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Fatigue and fracture of pultruded composite rods developed for overhead conductor cables

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Fatigue and fracture of pultruded composite rods developed for overhead conductor cables

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Content ii

FATIGUE AND FRACTURE OF PULTRUDED COMPOSITE RODS DEVELOPED
FOR OVERHEAD CONDUCTOR CABLES

by

Nikhil Kumar Kar

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)

August 2012

Copyright 2012 Nikhil Kumar Kar

iii
DEDICATION

This manuscript is dedicated to my family, who continue to provide unconditional love
and support in all aspects of my life.

ii
iv
ACKNOWLEDGEMENTS

I would like to thank Professor Steven R. Nutt for giving me a chance to prove
myself as a good scientist and engineer; worthy of the doctoral degree. Without his
support and patience, I would not have been able to get through graduate school, which
was at first, very difficult and arduous. His ability as an advisor goes beyond basic
scientific issues; rather he has a keen sense and deep understanding of how key problems
in civil and aerospace industries are the true motivation for the research we conduct.
With his guidance I learned how to become an independent researcher and I have learned
that we are the architects of our own success.
I would also like to thank Byungmin Ahn, Shad Thomas and Ehsan Barjasteh who
also provided support as the senior graduate students, whose suggestions and advice were
invaluable.
I would not have been able to complete this work without the scientific
discussions and collaborations with my cohorts Lessa Grunenfelder, Yinghui Hu,
Yuzheng Zhang, and Rohan Panikar.
The undergraduate students who I worked with Mike Asfaw, Will Price, Ryan
Van Schilfgaarde, and Chris Fisher made me a better teacher and forced me to think
outside the box. They also made me realize that there are strengths and weaknesses in all
intellectuals; all of whom are unique.
Finally, I would like to thank my high school sweetheart and fiancée, Susana.
You make me a better person, and your devotion to teaching is an example of why the
juice is always worth the squeeze.

iii
v
TABLE OF CONTENTS

Dedication ii

Acknowledgements iii

List of Tables vi

List of Figures vii

Abstract x

Chapter 1. Introduction 1
1.1 Overhead Conductors 1
1.2 Acoustic Emission Technique 5
1.3 Digital Image Correlation 10
1.4 Finite Element Method 13
Chapter 1 References 21

Chapter 2. Bending fatigue of hybrid composite rods 23
2.1 Abstract 23
2.2 Introduction 23
2.3 Experiments 25
2.3.1 Materials 25
2.3.2 Mechanical and Fatigue Tests 26
2.3.3 Finite Element Analysis 27
2.4 Monitoring Damage Development 27
2.4.1 Definition of Damage and Fatigue Failure 27
2.4.2 Acoustic Emission Technique 30
2.5 Results and Discussion 31
2.5.1 Bending Fatigue Response 31
2.5.2 Fatigue Life 34
2.5.3 Failure Mechanisms 40
2.5.4 Stress Distribution along the CF/GF Interface 44
2.5.5 Retained Mechanical Properties 47
2.6 Conclusion 49
Chapter 2 References 51

Chapter 3. Tension-tension fatigue of hybrid composite rods 54
3.1 Abstract 54
3.2 Introduction 55
3.3 Experiments 58
3.3.1 Materials 58
3.3.2 Stress State and Fatigue Tests 58
3.3.3 Finite Element Analysis 60
3.4 Monitoring Stiffness and Acoustic Emission 61
iv
vi
3.4.1 Definition of Secant Modulus 61
3.4.2 Acoustic Emission 61
3.5 Results and Discussion 62
3.5.1 Effect of R-ratio on Stiffness and S-N Diagram 62
3.5.2 Acoustic Emission Output 66
3.5.3 Failure Mechanisms 72
3.5.4 Effect of Failure Mechanisms on Crack initiation 73
3.5.5 Interface Separation 76
3.5.6 Design Considerations 78
3.6 Conclusion 79
Chapter 3 References 82

Chapter 4. Diametral compression of pultruded composite rods 85
4.1 Abstract 85
4.2 Introduction 85
4.3 Experimental Procedure 87
4.3.1 Materials 87
4.3.2 Diametral compression and Digital Image Correlation 88
4.3.3 Finite Element Analysis 90
4.3.4 Determination of transverse modulus 90
4.4 Experimental Results 91
4.4.1 Transverse Behavior 91
4.5 Analytical and Computational Results 96
4.5.1 Localized strain development 96
4.6 Discussion 101
4.7 Conclusion 104
Chapter 4 References 107

Chapter 5. Non-uniform radial deformation of hybrid composite rods 110
5.1 Abstract 110
5.2 Introduction 110
5.3 Experimental Procedure 112
5.3.1 Materials 112
5.3.2 Non uniform compression and Digital Image correlation 113
5.3.3 Finite Element Analysis 114
5.3.4 Elastic solution to uniform radial boundary condition 116
5.4 Results and Discussion 117
5.4.1 In plane deformation 117
5.4.2 Observation of failure and microcracking 121
5.4.3 Uniform radial displacement 124
5.5 Conclusions 127
Chapter 5 References 129

Chapter 6. Conclusions and Future Work 131

Comprehensive References (Alphabetical) 137
v
vii
LIST OF TABLES

Table 1.1. Comparison of properties between Al wire and Steel Core 2

Table 1.2. Comparison of ACCC and ACSR at same amperage 4

Table 2.1. Hybrid Composite Properties 26

Table 2.2. Retained Stress and Static Damage Accumulation 29

Table 2.3. Average Cycles to failure and Standard Deviation 35

Table 2.4. Weibull Parameters at Various Stress Levels 37

Table 2.5. Goodness of Fit Parameters 39

Table 2.6. Stress within the Matrix 46

Table 3.1. Radial Displacements as a Function of UTS 60

Table 3.2. Material Properties in Longitudinal and Transverse Directions 60

Table 3.3. Average Cycles and Standard Deviation 64

Table 3.4. Strain Amplitude at 3 R-ratios 66

vi
viii
LIST OF FIGURES

Figure 1.1. Comparison of traditional ACSR and ACCC conductor 3

Figure 1.2. Typical AE signal from an event source 7

Figure 1.3. Failure mode and AE frequency correlation for polymer composites 8

Figure 1.4. Schematic showing rectangular search structure for DIC 10

Figure 1.5. Displacement of two points and measured locations 12

Figure 1.6. Tracking of subset using speckle pattern 13

Figure 1.7. A triangular finite element with nodal displacements 15

Figure 1.8. Typical elements used in Abaqus Standard 18

Figure 2.1. Damage growth during Stage II bending fatigue at increasing
stress levels. 32

Figure 2.2. Damage rate versus number of cycles at increasing stress levels. 33

Figure 2.3. S-N Curve for bending fatigue behavior of hybrid composite. 34

Figure 2.4. S-N Curve utilizing failure probabilities. 38

Figure 2.5. AE events and damage versus fatigue life for a maximum stress level
of 68% FS. 39

Figure 2.6. (a) Damage initiates as transverse matrix cracks in the GF shell,
(b) brush-like feature formation at top surface of shell 40

Figure 2.7. AE Amplitude distribution as a function of position and life. 42

Figure 2.8. Damage saturation at end of fatigue life. 43

Figure 2.9. FEA showing stress concentration along GF/CF interface. 45

Figure 2.10. Retained mechanical properties after bending fatigue 47

Figure 3.1. CRC mechanical grip design 57

Figure 3.2. 2D diagram indicating relationship between longitudinal extension
on radial compression, and a cross sectional view of CF core and GF shell
under mechanical grip. 59
vii
ix

Figure 3.3. SM loss at 3 R-ratios and 4 stress levels 63

Figure 3.4. S-N Curve at 3 R-ratios showing endurance behavior 64

Figure 3.5. AE hits and damage versus fatigue life for a maximum stress level
of 70% UTS at 3 R-ratios 67

Figure 3.6. Damage initiates as cracks in the GF shell near rod/grip zone
along the CF/GF interface 68

Figure 3.7. Complete GF/CF separation termed bird caging 70

Figure 3.8. Catastrophic failure of CFs at end of fatigue life. 71

Figure 3.9. (a) Non uniform radial displacement of grip, (b) stress distribution
in plane with maximum radial displacement (c) stress distribution in plane
with minimum radial displacement 74

Figure 3.10. (a) Axial strain at 50% UTS along gauge length, (b) non-uniform
axial strain at interface 77

Figure 3.11. Tensile stress distribution with and without sleeve 78

Figure 4.1. Pultruded carbon fiber and glass fiber rods with common matrix 88

Figure 4.2. (a) Keyence microscope and Instron used for DIC, (b) cross section of
composite rod showing black and white random speckle pattern
(c) displacement of GF rod at 33 kN 89

Figure 4.3. (a) Typical load vs. crosshead displacement curves for the CF (left)
and GF rods and (b) Typical peak frequency 91

Figure 4.4. (a) Load vs. true displacement curve for CF rod, (b) Load vs. true
displacement curve for GF rod (c) Variation of apparent transverse modulus
as a function of true displacement 93

Figure 4.5. (a) Compressive and shear strain contours of CF rod from DIC (left)
and FEA analysis (right) under 17kN (b) Compressive strain distribution
along diameter line of CF rod at 17kN 97

Figure 4.6. Transverse tensile strain contours from DIC for GF rod at 23 kN, (b)
transverse tensile strain distribution along diameter line for GF rod 99

viii
x
Figure 4.7. Transverse tensile strain evolution in CF rod from DIC, formation of
microscopic crack perpendicular to tensile strain direction in the strain
concentration region 100

Figure 4.8(a) Diametral crack in GF and CF rod at failure with angled fracture
near loading edges (b) Fracture morphology showing bare CF fibers and
residual glass fiber/matrix adhesion. 102

Figure 5.1. (a) Hybrid composite rod after non-uniform radial compression
showing “V” cracks” near anvil gap, (b) Keyence microscope and Instron
used for DIC, (c) cross section of composite rod showing black
and white random speckle pattern 113

Figure 5.2. (a) Non uniform radial displacement boundary condition on GF shell
(b) uniform radial displacement boundary condition on GF shell 115

Figure 5.3. Typical load vs. crosshead displacement curve for the hybrid
composite rod with AE hits overlaid 117

Figure 5.4. (a) Vertical displacement contour of composite rod under ~7 kN, (b)
Horizontal displacement contour of composite rod at ~7 kN 118

Figure 5.5. Strain contours from DIC (top) and FEA analysis (bottom) under
~7kN 119

Figure 5.6. Stress contours from FE showing concentrations near anvil edges 120

Figure 5.7. Deformation, shear crack initiation and strain localization as near
as a function of applied load (GIF animation) 121

Figure 5.8. Shear crack propagation to GF/CF interface 122

Figure 5.9. (a) Longitudinal surface crack formation from inside the mechanical
anchors, (b) similar surface crack formation from non-uniform radial
compression anvils 123

Figure 5.10. (a) Radial and circumferential stress distribution under uniform
compression with associated strain distribution, (b) in plane stress distribution
after coordinate transformation 125

Figure 5.11. (a) Plastic strain (damage) accumulation under non-uniform radial
compression (b) no damage accumulation under uniform radial compression 126

ix
xi
ABSTRACT

Polymer matrix composites (PMCs) have been used extensively in the aerospace
industry for the past five decades. There has been an upsurge in the use of PMCs in other
industrials sectors such as civil infrastructure, automotive, marine and sporting
applications. The primary advantage of using PMCs over conventional metals and alloys
are the increase in weight savings, increased stiffness and strength properties. A new
application of PMCs has been developed and applied as the load bearing member for
overhead conductor cables. Traditional overhead conductor cables are comprised of an
aluminum cable with a steel reinforcement (ACSR). The new overhead conductor
replaces the steel core of the conductor with a single continuous hybrid composite
cylinder. The composite core is comprised of glass fibers and carbon fibers in a common
matrix, and the primary advantage of these composite reinforced conductors is the
reduction in sag and increase in ampacity over conventional ACSR conductors.
One of the major concerns of the hybrid composite core is long term durability
under various combined environments and loading conditions. Overhead conductor
cables are exposed to moisture, extreme ice and wind conditions, cyclic temperatures and
fatigue loads. The mechanical and physical properties of polymer composites can
degrade under such conditions, and the ability to understand degradation mechanisms is
important to create predictive models for long term durability. More specifically, the
basic mechanical properties, fatigue response of the composite rods, and the deformation
behavior under transverse loads is unknown, and the work here investigates such
behavior to shed light on design factors that can contribute to degradation in mechanical
properties while in service.
x
1

CHAPTER 1. INTRODUCTION
1.1 Overhead Conductors
The North American Electric Reliability Corporation stated in 2007 that by 2017
there will be a 17% increase in electrical energy demand with only a 5% increase in
electrical grid capacity [1, 2]. This alarming increase in power demand needs a
satisfactory solution that can be easily deployed. One solution is to increase the area of
the power grid infrastructure; however this is difficult because of resistance from the
public based on unsightly power stations in neighborhoods and natural environments.
Another problem with this solution is the necessary capital, man power, and land needed
to develop a sustainable infrastructure for many decades.
An alternative to power grid growth is to reconductor the electrical infrastructure
(densification) with more efficient overhead conductor cables that can meet peak
electricity demands. One such type of a high voltage (~100 kV) overhead conductor
cable uses helically wound round 1350-19 high purity Al (high conductivity 61.2%) as
the current carrying wires, with steel reinforced round wire core (ACSR). Overhead
conductors are designed to serve predefined mechanical and electrical loads, and they
vary in size and stranding ratios-which have similar electrical characteristics [3]. The
steel core wires are high strength (0.5 to 0.88% carbon) and low conductivity, and they
provide less sag then all aluminum overhead conductor cables [3], and their strength
allows them to be used to extreme environments of wind or ice loading, the properties of
which are shown in Table 1.1.

2
Table 1.1. Comparison of properties between Al wire and Steel Core
1350 Al wire Steel Core
Conductivity 61.20% 8%
CTE (x10
-6
/ºC) 23 11.5
E (GPa) 69 200
UTS (GPa) 1.65 1.376

The main drawback of this cable is the limit in operating temperature to 100 ºC
(Drake size) due to a high coefficient of thermal expansion (CTE). When there is an
increase in electricity demand, the conductors are forced to draw higher currents. These
higher currents lead to higher operating temperatures, which contribute to overall sag of
the conductor. The operating temperature limit is based on sag specifications that are
necessary to prevent unsafe clearances from occurring, which can lead to black outs,
short circuiting and catastrophic events. Increasing the thermal rating of a conductor (and
hence, current carrying capability (ampacity)) can satisfy electricity demands, but it also
causes higher operating temperatures which induce sag and heat loss in overhead lines.
The CTE of the steel reinforcement is 11.5x 10
-6
/ºC, so during high electricity demands,
the cable will expand, causing an increase in overall line length, inducing sag and greater
heat losses because of the increased resistivity of the line. Sag (D) is driven by operating
temperature, the weight of the conductor the length of the line as shown in equation 1.1
2
8
WS
D
H
= (1.1)

Where W= conductor weight per unit length, S= Span length, and H= horizontal load.
While the steel in the ACSR provides structural support, it also accounts for 11-40% of
the overall weight of the conductor (depending on conductor size) [3]. To meet or exceed
current energy demands, a new type of overhead conductor cable was developed by
3
Composite Technology Corporation and the primary design objectives were to increase
the overall strength of the conductor, rated ampacity, and improve sag at higher
temperatures when compared to the ACSR cable.
This new conductor replaces the steel core with a hybrid composite rod that
utilizes unidirectional glass and carbon fibers in a common epoxy matrix. The ECR
(electrical application, corrosion resistant) glass fibers resist stress corrosion cracking and
are boron free. The carbon fibers utilized are PAN based Toray T700s fibers. The
conductor is termed ACCC/TW- Aluminum conductor composite core/trapezoidal wire
as shown in Figure 1.1.

Figure 1.1. Comparison of traditional ACSR and ACCC conductor

The glass shell is used to prevent galvanic coupling between the aluminum and
the carbon and increases overall flexibility of the core. Recent studies showed that
aluminum in contact with carbon fibers in the presence of salt water causes galvanic
4
corrosion, by preventing the protective oxide layer to form on the aluminum (causing
corrosion of the aluminum). Instead, the reduction of oxygen occurs at carbon fiber ends
producing an electrical current [4]. The solid cylinder allows trapezoidal aluminum wires
to be used instead of round wires, and the interstices caused by the limited packing
efficiency of round wires are filled with more aluminum (achieving greater compactness),
increasing the overall area of aluminum by 28% (for a given overall diameter) allowing it
to carry twice the current as a conventional conductor. The ACCC/TW also utilizes
higher purity fully annealed aluminum wires (O-1350) which reduces resistivity
(increasing conductivity). While an increase in the amount of aluminum will increase the
weight of the conductor, the hybrid composite core is 60% lighter then the steel core.
The CTE of the hybrid composite core is 2.77 x 10
-6
/ºC, nearly ¼ that of the steel core
in the ACSR conductor. Sag and strength performance metrics were performed to
compare the ability of both conductors [5], as shown in Table 1.2.
Table 1.2. Comparison of ACCC and ACSR at same amperage
ACCC/TW ACSR
RTS(kN) 176.5 140
Span(m) 68.6 68.6
Current(Amps) 1500 1500
Operating Temp C 180 240
Initial Sag (mm) 220 260
Sag at Operating Temp (m) 0.34 1.9

Overall, the ACCC/TW showed a 25% higher rated tensile strength, which meant
that it could be tensioned to a higher horizontal load (minimizing sag). As shown in
Table 1.2, the ACCC/TW operated 60 ºC cooler than the ACSR for the same current
output and had nearly 1/6 the sag of the ACSR. Thus, the ACCC/TW can operate at
higher temperatures (satisfying peak electricity demands) with lower sag and greater
5
overall energy efficiency; but is 2.5 x the cost of the ACSR. These attributes would
result in an increase in overall transmission efficiency of the power grid system.
However, conductor cables are designed to provide service for multiple decades
with little to no maintenance. The long term durability of the hybrid composite core is
unknown, and the effect of combined environments such as cyclic temperature, oxidation,
moisture, and different loading modes are not well understood. Recent efforts have been
put forth to understand and characterize these environments separately, and have
provided insight on long term strength and durability of the composite core [6-8]. The
composite core must be able to sustain its functionality in harsh and extreme
environments, and this requires the study of the composite core under extreme loading
conditions, to understand weaknesses in the design and provide recommendations to
extend service life.
1.2 Acoustic Emission Technique
Acoustic emission occurs when a transient elastic wave is detected in a material,
generated by some abrupt and permanent change induced by a perturbation in the stress
field. AE sources release energy in the form of stress waves which propagate to the
material surface and are recorded by piezoelectric transducers. The transducers convert
mechanical energy into a voltage signal using a thin disk made up of small crystals of
zirconates. The acoustic emission technique has a range of industrial applications, but it
is primarily used to assess structural integrity, detect flaws and damage mechanisms
under in service or laboratory loading conditions. The detection of signals can be either
continuous or burst-type, which indicate a single discrete deformation event [9].
6
Acoustic emission systems cannot quantify damage; rather they qualitatively gauge how
much damage is in a specimen based on principal detection parameters.
A typical AE signal and its parameters are shown in Figure 1.2. The five
principal parameters used in AE are the following [9]:
• Amplitude: The highest peak voltage attained by an AE waveform is
responsible for determining the detectability of a AE source.
• Counts: The number of threshold crossing pulses is one of the oldest ways
of quantifying the AE signal.
• MARSE: Measured area under rectified signal is being used to replace
Counts as an indication of AE activity because it is a measure of all detected
events (total AE activity).
• Duration: The amount of time elapsed from the first detected threshold
voltage to the last detected voltage.
Rise Time: The time necessary from initial threshold crossing to the peak in the
waveform voltage.
Service environments can cause the formation of noise that is also detected by AE
sensors. As a result, overlap can occur between discrete signals from AE hits taking
place within a material and noise created by external sources. Filtering of noise is a
necessary task to capture data that is only relevant to the deformations taking place within
the material. The signals detected from one or more sensors are amplified and measured
according to the following equation [10]:
max
20log Pr ( )
1
V
dB eAmpGain dB
V μ
 
= −
 
 
(1.2)
7

Figure 1.2. Typical AE signal from a event source [10]
Where the detected amplitude is measured in dB and is based on the amplification
of the signal by the pre amplifier gain value. This method relies on the detection of
movement within the volume of a structure, where each AE source has a pulse like
velocity wave and a step wise displacement. The profiles are pulse like because they
represent distinct burst type events such as crack jumping, and precipitate fracture which
take place in a fraction of a microsecond [10]. The statistical aspects of AE are the most
important aspect for material science researchers because the statistical data gives an
indication of the dominant signals and parameters during a deformation process. This
allows one to detect the onset of various modes of damage, an indication which might not
be visible or detectable in an alternative fashion. Some researchers have isolated
different modes of damage in composite materials and characterized the failure modes
with frequency and amplitude ranges as shown in Figure 1.3 [11].
8

Figure 1.3. Failure mode and AE frequency correlation for polymer composites[11]

Another important aspect of the AE technique is signal attenuation. When a
source emits a transient elastic wave, the detected AE parameters might not be what they
were at the source because of the distance from the source to the AE sensor. The
transient elastic wave will attenuate because of the geometric spreading; or the decay of
the amplitude caused by conservation of energy. The elastic and kinetic energies of the
wave are also absorbed by the material and converted to heat. Discontinuities and
boundaries in the material can also lead to attenuation. Usually, the geometry of the
structure effects how the AE source can travel to the sensor, and many times the highest
detected peak in the wave form is caused by constructive interference of multiple path
9
components [9]. The waveform is a result of the AE wave bouncing around in the test
piece, repeatedly exciting the sensor which produces the waveform type in Figure 1.2.
As a result, it is sometimes difficult to relate only the signal voltage to exactly what is
happening in the structure.
The acoustic emission technique was used as a means to detect damage under
fatigue and cyclic loading conditions in a unidirectional hybrid composite rod, as a
complimentary tool to other damage evaluation techniques. Under bending fatigue
conditions, the onset of damage was detected by an increase in the number of detectable
events, and the distribution of amplitude levels at the source of each event was
determined. The location of each AE event was determined by utilizing two AE sensors
and this allowed an attenuation model to be used to determine the amplitude of the
detected event at a given source. Under tension tension fatigue conditions, a single AE
sensor was used primarily as a means to detect the onset of brittle and explosive cracking
by spikes in AE amplitudes as a function of the test duration. Diametral compression
tests were also performed and correlation between the AE amplitude and peak
frequencies were determined at different loads with the onset of debonding and matrix
cracking in the transverse plane. It should be noted that during fatigue loading,
significant noise from the hydraulic pump was detected, and this was filtered using a
graphical technique. Frictional sources were also detected by AE, and it was difficult to
distinguish separate signals caused only by friction and those damage mechanisms that
produce burst type emission. It was found that significant overlap can occur between
these types of signals [12].

10
1.3 Digital Image Correlation
The digital image correlation technique was developed by researchers at the
University of South Carolina in the early 1980s [13, 14]. The basics of the technique rely
on correlating pixel intensity (the gray scale value) between an undeformed and deformed
image. The gray scale value is tracked in small neighborhoods known as subsets during
the deformation process. Neighboring points in the undeformed image are formed by
creating a random black speckle pattern on a white surface. These neighboring points
remain neighboring after deformation, so the speckles act as digital markers for a
correlation algorithm that is used to find the same gray scale value in the deformed
image. The subset is a rectangular search structure (nxn pixel) window that is predefined
around grid nodes as shown in Figure 1.4 [15].
Figure 1.4. Schematic showing rectangular search structure for DIC [15]

The subset represents a neighborhood of digital pixels surrounding a center point
of interest. The nodes represent the coordinates of the center of the subset. The subset
11
acts as the initial gray scale value in the undeformed state. The correlation algorithm is
used to track and recognize the same gray scale value in the deformed state. The search
window (step size) is defined by a (NxN pixel) window, whereby in the calculation step
the subset is displaced inside the search window in the deformed state to find the best
position that has an equivalent gray scale value-that minimizes the correlation coefficient.
The correlation coefficient acts to compare the gray scale value of the deformed and
undeformed state, and when this value is minimized, it is assumed that the position of the
speckle patterns in the undeformed image have been found in the deformed image. From
this, the displacements and strains can be calculated.
Let f(x,y) and ( , )
d
f x y represent the gray scale value of the undeformed and
deformed image. For the subset S, the correlation coefficient can be defined as [16]:
[ ]
2
1, 1
2
( , ) ( )
( , )
n n d n n
n n
f x y f x y
C
f x y
  −
 
=
∑
∑
(1.3)
Where the summations are taken at all points within the subset S and S1 as shown in
Figure 1.5 [16].
From minimizing the correlation coefficient, the displacement fields u(x,y) and
v(x,y) can be calculated, and subsequently the in plane strains can be calculated from the
following equations:
1
, ,
2
xx yy xy
du dv du dv
dx dy dy dx
ε ε ε
 
= = = +
 
 
(1.4)
In general, the larger the subset size, the increase in accuracy. However, this causes an
averaging effect over the strain field and difficulty in measuring high strain gradients.
The subset size should be large enough to encompass a unique pattern from the area of
12

Figure 1.5. Displacement of two points and measured locations [16]
interest, but also small enough to distinguish strain differences in small regions. The step
size (search window) controls the density of the analyzed data. A smaller step size yields
slower results but denser data. An example of tracking a subset under tension is shown in
Figure 1.6 [17]. These results show that the subset is tracked correctly, and the
deformation of the window (subset) can be used to determine the displacements and
strains. Vic 2D software (Correlated Solutions) was used to determine the in plane
strains and displacements of unidirectional composite rods (under diametral and anvil
compression loads in the transverse plane). The experiments allowed us to develop an
accurate description of the in plane behavior (transverse) of the carbon fiber and glass
fiber composite rods. This technique was also utilized to examine the strain
concentrations under high loading regions in both materials.

13
Figure 1.6. Tracking of subset using speckle pattern [17]
1.4 Finite Element Method
The finite element method (FEM) was formally presented as a numerical
technique by Turner et al [18] and Argyris and Kelsey [19] and in the 1950s and 1960s.
The four most basic steps in any finite element technique are the following [20]:
1. Discretization: The region of interest is represented as a collection of a finite
number of elements. The collection of elements is known as the finite element
mesh.
2. Element equations: Each element has a set of governing equations used to
calculate the required property.
3. Assembly of element equations and solution: The assembly of element equations
is used to solve the problem for the structure.
4. Convergence and error estimate: The approximate solution is compared and the
error in the approximation is evaluated.
14
The basic equation that is utilized in the FEM is generalized Hooke’s Law:
[ ]{ } { } K D R = (1.5)

where [K] represents the global stiffness matrix, [D] is the nodal displacement, and {R} is
the force vector for the nodes. The global stiffness matrix is formed from the
combination of all the elements that make up the structure being analyzed. The
generalized Hooke’s Law equation is solved based on a system of equations to determine
nodal displacements of each finite element. From displacement values the strain can be
calculated, from which the stress can be determined. Load and boundary conditions are
utilized to assign known values to [D] and {R}.
While there is always a governing differential equation that describes a physical
behavior of a material, many times it cannot be solved for exactly, if the boundary
conditions or input data are complex. The weak form of the governing differential
equation can be found, and it is equivalent to the minimization of the total potential
energy of the problem [20]. The finite element method applies a variational technique
(such as the Rayleigh-Ritz) to each element. For example, the potential energy of an
elastic body is governed by internal strain energy (from stresses and strains) and external
loads and tractions. If we simply look at a bar under an axial load distributed as a
function of x (q=cx), the governing differential equation (strong form) is found in the
equation for potential energy (weak form) and both describe the same problem [21].
Differential equation:
2
2
0
d u
AE cx
dx
− − = (1.6)
Potential Energy equation:
2
2
1
2
p
d u
E Adx ucxdx
dx
∏ = −
∫ ∫
(1.7)

15
Setting d
p
∏ =0 with regards to the degrees of freedom will yield the differential
equation. The potential energy equation is known as a functional, and while there is
always a differential equation associated with a functional, there is not always a
functional associated with a differential equation. From the functional equation (
p
∏ ) a
Rayleigh-Ritz solution to the generalized Hooke’s Law is available.
For structural mechanics, the generalized functional for an assembly of N
elements of a structure with no initial strains or stresses is as follows [21]:
{ } [ ]{ } { } { } { } { } { } { }
1 1 1
1
2
N N N
T T T T
p
i i i
E dV u F dV u dS D P ε ε
= = =
 
∏ = − − Φ −
 
 
∑ ∑ ∑
∫ ∫ ∫
(1.8)

Where the integrations are done over each element, and then added for all elements, N.
{F} represents the body forces per unit volume in element i, and {P} are prescribed
boundary forces or surface tractions{ } Φ on element i. [E] are the isotropic or anisotropic
material properties of the element. Let { }
i
d represent the nodal displacements for each
element i. For example, a triangular finite element has the following nodal
displacements: { } d = { }
1 1 2 2 3 3
u v u v u v as shown in Figure 1.7 [21].
Figure 1.7. A triangular finite element with nodal displacements [21]

16
The variation of displacements within the element is important, and knowledge of this is
based on interpolation of displacements at the nodes. The derivation of interpolation
functions is only dependent on the type of element (geometry, number of nodes, and
unknowns per node). These interpolation functions have been determined for different
elements, and are available from a library of these functions. The displacements { } u
within element i are interpolated from:
{ } [ ]{ }
i
u N d = (1.9)

Where matrix [N] is a function of position within the element, and is known as the shape
function matrix. For the triangular element shown in Figure 1.7, the strain is found using
the following technique:
{ } [ ]{ } { } [ ]{ } [ ] [ ][ ] , , u B d B N ε ε = ∂ = = ∂ (1.10)

Where[ ] ∂ is of the form
0
0
x
y
y x
 
∂
 
∂
 
  ∂
 
∂
 
  ∂ ∂
 
∂ ∂
 
in 2 dimensions, [B] is known as the strain-
displacement matrix and is a derivative of the shape function matrix, [N]. For
completeness, the expanded form of the constant strain triangle is shown
below{ } [ ]{ } B d ε = :

17
1
1
2 2
2
3 2 3
2 2 3 2 3 3
3 3 2 3
2 3 2 2 3 2 3 3
1 1
0 0 0 0
1
0 0 0
1 1 1
0
x
y
xy
u
v
x x
u
x x x
v x y x y y
u x x x
x y x x y x y v
ε
ε
γ
    −
   
   
 
   
− −  
=
     
     
 
   
− − −
   
 
  
(1.11)

Substitution of this equation into equation (1.8) leads to the forms of the stiffness matrix
[k]
i
and load vector [r
e
] equations for an element, i:

[ ] [ ] [ ][ ]
T
i
k B E B dV =
∫
(1.12)
{ } [ ] { } [ ] { }
T T
e
i
r N F dV N ds = + Φ
∫ ∫
(1.13)

These element equations lead to the equations of equilibrium for nodal forces for the
entire structure, as shown in equation 1.5. Equation (1.5) is derived when setting
0
p
d
dD
∏
= where D is the global degrees of freedom, in the global coordinate system.
Thus, knowledge of the functional which describes the potential energy of the physical
problem, and the nodal interpolation for a specific element can allow us to find element
stiffness matrices. Generating the global stiffness matrix and global nodal force matrix
can allow us to solve for the nodal displacements from equation (1.5). From the nodal
displacements, strains can be calculated, and then subsequent stresses.
Abaqus Standard V. 6.10 is a common finite element tool used for research and
development in the materials science and mechanical engineering community. Abaqus
utilizes the theory of the finite element method to determine stresses, strains, flow
behavior and heat transfer characteristics of various materials. The basis of stress
analysis relies on knowledge of the displacements of the nodes, and are the fundamental
variables that need to be determined. The geometry of the structure is discretized into
18
finite elements, which share nodes; all of which make up the mesh of the structure. The
basic scheme for analysis is as follows [22]:
• Describe physical model by a 2D or 3D drawing
• Discretize the geometry and select an appropriate element type
• Input material properties, load and boundary conditions
The elements are characterized by the Family, Degrees of Freedom, Number of nodes,
Formulation and Integration. The most commonly used element families are shown in
Figure 1.8 below [22]:

Figure 1.8. Typical elements used in Abaqus Standard [22]

During the analysis of the simulation, the most important variables calculated are
based on the degrees of freedom of each node. For the case of stress analysis, there exists
6 possible degrees of freedom, translation in the x,y,z directions (1,2,3) and rotation the
x,y,z directions (4,5, 6). Beam elements with open sections can also have a warping type
of degree of freedom.
The displacements and rotations are determined at the nodes within the element,
and interelement displacements are based on interpolation functions as discussed
previously. Elements with nodes at the corners of the geometry utilize linear
interpolation, such as the C3D8R element shown in Figure 1.8. This is known as a first
order (linear interpolation), 3 dimensional, 8 node brick element with reduced integration.
19
Elements that have nodes at the midside utilize quadratic interpolation, and are second
order quadratic elements.
Formulation refers to the mathematical theory used to describe the elements
behavior [22]. The integration characterizes the way quantities are evaluated over an
element. Some choices of integration are full or reduced integration, using Gaussian
quadrature. The four element families are described as follows:
• Solid Elements: Used to model a wide variety of components. The element is
like a brick, or small block of a material making up the entire component. They
can model any shape and any loading. 3 dimensional continuum elements have 3
degrees of freedom ( translation in 3 directions) and 2 dimensional continuum
elements have 2 degrees of freedom ( translation in 2 directions). Whenever
possible, hexahedral (brick) elements should be utilized.
• Shell elements are used to model structures that are very thin, where the thickness
is much smaller than the other directions and stresses in the thickness direction
are small. A washer or Frisbee are examples of such structures.
• Beam elements are used to model structures where the length is much greater than
the width or thickness of the structure. The stress in the axial direction is only
significant, and they can undergo bending, tension and compression.
• Truss elements are used to model rods that only carry tensile or compressive
loads. They are useful when modeling pin jointed frames.
Computationally, Abaqus performs the following procedure to determine strains and
stresses in a structural member:
• Create element matrices that describe material behavior
20
• Combine element matrices to form the global structure (stiffness) matrix
• Assign specific nodes with loads, and other nodes with boundary conditions
• Solve set of algebraic equations to determine displacements at each node
• Compute gradients to determine strains and stresses within the structure
The finite element method was used in this thesis to model unidirectional
composite rods with two different fiber types. The composite rod was modeled to be
transversely isotropic, where the fiber and matrix were modeled as a continuum with very
high longitudinal properties. The models were used to determine the various stress and
strain states within the composite rod under 3 different loading conditions. Specifically,
the stress state along the glass fiber and carbon fiber interface were determined under 3
point bending. The effect of transverse compressive loads on longitudinal stress and
strains were also determined from a mechanical grip interaction used to maintain
longitudinal loads. In plane deformation and properties were simulated and confirmed
experimentally for glass fiber/epoxy and carbon fiber/epoxy rods respectively. In most
cases the C3D8R hexahedral(brick) elements were utilized.

21
Chapter 1 References
[1] North American Energy Reliability Corporation (NERC). 2008-2017
Regional and national peak demands and energy forecasts bandwidths.
Princeton, NJ; August 2008.

[2] Statement of David N. Cook general counsel north American electric
reliability counsel, National energy policy with respect to federal, State and
local impediments to the sitting of energy infrastructure, Senate committee on
energy and natural resources, Washington, D.C. (2001)

[3] Alawar A. Mechanical Behavior of a Composite Reinforced Conductor. PhD
Thesis, University of Southern California, August 2005.

[4] Boyd J, Speak S, Sheahen P. Galvanic corrosion effects on carbon fiber
composites. Results from accelerated tests. 37th International SAMPE
Symposium and Exhibition, March 9, 1992 - March 12, 1992; 1992;
Anaheim, CA, USA: Publ by SAMPE; 1992. p. 1184-98.

[5] Alawar A, Bosze EJ, Nutt SR. A composite core conductor for low sag at
high temperatures. IEEE Transactions on Power Delivery.
2005;20(3):2193-9.

[6] Bosze EJ, Alawar A, Bertschger O, Tsai Y-I, Nutt SR. High-temperature
strength and storage modulus in unidirectional hybrid composites.
Composites Science and Technology. 2006;66(Compendex):1963-9.

[7] Tsai YI, Bosze EJ, Barjasteh E, Nutt SR. Influence of hygrothermal
environment on thermal and mechanical properties of carbon
fiber/fiberglass hybrid composites. Composites Science and Technology.
2009;69(Copyright 2009, The Institution of Engineering and
Technology):432-7.

[8] Barjasteh E, Bosze EJ, Nutt SR. Thermal aging of fiberglass/carbon-fiber
hybrid composites. Comp A 2009; 40(12): 2038-2045

[9] Pollock AA. Acoustic Emission Inspection. Physical Acoustics
Corporation (PAC), Technical Report TR-103-96-12/89 (Copyright 2003,
Mistras Holding Group).

[10] Unpublished data from PCI-2 Based AE System User’s manual. Mistras
Group (Copyright 2003, Mistras Holding Group).

[11] De Groot, Peter J., Wijnen Peter A., and Roger Janssen. Real-Time
Frequency Determination of Acoustic Emission for Different Fracture
Mechanisms in Carbon/Epoxy Composites. Composite Science and
Technology, 55 1995 40
22

[12] Dzenis YA. Cycle based analysis of damage and failure in advanced
composites under fatigue 1. Experimental observation of damage
development within loading cycles. Int J Fatigue 2003;25:499–510

[13] Peters WH, Ranson WF. Digital Imaging Techniques in Experimental
Stress Analysis. Optical Engineering 1982; 21(3): 427-431.

[14] Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR.
Determination of displacements using an Improved Digital Image
Correlation Method. Image Vision Computing 1983; 1(3): 133-139.

[15] Dost M, Kieselstein E, Erb R. Displacement analysis by Means of Gray
Scale Correlation at Digitized Images and Image sequence Evaluation For
Micro-and Nanoscale Applications. Micromaterials and Nanomaterials
2002; 1(1):30-35.

[16] Huang YH, Quan C, Tay CJ, Chen LJ. Shape measurement by the use of
digital image correlation. Optical Engineering 2005; 44(8)

[17] CSI Application Note AN-525- Speckle Pattern Fundamentals. Correlated
Solutions, Inc., Columbia, SC, http://www.correlatedsolutions.com.

[18] Turner M, Clough R, Martin H, Topp L. Stiffness and Deflection
Analysis of Complex Structures. Journal of Aerospace Science 1956:
23:805-823

[19] Argyris JH, and Kelsey S. Energy theorems and Structural Analysis.
Butterworth Scientific Publications, London 1960.

[20] Reddy JN. An Introduction to the Finite Element Method. McGraw-Hill
Copyright 1984.

[21] Cook RD, Malkus DS, Plesha ME, Witt RJ. Concepts and Applications of
Finite Element Analysis. John Wiley and Sons Fourth Edition 2002. pg.
92,152-154

[22] Abaqus/Standard Version 6.10 Reference User Manual. Simulia 2010.

23
CHAPTER 2. BENDING FATIGUE OF HYBRID COMPOSITE RODS
2.1 Abstract

The bending fatigue behavior of hybrid composite rods comprised of
unidirectional carbon and glass fibers was investigated. Damage was evaluated by
monitoring stiffness loss as a function of cycle number, and bending fatigue failure was
defined in terms of flexural strength retention. The acoustic emission technique and
microscopic examination were used to characterize damage progression and failure
mechanisms. The number of cycles to failure depended on applied stress level, and a two-
parameter Weibull analysis was used to incorporate probability of failure to the S–N
curve. Damage initiated and propagated as a result of matrix cracking and fiber bundle
failures within the GF shell. Fatigue damage only initiated when the hybrid was exposed
to a deflection that produced a stress state in excess of 42% of the rod flexural strength.
Damage reached a saturation point along the GF/CF interface because of the stress
concentration that existed between the two material systems, resulting in asymptotic
behavior of the stiffness loss. Because damage did not extend into the CF core, static
mechanical properties were retained to 85% or more.
2.2 Introduction

Although polymer composites have been widely used in the aerospace industry
for decades, the use of composites in other industries has been limited in part by the
uncertainty in long-term durability [1]. However, this situation is changing, as evidence
of the emergence of non-aerospace applications, such as electrical power transmission
lines. Traditionally, overhead conductors feature conductive Al strands wrapped around a
steel cable (termed ACSR, for aluminum conductor steel reinforced). The next generation
24
of overhead conductors may involve replacement of the steel cable core in ACSR with a
unidirectional hybrid (carbon/glass fiber) composite rod [2]. Composite-supported
conductors (termed ACCC for aluminum conductor/composite core) will enable more
economic and efficient transmission of electrical power [3]. Other advantages of the
ACCC cables include greater strength, lower weight, and less sag at high temperatures
then traditional steel reinforced conductors.
The long-term durability of the ACCC conductor is an important issue because
overhead conductors are expected to operate maintenance free and retain mechanical
properties for decades. The effects of long-term exposure to heat and moisture on such
hybrid composites were reported recently, and showed that the oxidized surface layer
protected the bulk epoxy from further oxidation, and the complex intermingling of
GF/CF interface acted as a temporary moisture barrier [4,5]. In general, the mechanical
and physical properties of polymer composites are adversely affected by such
environmental factors, and the ability to forecast changes in material properties as a
function of environmental exposure is required to design for extended service life [6, 7].
Overhead conductors typically experience crosswinds, which in certain conditions
can result in galloping and Aeolian vibration, inducing dynamic tensile and flexural
stresses [8]. Typically, Aeolian vibrations are high-frequency (>150 Hz) and cause small
deflections. Nevertheless, such vibrations generate dynamic stresses that in some cases
have caused fatigue failures in conventional transmission lines [8, 9]. While composites
are generally resistant to fatigue damage, recent highly publicized failures of carbon–
fiber reinforced plastics (CFRP) have been partly attributed to fatigue [10, 11].
25
An unresolved issue surrounding fatigue of composites is the predominant
mechanism(s) responsible for fatigue failure. Some have concluded that local matrix
failures are the primary mechanism involved, while others have suggested that gradual
deterioration of the load-bearing fibers is primarily responsible [12, 13]. Supporting the
latter point of view, Agarwal et al. concluded that the dominating mechanism involved
fiber failures, and that fatigue resistance was not strongly dependent on interface
behavior [14]. Others have concluded that interfacial debonding is one of the most
important life-limiting parameters in fatigue of composites [15].
In this paper, the bending fatigue behavior and failure mechanisms in
unidirectional hybrid composite rods were investigated. The composite differs from most
conventional composite laminates, and is a solid rod featuring a CF core and a GF shell.
Experimental fatigue tests were performed, and statistical models were employed to
correlate fatigue life with stress level. The effect of bending fatigue on mechanical
property retention was also investigated and analyzed.
2.3 Experiments

2.3.1 Materials

Unidirectional composite rods were produced by pultrusion (Composite
Technology Corporation, Irvine, CA). The rods were comprised of a carbon fiber core
(CF) surrounded by a glass fiber shell (GF), as described in [4, 5]. The core consists of
carbon fiber reinforced epoxy, while the shell is comprised of glass fiber-reinforced
epoxy. Fiber volume fractions and core/shell radii are indicated in Table 2.1. The epoxy
matrix was designed to achieve a high glass transition temperature (T
g
= 205ºC) using a
propriety epoxy formulation and a curing agent.
26
2.3.2 Mechanical and Fatigue Tests
The influence of bending fatigue on mechanical properties was determined from
measurements of post-fatigue flexural strength. Production composite rods 9.5 mm in
Table 2.1. Hybrid Composite Properties

diameter were cut to a length of 305 mm using a diamond saw, and flexural static tests
were conducted on specimens using a three-point bend fixture to determine static flexural
properties according to ASTM D790-02. A span ratio (L/d) of 20 was chosen for static
and flexural fatigue tests to minimize the effect of the shear stress and to maximize the
effect of the flexural stress.
Fixed displacement, sinusoidal, bending fatigue tests were performed at a
frequency of 5 Hz using a load frame (Instron 8501) with a 100 kN load cell following
ISO 13003. The displacement ratio
d
R , which is the ratio of minimum displacement to the
maximum displacement, was zero for all tests. Tests were conducted at 5 cyclic
displacement levels (CDL), which corresponded to initial applied stress levels ranging
from 47% to 68% of the flexural strength (FS). To monitor the degradation in
mechanical properties, the dynamic stiffness was measured continuously as a function of
the number of cycles (along with acoustic emission, described below). Tests were
r
i
(mm) r
o
(mm) % glass
volume
% carbon
volume
% epoxy
volume
% cross
sectional
area
CF-
epoxy
core
0 3.4 0 69 31 51
GF-
epoxy
shell
3.4 4.75 64-69 0 36 49
27
terminated when the cyclic stiffness was reduced by a percentage of the initial cyclic
stiffness measured at each displacement.
Retained flexural strength and flexural modulus were determined after bending
fatigue at each CDL. The effect of flexural fatigue on retained tensile strength (TS) of
the composite core was measured according to ASTM Standard D3916 using a load
frame (Instron 5585). Composite rods were mounted in the load frame using custom-
made fixtures. The load was applied using a crosshead speed of 5mm/min until failure
occurred.
2.3.3 Finite Element Analysis
Finite element Analysis (FEA) was used to determine the stress distribution
between the CF core and the GF shell during flexural loading. The specimen was
modeled to represent the geometrical features of the test setup, using exact dimensions
from the experiment. Load and boundary conditions were simulated with commercially
available FEA software (Abaqus) using 22,494 elements and C3D8R element type. A 3D
model was implemented utilizing constituent properties of the GF shell and CF core
specified by the manufacturer.
2.4 Monitoring Damage Development
2.4.1 Definition of Damage and Fatigue Failure
Global damage caused by bending fatigue in composites can be effectively
monitored by measuring stiffness degradation [16]. A global damage index, D can be
defined as:
( )
1
( )
1
EI
n
D
EI
= −
 
 
 
 
(2.1)
28
where ( )
n
EI is the cyclic stiffness after the n
th
cycle, and
1
( ) EI is the stiffness measured
on the first cycle [17] at the tested CDL. The cyclic stiffness is different from the static
flexural stiffness in that it is measured at the tested CDL, and not at the static failure
displacement. The damage index D, is a measure of the degradation of the stiffness, and
can be determined with techniques developed by previous investigators [17]. All
individual damage mechanisms are assumed to contribute to this global damage
parameter [18]. If a composite sample loses the ability to sustain stress before the point
of separation, the definition of bending fatigue failure by catastrophic separation is of
limited value. Therefore, bending fatigue failure is sometimes defined as the point in
time when the composite can no longer sustain a specified stress level. Because of
different processing techniques used to produce composites and the wide range of
applications, these definitions are generally adapted to the loading environment.
Bending fatigue failure of composites is often defined as the point when a global
degradation percentage is reached, based on engineering justifications. For example,
Kukureka et al adopted a failure criterion of a 1.5% decrease in modulus because it
caused a 10% reduction in flexural strength [19]. The most widely used criterion for
bending fatigue failure is when the residual load bearing capacity falls to the level of
maximum stress in the fatigue cycle, at which point failure occurs [20]. However, this
criterion can only be used for load control fatigue tests, so different criteria have been
adopted for constant displacement fatigue tests. For example, Shih et al arbitrarily chose
a 10% drop in load as flexural fatigue failure for unidirectional fiberglass composites
produced by matched mold fabrication [15]. One standard (ISO 13003) defines the end
29
of a bending fatigue test when the damage level (related to a specific reduction in
specimen stiffness) reaches a value generally between 5% and 20%.
In the present study, we defined bending fatigue failure in terms of the retained
flexural strength after static loading. Quasi-static, three-point bend tests were performed
to determine the global maximum flexural stress (FS),
0
σ of the composite rod. Once the
composite failed at the static failure displacement (SFD), the load dropped sharply and
the maximum stress was determined based on the maximum load at failure, span length
and radius of the rod. A buckling surface crack was produced on the compression side of
the GF surface, and was visible at the point of contact between the composite and fixture
load pin, with cracks within the CF core also visible. This buckling behavior dominates
static bending failure of composite beams because of the relatively low compressive
strength of the fibers [21]. The composite was reloaded in a second three-point bend test
to determine the residual maximum flexural strength σ. Once the composite failed a
second time, the test was stopped. This procedure was performed on samples to
determine damage accumulation based on static bending failure. The results shown in
Table 2.2 indicate that after initial failure, the sample could subsequently support a load
that was roughly 80% of the FS. The flexural modulus could not be measured on
reloading because the static tests became non-linear after initial failure. However, to
induce a similar amount of damage during bending fatigue, a 20% drop in cyclic stiffness
was chosen based on the assumption that during bending fatigue, a relative drop in cyclic
stiffness (at a fixed displacement) will cause the same percentage drop in both the static
flexural modulus and static flexural strength.

30
Table 2.2. Retained Stress and Static Damage Accumulation
Test Maximum Flexure Stress(MPa) Retained Strength (%) Damage (%)
Initial Stress 1033.46 ± 36.77 - -
Retained Stress 857.19 ± 7.38 82.9 ± 3.4 17.1 ± 3.4

2.4.2 Acoustic Emission Technique
The acoustic emission (AE) technique is a non-destructive method that has been
used to determine the type of damage mechanisms occurring in composite fatigue. Any
type of damage event occurring in a fiber-reinforced composite releases energy and
produces a transient elastic wave [22]. Thus, direct information of fracture mechanisms
can be determined from knowledge of the AE signals generated during loading. AE
amplitude distributions have been used to identify damage mechanisms and monitor
failure processes, where a rise in the frequency of AE events has been attributed to an
increased level of damage in a material [23]. A single damage mechanism (such as
matrix cracking) can produce a wide range of AE signal parameters, and overlap of
parameter distributions can be caused by signal attenuation [24] Consequently, various
amplitude ranges have been assigned for specific failure modes, and this practice is
accepted within the context of a specified test setup [25]. To determine the dominant
failure mechanisms during bending fatigue, the AE amplitude and number of events were
plotted as a function of position and time.
Damage development was monitored during fatigue tests using an acoustic
emission system (Physical Acoustics PCI-2). Two 300 kHz resonance transducers
(Micro 30) were placed on the loading fixtures to determine when and where damage
events took place. The sensors were attached to model 2/4/6 preamps providing 40 dB of
gain and band-pass filtering of 200-400 kHz. The location of the AE source in the
31
specimen was determined using a linear location method. Only the events recorded
between the sensors were used to analyze the AE results. A threshold level of 30 dB was
used to filter out the interference caused by the hydraulics.
The most important AE parameters for burst-type signals are counts, amplitude,
duration and absolute energy. Counts represent the number of times the signal amplitude
crosses a set threshold level. Amplitude is the highest peak waveform voltage and is
directly related to the type of event taking place within the material. Duration represents
the time interval between the first threshold crossing and the last threshold crossing
during an event, and absolute energy represents the area under the rectified signal
envelope. A complexity associated with acoustic emission caused by fatigue arises from
friction sources caused by the fretting of crack faces [26]. One approach to eliminating
frictional sources involves varying AE parameters, although because both damage and
friction events are largely stochastic, the corresponding AE signal parameters are also
expected to overlap [27]. However Barre et al [23] showed that GF systems can exhibit
signature AE amplitudes depending on the fracture mode, and produce both high and low
amplitude events. Because both glass fibers and carbon fibers are present in this hybrid
composite, failure mechanisms occurring in the GF shell and CF core should be
distinguishable, because GF systems are more likely to emit high amplitude signals due
to their larger size and failure strain.
2.5 Results and Discussion
2.5.1 Bending fatigue response
The typical bending fatigue behavior of the hybrid composite is shown in Figure
2.1, where damage growth is plotted as a function of the number of cycles (N) at various
32
CDLs. As anticipated, increasing the displacement caused the number of cycles to failure
( N
f
) to decrease because of the higher stress exerted on the composite. Below 42% of
FS, no stiffness loss occurred up to 1 million cycles and thus, a minimum stress was
necessary to initiate damage.

The fatigue response is characterized by two stages. Stage I represents a “steady
state” response in which no change in the damage variable was detected despite visible
signs of degradation, while during Stage II, losses in the load-bearing capability of the
composite occurred. In the figure, only Stage II is depicted because most of the damage
took place during this stage. As the stress level increased, the number of cycles to initiate
Stage II decreased. Larger displacements produced larger stresses in the composite,
increasing the probability of initiating and propagating damage.
Figure 2.1. Damage growth during Stage II bending fatigue at increasing stress
levels.
33
The rate of damage accumulation during Stage II, (dD/dN) can be directly
determined by numerical differentiation, and a power-law equation can be used to relate
the rate of damage to the number of cycles, as shown below:
dD
B
AN
dN
= (2.2)
Here, A and B are empirical parameters, and A depends on the initial stress level,
while B is the slope in Figure 2.2. The damage rate decreases with increasing number of

cycles, as shown in Figure 2.2. The larger displacements correspond to more rapid initial
damage rates because of the greater cyclic stresses applied. This type of plot can be
explained with the following interpretation. At higher CDLs, a greater amount of stored
strain energy is initially released when damage occurs, leading to a higher initial damage
rate. At all CDLs, the damage rates were greater during the initiation of Stage II, and
decreased monotonically with increasing number of cycles as the composite approached
Figure 2.2. Damage rate versus number of cycles at increasing stress levels.

34
failure. The monotonic decrease in damage rate was attributed to depletion of sites for
damage development (with decreased stored strain energy) and a reduction of the stress
gradient within the composite, both of which reduced the driving force to initiate and
propagate damage [28]. When the stress was reduced, the increment of damage per cycle
decreased. Ultimately, the composite approached a saturated damage state near the end
of its fatigue life, as shown in Figure 2.1. The damage rate decreased

with the number of cycles independently of CDL, indicating that the applied stress levels
and the difference between strain rates within the range of tested displacements did not
affect the deceleration of the damage rate.
2.5.2 Fatigue Life
A log-linear relationship was developed between the number of cycles to failure
and applied stress level (Wöhler curve), as shown in equation (2.3):
1
log N E F
f
s
σ
σ
= +
 
 
 
(2.3)
Figure 2.3. S-N Curve for bending fatigue behavior of hybrid
composite.
35
where E and F are constants,
1
σ is the maximum cyclic stress on the first cycle, and
s
σ is
the FS. Samples were tested at each CDL to develop a comprehensive data set for the
statistical model, and a 95% confidence band for the constant E was computed using
statistical methods described in [29]. The average and standard deviation for each stress
level is shown in Table 2.3. Figure 2.3 shows the log-linear relationship and the
associated confidence intervals. As the stress increased, the number of cycles to fatigue
failure decreased in a log-linear fashion. The scatter in fatigue life can be attributed to
variability in the material properties, and to the anisotropic and inhomogeneous nature of
the composite.
Table 2.3. Average Cycles to failure and Standard Deviation

Figure 2.3 also shows the number of cycles to initiate Stage II (
II
N ) as a function
of CDL. The CDL had the same effect on
II
N as on
f
N , because the slopes for each linear
regression were almost identical, as shown in equation 2.4 (a) and (b):

2
1
log 6.7823 - 0.033 0.93 N R
II
s
σ
σ
= =
 
 
 
2.4 (a)

2
1
log 7.681- 0.0361 0.91 N R
f
s
σ
σ
= =
 
 
 
2.4 (b)
Both
II
N and the slope are useful indicators of the fatigue resistance of the
material [10], and can help designers to predict fatigue behavior when changes in
processing parameters and material properties are introduced. The Wöhler curve can be
% of FS applied Average Cycle to Failure Standard Deviation
47 1,024,658 134,633
53 544,693 83,652
58 384,986 24,143
63 318,757 105,116
68 174,222 34,419
36
used as a method for life prediction and is one way to present statistical data, although it
does not incorporate probability of failure into the S-N relationship. Instead, it indicates
to designers that 95% of the time, the composite will fail within the specified interval.
An alternative to the log-normal assumption is a two-parameter Weibull analysis,
which provides a way of computing failure probabilities so that designers can compare
the reliability of different designs or estimate the fatigue life at a given stress level for a
desired probability of failure. In this investigation, the cumulative distribution function
(CDF), F(x) was used to incorporate such a relationship, as shown below:
( ) 1
x
F x e
β
α
 
 
 
−
= − (2.5)
in which x is the specific value of the random variable (
f
N ), α is the scale parameter or
characteristic life at the specified CDL, andβ is the shape parameter. The scale and
shape parameters were determined at each CDL using Bernard’s Median Rank (MR)
formula:
0.3
0.4
i
MR
k
−
=
+
(2.6)
where i is the failure order number and k is the total number of samples tested at the CDL
[30]. A plot was constructed of ln(ln(1/1-MR)) versus ln(
f
N ), and a linear regression fit
was used to determine the Weibull parameters for the specified stress level (not shown).
The correlation coefficient for the linear regression fits was ~0.90 or greater, indicating
the suitability of Weibull analysis for the present study. The values for α and β obtained
for each CDL are shown in Table 2.4.

37
Table 2.4. Weibull Parameters at Various Stress Levels

Using these values and incorporating selected failure probabilities (
p
F ) fatigue life was
predicted according to the relation below:
1
ln ln ln
1
exp
F
p
N
f
β α
β
+
−
=
     
 
   
 
 
 
   
 
 
 
 
(2.7)
where the number of cycles at which the median population of the composites fail for a
given stress level could be determined [30]. The predicted fatigue lives of the hybrid
composite population at failure probabilities ranging from 25% to 95% are shown in
Figure 2.4. The plot shows that the number of cycles to failure, N
f
, declined with
increasing stress level in log-linear fashion, which is consistent with Figure 2.3. The plot
shows the percentage of the composite rod population that will fail at a given stress level,
as well as the distribution of predicted
f
N values.
The methods used here describe and determine fatigue life and damage modes of
hybrid composite rods providing different insights. The phenomenological approach
quantitatively described how damage accumulates with number of cycles and how
damage rate decreases with the number of cycles with strain energy dissipation. The
Wöhler curve provided a way to present the set of fatigue data and assumed that scatter
was independent of applied stress level, where fatigue life was log-normally distributed.
% of FS applied Scale Parameter(α) Shape Parameter(β)
47 1023447.06 6.53
53 543191.82 5.58
58 385437.46 13.74
63 309447.41 2.57
68 172992.79 4.33
38
Although this log-normal distribution function has been used extensively in fatigue
analysis, Gumbel showed that with the log-normal distribution, the probability of failure
after surviving a given number of cycles decreased with increasing time [31]. This
assertion is not valid when applied to degradation of engineering materials, and he argued
that there is no physical interpretation of the log-normal distribution for fatigue life. Thus
a two-parameter Weibull distribution was used to predict fatigue life at a specified
probability of failure, providing designers a way to predict life with a certain

level of confidence. To determine how well the Weibull model fit the set of
observations, the Kolmogorov-Smirnov (K-S) goodness of fit test was used as follows:
max ( )
1
k
i
D F x
i i
i
k
= −
=
 
 
 
(2.8)
Figure 2.4. S-N Curve utilizing failure probabilities.
39
Figure 2.5. AE events and damage versus fatigue life for a maximum stress level of 68%
FS.
where ( ) F x
i
is the cumulative distribution in Eq. (2.8) and
i
x is the cycles to failure for
the ith test. The maximum value of
i
D for each CDL was compared to
c
D values
obtained from a K-S table, and all values of
i
D were less than
c
D at a 5% level of
significance, as shown in Table 2.5. Thus, the two-parameter Weibull CDF was
appropriate to predict fatigue life and incorporated failure probabilities into the predicted
S-N curve.
Table 2.5. Goodness of Fit Parameters
% of FS applied i
D
c
D
47 0.22 0.57
53 0.23 0.62
58 0.2 0.49
63 0.31 0.62
68 0.25 0.62

40
2.5.3 Failure Mechanisms
Damage initiation and accumulation during bending fatigue occurred in two
stages, and the asymptotic growth in the damage variable (during Stage II) occurred in
the same fashion at all CDLs. Figure 2.5 shows the damage progression and AE events
as a function of fatigue life for a specimen loaded at 68% of the FS. Both Stages I and II
are shown and damage initiated in the GF shell at the midpoint of the sample on the
tensile surface where the bending moment was greatest. The rise in AE activity between
8 and 17% of life was attributed to matrix cracking.
Initial damage sites during Stage I appeared as light surface patches, and closer
SEM inspection revealed the development of matrix cracks, as shown in Figure 2.6 (a).
The limited cracking along the fiber/matrix interface indicated strong interfacial bonding,
while matrix cracks extended in transverse directions (radial and circumferential) normal
to the axial fibers. The interaction of such cracks resulted in a macroscopic brush-like

Figure 2.6. (a) Damage initiates as transverse matrix cracks in the GF shell, (b) brush-like
feature formation at top surface of shell

41
appearance on the tensile surface, at the outermost region of the glass fiber shell. The
brush-like appearance was caused by fiber fracture and the linkage of individual damage
zones, which caused the detachment of fiber bundles from the glass shell, as shown in
Figure 2.6 (b). The formation of broken fiber bundles was accompanied by a sharp rise in
the number of AE events near 17% life (see Figure 2.5), and an increase in the damage
variable, indicating the start of Stage II.
Figure 2.7 shows the AE amplitude distribution as a function of both position
(along the specimen length) and life during Stages I and II. Between the start of the test
and ~8% of flexural fatigue life, a reduction in AE was observed, which can be attributed
to the felicity effect (FE). The felicity effect is a phenomenon in which AE activity
decreases (from unloading and reloading) because AE from initial sources end, and AE
activity during reloading resumes at a fraction of the previously applied load [32]. AE
activity resumed when the first fatigue mechanism was activated, marking the onset of
Stage I damage (indicated on figure). This initial damage source exhibited an amplitude
42

range of 40-50 dB and was identified as matrix cracking. The start of Stage II is
distinguished by the green and red amplitude distribution in the center of the composite,
ranging between 60-70 dB. These high-amplitude events correspond to multiple fiber
bundle failures, where packets of GFs fail and could also be caused by continued matrix
decohesion and cracking. Between fiber bundle failures, there were periods of activity in
which only matrix cracking occurred. These periods occurred at ~33% of total life and
again at ~66% total life (absence of green/red, indicated by red ellipses). During these
periods, longitudinal splitting extended towards the specimen ends, creating crack
surfaces normal to the load axis, while matrix cracking simultaneously propagated in
transverse directions towards the neutral axis. Previous investigators have shown that
Figure 2.7. AE Amplitude distribution as a function of position and life.

43

friction caused by the fretting of crack faces can produce AE [33], and others have
suggested that friction sources are of short duration, resulting in low-energy AE counts
[19]. Thus, while frictional sources are present and produce AE counts, they account for
only a minor portion of the AE data displayed.
Initial GF bundle breaks and attendant matrix cracking caused a redistribution
of stress within the specimen. Matrix cracking effectively isolated certain fibers from
load transfer, causing load shedding to proximal fibers, which contributed to additional
fiber failures [34]. As Stage II proceeded, multiple fiber bundles failed, causing a
continuous redistribution of stress. Matrix cracks propagated in longitudinal (horizontal)
and radial directions, forming layer-like slabs that extended primarily in parallel planes
normal to the loading direction. These parallel layers were joined by shorter radial crack
segments that extended toward the CF/GF interface, as shown in Figure 2.8. The “slab
cracks” were a consequence of fiber bundle breaks that first occurred near the rod
surface. Additional matrix cracks subsequently developed on roughly parallel planes
successively deeper beneath the surface, creating additional slabs, and stopping at the
GF/CF interface (see Figure 2.8). The continuous loss in stiffness was attributed not to
such matrix cracks, but to the fracture of multiple fiber bundles in the GF shell. Both
Figure 2.8. Damage saturation at end of fatigue life.
44
fatigue mechanisms (matrix cracks and fiber bundle fractures) occurred concurrently
during Stage II, and were interactive, in that transverse matrix cracking led to the
formation of multiple fiber bundle failures, and vice versa. Figure 2.7 shows that most of
the high amplitude events (indicated by red dots) took place early in Stage II and
contributed to the majority of damage growth and the highest damage rate (as shown in
Figure 2.5). Near the end of the composite life, the number of AE events decreased,
indicating a deceleration in damage rate and a subsequent saturation of damage along the
interface. These phenomena are consistent with trends shown previously in Figure 2.1
and 2.2.
2.5.4 Stress Distribution along the CF/GF Interface
During bending fatigue, the maximum bending moment (
c
M ) occurred at the
center of the specimen, and was distributed to both the GF and CF regions. Although the
maximum strain occurred at the outer surface of the GF shell, the maximum stress arose
at the CF/GF interface because of the higher modulus of the CF/epoxy system. The axial
stress (
a
σ ), within the GF shell or CF core can be determined as follows:
/
a
GF CF
E r
σ
ρ
= (2.9)
GF GF CF CF
c
E I E I
M
ρ
+
= (2.10)
where ρ is the radius of curvature,
GF
E and
CF
E are the moduli of the respective fiber-
matrix systems, I is the second moment of inertia, and r is the distance from the neutral
axis. The value of E depends on the system for which the stress is to be calculated. The
axial stress distribution due to bending is shown in Figure 2.9 for a specimen loaded to
68% of the FS.
45

The maximum axial stress, σ
a
, occurs at the midpoint of the composite, and
decreases linearly towards the sample ends, as expected. The axial stress at the midpoint
varies with radial position, and is greatest at the CF/ GF interface (see Midpoint in Figure
2.9); where there is an abrupt discontinuity of stress that affects the way damage
propagates during flexural fatigue.
Fatigue damage first appeared in the form of matrix cracks followed by fiber
bundle breaks in the GF shell. Once cracks reached the GF/CF interface, they stopped
and did not penetrate into the CF core. The interface caused cracks to propagate along
this plane, causing the observed asymptotic behavior in the damage variable (Figure 2.5).
Because cracks failed to penetrate the CF core, the progressive reduction in stiffness
ceased. And while the interfacial portion of the CF system experienced the greatest
cyclic axial stress (1.2 GPa), the ultimate tensile strength of the CF material (~3.4 GPa)
prevented fatigue crack growth. Note that carbon fiber composites typically exhibit
greater resistance to fatigue when compared to comparable GF composites [35].
The distribution of strain during cyclic loading affected the matrix stress within
the GF and CF regions. During initial cyclic loading, the stress within the matrix at the
outer surface of the GF shell was greater than the matrix stress in the CF core. The axial
elastic stress within the matrix (
m
σ ) for each material system is given by:
Figure 2.9. FEA showing stress concentration along GF/CF interface.
46
Table 2.6. Stress within the Matrix
( )
m m CF CF
E σ ε
−
= (2.11)
( )
m m GF GF
E σ ε
−
= (2.12)
where
CF
ε is the maximum strain in the CF system,
GF
ε is the maximum strain in the GF
system and
m
E is the elastic modulus of the matrix. The elastic strain is calculated by:
r
ε
ρ
= (2.13)

Table 2.6 shows the respective stresses in the matrix at the tested stress levels.
During Stage I, the surface strain produced a larger axial matrix stress at the surface than
along the interface, causing the observed initiation of surface matrix cracks (and not
along the interface). The maximum matrix stress in the CF system at the CF/GF interface
was 26 MPa, which was nearly the same minimum matrix stress at the outer surface of
the GF shell, indicating that a minimum stress in the matrix was necessary to initiate
fatigue damage.
The development of matrix cracks is dependent on the modulus and strain-to-
failure of the fibers [32]. The carbon fibers, because of their proximity to the neutral
axis, experienced lower strains than the glass fibers. The CF modulus was also 3×
FS Curvature(m)
max
m GF
σ
−
(MPa)
max
m CF
σ
−
(MPa)
47% 0.67 25 18
53% 0.59 29 20
58% 0.54 32 22
63% 0.50 35 24
68% 0.46 37 26
47

greater than that of the GF modulus. These two factors limited the overall strain
of the carbon core, limiting matrix deformation which might initiate fatigue mechanisms.
Effectively, the GF shell acted as a protective buffer, preventing large strains in the
carbon core. The GF shell was exposed to the largest strain, and because of the lower
stiffness relative to the carbon fiber core, the working strains during fatigue led to matrix
damage.
2.5.5 Retained Mechanical Properties
The retained flexural strength (FS) and flexural modulus (FM) were determined
after flexural fatigue failure occurred at each CDL. Figure 2.10 shows that as the initial
applied stress level increased, the retained FS and FM decreased. Specimens cycled at
larger displacements were expected to retain less strength and stiffness, as higher stress
levels caused more damage. The extent to which larger displacements caused more
damage was evaluated by measuring retained properties. (Differences in damage from
Figure 2.10. Retained mechanical properties after bending fatigue
48
samples cycled at the various stress levels were not visibly discernable.) The retained FS
and FM dropped concurrently during cyclic loading, although both properties showed 85-
90% retention of original values. Note however that a 20% drop in cyclic stiffness during
flexural fatigue did not cause a 20% drop in static flexural modulus or flexural strength.
The difference arises because the cyclic stiffness is measured at the specified CDL, and
not at the SFD, and thus provides a measure of the relative stiffness. The extent of
damage to the hybrid composite was a function of the CDL. Thus, the quasi-static
flexural tests were more destructive to the hybrid composite than bending fatigue tests
(20% reduction in FS compared to 15%), because damage was introduced both to the GF
surface and to the CF core (not shown) at the static failure displacement.
After bending fatigue loading at 63% of the FS, samples were mounted in
tensile fixtures and uniaxial properties were measured. No loss in tensile strength of the
hybrid composite rods was observed after fatigue failure. A synergistic effect does not
exist for this composite, [3] and thus catastrophic failure occurred in tension as the hybrid
reached the failure strain of the carbon fibers (2.1%). Because the GF shell carried
20~25% of the applied tensile load and reached ~66% of its TS at failure, the maximum
strength was not utilized under tensile loads. The primary purpose of the GF shell is to
prevent galvanic coupling between the CF core and conducting aluminum wires. Thus,
fatigue damage to the GF shell will only affect the TS of the hybrid composite if the
strength of the GF shell declines by more than ~33%, or if fatigue damage propagated
into the CF core, neither of which was observed in this study.

49
2.6 Conclusion
The bending fatigue behavior of a GF/CF composite rod was investigated, and
damage development was monitored to predict fatigue life at specified stress levels.
Bending fatigue life was characterized by two distinct stages. Damage initiated by the
formation of microscopic transverse matrix cracks on the GF tensile surface during Stage
I. AE measurements revealed that during Stage II, both fiber bundle failures and matrix
crack propagation played an interactive role in the progression of damage and reduction
in stiffness. A distinctive failure pattern was observed, as radial and circumferential
cracks made up layer like formations that saturated along the CF/GF interface.
An issue of practical importance concerns the effect of fatigue on long-term
durability and retention of mechanical properties. Nearly 85-90% of the flexural strength
and modulus were retained and no loss in tensile strength was observed. The fatigue
damage was limited to the glass fiber shell, and did not penetrate into the carbon fiber
core. The GF shell effectively acted as a sacrificial barrier to fatigue, protecting the CF
core from damage.
Note that when supporting overhead conductors in actual service conditions,
Aeolian vibration due to wind loading will impose high frequency deflections onto the
conductor. But such deflections will be much smaller than those used in the present
investigation. Thus, while the composite core will be exposed to various cyclic stresses
(axial and flexural), this study shows that no fatigue damage initiated in the CF core. But,
understanding the fundamental fatigue damage mechanisms, the conditions necessary to
activate them, and the associated effects on property retention is important. The hybrid
composite design provides an effective means of limiting fatigue damage and delaying
50
the onset of fatigue failure, both of which serve to promote long-term durability of
composites used in infrastructure applications.

51
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[2] Alawar A, Bosze EJ, Nutt SR. A composite core conductor for low sag at
high temperatures. IEEE Transactions on Power Delivery, 2005; 20 (3):
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[3] Bosze EJ, Alawar A, Bertschger O, Tsai YI, Nutt SR. High-temperature
strength and storage modulus in unidirectional hybrid composites. Comp
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[4] Tsai YI, Bosze EJ, Barjasteh E, Nutt SR. Influence of Hygrothermal
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[6] Selzer R, Friedrich K. Mechanical properties and failure behavior of
carbon fibre-reinforced polymer composites under the influence of
moisture. Comp A 1997; 28(6): 595-604.

[7] Ellyin F, Master R. Environmental effects on the mechanical properties of
glass-fiber epoxy composite tubular specimens. Comp Sci Tech 2004;
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[8] IEEE Guide for Aeolian Vibration Field Measurement of Overhead
Conductors. IEEE Std 2006; 1368- p.1-35.

[9] Whapham R, Champa RJ. Wind induced vibrations of overhead shield
wires. In: Pacific Coast Electrical Association Engineering and Operating
Conference, CA, 1983.

[10] Bathias C. An engineering point of view about fatigue of polymer matrix
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[11] Harris B. Fatigue in composites.. CRC Press;2003. p. 4-5.

[12] Dharan CKH. Fatigue failurein fiber-reinforced materials. In:
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[13] Salvia M, Fiore L, Fournier P, Vincent L. Flexural fatigue of UDGFRP
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[14] Agarwal BD, Broutman LJ. Analysis and Performance of Fiber
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[17] Allah MH, Abdin EM, Selmy AI, Khashaba UA. Short Communication:
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[18] Poursartip A, Ashby MF, Beaumont PWR. The fatigue damage
mechanisms of a carbon fibre composite laminate: Development of the
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[19] Kukureka SN, Wei CY. Damage development in pultruded composites
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[20] Liu BY, Lessard LB.. Fatigue and damage-tolerance analysis of
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[22] Unpublished data from PCI-2 Based AE System User’s Manual. Mistras
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[23] Barre S, Benzeggagh ML. On the use of acoustic emission to investigate
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[24] Prosser WH, Jackson KE, Kellas S, Smith BT, Mackeon J, Friedman A.
Advanced waveform-based acoustic emission detection of matrix cracking
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[25] De Rosa IM, Santulli C, Sarasini F. Acoustic emission for monitoring the
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[26] Awerbuch J, Gorman MR, Madhukar M. Monitoring acoustic emission
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[27] Dzenis YA. Cycle based analysis of damage and failure in advanced
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[28] Wang SS, Chim ESM.. Fatigue damage and degradation in random
short-fiber SMC composite. Jour of Comp Mat 1983; 17(2): 114-134.

[29] ASTM E 739-91. Standard practice for statistical analysis of linear or
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[30] Bedi R, Chandra R. Fatigue-life distributions and failure probability for
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[31] Gumbel EJ. Parameters in the distribution of fatigue life. J. Eng. Mech
1963; ASCE: 45-63.

[32] De Rosa IM, Santulli C, Sarasini F. Acoustic emission for monitoring
the mechanical behaviour of Natural fibre composites: A literature review.
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[33] Awerbuch J, Ghaffari S. Monitoring progression of matrix splitting
during fatigue loading through acoustic emission in notched unidirectional
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[34] Matthews FL, Davies GAO, Hitchings D, Soutis C. Finite element
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1985; 6(3): 168-174.

54
CHAPTER 3. TENSION-TENSION FATIGUE OF HYBRID COMPOSITE RODS
3.1 Abstract
The tension-tension fatigue behavior was investigated for a hybrid composite rod
comprised of a unidirectional carbon fiber core and a glass fiber shell. Fatigue tests were
performed at three R-ratios and four maximum applied stress levels (MAS) while
recording the secant modulus at each cycle, and acoustic emission (AE) sensors were
employed to monitor the activation of fatigue mechanisms. Fatigue failure occurred
when the composite rod was no longer able to support the applied cyclic load. For a
MAS level of 70% of the ultimate tensile stress (UTS), composite rods tested at higher R-
ratios showed AE activity through a larger percentage of fatigue life, but exhibited a
greater resistance to fatigue failure, whereas samples cycled at lower R-ratios displayed
AE activity only near the end of fatigue life, and showed a lower resistance to fatigue
failure. The hybrid composite showed modes of progressive fatigue damage at high R-
ratios and low strain amplitudes in the form of longitudinal splitting of the GF shell. In
contrast, failure of the CF core was catastrophic and non-progressive. The fatigue
resistance and damage mechanisms of the composite rod were dependent on the MAS
level and R-ratio. Fatigue cracks initiated because of fretting between the GF shell and
grip surface, which led to the observed longitudinal splitting of the GF shell. Fatigue
damage occurred along the GF/CF interface where non-uniform strains developed
because of the clamping force of the grip on the GF surface. At an R-ratio of 0.85, a
fatigue stress of 70% UTS caused catastrophic fatigue failure, while at lower stresses,
composite rods did not fail and withstood cyclic loads up to 1 million cycles. The
research conducted is the first to investigate the degradation in fatigue performance
55
arising from grip/composite rod interactions and suggests that the results from the study
provide new information for composite materials in industries that utilize unidirectional
composites in cylindrical form.
3.2 Introduction
Overhead conductors in use today consist of aluminum strands wrapped around a
steel cable - the aluminum strands carry the current, and the steel cable supports the
mechanical loads. The major factor limiting the capacity of such conductors is sag at
high temperatures, which results from thermal expansion. To increase grid capacity, new
conductors have been introduced that feature low sag at high temperatures. One such
class of conductor is the high-voltage, composite-reinforced conductor (or CRC), in
which the steel cable used in conventional conductors is replaced with a solid composite
rod with low thermal expansion and high specific strength [1]. These conductors feature
reduced line losses, lower operating temperatures for a given current, and higher
strengths relative to conventional conductors. However, like conventional conductors,
they are expected to deliver decades of service with little or no maintenance. Thus, long-
term durability, which involves fatigue and aging phenomena, is an important issue that
must be addressed before the technology can be widely deployed.
High-voltage transmission lines are suspended between lattice towers by
tensioning during installation, and consequently CRCs will experience a static axial
tensile stress. In addition, cyclic tensile stresses arise from dynamic service conditions
that include wind, ambient temperature fluctuations, ice loading, and periods of high and
low electricity demand. The long-term effects of such dynamic service conditions on the
composite element of CRCs are not well understood. To date, no studies have been
56
undertaken to characterize tension-tension fatigue mechanisms in composite rods
developed for high voltage overhead transmission cables. However, studies have shown
that GRP insulator rods are susceptible to brittle failure where multiple cracks can
develop within fittings near rod/hardware interfaces [2, 3]. Thus, for CRCs, the tension-
tension fatigue behavior of the composite must be characterized and understood to
accurately predict lifetime within the range of anticipated service conditions, to develop
specifications for operating conditions, and to improve fatigue-resistant designs.
The strong dependence of tensile fatigue behavior on composite structure has led
to different, often contradictory conclusions. For example, some investigators have
concluded that tension fatigue is fiber-dominated, and fatigue failure mechanisms are no
different from those present in quasi-static loading [4, 5]. Others, however, observed that
higher modulus and strength fibers in the same epoxy matrix resulted in little
improvement in fatigue behavior of unidirectional composites, and argued that fatigue
depended more strongly on matrix strain [6]. These and similar discrepancies stem from
factors such as the particular loading configuration, the fiber architecture, and the
associated anisotropy.
Tension-tension fatigue testing of composites presents special challenges, some of
which stem from the inherent anisotropy. This anisotropy generally causes cracks to
grow more readily along fiber directions, which leads to splitting parallel to the fibers [7],
often initiated at the grips. (Some test methods suggest gauge length failures are required
to mimic damage that would occur in service conditions [8].) While failure initiation at
grips is generally regarded as an unwanted artifact in lab tests, recent experience with
overhead conductors has shown that failures of conventional overhead conductors
57

typically originate at the node where the conductor cable is attached to the lattice tower
[9, 10]. While fatigue mechanisms for composites have been developed and explained
for gauge-length-related failures, grip induced failures have largely been considered
invalid for coupon testing, [11] and have received little attention. Such observations
underscore the importance of stress concentrations associated with gripping, both in
service and in fatigue testing. This is particularly critical for unidirectional composite
rods, such as those used in CRCs. Figure 3.1 shows the design of a new self-tightening,
collet fixture used to grip the composite core in service. As the axial tensile load
increases, the compressive pressure exerted on the composite rod increases, preventing
slip. Because the transverse strength properties of unidirectional FRCs are much lower
than longitudinal values, failure mechanisms can originate and grow due to stress
variations where transverse loads are the greatest.
The objective of this study is to characterize the effect of stress concentrations
induced by hardware fixtures on tensile fatigue life and failure mechanisms of a hybrid
composite rod similar to those designed for CRCs. Tension-tension fatigue tests were
conducted using collet grip fixtures similar to those designed for attaching CRCs to
splices and dead ends. Experiments using load-control fatigue tests suggest fatigue failure
occurs when the residual strength of the composite reaches the cyclic stress, and
Figure 3.1. CRC mechanical grip design
58
catastrophic failure ensues [12, 13]. S-N curves are developed to illustrate the lifetime of
the composite under varying load conditions, and failure modes are observed and
characterized using microscopy, acoustic emission and finite element analysis.
3.3 Experiments
3.3.1 Materials
Unidirectional hybrid composite rods were acquired for fatigue testing
(Composite Technology Corporation, Irvine, CA). Each rod consisted of a unidirectional
carbon fiber core (CF) surrounded by a glass fiber shell (GF), and an epoxy matrix, as
described elsewhere [14, 15]. The CF core and GF shell regions comprised 44 and 56%
of the composite volume, and the carbon fiber and glass fiber volume fractions for core
and shell were ~69%. The epoxy matrix was formulated for a high glass transition
temperature (T
g
=205ºC). Test specimens were cut to lengths of 610 mm from production
composite rods with a ~6 mm diameter.
3.3.2 Stress State and Fatigue Tests
Static tensile tests and tension-tension fatigue tests were conducted using a
hydraulic load frame (Instron 8500) with a 100 kN load cell. Static tensile tests were
conducted on specimens using custom made tensile test fixtures in accordance with
ASTM D3916. The average ultimate tensile strength (UTS) was 2.24 GPa, and
catastrophic failure occurred when the composite strain reached the carbon fiber failure
strain of ~2%. Load control fatigue tests were performed at three R-ratios (minimum
stress/maximum stress) ranging from 0.5 to 0.85 at a fixed frequency of 5 Hz following
ASTM D 3479. The maximum applied stress (MAS), ranged from 50% to 80% of the
UTS.
59

A set of mechanical grips similar to those used in service (Figure 3.1) were
designed and fabricated for conducting tension-tension fatigue tests. As shown in Figure
3.2, the grips employ a long collet that exerts a radial clamping force that increases as the
tensile load is applied. The collet grip design utilizes two concave anvils to ensure that
the gripping pressure applied to the surface of the rod is sufficient to prevent slip. This
leads to a variation in radial displacements, with the maximum displacement occurring on
the GF shell surface in regions farthest from the gap spacing, indicated in Figure 3.2. The
friction force between the grip and the rod increases with radial displacement, which
resists slippage under higher axial loads. The maximum radial displacement (
max
u ) is a
function of the applied tensile displacement (
z
L ε ) and the grip angle (α ):
max
tan
z
u L ε α = (3.1)

To verify the accuracy of the estimated maximum radial displacement, the gap spacing
was measured as a function of applied axial load and is shown in Table 3.1, compared
Figure 3.2. 2D diagram indicating relationship between longitudinal extension on
radial compression, and a cross sectional view of CF core and GF shell under
mechanical grip.

60
with estimated values. The corresponding maximum radial load that results from the
maximum radial displacement was determined by compressing the rod surface using two
concave anvils with the same geometry as the grips.
Table 3.1. Radial Displacements as a Function of UTS
Axial Load
Calculated Max Radial
displacement(mm)
Measured Max Radial
displacement(mm)
50% of UTS 0.18
0.20
60% of UTS 0.21
0.23
70% of UTS 0.25
0.24
80% of UTS 0.28
0.24

3.3.3 Finite Element Analysis
Finite element analysis (FEA) was performed to determine the stress distribution
within the composite rod subject to an imposed radial displacement and an applied axial
load. The composite rod properties were taken to be transversely isotropic [3], (where x
and y are the transverse directions) and are described in Table 3.2.
Table 3.2. Material Properties in Longitudinal and Transverse Directions

GF/Epoxy CF/Epoxy
( )
z
E GPa
47 139.4
( )
x y
E E GPa =
10.8 7

zx zy xy
ν ν ν = =
0.214 0.27

zx zy
G G = (GPa)
6.3 2.9

A 3D model was developed using constituent properties, and the specimen was modeled
to represent the geometrical features of the test setup, using exact dimensions from the
experiment. Load and boundary conditions were simulated with commercially available
FEA software (ABAQUS) using 183,000 elements with a four-node, bilinear,
61
axisymmetric, quadrilateral element (CAX4R, commonly used in ABAQUS) in the 2D
model, and 47,995 C3D8R elements in the 3D model. The analysis involved two load
steps. In the first step, a radial displacement was applied, and in the second step, an axial
load was applied. The analysis was performed to determine the stress distribution
resulting from the grip design.
3.4 Monitoring Stiffness and Acoustic Emission
3.4.1 Definition of Secant Modulus
Stiffness measurements were performed during fatigue tests as a non-destructive
means to quantitatively monitor the accumulation of damage. During load-controlled
fatigue tests, the maximum and minimum loads during each cycle were recorded, as well
as the elongation. The secant structural modulus (SM) was calculated from:
max min
max min
( ) ( )
( )
( ) ( )
F N F N
SM N
l N l N
−
=
−
(3.2)

where l is the displacement and the subscripts max and min are the maximum and
minimum values of the load or displacement for cycle N [16]. The normalized SM was
calculated by dividing SM(N) by SM(0), which was recorded on the first cycle of each
test. For a given R-ratio and stress level, catastrophic failure occurred when the applied
stress reached the residual strength of the composite. The number of cycles to failure
(
f
N ) was then determined. Specimens that exceeded 1 million cycles without failure
were considered run-outs.
3.4.2 Acoustic Emission
The acoustic emission (AE) technique was used as an in situ, qualitative method
to detect different modes of fatigue damage. In the present work, two acoustic emission
62
resonance transducers (300 kHz Micro 30, Physical Acoustics PCI-2) were placed on
each grip edge to detect damage events. A graphical amplitude filter was employed to
exclude noise caused by the hydraulic pump. The transducer positioned closer to the
hydraulic piston (attached to bottom grip) detected significant noise from the pump and
was in constant cyclic motion, which compromised the ability to locate AE sources. The
transducer farthest from the pump (attached to the stationary top grip) also detected
hydraulic noise, but the amplitude of this signal was attenuated, allowing the transducer
to detect a wider range of amplitudes caused by damage events. Thus, only data
collected from this sensor was used. In fiber reinforced composites, a damage event
releases energy and produces a transient elastic wave [17]. The most important AE
parameters for burst type signals are counts, amplitude, duration and absolute energy
[18]. The AE response was continuously monitored during fatigue tests, and detected AE
decibel hit signals were correlated with fatigue failure mechanisms.
3.5 Results and Discussion
3.5.1 Effect of R-ratio on Stiffness and S-N Diagram
The tension-tension fatigue response for the three R-ratios and four MAS levels is
shown in Figure 3.3, where the normalized SM is plotted against the number of cycles.
At all R-ratios, increasing the MAS caused the number of cycles to failure to decrease.
Increasing the R-ratio caused the fatigue stress (taken as the MAS to cause catastrophic
fatigue failure) to increase. At R=0.50, catastrophic failure occurred for all four MAS
levels, while at R=0.68, failure occurred only for MAS ≥ 60% UTS, and at R=0.85,
failure occurred for MAS stress ≥ 70% UTS. All R-ratios show the same trend in
modulus loss - the SM remains constant for the initial portion of the fatigue life until
63

damage events cause abrupt SM drops, with ensuing catastrophic failure. The first drop
in SM indicated that composite damage had occurred, but was still able to carry the cyclic
load. The applied cyclic load was redistributed and a slightly lower, steady SM was
maintained temporarily while the load cycles continued. Subsequent modulus drops
transpire, with plateaus at lower SM values. Eventually the fatigue damage saturated, and
catastrophic failure occurred, manifested as a precipitous drop in SM, taken as the fatigue
life (
f
N ). Figure 3.3 also shows that for any fixed R-ratio, a shift in material behavior
occurs as the MAS level increases. In particular, for small MAS values, multiple small
decrements in SM are observed, while for larger MAS values, the SM remains nearly
constant over most of the fatigue life, and rapid failure and modulus loss occurs near the
end of fatigue life. The tension-tension fatigue behavior of the hybrid composite rod
differs from that of typical composite laminates, where investigators normally observe a

Figure 3.3. SM loss at 3 R-ratios and 4 stress levels
64

sigmoidal response of stiffness deterioration earlier in life, followed by a steady loss in
stiffness and eventual catastrophic failure [19].
The S-N curves in Figure 3.4 show the effects of the MAS level and R-ratio on
fatigue life. Increasing the MAS level (for any R-ratio) reduced fatigue life. The S-N
curves show that for a fixed MAS level, lower R-ratios resulted in a shorter fatigue life.
At 80% UTS, the R-ratio had little effect on fatigue life, as
f
N varied slightly between
1000 and 1200 cycles for R-ratios 0.50 and 0.68, and increased to ~7000 cycles for
R=0.85. However, at a MAS level of 60% UTS, the fatigue life increased from ~3000
(for R=0.50) to 15000 cycles (for R=0.68) and was beyond 1 million cycles for R=0.85;
with the average and standard deviations shown in Table 3.3. Thus, the effect of R-ratio
on fatigue life was more pronounced at lower stress levels.
Table 3.3. Average Cycles and Standard Deviation
50% UTS 60% UTS 70% UTS 80% UTS
R=0.5 16,188±6,349 3,221±520 1,341±673 1,199±378
R=0.68 - 15,058±334 4,739±909 1,210±204
R=0.85 - - 10,322±2,777 6,723±154

Figure 3.4. S-N Curve at 3 R-ratios showing endurance behavior
65
The effect of frequency on fatigue life was also investigated. Variation in
frequency can affect both specimen temperature and strain rate. Research has shown CF
composites are relatively insensitive to strain rate in the longitudinal direction, although
the mechanical properties of GF composites show stronger rate dependence [20].
Reducing the cycle frequency to 2.5 Hz caused no significant deviation in fatigue life, as
shown in Figure 3.4, indicating that the load frequency had little effect for this study.
Also, because the frequencies used were relatively low, sample heating was negligible.
The testing of multiple samples resulted in statistical scatter in fatigue life, and a
regression model was used to relate the fatigue life to the stress level, as shown in the
power-law relationship below:
B
f
UTS
N A
σ
σ
 
=
 
 
(3.3)

where A and B are empirical parameters. The data conform to this relationship, as shown
in Figure 3.4, indicating the existence of an endurance limit, below which fatigue failure
does not occur. As shown in the plots, fatigue life is affected by the R-ratio. This is
particularly apparent when observing the log-log relationship at the two lower R-ratios
(R= 0.5 and R=0.68):
R = 0.50 2
R = 0.68 2
-ratio 0.50 log( ) 15.843 6.85log 0.89
-ratio 0.68 log( ) 20.45 9.09log 0.97
f
UTS
f
UTS
R N r
R N r
σ
σ
σ
σ
 
= = − =
 
 
 
= = − =
 
 
(3.4)
The high correlation coefficients in equation (4) (r
2
= 0.89 and 0.97) indicate a
strong relationship between fatigue life and stress level. On the other hand, the effect of
the R-ratio is reflected in the pre-logarithmic term (equal to B in equation (3.3)). This
66
term, effectively the value of the slope in equation (3.4), quantitatively relates the effect
of the R-ratio on fatigue life, and is an indicator of fatigue resistance. For example, a
slope of -9.09 compared to -6.85 indicates that a longer fatigue life is predicted at larger
R-ratios and lower MAS levels. Thus, the hybrid composite is more fatigue-resistant at
higher R-ratios, which is a result of lower cyclic strain amplitudes at high R-ratios.
Table 3.4. Strain Amplitude at 3 R-ratios

The initial strain amplitudes ((
max min z z
ε ε − ) within the gauge length) of the
composite at the three R-ratios and four MAS levels are shown in Table 3.4. The table
indicates that at R=0.85, the cyclic strain amplitude varied between 0.17% - 0.27%, the
lowest range of strain values of all the three R-ratios regardless of stress level. Note that
CFRPs reportedly do not experience fatigue damage when cyclic strain amplitudes are
sufficiently low [8]. Thus, the low strain amplitudes at R=0.85 are an indication of why
composite rods cycled at MAS levels of 50% UTS and 60% UTS survived over 1 million
cycles without catastrophic failure. Although fatigue damage occurred in the GF shell,
the cyclic applied load was supported primarily by the CF core, which showed no
evidence of fatigue damage at low strain amplitudes.
3.5.2 Acoustic Emission output
The AE amplitude response is shown concurrently with the SM loss in Figure 3.5
for a fixed MAS level of 70% UTS at the three R-ratios. Each red dot represents a single
hit, corresponding to the detection of an AE signal arising from an active damage mode.

R=0.5 Strain
Amplitude (%)
R=0.68 Strain
Amplitude (%)
R=0.85 Strain
Amplitude (%)
50% of UTS 0.56 0.36 0.17
60% of UTS 0.67 0.43 0.20
70% of UTS 0.78 0.50 0.24
80% of UTS 0.90 0.57 0.27
67
Figure 3.5. AE hits and damage versus fatigue life for a maximum stress level of
70% UTS at 3 R-ratios

68

The data in Figure 3.5 show that during the early stage of tension-tension fatigue, the SM
was nearly constant, and no AE signals were detected, indicating negligible damage. The
end of the early stage was marked by a sharp drop in the secant modulus, accompanied
by a rise in the value and number of AE hits, indicating the onset of a fatigue damage
mechanism. The audible damage events occurred within the GF shell and originated near
the grip/gauge length transition region, shown in Figure 3.6. Fretting fatigue damage at
the GF surface, caused by the collet fixture, led to the formation and propagation of a
radial crack through the GF shell, which was subsequently deflected at the GF/CF
interface and propagated as a longitudinal crack along the gauge length (see micrograph
in Figure 3.6). This pattern of initial failure manifested as bundles of GF fibers
separating from the GF/CF interface, as shown in Figure 3.6.
Prominent drops and plateaus in SM occur after the initial SM loss, as shown in
Figure 3.5(b) and (c). In particular, for R ratios of 0.68 and 0.85, progressive damage
occurs within the GF shell, where each drop in SM corresponds to an AE amplitude peak.
The damage mode was progressive because each SM drop was correlated with a
macroscopic damage event accompanied by a burst of AE signals. The peaks in AE
Figure 3.6. Damage initiates as cracks in the GF shell near rod/grip zone along the
CF/GF interface

69
amplitude in Figure 3.5 (b) and (c) represent progressive longitudinal splitting of the GF
shell, and are characterized by a high amplitude output range of 80-95 dB. Each
longitudinal split in the GF shell originated within a grip and propagated along the gauge
length, both as a radial crack in the GF shell and a longitudinal crack at the GF/CF
interface. The fatigue resistance of unidirectional composites reportedly depends on the
susceptibility to longitudinal splitting [21]. In the present investigation, the GF shell
showed clear signs of this mechanism. These wedge-shaped GF bundle cracks grew
parallel to the fiber direction, and were responsible for the progressive step-wise losses in
the SM.
Two mechanisms of fretting damage in the GF shell were apparent during
tension-tension fatigue tests, and these were detectable only by analyzing the AE data and
observing the fracture surfaces. As the GF shell debonded from the CF core, broken
sections of the GF shell continued to slide and abrade unbroken fibers, a phenomenon
that was both visible and audible. Signs of fretting damage were also evident along the
surface of the GF shell that was in contact with the collet grip (Figure 3.6). Fretting
fatigue damage was manifested in the AE data as signals of repeated low-AE-amplitude
(60-70 dB, Figure 3.5). These signals increased in frequency with fatigue life,
demonstrating that fretting fatigue of the GF shell was an important damage mechanism
contributing to fatigue failure. Kim and Ebert [22] determined that the surface integrity of
the glass fiber was the most critical factor limiting the fatigue life of a GF composite, and
surface integrity can be compromised during fatigue loading because of fiber-fiber
contact (fretting type damage) produced during high-amplitude stress cycling [23].

70

The tension-tension fatigue behavior of the hybrid composite led to complete
failure of the CF core because of a transition in damage mechanisms and load sharing
behavior. The growth of multiple longitudinal cracks (along the CF/GF interface) led to a
10-20% loss in SM after ~70% of the fatigue life, (see arrow in Figure 3.5 (b) and (c)).
Eventually, these cracks led to complete separation of the GF shell from the carbon fiber
core, corresponding to the lowest SM plateau prior to catastrophic failure. This resulted in
a bird cage morphology, as shown in Figure 3.7. At this stage, (complete shell/core
separation), the CF core supported all of the applied cyclic loads. Figure 3.5(b) and (c)
show that after the bird-caging effect, the SM remained constant until final failure, and
there were no prominent peaks in AE signals until the CF core failed catastrophically.
The failure-causing damage to the CF core was characterized by multiple fiber
breaks and fiber/matrix interface separation, as shown in Figure 3.8. While some of the
outermost fibers of the CF core detached with portions of the GF shell during bird-
caging, the bulk of the CFs did not separate, and the majority of the core remained intact
until catastrophic failure occurred. There was no evidence of progressive fatigue damage
in the CF core, and the fracture surfaces were similar to the failures observed in tensile
strength tests. Supporting this contention, the normalized SM remained nearly constant
during the final 20-30% of fatigue life (at 80-90% of SM), a period during which the load
Figure 3.7. Complete GF/CF separation termed bird caging

71

Figure 3.8. Catastrophic failure of CFs at end of fatigue life.
72
was supported solely by the CF core (see Figures 3.5 (b) and (c)). During this period, the
number of random fiber breaks increased with the number of cycles, but because the SM
remained constant, the damage was negligible and the failure of the CF core was non-
progressive. Eventually, the distribution of broken carbon fibers reached a critical stage
at which point catastrophic failure occurred, corresponding to a final peak in AE
amplitude (near 95 dB) and a drop in SM to zero.
3.5.3 Failure Mechanisms
Figure 3.3 shows that the hybrid composite undergoes a transition from
continuous degradation of the SM to a sudden-death failure with increasing MAS levels
and strain amplitudes. In previous fatigue studies, progressive damage mechanisms were
responsible for the steady degradation of the SM where a zone of damage was traced,
while non-progressive damage mechanisms were indicated by a sudden-death behavior of
the SM [24, 25]. Progressive damage mechanisms in composites are matrix-dependent
failure modes, and typically start within the matrix and propagate along the fiber/matrix
interface. In contrast, non-progressive damage mechanisms are fiber-dominated failure
modes, and are catastrophic in nature. Table 3.4 shows that lower R-ratios corresponded
to higher initial strain amplitudes, ranging from 0.17% to 0.9% within the gauge length.
The strain amplitude was 0.78% for R=0.50, and was lowest (0.24%) for R=0.85, at a
MAS of 70% UTS.
The high strain amplitude of 0.78% led to sudden-death failure of the entire
hybrid composite, as shown in Figure 3.5(a). This trend is consistent with Talreja’s
investigations showing that higher maximum strain amplitudes corresponded to non-
progressive catastrophic failure [26]. In Figure 3.5(a), AE activity occurred only in the
73
last 20% of the fatigue life, while at higher R-ratios, AE activity initiated within the first
20-50% of life, and was present throughout, as shown in Figure 3.5(b) and (c). This
continuous AE activity throughout most of the fatigue life reflects a progressive damage
mechanism. The scaled AE activity early in fatigue life was an indication that increasing
the R-ratio led to the activation of progressive damage mechanisms, at lower strain
amplitudes. Lower MAS levels and higher R-ratios produced lower strain amplitudes,
leading to early, progressive damage of the GF shell and higher fatigue lives. On the
other hand, higher MAS levels and lower R-ratios produced higher strain amplitudes,
leading to non-progressive, sudden-death failure of the entire hybrid composite and
shorter fatigue lives.
3.5.4 Effect of Stress Distribution on Crack Initiation
The stress distribution in the composite rod during tension-tension fatigue tests
affected the observed fatigue mechanisms. Portnov and Bakis [27] showed that for all
types of methods used to grip and pull pultruded composite rods; the tensile load is
maintained by the shear stress acting on the surface of the rod within the grips. Near the
grip edges, tensile and hoop stresses are concentrated, and are related to the value and
distribution of the surface shear stress. In the case of flat laminate coupons, stress
concentrations within grips are commonly mitigated by the use of tabs, although
conventional tabs cannot be deployed with cylindrical rods.

74

Stress concentrations within the grip were a function of the distribution of radial
displacements, which were determined by finite element (FE) analysis. Figure 3.9(a)
shows the distribution of radial displacements at 50% UTS (axial load) under an imposed
radial displacement in a 3D FE model. The radial displacements were slightly non-
uniform as a result of the slit spacing inherent in the collet grip design (see Figure 2).
The analysis revealed that the greatest radial displacements occurred near the top and
bottom of the grip (u
max
in Figure 3.2), where the greatest radial loads occurred. These
regions experienced minimal fretting damage because the high radial displacements
prevented axial displacements (slippage). Large radial displacements can cause high
transverse compressive stresses to develop that can crush composites [28]. Thus, radial
displacements ideally should be sufficiently large to prevent fretting and slip, but small
enough to prevent compressive overload and crushing (not observed in this study). The
smallest radial displacements (u
min
in Figure 3.9(a)) occur near the collet slit where the
two concave anvils of the collet meet. This analysis is consistent with Figure 3.6, which
shows the formation of fatigue cracks in regions where radial displacements are minimal
and where the sharp edges of the collet exist. These sharp edges created grooves on the
Figure 3.9. (a) Non uniform radial displacement of grip, (b) stress distribution in plane with
maximum radial displacement (c) stress distribution in plane with minimum radial
displacement
75
GF surface (see Figure 3.6), and allowed the composite rod to slip and fret during tensile
fatigue.
The effects of the radial displacements on the tensile stress distribution in the
composite rod are shown in Figures 3.9(b) and (c). Figure 3.9(b) shows the 3D
distribution of stress within the gauge length, and near the grip edge (MAS =50% UTS)
in the plane where the greatest radial displacement occurred. The stress distribution
along the gauge length is uniform within the CF core (1.7 GPa) and the GF shell (0.57
GPa). However, the discontinuity in stress arises at the core-shell interface because of the
abrupt modulus mismatch between the two material systems (see Table 3.1). The
longitudinal composite stress (
c
σ ) can be evaluated as:
( )
c c c GF GF CF CF c
E E V E V σ ε ε = = + (3.5)
where subscripts GF and CF represent the homogenized material systems (fiber and
matrix), and an isostrain condition is assumed within the gauge length region. Using
equation (3.5) and the longitudinal elastic constants shown in Table 3.1, one can show
that the CF core bears 70~80% of the applied load, while the GF shell bears the
remaining 20~30% depending on rod diameter. The distribution of tensile stress
becomes non-uniform near the grip entrance in both material systems, where non-uniform
radial displacements (and loads) are introduced. Figures 3.9(b) and (c) show that a
transition from longitudinal tension (caused by surface shear stresses) to longitudinal and
transverse compression (caused by the radial load) occurs deeper within the grip. The
plane in which the radial displacement is greatest causes the maximum longitudinal
tensile stress (in both the GF shell and CF core) to increase to ~0.8 GPa and ~1.83 GPa,
respectively. Figure 3.9(c) shows that in the plane with the lowest radial displacement,
76
the stress concentration region was smaller, indicating that lower radial displacements
reduced stress concentrations.
These results show that during tension-tension fatigue, the non-uniform
distribution of longitudinal stress near the grip ends caused the composite to experience
larger cyclic stresses within the collet grip than within the gauge length. The
concentrated cyclic stresses within the grip increased the probability of initiating and
propagating cracks during tension-tension fatigue. Table 3.1 indicates that higher tensile
loads generate larger radial displacements which are necessary to prevent slip, but
increases the severity of stress concentrations. Thus, the probability of crack propagation
increases at higher MAS levels because of the greater radial displacement required to
prevent slip within the grips.
3.5.5 Interfacial Separation
Crack growth parallel to the fiber direction and along interfaces occurred during
tension-tension fatigue of the hybrid composite rod. Cracks grew and propagated along
the GF/CF interface into the gauge length, and led to complete separation of the GF/CF
systems. The interface between two materials is often weak relative to fiber strengths,
providing preferred pathways for crack propagation [29]. Multiple factors can cause
materials to separate along interfaces, one of which is the abrupt change in elastic
modulus between the CF and GF systems. In the present case, the modulus mismatch
caused a discontinuity of stress to arise at the interface that was amplified within the
collet grip. In this region, shear stresses can also develop if there is relative motion
between the two material systems.

77

Figure 3.10(a) shows the longitudinal strain distribution within the gauge length at
50% UTS, where an isostrain condition exists at 1.1% strain. During tension fatigue, the
composite was initially cycled between two positions where the two fiber types and the
matrix reached uniform strains (within the gauge length). Figure 3.10(b) shows that the
axial strain increases along the GF/CF interface near the grip entrance, rising to a
maximum of 1.4% in the GF shell. This distribution constitutes a strain gradient within
the matrix near the GF/CF interface. During tension-tension fatigue, the strain gradient
along the interface produced a shearing effect in the matrix and caused separation of the
GF shell from the CF core, resulting in relative sliding between the CF core and the GF
shell. These observations are consistent with previous observations of fatigue cracks
initiating in regions of high matrix strain and propagating along stress concentration sites
[18].

Figure 3.10. (a) Axial strain at 50% UTS along gauge length, (b) non-uniform axial
strain at interface
78
3.5.6 Design considerations
To mitigate the issues of high interfacial stress concentrations and fretting fatigue
within the grip, a new design consideration was proposed. The addition of a thin sleeve,
(25 mm in length) near the grip/gauge length interface is contemplated to reduce the
friction coefficient and the maximum radial displacement (within the region). The radial
displacement was reduced from 0.18 mm to 0.10 mm and the friction coefficient was
reduced by 20% in the 25 mm length region to hypothetically model the effect of a

sleeve. The effect of such a sleeve on the stress distribution in the rod was analyzed
using a 2D FE model, and the results are shown in Figure 3.11. The simulation shows
Figure 3.11. Tensile stress distribution with and without sleeve

79
that stress concentrations were reduced by ~10% in both the GF and CF systems. The
corresponding stress states in the 2D model are similar to those determined by the 3D
model. If similar sleeves were implemented in service, they would reduce stress
concentrations in the grip while allowing a lower more uniform distribution of radial
displacement. This sleeve would also protect the GF shell from fretting fatigue damage
caused by the sharp grooves in the grip design.
To validate the model predictions and determine the effect of a protective sleeve
on fatigue life, a PTFE (polytetrafluoroethylene) film was wrapped on the composite rod
within the grip/gauge length transition region. As shown in Figure 3.4, at R=0.50 and
50% UTS, the fatigue life more than doubled after application of the PTFE film,
increasing from an average of ~17,000 (no coating) to 38,194 cycles. At 60 and 70%
UTS, the fatigue life with the PTFE sleeve was 5,433 and 2,835 cycles, both nearly
double the average fatigue life of control samples at the respective stress levels. A
statistical analysis of the fatigue life distributions of sleeveless samples indicates that
only a 1% probability of the population would reach such high fatigue lives.
Observations of the crack initiation sites revealed that the sleeve delayed the onset of GF
shell fretting cracks, acting as a protective sliding contact. Thus, the sleeve strongly
affected the fatigue life and similar measures are expected to reduce fatigue cracks and
extend fatigue life for hybrid composite rods in service applications.
3.6 Conclusions
The tension-tension fatigue behavior of a hybrid composite rod comprised of
unidirectional carbon and glass fibers was investigated. The technique used to grip the
composite influenced the observed fatigue behavior and damage mechanisms, and the
80
stress distributions showed that regions within the collet grip having the greatest radial
displacement experienced the greatest tensile stresses. Cracks initiated in regions with
low radial displacements, where the sharp collet edges rubbed against the GF shell.
Longitudinal cracks grew along the GF/CF interface until complete shell/core separation
occurred. Lower R-ratios and higher MAS levels led to shorter fatigue lives because of
the transition from progressive fatigue failure to non-progressive fatigue failure.
Modifications to the grip design were considered that would increase the overall
durability of the composite component in CRCs under both laboratory conditions and
service conditions. In service, conductors are expected to be tensioned to a maximum
stress level of 25% UTS, much lower than the levels of 50-80% UTS used for fatigue
tests described here. However, overstressed conditions routinely arise in service, and it is
important to understand the effects of stress concentrations that will develop at dead-ends
and splices where hardware is used to attach the conductor to support towers. The results
of this study suggest that while the gripping technique is adequate to support the
appropriate loads, stress concentrations arise near the grip edges, where fretting damage
can be induced under cyclic loading. FEA simulations and trial experiments showed that
a thin protective sleeve over the composite rod would reduce fretting and stress
concentrations, and thus extend fatigue life.
The hybrid composite design exhibited robust fatigue behavior - rods supported
high cyclic loading levels (60% UTS) for more than 1 million cycles. The fatigue
resistance stems from the fact that damage was confined to the GF shell, while the major
load-bearing component (the CF core) was largely immune to fatigue damage.
Improvements in interfacial adhesion or a gradual transition zone between CF and GF
81
components (as opposed to the abrupt material transition) could delay or prevent core-
shell debonding (as well as the attendant bird-caging phenomenon), and these approaches
are presently being explored. With the advent of new conductor designs such as the
CRCs, fatigue damage modes must be analyzed and understood to prevent failure from
occurring in service. Because most service-related material failures are caused by some
form of fatigue and service lives for infrastructure applications typically span multiple
decades, composite designs for applications like CRCs will require consideration of
fatigue resistance. Furthermore, CRCs will be deployed in outdoor environments with
minimal protection, and thus aging factors such as thermal oxidation and degradation and
moisture uptake will further limit fatigue life of composites. These aging factors have
been studied for CRC composites [14, 15, 18], although the interaction of their combined
effects on long-term durability has not yet been considered. Accounting for such
interactions, which are undoubtedly complex, will be necessary to develop a realistic and
accurate model for CRC lifetime prediction.

82
Chapter 3 References
[1] Alawar A, Bosze EJ, Nutt SR. A composite core conductor for low sag at
high temperatures. IEEE Trans Power Deliv 2005; 20(3):2193-9.

[2] Bansal A, Schubert A, Balakrishnan MV and M Kumosa. Finite Element
Analysis of Substation Composite Insulators. Composites Science and
Technology, 1995. 55: p. 375-389.

[3] Lanteigne J, C De Tourreil. The Mechanical Performance of GRP used in
Electrical Suspension Insulators. Composites and Mathematics with
Applications, 1985. 11(10): p. 1007-1021.

[4] Keller T, Tirelli T and A Zhou. Tensile Fatigue Performance of Pultruded
Glass Fiber reinforced Polymer Profiles. Composite Structures, 2005. 68:
p.235-245

[5] Zhang Y, Vassilopoulos AP and T Keller. Stiffness Degradation and
fatigue life prediction of adhesively-bonded joints for fiber-reinforced
polymer composites. International Journal of Fatigue, 2008. 30: p.1813-
1820.

[6] Curtis P.T. The Fatigue Behaviour of fibrous composite materials.
Journal of Strain Analysis. 24 No. 4, 1989.

[7] Meziere, Y., A.R. Bunsell, Y. Favry, J.C. Teissedre and A.T. Do. Large
Strain Cyclic fatigue testing of unidirectional carbon fibre reinforced
epoxy resin. Composites Part A, 2005 (36). P. 1627-1636.

[8] ASTM D 3479. Standard Test Method for Tension-Tension Fatigue of
Polymer Matrix Composite Materials. ASTM; 2007.

[9] Brunair R.M., Ramey G. E. and R.R. Duncan III. An Experimental
Evaluation of S-N Curves and Validity of Miner’s Cumulative Damage
Hypothesis for An ACSR Conductor. IEEE Transactions on Power
Delivery, 1988. Vol. 3, No. 3.

[10] Cardou A, Cloutier L, Lanteigne J and P M’Boup. Fatigue Strength
Characterization of ACSR Electrical Conductors at Suspension Clamps.
Electrical Power Systems Research, 1990. 19: p. 61-71.

[11] Hodgkinson JM. Mechanical Testing of Advanced Composites. CRC
Press, 2000; 65.

83
[12] Kawai M. A phenomenological model for off-axis fatigue behavior of
unidirectional polymer matrix composites under different stress ratios.
Composites: Part A, 2004 35: 955-963.

[13] Epaarachchi JA, and PD Clausen. An empirical model for fatigue
behavior prediction of glass fibre-reinforced plastic composites for various
stress ratios and test frequencies. Composites:Part A, 2003. 34: 313-326.

[14] Tsai YI, Bosze EJ, Barjasteh E, Nutt SR. Influence of Hygrothermal
environment on thermal and mechanical properties of carbon fiber/fiber
glass composites. Comp Sci Tech 2009; 69(3-4): 432–437.

[15] Barjasteh E, Bosze EJ, Nutt SR. Thermal aging of fiberglass/carbon-fiber
hybrid composites. Comp A 2009; 40(12): 2038-2045.

[16] Zhang Y, AP Vassilopoulos, and T Keller. Environmental effects on
fatigue behavior of adhesively-bonded pultruded structural joints.
Composites Science and Technology, 2009. 69: p. 1022-1028.

[17] Unpublished data from PCI-2 Based AE System User’s manual. Mistras
Group.

[18] Kar NK, Barjasteh E, Hu Y, and SR Nutt. Bending fatigue of hybrid
composite rods. Composites Part: A, 2011. In press.

[19] Ferreira JAM, Costa JDM, Reis PNB, Richardson MOW. Analysis of
fatigue and damage in glass-fibre-reinforced polypropylene composite
materials. Composites Science and Technology 1999; 59: 1461-1467.

[20] Harris B. Fatigue in Composites. CRC Press, 2003; 45-46, 283.

[21] Curtis PT. Tensile fatigue mechanisms in unidirectional polymer matrix
composite materials. International Journal of Fatigue, 1991; 13(5): 377-
382.

[22] Kim HC, Ebert LJ. Fatigue life-limiting parameters in fiberglass
composites. Journal of Materials Science 1979; 14:2616-2624.

[23] Mandell JF, McGarry FJ, Hsieh AJY, Li CG. Tensile fatigue of glass
fibers and composites with conventional and surface compressed fibers.
Journal of Polymer Composites 1985; 6(3):168-174.

[24] Bader MG, Pickering KL, Buzton A, Rezifard A, Smith PA. Failure
micromechanisms in continuous carbon-fiber/epoxy-resin composites.
Compos Sci Technol 1993;48(1–4):135–42.

84
[25] Gamstedt EK, Berglund LA, T Peijs. Fatigue mechanisms in
unidirectional glass-fibre-reinforced polypropylene. Compos Sci Technol,
1999. 59:759-768.

[26] Talreja R. Fatigue of composite materials: damage mechanisms and
fatigue-life diagrams. Proc. R. Soc. Lond. A 1981; 378: 461-475.

[27] Portnov G, CE Bakis. Analysis of stress concentration during tension of
round pultruded composite rods. Composite Structures, 2008. 83: 100-
109.

[28] Woldesenbet E. Finite Element Stress Analysis of Composite Sucker
Rods. Journal of Energy Resources, 2003.

[29] Krishnan A, LR Xu. Effect of the interfacial stress distribution on the
Material Interfacial Shear Strength Measurement. Experimental
Mechanics, 2009.

85
CHAPTER 4. DIAMETRAL COMPRESSION OF PULTRUDED
COMPOSITE RODS

4.1 Abstract

Diametral compression tests were performed on pultruded composite rods
comprised of unidirectional glass or carbon fibers in a common matrix. During
compression tests, acoustic emission (AE) activity was recorded and images were
acquired from the sample for analysis by digital image correlation (DIC). In both
composite systems, localized tensile strain developed in the transverse plane under the
load platens prior to failure, producing non-linearity in the load-displacement curve and
AE signals. In situ SEM diametral compression tests revealed the development of matrix
microcracking and debonding in regions of localized strain, perpendicular to the tensile
strain direction (parallel to the load axis). Comparison of linear finite element
simulations and experimental results showed a deviation from linear elastic behavior in
the load displacement curve. The apparent transverse modulus, in plane shear modulus,
and transverse tensile strength of the GF rod was greater than that of the CF rod, and
fracture surfaces indicated greater fiber/matrix adhesion in the GF system compared to
the CF system. A mixed mode fracture surface showed that two failure modes were
active - matrix tensile failure and matrix compression failure by shear near the loading
edge.
4.2 Introduction
High-voltage composite reinforced conductors (CRCs) generally consist of Al
wires (to carry current) wrapped around a hybrid composite rod (to provide mechanical
support) comprised of a glass fiber (GF) shell and a carbon fiber (CF) core [1-5]. The
advent of CRCs has led to investigations to determine the effect of intense mechanical
86
loads, thermal and moisture exposures on such hybrid composite rods. Overhead
conductors (power cables) must retain load-bearing capability for several decades with
little or no maintenance. As a result, studies have focused on retention of mechanical
properties, particularly longitudinal strength, under aggressive environmental conditions
and loads [2, 3]. Progress has been made to better understand factors affecting the
durability of CRCs, although several fundamental issues have not yet been addressed.
One such issue concerns the effects of stress concentrations and the associated
development of localized strains and modes of failure under complex loading conditions.
For example, mechanical collets are used to attach the composite rods at lattice tower
nodes, and these fixtures achieve traction by applying transverse loads on the rod surface.
Recent studies have shown that transverse loads on the composite core can increase
longitudinal stresses and promote fatigue crack propagation under cyclic tensile loads [5].
However, the effect of transverse loads on the in-plane behavior of pultruded composite
rods is not yet fully understood.
Because of the cylindrical geometry and the intermingling of carbon and glass
fibers in the core/shell design of the hybrid composite rod, accurate measurement of
transverse properties poses difficulties, and conventional composite laminate test
methods cannot be used. Thus, alternative techniques must be considered to measure
transverse properties and understand fundamental behavior in the transverse plane. The
diametral compression test (also known as the Brazilian Disk test) has been used to
measure the hardness and strength of pharmaceutical pills [6], the splitting tensile
strength of rock core and concrete specimens [7-9], and the apparent tensile strength of
brittle materials that cannot be machined into conventional dog bone specimens [10].
87
Because of the simplicity of the test setup, the diametral compression test has also been
used to measure transverse properties of oriented polymeric fibers [11]. Some studies
have shown that flattening the ends of brittle cylindrical disks increased transverse tensile
strength values by altering the modes of failure [12].
The analysis of a cylinder exposed to a concentrated line force applied at opposite
sides is a classical problem for verification of theoretical and experimental methods to
determine the exact state of stress or strain in a structural member [13]. The objective of
this study is to understand the transverse material response of two pultruded composite
rods subject to diametral compression loading. Diametral compression tests were
conducted and the material response was observed and analyzed using acoustic emission
(AE), digital image correlation (DIC), and finite element analysis (FEA). The mode of
failure in the plane was determined by in-situ SEM investigations.
4.3 Experimental Procedure

4.3.1 Materials

Two types of unidirectional composite rods were acquired for diametral
compression testing (Composite Technology Corporation, Irvine, CA). The rods
consisted of unidirectional carbon (CF) or glass fibers (GF) in an epoxy matrix
(proprietary). The two composite rods featured the same epoxy and fibers used for the
core (CF) and shell (GF) of the hybrid composite rod in CRCs. The all-carbon and all-
glass rods (7 mm diameter) were produced by pultrusion, and are shown in Figure 4.1.
The fiber volume fraction was ~70% in both rods, with fiber diameters of ~8 μm (CF)
and ~25μm (GF). Test specimens were cut to a length of 152 mm, the length of
compression platens used in the experiment.
88
4.3.2 Diametral compression and Digital Image Correlation
A mechanical testing machine (Instron 5585) was used to apply diametral
compression to the samples at a loading rate of 0.1 mm/min. The acoustic emission (AE)

technique was employed during the tests to detect signals associated with damage. A
single acoustic emission resonance transducer (300 kHz Micro 30, Physical Acoustics
PCI-2) was placed on each rod to detect acoustic emission activity. Additionally, as each
composite rod was compressed, a microscope was used to record images during loading
to determine true displacements at the cylinder edges, as shown in Figure 4.2(a).
Figure 4.1. Pultruded carbon fiber and glass fiber rods with
common matrix

89
Digital image correlation (DIC) is a non-contact strain measurement technique
that is used to measure non-uniform full-field displacements. To measure in-plane strains,
white and black paint were sprayed in succession onto the rod surface to produce a

random speckle pattern, as shown in Figure 4.2(b). The vertical displacements shown in
Figure 4.2(c) were determined by direct DIC measurements provided inputs for an
Figure 4.2. (a) Keyence microscope and Instron used for DIC, (b) cross section of composite
rod showing black and white random speckle pattern (c) displacement of GF rod at 33 kN

90
analytical solution and a finite element model. Two-dimensional DIC was performed
using commercial software (VIC-2D, Correlated Solution, Inc).
4.3.3 Finite Element Analysis

Finite element analysis was performed to simulate the load-displacement response
and strain distribution during diametral compression tests. A 3D, transversely isotropic,
linear elastic model was developed using measured transverse properties ( , ,
T xy yx
E G ν ),
determined experimentally. The specimens were modeled to represent the geometrical
features of the test setup using exact dimensions from the experiment. Load and
boundary conditions were simulated with FEA software (ABAQUS) using 50,160
elements and a general-purpose brick element (C3D8R). The analysis involved a single
step, in which a vertical displacement (determined via DIC) was applied using an
analytically rigid surface and the reaction load was obtained.
4.3.4 Determination of transverse modulus

Jawad and Ward [14] developed a relationship for transversely isotropic materials
from elasticity theory, relating the apparent transverse modulus (
T
E ) to the vertical
displacement (
y
u ), load (F), length (L) and radius (R) for a diametral compression test:
1
4
0.19 sinh
4
T
y
T
RE L F
u
LE F
π
π
−
   
= +    
   
   
(4.1)

Equation (4.1) is valid when the contact area under the loading platens is much
less than the diameter of the cylinder, and has been used to determine transverse modulus
values for continuous fibers [11], and was used to determine the transverse modulus of
91
the composite rods from experimentally determined load and vertical displacement
values.
4.4 Experimental Results

4.4.1 Transverse behavior

The in-plane behavior and apparent transverse modulus (
T
E ) of each CF and GF
composite rod were determined from diametral displacement(s) and corresponding

load(s). Figure 4.3 (a) shows typical load- crosshead displacement curves for both
composite rods and the amplitude decibel (dB) output for each detected AE hit.
Figure 4.3. (a) Typical load vs. crosshead displacement curves for
the CF (left) and GF rods and (b) Typical peak frequency
distribution for each CF and GF rod
92
Correlation of AE amplitude distributions with different failure modes has been reported
previously [15]. In many cases, authors use the AE amplitude distribution to identify
specific damage mechanisms [15]. The initial, non-linear concave inflection of the curve
is characteristic of Hertzian contact behavior [14]. The first burst of AE emission shown
in the figure corresponds to this initial contact region. After this inflection, the load
response was approximately linear up to failure, at which point the load dropped and a
diametral crack appeared within the plane in both composite rods. Clusters of AE
activity were apparent, showing detection in a dB output range of 30-60 dB, and final
failure producing an output of 80-95 dB, corresponding to the diametral crack and the
load drop. The increase in AE emission behavior before the load drop was an indication
that damage mechanisms were active because the increase in the number of AE events is
usually associated with increased damage [15]. However, it is incorrect to assume that
the all the detected AE hits correspond to active damage mechanisms. The peak
frequencies of the detected AE hits were also determined, and it was found that the initial
peak frequencies for both rods up to the concave inflection point (at lower loads) were
low, between 30-90 kHz. A typical waveform of a detected AE hit before final failure is
also shown at the top of Figure 4.3 (a). The waveform of the indicated hit before final
failure shows a decibel output of 48 dB with a peak frequency of 173 kHz. Figure 3 (b)
shows the maximum frequency distribution for the detected AE hits after Hertzian
contact (post inflection point) and before the final failure AE burst. The majority of these
detected peak frequencies for both composite rods were between 120-240 kHz, a
frequency range which has been shown to be associated with matrix cracking in polymer
composites [16]. Figure 4.2 (c) shows a vertical displacement field (measured by
93
DIC) at ~33 kN for the GF composite rod. The measured DIC surface displacements in
the figure show that the top and bottom regions of each composite surface were displaced
downward because of vertical motion of both platens under the imposed load. The true
displacement (
true
u ) is the difference between the displacement from the top (
top
u ) and
bottom (
bottom
u ) regions of the composite surface, (
true top bottom
u u u = − ). The true
displacement (
true
u ) was determined from successive images recorded at incremental
loads.

Figure 4.4. (a) Load vs. true displacement curve for CF rod, (b) Load vs. true
displacement curve for GF rod (c) Variation of apparent transverse modulus as a
function of true displacement

94
The load versus true displacement (
true
u ) curve is shown in Figure 4.4 (a) and (b)
for both the CF and GF composite rods, indicating different behavior than shown in
Figure 4.3. The curves show three stages of deformation. Stage I represents the initial
Hertzian contact region, while Stage II represents a linear elastic response of each rod.
As both composites deformed in compression, a displacement and load were reached
where inelastic behavior was apparent. The deviation from linearity was not observable
in the load-displacement curves of Figure 4.3, but was consistent with AE data which
indicated active damage mechanisms. The reduction in slope shown in Figure 4.4 (a) and
(b) reflects this behavior and is denoted as Stage III. While the composite rods continued
to deform, the reduction was permanent, although both rods continued to support higher
loads up to the point of failure.
Equation (4.1) was solved numerically for
T
E by inputting an experimental load
value, assuming an initial value for
T
E , and comparing the analytical displacement (
y
u )
with the true displacement (
true
u ) at the given load. Iterations were performed to
minimize error in the value of
T
E and promote convergence between the analytical and
true displacements. Thus, the value of
T
E was adjusted so that
y
u equaled
true
u for a
specific load, shown in Figure 4 (a) and (b) as the analytical solution data.
The adjustment of the apparent transverse modulus for both the CF and GF rods
as a function of true displacement is shown in Figure 4.4 (c). Both curves show an
increase in
T
E for Stage I, with a peak and plateau in Stage II. The steady state value of
T
E occurs in Stage II, where the CF and GF rods had average values of 10.78±0.26 GPa
and 12.8±0.48 GPa respectively. While equation (4.1) is appropriate for determining
95
elastic constants only in the linear elastic region (Stage II), values were determined for
Stage III to quantify the effect of localized damage on bulk transverse properties, as
shown in Figure 4.4 (c). During Stage III,
T
E decreased for both the CF and GF rods, but
the CF rod showed a greater loss in apparent modulus compared to the GF rod (~ 25%
versus ~15% loss) at the end of Stage III (before final failure). Thus, damage
mechanisms caused a reduction in the load-displacement response, with greater
deformation and softening occurring in the CF rod. The transverse behavior of a
composite is typically matrix dependent, but the fiber type and fiber architecture also
contribute to the strength and modulus values. The GF rod showed a slightly greater
apparent transverse modulus than the CF rod with equivalent fiber volume fraction and
matrix. Studies have shown that
T
E increases with an increasing :
f m
E E ratio, and
T
E
also shows a greater dependence at a higher
f
V , where subscripts f and m are fiber and
matrix, respectively [17]. The glass fiber is isotropic, with equivalent longitudinal and
transverse properties that are ~6× greater than the transverse modulus of the transversely-
isotropic carbon-fiber, which contributes to the observed greater
T
E value for the GF rod.
The load-displacement behavior for diametral compression was simulated using a
linear FE model. The transverse property inputs used were the average values of
T
E from
Stage II (10.78 and 12.8 GPa for the CF and GF respectively) for both composite rods as
determined from equation (4.1), and longitudinal properties were used from a previous
paper (5). The load-displacement curves for the FE simulation for each composite rod
are also shown in Figure 4.4 (a) and (b), and simulated curves match the measured curves
within 5% in the linear elastic region (Stage II). The agreement between the
96
experimental and simulation results during Stage II indicate that the diametral
compression test is a suitable method for determining the transverse modulus of
pultruded composite rods. The experiments show deviations from linearity for both
composite rods in Stage III. This bifurcation from linearity was more pronounced in the
CF rod, as the GF rod behaved linearly for a greater portion of the curve.
4.5 Analytical and Computational Results

4.5.1 Localized strain development

During diametral compression, a contact zone developed near the platen edges
where the applied load became distributed over a finite region on the composite surface
[18], which led to the development of in-plane shear and compressive strains. Figure 4.5
(a) shows the development of compressive (
y
ε ) and shear strains (
xy
γ ) near the loading
edges from DIC and FE simulation for the CF composite rod at ~17 kN (Stage II). The
shear strains arise on either side of the diametral line, but are zero along the line (x=0),
and axial-symmetry exists in both DIC and FE contours. The shear stress state at any
point within a cylinder under diametral compression can be determined from [19, 20]:
2 2
2 2 2 2 2 2
2 ( ) ( )
[ ( ) ] [ ( ) ]
xy
P x R y x R y
L x R y x R y
τ
π
  − +
= −
 
+ − + +
 
(4.2)
The shear stress for a given load in the linear elastic Stage II region was
determined for both composite rods using equation (4.2). The (x, y) coordinates and the
measured DIC shear strains (on either side of the diametral line-see Figure 4.5) at each
load value were determined from the contour maps via DIC. The analytical shear stresses
and experimentally measured shear strains at specific loads (in Stage II) were used in
97

combination with Hooke’s Law
xy
xy
xy
G
τ
γ
 
=
 
 
 
to determine the in plane shear modulus.
The values of the in plane shear modulus (G
xy
) were 5.65±1.05 GPa and 6.5±0.96 GPa
for the CF and GF rod, respectively and these values were used as transverse property
inputs in the FE model.
The development of transverse tensile (
x
ε ) and compressive strains can also be
determined analytically. The transverse tensile stress (
x
σ ) and compressive stress (
y
σ ) in
the plane of a cylinder (with a diameter, D) under diametral compression are independent
of material properties and orientation [15], and have been solved by Hertz with the
following distribution along the diametral line (x=0):
2 2 2 1
,
x y
F F F
DL DL L R y
σ σ
π π π
  −
= = −
 
−
 
(4.3)

Although this solution is for a point load, it is appropriate within the transverse plane.
However, disagreement occurs near the rigid boundary contact point, [10] where
Figure 4.5. (a) Compressive and shear strain contours of CF rod from DIC (left) and FEA
analysis (right) under 17kN (b) Compressive strain distribution along diameter line of CF
rod at 17kN

98
analytical solutions are invalid. The stress field formed within the plane is the same for
either plane stress or plane strain conditions [18]. The analytical expressions show that
the transverse tensile stress
x
σ is maximum and constant along the diametral line (x=0),
while at the center of the cylinder (y=0), the compressive stress (parallel to the load
direction) is equal to -3
x
σ and increases towards either loading edge. To determine the
corresponding analytical strains, Hooke’s law was used with a transverse Poisson’s ratio
(
x
yx
y
ε
υ
ε
=− ). The Poisson’s ratio used for the FE model was ~0.69 for both composite
rods. However, significant variation was evident, with values ranging from 0.40-0.69 for
both the CF and GF rods determined at various loads (in Stage II) and was markedly
higher from typical values of 0.21-0.28 [5]. Under pure transverse compression tests, the
initial Poisson’s ratio was 0.3-0.4, and with increasing load this value reached 0.6-0.7,
due to micromechanical behavior including debonding between fiber and matrix. There
have also been reports of Poisson’s ratio values equal to 0.66 for unidirectional
composites with high volume fraction of fibers [26].
The FE simulations were performed using measured transverse properties
( , ,
T xy yx
E G ν ), and Figure 4.5 (b) shows the compressive strain distribution along the
diametral line (x=0) up to the loading edge. Simulations were also performed at a lower
transverse Poisson’s ratio (see Figure 4.5 (b)). The strain distributions from DIC, FE
(
yx
υ =0.21 and 0.69), and analytical compressive strains at ~17 kN (Stage II) are shown
for the CF rod. The results in Figure 4.5(b) show that compressive strain was greatest
just under the loading edges. The large compressive strains showed a weak dependence
99
on the Poisson’s ratio, as the compressive strain simulation for
yx
υ =0.21 was similar to
the simulation for
yx
υ =0.69 along the diametral line.
The transverse tensile strain distribution determined from DIC at a load of 23 kN
(Stage II) is shown in Figure 4.6 (a) for the GF composite rod. Figure 4.6 (b) shows the

distribution of transverse tensile strains extending vertically from the center of the rod,
approaching the rod edges for the DIC measurement, the FE simulation, and the
analytical solution. The results show that the most intense transverse tensile strain occurs
in a region ½ mm below the contact points. However, the tensile strains were roughly
constant along the diametral line when a Poisson’s ratio of 0.21 was used (under the same
load). Tensile strain concentrations occurred in both composite rods under the loading
edges as a result of localized debonding and microcracking. These cracks formed by
transverse tension, caused by the high compressive strains under the loading edge,
Figure 4.6. Transverse tensile strain contours from DIC for GF rod at 23 kN, (b)
transverse tensile strain distribution along diameter line for GF rod
100
leading to a high
x
y
ε
ε
− ratio measurement. The transverse Poisson’s ratio input of 0.69
for the FE model characterizes this localized strain effect. The measured (DIC) and FE
transverse strain distribution both show high strain values (~1%) in a localized region.

Figure 4.7 shows the evolution of tensile strain (measured by DIC) in the CF rod
as a function of applied load along the diametral line. At higher loads in Stage III, the
tensile strain concentration increased significantly and became more localized under the
platen edge, up to 2%. In situ SEM diametral compression tests were performed on CF
Figure 4.7. Transverse tensile strain evolution in CF rod from DIC, formation of
microscopic crack perpendicular to tensile strain direction in the strain concentration
region

101
samples to determine if and where damage mechanisms occurred during Stage III.
Evidence of microcracking and debonding that led to the observed weakening in Stage III
under the loading edges is shown in the SEM image. The localized
x
ε strain
concentrations were a result of the development of matrix microcracks along the
fiber/matrix interface, extending perpendicular to the direction of the concentrated
transverse tensile strain (parallel to the loading axis). These microscopic damage
mechanisms coincided with the early AE activity shown in Figure 4.3, and are consistent
with studies indicating that lower amplitudes correspond with matrix cracking [21]. The
onset of Stage III shown in Figure 4.4 reflects the development of multiple matrix
microcracks and high tensile strain concentrations in both composite rods. The top and
bottom regions of the cylinder in Figure 4.6 and 4.7 show the distribution of transverse
tensile strain was localized, indicating that the bulk of the material in the plane continued
to deform elastically (without microcracks) until final failure.
4.6 Discussion

The centers (x=0, y=0) of both composite rods were exposed to a biaxial stress
state of transverse compression and transverse tension in the linear elastic region. It has
been shown that the apparent transverse tensile strength (TTS) (using equation (4.3) and
the load at failure) measured by diametral compression is expected to be approximately
equal to the uniaxial transverse tensile strength of pultruded composite rods [22]. This
assertion relies on the assumption that failure initiates from the rod center. For
comparative purposes, the apparent TTS values (from an average of 5 samples) for the
CF and GF composite rods were 21.62±0.66 MPa, and 23.96±0.85 MPa respectively.
The transverse compressive stress is three times the tensile stress at the rod center, and
102
increases significantly near the loading edges. These high transverse compressive
stresses lead to transverse tensile strains, contributing to the formation of localized
microcracking and debonding under the loading edges in the tensile direction. This form
of tensile damage indicates that compressive stresses will reduce the nominal tensile
stress to cause failure because of induced initial tensile strains. Thus, the apparent TTS

Figure 4.8(a) Diametral crack in GF and CF rod at failure with angled fracture near
loading edges (b) Fracture morphology showing bare CF fibers and residual glass
fiber/matrix adhesion.

can be a useful global indicator of relative transverse tensile strength among different
composite rods (with different diameters and fiber types), but is a conservative estimate
of TTS since the loading geometry forces a biaxial stress state, where the transverse
compressive stress contributes to transverse tensile failure.
103
Microcrack coalescence led to a macroscopic crack along the diametral line (at
the failure load) with a corresponding peak in AE activity, as shown in Figure 4.8 (a) for
the GF rod and CF rod. Final failure was confined to the central region of the cylinder,
and was brittle and catastrophic in nature; causing an instantaneous drop in load. Figure
4.8 (b) shows the deflection of the crack at an angle near the loading edges. Figure 4.5 (a)
and (b) showed that both shear and compressive strains develop on either side of the
diametral line, and this corresponded to the region where crack deflection occurred. The
initial microcracking in the composite rods was governed by the principal direction of
tensile strain, and final failure occurred along the diametral line where tensile stresses and
strains were the highest. Since this was the only form of localized damage occurring
before final failure, the orientation of the shear fracture planes depended on the shear (τ )
and normal (σ ) tractions, (obtained from the components of the stress tensor at failure)
and fracture angle at a specific point, as discussed in [23]. Since the fracture angle was
no longer perpendicular to the tensile direction, the fracture criteria changed, and showed
similar failure angles produced by pure transverse compression [24]. Crack angles under
transverse compression can be greater than 45º because failure occurs on a plane where
the shear traction (τ ) reaches a critical value that is dependent on the normal
compressive traction (σ ) based on the Mohr-Coulomb criteria [24, 25]. Thus, mixed
mode final fracture was observed, showing both matrix failure by tension along the
diameter and shear failure due to dominant compressive and shear traction near the
loading edges.
Figure 4.8 (b) shows the fracture surfaces of the GF and CF rod in the
longitudinal direction. The CF surface reveals bare fibers with little residual matrix
104
attached, and regions of pure matrix with no fibers, indicating complete fiber-matrix
separation. The GF fracture surface shows some residual adhesion of matrix to fibers,
and some fibers embedded in the matrix. The fiber-matrix bond strength strongly
affected the transverse behavior of the composite rods. The fracture surfaces indicated
that the fiber/matrix bond in the CF rod was more prone to separation under transverse
conditions when compared to the GF rod, and this was reflected in lower transverse
modulus, strength values, and fractography. The mechanisms of interfacial bond strength
depend primarily on the chemical bond and reactivity between fiber and matrix. Sizing
coupling agents are applied to fiber surfaces as a means to provide a chemical link
between the fiber and matrix, where co-reactivity of the sizing agent with both the fiber
and matrix through covalent bonds produces molecular continuity [26]. The mechanisms
of interfacial bonding of carbon fibers and polymer matrices have complications
primarily caused by the high reactivity and absorbing nature of the carbon fiber surface
[27]. However, such coupling agents used on the fibers in this study are proprietary, so
the exact chemical cause for the higher degree of adhesion in the GF composite rod over
the CF composite rod is speculative, and requires analysis that is beyond the scope of this
work.
4.7 Conclusions

Diametral compression tests were performed on CF and GF pultruded composite
rods to determine the effect of transverse loads on in-plane behavior and the GF
composite showed greater resistance to transverse deformations and fracture than the CF
rod. DIC was used to capture displacement and strain, and inelastic behavior was
observed through changes in the load-displacement curve. The distribution of strains in
105
the transverse plane of the composite rod showed a region of localized tensile strains
under the loading edges which resulted from the formation of matrix microcracks and
debonding. These cracks caused a reduction in load-bearing capability of both rods.
Final failure occurred along the diameter, as a crack formed parallel to the direction of
applied load, with shear failure near the loading edges.
While service loads will produce stress and strain conditions more complex than
those considered here, the results provide insights into basic transverse behavior and
development of associated damage mechanisms. The diametral compression test
combined with DIC provides a means to directly measure transverse and in plane shear
modulus, while in previous studies, an adapted Eshelby model was used to provide
estimates of these properties [28, 29]. Although approximations of material properties
are often useful to provide engineering estimates, accurate property measurements in both
the transverse and longitudinal directions are preferable for predictive modeling of
component durability and lifetime. The deformations produced in this study were
relatively simple, but yielded combined fracture modes, an indication of the complexity
of composite fracture mechanics.
The findings presented here have implications for the intended application of such
rods in overhead conductors (CRCs), which generally feature a GF shell around a CF
core. The primary purpose of the GF shell of the rods is to prevent galvanic coupling
between the CF core and the over-wrapped Al wires [4]. Attaching the conductors to
lattice towers requires collet fixtures that grip the composite rods. In doing so, the collets
introduce contact and transverse loads that include simple diametral compression, but
generally are more complex. The well-documented susceptibility of unidirectional
106
composites to surface wear and transverse crack damage may dictate measures to
mitigate stress concentrations, or consider alternative fiber architectures to provide
greater resistance to surface damage from localized stresses resulting from such grips.

107
Chapter 4 References

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composite rods. Composites Part A 2011; 42(3): 328-336.

[2] Barjasteh E, Bosze EJ, Nutt SR. Thermal aging of fiberglass/carbon-fiber
hybrid composites. Comp A 2009; 40(12): 2038-2045

[3] Tsai YI, Bosze EJ, Barjasteh E, Nutt SR. Influence of Hygrothermal
environment on thermal and mechanical properties of carbon fiber/fiber
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[4] Bosze EJ, Alawar A, Bertschger O, Tsai YI, Nutt SR. High-temperature
strength and storage modulus in unidirectional hybrid composites. Comp
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[5] Kar NK, Hu Y, Barjasteh E, Nutt SR. Tension tension fatigue of hybrid
composite rods. Composites: Part B, 2012, in press.

[6] Cartensen, JT. Pharmaceutics of Solids and Solid Dosage Forms. John
Wiley and Sons, New York 1977.

[7] Standard Test Method for Splitting Tensile Strength of Intact Rock Core
Specimens. ASTM D3967-86. 10 pp 504-506.

[8] Mellor, M and Hawkes I. Measurement of tensile strength by diametral
compression of discs and annuli. Engineering Geology 1971; 5(3): 173–
225.

[9] Hudson, J A, Brown, E T and Rummel, F. The controlled failure of rock
discs and rings loaded in diametral compression. International Journal of
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[10] Procopio AT, Zavaliangos A, Cunningham JC. Analysis of the
diametrical compression test and the applicability to plastically deforming
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[11] Singletary J, Davis H, Song Y, Ramasubramanian MK,, Knoff W. The
transverse compression of PPTA fibers. Journal of Materials Science
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[12] Fahad MK. Stresses and failure in the diametral compression test. Journal
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108
[13] Tokovyy YV, Hung KM, Ma CC. Determination of stresses and
displacements in a thin annular disk subjected to diametral compression.
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[14] Jawad SA, Ward IM. The transverse compression of oriented nylon and
polyethylene extrudates. Journal of Materials Science 1978; 13(7):1381-
1387.

[15] Barre´ S, Benzeggagh ML. On the use of acoustic emission to investigate
damage mechanisms in glass-fibre reinforced polypropylene. Composites
Science and Technology 1994; 52: 369-376

[16] Groot PJ de, Wijnen PAM, Janssen BF. Real time frequency
determination of acoustic emission for different fracture mechanisms in
carbon/epoxy composites. Composites Science and Technology 1995;
55:405-412.

[17] Kaw, AK. Mechanics of Composite Materials. Second Edition, CRC
Press, 2006; 223-224.

[18] Liu C, Lovato ML. Elastic constants determination and deformation
observation using brazilian disk geometry. Proceedings of the XIth
International Congress and Exposition. Society for Experimental
Mechanics 2008.

[19] Timoshenko SP, Goodier JN. Theory of Elasticity. McGraw-Hill, New
York, 1970.

[20] Frocht MM. Photoelasticity. John Wiley and Sons, New York, 1947.

[21] Berthelot JM, Rhazi J. Acoustic emission in carbon fibre composites.
Composites Science and Technology 1990; 37: 411-428.

[22] Chisholm JM, Hahn HT, Williams JG. Diametral compression of
pultruded composite rods as a quality control test. Composites 1989;
20(6): 553-558.

[23] Pinho ST, Iannucci L, Robinson P. Physically-based failure models and
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kinking: Part I: Development. Composites Part A 2006; 37(1): 63-73.

[24] Gonzalez C, LLorca J. Mechanical behavior of unidirectional fiber-
reinforced polymers under transverse compression: Microscopic
mechanisms and modeling. Composites Science and Technology 2007;
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109
[25] Collings, TA. Transverse compressive behaviour of unidirectional carbon
fibre reinforced plastics. Composites 1974; 5(3): 108-116.

[26] Koenig JL, Emadipour H. Mechanical characterization of the interfacial
strength of glass reinforced composites. Polymer Composites 1985, 6:
142-150.

[27] Kim JK, Mai YW. Engineered Interfaces in Fiber Reinforced Composites.
Elsevier Science 1998; 170-180.

[28] Burks BM. Short-term failure analysis of aluminum conducting
composite core transmission lines. Master’s Thesis, University of Denver
2009.

[29] Burks B, Armentrout D, Kumosa M. Characterization of the fatigue
properties of a hybrid composite utilized in high voltage electric
transmission. Composites: Part A 2011; 42:1138-1147.

110
CHAPTER 5. NON-UNIFORM RADIAL DEFORMATION OF HYBRID
COMPOSITE RODS

5.1 Abstract

Hemispherical anvil compression tests were performed on a hybrid composite rod
comprised of a unidirectional glass fiber shell (GF) and a carbon fiber core (CF) in a
common matrix. During compression tests, acoustic emission (AE) activity was recorded
and images were acquired from the sample for analysis by digital image correlation
(DIC). Prior to local crack formation, a biaxial strain state developed in the CF core,
while shear and localized strains formed in the GF shell. Finite element simulations and
experimental results showed stress concentrations developed near the anvil corners.
Dynamic microscopy revealed initial sites of matrix microcracking via shear in the GF
shell, and debonding at the GF/CF interface. Crack initiation coincided with a rise in AE
activity and DIC strain contour localization. Macroscopic “V” cracks formed where the
composite was unconstrained and underwent lateral expansion. The experiments
revealed that anchor design features caused crack initiation. An alternate anchor design
was proposed that produced uniform radial compression. The resulting compressive
stresses did not exceed the Mohr-Coulomb failure criterion and would reduce the
likelihood of surface cracks in composite rods used in overhead conductors.
5.2 Introduction
Polymer matrix composites are increasingly utilized as primary load-bearing
components in civil infrastructure applications. As one example, unidirectional glass
composite rods have been used as suspension and tension insulators for overhead power
lines in place of conventional ceramic insulators [1, 2]. Called non-ceramic insulators
(NCIs), these products are simple unidirectional fiberglass rods of high strength and low
111
density. In a second example, a pultruded hybrid composite rod comprised of a CF core
and a GF shell has been developed to replace the strength member (steel cable) in
traditional overhead conductors (called ACSR, for aluminum conductor steel reinforced).
The composite reinforced conductor, called ACCC, for aluminum conductor-composite
core, features superior strength, greater ampacity, and low sag at high temperatures [3-6].
A primary concern for the replacement of conventional insulators and ACSR conductors
with composite reinforcement is the damage tolerance and long-term durability of the
composite. While these composites are designed for superior mechanical properties in
the longitudinal direction, transverse properties are poor, and thus excessive transverse
loads combined with various service conditions can cause premature cracking and even
catastrophic failure [7].
Durability studies on all-glass composite rods used in suspension insulators and
hybrid rods used in composite reinforced conductors have shown susceptibility to
damage. Reported failures for suspension insulators in service have shown that cracks
originated where mechanical anchors were used to grip and attach the composite to other
structural components [8]. These cracks propagated with time and significantly reduced
the lifespan of the structure. Mechanical anchors are used to transfer applied load to the
composite via transverse displacements and surface traction. Previous durability studies
on hybrid composite rods have shown that the transverse displacements play a critical
role in fatigue life [9, 10]. Significant fretting and surface wear of the glass fiber shell
initiated transverse cracks, which then propagated to the GF/CF interface, with
subsequent longitudinal propagation. Fatigue life was extended by introducing a
compliant sleeve within the anchor to mitigate friction and wear.
112
In service, the anchor design is used to maintain tensile load on the conductor and
attach it to the lattice tower. A mechanical wedge is placed at dead ends and splices to
hold the hybrid composite rod in tension. However, there have been no reports of efforts
to characterize the effects of such anchors on deformation in the transverse plane and the
relation to premature failure. The objective of this study is to understand deformation in
the transverse plane of a hybrid composite rod using hemispherical anvils to apply a non-
uniform radial displacement on the glass fiber shell. Digital image correlation (DIC),
acoustic emission (AE), and finite element simulations are used to analyze the behavior
under increasing non-uniform transverse loads. Finally, measures are proposed to
minimize concentrations for in-service applications based on the results.
5.3 Experimental Procedure
5.3.1 Materials
Hybrid unidirectional composite rods were acquired for hemispherical anvil
compression testing (Composite Technology Corporation, Irvine, CA). The rod consisted
of unidirectional carbon fibers (CF) and glass fibers (GF) in an epoxy matrix (proprietary
formulation). The composite rod featured the same epoxy and fibers used for the core
(CF) and shell (GF) of the hybrid composite rod deployed in the ACCC. The rod (7 mm
diameter) was produced by pultrusion, and is shown in Figure 5.1 (a). The fiber volume
fraction was ~70% in both the CF core and GF shell, with fiber diameters of ~8 μm (CF)
and ~25μm (GF). Test specimens were cut to a length of 11 mm, the length of
hemispherical anvils used in the experiment.

113

Figure 5.1. (a) Hybrid composite rod after compression showing “V” cracks” near
anvil gap, (b) Keyence microscope and Instron used for DIC, (c) cross section of
composite rod showing black and white random speckle pattern

5.3.2 Non uniform compression and digital image correlation
A mechanical test machine (Instron 5567) was used to apply compression to the
anvils at a loading rate of 0.1 mm/min. Custom-made hemispherical anvils were
produced to replicate surface displacements that are applied to composite rods by
mechanical anchors at dead ends and splices while in service, as shown in Figure 5.1. The
acoustic emission (AE) technique was employed during the tests to detect damage events
and mechanisms. A single acoustic emission resonance transducer (300 kHz Micro 30,
Physical Acoustics PCI-2) was positioned and attached on the compression platen to
detect acoustic emission activity, shown in Figure 5.1 (b). Additionally, a microscope
was used to record images during loading, from which true displacements and strains
within the transverse plane were determined.
Digital image correlation (DIC) is a non-contact strain measurement technique
used to measure non-uniform full-field displacements [11, 12]. The technique involves
mathematical tracking of patterns (pixels) from successive images. In-plane strains were
measured by applying a black and white speckle pattern on the rod surface, as shown in
Figure 5.1 (c). The strains were calculated from in-plane displacements using
114
commercial software (VIC-2D, Correlated Solutions, Inc). For suitable resolution and
reliable results, a proper subset size (49 pixels) and step size (5 pixels) were selected, and
these conditions were sufficient to produce a satisfactory unique speckle pattern.
5.3.3 Finite Element Analysis
The deformation behavior was simulated using a plane strain 2D quarter circle
with 4768 linear quadrilateral (CPE4R) and triangular elements (CPE3) (Abaqus,
Simulia). Elastic properties used were E
T
= 11 and 13 GPa for the carbon and glass
systems respectively, with a Poisson’s ratio of ~0.40. The transverse plane was modeled
as a continuum. The Mohr Coulomb failure criterion was implemented because failure of
unidirectional composite systems under pure transverse compression was shown to be
greater than 45 degrees, and transverse compression strengths (TCS) were greater than
the transverse tensile strengths (TTS) in both composite systems [13-15].
The Mohr-Coulomb criterion assumes failure takes place when the shear stress
(τ ) acting on a specific plane reaches a critical value that depends on the normal stress
(σ ) acting on the same plane [13]. The parameters necessary to characterize the failure
criterion are cohesion (c), which is the transverse shear strength under a pure shear stress
state, and the friction angle (φ ), which is related to the failure angle (= (φ +90)/2) under
pure transverse compression. The cohesion and friction angle were measured from
transverse compression tests on cuboids cut from GF and CF composite rods, where TCS
and (φ ) were measured directly, and c was determined from Equation (1).
cos
2
1 sin
TCS c
φ
φ
=
−
(5.1)

115

Figure 5.2. (a) Non uniform radial displacement boundary condition on GF shell (b)
uniform radial displacement boundary condition on GF shell

The cohesion values used were 32 and 29 MPa for the GF and CF systems,
respectively, and both composite systems featured an equal friction angle of 30 degrees.
Because the behavior was modeled as a continuum, the failure criterion was simply used
as an indicator of damage to show whether a prescribed boundary condition caused a
local stress state to exceed the elastic limit of the material, not to model post-failure
behavior under the prescribed loading condition.
A non-uniform radial displacement (U
r
) boundary condition was applied as shown
in Figure 5.2(a), where G is the horizontal displacement (mm) measured via DIC, and J is
related to the maximum vertical displacement (mm) measured by DIC at a given load.
The boundary condition was applied only to a segment of the GF shell, to simulate the
implications of the anvil spacing. Because of axial symmetry, the J value used in the FE
model was calculated from the difference between the vertical displacement from the top
(
top
V ) and bottom (
bottom
V ) regions of the composite surface, (
2
top bottom
V V
J
−
= ). The
displacement fields were determined from successive images recorded at incremental
116
loads during the non-uniform compression tests. The FE strain distribution under a
specified boundary condition was compared with the strain fields determined from DIC.
5.3.4 Elastic solution to uniform radial boundary condition
As a means to reduce the stress concentrations caused by the anvil design, the
deformation of the composite rod to a uniform radial boundary condition was also
determined, with proposed boundary conditions shown in Figure 2(b). Because the
problem is axisymmetric, no shear stresses or strains existed in the (r,θ) coordinate
system.
Radial displacement and stress continuity were assumed at the interface, where U
r

is the radial displacement and
r
σ is the radial stress for the CF and GF system
respectively. Because the boundary condition is uniform, a closed-form solution for
strain existed, where the strain-displacement equations for an axial symmetric response
are ,
r r
r
dU U
dr r
θ
ε ε = = . Combined with Hooke’s Law and the equilibrium equation in
the radial direction ( 0
r r
d
dr r
θ
σ σ σ −
+ = ), a linear ordinary differential equation was
solved for the radial displacement, with the following solution:
2
2 2
, 0
,
1
0

0
r r r
GF
r GF GF C
r CF CF C
d U dU U
dr r dr r
B
U A r R r R
r
U A r r R
+ − =
= + ≤ ≤
= ≤ ≤
(5.2)

where the constants A, B were determined from the boundary conditions shown in Figure
5.2(b). From the radial displacement distribution, the strain distribution was determined
and compared with FE results.
117
5.4 Results and Discussion
5.4.1 In-plane deformation
The deformation behavior of the hybrid composite rod under hemispherical anvil
compression was determined from in-plane displacements and the applied load. Figure
5.3 shows a typical load-crosshead displacement curve and the cumulative number of
detected AE hits superimposed under the curve. The plot shows that AE activity was
negligible until a load of 11~12 kN was reached, after which the number of AE hits
increased sharply, an indication that damage mechanisms were active [16]. The behavior
in Figure 3 shows no catastrophic loss in load-bearing capability, although there is
significant AE activity above a critical load and displacement.

Figure 5.3. Typical load vs. crosshead displacement curve for the hybrid composite rod
with AE hits overlaid

118

Figure 5.4. (a) Vertical displacement contour of composite rod under ~7 kN, (b)
Horizontal displacement contour of composite rod at ~7 kN

Figure 5.4 (a) and (b) show the displacement field (measured by DIC in
rectangular coordinates) at ~7 kN (prior to damage initiation) for the hybrid composite
rod. DIC measurements were obtained before the burst in AE, to understand the
deformation process prior to damage initiation. The constraint imposed by the
hemispherical anvils forced the circular cross section to deform to an elliptical shape, as
indicated by the displacement contours, producing distortional stresses. The DIC
displacements in Figure 5.4 (a) show that the top and bottom regions of the composite
surface were displaced vertically because of the movement of both anvils under the
imposed compressive load. The anvil spacing allowed expansion of the composite rod in
the x-direction as shown in Figure 5.4 (b), with compression occurring in the x direction
near the top and bottom regions of the anvils.
Figure 5.5 shows the strain fields determined from DIC and FE analysis (using the
assumed boundary conditions) at an applied load of ~7 kN. The simulation contours
119

Figure 5.5. Strain contours from DIC (top) and FEA analysis (bottom) at ~7kN

were validated by the measured contours, as the DIC and the FE plots show similar
trends. Slight variations in the experimental data (particularly the shear strains) can be
attributed to geometric non-uniformity of the anvil boundary, microstructural variations,
and/or the accuracy of the correlation technique. The anvil surface undoubtedly induced
non-uniform displacements, and this was most likely the cause for contour variation.
However, heterogeneity in strain contours determined by DIC has also been attributed to
microstructural variations [17]. Nevertheless, the contour plots show similar behavior,
where large negative compressive strains (
y
ε ) of 2-3% developed in the central region of
the composite rod, and these strains decreased near the rod edges where there was no
constraint. Conversely, large positive tensile strains (
x
ε ) of 1-1.5% developed in the
central region and decreased toward the edges. A biaxial state of strain was produced
within the CF core in response to the non-uniform loading conditions (prior to failure).
Shear strains (
xy
γ ) arose near the top and bottom portions of the GF shell, as well as at
120

Figure 5.6. Stress contours from FEA showing concentrations near anvil corners

the corners of the hemispherical anvils, as shown in Figure 5.5 (see red arrows). Thus,
the CF core was strained biaxially, while the GF shell underwent shear strain. Both
FEA and DIC contours showed strain localization at the anvil corners, where contact
between the anvils and the composite rod ceased (indicated by red arrows in Figure 5).
This transition point played a major role in the formation of localized stresses in the GF
shell, which influenced the way cracks formed in the composite.
Figure 5.6 shows the stress fields before the rise in AE activity, as determined
from the FE model using the same boundary conditions from Figure 5.5. The results
indicate that the CF core developed compressive (
y
σ ) and tensile stresses (
x
σ ) of -200
MPa and 45 MPa in the central core, and severe stress concentrations arose at the anvil
corners, where biaxial tensile stresses (
x
σ =240 MPa,
y
σ =160 MPa) were produced,
along with a shear stress component. The highest stress state was produced at these
loading edges, providing an indicator of where damage was likely to initiate. Light
microscopy was performed dynamically, and images of a polished cross section were
recorded as the compressive load was increased.

121
5.4.2 Observation of Failure and Microcracking
Figure 5.7 (a) shows deformation of the composite rod near one of the anvil edges
at loads between 7kN and 20 kN, and the corresponding strain contour development
(DIC) is shown in Figures 7(b)-(d). As the load was increased, the composite rod showed
symmetric lateral expansion about the centerline, and the GF shell was pushed against the
hemispherical anvil edges. Damage and failure initiated near the anvil corners, where the
unconstrained region of the GF shell expanded laterally as the anvil descended, at an
applied load of ~11-12 kN. DIC shows the onset of strain localization at the anvil
corners, resulting in failure at these locations. The DIC technique cannot be used as a
measure of true strain after failure because crack initiation and propagation in the plane
distorts the speckle pattern and thus the associated displacements, causing the software to
indicate regions of abnormally high strain (over 5%).

Figure 5.7. (a) Deformation, shear crack initiation and (b)-(d) strain localization as a
function of applied load (GIF animation)
122
The abnormal “strains” detected were caused by localized cracking near the anvil
corners, and were not an indication of true strain. However, these strain localizations
were used as a means to detect damage in the composite rod by showing significant
changes in strain contour behavior.
The rise in AE activity shown in Figure 5.3 was a result of shear microcracks in
the epoxy matrix and debonding along fiber/matrix interfaces. Symmetric shear cracks
formed a “V” pattern about the GF/CF interface, as shown schematically in Figure 5.1(a).
The crack angle (30~40º measured from the vertical) was an indication that failure
initiated when the shear stress on the failure plane reached a critical value. Figure 5.8
shows a detailed SEM image of the GF/CF interfacial microstructure with “V” shaped
matrix microcracking.

Figure 5.8. Shear crack propagation to GF/CF interface

123
Figures 5.7 and 5.8 indicate that debonding occurred as microcracks propagated to the
GF/CF interfacial boundary, with limited propagation into the CF core.
The results of this analysis have implications for the anchor design used in
overhead conductor cables. In previous studies, longitudinal fatigue cracks initiated
within the mechanical collet, primarily due to the fretting behavior of the collet on the GF
shell [9]. However, GF surface cracks were also observed as a result of the collet design,
shown in Figure 5.9 (a), which featured similar diametrically opposed gaps to ensure
sufficient compression to prevent slip. While the stress state of the composite rod within
the mechanical collet is different than from hemispherical anvil compression (because of
both axial and transverse loads), the formation of surface cracks is a result of the anvil
spacing. These longitudinal cracks along the surface of the GF shell exhibited the same
pattern as those shown in Figure 5.9 (b), and resulted from the non-uniform clamping of
the GF surface and the stress concentrations near the anvil corners. A more uniform
radial displacement boundary condition, described below, prevents such stress
concentrations.

Figure 5.9. (a) Longitudinal surface crack formation from inside the mechanical
anchors, (b) similar surface crack formation from hemispherical anvils

124
5.4.3 Uniform Radial Displacement
The deformation of the hybrid composite rod subjected to a uniform radial
displacement was investigated using an elasticity solution and FE model. Figure 5.10 (a)
shows the contour plot that results from a uniform radial displacement equal to the
vertical displacement (J) used in Figures 4 and 5. Equal compressive strains (-1.7%) and
stresses (-664 MPa) form within the carbon fiber core, where and
r r θ θ
ε ε σ σ = = . The
GF shell withstands compressive stresses, although a discontinuous jump in both
θ
σ
and
r
ε occurs at the GF/CF interface. The GF shell exhibits small variations in
both
r
σ and
θ
σ , with the greatest difference between the two stresses occurring at the
GF/CF interface. The strains resulting from the elasticity solution and the FE model differ
by less than 10% and show strain discontinuity (
r
ε ) at the GF/CF interface. Because the
composite rod was fully constrained, no positive strains or stresses developed in the
transverse plane. The rod remained circular in cross section, with negligible deformation
in the transverse direction.
Figure 5.10 (b) shows the stresses in the x and y directions after a rectangular
coordinate transformation. Equal compressive stresses develop in the CF core, and
unequal compressive stresses in the GF shell exist in both the x and y directions, with
discontinuities at the GF/CF interface. Maximum shear occur at an angle of 45 degrees
from the rod center. This can be explained by the coordinate transformation equation:
( )sin cos
xy r θ
τ σ σ θ θ = − (3)
which shows that shear stresses were maximized when a difference in
r
σ and
θ
σ was
greatest (at the GF/CF interface) and when θ equaled 45 degrees. These stress and strain
125

Figure 5.10. (a) Radial and circumferential stress distribution under uniform
compression with associated strain distribution, (b) in plane stress distribution after
coordinate transformation

discontinuities were a result of the transverse modulus mismatch between the CF core
(~11 GPa) and the GF shell (~13 GPa). The elastic mismatch led to shear stresses at the
interface. The analysis shows that under a uniform radial displacement condition,
compressive stresses/strains form, with no stress concentration development.
The Mohr Coulomb failure criterion was employed in the FE model as a means to
identify regions where the elastic limit was exceeded, a result of local stress conditions in
the transverse plane. Because the material was modeled as a continuum, the occurrence
of plastic strain was used to indicate regions of damage. The FEA simulation in Figure
11 (a) shows that plastic strains developed under non-uniform loading conditions in the
regions where shear matrix cracks were observed (see Figure 5.7). The simulation also
shows that localized plastic strain arose at a relatively low applied load (2-3 kN),
although localized damage was not detected using DIC until higher loads were reached

126

Figure 5.11. (a) Plastic strain (damage) accumulation under non-uniform radial
compression (b) no damage accumulation under uniform radial compression

(11-12 kN), at which point matrix cracks propagated and generated significant AE
activity, as discussed previously.
The development of plastic strain in Figure 5.11 shows that material strength
variation (TTS, TCS) in the transverse plane of unidirectional composite rods can lead to
localized damage, and that damage accumulates with increasing loads. Clearly,
alternative gripping techniques are necessary to prevent such micromechanical damage
from occurring. Applying the Mohr Coulomb failure criterion under uniform radial
conditions (Figure 5.11 (b)) shows no development of plastic strain, an indication that no
damage mechanisms are active when only compressive states of stress and strain exists in
the transverse plane. Unidirectional composites under hydrostatic stress states have been
shown not to fail, and under biaxial transverse compression, composites have been shown
to withstand transverse compression stresses 4× the TCS before failure [18]. Thus, new
127
anchor designs must be developed that can sustain service loads of overhead conductors
without compromising the structural integrity of the composite core.
5.5 Conclusions
Compression tests were performed on a hybrid composite rod using hemispherical
anvils to determine the effects of non-uniform loading on transverse plane behavior. DIC
was used to capture displacement and strain, and damage mechanisms were observed
through changes in the strain contours that occurred simultaneously with bursts in AE.
Before damage initiation, localized (shear) strain concentrations developed in the GF
shell near the anvil corners, while primarily biaxial strains developed in the CF core. The
distribution of strains in the transverse plane of the composite rod shifted when failure
began, and regions of large localized strains resulted from shear matrix microcracks that
formed near the anvil corners. The lack of constraint caused the composite to expand
against the anvils, initiating longitudinal cracks in the GF shell. The in-plane shear failure
that occurred near the anvil corners was dictated by the Mohr Coulomb failure criterion.
The results provided insight into the material response to stress concentrations
and development of associated damage mechanisms for unidirectional composite rods.
The hemispherical anvil compression tests simulated the loads and associated stresses
resulting from hardware used in the utility industry to grip composite rods in overhead
conductors. To mitigate stress concentrations and prevent crack initiation/propagation
resulting from such hardware, an alternative gripping method was proposed. The method
yields uniform radial displacements and reduces stress concentrations. These factors
reduce the risk of crack initiation and failure in the composite rod, and thus enhance
component durability.
128
The findings presented here have implications for the intended application of
composite rods in overhead conductors. Attaching the conductors to lattice towers
requires anchors that grip the composite rods, and the method of gripping can influence
crack growth and propagation. Crimped end fittings are widely used to attach composite
insulators to structures, primarily because of the low-cost design and roughly uniform
radial loading [8]. However, in recent years, fiber-reinforced tendons used in anchorage
systems for mooring platforms and bridges feature a thin inner sleeve of ductile metal to
distribute the radial loads more uniformly around the tendon and to protect the composite
from damage [19]. The susceptibility of unidirectional composites to damage from
concentrated transverse loads also highlights the need to consider alternative fiber
architectures for composite reinforced conductors, particularly for the outer shell, where
damage initiates. Designs with greater resistance to damage from transverse loading will
improve long-term durability, although possibly at the expense of axial properties and
processing ease. Exploring such tradeoffs is likely to lead to an optimized design that
will accelerate acceptance and adoption by power utilities.

129
Chapter 5 References
[1] Kumosa M, Narayan HS, Qiu Q, Bansal A. Brittle fracture of non-
ceramic suspension insulators with epoxy cone end fittings. Composites
Science and Technology 1997; 57: 739-751.

[2] Owen MJ, Harris SJ, Noble B. Failure of high voltage electrical insulators
with pultruded glass fibre-reinforced plastic cores. Composites 1986;
17(3): 217-226.

[3] Bosze EJ, Alawar A, Bertschger O, Tsai YI, Nutt SR. High-temperature
strength and storage modulus in unidirectional hybrid composites. Comp
Sci Tech 2006; 66(13): 1963–1969.

[4] Tsai YI, Bosze EJ, Barjasteh E, Nutt SR. Influence of Hygrothermal
environment on thermal and mechanical properties of carbon fiber/fiber
glass composites. Comp Sci Tech 2009; 69(3-4): 432–437.

[5] Barjasteh E, Bosze EJ, Nutt SR. Thermal aging of fiberglass/carbon-fiber
hybrid composites. Comp A 2009; 40(12): 2038-2045

[6] Alawar A, Bosze EJ, Nutt SR. A composite core conductor for low sag at
high temperatures. IEEE Transactions on Power Delivery 2005; 20 (3):
2193-2199.

[7] Bansal A. Finite element simulation and mechanical characterization of
composite insulators. PhD dissertation, Portland, OR: Oregon Graduate
Institute of Science and Technology; 1996.

[8] Kumosa M, Han Y, Kumosa L. Analysis of composite insulators with
crimped end fittings: Part I-non linear finite element computations.
Composites Science and Technology 2002; 62:1191-1207.

[9] Kar NK, Hu Y, Barjasteh E, Nutt SR. Tension tension fatigue of hybrid
composite rods. Composites: Part B 2012, in press.

[10] Burks B, Armentout D, Kumosa M. Characterization of the fatigue
properties of a hybrid composite utilized in high voltage electric
transmission. Composites: Part A 2011; 42: 1138-1147.

[11] Peters WH, Ranson WF. Digital Imaging Techniques in Experimental
Stress Analysis. Optical Engineering 1982; 21(3): 427-431.

130
[12] Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR.
Determination of displacements using an Improved Digital Image
Correlation Method. Image Vision Computing 1983; 1(3): 133-139.

[13] Gonzalez C, LLorca J. Mechanical behavior of unidirectional fiber-
reinforced polymers under transverse compression: Microscopic
mechanisms and modeling. Composites Science and Technology 2007;
67(13): 2795-2806.

[14] Collings, TA. Transverse compressive behaviour of unidirectional carbon
fibre reinforced plastics. Composites 1974; 5(3): 108-116.

[15] Ugural AC, Fenster SK. Advanced Strength and Applied Elasticity. 4
th

edition, Prentice Hall. 159-163.

[16] Barre´ S, Benzeggagh ML. On the use of acoustic emission to investigate
damage mechanisms in glass-fibre reinforced polypropylene. Composites
Science and Technology 1994; 52: 369-376

[17] Godara A, Raabe D, Bergmann I, Putz R, Muller U. Influence of additives
on the global mechanical behavior and the microscopic strain localization
in wood reinforced polypropylene composites during tensile deformation
investigated using digital image correlation. Composites Science and
Technology 2009; 69: 139-146.

[18] DeTeresa SJ, Larsen GJ. Derived interaction Parameters for the Tsai-Wu
Tensor polynomial theory of strength for composite materials. ASME
International Mechanical Engineering Congress and Exposition 2001.

[19] Schmidt JW, Bennitz A, Taljsten B, Goltermann P, Pedersen H.
Mechanical anchorage of FRP tendons- A literature review. Construction
and Building Materials 2012; 32: 110-121.

131
CHAPTER 6. CONCLUSIONS AND FUTURE WORK
The mechanical behavior of composite rods used in overhead conductors was
investigated in this work. The ACCC is comprised of trapezoidal aluminum wires
wrapped around a solid cylinder comprised of glass fibers and carbon fibers in a common
matrix. This conductor has considerable advantages over the traditional ACSR, having
greater strength, being lighter weight and capable of producing greater ampacity. The
limiting factor for traditional overhead conductors is sag during peak electricity demands.
When electricity demands increase across the world, overhead conductors are forced to
draw and transfer larger amounts of current. Increasing the line current causes the
continuous operating temperature of the conductor to increase, leading to excessive line
expansion (from large CTE’s from the steel and aluminum); causing considerable sag.
Sag of overhead conductors has led to short circuiting (brown out and black outs), where
the lines can come into contact with tall structures, and power utilities have implemented
strict continuous operating temperatures to limit sag to prevent potential failures. The
main advantage of the ACCC cable is the ability to operate continuously at high
temperature (high ampacity) while producing low sag. This attribute stems from the
polymer composite core, which has a coefficient of thermal expansion that is ¼ that of
the steel reinforcement used in ACSR cables. The advantages of the ACCC over the
ACSR can reduce infrastructure costs by reconductoring the power grid with more
efficient cables that can have larger overall span lengths, reducing the number of
necessary tower nodes.
However, overhead conductors are exposed to various environments, the
combination of which can lead to premature failure. Ice and wind loading, cyclic tensile
132
loads, thermal cycling, moisture exposure, and ozone are the types of environments that
can lead to failure of such structures. Because overhead conductor cables are meant to
withstand such environments with little to no maintenance, long term durability of
conductors utilizing polymer composite rods is a major concern for the power utility
industry. The scope of this dissertation focused on the fatigue and fracture behavior of
newly developed hybrid composite rods under various loading conditions. Specifically,
the effect of bending fatigue on the failure evolution of the composite rod was
investigated; and how such effects reduced strength and modulus. The ability of the
composite rod to withstand tension-tension fatigue conditions was analyzed, and fretting
and wear behavior was caused by the mechanical anchor used to grip and hold the
composite. Diametral compression tests were performed on all glass and all carbon
composite rods, to measure in plane strength and modulus. The fracture surfaces and
deformation behavior were also analyzed. Non-uniform radial deformation tests on
hybrid composite rods were also investigated as a means to understand how mechanical
anchors used to grip and hold composite rods can induce premature cracks that can limit
long term durability. The goal of this dissertation was to improve the understanding of
the mechanical behavior of such composite materials from a scientific standpoint, while
producing results that can be applied to in service conditions.
In Chapter 2, the bending fatigue behavior of a GF/CF composite rod was
investigated, and damage development was monitored to predict fatigue life at specified
stress levels. Damage initiated by the formation of microscopic transverse matrix cracks
on the GF tensile surface during Stage I. AE measurements revealed that during Stage II,
both fiber bundle failures and matrix crack propagation played an interactive role in the
133
progression of damage and reduction in stiffness. A distinctive failure pattern was
observed, as radial and circumferential cracks made up layer like formations that
saturated along the CF/GF interface. This saturation behavior was reflected in the
damage variable growth as a function of the number of cycles in both stages. Nearly 85-
90% of the flexural strength and modulus were retained and no loss in tensile strength
was observed. The GF shell was exposed to the highest cyclic tensile strains, and
damage initiated on the tensile surface. However the CF core underwent the greatest
cyclic tensile stresses, but did not show any signs damage; indicating a greater resistance
to fatigue damage.
In Chapter 3, the tension-tension fatigue behavior of a hybrid composite rod
comprised of unidirectional carbon and glass fibers was investigated. The mechanical
grip used on the composite influenced the observed fatigue behavior and damage
mechanisms, and the stress distributions showed that regions within the collet grip having
the greatest radial displacement experienced the greatest tensile stresses. Cracks initiated
in regions with low radial displacements, where the sharp collet edges rubbed against the
GF shell. Longitudinal cracks grew along the GF/CF interface until complete shell/core
separation occurred. Lower R-ratios and higher MAS levels led to shorter fatigue lives
because of higher strain amplitudes, and the transition from progressive fatigue failure to
non-progressive fatigue failure.
The gripping technique is adequate to support the appropriate service loads,
however stress concentrations arise near the grip edges, where fretting damage can be
induced under cyclic loading. FEA simulations and trial experiments showed that a thin
134
protective sleeve over the composite rod would reduce fretting and stress concentrations,
and thus extend fatigue life.
In Chapter 4, diametral compression tests were performed on CF and GF
pultruded composite rods to determine the effect of transverse loads on in-plane behavior,
and measure in plane properties and strength. The GF composite showed greater
resistance to transverse deformations and fracture than the CF rod and this was reflected
in the fracture surfaces of both systems. The GF surface after failure showed residual
fiber and matrix adhesion, while the CF system showed bare fibers, with little residual
adhesion. The distribution of strains in the transverse plane of the composite rod showed
a region of localized tensile strains under the loading edges which resulted from the
formation of matrix microcracks and debonding. Final failure occurred along the
diameter, with shear failure near the loading edges. The diametral compression test
combined with DIC provides a means to directly measure transverse and in plane shear
modulus.
In Chapter 5, compression tests were performed on a hybrid composite rod using
hemispherical anvils to determine the effects of non-uniform loading on transverse plane
behavior; the purpose of which was to understand how mechanical anchors deform the
composite rod. Damage mechanisms were observed through changes in the strain
contours that occurred simultaneously with bursts in AE. The anvil corners were sites
where failure began, and regions of large localized strains resulted from shear matrix
microcracks that formed at these points. The lack of constraint caused the composite to
expand against the anvils, initiating longitudinal cracks in the GF shell. An alternative
gripping method was proposed that yielded uniform radial displacements and reduces
135
stress concentrations. These factors reduce the risk of crack initiation and failure in the
composite rod, and thus enhance component durability.
Actual service conditions utilize combined transverse loads near the mechanical
anchors with along with longitudinal tensile loads. Aeolian vibration due to wind loading
will impose high frequency deflections onto the conductor that can induce bending loads.
Thus, the composite core will be exposed to various cyclic stresses (axial, bending,
transverse), and these studies show that fatigue damage was mainly limited to the GF
shell, protecting CF core. The hybrid composite design provides an effective means of
limiting fatigue damage (especially caused by fretting near the mechanical grips).
However, protection of the GF shell surface would also promote long-term durability for
composites used in infrastructure applications.
Improvement in the composite design would also limit the type of interface
separation behavior observed during mechanical testing. The GF/CF interface played a
critical role in the observed failure modes, and a gradual transition zone between CF and
GF components (as opposed to the abrupt material transition) could delay or prevent
core-shell debonding as well as the attendant bird-caging phenomenon. Most service-
related material failures are caused by some form of fatigue, and composite designs for
applications like composite reinforced conductors will require understanding of fatigue
and failure mechanisms.
Attaching the conductors to lattice towers requires collet fixtures that grip the
composite rods. Because the hybrid composite utilizes unidirectional fibers, the inherent
anisotropy in the design leads to weakness in the transverse plane. As such, the
mechanical collets introduce contact and transverse loads that primarily use compression
136
and surface traction to prevent slip, which has been shown to initiate forms of
micromechanical damage. Alternative fiber architectures may provide greater resistance
to surface damage from localized stresses resulting from such grips.
Future research should focus on design improvements that would promote long
term durability, and the effect of combined environments on fatigue life. A thin inner
sleeve of ductile metal to distribute the radial loads uniformly around the hybrid
composite rod would act to protect the composite from damage; however such
experiments have yet to be investigated. Alternative fiber architectures such as a woven
glass fabric for the outer shell might increase fracture and fatigue resistance in the
transverse plane. The effect of thermal oxidation, moisture and ozone on fatigue life is
also an important area of research yet to be investigated, as it would lead to an
understanding of how combined environments affect long term durability.

137
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International Journal of Fatigue, 2008. 30: p.1813- 1820

Abstract (if available)

Abstract Polymer matrix composites (PMCs) have been used extensively in the aerospace industry for the past five decades. There has been an upsurge in the use of PMCs in other industrials sectors such as civil infrastructure, automotive, marine and sporting applications. The primary advantage of using PMCs over conventional metals and alloys are the increase in weight savings, increased stiffness and strength properties. A new application of PMCs has been developed and applied as the load bearing member for overhead conductor cables. Traditional overhead conductor cables are comprised of an aluminum cable with a steel reinforcement (ACSR). The new overhead conductor replaces the steel core of the conductor with a single continuous hybrid composite cylinder. The composite core is comprised of glass fibers and carbon fibers in a common matrix, and the primary advantage of these composite reinforced conductors is the reduction in sag and increase in ampacity over conventional ACSR conductors. ❧ One of the major concerns of the hybrid composite core is long term durability under various combined environments and loading conditions. Overhead conductor cables are exposed to moisture, extreme ice and wind conditions, cyclic temperatures and fatigue loads. The mechanical and physical properties of polymer composites can degrade under such conditions, and the ability to understand degradation mechanisms is important to create predictive models for long term durability. More specifically, the basic mechanical properties, fatigue response of the composite rods, and the deformation behavior under transverse loads is unknown, and the work here investigates such behavior to shed light on design factors that can contribute to degradation in mechanical properties while in service.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Kar, Nikhil Kumar (author)

Core Title Fatigue and fracture of pultruded composite rods developed for overhead conductor cables

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 07/12/2012

Defense Date 06/04/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag composites,durability,fatigue,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nutt, Steven R. (committee chair), Goo, Edward K. (committee member), Kassner, Michael E. (committee member)

Creator Email nkar@usc.edu,nkarusc@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-56090

Unique identifier UC11289007

Identifier usctheses-c3-56090 (legacy record id)

Legacy Identifier etd-KarNikhilK-940.pdf

Dmrecord 56090

Document Type Dissertation

Rights Kar, Nikhil Kumar

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA