In this technique, laser beam microscope is used to
measure critical compressive strain and molecular deformation during and after the failure.
Also, the compressive modulus and critical compressive stress are calculated based on the
strain dependence of individual fiber Raman frequencies [10].
In bending beam method, failure can be detected only when kink band is observed
optically and the film shrinkage is not taken into consideration while calculating the results. To
overcome these drawbacks, a modified version of bending beam method was introduced. In
this method [10], fiber is subject to load and molecular deformation is observed by scanning
the fiber with laser Raman microscope (LRM). LRM is used in such a way that the Raman
frequencies show higher values in case of compression and lower values for tension.
Similar to a typical bending beam test, the fiber filament is bonded on an elastic bar
with the help of an acrylic adhesive and the film is dried for several hours. The cantilever beam
is deflected with the help of flat screw. Deflection in fiber is observed in-situ, with laser Raman
microscope placed above the fiber, as shown in figure (2.15).
Figure (2.15) Schematic diagram of experimental set up of bending beam test [10]
19
Before testing, all the fibers are examined without bonding fiber to the beam. If any specimen
is found to experience stress due to shrinkage or mishandling, then it is rejected. Raman spectra
is 515 nm argon ion laser. A microscope must be used to focus laser beam incident on the fiber.
Maximum laser frequency should not exceed 1-2 MW to prevent the fiber from overheating.
Typical cantilever compression plot is used to find out desirable results. This graph is
plotted in a way that y-axis represents the difference of Raman frequencies of embedded fibers
and stress-free fibers tested before the experiment. Whereas, the x-axis represents compressive
strain calculated along the fiber with the formula used in bending beam test as shown in
equation (2.8).
𝑒(𝑥) =3𝑡𝑑
3𝐿2 (1 −𝑥
𝐿) (2.8)
This Raman frequencies v/s compressive strain curve can be plotted for both compression and
tension. It has been observed from experiments that up to some point graph depicts linear
increment in values. Continuingly, it starts dropping and tends to achieve much lower values.
The significance of this behaviour is that till the point where Raman frequencies increases
linearly, the applied compressive strain is sustainable for the fibers. In other words,
intermolecular bonds are contracted but do not fail. Now, if the stress is increased, kink band
is formed as the result of damage in intermolecular bonds. Kink band formation executes
relaxation of intermolecular bonds which result in the drop of Raman frequencies. An example
of Raman frequencies v/s compressive strain graph is shown in figure (2.16). This graph is
plotted for Kevlar 29 fiber with tensile modulus value of 80 GPa [10].
20
Figure (2.16) Raman frequency shift as a function of compressive strain for a Kevlar 29 fiber, represents Onset of visible kink band formation [10]
Then, the value of % compressive strain, obtained from the figure (2.16) is used to calculate
compressive strength assuming Hookean behaviour till failure, Bending beam technique with
laser Raman microscope can provide data in both tension and compression field. Critical
compressive strain calculation is more accurate in this technique.
Tensile compressive strength of some PAN and Pitch based carbon fibers obtained
from bending beam methods is shown in figure (2.17).
Figure (2.17) Compressive strength of carbon fibers obtained from bending beam method [5,10]
00.10.20.30.40.50.60.70.8
Com
pres
sive
stre
ngth
(GPa
)
Fibers
21
2.3.5 Direct axial compression test method
In an attempt to avoid indirect measurement and assumptions, direct method was
introduced by researchers where the load is applied directly to the filament with no
constrictions around the fibers. Fibers are observed directly by an optical microscope to detect
failure [4].
Kazuhiro Fujita and others measured compressive strength with apparatus consists of
two bases on which fiber ends are bonded with the help of epoxy resin. One base is connected
to the load cell and another one is connected to three-dimensional drive actuator to achieve
smooth displacement and avoid off-axis loading. An optical microscope is fitted to observe the
fiber behaviour as shown in figure (2.18). Voltage is applied to the actuator which induces
strain in fiber filament and the applied load is experienced by a load cell. The load is gradually
increased until the shear failure or buckling failure is observed in fiber through the optical
microscope.
Figure (2.18) Experimental set up of direct axial compression test [4]
Fujita, Shioyama, and Sawada [4] studied many Pitch-based and PAN-based carbon fibers and
concluded that almost all pitch-based carbon fiber shows shear failure whereas, Pan-based
shows buckling failure. Secondly, they found out that gauge length-diameter ratio for this test
22
should be less than 10 for PAN based carbon fibers and less than 5 for Pitch-based carbon
fibers. Length- diameter ratio is an important thing to be considered to avoid buckling effect.
2.3.6 Direct measurement with bending beam test method
A method was reported by Naoyuki Oya, David J. Johnson in 1998, to eliminate the
effects of buckling which is one of the drawbacks of direct compression methods [16]. Carbon
fiber of about 45-200 mm gage length is mounted on the fixed sample stage. The experimental
setup consists of an elastic material cantilever beam attached to the strain gauge and an
elliptical cam, as shown in figure (2.19). The elastic beam moves as the elliptical cam rotate
(DC motor is connected to the cam). While cantilever beam bents, it applies the compressive
force to fiber filament. Compressive load experienced by the fiber is proportional to the strain
applied to cantilever beam and it is observed by the strain gauge attached to the beam.
Figure (2.19) Schematic diagram of direct method [16]
Using this method, fiber specimens were examined with different gage lengths for different
fibers and they concluded that strength was highest at the gage length of 45 micrometers, as
shown in figure (2.20).
23
Figure (2.20) Resultant graph plotted for longitudinal compressive strength with respect to different gage lengths [16]
2.3.7 Direct measurement method
There was another method used by N. Oya, D. J. Johnson with H. Hamada and others
in 2000 [7], to measure compressive strength directly under the microscope. In this method,
fiber filament is glued on the brass stage with the help of a super glue. A portion of the filament
(20-500 micrometers) is kept out of the brass stage with the help of a microscope and the length
is considered as the gage length. Then the brass stage is placed on the assembly of DC motor
with micrometer screw thread and mechanically moved with the speed of 0.13 micrometer per
second [7]. At a certain distance, a cantilever beam is fixed with the strain gauge attached to it
as shown in the figure (2.21).
As the gear rotates, fiber filament gets in contact with cantilever beam and ultimately
gets compressed axially. Strain gauge detects the deflection experienced by the cantilever
beam. These signals are amplified and calculated digitally in terms of force. With the help of
force-time graph obtained in a computer, longitudinal compressive strength is observed by
dividing ultimate force with the cross-sectional area of the specimen.
24
Figure (2.21) schematic diagram of experimental set up of direct measurement method [7]
This process takes place under a light microscope and fiber failure is observed in the form of
kink bands or splitting. Some pictures of in situ observation of fiber behaviour under
compression are shown in figure (2.22).
Figure (2.22) Kink band formation and post kink splitting of fiber filament under direct compression [7]
25
The tensile compressive strength of some PAN and Pitch-based carbon fibers obtained from
different direct methods is shown in figure (2.23).
Figure (2.23) Compressive strength of carbon fibers obtained from direct method [4,19,8,7]
0
0.5
1
1.5
2
2.5
3
Com
pres
sive
stre
ngth
(GPa
)
Fiber
26
CHAPTER 3
RESEARCH OBJECTIVE
The objective of this research is to measure mechanical properties of single carbon fiber
filament-‘TOHO HTS-40’. In an effort to advance the existing understanding and behaviour of
single fiber filament when subjected to different loadings, the following attempts were made;
➢ Fiber filament behaviour was examined under tensile loading. Tensile testing was
conducted to measure the maximum tensile stress that a filament can withstand.
Tensile modulus and failure strain of fiber filament was measured using different gage
lengths to examine effects of gage length on tensile properties.
➢ Compressive strength of single fiber filament was measured by bending the fiber in a
loop, by using the elastic loop method. Loop dimensions were used to measure the
compressive strength.
27
CHAPTER 4
EXPERIMENTAL PROGRAM
The experimental program was conducted in 3 groups. Firstly, the diameter of the
filament was measured. Secondly, the fiber was examined under the application of axial tensile
load. Lastly, compressive properties of the fiber were measured using elastic loop method.
4.1 Diameter measurement
Fiber diameter is a very important parameter to be measured before the conduction of
tensile and compressive testing. The diameter of fiber filament was measured using an
advanced optical microscope (Zeiss Axio Imager microscope) with the magnification of 500×.
Images of 10 fiber filaments were captured and their diameters were measured directly by the
Axio vision software [2]. Some images of the fibers and measured diameters are shown in
figure (4.1).
Figure 4.1 Fiber diameter images taken from optical microscope
28
Lastly, mean of the diameters of 10 fiber filaments were calculated to be considered as the
diameter of the fiber for further calculation, as shown in the table (4.1). Hence, the diameter of
TOHO HTS 40 carbon fiber was ranging from 7.2-8.4 m and the average of 10 observations
was 7.71 m.
Table 4.1 Observations of the diameter of fiber filaments
Filament No. Diameter (m)
1 7.615
2 7.333
3 7.99
4 7.621
5 7.99
6 7.358
7 7.87
8 7.63
9 7.225
10 8.44
Average 7.71
4.2 Tensile Testing
The test was performed with a set up that consists of one fixed slider (free movement
across the axis of the filament) to avoid off-axis loading, one moving slider (free movement
along the fiber filament) for application of load, a force transducer load cell (Interface model
ULC-0.5 N with 0.5 N maximum capacity [14]). A load cell was fixed on a screw threaded
base, an extensometer was used with test work 4 software support as shown in figure (4.2) and
figure (4.3). A spring was attached between the load cell and the slider for smooth and slow
application of load.
29
Figure (4.2) Tensile testing experimental set up
Figure (4.3) Schematic diagram of tensile testing experimental set up
The specimens were prepared by sticking a fiber filament on the paper by using a super glue.
A slot in the paper was cut in such a way that cut out was exactly equal to gage length of the
specimen, as shown in figure (4.4).
30
Figure (4.4) Schematic diagram of test sample for tensile testing
Before, starting the test, load condition was set to zero. One end of the paper was attached to a
fixed base and another end to the moving slider base. Now the paper was cut carefully from
the middle of the slot. The tensile load was applied to the filament by moving the slider and
load applied was experienced and recorded with the help of load cell. Fiber extension was
recorded by using laser extensometer in graphical form with the help of ‘Test work 4’ software
application.
Set of 10 experiments were conducted for each gage length ranging from 0.5 to 3 inches
in order to analyse the effects of gage length on tensile properties of the fiber. Output was
obtained in the form of force(N)-extension(in) graphs as shown in figure (4.5).
Figure (4.5) Force-extension graph obtained from tensile testing
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 0.002 0.004 0.006 0.008 0.01
Forc
e (N
)
Extension (in.)
31
4.2.1 Elastic modulus measurement
Force-extension coordinates were used to plot stress-strain graphs by dividing the force
by cross-section area and extension by respective gage lengths as shown in figure (4.6). The
slope of best-fitted trendline of the curve is the value of tensile elastic modulus. Hence, the
average of slopes obtained from the stress-strain curve was considered as the elastic modulus
value as shown in figure (4.6). Stress-strain graphs plotted using different gage lengths are
represented in Appendix-B.
Figure (4.6) Stress-Strain graph plotted with 0.5 inches gage length
The tensile test was conducted with 5 different gage lengths of 0.5, 1, 1.5, 2 and 3 inches to
study effects of gage length on tensile properties of the fiber. It was observed that with the
increase in gage length, stress-strain graphs tend to show more scattered values. The gage
length has considerable effects on the linearity of the graph, as shown in figure (4.7). Hence,
for better understanding and measurement of fiber properties, it is recommended to use shorter
gage lengths while conducting the tensile test.
0
500
1000
1500
2000
2500
3000
0 0.005 0.01 0.015 0.02
STR
ESS
(MP
a)
STRAIN
Average E= 181.68 GPa
32
Figure (4.7) Stress-strain graphs plotted for different gage lengths
Furthermore, figure (4.8) explains the fact that gage length of the specimen does not affect the
value of elastic modulus. A graph was plotted to demonstrate values of average elastic modulus
with respect to gage lengths. Average value of elastic modulus obtained from different gage
lengths was 192 GPa.
Figure (4.8 ) Elastic modulus measured using different gage lengths
33
4.2.2 Failure strain measurement
Failure strain of the fiber was determined by dividing maximum extension of the filament by
gage length. A constant decrease in strain value was observed with the increase in gage
length as depicted in figure (4.9). Hence, average failure strain of the fiber was obtained as
1.7 % with the strain decreasing from an average value of 2.2% at a gage length of 0.5 inches
to 1.3% at a gage length of 3 inches.
Figure (4.9) Failure strains measured using different gage lengths
4.2.3 Tensile strength Measurement
Tensile strength is the maximum tensile stress (force per unit area), a material can
withstand when subjected to a pure tensile load. The tensile strength was calculated by
multiplying maximum strain with elastic modulus obtained from different gage lengths. A
graph was plotted for tensile strength with respect to gage length as shown in figure (4.10).
The tensile strength value for the fiber filaments was 2.52-4.00 GPa as shown in figure
(4.10). A constant decrease in tensile strength with increasing gage length depicts that strength
of the fiber is dictated by the presence of flows distributed randomly along the length of the
fiber. Shorter gage length shows higher tensile strength value because of absence of larger
flows.
0.022
0.0200.016
0.0140.013
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0 20 40 60 80 100
Stra
in
Gage Length (mm)
Failure Strain = 0.017
34
Figure (4.10) Tensile strengths measured using different gage lengths
4.3 Compression Testing
The experimental set up for elastic loop test is shown in figure (4.11). A microscope
slide was placed on the illuminated light base and 2 sliders were fixed on both the sides of the
microscope slide (with accurate horizontal and vertical alignment). A calibration slide was
placed beneath the microscope slide to measure the loop dimensions.
Carbon fiber filament was placed in light oil and a loop of about 1mm length was made on the
microscope slide by sticking ends of the filament on the slider bases as shown in the figure
(4.11).
Figure (4.11) Schematic diagram of elastic loop test set up [5]
4.003.42 3.29
2.67 2.52
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0 20 40 60 80 100
Tens
ile st
reng
th (G
Pa)
Gage Length (mm)
Tensile Strength = 4-2.52 GPa
35
In this work, a lens with the magnification of 100-150× and Dino Capture software was used.
Pictures of reducing loop were captured with an interval of 1 second with the help of a
microscope. In all the pictures, loop geometry was defined by the length of the loop (L) mm
and diameter of the loop (D) mm as shown in figure (4.12). Images of fiber loops captured
from the microscope is shown in figure (4.12).
Figure (4.12) Fiber loop images with dimensions
The elastic loop test is based on the fact that L/D ratio of loops is 1.34 (considered as the elastic
region) at the critical point and starts increasing after this point, as shown in figure (4.13).
Failure was observed to occur on the compression side of the looped fiber at the critical point.
Figure (4.13) L/D - Length graph from loop test method
36
Loop dimensions were noted at the critical point in order to calculate the compressive strength
of the fiber. The value of 𝑒𝑐𝑟 was the critical compressive strain obtained from the elastic loop
test (equation 4.4). 𝑒𝑐𝑟 was then multiplied by tensile modulus to obtain the value of
compressive strength of the fiber. The average of 10 values, as shown in the table (4.2), was
considered as compressive strength of filament.
𝑒𝑐𝑟 =𝑟
𝑟𝑚=
𝑓𝑖𝑏𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠
𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑙𝑜𝑜𝑝 (4.4)
Table (4.2) Values of Length and diameter of a loop at critical point
S No. Length (L)
(mm)
Diameter (D)
(mm)
L/D Compressive strain
(𝑒𝑐𝑟)
Compressive Strength
(GPa)
1 .699 .518 1.349 0.015 2.85
2 .617 .459 1.344 0.017 3.22
3 .435 .320 1.35 0.024 4.62
4 .486 .361 1.346 0.021 4.10
5 .865 .641 1.349 0.012 2.31
6 .425 .317 1.34 0.024 4.66
7 .522 .387 1.348 0.020 3.82
8 .517 .385 1.342 0.020 3.84
9 .462 .344 1.34 0.022 4.30
10 .405 .301 1.345 0.026 4.91
AVG .543 .4033 1.34 0.020 3.86
37
CHAPTER 5
RESULTS AND CONCLUSION
Tensile and compressive tests were conducted on ‘TOHO HTS 40’ carbon fibers to
investigate the behaviour of the fiber when subjected to tensile and compressive loading. The
following prominent observations were made from the experiments.
1. The average diameter of fiber filament measured with the help of an optical microscope
was 7.71 m.
2. The tensile test was conducted with 5 different gage lengths of 0.5, 1, 1.5, 2 and 3 inches
to study effects of gage length on tensile properties of the fiber. It was observed that with
the increase in gage length, stress-strain graphs tend to show more scattered values. Hence,
for better understanding and linearity in the measurement of fiber properties, it is
recommended to use shorter gage lengths.
3. Average tensile elastic modulus, determined by the slope of the stress-strain curve was 192
GPa. It was observed that gage length of the specimen does not greatly affect the elastic
modulus. However, there is a slight variation in elastic modulus obtained from different
gage lengths.
4. Average failure strain of the fiber was measured as 1.7% with the strain decreasing from
an average value of 2.2% at a gage length of 0.5 inches to 1.3% at a gage length of 3
inches. It was observed that strain of the fiber decreased with increase in gage length.
5. The tensile strength, calculated as the product of strain and elastic modulus obtained from
different gage lengths was 2.52-4.00 GPa. A decrease in tensile strength was observed with
increase in gage length, because of the presence of flaws distributed randomly along the
gage length. Shorter gage length shows higher tensile strength value because of the absence
of larger flows [25].
38
6. Calculation of the compressive strength is a length independent process. The average
compressive strength of the fiber, calculated using elastic loop method was 3.8 GPa.
7. Table (5.1) shows the range of properties for carbon fiber family and ‘TOHO HTS-40’
Carbon fiber. Table (5.1) demonstrates that experimental results are in good agreement with
existing carbon fiber properties in open publications.
Table 5.2 comparison for Pan-based Carbon fibers with experimental results of Carbon fiber TOHO-HTS 40
S. no. Property Carbon Fibers
(PAN-Based)
[23,27]
Carbon fiber
(TOHO-HTS 40)
[26]
Carbon Fiber
(TOHO-HTS 40)
(experimental)
1 Diameter 5 - 8 m 7 m 7.2-8.4 m
2 Elastic Modulus 200–520 GPa 230 GPa 181.68-210.42 GPa
3 Failure strain 0.6 – 2.2 % 1.80 % 1.7-2.2 %
4 Tensile Strength 1.8 – 5.7 GPa 4.2 GPa 2.52 – 4.00 GPa
5 Compressive
Strength
0.8 – 4 GPa 2.3-4.6 GPa
39
CHAPTER 6
FUTURE WORK
Results of diameter, elastic modulus, failure strain and tensile strength are in
good agreement with the existing recorders [26]. However, the compressive strength of
‘TOHO HTS 40’ carbon fiber is not reported in the open publication. Hence, there is a wide
scope for determining the compressive strength by using alternative techniques such as
recoil method, bending beam method and/or direct method.
In this research, elastic loop method was used to measure compressive
properties. This method states that ratio of major to minor axis of the fiber loop in the elastic
region is 1.34 and increases rapidly as the fiber enters in the plastic region [3,5]. As shown
in figure (4.14), L/D ratio of the loop constantly decreases till 1.34 (critical point) and starts
increasing after the critical point. However, ideally L/D ratio should be 1.34 in the elastic
region, to overcome this experimental limitation, it is recommended to keep loop arms as
short as possible to maintain the loop arms alignment. This can be achieved by keeping the
loop’s major axis along the length of the microscope slide or by using a smaller size
microscope slide.
Loop dimensions were measured using an optical microscope to determine the
critical point. Alternatively, the critical point may be determined by observation of kink
bands using scanning electron microscopy [5].
It is recommended to determine shear modulus of fiber filament for the detailed
examination of fiber properties. Some factors may influence the compressive strength and
shear modulus simultaneously, such as lattice imperfection, molecular bonding etc [1].
The density of filament is suggested to be determined since it gives the value of specific
modulus and specific strength of the fiber [25] and used in micromechanics modelling and
analysis extensively.
40
REFERENCES
41
REFERENCES
[1] C.Wang, B.A.P. Francis, E.S.M. Chia, “Mechanical and Interfacial Properties Characterisation of Single Carbon Fibres for Composite Applications”, Society for Experimental Mechanics, Singapore, March 2015.
[2] I.P. Kumar et al., “Axial compressive strength testing of single carbon fibers” in Archives of Mechanics, Institute of Fundamental Technological Research, Vol 65, No 1, 2013.
[3] A. Andres Leal, Joseph M. Deitzel, and John W. Gillespie, JR, “Compressive Strength Analysis for High-Performance Fibers with Different Modulus in Tension and Compression” Sage, Newark, USA, March 2009.
[4] Kazuhiro Fujita et al., “Direct Evaluation of Axial Compressive Properties of Carbon Filament” in “Osaka National Research Institute”, AIST, Midorigaoka, Ikeda, Osaka, 563-8577 Japan, data accessed Nov 2017
[5] Sukru Fidan, “Experimentation and analysis of compression test methods for single filament high-performance fibers” department of the air force, Wright-Patterson air force base, Ohio, 1989.
[6] P. D. Ewins, “A compressive test specimen for unidirectional carbon fiber reinforced plastics” Structures Department, R.A.E., Farnborough, January 1970.
[7] N. Oya, D. J. Johnson, and H. Hamada “Longitudinal compressive behaviour of carbon
fibers” West Yorkshire, LS2 9JT, UK, Sakyo-Ku, Kyoto, Japan, May 2000
[8] K. S. Macturk and R. K. Eby, and W. W. Adams, “Characterization of compressive properties of high-performance polymer fibers with a new micro-compression apparatus” The University of Akron, and Institute of Polymer Science, OH, USA, Air Force Wright Research and Development Center, Dayton, OH, USA, 1990.
[9] A. Andres Leal, Joseph M. Deitzel, John W. Gillespie Jr., “Assessment of compressive properties of high-performance organic fibers” Newark USA, 2007.
[10] C. Vlattas and C. Galiotist, “Monitoring the behaviour of polymer fibers under axial compression” Department of Materials, Queen Mary and Westfield College, The Johns Hopkins University, Baltimore, MD, USA, 1990.
42
[11] Yoshiki Sugimoto, Masatoshi Shioya, Katsuhiro Yamamoto, Shinichi Sakurai “Relationship between axial compression strength and longitudinal microvoid size for PAN-based carbon fibers”, Japan, 2012.
[12] Naoyuki Oya, David J. Johnson, “Longitudinal compressive behaviour and microstructure of PAN-based carbon fibers”, Textile Physics Laboratory, School of Textile Industries, University of Leeds, Leeds, West Yorkshire LS2 9JT, UK, 30 May 2000.
[13] M. Nakatani, M. Shioya, J. Yamashita, “Axial compressive fracture of carbon fibers”, Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1 O-okayama,, Meguro-Ku, Tokyo 152, Japan, August 1998.
[14] Next Day Automation Interface, “ULC-0.5N Ultra Load Cell Capacity Interface: 0.5N”, URL:https://www.ebay.com/itm/Interface-ULC-0-5N-Ultra-Low-Capacity-Load-Cell-Capacity-0-5N-0-112lbs-/331950923716?_ul=BR, data accessed Nov 2017.
[15] J.P. Attwood et al., “The compressive response of ultra-high molecular weight polyethylene fibers and composites”, VA USA, 2015.
[16] Naoyuki Oya, David J. Johnson “Direct measurement of longitudinal compressive strength in carbon fibers” in “Carbon”, Vol 37, pp. 1539-1544, Issue 10, 1999.
[17] A. Andres Leal, Joseph M. Deitzel, Steven H. McKnight, John W. Gillespie, Jr., “Effect of hydrogen bonding and moisture cycling on the compressive performance of poly-pyridobisimidazole (M5) fiber” USA, 2009.
[18] Tao Zhang, Junhong Jin, Shenglin Yang, Guang Li, Jianming Jiang, “A rigid rod dihydroxy poly (p-phenylene benzobisoxazole) fiber with improved compressive strength” State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, College of Material Science and Engineering, Donghua University, Shanghai 2009, China.
[19] M. Shioya, M. Nakatani, “Compressive strengths of single carbon fibers and composite strands”, Department of Organic and Polymeric Materials, Tokyo Institute of Technology, Meguro-Ku, Tokyo, Japan, August 1999.
[20] Masatoshi Furuyama, Masakazu Higuchi, Kenji Kubomura, Hirofumi Sunago, hao jiang, S. Kumar, “Compressive properties of single-filament carbon fibers” R and D Laboratories-l, Kawasaki Japan, GA USA, 1993.
43
[21] S. R. Allen, “Tensile recoil measurement of compressive strength for polymeric high performance fibers”, Pioneering Research Laboratory, Textile Fibers Department, Wilmington, Delaware, USA, 1987.
[22] Prasanna Kumar Ilankeeran et al, “Axial tensile testing of single fibers” Modern Mechanical Engineering, 2, 151-156, Kanpur, India, July 2012.
[23] Michael R., Vijay Kumar et. al, “Handbook of composites from renewable materials”, volume-2, Scrivener Publishing, 2017
[24] Teijin, “What is Carbon Fiber?” URL: https://www.tohotenax.com/products/what- is- carbon-fiber/, data accessed Oct 2017.
[25] Issac M. Daniel, Ori Ishai, in “Engineering Mechanics of Composite materials”, 2nd Edition, Oxford University Press, 2005.
[26] TEIJIN, Toho Tenax, “Suter-kunststoffe”, URL: https://www.swisscomposite.ch/pdf/t-Tenax-Datenblatt.pdf, Dec 2010, data accessed July 2017.
[27] Deborah D.L. Chung, “Properties of Carbon Fibers” in Carbon Fiber composites, Butterworth-Heinemann, 1st Edition, pp. 65-78, Oct 1994.
[28] Pulwell Composites Co. Ltd., Basalt Fiber Rebars, ”Pulwell Basalt fiber rebar, Basalt Composite rebar”, URL:http://www.pulwellfrp.com/en/Products.aspx?id=275, data accessed Nov 2017.
[29] ZEISS, “Axio Imager Pol”, URL:https://www.zeiss.com/microscopy/us/products/light-microscopes/axio-imager- for-polarized- light.html, data accessed Nov 2017.
44
APPENDIXES
45
APPENDIX-A
The following figures shows calibration of fiber diameter, measured by optical microscope.
46
47
APPENDIX-B
The following figures shows the stress-strain graph obtained from tensile testing using different
gage lengths.
Stress – strain curves for 0.5 in. gage length
Stress – strain curves for 1 in. gage length
0
500
1000
1500
2000
2500
3000
0 0.005 0.01 0.015 0.02
STR
ESS
(MP
a)
STRAIN
Average E= 181.68 GPaStandard Deviation = 28.15 GPa
0
500
1000
1500
2000
2500
3000
3500
0 0.005 0.01 0.015 0.02
STR
ESS
(MP
a)
STRAIN
Avaerage E= 170.78 GPaStandard Deviation = 32.45 GPa
48
Stress – strain curves for 1.5 in. gage length
Stress – strain curves for 2 in. gage length
0
500
1000
1500
2000
2500
3000
3500
0 0.005 0.01 0.015 0.02 0.025
STR
ESS
(MP
a)
STRAIN
Average E= 205.40 GPaStandard Deviation = 49.83 GPa
0
500
1000
1500
2000
2500
3000
3500
0 0.005 0.01 0.015 0.02 0.025
STR
ESS
(MP
a)
STRAIN
Average E= 190.48 GPaStandard Deviation = 27.31 GPa
49
Stress – strain curves for 3 in. gage length
0
500
1000
1500
2000
2500
3000
3500
0 0.005 0.01 0.015 0.02 0.025 0.03
STR
ESS
(MP
a)
STRAIN
Average E = 210.42 GPaStandard Deviation = 30.78 GPa
50
APPENDIX-C
The following figures shows the L/D Vs Length(mm) graph obtained from compression testing.
The graphs shows sudden increments in values after the L/D reaches value of 1.34 (critical
Point).
1.338
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
L/D
Length (mm)
1.34
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
L/D
Length (mm)
51
1.34
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
L/D
Length (mm)
1.344
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 0.3 0.4 0.5 0.6 0.7 0.8
L/D
Length (mm)
1.34
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 0.4 0.6 0.8 1
L/D
Length (mm)
52
1.34
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
L/D
Length (mm)
1.34
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
L/D
Length (mm)
1.349
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.5 0.6 0.7 0.8 0.9 1
L/D
Length (mm)
