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MICHIGAN STAT

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H! M II!!! Milli/"Ill”ill/l

3 129lt/3 00900 8834

 

 

 

This is to certify that the

dissertation entitled \

Interfacial Changes During the Processing of a
Typical Carbon Fiber/Epoxy Composite Material

presented by

Venkatesh Rao

has been accepted towards fulﬁllment
of the requirements for

Ph . D . degree in Chemical Engr .

 

 

MS U is an Afﬁrmative Action/Equal Opportunity Institution 0-12771

‘ LIEMRY 1
Michigan State
University

 

 

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MSU lo An Affirmative Action/Equal Opportunlty Institution
owns-9.1

INTERFACIAL CHANGES DURING THE
PROCESSING OF A TYPICAL
CARBON FIBER/EPOXY
COMPOSITE MATERIAL

by

Venkatesh Rao

A DISSERTATION

Submitted to
Michigan State University

in partial ﬁdﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering

1991

x’d

/ ‘5, ‘74 / 11'

ABSTRACT

INTERFACIAL CHANGES DURING THE
PROCESSING OF A TYPICAL
CARBON FIBER/EPOXY COMPOSITE MATERIAL

By
Venkatesh Rao

The effect of the processing cycle on the interfacial shear strength of a thermoset
mPDA/DGEBA matrix reinforced with earbon, A84 ﬁbers was investigated. The
processing cycle of a thermoset can be conveniently divided into three different regimes:
the ﬂuid regime (up to the point of matrix gelation), the ambient temperature regime
(room temperature), and the elevated temperature regime. In each of these regimes,
readily measurable material properties of the matrix will be related to the ﬁber-matrix
interfacial shear strength using model single ﬁber techniques to quantify the interfacial
shear strength.

In the ﬂuid regime, the kinetics of crosslinking are used to determine gelation times.
A modiﬁed Williams-Iandel—Ferry (WLF) equation is then used to model the viscosity
changes as a function of the extent of cure. Gravimetric pull-out tests are conducted to
relate the viscoelastic properties of the matrix to an interfacial pull-out strength. Results
indieate that in the ﬂuid regime, the interfacial strength begins to develop and increases
with increasing viscosity of the reacting matrix. A modiﬁed WLF-type model is used
to describe the dependence of interfacial pull-out strength on extent of cure.

At ambient conditions, constant interfacial and matrix chemistry is used to
systematically vary the matrix properties from ductile to brittle in order to simulate the
actual processing cycle. These matrix properties are then related to the interfacial shear
strength (the single ﬁber fragmentation test is used to quantify the interfacial shear
strength). Different length polyether diamine curing agents are used to alter the matrix
properties while keeping the chemical bonding and chemistry at the interface constant.
It will be shown that the interfacial shear strength decreases monotonically with
decreasing modulus of matrix. A shear lag model is shown to model the changes in
interfacial shear strength as a function of matrix properties down to a matrix shear
modulus of 1 GPa. Radial compressive stresses as well as the ﬁber wettability
characteristics are shown to play a minor role in comparison to the changing material
properties of the matrix in determining the level of adhesion at the interface.

At elevated temperatures, interfacial (single ﬁber) shear strength measurements
conﬁrm the reduction in interfacial shear strength with a reduction in matrix modulus.
As the glass transition of the matrix is approached, a large decrease in interfacial shear
strength is noted parallel to the decrease in matrix modulus. The results were used to
generate a master curve capable of predicting the changes in interfacial shear strength as
a function of temperature. Additionally, epoxy sized ﬁbers were used to study and
model the formation of an interphase by preferential diffusion of the curing agent into
the coating and creating an interphase with different mechanical properties than the bulk
matrix. A model for the formation of the interphase is presented.

TO:

MY DAD AND MOM

Dr. S. Tyagaraja Rao and Lalitha Rao

iv

ACKNOWLEDGEMENTS

As with any undertaking of this size and magnitude, many people need to be thanked
and form the backbone necessary for proper completion of the task. I start with my
sincere appreciation to Dr. Lawrence T. Drzal for his guidance, support, encouragement,
and ﬂexibility throughout the duration of this project. It has been a pleasure to work
with him and I have certainly learned a great deal during my stay here at Michigan State
University.

I also wish to thank my fellow chemical engineering graduate students at the
Composites center past and present-Raj, Shri, Javad, Brent, Craig, Greg, Ed, Sanjay
and many others for their assistance and friendship and for making my stay here a very
enjoyable one. In addition, I wish to thank Mike Rich, Brian Rook, Hassan Al-
Moussawi, Pedro Franco-Herrera and Shekar for their help in equipment operation,
experimental analysis as well as their friendship. My thanks also go to Steve Kahl and
Ethan Russell for their help in some of the data acquisition.

I am thankful to the other members of my committee—Dr. E. A. Grulke, Dr. M.
Hawley, Dr. S. Selke and Dr. D. Liu for the time they dedieated to this dissertation.

I thank my parents and family for their emotional and ﬁnancial support and their
never-ending encouragement throughout my educational career.

Finally, I thank my wife Revathy for her love and support in enabling me to
complete this work and for her ability to adjust to a new lifestyle in this country while
at the same time enduring my sometimes long, irregular work hours over the past two

years.

TABLE OF CONTENTS

List of Tables x
List of Figures xii
Nomenclature xvi
CHAPTER 1 INTRODUCTION AND BACKGROUND 1
CHAPTER 2 EXPERIMENTAL MATERIALS AND METHODS 10
2.1 MATERIAL SELECTION 10
2.1.1 EPOXY RESINS 10
2.1.2 CURING AGENTS 11
2.1.3 FIBER REINFORCEMENTS 15
2.2 EXPERIMENTAL METHODS 16
2.2.1 SINGLE FIBER FRAGMENTATION TEST 16
2.2.2 MICROBOND TEST 22
2.2.3 INTERFACIAL PULL-OUT TEST 23
2.2.4 INTERFACIAL TRANSVERSE STRENGTH TEST 27
2.2.5 MATERIAL PROPERTIES OF THE MATRICES 27
2.2.6 THERMAL PROPERTIES OF THE MATRICES 29
2.2.7 VISCOSITY MEASUREMENTS 31
2.2.8 SURFACE ENERGY MEASUREMENTS 31
2.2.9 MICROSCOPY 33
CHAPTER 3 BEHAVIOR OF THE INTERFACE IN 34

THE VISCOUS REGIME

vi

3.1 INTRODUCTION
3.2 EXPERIMENTAL ANALYSIS
3.3 RESULTS AND DISCUSSION
3.3.1 KINETICS OF DGEBA/mPDA
3.3.2 VISCOSITY AND GEL POINT OF mPDA/DGEBA
3.3.3 INTERFACIAL PULL-OUT STRENGTH
3.4 CONCLUSIONS
CHAPTER 4 MICROBOND TECHNIQUE
4.1 INTRODUCTION
4.2 EXPERIMENTAL
4.3 RESULTS AND DISCUSSION
4.4 THIN FILMS
4.5 MODELING OF THE DIFFUSION PROCESS
4.6 CONCLUSIONS

CHAPTER 5 THE DEPENDENCE OF INTERFA CIAL SHEAR

SHEAR STRENGTH ON MATRDI AND INTERPHASE
PROPERTIES AT AMBIENT CONDITIONS

5.1 INTRODUCTION
5.2 EXPERIMENTAL
5.3 RESULTS AND DISCUSSION
5.3.1 EFFECT OF MATRIX PROPERTIES ON 188
5.4 CONCLUSIONS

CHAPTER 6 THE DEPENDENCE OF INTERFA CIAL SHEAR

STRENGTH ON TEMPERATURE AND
ASSOCIATED INIERPHASE FORMATION

6.1 INTRODUCTION
6.2 EXPERIMENTAL
6.3 RESULTS AND DISCUSSION

vii

34
35

45
52
56
57
57
59
59
70
74
75

8

81
100
102

102
104
105

6.3.1 CHEMICAL BONDING

6.3.2 INTERFACIAL SHEAR STRENGTH
6.3.3 LINEAR SUPERPOSITION

6.3.4 RESIDUAL STRESSES

6.3.5 FORMATION OF AN INTERPHASE (AS4C-mPDA-

DGEBA SYSTEM)

6.4 MODELING OF THE FORMATION OF AN INTERPHASE

6.5 CONCLUSIONS

CHAPTER 7 INTERFA CIAL TRANS VERSE STRENGTH MEASUREMENTS

7.1 INTRODUCTION

7.2 EXPERIMENTAL

7.3 RESULTS AND DISCUSSION
7.4 CONCLUSIONS

CHAPTER 8 ADHESIVE BEHAVIOR OF CARBON FIBERS IN
THERMOPLASTIC POLYCARBONATE MATRDI

8.1 INTRODUCTION

8.2 EXPERIMENTAL

8.3 RESULTS AND DISCUSSION
8.4 CONCLUSIONS

CHAPTER 9 CONCLUSIONS AND RECOMMENDATIONS

9.1 CONCLUSIONS

9.2 RECOMMENDATIONS FOR FUTURE WORK

APPENDICES:
APPENDIX A

APPENDIX B

"PEAK" POINT ANALYSIS OF ISOTHERMAL

KINETIC DATA

MODEL FOR DIFFUSION OF CURING AGENT

OUT OF DROPLETS

viii

105
106
112
112
115

118
133
134
134
134
135
141
142

142
143
145
147
153
153
154

156

161

APPENDIX C A MODEL TO DESCRIBE INTERPHASE FORMATION 165
LIST OF REFERENCES 169

Table 1.1:
Table 1.2:
Table 2.1:
Table 2.2:
Table 2.3:
Table 3.1:
Table 3.2:
Table 3.3:
Table 4.1:
Table 4.2:
Table 5.1:
Table 5.2:
Table 5.3:
Table 5.4:
Table 6.1:

Table 6.2:

Table 6.3:

Table 6.4:

LIST OF TABLES

Properties of carbon, glass and Kevlar 49 ﬁbers at 20°C
Properties of a typical epoxy resin

Curing schedules used in study

Stoichiometry of curing agents used

Surface energies of characterizing liquids

Kinetic model parameters

T, as a function of 0:

Prediction of gel times

Curing schedules and conditions

Fully cured T,’s of the matrices

Interfacial and material properties of DGEBA system
Interfacial and material properties of MY720 system
Radial compressive stresses

Wetting characteristics of matrices and ﬁbers

Interfacial, mechanieal and thermal properties
of the DGEBA system

Critical length data for DGEBA/mPDA system at
elevated temperatures

Critical length data for DGEBA/1230 system at
elevated temperatures

Critical length data for DGEBA/1403 system at
elevated temperatures

14
14
32
45
47
52
62
72
81
82
96
100
104

107

107

108

Table 6.5:

Table 6.6:

Table 7.1:
Table 8.1:
Table 8.2:

Table A1:
Table A2:
Table A3:

Critical length data for DGEBA/I403/J 700 system
at elevated temperatures

Critical length data for DGEBA/J 700 system at
elevated temperatures

Transverse strengths in DGEBA/mPDA matrix
Processing cycle for Lexan thermoplastic

Critical length distribution for Lexan reinforced
with A84 ﬁber

Peak kinetic parameters
Peak times and reaction rates

Comparison of kinetic parameters

108

109

139
144
145

159
159
160

Figure 1.1:
Figure 1.2:
Figure 2.1:
Figure 2.2:
Figure 2.3:
Figure 2.4:
Figure 2.5:
Figure 2.6:
Figure 2.7:
Figure 2.8:
Figure 2.9:
Figure 3.1:
Figure 3.2:
Figure 3.3:
Figure 3.4:

Figure 3.5:
Figure 3.6:

Figure 3.7:
Figure 3.8:

LIST OF FIGURES

Possible failure of thick composite

TIT diagram for epoxy resin

Chemical structure of resins

Chemical structure of curing agents

Scanning electron micrograph of carbon, A84 ﬁber
Tensile jig used for conducting fragmentation tests
Process of fragmentation

Scanning electron micrograph of microdrops on ﬁbers
Schematic of microbond apparatus

Schematic of pull-out experiment apparatus

Schematic of transverse strength specimens

Viscosity vs. time for DGEBA/mPDA system at 125°C
Viscosity vs. temperature for neat DGEBA resin
Viscosity vs. pull-out force for neat DGEBA resin

Extent of conversion, 0:, vs. time for
isothermal la'netic data

Reaction rate, da/dt, vs. time for

isothermal data

Comparison of kinetic model to data at 55°C,
75°C and 125°C

T, vs. extent of cure, a

Reduced, modiﬁed WLF plot of kinetic data

12
l3
17
19
20
24
25
26
28
37
38
39
41

43

46
48

Figure 3.9:

Figure 3.10:
Figure 3.11:

Figure 3.12:
Figure 4.1:
Figure 4.2:

Figure 4.3:
Figure 4.4:

Figure 4.5:

Figure 4.6:

Figure 4.7:
Figure 4.8:

Figure 5.1:

Figure 5.2:
Figure 5.3:
Figure 5.4:
Figure 5.5:
Figure 5.6:
Figure 5.7:

Figure 5.8:

Comparison of WLF viscosity model to RMS data at
80°C, 100°C and 125°C

6’ and G' data for DGEBA/mPDA at 80°C

Temperature vs. time to gel as predicted by
various techniques

Comparison of pull-out model to gravimetric data
Schematic of incompletely cured microdroplets

T, as a function of microdroplet size for various
curing schemes

T, vs. amount of mPDA in bulk samples

Amount of curing agent, mPDA, lost as a function
of microdroplet size

Microbond data for mPDA/DGEBA formulation with
various curing schemes and atmospheres

A comparison of the microbond test and the
fragmentation test for mPDA/DGEBA matrix
and WOO/DGEBA matrix

Microbond data for WOO/DGEBA formulation

T as a function of ﬁlm size for mPDA/DGEBA,
J403IDGEBA and WOO/DGEBA formulations

Interfacial shear strength as a function of
bulk matrix shear modulus

Interfacial failure mode of mPDA/DGEBA formulation
Interfacial failure mode of J230/DGEBA formulation
Interfacial failure mode of J403IDGEBA formulation
Interfacial failure mode of WOO/DGEBA formulation
Interfacial failure mode of I700/MY720 formulation
Interfacial shear strength as a function of the

product of squareroot of matrix shear modulus

and strain at ﬁnal break

Stress/ strain curves for all DGEBA formulations

50

51
53

55
61
63

65

67

68

71
73

87
88
89

93

Figure 5.9:
Figure 5.10:
Figure 6.1:
Figure 6.2:
Figure 6.3:

Figure 6.4:

Figure 6.5:

Figure 6.6:

Figure 6.7:
Figure 7.1:
Figure 7.2:

Figure 7.3:

Figure 8.1:

Figure 8.2:
Figure 8.3:
Figure 8.4:
Figure 8.5:

Radial compressive stress and interfacial shear
strength as a function of matrix shear modulus

Interfacial shear strength as a function of T:
of the fully cured matrix

Interfacial shear strength as a function of test
temperature for DGEBA resin cured with different
amine curing agents

Shift factor as a function of temperature

Master curve for prediction of interfacial shear strength
as a function of shift factor and temperature

Loss modulus of mPDA/DGEBA matrix and interfacial
shear strength of mPDA/DGEBA matrix reinforced
with carbon A84, and A84-C ﬁbers as a function

of temperature

Schematic of interphase formation by diffusion of
curing agent

Model prediction curing agent concentration proﬁle
within rnterphase region as a function of diffusion
coefﬁcient, reaction rate constant and temperature

Effective diffusion coefﬁcient as a function of
interphase thickness

Transverse interfacial mode of failure for Si Coated
A84 ﬁber in mPDA/DGEBA matrix

Transverse interfacial mode of failure for Kevlar ﬁber
in mPDA/DGEBA matrix

Interfacial transverse strengths of carbon, Kevlar and
Si-coated carbon ﬁbers in mPDA/DGEBA matrix

Interfacial shear strength as a function of test temperature
for thermoplastic Lexan matrix reinforced with carbon,
A84 ﬁbers

Interfacial failure mode for Lexan/A84 at 25°C
Interfacial failure mode for Lexan/A84 at 45°C
Interfacial failure mode for Lexan/AS4 at 65°C

Interfacial failure mode for Lexan/A84 at 85°C

xiv

95

110

113

114

116

121

126

128

137

138

140

146

148

149

150
151

Figure 8.6: Interfacial failure mode for Lexan/AS4 at 120°C 152
Figure B1: Diffusion process in microdrop 161

XV

NOMENCLATURE

Dimensionless parameter (k/D °5, deﬁned by Equation D2
WLF shift factor

Concentration of curing agent (in interphase region)

Bulk concentration of curing agent

WLF constants deﬁned by Equations 3.1 and 3.2
Diameter of ﬁber

Average diameter of ﬁber

Average, effective diffusion coefﬁcients

Concentration dependent diffusion coefﬁcient

Differential scanning calorimeter

Dynamic mechanical analyzer

Error function

Complimentary error function (1-erf)

Immersion depth

Tensile modulus of ﬁber

Tensile (Young’s) modulus of matrix

Ratio of activation energy to gas constant deﬁned in Table 3.1
Pull-out or debonding force

xvi

6,6.
6’
GI

ISS

R(C)

Fir-1"

Steady—state pull-out force deﬁned by Equation 2.4
Acceleration due to gravity (9.80665 ml sec?)

Shear modulus of matrix

Storage modulus of matrix

Loss modulus of matrix

Interfacial shear strength

Pseudo ﬁrst order rate constant of epoxy/amine reaction
Arrenhius based reaction rate constants

Critical length deﬁned by Equation 2.1

Embedment length

Kinetic exponent deﬁned by Equation 3.3

Kinetic exponent deﬁned by Equation 3.3

Applied load

Radial distance from center of ﬁber to edge of interphase region
Radius of ﬁber

Universal gas constant (1.987 Kcal/mole—K)

Interﬁber spacing in composites as deﬁned by Equation 5.1
Concentration dependent reaction rate deﬁned by Equation 6.1
time

Gelation time (time required to reach gel point)

Time to reach peak in reaction rate

Temperature

xvii

 

Glass transition temperature
Reference temperature chosen for shifting data (346°K)
Thermal mechanical analyzer

Radial distance parameters

GREEK SYMBOLS

“9%

”a

AT

Weibull model scale parameter deﬁned by Equation 2.2

Extent of reaction (conversion) deﬁned by Equation 3.3
Conversion at peak reaction rate

Reaction rate, da/dt

Peak (maximum) reaction rate

Weibull model shape parameter deﬁned by Equation 2.2

Fiber scaling parameter deﬁned by Equation 5 .1

Fracture strain of matrix

Strain at which ﬁnal break occurs in fragmentation test
Dimensionless distance deﬁned by Equation 4.4

'pi", 3.14151629

Dimensionless distance deﬁned by Equation B2

Viscosity deﬁned by Equations 3.1 and 3.2

Viscosity of fully cured matrix, 10” cP, deﬁned by Equation 3.1
Interphase thickness

T-T

x .0.

0r

7‘: 713

“:74
7'.»

Tensile strength of ﬁber

Dimensionless modulus deﬁned by Equation 6.5
Dimensionless radial distance deﬁned by Equation 6.5
Total surface free energy of material

Dispersive component of surface free energy

Polar component of surface free energy

Contact angle in Wilhelmy experiments

Partial differential operator

micrometers (microns)

Poisson’s ratio

Gamma function deﬁned by Equation 2.2

CHAPTER 1

W

There are three main points to be included in the deﬁnition of an acceptable
composite material for use in structural applications [1]:

( 1) It consists of two or more physically distinct and mechanically separable
materials.

(2) It can be made by mixing the separate materials in such a way that the
dispersion of one material in another can be done in a controlled way to
achieve optimum properties.

(3) The properties are superior, and possibly unique in some speciﬁc respects
to the properties of the individual components.

The last point provides the main impetus for the development of composite materials.
They may be broadly classiﬁed as ﬁbrous composites (consisting of ﬁbers embedded in
a matrix), laminated composites (layers of various ﬁbrous composites), and particulate
composites (consisting of particles in a matrix). The discussion in this work will be
restricted to ﬁbrous composites.

Fibrous composites are composed of ﬁbers, which are usually aligned and embedded
in a polymeric matrix. The ﬁbers themselves can be of various types, the most
prominent being carbon, glass and Kevlar ﬁbers. Comparison of the typical properties
of these ﬁbers [1] are illustrated in Table 1.1 below.

All polymers are potential candidates for matrix materials. But limitations such as
end properties and processability rule out quite a number of them [2]. Epoxy resins are
the most widely used thermosetting matrices, due to their ease of processability and good
properties at low to moderate temperatures. Typical mechanical and thermal properties
[3] of an epoxy resin are illustrated in Table 1.2 below.

A typical process for producing epoxy/carbon ﬁber composites involves drawing

2

carbon ﬁbers through a vat of epoxy resin and winding the epoxy coated ﬁbers onto a

 

 

 

 

 

 

 

 

 

i

 

 

 

 

Property Carbon Fibers E Glass Fibers Kevlar 49 Fibers
(PAN Based)
Diameter 7-8 8-14 11-12
(microns)
Density 1.75 2.56 1.45
(103 lie-m")
Young’s 250 76 125
Modulus
(GN-m")
Transverse 20 76 --
Modulus
(GN-m")
Tensile 2.70 1.4-2.5 2.8-3.6
Strength
(GN-m")
Strain to 1.0-1.5 1.8-3.2 2.2-2.8
Failure (96)

 

 

 

3
mandrel. The mandrel containing the wound ﬁbers in epoxy matrix is then subject to a
thermally driven processing cycle which initiates devolatilization [4]. The curing occurs
in two stages. In stage I, the material is reacted to produce a lightly crosslinked
structure at moderate temperatures. In stage II, the material is post cured at higher

 

 

 

 

 

 

 

 

 

 

 

 

Property Typical Epoxy Resin T
Density (Mg-m") 1.1-1.4
Tensile Modulus (GN-m") 3-6 ]
Poisson’s Ratio 0.38-0.40
Tensile Strength (MN-m") 35-100
Compressive Strength (MN -m”) 100-200
Strain to Failure (96) 1-6
Coefﬁcient of Thermal Expansion 60-65
(10*s °C‘)
Heat Distortion Temp. (C) 50-300
Shrinkage upon Curing (96) 1-2 _J

 

 

 

temperatures and longer times to arrive at the ﬁnal composite. After curing and post
curing are completed, the composite is cooled to ambient conditions.

There is a major problem associated with epoxy/carbon ﬁber composites and any
thermoset composite made in this fashion. During processing, defects are produced and

4
appear as large wavy regions of ﬁbers in the interior of the composite (see Figure 1.1
below).

When exposed to high pressure differences between the interior and exterior, it is
possible that these defects cause the composite to crack and fail in a direction normal to
the wavy regions, due to compression and shear [5]. It is believed that these defects are
formed during the curing process.

Upon cooling, especially below the glass transition temperature (T,), internal stresses
build up as a result of the different volume expansions in regions of differing temperature
and extent of cure [6]. During the curing process, large temperature gradients occur in
the composite caused by the heat transfer to the material through both the inner and outer
surfaces of the cylinder and by the exotherm of the curing reaction. A temperature front
begins at both inner and outer surfaces and travels towards the interior during curing.
It is likely that a region of high temperature greater than the processing temperature
exists where the two fronts meet in the interior of the composite. These high
temperatures may lead to decomposition and/or charting of the matrix material and
stress build-up during cooling. The region of maximum temperature during curing will
remain the region of maximum temperature during cooling. The regions near the inner
and outer surfaces during cooling will be at or below T" whereas at some region within
the composite the temperature is at or above T,. The stress build up in the regions near
the surface may cause the material within the inner high temperature region to deform
into the observed wavy patterns or delaminate the composite in this region. These
defects are especially evident in the production of thick section composite structures
(> 0.5” thick) used in a variety of aerospace and naval applications [7,8].

It is the ability of the matrix to transmit stresses from ﬁber to ﬁber (through the
interface) at the microscopic level that is responsible for internal stress development in
a composite, which in turn is responsible for causing the generated defects.

 

POSSIBLE FAILURE

 

HIGH PRESSURE

 

 

 

Figure 1.1: Possible failure of thick componite

Experimentally veriﬁed data on the generation of interfacial stresses and their variation

6

with temperature, extent of cure and time is needed. Interfacial properties are dependent
on the matrix modulus and the interactions at the ﬁber-matrix interface. During
processing there is a simultaneous increase in modulus with time and temperature. A
typical time-temperature transformation (TIT) diagram [9,10] is shown in Figure 1.2 for
a reacting thermoset system. It is critical that the mechanism by which the interfacial
and mechanical properties are generated is understood and the mechanical properties
known as a function of temperature, extent of cure and processing time. Interfacial
shear strength and interfacial normal strength measurements have not been determined
as a function of processing conditions.

While it is not possible to directly probe the in-situ stresses within a composite with
high enough resolution, a separate study is required to generate this data. It is the
objective of this study to measure interfacial shear properties during the entire processing
cycle of a carbon ﬁber/thermoset material. In this study, single ﬁber methods [11],
which allow for the isolation and measurement of interfacial properties will be combined
with processing data to obtain the variation in interfacial (shear and normal) properties
as a function of extent of processing. The interfacial shear strength will be directly
measured as a function of the relevant material properties of the matrix being processed.
As a result of this study, it will be possible to predict the interfacial shear strength given
the changing material properties of the matrix during processing. This will ultimately
allow for probing of the processing cycle in an attempt to identify where defects may
begin occurring in the composite material.

The chapters in this thesis are generally arranged according to the regime of the
processing cycle being discussed. The appendices contain some of the mathematical
derivations as well as some of the experimental data. All the chapters are self contained
in that there is an introduction section to overview the existing literature, an experimental

section, a results and discussion section, a modeling section and ﬁnally, a set of

 

 

 

 

 

e'e’e'e’e’e'e
o‘e’e’e’e‘o‘e
eeeeee

 

 

Figure 1.2: TTT diagram for epoxy resin

conclusions. Speciﬁcally, the chapters are arranged in the following order:

(1) Chapter 2 discusses the materials used and the experimental techniques employed

(2)

(3)

in this study.

Chapter 3 focuses on the kinetics of crosslinking, time to gelation, and in
general, how the interface behaves in the viscous regime (up to the point of
matrix gelation). Interfacial parameters are quantiﬁed with a single ﬁber
gravimetric pull-out test.

Chapter 4 deals with the microbond test for measuring the interfacial shear
strength of brittle systems. It will be shown that diffusion of curing agent in
small sized samples can alter the mechanical properties of the droplet specimens

leading to misleading measurements of interfacial shear strength.

8

(4) Chapter 5 describes how the interface behaves at ambient conditions (after
matrix gels and sets) as a function of bulk matrix and interfacial
properties. Interfacial shear strength is quantiﬁed using the single ﬁber
fragmentation test.

(5) Chapter 6 examines the role of elevated temperatures on interfacial shear
strength. Single ﬁber fragmentation tests are conducted in a specially designed
temperature chamber. Arguments will be made, using the data, for the formation
of an interphase region.

(6) Chapter 7 describes normal strength measurements of the interface.

(7) Chapter 8 describes interfacial shear strength measurements on a thermoplastic
system (Polycarbonate-Lexan) as a function of temperature.

(8) Chapter 9 presents the conclusions in a manner to coherently tie together the
material in Chapters 3, 4 and 6. Also, Chapter 9 attempts to provide proper
guidelines for future work that needs to be addressed in determining and
modeling the changes at the interface during processing.

Additionally, in chapters 3-6 mathematical models will be presented for the
prediction of interfacial properties based on material properties of the matrix. In chapter
3, a modiﬁed WLF equation [12] will be used to predict the interfacial pull-out force as
a function of the changing viscosity of the reacting ﬂuid medium. In chapter 4, an
unsteady state Fickian-type [l3] diffusion model will be used to analyze the transient
diffusion characteristics of the curing agent out of the samples. In chapter 5 , an existing
shear-lag model proposed by Cox and modiﬁed later by Cooke [14] will be used to
model the interfacial shear strength as a function of the changing material properties of
the matrix. Finally, in Chapter 6, a predictive model will be presented for the
description of the interfacial shear strength as a function of the modulus (or T,) of the
matrix. In addition, the steady-state Fickian diffusion equation (with a reaction term

9
[15]) will be used to mathematically explain the formation of an interphase region, whose
properties (different from the bulk matrix) play a major role in determining the level of
ﬁber/ matrix adhesion. The elevated temperature interfacial shear strength data will be
used to predict an effective diffusion coefﬁcient in the interphase region, the thickness
of the interphase region as well as to validate the model.

 

2.1 MATERIAIS SELECTION
W

The term ”epoxy" refers to a reactive chemical group consisting of an oxygen atom
bonded to two other atoms already united in some way [16]. Since their discovery,
epoxy resins have been the subject of a plethora of patents and technical publications.
There has been more written about these products per pound of sales [3] than any other
commercially available thermosetting resins. This broad interest in epoxy resins comes
from the wide variety of chemical reactions and materials that can be used for the curing
and the wide spectrum of different properties that result. The chemistry is unique among
the thermosetting resins. In contrast to formaldehyde resins [3], for example, an addition
reaction takes place instead of a condensation reaction insuring that no volatiles are given
off during cure. This means that only minimum pressures are required for the
fabrication techniques normally used on these materials. The volumetric shrinkage [17]
during curing is also much less than encountered in many other systems. This means
reduced stresses in the cured ﬁnal product. Moreover, a knowledge of the chemistry
involved permits the user to process epoxy resins over a wide range of temperatures and
to control the degree of crosslinking. As will be seen in later chapters, this last point
plays an important role in the physical and interfacial properties of epoxy thermosets.

Considering the range of attainable properties, the versatility of epoxy resins becomes
even more apparent. Depending on the chemical nature and structure of the curing agent
and curing conditions, it is possible to obtain mechanical properties with a wide range
of ﬂexibility, strength, hardness, adhesive strength and electrical resistance [3].
Uncured, the resins have a variety of physical forms, ranging from low viscosity liquids

10

11
to tack-free solids, that, along with the curing agent, afford the experimentalist a wide
range of processing conditions. In the absence of curing agents, the epoxies are also
useful as plasticizers and coatings [3].

Two different types of epoxy resins were used as representative composite matrices
in this particular study. A diglycidyl ether of Bisphenol-A (DGEBA)--EPON 828-Shell
Chemical Company-—was used for the majority of the study as the representative
difunctional (with and Epoxy Equivalent Weight of about 180) epoxy resin while MY720
(Araldite, Ciba Geigy, EEW of about 125) was used as the representative tetrafunctional
epoxy resin. The structures of both these compounds are illustrated in Figure 2.1.
W

Epoxides are notable for their high degree of reactivity towards a variety of
nucleophilic and electrophilic reagents. Extensive and detailed reviews of curing agents
are available elsewhere, see for example Tanaka and Mika [18] and Mika [19]. In
general, epoxy resin curing reactions involve opening of the epoxide ring followed either
by a homopolymerization reaction with further epoxides or reaction with the ”curing
agent" to form addition products.

Amongst the curing agents of greatest technological and structural importance [20]
are the polycarboxylic anhydrides, polyamines, and anionic or cationic catalysts. In this
work, all curing agents used were polyarnines (dianrines and triamines).

Figure 2.2 shows the chemical structures of all the curing agents employed in this
study. Meta-phenylenediamine (mPDA) was used as the baseline curing agent. The
other curing agents used were diamino-diphenyl sulfone (DDS) and a series of
polyetheramines (Jeffamines, Texaco Co.) having oxypropylene units of varying length
between the end amines. These different curing agents resulted in ﬁnal properties of the
mauix varying from brittle to ductile while at the same time preserving the interfacial

1 1
to tack-free solids, that, along with the curing agent, afford the experimentalist a wide
range of processing conditions. In the absence of curing agents, the epoxies are also
useful as plasticizers and coatings [3] .

Two different types of epoxy resins were used as representative composite matrices
in this particular study. A diglycidyl ether of Bisphenol-A (DGEBA)--EPON 828-Shell
Chemical Company-—was used for the majority of the study as the representative
difunctional (with and Epoxy Equivalent Weight of about 180) epoxy resin while MY720
(Araldite, Ciba Geigy, EEW of about 125) was used as the representative tetrafunctional
epoxy resin. The structures of both these compounds are illustrated in Figure 2.1.
W

Epoxides are notable for their high degree of reactivity towards a variety of
nucleophilic and electrophilic reagents. Extensive and detailed reviews of curing agents
are available elsewhere, see for example Tanaka and Mika [18] and Mika [19]. In
general, epoxy resin curing reactions involve opening of the epoxide ring followed either
by a homopolymerization reaction with further epoxides or reaction with the ”curing
agent” to form addition products.

Amongst the curing agents of greatest technological and structural importance [20]
are the polycarboxylic anhydrides, polyamines, and anionic or cationic catalysts. In this
work, all curing agents used were polyamines (diamines and triamines).

Figure 2.2 shows the chemical structures of all the curing agents employed in this
study. Meta-phenylenediamine (mPDA) was used as the baseline curing agent. The
other curing agents used were diamino—diphenyl sulfone (DDS) and a series of
polyetlrerarnines (Jeffamines, Texaco Co.) having oxypropylene units of varying length
between the end amines. These different curing agents resulted in ﬁnal properties of the
matrix varying from brittle to ductile while at the same time preserving the interfacial

12

aea-a.][oQ?_©_o-a.-ii_c..]l QEQMWL.

DIGLYCIDYL ETHER OF BISPHENOL A (DGEBA)
(DIFUNCTIONAL RESIN)

N.N.N‘.N-Tetragchidyt-4.4'-methylenebtsbenzenamine

R R
\N CH N/
/ ’ \

/°\

= org—cu—cu,

MY720 ARALDITE RESIN
(TETRAFUNCTIONAL RESIN)

Figure 2.1: Chemical structure of resins

NH,
I

@\

NH,

mPDA

JEFFAMINE CURING AGENTS:

HZNCISHCHz-fOCHZCfoNl-tz
l

CH3 CH3

DI-AMINES

13

H,NHNH,

DDS

°== =0

CH2+OCH20H(CH3)+.NH2
CH;CH2(IZCH2+OCH20H(CH,)+YNH2
CﬂszCHchmHahNHz

TRI-AMINES

Figure 2.2: Chemical structure of curing agents

14
chemistry. Unless otherwise noted, the standard curing cycles used for the various
systems is listed below in Table 2.1.

 

 

 

IIIZI-C' III I‘ 1
CURING AGENT CURING SCHEDULE I
mPDA 75°C-2hr, 125°C-2hr I

DDS 180°C-lhr, 220°C-2hr I

All Jeffamines 80°C-2 hr, 125°C-3hr _|

 

 

 

Unless otherwise noted, all matrix formulations in this study employed a stoichiometric
amount of curing agent based on the epoxy equivalent weight of the resin and the amine
equivalent weight of the curing agent. Table 2.2 below shows the proportions used for
the different curing agents employed in this study.

 

 

 

 

 

 

 

I n 22, s .l. E . I
I CURING AGENT AMOUNT USED (phr)
I mPDA 14.5
I DDS 35.8

1230 33.0

1400 56.0

1403 45.0
I 1700 117.0

 

 

One note of caution must be mentioned about the longer chained Jeffamine curing agents.
Our results have shown that these curing agents have a tendency to degrade over time
[21] leading to differing mechanical properties of the ﬁnal, neat specimens. Care must
be exercised in storing these curing agents properly in dark, airtight containers.

15
W
By 1960, it had been shown that cellulose textile ﬁbers could be carbonized in

reasonably large quantities to give low-grade carbon ﬁbers [22]. The original earbon
ﬁbers were made from textile grades of PAN (poly-AcryloNitrile) and fortuitously many
of their features proved to be advantageous. PAN has a -CH2-CH backbone with CN side
groups [23]. The polarity of the nitrile side groups produces relatively strong
intermolecular forces resulting in an amorphous structure.

The properties of the ﬁber-matrix interface are most signiﬁcant. Carbon ﬁbers
straight from the ﬁnal heat treatment furnace do not adhere well to polymeric matrices.
They are usually given an oxidative surface treatment which increases the ﬁber—matrix
bond strength but which can reduce the composite toughness. The level of surface
treatment needs to be adjusted to give optimum overall properties. Fitzer [24] has
presented an excellent review of the production of high performance carbon ﬁbers and
their applications.

The carbon ﬁbers chosen for this study are the "A' type. These are produced by
high temperature inert gas graphitization of PAN ﬁber. The morphology of the resulting
carbon ﬁber is axially and radially symmetric composed of ribbons of graphitic crystals
formed in turbostatic layers oriented almost parallel to the ﬁber axis as well as varying
in orientation across the ﬁber diameter. Adhesion to these ﬁbers, as mentioned above,
in their untreated state by a typical amine cured epoxy results in very low values of
interfacial shear strength [25]. Many surface treatments for improving the adhesion to
carbon ﬁbers have been proposed and various commercial ones are extensively described
in existing patent literature [26].

ThespeciﬁcPANbasedearbon ﬁbersusedinthis studyarethe 'A-4" typeCI-Iercules
Co.) having a ﬁber tensile modulus of about 238 GPa and a tensile strength of 3.5 GPa
whenmeasuredataZSmmgagelength. Theyarecircularincross section. Theﬁbers

16

used in this study had two different surface conditions: (1) 'AS4" ﬁbers are surface
treated with an electrochemical oxidation process which optimizes their adhesion to epoxy
matrices and (2) 'AS4-C" ﬁbers, in addition to being surface treated, are coated with a
100-200 nm layer of epoxy applied from a organic solvent directly onto the A84 ﬁber
surface. A typical SEM micrograph showing the surface morphology of A84 ﬁbers is
shown in Figure 2.3. The surface energetics and details on the surface morphology
have been studied in detail by Dual et al. and reported elsewhere [27].

2.2 EXPERIMENTAL METHODS

Many methods are available for determining the interfacial shear strength in a single
ﬁber composite. Extensive reviews are available [11,28,149]. In this section, three
different protocols for determining the interfacial shear strength of single ﬁber systems
will be outlined. Also, in this section, experimental procedures for determining the
material, thermal and optieal properties of the matrices will be given. Finally, an
experimental protocol will be given for determination of the surface free energies of the
matrices and ﬁbers used.
W

The single ﬁber fragmentation test was originally used by Kelly and Tyson [29] who
used some brittle ﬁbers embedded in a copper matrix. They observed that upon
application of a tensile load to the matrix, a multiple ﬁber fracturing phenomenon took
place. Since then, many experimenters [30,31,32,33,34] have used this technique to
study ﬁber/ matrix adhesion in single ﬁlament thermoset as well as thermoplastic systems.

In general, the fragmentation test involves fabrieation of single ﬁber specimens. This
is achieved by mixing of the curing agent and resin in proper proportions and pouring
into a mold with a ﬁber aligned axially within it followed by appropriate curing. The
mold itself is a silicone room temperature vuleanizing (RTV 664) eight eavity mold.

l7

15m xsaaa 1682 1.?0 135091

 

Figure 2.3: Seanning electron micrograph of earbon, A84 ﬁber

18
Standard ASTM 64 mm 'dogbone" specimen eavities with a 3.18 mm wide by 1.59 mm
thick by 25.4 mm gage section are molded into a 76.2 x 203.2 x 12.7 mm silicone piece.
Sprue slots are molded in the middle of each dog bone to a depth of 1/32' and through
the end of the silicone piece. A more detailed description of the dimensions of the molds
used has been given by Herrera-Franco et al. [28].

Single ﬁbers approximately 5" length are selected by hand from a ﬁber bundle kept
inside of aluminum foil. Single ﬁlaments are carefully separated from the tow without
touching the ﬁbers, except at the ends. Once selected, a ﬁlament is mounted in the mold
and held in place with a small amount of rubber cement at the end of the sprue. After
the rubber cement sets, the liquid matrix is carefully pipetted into the molds and cured.
More details on this procedure have been provided by Herrera-Franco et al. [28,35].

After the ﬁber is totally encapsulated in a matrix coupon and cured, a tensile load
is applied to the coupon, and an interfacial shear stress transfer mechanism is relied upon
to transfer the coupon tensile forces to the encapsulated ﬁber through the interface. The
tensile jig used for straining the specimens is shown in Figure 2.4. As the load is
increased on the specimen, shear forces are transmitted to the ﬁber along the interface.
The ﬁber tensile stress increases to the point where the fracture strength of the ﬁber is
exceeded and the ﬁber breaks inside the matrix. This process is repeated producing
shorter and shorter fragments until the remaining fragment lengths are no longer
sufﬁcient in size to produce additional fracture through this stress transfer mechanism.
At this point, the critieal length (1,) is said to have been reached. This fragment process
is shown schematieally in Figure 2.5. The fragment critieal length-to-diameter (Lid) is
measured with the aid of the optical microscope, under which all the tests are conducted.
A shear lag analysis is completed (force balance at the interface) on the fragments in
order to calculate an interfacial shear strength, 1, according to:

l9

 

 

Tensile jig used for conducting fragmentation tests

Figure 2.4

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0
E
(I)
LENGTH
(I)
0)
LL!
0)
* LENGTH
(I)
(0
LL]
c - — _ — E
(O
LENGTH I ,
c

Figure 2.5: Process of fragmentation

 

21

“r d
=__ (2.1)
t 2 1c

Different statistical analyses exist and have been used for ﬁtting the distribution of
critieal lengths [28,36,37]. Throughout this work, the distribution of critical lengths will
be ﬁt to a two—parameter Weibull statistical model [30,36,51] and the following equation
will be used to calculate r, the interfacial shear strength. Where a and B are the shape

0
t=——f-I‘(1-%) (2.2)

29

and scale parameters, respectively, and 1‘ is the Gamma function. or, represents the ﬁber
tensile strength at the gage length in question and for this work was obtained from the
literature [38] for all ﬁbers used.

The embedded single ﬁber technique has several advantages. A large number of data
points can be gathered in each observation, the failure process itself can be observed in
transmitted (polarized) light, the locus of failure is identiﬁed and the process replicates
the in-situ events in the actual composite itself. A plethora of experimental data has been
generated with this method and published elsewhere [31,32,34,39,40].

A specially designed heated cell was constructed to conduct the single ﬁber
measurements at elevated temperatures. The dimensions of the cell (2"x1.25"xl") are
such that it ﬁts snugly around the dogbone coupon and in the straining device shown in
Figure 2.4. The cell is constructed entirely out of teﬂon which has thermal capabilities
up to 300°C. Two aluminum blocks, which house the 'ﬁrerods" (1/4'xl' and 40 Watts,
Watlow Co.) used for heating the interior of the cell, are built into the two outside teﬂon
walls. Quartz glass windows above and below the specimen allow for experimental
observation under an optical microscope. Elongated dogbone shaped specimens (2" gage

22

length) are inserted in the chamber and the gage length is heated to the desired
temperature. Tests are conducted as mentioned previously. Temperature calibration runs
have shown that the entire gage length attains constant temperature to within 5 % of the
set point temperature after equilibration. The time for equilibration is dependant upon
the set point temperature and ranges from 5-15 minutes. Even at the highest
temperatures used in this study (about 120°C), the equilibration time is less than 15
minutes.

W

The procedure used to fabricate samples for the microbond test is similar to that
described by Miller et al. [41,42]. It involves deposition of a small amount of resin onto
a clean surface of a ﬁber in the form of several microdroplets. The droplets form
concentrieally around the ﬁber in the shape of ellipsoids and retain their shape after
appropriate curing. Once cured, the microdroplet specimens and ﬁber diameter are
measured with the aid of an optical microscope. The embedded length is ﬁxed by the
diameter of the microdroplet along the ﬁber axis, which is dependant on the amount of
resin deposited on the ﬁber. In these experiments, 6" lengths of ﬁbers were stretched
across a rectangular frame and held in tension (with tape) while random drops of various
sizes were deposited on the ﬁbers with the aid of a very thin (30 gage) needle, the ﬁber
collection was then appropriately cured. The practical minimum limit for embedment
length using this technique is about 70 microns.

In this work, a ﬁber holder and straining device, mounted horizontally and positioned
under an optieal microscope, was used to collect the data. One end of the ﬁber specimen
is ﬁxed adhesive to a metal tab which is connected to a loadcell (the microdroplets are
sheared off the ﬁber at a rate of about 100 microns/min using a moveable stage). To
grip the droplet, an adjustable micrometer equipped with ﬂat, rectangular cross-section
blades is used. The blades of the micrometer are ﬁrst positioned on one side of the

23
droplet, then the blades are brought into contact with the ﬁber and then opened slightly
to let the ﬁber, but not the droplet, move between them. This process reproducibly
positions the blades properly in relation to the droplet and ﬁber. The moveable stage is
used to translate the ﬁber and droplet laterally in the horizontal plane. As the blades
continue to move, they make full contact with the droplet and an axial force is exerted
on the droplet. The axial force on the droplet is then transformed to the ﬁber through
a shearing force at the ﬁber/ matrix interface. When the shearing force exceeds the
interfacial bond strength, detachment occurs, and the droplet is displaced horizontally
along the axis of the ﬁber. The maximum in the force curve is taken as the point at
which the droplet has debonded from the ﬁber. A simple force balance at the interface
gives the following relation for determining the interfacial shear strength. Here, F is the

F

1": ndL ”'3’

 

maximum force recorded, (1 is the ﬁber diameter, and L is the embedment length.
Figures 2.6 and 2.7 show typical droplets on ﬁbers and the apparatus used.
W

To determine the interfacial characteristics of the matrix when in a ﬂuid state, pull-
out experiments were conducted with a gravimetric electrobalance (see section 2.2.8 for
a more detailed description of the electrobalance itself) apparatus. A schematic of the
apparatus is shown below in Figure 2.8.
The pull-out tests were conducted as follows:
(1) Immerse a single ﬁlament of carbon ﬁber to a known depth (controlled by the motor
and usually about 7 mm) in the resin which is maintained at a temperature, T and
Vlscosuy, n.
(2) Pull out the ﬁlament at an roximate rate of 25 microns/min (preset by

motor). Alternatively, it was also ound that it was as convenient to manually move the
stand that the resin rests upon. Either technique resulted in very reproducible results.

24

 

Figure 2.6: Scanning electron micrograph of microdrops on ﬁbers

25

 

Figure 2.7: Schematic of microbond apparatus

26

 

' PULL-OUT WITH moron- DRNE

CARBON FIBER\

ooooooooooooooooooooooooooooooooooooooooooooo

ooooooooooooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooo

ooooooooooooooooooooooooooooooooooooooooooooo

 

uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu

 

............................................
.............................................

.............................................
.............................................

.............................................

 

 

 

 

 

Figure 2.8: Schematic of pull-out experiment apparatue

(3) Take the steady-state value (after initial transient behavior dies out) in the force
versus time curve as force at pull out.

(4) Calculate an approximate interfacial pull-out (shear) strength, 7, according to:

1': 88 (2.4)

7‘ drEr

 

where,
r = Interfacial pull-out strength (Pa)
F. = Steady-State pull-out force (gms)
d, = Diameter of ﬁber (about 7.4 microns)
E, = Immersion depth (usually about 7 mm)

(5) Relate r of the known viscoelastic properties of the matrix.

27
Piggott et al. [43] and Gent et al. [44] have used this type of experimental methodology
to calculate interfacial tensions and pull-out forces in cured epoxies and polymers.
Two types of pull-out experiments were conducted. Neat DGEBA resin was used
to conduct pull-out tests at various temperatures (and thus, at different viscosities).
Additional experiments were conducted after the matrix was allowed to react for a given

amount of time at an isothermal temperature. These samples were quenched at speciﬁc

times (at known extent of cures) and pull-out experiments were conducted.

 

Normal strength measurements of the interface were made by aligning the ﬁber in
a direction perpendicular to the plane of load application. Figure 2.9 shows a schematic
of the samples. Sample preparation technique was similar to the single ﬁber
fragmentation sample preparation technique discussed in section 2.2.1. Once the dog
bone shaped samples are cured, they are polished and subject to a tensile load. In this
set of experiments, however, a pneumatic controller was used to apply load in order to
measure the amount of load applied to the sample. An optical microscope was used to
detect the ﬁrst signs of debonding. Once detected, the load is recorded and multiplied
by an appropriate stress concentration factor [45] to arrive at a load at debonding.

 

The matrix property data (Young’s modulus, strain to failure and Poisson’s ratio of
the matrix materials) used in this study was obtained using a Materials Testing System
(MTS). The speciﬁc instrument used was a MTS-880 servo-hydraulic instrument
equipped with a biaxial extensiometer. Samples were cured into standard 4.5'
gagelength (or 1" gagelength) hourglass shaped specimens suitable for material property
testing. Load/displacement data was obtained directly from the MTS at a rate of
approximately 0.02 inches! min.

28

Ps’——- | ——>p

 

___\ /___.
\—

 

 

TOP VIEW

P< 9
/
interfaé A matrix

I
CYLINDRICAL FIBER
CAUSES STRESS CONCENTRATION

matri

 

 
  

 

 

 

__:>P

 

 

 

 

 

Figure 2.9: Schematic of transverse strength specimens

29
The Young’s modulus, E, was computed by extending the initial portion of the
stress/ strain curves and by measuring the slopes of these relatively linear regions. The
shear modulus, G, was then estimated by measuring the Poisson’s ratio, P, of the matrix
material and by assuming the matrix material to be isotropic; whereby the following
relation can be used [46]:

E
G:______.. (2.5)
2(1+v)

The strain to failure, cf, of the various matrices were determined directly from the
endpoints of the stress/ strain curves and by knowing the exact gage length of the
specimens. The strain at ﬁnal ﬁber (i.e. at critical length) break, 5,, represents the strain

at which the ﬁnal break occurs in the fragmentation test (section 2.2.1) and is always less

 

Two methods were used to determine the glass transition temperature (T‘) of samples
used in this work. For bulk samples, a Differential Scanning Calorimeter (DSC, DuPont
9900) was used. DSC scans of cured matrices, as well as cured droplets were made at
5°C/rnin under nitrogen purge using open pans. The T,’s were estimated from the
midpoints of the transition regions. _

For individual as well as clusters of droplets (section 2.2.2) too small to test on
DSC, a Thermal Mechanical Analyzer (TMA, DuPont 9900) was used. In this method,
the thermal expansion coefﬁcient is used as an indicator of thermal transitions. This
method is a novel application of TMA, not attempted or found successful by others, for
measuring thermal properties of very small quantities of polymer. Individual droplets
were prepared on ﬁbers as mentioned in section 2.2.2 and subsequently, after

30
measurement of droplet dimensions, cut from ﬁbers and placed under the TMA probe
for T, determination. For droplets less than about 600 microns (0.6 mm) in diameter,
a cluster of droplets of similar size was used to generate the necessary Signal (which is
approximately 0.8-1.0 mm) for determining the T,. Care must be taken with this
technique since the small quantities of polymer have a tendency to adhere to the TMA
probe which would necessitate a bakeout of the probe before the next set of experiments
can be conducted. A careful check was made between these two experimental techniques
(DSC and TMA) to assure that consistent T,’s were obtained for identical bulk samples.

DSC was also used to carry out kinetic experiments. Sample size was 15-35 mg.
Isothermal runs were used to calculate extent of reaction (cure). Samples were cured
outside the calorimeter at the desired temperature. After various times, the samples were
quenched with ice (water) and residual cure was measured by DSC at a heating rate of
5°C/min. The fraction reacted, a, was calculated as that fraction of the total possible
enthalpy of exothermic reaction [48,64,78]. DSC was also used to determine T, as a
function of extent of cure, 0:. Samples were quenched after exposure to a temperature
for a given time and subsequently analyzed (as described previously) for T:-

A Dynamic Mechanical Analyzer (DMA, DuPont 9900) coupled to the Dupont 9900
Thermal Analyzer System was used to carry out viscoelastic experiments on the matrices
[47]. Loss (G’) and storage modulus (6") data was obtained as a function of
temperature. The instrument was operated at a ﬁxed frequency of 1 Hz. and amplitude
of 0.6 mm. The modulus data reported here refer to flexural moduli, which are closer
to tensile modulus than to the shear modulus because of the sample dimension utilized.
The sample dimensions were approximately 3.5x0.5x0.2 inches. Dynamic Viscoelastic
experiments were performed at an initial ambient temperature up to the matrix T, at a
rate of 5°C/ min. The experiments were discontinued at temperatures close to the T, due
to the fact that large scale deformations are expected to occur in the vicinity of T,.

31
W

Viscosity measurements were made with two different pieces of equipment. A
tabletop Brookﬁeld Viscometer was used to gather data at low viscosities (< 500 cp).
Different spindle sizes were used to get the maximum amount of sensitivity. The bulk
of the viscosity and gelation measurements, however, were made using a Rheometrics
Mechanical Spectrometer (RMS 800). Simple temperature sweeps were made at
isothermal temperatures and a ﬁxed frequency of 1 rad/ sec. Parallel plate geometry
(with a gap width of about 1 mm) in the dynamic, oscillating mode was then used to
measure dynamic properties (viscosity, storage modulus and loss modulus) as a function
of time at a ﬁxed frequency (1 rad/ sec) and temperature. Further details on the
experimentation technique is available elsewhere [48].
WW

Surface energy measurements were done by measurement of dynamic contact angles
(advancing and receding) for single ﬁbers as well as cured matrices using a micro-
Wilhelmy technique with water, methylene iodide and ethylene glycol as characterizing
liquids (see Table 2.3 below).

Fibers, about 10 mm in length, were attached with cyanoacrylate (”super glue”)
adhesive to a nickel hook which hung on a Cahn RG Electrobalance which measured the
force on the ﬁber as it was raised and lowered in the characterizing liquid.
Approximately 2.5 mm of the ﬁber (or matrix sample) was immersed in the liquid of
interest before being moved in and out of the liquid at the rate of 25 microns/sec. The
nickel hooks were dipped into the matrices of interest and allowed to cure for testing of
the various matrix materials. Once cured, the uneven ends were snipped off leaving
behind a thin ﬁlm which was dipped into the liquid of interest and tested.

32

 

WATER

 

ETHYLENE
GLYCOL

 

METHYLENE
IODIDE

 

 

 

 

 

The samples were allowed to stabilize 30 seconds before the static force measurement
was taken. The entire apparatus was enclosed in an environmentally controlled chamber
to eliminate wind currents, reduce contamination of the characterizing liquid, insulate the
apparatus from vibrations, and maintain constant temperature. All glassware (and other
materials) was thoroughly cleaned with a strong mineral acid ('Chromerge') and baked
out to avoid any type of contamination.

Contact angles (0) were determined (neglecting the buoyant force) according to the

following equation:

F=nrg=y 1' c'PCOSe (2-6)

where m is the mass measured by the electrobalance, g is the acceleration due to gravity,
and P is the perimeter (=rd for circular cross section samples) of the sample. A
minimum of 35 measurements were taken for each sample to assure statistical
signiﬁcance.

Surface energy analyses of the samples was determined from the contact angles in
the manner described by Kaelble et al. [49]. This method assumes, for low surface

33

energy solids such as polymers, that the total surface free energy across the interface,
1“, is composed of a polar, 7“,, and dispersive part, 71.43 7L, = 7“ + 7L, where i stands
for the ﬁber, matrix or liquid. Due to the simplicity of this analysis for determining
surface free energies, many experimenters have resorted to using it [27,50,105] for
determining the surface energy characteristics of both ﬁbers as well as polymeric
matrices.
W

Some common polymeric matrices, when undeformed, can be considered optically
isotropic. However, when subjected to stresses, whether due to externally applied loads
or thermally induced stresses from differential shrinkage during sample preparation, the
material becomes optically anisotropic (birefringent). Since 828 epoxy resin is
transparent and exhibits birefringent behavior when subjected to stresses, it would be
beneﬁcial, for a better understanding of ﬁber-matrix interactions, to study the stress
birefringence adjacent to the ﬁbers, before, during, and after application of load in the
single—ﬁber embedded test described above. Drzal et al. [51] observed qualitative
differences in the stress pattern resulting from interface changes and levels of adhesion
when working on carbon ﬁbers and epoxy matrices. Recently, Marshall et al. [52] have
reported that visual observation of the events taking place at the interface during a
different type of single ﬁber pull-out test is also valuable in determining the type of
adhesion that exists there. Scanning electron microscopy (SEM, JEOL 2200) was also
used to identify fracture surfaces and the surface morphology of carbon ﬁbers. Bascom
et al. [53] have demonstrated how SEM of fractured surfaces can be used to detect levels
of adhesion in thermoplastic composites.

 

This chapter focuses on the kinetics of crosslinking, time to gelation, and in general,
how the interface behaves in the viscous regime (up to the point of matrix gelation).
Interfacial parameters are quantiﬁed with a single ﬁber gravimetric pull-out test and the
data is modeled with a modiﬁed WLF-type equation. This Chapter is based on work to
be published by Rao et al. [54].

3.1 INTRODUCTION

In order to make optimum use of epoxies as structural materials, it is important to
know what the curing process is, to what extent it proceeds, and the Structure of the
cured material as a function of curing time and temperature. Interfacial properties
likewise play a major role in developing the ﬁnal properties of the epoxy based
composite material. Conventional isothermal processing of thick section composites, for
example, have been found [5,7] to fail due to interfacial defects formed at some point
during the curing process. The development of non-conventional curing methods
requires knowledge of the process by which interfacial strength develops during the entire
processing cycle of these types of composite materials to be able to determine where
these defects initiate and propagate. Moreover, interfacial properties need to be related
to readily measurable properties of the reacting matrix material if they are to be used
effectively. Extensive studies [l4,55,56,57] have been conducted relating interfacial
properties to matrix and ﬁber properties in the solid state (after matrix gels and sets).
Recent studies [36,5 8,59] have investigated the variation of interfacial properties as a
function of matrix properties at elevated temperatures. However, very little work has

34

35

been done in an attempt to understand the behavior of the interface during the initial
stages of cure when the matrix is in a ﬂuid state. Though the matrix will be unable to
transfer stress to the interface when the matrix is motionless in the fluid state, as the
consolidation process moves ﬁbers past the matrix shear Stresses will be introduced.
Concurrently the matrix reacts and its viscosity increases the magnitude of these stresses.
The ability of the interface to withstand these stresses during the early stages of
processing can reduce the tendency to separate matrix from the ﬁber and hence produce
voids. Such information would be desirable for process models. The early stages of
cure of the matrix mass will be characterized for extent of cure, viscosity and modulus.
These data will then be combined with gravimetric pull-out experiments to measure a
"pseudo” interfacial pull—out force based on the changing viscosity of the reacting
material. A model for this process has been developed.

3.2 EXPERIMENTAL ANALYSIS

DGEBA resin was processed at stoichiometric conditions with the hardener meta-
phenylene diamine (mPDA). The hardener was melted at 70°C before being mixed with
the DGEBA resin at about 70°C. Fresh samples were used for all experiments.

The ﬁber used for the pull-out experiments was a carbon, AS4 ﬁber described in
detail in Section 2.1.3.

All kinetic experiments were carried out on a DuPont 9900 model differential
scanning calorimeter as described in Section 2.2.6. DSC was also used to obtain the T,
data as a function of extent of cure of the matrix. Since resin and hardener were mixed
at 70°C, most of the discussion in this chapter will center on kinetic data above 70°C.
Viscosity and gel point data were collected, as described in Section 2.2.7, on two
different pieces of equipment. A Brookﬁeld viscometer was used to gather data at low

viscosities. At higher viscosities (> 5000 cp) a Rheometrics RMS was used, in the cone

36

and plate mode with a gap width of 1 mm, to collect the appropriate data. Isothermal
data was collected to the maximum extent of cure possible (i.e. to the point of gelation)
for a given temperature. The raw data (obtained from RMS) is shown, for the reacting
system, in Figure 3.1 for a temperature of 125°C. Viscosity for the DGEBA resin alone
was also measured as a function of temperature. The results are shown in Figure 3.2.
As expected, the data in Figure 3.2 show the DGEBA resin to be a Newtonian ﬂuid [12].

Many authors have used [60,61,621 viscosity measurements to track the progress of
a reacting, crosslinking system. Most of this work focuses on relating the viscosity to

the temperature and degree of cure according to a WLF-type relationship shown below:

-C1(T-TL) (3.1)

log(n/ng) C2+T-Tg
where,
r) = viscosity (cP)
= viscosity in ”fully cured“ state (constant [63,78] at 10“ cP)
(I1, C, = characteristic "WLF” constants for this system
T = reaction temperature (°C)
T, = glass transition temp. , function of extent of cure, a

In order to evaluate the constants C, and C2, Equation 3.1 is rearranged to give,
.. c1 ( T- T!) _ C2

1 _'L
ogt 11,)

Equations 3.1 and 3.2 are the basis of the analysis presented in this particular chapter.

 

(T'Tg) = (3.2)

Pull-out experiments were conducted in a gravimetric, Wilhelmy type apparatus
described earlier in Section 2.2.8 (Figure 2.8). Similar to the viscosity experiments
described above, two types of pull-out experiments were conducted. Neat DGEBA resin
was used to conduct pull-out tests at various temperatures (and thus, at various
viscosities). This data is shown in Figure 3.3. Additional experiments were conducted

Viscosity (cP)

37

10’

 

 

Lo Data at 125°C]

 

10' o
10’ o
0
0
10‘ 0°00 0° 0 o o
0
00
3
10 0
0
101 r I f I T I r r T j “—7— I T.
0 2 4 6 8 10 12

TIme (minutes)

Figure 3.1: Viscosity vs. time for DGEBA/mPDA system at 125°C

 

Viscosity [PG 3]

38

 

 

 

 

 

100
4 O DGEBAR '
3I 83“] nogcn) = B(0)*1000/W'-t 8(1)
8(1) = —16.7689
8(0) = 5.3204
10':
1 I I I r I I I
3.20 3.25 3.30 3.35 3.40

 

1000/(I[K])

Figure 3.2: Viscosity vs. temperature for neat DGEBA resin

roximate Interfacial

App
Pu I—Out Strength (PG)

39

 

 

260—Lo GRAVIMETRIC DATA FOR NEAT DGEBA REsm

.J
.4

220~

d

 

180—
140~
100*
" O

‘ O
60—

hi 1

 

 

20 ﬂ T f j j T I I I r I

O 20 4O 60 80 100

Viscosity (Poise)

Figure 3.3: Viscosity vs. pull-out force for neat DGEBA resin

 

40

after the matrix was allowed to react for a given amount of time at an isothermal
temperature. These samples were quenched at speciﬁc times (at known extent of cures)
and pull-out experiments were conducted up to the gel point of the system. Pull-out
experiments (with the reacting system) are tedious to conduct as the gel point of the
system is approached. The reacting system has a tendency to exotherm, as the gel point
is approached, and instantaneously gel causing the termination of the run and the
experimental apparatus to malfunction, usually necessitating recalibration.

3.3 RESULTS AND DISCUSSION
W

An extensive amount of kinetic studies have been conducted on epoxy reactions
[9] . Lee et al. have suggested an autocatalytic mechanism to describe the crosslinking
process [64], while others [65,66] have suggested an initial autocatalytic mechanism
followed by a pseudo-ﬁrst order diffusion controlled regime. Prime et al. have
cOnducted an extensive amount of kinetic experiments with this system (DGEBA/m-PDA)
at a non-stoichiometric ratio of resin to curing agent. Much of Prime’s work [9,67], as
well as work done by Kamal [68] indicate that these type of crosslinking epoxy reactions
proceed autocatalytically with an overall kinetic order of two until the diffusion-
controlled regime is reached, whereby they become pseudo—ﬁrst order. In this analysis,
the autocatalytic model with an overall ln'netic exponent of two is used and validated with
appropriate DSC data.

Isothermal experiments were carried out as discussed previously and the resulting
data is presented in Figure 3.4 as extent of cure, 01, versus time. As expected the nature
of the curves (at elevated temperatures) indicate an autocatalytic reaction [69]
mechanism. The data in Figure 3.4 also Show that diffusion limits the maximum extent

41

 

 

50 C
80 C
90 C
110 C
120 C
140 C

 

 

ODBOGO

 

 

 

 

 

I —I l
O 50 100 150 200 250

Isothermal Time (minutes)

Figure 3.4: Extent of conversion, 0:, vs. time for isothermal kinetic data

42
of cure at lower temperatures; only at about 110°C is a cure of 95 % achieved. A widely-
used [68] three parameter kinetic model was used to monitor reaction rate:

%:-=(k1+k2a’") (1-a)” (3.2)

Wherii, k2 = Arrenhius-based reaction rate wnstants (min")
da/dt = Reduced reaction rate (min")
m,n = Kinetic exponents (overall order of reaction = m+n)
at = extent of cure

A plot of reduced reaction rate, da/dt, versus time is shown, for various isothermal
temperatures ranging from 50-140°C, in Figure 3.5. AS expected, the maximum in
reaction rate occurs at lower times for higher temperatures. A non-linear regression
analysis [15] was used to ﬁt all of the data in Figures 3.4 and 3.5 to Equation 3.3 above.
The resulting relevant parameters are shown in Table 3.1.

In Table 3.1 below, the reaction rate constants (km) are incorporated into an
Arrenhius form while the kinetic exponents are incorporated as a function of temperature.
The activation energies determined for this system are in excellent agreement with values
in the literature reported for similar systems by Prime et al. [9,67], and Acitelli et al.
[70]. A comparison of the model prediction (Equation 3.3 with the appropriate
parameters from Table 3.1) and experimental values of the reduced reaction rate (versus
time) is shown in Figure 3.6. It can be seen that the agreement is good at high
temperatures. This close agreement indicates that the previous assumption of the overall
reaction order (m +n) being two is valid. At the lower temperatures (less than about
85°C), however, the reaction is less autocatalytic and the reaction kinetics can be
adequately described by a pseudo-ﬁrst order reaction mechanism (see Appendix A).

An equally elegant alternative way of determining these kinetic parameters from
dynamic DSC data has been suggested by Kissinger et al. [71] and used by others

43

 

  

 

 

 

 

 

 

t; O 100 C
0.1000 ff‘ e 90 C
”'1' 0.0500? \ g ”0 C
E " ‘ 120
E .‘\- - A 130 c
«as 00100:,— . .. _
CD I
“‘6 0.0050:
Q: ~ 0
C “ 9
-9
‘8 00010-5
O 2
cu 00005-—
C: ‘
0.0001 E , , j 1 r
0 20 40 60 80

Figure 3.5: Reaction rate, da/dt, vs. time for isothermal data

Isothermal Time (minutes)

 

100

Reaction Rate

dcr/dt (min-I)

0.1—4-

 

0.12-

l

0.10-

0.08-

0.06-

0.04-

0.02-

0.00

 

 

G-O MODEL AT 55'C

6—0 MODEL AT 75'C

A—A MODEL AT 125'C
A DATA AT 125'C
9 DATA AT 75'C

 

 

 

0 DATA AT 55°C ‘

O

I I I v u v I 1
0.0 0.2 0.4 0.5

extent of cure, or

 

Figure 3.6: Comparison of kinetic model to data at 55°C, 75 °C and 125°C

45
[72,73]. In their method, different heating rates are used to determine “peak” values and
these are used, after algebraic manipulation of Equation 3.3, to determine the kinetic
parameters in Table 3.1. Appendix A outlines the usage of this method (with isothermal
DSC data)

Illﬂl'K' . ll

Reaction Rate Constants of the form, k=Ae‘B’":

k, = 1.693xlO‘e"7°"‘m
k2 = 9.505x103¢(4l96m

A, knareinmin“
Tisin°K
E/Risianal-°K

Kinetic Exponents:

m = -2.75x10’T+l.43, for T > 85°C
n=2-m

Tisin°C

 

to determine the kinetic parameters for this particular system. It will be seen that the
agreement, with the isothermal rigorous regression technique used above, is good.
Equation 3.3 can be next used to predict the gel time as a function of temperature once
the extent of cure at the gel point, a“, is known.
W

In order to use Equation 3.1 to predict viscosities, the constants C, and Q need to
be determined for the system at hand. Equations 3.1 and 3.2 require the knowledge of
T, as a function of extent of cure. The appropriate experiments were conducted as
described in Sections 2.2.6 and 2.2.7 and all of the data have been combined and
condensed into Figure 3.7. These data agree quite well with the semi-empirical
relationship suggested by Pascault et al. [74] for the dependence of T, on the extent of

46

 

 

 

 

 

 

 

 

 

ﬂ 180
0 4 0 Region I. «(0.6
L , e Region II, a>0.6
8 4
3
46 140-I
L -1
Q)
o_ .
E I
n)
I" 1004
C ..
.9
:1: 'I
g .
O
E 50" O o
l— 1 o
m d
to
.9. 4
O
20 Testerrseveseerr+wre
0.0 0.2 0.4 0.6 0.8 1.0

Extent Of Cure, or

Figure 3.7: T, vs. extent of cure, a

47
cure for crosslinking systems. The data in Figure 3.7 fall into two distinct regimes; one
for a < 0.6 and one for at > 0.6. The appropriate ”best-ﬁt" relationships are shown for
the two regimes in Table 3.2 below:

WW

FOR 0150.6. , = 35.89+52.1a ‘
; FOR a>0.6, T, = 335615001

The dramatic increase in T, after crossing the gel point of the system is expected and has

 
     

been observed before for similar epoxy systems [75]. At the lower curing temperatures,
measured T,’s exceed the curing temperature at the higher extent of cures due to
vitriﬁcation [10]. Because the model (Equation 3.2) is very sensitive to changes in T-T,,
data that fall into the ’vitriﬁed’ regime are not used.

Using the viscosity data from Figure 3.1 (the data for 125°C is shown; however,
similar data was generated for different temperatures and used in this analysis) and the
T, data from Table 3.2, the constants C, and Q can be determined from Equation 3.2.
The appropriate linear form of Equation 3.2 is shown in Figure 3.8 for three different
temperatures. The constants C, and Q were determined as slope and Y—intercept of a
”best-ﬁt" line through all of the data. The appropriate calculations of slope and intercept
result in C,=11.30 and Q=0.580 for this thermoset system. Nielsen [12] has suggested
that the constant C, should be approximately 14 for many polymeric matrices and the
constant Q varies depending upon the viscokinetic behavior of the particular polymeric
system. It should be noted that if additional data at temperatures down to 80°C are
added to Figure 3.8 in appropriate form, the slope and y-intercept change less than 5%.

(T-Tq) (°C)

48

 

 

 

 

 

 

80
o T=100'C
. a T-125'C
50* A A 7-117-c
.J A 7
4.0..
204
.1
0...
1
-20«
~40 T r '— r r T 7 r f I —r I r f r

 

 

 

-7 -6 -5 -4 :3 ~12 -1 O 1 5
(T—Tg)/log(n/n,) (°C)

Figure 3.8: Reduced, modiﬁed WLF plot of kinetic data

49
Insertion of the constants C, and Q and the relationships for the T,’s from Table 3.2
into Equation 3.1 and slight rearrangement gives the following viscosity model for the
reacting DGEBA/mPDA system.
For 0250.6 and for T in (°C),

(-11.3)(1~3s.89-52.1a)

(3.4)
(0 . 58+T-35 . 89-52 . 1a)

logn=15+

and for a>0.6,

(-11.3)(IL335.6a+150)

(3.5)
(0.58+I~33s.6a+150)

 

logn=15+

Viscosity values predicted by Equations 3.4 and 3.5 at temperatures of 80°C, 117°C
and 125°C are shown in Figure 3.9. Actual RMS data (as described in Section 2.2.7)
is also shown at these temperatures. At all temperatures, the model predicts changes in
viscosity with time and degree of cure. At lower extents of cure (low viscosities) there
is seen to be some discrepancy between experimental and predicted viscosities at all
temperatures. This is mainly due to the lack of sensitivity in the equipment used to
measure very low viscosities (< 200 cP). Additionally, there is an initial temperature
effect which causes the viscosity to go to a minimum [76] before the crosslinking
reaction occurs causing the viscosity to increase.

Three different methods were used to determine the time to gel. In method I, the
time at which the storage modulus (G’) crosses the loss modulus (G') at a given
temperature was used as the characteristic time to gel [75]. A typieal plot of G’ and G"
(RMS data) is shown in Figure 3.10 for a temperature of 80°C. As expected, when all
of the data was analyzed for a“, it was found to be constant between 0.67-0.73. Flory’s
theory [77] predicts an a... of about 0.6 for this stoichiometrically cured difunctional

50

 

 

 
  
 
 
 

 

 

 

 

 

 

107
H Model at 80'C
0 Data at 80'C
H Modal ot 100'C
10‘ D Data at 1oo'c A
H Modal ot 125'C
E: A Data at 125'0
3 10-
>,
.4:
8
8 10“ A:
'5 A Au 0 0 ‘9
10’ A D o
O
we vervTWWr e e+v+ﬁ
1 5 10 50 100

Time (minutes)

Figure 3.9: Comparison of WLF viscosity model to RMS data at
80°C, 100°C and 125°C

G' (Pa)

51

 

 

 

 

 

 

 

10¢ - 10'
o 0' Data at 80°C (Pa)
105 O G" Data at 80°C (Po) 8 O 105
104 104
10: 10’
102 102 ”c?
E,
10‘ 10‘ z
. 0
10° 10o
.
-q . . --1
10 o o o 10
10" o 10"
10., r r 1 r I f f v T ' I ' 1 7 I T T T ' 10-,
0 10 20 3O 40 50 50 7O 80 90

Time (min)

Figure 3.10: G’ and 6" data for DGEBA/mPDA at 80°C

52

system. The slight discrepancy between experimental values and the absolute value
predicted by Flory’s ”chain” theory could be due, in part, to slight stoichiometric
variations during experimental preparation techniques. In method II for determining t“,
the time to reach a viscosity of 10‘ Pa—S was used as the characteristic time. Finally in
method 111, a“, was substituted into the kinetic Equation 3.3, with the appropriate
parameters from Table 3.1, and the resulting expression numerically integrated for t",
[78]. The calculations from all three methods are summarized in Table 3.3.

The data shown in Table 3.3 is shown graphically in Figure 3.11. It can be seen that
the 6’ =6” data (method I) and the viscosity data (method 11) agree closely throughout.
The kinetic model predicts slightly lower t,.,’s at the lower temperatures. This may be
partially due to lack of accurate kinetic and network formation data at these temperatures.
In general, the data in Figure 3.11 agree very well with work done by Prime et al. on

the same system [9].

 

 

 

 

 

 

 

 

The viscosity versus pull-out data (for the unreacting, DGEBA resin system) shown

in Figure 3.3 was ”best-ﬁt” to the following regression line,

53

 

 

 

 

 

 

 

 

 

80
”a _
B 60—
3
.E ‘
E, a
(D
E 40
C .
.9 .
P. 20—
CD
0 ‘ . . EB
q 0 Kinetic Model .
O
. EB \flsc. Model
G~€ G'=G" Values
0 1 1 s T 1 T T T v f '
7O 80 90 100 110 120 130

Temperature (°C)

Figure 3.11: Temperature vs. time to gel as predicted by various techniques

54
n=54.481:-2050 ”-6)

where,

n is in cP

r in in Pa

Insertion of Equation 3.6 into Equations 3.4 and 3.5 yields, for «50.6

15,, (-11.3) (T-35.89-52.1a)

 

 

 

 

10 70.sa+1"-3s.39-52.1a) +2050 (3.7)
t:
54 .48
where,
ris in Pa
T is in °C
and for a>0.6
15, (-11.3) gr—335.5a+150)
10 (o.sa+r-335.6a+150) +2050 (3.8)
t:
54 .48

the units are the same as in Equation 3.7 above. Equation 3.8 cannot be veriﬁed
experimentally since pull-out experiments cannot be conducted above the gel point of the
system (which experimentally occurs between 0.65-0.70 extent of conversion).
Comparison was made between the model prediction for pull-out strength at given
extent of cures (Equations 3.7 and 3. 8) and actual pull-out data as measured by the
gravimetric technique discussed earlier is shown in Figure 3.12. For all temperatures
and extent of cures, the agreement is good except at low conversions, where as discussed
earlier, viscosities were difﬁcult to measure with any degree of accuracy. Thus,
Equations 3.6 and 3.7 as well as Figure 3.12, allow for the estimation of the interfacial
pull-out strength of A84 ﬁber and mPDA/DGEBA thermosetting matrix at any point
during cure. To the best of the authors’ knowledge, this type of experimental
methodology has not been attempted before to relate the pull-out strength to matrix

55

 

 

‘1 O WLF model at 117'C f
4 C Data at 117'C

a B-El WLF model at 100'C
" I DATA ot 100'C

j A WLF model at ao'c
~ A Data at 80'C

 

 

 

 

Interfacial Pull—Out Strength (Po)

 

 

 

100 TT I' UTj'rrW VrfT TTrj—fj’

...... Te..-r..,
5000 8000 1 0000 12000 1 4000
Wscosity (cP)

Figure 3.12: Comparison of pull-out model to gravimetric data

56
viscosity and extent of cure up to the gel point. These data provide an estimate on the
upper bound for the amount of stress the interface can withstand in this regime as a
function of viscosity. Imposed stresses that exceed these values in the early stages of
processing may lead to ﬁber/ matrix separation causing void formation in the ﬁnal
product. As expected, the measured pull-out forces are quite small (in the order of
Pascale-whereas solid state interfacial shear strengths are on the order of million Pascals

for this same system).

3.4 CONCLUSIONS

In this chapter, an extensive viscokinetic model was constructed for the reacting
mPDA/DGEBA system. This model predicts the viscokinetic behavior up to the gel
point of the matrix. The crosslinking kinetics were found to be adequately described by
a three parameter autocatalytic model at temperatures above about 85 °C and by a pseudo
ﬁrst order model below 85°C. The changing viscosity was modeled using a modiﬁed
WLF-type relationship. The kinetic and viscosity models were then combined with
gravimetric pull-out experiments to predict the relationship between extent of cure and
the interfacial pull-out strength (using carbon AS4 ﬁbers). Pull-out experiments at

various stages of cure revealed the data to match up satisfactorily with model predictions.

CHAPTER 4

W

In this chapter, results will be reported on the use of the microbond technique for
determining the interfacial shear strength of mPDA/DGEBA matrix with AS4 carbon
ﬁbers. Results will be presented which show that diffusion of the curing agent, mPDA,
at early stages of the cure cycle leads to mechanical property variations in the droplets
and low values of interfacial shear strengths when compared to results obtained for the
same system with the fragmentation test.

A distinct relationship between the glass transition temperature of the droplets and
their size have been found. Smaller dr0plets (< 150 microns) have very low T,’s and
are incompletely cured. It will also be shown that alteration of the curing cycle and
droplet environment has little effect on reducing the loss of curing agent. Additionally,
for the mPDA/DGEBA system, ﬁlms in thicknesses up to 3 mm also are susceptible to
loss of curing agent by diffusion and evaporation. The research reported in this chapter
has been published previously as two different journal articles by Rao et al. [79,80] and

one by Herrera-Franco et a1. [81].

4.1 INTRODUCTION

The interface between polymer matrix and reinforcing ﬁber plays a key role in
determining the ﬁnal mechanical properties of the composite material. “Good" adhesion
and bonding at the interface is paramount for achieving high interfacial shear and off-axis
strength. ”Good” adhesion is also necessary for efﬁcient load transfer and long term
property retention. Since the interface plays a key role in transferring stress from matrix
to the ﬁber, it is important to be able to characterize the interface and level of adhesion

57

58
to understand composite performance properly. Thus, it is essential to have reliable
laboratory techniques to study ﬁber-matrix interfacial interactions.

Several techniques have been developed in an effort to measure the interfacial shear
strength directly. In one technique, a single ﬁber embedded in an epoxy material is
loaded in tension in the ﬁber direction. The ﬁber repeatedly fractures until a ﬁnal
critical length is reached (see Section 2.2.2). These fragmentation tests have been used
to study glass ﬁber/resin interactions by Frazer et al. [82], carbon ﬁber/epoxy
interactions by Drzal et al. [30,83] and highly cross-linked brittle systems by Lee et al.
[84]. A second method is the single ﬁber pull-out test. A small length of ﬁber is
embedded in a thin disk of resin and the force needed to extract the ﬁber from the resin
is measured and used to calculate the interfacial shear strength, 1, using the equation:

F
t: (4.1)
udL

 

This test has also been used, with some success, to study the adhesion of thermosetting
resins to glass and carbon ﬁbers [85,86]. A limitation inherent in these types of pull-out
tests is met when small ﬁbers having diameters of 10 microns or less are used. If the
pull-out force exceeds the ﬁber tensile strength, the ﬁber breaks before successful pull-
out occurs. Thus, very short embedment lengths (.04-.05 mm) are necessary to complete
these pull-out tests successfully. Such small embedment lengths are difﬁcult to work
with in practice, although some investigators have reported limited success with specially
designed apparatus [87] for such tests.

Due to problems inherent with conventional pull-out methods and with other
interfacial testing methods, a modiﬁed pull-out test version has been developed by Miller
et al. [41,42] and used by others [88,89,90]. This method provides a more convenient
method for measurement of interfacial shear strengths of ﬁber/resin interfaces. Because

59
this method uses very small amounts of resin, it is commonly referred to as the
microbond pullout technique or test.
The study in this chapter was undertaken to examine the microbond technique as it
applies to determination of interfacial shear strengths of carbon ﬁbers (AS4) with epoxy
thermoset matrices as well as to compare it to the more established fragmentation test

described earlier.

4.2 EXPERIMENTAL

The experimental methods involved are outlined in detail in Chapter 2 (section
2.2.2). In this chapter, two different curing cycles are used. The ”normal” curing
cycles (2 hr-75°C, 2 hr-125°C) and for the mPDA/DGEBA system a modiﬁed curing
cycle (room temperature-24 or 36 hr, 75°C-2 hr, 125°C-2 hr).

Thin ﬁlm samples were prepared by combining the resin with the appropriate amount
of curing agent and mixing well. Hooks were then dipped into these mixtures and
allowed to cure vertically in a glass chamber. Repeated clippings resulted in maximum
sample thickness of about 4 mm.

4.3 RESULTS AND DISCUSSION

Initially an attempt was made to perform the microbond test after curing the
mPDA/DGEBA droplets with the "normal“ curing cycle listed in Table 2.1. For the
AS4 ﬁber/mPDAlDGEBA system the critical length in the fragmentation test is found
[51,30] to be about 300 microns, so that the droplet sizes cannot be greater than about
200 microns for the microbond test to be conducted. However, the experiments could
not be conducted because the smaller droplets (< 110 microns) were incompletely cured
as evidenced by the fact that they were "tacky” to the touch or ”distorted" during initial
stages of testing. This phenomenon is clearly illustrated in the two micrographs shown

60
in Figure 4.1. It can be seen that the smaller droplets are incompletely cured. For the
larger droplets, as soon as the blades make contact with the droplet, large droplet
deformations take place.

To investigate this phenomenon more closely, the T, of mPDA/DGEBA droplets
cured with the ”normal" curing cycle was measured using the Thermal Mechanical
Analyzer (TMA) and Differential Scanning Calorimeter (for larger droplets) as described
in Chapter 2. The results are plotted in Figure 4.2 (triangular points) as droplet size
versus T, of the droplets. It can be seen that there is a strong correlation between
droplet size and T,. At small droplet sizes, the curing agent diffuses out of the samples,
and the difference between the bulk T, (T, for the fully cured bulk DGEBA/mPDA
matrix is about 135-140°C) and T, of the droplet is about 70°C. As the droplet size
increases, the T, of the droplet also increases until at a droplet size of about 600 microns
the difference between bulk T, and the droplet T, is about 30°C. Since T, reﬂects the
matrix structure and hence its mechanical properties, the droplet mechanical properties
also must change with size. Therefore, measurement of ﬁber-matrix adhesion by the
microbond test can produce artifacts at small droplet size in systems with volatile
components because of changes in droplet stoichiometry. A recently published study by
Rao and Drzal [55] has demonstrated that matrix modulus itself directly affects the
interfacial shear strength. Thus, microbond tests will produce artifacts and cannot get
representative values of interfacial shear strength for these systems unless account is
taken of the change in material properties.

Since microbond tests failed when run with droplets cured with the ”normal" curing
cycle, an attempt to retard the process of diffusion and loss of the curing agent at high
temperatures of cure was made. Droplets were cured with different, modiﬁed curing
cycles as well as in mPDA-rich curing environments. The experimental procedure, in
the case of the systems in which a mPDA atmosphere was used, was altered slightly.

61

 

Droplets of 200 Microns Ready to be Tested

Figure 4.1: Schematic of incompletely cured microdroplets

62

Droplet specimens were prepared as usual and mounted on frames; these frames were,
in turn, placed inside a sealed glass chamber containing an excess of mPDA at the
bottom of the chamber. At processing temperatures the mPDA melted and its vapor
saturated the chamber. The droplets were then cured either with the normal or modiﬁed
curing cycles in contact with the mPDA vapor. The various curing schemes are shown
in Table 4.1. In Table 4.1, all mixes contain a stoichiometric amount of mPDA except
curing scheme C, which contains twice the stoichiometric amount. Interfacial shear
strength for all the systems listed in Table 4.1, determined from the fragmentation test
is 65-70 MPa.

The variation of T, with droplet size, for the different curing schemes, is

IEEIEII'C' ll] 1 1..

 

 

 

 

 

 

 

CURING AMT. OF MICROBOND
CONDITIONS MELTED mPDA 188 (MPa)
NORMAL 6.667 g 38.9
NORMAL 37.42 g 36.8
NORMAL 6.787 g 35.7
25°C-24 m 6.699 g 45.3

NORMAL
25°C-24 hr NONE 41.6
NORMAL
25°C-24 hr NONE 54.7
NORMAL

 

 

 

 

 

shown in Figure 4.2. It can be seen that, at small droplet sizes (<150 microns),
regardless of whether a mPDA atmosphere or a modiﬁed curing cycle is used, the T, is
lower that the bulk T, (even though it has increased when compared with the data from
the “normal" curing cycle alone). At larger droplet sizes, the T, has increased.
However, the values are still low when compared with bulk values of T, for this

particular system. To estimate how much of the amine curing agent is diffusing out of

63

 

 

(Au-9"" e-e MPDA ATM.
o-o MODIFIED

._A_N.QBMAL_
70 if I t l T l t I I I I l j I 1 l r
0 1 00 200 .300 400 500 600 700 800 900

Glass Transition Temperature (°C)

 

 

 

 

 

Approximate Droplet Size (microns)

Figure 4.2: T, as a function of microdroplet size for various curing schemes

64

the droplets, a relationship between T, and amount of curing agent (mPDA) in the sample
is necessary. The plot shown in Figure 4.3 used DSC to determine the relationship
between amount of mPDA in the bulk sample and T, of the sample. By combining the
data from Figures 4.2 and 4.3 an estimate can be made of the droplet mPDA content as
a function of droplet size. These data are plotted in Figure 4.4 where it is evident that,
for the "normal” curing cycle, close to 40% of the amine curing agent may have been
lost in small droplets. Even with the "modiﬁed“ curing cycle, at small droplet sizes,
about 25 % of the amine curing agent is estimated to have been lost by diffusion. Ozzello
et al. [91] and Haaksma et al. [92] have also made references to diffusion being a
problem when conducting microbond tests though no attempts were made to quantify the
phenomenon. Because the modiﬁed curing cycle as well as the mPDA-rich curing
environment data showed less dependency of T, on droplet size when compared with the
normal curing cycle data, microbond experiments were conducted with various
combinations of these conditions (Table 4.1) to compare the fragmentation test with the
microbond test. Figure 4.5 shows the relationship between embedment area and
debonding force, according to Equation 15 , for the various curing schemes. In Figure
4.5, data is shown only for a limited range of embedment lengths. This is due to the fact
that the carbon ﬁbers tend to rupture if droplet sizes greater than about one-half of the
critical length determined from the fragmentation test. The range of data shown in
Figure 4.5 corresponds to embedment lengths generally between one-third and onehalf
of the critical length. It can be seen that all the plots are linear in the range of testing
and the values of interfacial shear strength (1) shown in Table 4.1 represent the slope of
the ”best-ﬁt” line forced through the origin.

Figure 4.5 represents microbond data taken using curing schemes A through F listed
in Table 4.1 and plotted separately in Figure,4.6. From Figure 4.6 it is evident that the
microbond interfacial shear strength calculated for all cases is low when compared with

ogyRE AS

GLASS TRANSITION TEMPE
MEASURED BY DSC

65

 

 

 

 

. ,
180] O NORMAL CURING CYCLE (75'0-2HR. 125°C-2HR)
o MOD. CURING cvcuz (RT—24HR,7s-c—2HR125-c—2NR
14o— ......... o
s g
1204
ﬁ 0......
1004 ,9'
80- o
4 ’96
60-
. 0 ,.-‘B
9 o ,...."
40..., O ...........
‘l
29 —' r— ﬁ T *r r “a r T T T 1 r
2 4 6 a to 12 14 16

Phr OF CURING AGENT (mPDA)

menr43:1,vsinmmmuofnﬂHLAinbmﬂummmmw

 

0.44

.

a...
0.3%
. .... 0“
.......................... e

l A ........ e

0.24- '

 

0.04

 

PERCENTAGE OF AMINE ESTIMATED TO
HAVE DIFFUSED OUT OF DROPLEI' S

 

 

TT'FTTUT'T'T'T‘TT
O 100 200 300 400 500 600 700 800 900

Approximate Droplet Size (microns)

Figure 4.4: Amount of curing agent, mPDA, lost as a function of microdroplet size

67

 

 

 

 

 

 

 

 

28; o (B)NCC + 37.4 g m—PDA
A 3 ate (C)NCC + 245 + 6.78 g m—PDA
E . EB (D)RT—24hr+NCC + 6.67 g m—PDA
O 24': A (E)RT—24hr + NCC
a 4 o (F)RT—36hr + NCC
v 20; A (A)NCC + 6.67 g m—PDA
16— C 33
o .
. / o
0 12—4
:4 1 /
Q i
6 8— //— /
33 1 //
c3 4: //
V
0 w r 1 T ‘ T T l
0 1000 2000 3000 4000

EMBEDMENT AREA, TI'DL (micronz)

Figure 4.5: Microbond data for mPDA/DGEBA formulation with various
curing schemes and atmospheres

 

68

 

   
     
   
   
   
     
 

 

 

 

A

o 100

°- I7:

3 E

I 80-1 (5

s—

0

2 E

E - MICROBOND

i3 SCH I f u. '5 %

cr 0 I3 m

- 0

at] ° ' < in o u o 8
.4 . .

5 4° ... E3

.1 w.

55 '0'

0 20- :’j

6‘. .1. SE

0: ~9-

LrJ .,,

I— . .

Z 0- AA 7 7 , 7 7 ,

— m-PDA/DGEBA J700/DGEBA

Figure 4.6: A comparison of the microbond test and the fragmentation
test for mPDA/DGEBA matrix and WOO/DGEBA matrix

69

the corresponding fragmentation test result of about 65-70 MPa (fragmentation tests
conducted on specimens subjected to curing schemes A-F all showed a interfacial shear
strength between 65 and 70 MPa). The two lines shown in Figure 4.5 are representative
of the data with (curing schemes A, B, and C) without (curing schemes D, E, and F) a
room temperature cure portion. The lines illustrate the fact that with the room
temperature cure the microbond interfacial shear strength (the slope) has increased.

The mPDA environment (curing schemes A, B, and C) is not able to retard the loss
of mPDA due to diffusion to any great extent. Changing the initial stoichiometry of the
droplet (curing scheme C) also does not compensate for the amount of curing agent loss
by the diffusion process. In curing schemes D-F, the ”normal" curing cycle is preceded
by a room temperature cure portion. It can be seen from Figures 4.5 and 4.6 that the
interfacial shear strengths calculated for these curing schemes are slightly higher and thus
closer to the interfacial shear strength values measured using the fragmentation test. The
room temperature step allows some reaction to occur between amine and epoxy which
retards the diffusion process as indicated by the higher interfacial shear strength results.
Providing a mPDA atmosphere does not seem to inﬂuence the results as evidenced by
the fact that the data from scheme D (with melted mPDA environment) results in lower
interfacial shear strength when compared with scheme E (with no melted mPDA).
Scheme F, which has a 36 hour room temperature cure-compared with 24 hours in
schemes D and E—results in the highest microbond interfacial shear strength measured.
This again points to the fact that allowing the droplets to cure at room temperature before
being exposed to a high temperature environment effectively causes the system to gel so
that the loss of curing agent at high temperatures is reduced.

Figure 4.6 also shows microbond data taken from another diamine curing agent
system. In this case, a high molecular weight polyether diamine curing agent (Jeffamine
700) with reduced volatility was used (with curing schedule listed in Table 3) and hence

70

retarded the diffusion process. The data are shown in Figure 4.7 as embedment area
versus force of debonding. The slope of the best-ﬁt line through the origin results in a
microbond interfacial shear strength of about 35 MPa. From Figure 4.6 it can be seen
that this is within 5 % of the interfacial shear strength measured using the fragmentation
test for this system [55]. These results are consistent with the fact that the 1700 curing
agent has a lower vapor pressure and thus the amount of curing agent lost by diffusion
and vaporization is minimized when compared with a more volatile system such as
mPDA/DGEBA. Figure 4.7 also shows that the range of embedment lengths tested with
the 1700 system is greater than with the mPDA systems. This is due to the
1700/DGEBA matrix being more compliant (the 1700 matrix has a strain to failure of
about 90% while the mPDA matrices have strain to failures of about 6%) leading to
lower ﬁber-matrix adhesion. This lower adhesion allows larger drops to be tested
(because the ﬁber does not tend to break) while the viscous nature of the 1700 curing
agent allows for smaller drops to be tested.

Recent work done, using photoelastic and ﬁnite element analysis, by Herrera-Franco
et al. [81] has shown that the method of loading the microdrop in the droplet test affects
the measured debonding force and can lead to a large amount of scatter in the data. The
relative position of the blades with respect to the center of the drop (the contact angle
between the blade and the microdrop) changes the stress distribution on the microdroplet.
Thus, gripping the microdrop ”incorrectly” may affect the measured debonding force by
introducing large scatter in the data. This is especially true for the brittle mPDA systems
studied; the 1700 curing agent gives a much more compliant matrix making blade

position and location less critical.

DEBONDING FORCE (grams)

71

 

 

 

 

 

 

 

32
[O J7otyDcEBA/AS4. TAU = 32.1 MPa]
24-1
16-1
/
8a /
/
/
0 I T f a
0.0 2000.0 4000.0 6000.0 8000.0

EMBEDMENT AREA, 1rDL (micronz)

Figure 4.7: Microbond data for 1700/DGEBA formulation

1 0000.0

72

4.4 THIN FILMS

Thin ﬁlms of upto 4 mm in size were prepared and tested (as described in Chapter
2 and above) to discern the amount of curing agent being lost by diffusion for the three
of the matrices used in this work. The three different systems chosen for this portion of
the study are all based on DGEBA resin cured with stoichiometric amounts of amine
curing agents mPDA, 1403 and 1700. Glass transition temperatures of the "fully" cured
samples were used as a measure of how much curing agent was lost during the curing
process. As reported in Chapter 2, glass transition temperatures were measured both
with a Thermal Mechanical Analyzer (TMA) as well as with Differential Scanning
Calorimeter (DSC). The fully cured glass transition temperatures for the three different
systems studied are shown below in Table 4.2.

 

 

 

 

 

SYSTEM T. (C) _|
mPDA/DGEBA 137:7
1403/DGEBA 751:3
1700/DGEBA 20:3 I

 

The data shown in Figure 4.8 are a combination of the data Shown in Figure 4.2 (for
the normal curing cycle, mPDA/DGEBA system) and the data obtained from the thin
ﬁlm experiments described earlier. As expected, the two Jeffamine-based systems (which
have a higher viscosity and lower volatility when compared to the mPDA system) Show
nearly constant glass transition temperature throughout the testing regime. On the other
hand, the mPDA system, even at Sizes of about 3000 microns (3 mm), shows that the
measured T, deviates from the bulk T, by about 10°C. This indicates that even at such

73

 

 

e—a mPDA/DGEBA
H J403/DGEBA
A—A J700/DGEBA

     

 

 

 

 

 

 

 

 

A

C.)

3.,

[U

Of.

2

[E 100‘

LLJ

0..

E 80'"I __..

lt—

E 60

E ..

(I)

Z 40—

<(

95 1 , . A , A

(f)

(I) J

a 0 T a I T T r ﬂ I
0 1 000 2000 3000 4000

APPROXIMATE FILM SIZE (microns)

Figure 4.8: T, as a function of ﬁlm size for mPDA/DGEBA, 1403/DGEBA
and 1700/DGEBA formulations

74
large ﬁlm sizes, the mechanical properties could be different from those of the bulk
matrix. Thus, extreme care must be taken to ensure careful measurement of mechanical
properties os small dimension samples for the mPDA/DGEBA system or any system

where a volatile curing agent is used.

4.5 MODELING OF THE DIFFUSION PROCESS

The diffusion in a semi-inﬁnite slab has been extensively studied by many authors
[13]. The slab initially contains a uniform concentration of solute. At some time,
chosen conveniently as time zero (t =0), the concentration at the interface is suddenly and
abruptly increased. In the case of droplet testing, t=0 would correspond to the time at
which the droplets are placed on the ﬁber. This sudden concentration increment ate the
ﬁber/ matrix interface produces a time dependent concentration proﬁle that develops as
the solute (curing agent) diffuses out of the droplet.

If a mass balance of the diffusing species is combined with Fick’s law, and assuming
that the diffusion coefﬁcient is independent of concentration (i.e. constant), we can arrive
at the following well—known relation for diffusion of the curing agent:

%—E =De-g—Z-g- (4 - 2)
where, C is the concentration of the curing agent, and z is radial distance from interface
out, and D, is the effective diffusion coefﬁcient. In this case, the boundary conditions
become:

at t=0, all z, C=C.=0
at t>0, z=0, C=C,,..
at t>0, z=oo, C=C.,=0
It can be shown [12,13] (Appendix C) that the solution of this differential equation with
the above boundary conditions is:

75

C
bulk

=1-erf(€) (4.3)

 

Z
E= (4.4)

,F—4D,t

If a diffusion coefﬁcient of 10” cm2/ sec is assumed for the mPDA/DGEBA system [93]

 

(see Appendix B), the time required to reach 10% of the bulk concentration in a 200
micron droplet is about 2 seconds. Whereas, for the Jeffamine based curing agents, the
diffusion coefﬁcient is expected to be lower (in the order of 10" cm’lsec) and thus the
time to reach the same concentration proﬁle (and ratio) would be an order of magnitude
or greater. This analysis validates and explains some of the curing observations made
earlier with the volatile mPDA system.

4.6 CONCLUSIONS

In this chapter, experiments were conducted to compare the fragmentation test with
the microbond test for determining the interfacial shear strength of carbon ﬁbers in two
different epoxy-amine thermoset matrices. Lack of agreement in the interfacial shear
strength between the two testing methods has been attributed to loss of curing agent by
diffusion from small droplets of resin which signiﬁcantly changes the droplet mechanical
properties. There is a strong correlation between droplet size and the amount of curing
agent (mPDA) lost. Droplets less than about 150 microns in diameter lose up to 40%
of the curing agent by diffusion and evaporation during the ”normal” curing cycle in
which the droplets are exposed immediately to a high temperature. This loss of curing
agent lowers the T, of the droplets by 60°C. Adding excess curing agent to the curing
atmosphere does not seem to reduce the loss of curing agent from the small drops.

76
Modifying the cure cycle to include a protracted room temperature portion reduces the
loss of curing agent.

A model developed here indicates that the diffusion of amine out of the droplets, at
high temperatures, is very fast when the curing agent is the volatile mPDA curing agent.
The use of less volatile curing agents (e. g. 1700) with the same epoxy resin and ﬁber
result in close agreement between the two tests without modiﬁcation of the cure cycle or

the cure atmosphere.

CHAPTER 5

EN F AR
0\ u; [L D; an" laIlLLHjJ_ -_ 110,531 '1. it 4,111.11-“ 0;” H 0;

This chapter focuses on the dependence of interfacial shear strength (188) on the bulk
material matrix properties (at ambient conditions) using model compounds based on
epoxy/amine chemistry discussed earlier. Carbon, AS4 ﬁbers were used as the subject
for these measurements with both a difunctional epoxy (DGEBA) as well as a
tetrafunctional epoxy (MY720) system. Amine curing agents were carefully chosen to
produce matrices which resulted in a range of matrix properties from brittle, elastic
(shorter chained curing agents) to ductile, plastic (longer chained curing agents). The
ﬁber-matrix interfacial chemistry was kept constant throughout this study (this chapter)
by always using a stoichiometric amount of curing agent. The interfacial shear strength
was quantiﬁed using the single ﬁber fragmentation test. This work has been previously
published by Rao and Drzal [55].

5.1 INTRODUCTION

The determination of interfacial shear strength between ﬁber and matrix in composite
materials is possible with a variety of methods ranging from single ﬁber to composite
specimens [25 ,30,3l,94]. While advances are being made in experimental methods that
probe the ﬁber-matrix interface, the ultimate goal is to predict interfacial shear strength
and to relate interfacial shear strength to ﬁber, matrix and interphase properties.

Many authors have proposed theoretical relationships between interfacial properties
and bulk material properties. These models allow the local stresses to be computed
based on the constituent properties. One of the ﬁrst approaches was developed by Cox

78
[95] and later again by Cooke [14] who considered an elastic ﬁber of length, l, embedded
in an elastic matrix, under general strain, 6. Cox and Cooke assumed “perfect bonding“
between the two phases, as well as lateral contraction of the ﬁber and matrix. Using the
assumption of load transfer through the ends of the ﬁber, leads to the following equation
[14,95]:

)o,5 sinhp (0 . SL-x)

G
:3 I ..
1.’ te.(2E,1n(—§) cashpL/z (5.1)

 

 

where, E = Tensile modulus of ﬁber

6,, = Strain in the matrix

G. = Shear modulus of matrix

R = Interﬁber spacing

r = Radius of the ﬁber

B = Scaling factor

L = Length of embedded ﬁber

x = Radial distance outward

r = Interfacial shear stress at ﬁxed point
As is evident from Equation 5.1, if the specimen geometry is ﬁxed and the same ﬁber
is used in each case, the theory predicts a direct dependence of the interfacial shear
strength on the product of the matrix strain and the square root of the shear modulus of
the matrix. This square-root dependency of the interfacial shear strength on the matrix
shear modulus has also shown to hold in other single ﬁber tests. Kendall [96], for
example, has shown that in single ﬁber pull-out tests, the force required to pull a single
ﬁber out of an elastic matrix is directly proportional to the square root of the shear
modulus of the matrix. Rosen [97,98] also has analyzed the shear stress ﬁeld along the
ﬁbers between parallel ﬁbers in a composite loaded in tension. His model consists of a
ﬁber surrounded by matrix, which in turn is embedded within a composite material
exhibiting average composite properties. The ﬁber is assumed to carry only extensional
loads and the matrix to transmit only shear stresses. He used an equilibrium approach

to derive the relationship between, 7, the shear stress at the interface and properties of

79
the ﬁber and matrix. Dow [97 ,99] has evaluated a more general case in which the load
is applied to both ﬁber and matrix. The theory used is Similar to that considered by Cox
and Cooke, except that no matrix was present at the end of the ﬁber.

In all of these models, the matrix is the medium by which Shear stresses are
transferred to the ﬁber. The models show an explicit dependency on matrix shear
properties. Yet, most adhesion studies focus entirely on the interfacial interactions
(chemical and physical) between ﬁber and matrix and tend to neglect the matrix itself as
having a causal effect on ﬁber-matrix adhesion.

In other work previously published it has been shown that the maximum extent of
chemical bonding between amine and/ or epoxy groups with the surface chemical groups
present on the ﬁber surface is less than 5% [100]. Experimental veriﬁcation of the
extent of chemical interaction between epoxy and amine groups with the AS4 ﬁber
surface [100] has been completed in the following fashion. Monofunctional epoxy and
amine compounds were dissolved in an inert solvent and placed in a closed container with
a aliquot of AS4 carbon ﬁbers. The system was sealed, taken up to the typical
processing temperatures encountered in curing epoxy composites, and then cooled to
room temperature. The ﬁbers were Soxhlet extracted in pure solvent and the surfaces
of the A84 ﬁbers were compared by Xray photoelectron spectroscopy with the ”as-
received” ﬁbers. Epoxy and amine chemical bonding to AS4 ﬁber surfaces has been
showntobelessthan5%andoccurattemperaturesabove100°Csupportingthe
assumption that the extent of chemical bonding in this set of experiments (in this study)
to be both small and constant for all of these systems.

It is very tenuous to try to extrapolate interfacial properties from one system to
another if the matrix properties are not taken into account. Little experimental
veriﬁcation has been attempted where the interfacial chemistry remains unchanged but
the matrix properties are systematically varied. This study presented in this chapter was

80
undertaken to experimentally investigate the effect of changing matrix properties from
stiff and brittle (characteristic of most thermoset matrices) to compliant and ductile
(characteristic of thermoplastic matrices) on ﬁber-matrix interfacial shear Strength.

5.2 EXPERIMENTAL

AS4 ﬁbers were used throughout the study presented in this chapter. All curing
agents were either di- or tri- amines illustrated in Figure 2.2. Material properties of the
different matrices was obtained, as described in Chapter 2, using a MTS-880 system.
Thermal analysis (T, determinations) were performed on a DSC unit.

The single ﬁber fragmentation test was used (Equation 2.2) to quantify the interfacial
shear strength. A single parameter like the interfacial Shear strength is of limited value
when the mode of failure between ﬁber and matrix is unknown or changing. A very
useful additional feature of the fragmentation test described in Chapter 2 is that in-situ
observation of the ﬁber-matrix region can be made during testing. Observation of the
fragmentation test with either transmitted or polarized light provides information about
local stresses and failure modes. The highly stressed polymer near the ends of the ﬁber
fragments is birefringent and pronounced changes in the photoelastic stress pattern of this
region occur with each ﬁber-matrix combination. The change in this pattern with
increasing sample strain has been shown to be a qualitative indicator of different types
of ﬁber-matrix failure modes [30,31].

The wetting characteristics of the ﬁbers and matrices were determined by using a
Wilhelmy apparatus for measuring contact angles as described in Chapter 2. A three
liquid analysis (deionized water, ethylene glycol and methylene iodide) was completed
to compute the polar and dispersive components of the surface free energies.

81

5.3 RESULTS AND DISCUSSION
WISE

All material and interfacial properties of the different matrices are listed below in
Tables 5 .1 and 5.2. In Table 5.1, the DDS system did not reach critical length due to
the matrix being too brittle. The standard deviations associated with the interfacial shear
Strengths, 1', measured are on the order of 10-15%. For details on the error in
measurements, consult ref. [55]. It can be seen from Table 5.2 that there are fewer data
points for the more reactive tetrafunctional MY720 resin system and that all of the
mixtures have at least a few phr of 1700 curing agent in them. This is due to the fact

that the MY720 resin system, which is a. gummy solid at room temperature,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WITH: (MP3) (GPa) (GPa) (95) (95)
mPDA 72.7 3.30 0.35 1.17 5.30 4.10
DDS 64.3 3.40 0.31 1.30 4.40 4.40
1230 56.7 2.95 0.35 1.09 7.10 6.00 I
1400 51.3 2.73 0.34 1.01 8.00 7.3
1403 47.0 2.31 0.36 0.85 12.2 9.8
1700 39.0 0.67 0.44 0.23 96.3 28.0

 

82
reacts very quickly with any of the smaller Sized curing agents leading to an uncontrolled
exothermic crosslinking reaction upon mixture of the resin and curing agent. Various

methods (such as aliquoting the curing agent into the resin, cooling the resin to a lower

 

 

 

 

MY720 Cured 1' E G e, 6,,
With: (MPa) (GPa) (GPa) G) (95)
1700 40.8 1.26 0.45 86.0 25.0

1700/1403 48.8 2.67 0.99 8.30 7.80
1700/1400 53.8 2.92 1.08 7.10 6.50

 

 

 

 

 

temperature before mixing, etc.) were attempted with little success. A controlled
reaction could be initiated only with the addition of a few phr of 1700 to the other curing
agents before mixing. The reaction could not be controlled (even after the addition of
1700) with the 1230, mPDA and DDS curing agents. However, a stable controlled
reaction was obtained with the 1400 and 1403 curing agents.

As can be seen from Tables 5.1 and 5.2, the interfacial shear strength (as calculated
using Equation 2.2) is seen to decrease as the modulus ofthe matrix material decreases.
This relationship is seen clearly in Figure 5.1 where the interfacial shear strength, 7, is
plotted versus the shear modulus, G, for both the difunctional as well as the
tetrafunctional resin systems. From Figure 5.1 it can be seen that, for both systems, as
themodulusofthematrixdecreases, theinterfacialshearstrengthalsodecreasesina
non-linear fashion. This suggests that as the matrix material near the ﬁber surface, in
which the ﬁber is embedded, becomes more compliant, the transfer of stress between it
and the AS4 carbon ﬁber is reduced.

Microscopic observation of the single AS4 carbon ﬁber in various matrices during
the interfacial shear strength measurement provides additional insights into the processes

83
occurring during the interfacial fragmentation test. Figures 5.2-5.6 Show a series of
photomicrographs, using both transmitted light and transmitted polarized light, depicting
the ﬁber in the various systems studied. For comparative purposes all micrographs were
selected at a point at approximately 50% of the strain required to reach critical length.
From these micrographs it is possible to identify the failure modes in the various
systems.

Figure 5 .2 displays a micrograph of the relatively high modulus DGEBA/mPDA
system. Under polarized light the stresses that develop around the ﬁber fragment ends
can be easily observed due to the photoelastic nature of the matrix. The large elliptical
photoelastically active area represents the tip of a growing interfacial crack. This
elliptical region was seen to be initially present at the end of a ﬁber fragment. With
increasing sample strain, this region moves away from the ﬁber along the ﬁber-matrix
interface leaving behind an intense narrow region between itself and the ﬁber fragment
end. Previous studies [30,101] have used transmission electron microscopic analysis of
ultramicrotomed sections to show that this pattern is associated with a fracture path
between the ﬁber and the epoxy matrix which is purely interfacial (this phenomena can
be seen in the transmitted light micrograph in Figure 5.2).

In the next two sets of photomicrographs (Figures 5 .3 and 5.4), failure modes for
two of the Jeffamine based curing agents, which have a lower modulus than the mPDA
system, are shown. The tensile modulus of the 1230 cured system is 2.95 GPa while for
the 1403 cured system it is 2.31 GPa (compared to 3.30 GPa for the mPDA cured
system). In each case, the photoelastic Stress pattern is less intense (indicating lower
adhesion) than the mPDA system described above. In the case of the 1230 curing agent
(Figure 5.3), the polarized light micrograph shows a more diffuse photoelastically active
area with a narrow intense region at the interface extending away from the ﬁber break.

These regions again represent the elastic zone at the tip ofa growing interfacial crack.

130.0

 

 

O tetrafunctional resin (MY720)
A difunctional resin (DGEBA)

 

 

 

105.0—

80.0-

55.0—

strength (MPa)

 

 

30.04

Average Interfacial shear

 

 

500 T
200

 

T . I
600 1000 1400

Shear modulus Of matrix, G (MPa)

Figure 5.1: Interfacial shear strength as a function of bulk matrix shear modulus

85

 

Polarized Light Micrograph

 

Transmitted Light Micrograph
(ﬁber diameter~ 7 pm)

Figure 5.2: Interfacial failure mode of mPDA/DGEBA formulation

86

 

Polarized Light Micrograph

 

Transmitted Light Micrograph
(ﬁber diameter-7 pm)

Figure 5.3: Interfacial failure mode of 1230/DGEBA formulation

 

Polarized Light Micrograph

Transmitted Light Micrograph
(ﬁber diameter~7 pm)

Figure 5.4: Interfacial failure mode of 1403/DGEBA formulation

88

 

Polarized Light Micrograph

 

Transmitted Light Micrograph
(ﬁber diameter~ 7 pm)

Figure 5 .5 : Interfacial failure mode of 1700/DGEBA formulation

89

 

Polarized Light Micrograph

 

Transmitted Light Micrograph
(ﬁber diameter~7 um)

Figure 5.6: Interfacial failure mode of 1700/MY720 formulation

90

As with the mPDA curing agent, as the strain is increased, this region moves away from
the ﬁber break leaving behind a less intense narrow region between itself and the ﬁber
fragment end. The transmitted light micrograph reveals that the interface fails with the
simultaneous creation of a transverse crack and interfacial debonding. For the
DGEBA/1403 system, and for which the micrographs are shown in Figure 5.4, the
failure process is similar to those described above as characterized by the photoelastically
active area. As before, the debonding is seen to be interfacial along with a small amount
of matrix tearing as seen in the transmitted light micrograph. This feature is seen as a
small sharp crack going into the matrix in a direction perpendicular to the ﬁber. This
type of matrix failure was completely absent in the mPDA system and was barely
detectable in the 1230 system.

The micrographs shown in Figure 5.5 is that of the very compliant 1700/DGEBA
system. This system (along with 1700/MY720 (Figure 5.6) which behaves identically)
is quite different when compared to the other systems studied. This system shows very
large amounts of matrix damage (matrix tearing away from interface) occurring from the
initial stages of the single ﬁber test when the sample strain is very low due to the low
yield stress of the matrix. At the point when the ﬁrst break occurs in the single ﬁber
test, a large amount of matrix damage is already present. As the sample strain is
increased thematrixfractureassociated withthebreaks increases and thefractureopens
creating the characteristic double-diamond shaped pattern depicted in the micrograph.
The photoelastic stress pattern, representing the plastic zone at the tip of the crack, has
no geometrical shape associated with it and is less intense when compared to the other
systems studied. The debonding, however, still takes place interfacially.

It is obvious from the failure-mode micrographs that the fracture toughness of the
matrices is changing and is partly responsible for the changes which are observed. Since
the ﬁber geometry is constant in these experiments, the stresses at the ﬁber fracture point

91
should be similar. The matrix formulations which are lower in toughness would be
expected to produce less damage.

The theory presented by Cox and Cooke (Equation 5.1) relates the interfacial shear
strength to the material properties of the matrix and properties of the ﬁber. For a ﬁxed
geometry, a linear relationship is predicted between the interfacial shear stress, 1, and
the product of the matrix strain and the square root of the shear modulus of the matrix,
5J6,” provided that all of the other variables are held constant. In the present work,
the interfacial chemistry and specimen geometry are constant. The linear relationship
suggested by Cooke is plotted in Figure 5 .7 with a minor adjustment. Instead of plotting
the quantity 6.1/6., the group 6.1/G. is plotted in Figure 5.7 versus the interfacial shear
strength. For these experiments, 6,, is selected as a better measure of the physical events
takingplaceattheinterfacethang. 6,,isthestraininthematrixwheretheﬁberhas
reached its critical length rather than the yield point of the matrix.

Figure 5.7 shows a nearly linear relationship, for both the difunctional as well as the
tetrafunctional resin systems, for all the points except when pure 1700 is used as the
curing agent. One possible reason for the 1700 cured systems not following the linear
relationship as the other curing agents could be due to the fact that the modulus of the
system is so low that its behavior is more plastic than elastic. Signiﬁcant necking was
seen to occur while conducting the stress! strain experiments for this system. From the
stress/strain curves depicted in Figure 5.8, it is evident that the total strain is much
greater for this system than for any of the other systems studied. From Figure 5.7 it is
seenthatthelineardependencebetweentheinterfacial shear strengthandtheproductof
thestraintofailureatthecriticallength ofeach system timesthesquarerootoftheshear
modulusofthematrixisvaliduntiltheshearmodulusofthematrixdecreasestobelow
about 1 GPa. Cooke’smodeluseslinearelasticﬂreorytopredicttheinterfacialshear
stress as a function of matrix and ﬁber properties. It is therefore rather surprising that

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

155.0
0 tetrafunctional resin (MY720)

Cl: EB difunctional resin (DGEBA)
6 130.04
I
(DA

0
2'0. 105.O~
0?,
s _._.
0111—: 80.0-1 EB
LLJQ ‘
t‘z
ém EB 3:
— __ E
895 “9&1

(f) T
g o E :1;

30. 4
>
<
5-0 r I —l a I
O 1 2 3 4 5

£b[G]o.5 (M p0)0.5

Figure 5.7: Interfacial shear strength as a function of the product of
squareroot of matrix shear modulus and strain at ﬁnal break

Stress (MPG)

93

 

 

 

 

 

 

 

 

 

 

120.4 DGEBA resin cured with: 0-6 m-PDA
H J—230
J E—E J-403
A—A J—7OO
ﬂit—r
O I'I‘IY'ferYTTTTjjjT'"IIYrYfTTTII
0 5 10 15 20 25 30

Strain (70)

Figure 5 . 8: Stress/Strain curves for all DGEBA formulations

35

94

for the elastic/plastic systems studied, the model seems to predict interfacial phenomena
as a function of matrix and fiber properties rather well down to approximately 1 GPa for
matrix shear modulus. Figure 5 .7 indicates that there is a lower limit of the matrix
modulus on ﬁber-matrix adhesion. Netravali et al. [56] have also shown that the effect
of matrix properties (modulus) on interfacial shear strength is minimal for these types of
systems below about 1.3 GPa modulus for the matrix material. The matrix material in
the interphase may behave in a more linearly elastic manner under the superimposed
triaxial compressive interfacial stress. This mechanism will be explained in detail in the
next chapter where the effect of elevated temperature on interfacial shear strengths will
be discussed.

All experimental values of the interfacial shear strengths have been determined by
Equation 2.2. However, the effects of thermal stresses and Poisson’s radial contractions
are not explicitly present in the equation. Interfacial shear strengths calculated using
Equation 2.2 agree well with Cox’s and Cooke’s model until the matrix begins to become
very compliant (about 1000 MPa) at which point the agreement between the two is seen
to decrease. Better agreement with Equation 2.2 ean be obtained when a three-
dimensional model proposed by Whitney and Drzal [102] is used to compute the
interfacial shear strengths. This three dimensional stress model proposed by Whitney can
be used to compute the complete state of interfacial stresses. For example, the radial
compressive stress (which results from thermal stresses and shrinkage in the matrix and
ﬁber), in the various systems studied, is calculated using Whitney’s model and tabulated
in Table 5.3. These data are plotted in Figure 5.9 as shear modulus of the matrix versus
the radial compressive stress. Also shown in Figure 5.9 is the variation of the interfacial
shear strength as a function of the shear modulus of the matrix. The vertical line drawn
in Figure 5.9 at a shear modulus value of 1180 MPa reﬂects previous work [39] done
on a similar ﬁber/matrix system in which the effect of cure temperature on interfacial

AVERAGE INTERFACIAL SHEAR
STRENGTH (MP0)

95

 

 

 

 

 

 

 

 

 

1 35 1 35
O difunctional resin
1 201 A tetrafunctional resin L 120
B difunctional resin
1 05_ A tetrafunctional resin L105
H ISS as a f(T)
90-i *- 90
5C
75— U12 L75
_‘ 0
60d 1-60
45- P45
8
30- - 30
15“ — 1 5
E A
91 L0
0 ‘T j T n 1 T
200 400 600 800 1 000 1200 1400 1 600

SHEAR MODULUS OF MATRIX (MPO)

Figure 5.9: Radial compressive stress and interfacial shear strength

as a function of matrix shear modulus

RADIAL COMPRESSIVE STRESS USING
WHITNEY'S MODEL (MP0)

96
strength was studied. The lower point represents the interfacial shear strength for an
epoxy/amine system that was fully cured at ambient condition. The difference should
be entirely attributable to differences in radial residual compressive stress. Higher cure
temperatures produce a higher (beneficial) radial residual compressive stress at the
interface. From Figure 5.9 it can be seen that the radial compressive stress, for a given
system of modulus G, is only about 25 96 of the interfacial shear strengths for the high
modulus systems and is virtually non-existent for the low modulus systems.

To aid in identifying the role that the radial compressive stress plays determining the

 

 

 

 

 

 

 

 

 

 

 

IEEIEH-B 1'! .v
SYSTEM T T-T, ISS RADIAL
(“5) (°C) (MPa) COMP.
STRESS
(MPa)
DGEBA
CURED
WITH:
mPDA 130 -110 72.9 20.9
DDS 198 -178 -- 33.9
1230 73 -53 56.7 10.7
1400 45 -25 51.3 6.0
1403 75 -55 48.4 6.0
1700 18 2 38.6 0.56
MY720 CURED
WITH:
1700/1400 40 -20 53.8 5.70
1700/1403 43 -23 48.8 5.62
1700 f 22 -2 40.8 e. 1.31

 

 

 

 

change in interfacial Shear strength of a given system, the analysis presented by Adamson
[103] can be used. Van der Waal’s forces, chemieal bonding, molecular interactions as

97

well as frictional forces contribute to the interfacial shear strength. The vertical line
drawn in Figure 5 .9 represents a constant chemistry system in which only the cure
temperature was altered. Thus by equating the frictional force component of the
interfacial shear strength to a coefﬁcient of friction times the normal force (r=uN) an
estimate of the friction coefﬁcient can be made. From the vertical line in Figure 5.9,
it can be seen that the change in interfacial shear strength between the two temperatures
is about 13 MPa; the corresponding change in normal force is just the radial compressive
stress at 125°C Since the contribution from 25°C is negligible (due to AT being small).
The coefﬁcient of friction ealculated in this manner is about 0.6, so that Ar=0.6N.
Using this equation, the effect of the normal force on the change in interfacial shear
strength can be calculated for all the systems. For example, the DGEBA/mPDA system
shows that Ar= 12 MPa due to normal forces while the compliant DGEBA/J 700 system
shows that A1=0.34 MPa due to normal forces. Generally speaking, the effect of radial
compressive stress on interfacial shear strength diminishes as the modulus (and T,) of the
system decreases. Therefore, it can be said that the effect of radial compressive stresses
on changes in the interfacial shear strength are signiﬁeant but generally small. By
extrapolating the interfacial shear strengths to zero thermal stresses, it is evident, beeause
of the minor contribution of radial stresses, that a plot of G versus A1 will be very
similar to the G versus 7 curve shown in Figure 5.9. It can then be concluded that the
changes in interfacial shear strengths seen in this study are mainly due to the modulus
differences in the various systems and not to the effect of residual thermal stresses.

These epoxy polymers are glasses below T,. At temperatures above T, the polymer
is soft and ﬂexible. Mechanieal properties Show profound changes in the region of glass
transition. For instance, the elastic modulus may decrease by a factor of over 1000 times
as the temperature is raised through T, [12]. Above T, virtually all possible motions for

a polymer chain occur while below T, many molecular motions are frozen and cannot

98

occur. Beeause the glass transition temperatures are a parameter characteristic of a given
matrix system and are different for each of the matrix systems chosen for this study, the
interfacial shear strength has been measured at different temperatures in relation to the
glass transition temperature. A plot of T-T, (where T is the temperature at which the
experiments are conducted and T, is the glass transition temperature of the fully cured
matrix) versus the interfacial shear strength would compare the interfacial shear strength
results at equivalent matrix conditions.

Figure 5 . 10 is a plot of the interfacial shear strength versus difference in temperature
between test temperature and T,. It can be seen that a nearly linear relationship exists
over the entire range of matrix systems tested.

It is evident that as the T, of the matrix increases, the interfacial shear strength also
increases. From a network structure point of view, materials which have a higher T,
would tend to have a higher modulus and transfer stress better to the interface leading
to an increase in the interfacial shear strength. Materials with a higher transition
temperature would, in general, also lead to higher thermal stresses in the system which
would cause shrinkage of the matrix around the ﬁber and consequently increase the
interfacial shear strength a noted earlier by Kalantar and Drzal [39]. For constant
interfacial chemistry, Figure 5.10 also shows that the interfacial shear strength can be
predicted by knowing a fundamental material parameter such as the T,. By conducting
experiments such as these at different temperatures it may be possible to predict the
interfacial shear strength as a function of modulus or temperature. This is the subject
of the next chapter.

In the above discussion, it has been Shown that the changes in interfacial shear
strength seen in the experiments conducted in this chapter are mainly due to modulus
changes of the bulk matrix (and interphase). Recently, however, experimenters have
published results [104,105,106] indicating that wetting of the matrix and ﬁber, as well

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100
d O tetrafunctional resin
If: B difunctional resin
LrJ 90‘
I .1
(f)
j; 80..
<0— . ’7—
as; i
E 70-4 _A__
crE .
“JO
i—Z 60— r— _
ZLLJ 4 R
O: ___1
LLJ|.-— ﬁr—
om 50'7 35 Ba
E A ____ .._i_ -
L1J
> 40-1 \
< . E
30 I r ' I ' I I j I j
-120 —‘|00 —80 —60 —40 -20 0 20
T—Tg (°C)

Figure 5.10: Interfacial shear strength as a function of T, of the fully cured matrix

100
as the acid-base characteristics of the ﬁber-matrix combination, could play a major role
on determining the ﬁnal level of ﬁber-matrix adhesion.
Using deionized water, ethylene glycol and methylene iodide as the liquids, a
dispersive and polar component of ﬁbers and matrices were calculated. The results are
tabulated below in Table 5.4. It can be seen that the changes in the polar component

MATERIAL

 

AS4 FIBER

35.8;30

11.5;13

47.3 g 4.2

 

mPDA/DGEBA

 

34.3i3.1

13.1;13

47.8 4.9

 

1230/DGEBA

 

25.4;46

11.9;35

37.3 6.8

 

1400/ DGEBA

 

26.1;45

1222.9

38915.9

 

1403/DGEBA

 

25.9;39

13.0;27

38.91353

 

_ J700/DEBGA

 

 

0.8 2.

 

10.8:tl.7

 

 

31.6;t4.3

(which is the parameter most sensitive to changes in level of ﬁber/ matrix adhesion [27])
of the surface free energies is quite small for the different systems (only the 1700 system-
which has the lowest ﬁber-matrix adhesion shows a signiﬁcant decrease in the polar
component-and even that is only a change of about 5 96) and thus it can be concluded
tint the changes seen in interfacial shear strengths in this chapter were due to

modulus changes in the matrix materials.

5 .4 CONCLUSIONS

In this chapter, a series of experiments were conducted wherein the ﬁber-matrix
interfacial chemistry was kept constant while the matrix modulus was altered. A
monotonically increasing dependence of interfacial shear strength on the shear modulus
of the matrix was determined for both a difunctional and a tetrafunctional epoxy system

101

cured with polyamines using carbon ﬁbers (AS4) as reinforcement. A linear dependence
is observed between the interfacial Shear strength and the product of the strain to failure
at the critical length of the system times the square root of the shear modulus until the
shear modulus decreases below approximately 1 GPa. When the interfacial shear
strength is plotted against the difference between the test temperature and the glass
transition temperature of the fully cured matrix, a linear relationship also results. The
conclusions from these results are that a dependence exists between matrix modulus and
interfacial shear strength because of the stress transfer function of the matrix. A
decrease in modulus, all other things being equal, causes a corresponding decrease in
interfacial shear strength.

CHAPTER 6

 

In this chapter, the dependence of interfacial shear strength on temperature will be
will be investigated. The same epoxy matrices (reinforced with carbon, AS4 ﬁbers)
studied in Chapter 5 will be used to construct a master curve which has the ability to
predict the interfacial shear strength by knowing the test and glass transition temperature
of the matrix. Additionally, a diffusion model will be presented to predict the formation
of an interphase using epoxy-sized carbon ﬁbers in mPDA/DGEBA matrix. Most of the
work presented in this chapter has been published separately by Rao and Drzal [5 8].

6.1 INTRODUCTION

As described in Chapter 1, the ability of the matrix to transmit stresses from ﬁber
to ﬁber at the microscopic level is responsible for internal stress development in the
composite during processing which in turn, may be responsible for generating defects.
During the early stages in processing, the matrix is in a ﬂuid state and can only transmit
minimal amount of stresses (Chapter 3). As processing progresses, however, there is an
increase in modulus with time and temperature. Interfacial properties have been shown
to be heavily dependent on the matrix modulus and the interactions at the ﬁber matrix
interface [55]. In thick parts, with an exothermic reacting matrix, simultaneously the
matrix properties, and consequently the interfacial properties, can vary throughout the
thickness of the material because of temperature non-uniformity. Hence it is critieal that
the mechanism by which the interfacial (and adhesive) properties are generated during
composite processing is understood so that the mechanical properties can be known as
a function of temperature and time in order to optimize composite processing.

102

103

Though various authors [36,5 8,59] have studied how temperature and modulus affect
polymeric composites, the role that residual stresses [107] play in determining the ﬁnal
mechanical properties of composites as well as the dependence of temperature on
mechanical strength of composites [108], little work has been done to elucidate the
alteration of interfacial shear strength as a function of processing conditions.

An added complexity results from the fact that in most cases an "interphase“ exists
at the ﬁber-matrix interface. This region, ﬁrst introduced by Sharpe [109], is a three
dimensional region of some ﬁnite thickness extending, depending on the system
constituents, from within the ﬁber surface to some point in the matrix where local
properties approach bulk properties. Its size and composition can vary with each system
and can include unreacted polymer components, polymer reaction byproducts, weak
surface layers of the ﬁber, amongst other things. Throughout this chapter the term
"interface” will mean the actual contact surface between the ﬁber and matrix while the
term ”interphase" will be the region near and on b0th sides of the interface. Numerous
other publications referenced throughout this dissertation, have shown the effect of this
interphase itself on ﬁber-matrix adhesion and composite performance.

It is the objective of this chapter to determine the inﬂuence of processing temperature
on the interfacial shear strength of various model, polymeric matrices (see "materials“
section-Chapter 2) reinforced with AS4 earbon ﬁbers. An AS4-C ﬁber (embedded in
mPDA/DGEBA matrix) was selected to investigate the effect of a low temperature epoxy
sizing on the interfacial shear strength behavior at elevated temperatures. The data from
the AS4C system will be used to model the formation of an interphase region. Linear
superposition methods will be used to generate a master curve (for the A84 systems)
from which the interfacial shear strength can be predicted as a function of the processing
temperature of the composite material.

104
6.2 EXPERIMENTAL
Two earbon ﬁbers (AS4 and AS4C), described in Chapter 2, were used for the
studies in this chapter. The representative polymeric matrices used in this chapter are
described in detail in Chapters 2 and 5. A brief summary of the interfacial, mechanical
and thermal properties of the matrices used in this chapter are shown below in Table 6.1.
It can be seen from Table 6.1 that the thermoset matrices used in this chapter have
a wide range of mechanical and interfacial properties. The mPDA system is seen to have
a strain to failure of about 6% and a fully cured T, of about 135°C while the compliant
1700 system is seen to have a strain to failure of over 90% and a T, just below room
temperature. It can also be seen that lower adhesion results in systems with lower
moduli (Chapter 5). Finally, it can be observed that the AS4C/mPDA/DGEBA system
has a higher level of adhesion at ambient temperatures when compared to the same AS4
system.

 

mPDA
J 230
1700/1403
J 403
J 700
mPDA

 

 

 

 

 

 

 

 

 

 

As mentioned previously in Chapter 5, an important factor in selecting these curing

agents to increase the polyether amine length as opposed to the epoxy length is the

105
preservation of epoxy-amine chemistry throughout the series by the use of polyether
diamines (Jeffamine based curing agents). If epoxy oligomers are selected, additional
hydroxyl functional groups are present along the oligomer backbone. These hydroxyls,
could in fact interact (e.g. hydrogen bonding) with each other as well as the ﬁber surface
and unnecessarily complicate the analysis.

The single ﬁber fragmentation test was used to quantify the interface in all the tests.
The specially designed heated cell (described in Chapter 2) was used to conduct the high
temperature experiments. A dynamic mechanical analyzer (DMA-9900) was used to
gather modulus data for the DGEBA/mPDA system as a function of temperature. The
procedure is outlined in section 2.2.6.

6.3 RESULTS AND DISCUSSION
W

New surface analytical techniques allow the chemical nature of the carbon surface
to be determined. X-ray photoelectron spectroscopy [100,110] provides not only atomic
information but also molecular information about the surface characteristics and can be
used to determine the extent of chemical bonding between matrix and reinforcing ﬁber.

AS discussed brieﬂy in Chapter 5, to determine the extent of chemical bonding, a
series of experiments were performed with model monofunctional epoxy compounds,
amines and epoxy-amine adducts whereby these components were dissolved in an inert
aromatic solvent and placed in contact with carbon ﬁbers under the same temperature
conditions experienced in the processing of the composite [100]. Afterwards, the ﬁbers
were extracted with pure solvent, dried and then their surface composition determined
with XPS. Subsequent comparison of the carbon ﬁber spectra before and after this
exposure to the matrix components conﬁrmed that chemical adsorption had taken place.
Both the epoxy group and the amine group can chemically react with the surface oxygen

106
present. Surprisingly, on an absolute basis only about 5% of the surface sites of the
carbon ﬁber were found to be involved in chemical bonding. One would expect chemical
bonding to create a stronger interaction than physical bonding.

For the epoxy-aminecarbon ﬁber system studied here, it is expected that chemical
bonding would be similar for all systems and because of the small number of chemical
bonds formed, it is expected that the role of chemical bonding between ﬁber and matrix
would be small and constant. At most, under the processing conditions of interest in this
study (up to about 125°C), only 5% of the available carbon ﬁber surface sites can react
with the epoxy matrix. Moreover, previous work has shown [55] that the bulk properties
of the matrix and interphase properties themselves play a much more signiﬁcant role on
ﬁber-matrix adhesion than does the chemical bonding between ﬁber and matrix itself.
Since temperature signiﬁcantly alters the bulk mechanical properties of the matrix, one
would expect it to play a more important role than chemical bonding in affecting ﬁber-
matrix adhesion in these systems studied in this chapter.
W

At ambient temperatures the interfacial shear strength was measured for all the
formulations and averaged according to Equation 2.2. The data is plotted in Figure 5.1
as interfacial shear strength vs. shear modulus of the bulk matrix. Since the T, of a
material is related to the crosslink density of a material, the difference in compliance in
the matrices studied can be seen by examining the T,’s listed for the various formulation
in Table 6.1. From Figure 5.1 it is seen that all of the matrix formulations fall on a
single smooth curve showing an increasing interfacial shear strength with increasing shear
modulus of the matrix (and of the interphase). Further discussion on the relationship is
presented in Chapter 5.

For elevated temperature measurements, using the specially designed cell,
measurements were made at 30°C increments up to the T, for each of the different

107
DGEBA formulations listed in Table 6.1. At each temperature replicate samples (a
minimum of 5 samples were tested at each ﬁber/ matrix/ temperature combination) were
tested to insure statistical signiﬁcance. Tables 6.2-6.6 below provide a summary of the

critical length distribution and data for all of the various formulations tested.

 

 

 

 

 

 

 

._. - . - ..". -,~_, .39., . is, ,:,_ "is, ;.. . ‘a.,‘.,o .-...,—.,“‘(-,
— " TH i h i if d.,, if i if i a i i 1’
(°C) (micrODS) (Bald) (MPa)
AMBIENT 7.3i0.26 392/7.3 2.7032 68.4150
44911.6 7.210.34 384/7.2 2.8169 67.0143
57.8;t1.9 7.3;t0.30 409/7.3 2.8986 62.8:t5.8
65.2;t1.9 7.410.19 422/7.4 2.9418 61.21343
79.2:t2.5 7.2i0.21 412/7.2 2.9420 61.0:t4.3
99.8123 7.1i0.32 438/7.1 2.9851 56.2:t4.0
114.2:I:3.6 7.0:t0.18 667/7.0 2.7030 38.3zt7.8

 

 

 

-‘ll- ”-1..

-V.‘

 

(11.191111.

1'

 

 

 

 

(microns) (MPa)
AMBIENT 7.2:t0.26 393/72 57.9 is .9
36.21: 1.8 7.11:0.13 404/7.1 3.3714 56.9:t6.0
45.31: 1.9 7.43:0.20 454/7 .4 3.3333 54.11143

 

 

 

 

 

108

 

59.3 i2.3

7.2i0. 18

469/72

51.3:t5.8

 

71.3:l:3.0

 

7.010.22

 

583/7.0

 

 

42.6i6.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

91114-1 '- 9’s 0 h . ‘J H ‘ a - 5v) .' H 0.‘ r- t (v.5
a... i a... a 1'
(°C) (microns) (5",) (MPa)
AMBIENT 7.11020 469/71 4.0006 47.6:t5.3
35812.1 74320.23 502/74 4.1667 46.6i5.1
I 43353.0 7.31:0.16 497/73 3.7037 45.8;t4.9
54513.1 7.3;t0.l8 557/73 4.0003 41.1:39
69.8133 7510.20 634/75 4.3478 36.2158
-.0 0 1.0:? 611%-! t... 0 h . ‘J U ‘ ‘1-” ll ' a - .‘vJ -‘ Hirer-1.165
T d" U4». 0 1'
(°C) (microns) (Bu) (MPa)
AMBIENT 7210.20 525/72 4.5454 41.6142
29.8;t2.6 7.31019 531/73 4.7619 41314.0
36313.3 \ 7.4:t0.16 550/74 4.5386 40814.1
41.2;t3.6 7110.20 589/7.1 4.6329 36.3163
43.0130 7,210.23 701/72 5.1237 30316.9

109

 

 

 

 

 

 

 

 

 

.3 ‘ s ' g1” ,. f.“ ‘41 0,1; is) I; _: 5 LI ‘1 g u . ' a; . 3,1 ; ll .3qu (g
T d", leld", a 1
(°C) (micronS) (B...) (MPa)
AMBIENT 7.010.22 525/70 5.2632 39215.0
31212.8 7510.21 611/75 5.1924 36.3163
38.3133 7.410.13 702/74 5.3333 30.9183
|___

In all these data, the tensile strength of the carbon AS4 ﬁber is assumed to be
approximately 5101 MPa [38] at the critical length. Each measurement corresponds to
an average of between 8-16 samples. The a and B shown in the tables above
corresponds to the shape and scale parameters in the Weibull statistical model [30,36].
These parameters deﬁne the distribution of critical lengths according to Equation 2 in
Chapter 2.

The interfacial shear strength, for all the matrix formulations reinforced with AS4
ﬁbers, as a function of test temperature is shown in Figure 6.1. It can be seen that in
all cases the interfacial shear strength slowly decreases (as the modulus ofthe matrix also
slowly decreases-Chapter 5) with increasing temperature until at some point a signiﬁcant
decrease in the interfacial shear strength is noted. This point is near the bulk T, of the
matrix. These results are similar to those obtained by Wimolkiatsak and Bell [36] where
it was shown that for uncoated carbon ﬁbers embedded in a thermoset matrix, the
interfacial shear strength decreased with increasing temperature slowly initially (they
suggest that the interfacial shear strength is interface controlled in this regime) with a
steep decrease at higher temperatures (in this regime, they suggest that the interfacial
shear strength is matrix controlled). In our experimental protocol, interfacial shear

110

 

(N
O
L

 

L

AVERAGE INTERFACIAL
SHEAR STRENGTH (MPO)
4: UT
0 O
r l r 1

EB—EB J403/J700,Tg=46°C
H J403,Tg=75°C
A—A J230,Tg=73°C
H J700.Tg=18°C

e—e MPDA.Tg=135°C
T T T I T I I I ﬁr I T r 1' T ﬁ— f 7 I I

20 30 40 50 60 70 80 90 100 110 120
TEST TEMPERATURE (°C)

N
O
L l

 

 

 

O

 

 

 

Figure 6.1: Interfacial shear strength as a function of test temperature
for DGEBA resin cured with different amine curing agents

11 l

strength measurements were difﬁcult to make at or above T, of the bulk matrix due to
the matrix being too ductile causing an excessive amount of necking and tearing upon
tensile load application. Since the Ieffamine based systems have lower bulk glass
transition, less interfacial shear strength data could be obtained at elevated temperatures
for these more ductile systems. Previous work by Rao and Drzal [55] has shown that
decreasing the modulus of the matrix (and interphase) leads to lower values of interfacial
shear strength for systems with constant interfacial chemistry. As the temperature of the
matrix is increased from room temperature towards T, of the matrix, the modulus of the
matrix decreases thereby reducing the ability of the matrix adjacent to the ﬁber surface
to transfer stress.

The glass transition temperatures for all of the different thermoset formulations used
in this Chapter are listed in Table 6.1. In all cases itcan be seen from Figure 6.1 that
the interfacial shear strength is seen to decrease as the T, of each system is approached.
It would be expected that at T,, since the modulus of the matrix drops by orders of
magnitude [12], the interfacial shear strength would also rapidly decrease at that point.
However, in all cases, and especially in the case of the brittle mPDA/DGEBA system,
the interfacial shear strength is seen to decrease well before T, of the bulk matrix is
reached. The mPDA/DGEBA system is seen to have a bulk T, of about 135-140°C, but
the interfacial shear strength is seen to decrease steeply well before this at a temperature
of about 1001 10°C. These results support the concept of the formation of an interphase
whose glass transition temperature, and thus its mechanical properties [111,112], are
different than that of the bulk matrix. Other experimenters [113] have also reported the
formation of an interphase having mechanical and Viscoelastic properties different from
the bulk matrix material.

112

W

Since all the matrices used in this study and this chapter are cured with diamine type
curing agents and the ﬁber-matrix chemical interactions would be constant, it should be
possible to combine all of the data from Figure 6.1 into one ”master” curve. The
interfacial shear strength data was analyzed using linear superposition in the same manner
that the WLF equation [12] of state is used to describe polymer matrix temperature
dependence. The J 230 system was chosen randomly as the reference system and all of
the other data in Figure 6.1 were either shifted to the left or to the right to coincide with
the chosen reference matrix. The shift factor was ”best-ﬁt” and manually optimized with
temperature and the resulting plot is shown in Figure 6.2. These shift factors were then
used to linearly superpose the data. The resulting plot in shown in Figure 6.3. The
ordinate in Figure 6.3 is the “corrected" interfacial shear strength; the data has all been
multiplied by the numerical factor T/T,. In this notation T is the measured temperature
and T, is the reference temperature chosen (T, of the 1230 system), 346°K. This TIT.
factor is the standard factor used [12] for correcting data with the WLF equation of state
for superpositioning data. It can be seen that the shifted data is seen to cover a wide
range of temperatures and interfacial shear strengths. As expected, at lower temperatures
(and higher moduli) the interfacial shear strength is seen to be higher. Figure 6.3 then
allows for the prediction of interfacial shear strength by knowing just the modulus (or
processing temperature at a given time) and the glass transition temperature.
W

In addition to chemical and structural considerations, the state of stresses which result
from the processing of the material itself can inﬂuence the degree of ﬁber-matrix
adhesion. In the case of carbon ﬁbers, the coefﬁcient of thermal expansion is quite small
and can actually be negative [114]. The ﬁber itself is anisotropic and the radial and
longitudinal thermal expansions can be quite different. The matrix is isotropic but has

Shift Factor, At

113

 

2144
2124

  
  

O

J700/DGEBA

J403/J700/DGEBA

   

J403/DGEBA

 
   

rnPDA/DGEBA

 

 

280

f T T

300

T
320

j T j

T
340 360

j

T’ T
380 400

Temperature (°K)

Figure 6.2: Shift factor as a function of temperature

 

GDRREGTED INTERFACIAL
SHEAR STRENGTH (MP0)

114

 

 

 

 

 

 

80
, TO=346OK o mPDA
Q J403
70“ . J700
4 E1 .1230 (ref.)
are J700/.1403
501 (2% G—O Fitted Curve
50*
404
30—
20 I

 

 

 

. T . ' I ' T T I ' T I I ' l '
-200 -100 0 100 200 300 400 500 600 700
At*(T-TO) <°+<>

Figure 6.3: Master curve for prediction of interfacial shear strength
as a function of Shift factor and temperature

115
a coefﬁcient of thermal expansion a factor of thirty larger than the ﬁber. As described
previously in Chapter 5, this disparity becomes increasingly Signiﬁcant as higher
processing temperatures are reached with the absolute difference between the glass
transition temperature and the use temperature determining the magnitude of these
residual thermal stresses [55].

Epoxy matrices also reduce their volume as they begin to crosslink. This volumetric
shrinkage also contributes to the state of Stress at the ﬁber-matrix interphase. For ﬁbers
surrounded by matrix, the resulting cure shrinkage produces a beneﬁcial compressive
interfacial force while for matrix conﬁned between a row of ﬁbers, a net tensile
interfacial state of stress may result. The resulting state of stress can reduce the level
of adhesion attainable between ﬁber and matrix. Calculations of interfacial stresses have
been nrade previously for these thermoset systems and are discussed in depth in Chapter
5. The calculations Show that although the radial component of the stress changes in the
same manner as the measured interfacial shear stress, the magnitude of the radial
compressive stress is small and is considered to be a minor factor. Thus, it is concluded
that it is the changes in the matrix material properties themselves, that are primarily
responsible for the changes in the interfacial shear strengths in this chapter.

. {LOLA/1 '0; 0 it lkﬂmilis. 1,.‘--uJ|1|x .31 I310.

The AS4-C/epoxy system was chosen as an example where an interphase of known
composition different than the bulk is present. It has been proposed and indirectly
veriﬁed [115] that this interphase consists of a low T, epoxy material. Kalantar and
Drzal [116] have given an excellent review of the possible interphase interactions that
may control the level of ﬁber-matrix adhesion.

The plot of interfacial shear strength versus temperature for this particular system is
shown in Figure 6.4. For comparison purposes, both the AS4/mPDA/DGEBA as well
as the AS4C/mPDA/DGEBA data is Shown. At ambient temperatures, it can be seen that

116

 

 

 
      

 

 

 

 

 

90 * 1.4 ’8
L 0..
I: g
g 80 v ; = ¢ , i‘1-2 {D
_.I " -. w
51% 70— ’ e i m-
0V _ *1 0
< - ‘ - - D
“-I 50- - , . 5!
[K].— <___ u
LIJQ 4 ~0.8 G
1—2 0
ZUJ 50‘ . E
DIE * —0 6 LL]
2m 40— - 2
0105 ~ 0 CK
L11< -O.4 Q
>LIJ 30‘ __> I'—
((30: J G-Q 7.25 phr mPDA " (f)
20__ F g 14.5 phr mPDA I-O.2 5
q H mPDA/DGEBA, AS4C fiber . E;
. ° <(
10 I t T I T T I T I T T T TV T r Y T T T 000 2

20 40 60 80 100 111201 I 1110 I100, r180
TEST TEMPERATURE (°C)

Figure 6.4: Loss modulus of mPDA/DGEBA matrix and interfacial shear strength
of mPDA/DGEBA matrix reinforced with carbon, AS4, and AS4»C ﬁbers
as a function of temperature

117

the AS4C system has a 15% higher interfacial shear strength due to the interphase
resulting from the coating placed on the ﬁber during processing. Its modulus is higher
than the stoichiometric bulk epoxy modulus. As the test temperature is increased,
however, the AS4C system is seen to exhibit a measurable decrease in interfacial shear
strength (indicating a lower level of adhesion). As the temperature is increased, there
is a distinct decrease starting at about 70°C well before the expected decrease in
interfacial shear strength when the T, of the bulk matrix is approached. The drop in
measured interfacial shear strength at about 40°C may be attributed to the interphase
epoxy softening thereby leading to a lower modulus in the interphase region eausing a
corresponding lowering of the interfacial shear strength.

The interphase that results from the diffusion controlled interaction of the pure epoxy
coating with the bulk stoichiometric matrix will produce a region around the ﬁber having
less than the stoichiometric amount of amine curing agent. A model this phenomenon
is presented in the next section in this chapter. Separate measurements of the T, and the
modulus of this material [79,117] which is subject to the same curing schedule as the
bulk matrix indicates that the glass transition temperature ean decrease from the bulk
value to about 70-75°C at 50% of the stoichiometric amine level. Netravali et al. [56]
have also shown that interphase interactions play a major role in determining the
interfacial shear strength of coated earbon ﬁbers. They speculate, as Drzal et al. [118]
did earlier, that the interphase region is more brittle due to migration and diffusion of
the curing agent thereby leading to a more brittle interphase with thermal and mechanieal
properties different than that of the bulk matrix.

Figure 6.4 also shows the relationship between bulk matrix storage modulus and
temperature for DGEBA resin cured with a stoichiometric amount (14.5 phr) of mPDA
(open inverted triangles in Figure 6.4) as well as DGEBA resin cured with a 50% of
stoichiometric amount (7 .3 phr; open circles in Figure 6.4) of mPDA. It can be seen

l 18
that for the stoichiometrically cured system, the T, of the matrix falls in the range of
130-145°C while for the 50% stoichiometrieally cured system the T, is in the range 70-
90°C.

Since pure DGEBA monomer melts at about 40°C [5], the ﬁrst drop for the AS4C
data in Figure 6.4 at about 40°C may be due to melting of the unreacted excess DGEBA
in this region. Following this decrease the interfacial shear strength remains higher than
the AS4 system until about 70°C. At this point, a precipitous drop is interfacial shear
strength is measured. The temperature at which this occurs corresponds approximately
to the T, of a 50% of stoichiometric amine/epoxy mixture. This indieates that the curing
agent has diffused and migrated to the interphase through the initially pure epoxy resin
interphase region. Additionally, the decrease in interfacial shear strength at 70°C for the
AS4C system indicates that the interface composition is approximately 50% of the
stoichiometric (bulk matrix) amount. These results show that the composition of the
interphase region is different than that of the bulk matrix and plays a major role in
determining the ﬁnal level of ﬁber-matrix adhesion.

6.4 MODELING OF THE FORMATION OF THE INTERPHASE

The role of the interface/interphase region in determining the mechanical and
adhesive properties of ﬁber reinforced composite materials has gained increasing attention
in recent years [119,120,121,122,123,124,125,126]. The use of simple ”rule of
mixtures” models in which the properties of matrix and ﬁber are weighed to predict
various composite properties often fails to predict accurate values [127]. Interaction
between ﬁber and matrix extending away from the interface region has a strong effect
on composite properties such as interlaminar shear strength [25,94].

Kalantar and Drzal [116] have provided an excellent review of various interfacial
factors, both at the microscopic as well as macroscopic level, which could effect the level

l 19

of ﬁber/ matrix adhesion. Delong et al. [115] have attempted to quantify the interphase
region spectroscopically. Cazeneuve et al. [128] have used Auger microscopy to study
the structure of the interface in carbon ﬁber composites. Others have measured
interfacial properties and concluded that the interphase and its properties play a major
role in determining the level of adhesion at the interface. For example, Zultas et al.
[129] have shown, with metal-matrix composites, that kinetic interactions at the
interphase are different than that in the bulk and that these kinetics lead to different levels
of exotherm and adhesion at the interface. Robertson [130] has also speculated on the
formation of a weak boundary layer leading to low levels of adhesion at the interphase.
Recently, Netravali et al. [56,131] have shown that diffusion of the curing agent into the
epoxy rich interphase creates a brittle interface giving rise to higher levels of adhesion.
Drzal et al. [118] had also noticed this same phenomena earlier with earbonlepoxy
microcomposites. It is this phenomena of diffusion that will be modeled here in this
section.

Virtually no models exist in describing diffusion of curing agent into an epoxy rich
interphase region resulting in alteration of the mechanieal properties of the interphase
region. Theocaris et al. [132] have presented models relating properties of the bulk
matrix to properties in the interphase region using the theory of elasticity and plasticity.
Recently [133] he considered the concept of diffusion of material into the interphase
eausing a change in the mechanical properties of the interface region. While he does not
rigorously solve this particular diffusion problem, he suggests a possible solution using
some idealized conditions. This analysis has been extended below to arrive at a
predictive model for relating the measured interfacial shear strength to the composition
of curing agent at the interface between ﬁber and matrix.

The effect of the interphase region on interfacial properties of a composite can be
visualized by considering an epoxy coated ﬁber embedded in a bulk epoxy/amine matrix,

120

as shown in Figure 6.5 . Here the system initially consists of a stoichiometric mixture
of epoxy and amine in the bulk and epoxy only on the ﬁber coating. During cure, the
amine curing agent diffuses into the coating, creating an interphase having a gradient of
low amine concentration near the ﬁber to the stoichiometric concentration in the bulk.
Because the material properties of amine cured epoxies are greatly dependent on the
amine-epoxy ratio [117,134,135], the interphase will possess unique properties different
from the bulk cured epoxy. Quantiﬁeation of interphase diffusion will enable realistic
modelling of the interphase and its effect on material properties, which in turn will
facilitate accurate prediction of these properties.

It can be seen from Figure 6.5 that three different physical phenomena are occurring
simultaneously in describing the diffusion process into the interphase region. and all three
must be included in a rigorous mathematieal model. Bulk, convective diffusion of the
curing agent into the pure epoxy sizing, chemical reaction between epoxy and curing
agent, and accumulation of curing agent are all occurring simultaneously in the interphase
region. Thus, we have the classical problem of diffusion in a slab (one-dimensional)
with reaction

%=§;(D(o-:—f)+k(c> (6.1)
here the concentration, C, represents the concentration of curing agent in the interphase
region. As a ﬁrst step in the analysis, it will be assumed that the diffusivity is constant
(represented by an ”effective” diffusion coefﬁcient) and the reaction rate linear (i.e.

R=kC). With these assumptions we arrive at:

121

INTERPHASE FORMATION
BY DIFFUSION AND REACTION

 

BULK MATRIX “I

i

E /l'\ (14.5 PHR)
; rxn.

l x \

   

E BULK MATRIX
I

 

 

/ \
INTERPHASE INTERFACE
REGION r=rf
(< 14.5 PHR)
r =r I

Figure 6.5: Schematic of interphase formation by diffusion of curing agent

122

1
ﬂab—E -bC (5,2)
51 ﬁx”

with the following boundary and initial conditions:
Initial Condition: C=0 @ t=O, 0<r<ri
Boundary Conditions: C=C.,...K @ t20, r=ri
dc/dx=0 @ tZO, r=r,
Because this problem does not lend itself to an analytical solution, usually separation of
variables is used to lead to an approximate series solution for the problem (usually
solved without reaction). It has been shown by Finlayson [15,136] that the solution to the

above problem is given by the following series solution.

(2n+1)r,-r +010 (2n+l)r,+r
Mat) 2m

—=2:(-1e'>wc—— (6.3)

In Equation (6.3), n is summed from zero to inﬁnity and erfc is the complimentary error
function. This solution, though rigorous, has limited capability since the time needed to
achieve a concentration of 10% of the bulk at the interface is calculated to be on the
order of microseconds. This does not allow for proper analysis for comparison to the
interfacial data collected earlier in the chapter. This estimate of time needed to achieve
a given concentration at the interface results from the fact that an accurate value for the
diffusion coefﬁcient was not available or determined experimentally. The diffusion
coefﬁcient could change over orders of magnitude as the reaction proceeds in the
interphase and must be accounted for in the model above. The calculated times are very
sensitive to the value of diffusion coefﬁcient used in the analysis. While Theoearis

[133] has speculated on the numerical value of diffusion coefﬁcients for a reacting system

123
(they suggest values anywhere from 10'2cm2/ sec to 10"cm’lsec), they do not make an
effort to estimate the diffusion coefﬁcient as a function of reaction extent. Using a
simpliﬁed form of Equation (6.2), a model is presented below that allows for both the
estimation of interphase thickness as well as well as the variation of diffusion coefﬁcient
within the interphase thickness and perhaps most importantly an estimate of an
”effective” diffusion coefﬁcient in the interphase region.

As mentioned above, very little experimental work has been done on investigating
how the diffusion coefﬁcient changes with extent of cure for a crosslinking reaction. It
would be expected that if the curing agent diffuses from the bulk towards the interface
in a ”reaction-front” type mechanism, the local diffusion coefﬁcient will initially be low
(characteristic of liquid-liquid diffusion) and then quickly diminish as reaction occurs and
liquid-solid diffusion begins to occur. Liquid-liquid diffusion is characterized by
diffusion coefﬁcients in the order of 107 to 10’ cm’lsec while liquid-solid diffusion ean
lead to diffusion coefﬁcients of 10" cm’lsec or lower [13,136]. It is difﬁcult to average
over such large orders of magnitude; Theoearis [133] has suggested effective values for
the diffusion coefﬁcient which fall in the middle of this range (about 10“cm’/sec)
without experimentation. In the analysis below, the thermal response and interfacial
shear strength data of coated AS4 ﬁber data will be used, via a simple model. to arrive
at a relationship between "effective” diffusion coefﬁcient in the interphase and the
thickness of the interphase. It will be shown that the effective diffusion coefﬁcient must
be about lO'“cm’/sec to arrive at the approximate interphase thickness speciﬁed by the
manufacturer.

Because Equation 6.3 above gives a minimal understanding of the physical situation
that is occurring (due to limitations in determining the diffusion coefﬁcient as well as
lack of an analytical solution for the model in Equation 6.2), a suggestion made by

124
Theoearis [133] is used to arrive at an analytical solution for the diffusion of curing agent
into the interphase region for epoxy coated ﬁbers.
The following assumptions are made:
1. One-dimensional diffusion
2. Slab geometry can be approximated (interphase region small)
3. First-order reaction
4

. Adsorption of curing agent onto ﬁber surface (no accumulation of curing
agent 1n the interphase region.

5 . Diffusion coefﬁcient constant (effective diffusion coefﬁcient)

These assumptions lead to Equation 6.1 being simpliﬁed to:

2
99.2 -520 (6.4)
b’r

here, C is the concentration of curing agent in the interphase, D is the diffusion
coefﬁcient of the curing agent into the liquid epoxy, r is the radial direction outward
from the ﬁber surface and k is the pseudo-ﬁrst order reaction rate constant for the
mPDA/DGEBA matrix. The following boundary conditions are valid in this case

at r=r, dC/dr=0

at r=ri C =C.,,,.

the ﬁrst boundary condition is the “no-slip” (i.e. no net ﬂux) condition at the ﬁber
surface and the second boundary condition simply states that bulk concentration (14.5
phr) of curing agent exists at the interphase boundary with matrix. After some involved
mathematical manipulations (see Appendix C for appropriate derivation), it ean be shown
that a closed form analytieal solution of the following form is obtained:

125

6.5)
,0“ -¢ (

 

can:
here C is the concentration of curing agent in the interphase region, and the greek

symbols are the following dimensionless quantities:

4’ =aAr=a(ri’rr) =(k/D)m (ri'rf)

(I: =ri—r/ri-r, = ri-r/ Ar

Figure 6.6 shows the relationship between the concentration of curing agent in the
interphase (normalized to the bulk concentration) and the radial distance in from the
interphase to the ﬁber surface according to Equation 6.5 above. In Figure 6.6 the value
of phi, d: (ratio of the squareroot of reaction rate constant to diffusion coefﬁcient) is
randomly varied from 0.5 to 2.5. It can be seen that the gradient is essentially ﬂat
(unchanging) for low values of 4» and changes to an exponential type behavior for higher
values of c. It was seen in section 6.3.5 above that the concentration of curing agent at
the interface for AS4C (coated) ﬁbers was estimated to be approximately 50% of
stoichiometric value (based on the point at which the interfacial shear strength began to
decrease). From Figure 6.5 it can be seen that a 4> value of 1.45 can be extrapolated
back to a value of approximately 50% of stoichiometric value of curing agent
concentration at the interface (at r=r,).

Slight rearrangement of the deﬁnition of «b above gives:

 

‘ 4, 2 (6.6)

126

 

 

 

 

 

 

1.0 3 {‘r c A G
¢=o.05 _05 T
0.9“ . I: ll — . + a
0.84
=1.0
0.7- ¢
a, 0.64
03 _ ’ ¢=1.5
b 0.5 .
0.4—
0.3— ¢=2.25
0.2—
0.1- . ¢=5.o
00 I I T I V f I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
r'— r/ri—rf=1//

Figure 6.6: Model prediction curing agent concentration proﬁle within
interphase region as a function of diffusion coefﬁcient, reaction
rate constant and temperature

 

127

Since the pseudo-ﬁrst order constant for the crosslinking reaction can be calculated to be
approximately 1.58x104 sec‘l from the data in Chapter 3, Equation 6.6 ean be used to
derive a relationship between the effective diffusion coefﬁcient in the interphase region
and the thickness of the interphase. Figure 6.7 shows this relationship. It can be seen
from Figure 6.7 that for the interphase thiclmess to be 100—300 nm (the approximate
value of the initial epoxy layer reported by the manufacturer, Hercules Corporation,
placed on the ﬁber is about 100 nm) the effective diffusion coefﬁcient in the interphase
region calculates to be between 10'3cm2/ sec and 10“cm’/sec (as suggested without proof
by Theocaris [133]). Thus, for the AS4C data taken here, if D, is taken to be an average
value of 5.5x10“ cm’lsec, Ar calculates to be about 250 nm. Also, it is noted from
Figure 6.6 that as the interphase thickness becomes small (on the order of angstroms)
that the effective diffusion coefﬁcient is about 10‘9cm2/sec which is characteristic of
liquid-solid diffusion. On the other hand, as the interphase thickness approaches a large
value (on the order of microns) the effective diffusion coefﬁcient increases to about
10'9cm2/sec which is more characteristic of liquid-liquid diffusion.

This analysis thus gives a valuable starting point for the value of effective diffusion
coefﬁcient for mPDA/DGEBA matrix. If the cure temperature or matrix is changed,
only the new reaction rate constant is needed (in Equation 6.6) to arrive at a new
effective diffusion coefﬁcient. Furthermore, by measuring the interfacial shear strengths
at elevated temperatures and by using the ”effective” diffusion coefﬁcient calculated
above, an interphase thickness can be computed for any type of epoxy sizing placed on
a ﬁber.

Thus, this rather simpliﬁed model seems to predict the thickness of the interphase
rather accurately based on the diffusion characteristics of the curing agent and
measurement of the interfacial shear strength. This model has the advantage of providing
a closed, analytical solution for the concentration of curing agent in the interphase

ion

ffus

Effective ,lrgterphase
Coefflcrent (cm2 sec)

10“|
10"

128

 

 

LG-E) mPDA/DGEBA matrix at 70‘Cj

10-7 _

1 0".

1 0"
1 o-aa
I 0""
1 0-41
1 0-13
1 0-14
1 o-ra

1 o-'-

10-47
1 0-1-
1 0-1-

10"

1 0"

10“ 10“ 10“ 10" 10“

Interphose Thickness (cm)

10“

 

10°

Figure 6.7: Effective diffusion coefﬁcient as a function of interphase thickness

 

129

region. The predictive capability of the model (which is based on "average" values of
diffusion coefﬁcient and reaction rate constant in the interphase region) can be further
improved by experimentally determining the diffusion coefﬁcient as a function of extent
of cure (i.e. determination of the concentration proﬁle of curing agent in the interphase
region). This would provide a relationship between diffusion coefﬁcient and time which
could be used in Equation 6.1 above to arrive at a more complete solution. In addition,
a more complete non-stoichiometric kinetic study could be conducted to more accurately
describe the epoxy/amine reaction occurring in the interphase region.

The solution presented above is strictly applicable only to sized (or coated) ﬁbers in
which there is a region of pure epoxy initially where the curing agent is free to diffuse
into. From section 6.3.5 it was seen that the AS4 ﬁber/epoxy interface behaved as
though the stoichiometry was about 70-75 96 of bulk. If this model applied here, it
results in an interphase thickness of about 140 nm using an effective diffusion coefﬁcient
of 5.5x10'“cm2/sec. While the trend of the interphase thickness being smaller for a
unsized ﬁber is expected, the model is apparently not able to differentiate between the
two systems to any great deal. This is due to the fact that one of the boundary conditions
may no longer be valid for AS4 ﬁbers. Since there is no pure epoxy sizing (initially),
there is no boundary (no interphase) where the concentration of curing agent ean be set
to the standard stoichiometric value. It is therefore difﬁcult to gage the accuracy of this
model for the unsized AS4 system.

With AS4 ﬁbers, the curing agent diffuses to the interface (during the time that it
takes for the matrix to gel at 70°C) and adsorbs onto the ﬁber surface by either
chemisorption, physisorption or both. This process leaves behind a concentration of
curing agent at the interface which is less than stoichiometric. This is clearly a more
complieated situation to model than the sized system described above beeause the
boundary conditions are difﬁcult to enforce with any degree of accuracy. The

130

stoichiometry at the interface has been inferred from the interfacial shear strength
measurements earlier in this chapter to be about 75-80% of stoichiometric for this
AS4/mPDA/DGEBA system. In this procedure below, different methods will be
attempted to try and estimate interphase thickness from the inferred interfacial
stoichiometry. It will be seen that because the boundary conditions are difﬁcult to
deﬁne, a more accurate model of how the diffusion coefﬁcient changes with time and
concentration of curing agent is required for accurate results.

Initially if we consider a steady-state situation with no reaction (the diffusion is much
slower than chemisorption and thus rate limiting) and a constant diffusion coefﬁcient,

Equation (6. 1) can be reduced to:

2
fig :0 (6-7)
dr:

here, C is the concentration of curing agent in the interphase region and r is the radial
distance outward from the ﬁber surface, with boundary conditions:

at r=r,, C =xC.,.,.K

at r=r,, C =Ch.
the ﬁrst boundary condition contains a factor, x, which corresponds to the amount of
curing agent adsorbed onto the ﬁber surface by chemisorption, physisorption or both.
The second boundary condition is an inferred one beeause it is assumed that bulk
properties are reached at the interphase boundary. The solution to Equation (6.7) with
these boundary conditions is straightforward. The ﬁnal solution reduces to:

—C—=1-¢(r-x) (6.8)

Cu:
where (I is the dimensionless radial distance deﬁned earlier. Equation (6. 8) suggests that
for the stoichiometry to be 80% (as suggested by the elevated high temperature data) that

 

131

the amount of curing agent adsorbed onto the ﬁber surface, x, must also be about 80%
since the solution is linear. Since earlier ESCA studies (Chapter 5) revealed that
chemisorption contributes only 5 % of the total interactions at the interface, there must
also be physisorption occurring whereby a monolayer or more of curing agent adsorbs
onto the ﬁber according to this model. The interphase thickness can only be estimated
if an assumption is made that the amount adsorbed onto the ﬁber (x) is slightly different
than the actual fraction (C/C...) of curing agent at the interface. If this difference is
assumed to be very small (1%), then Equation (6.8) can be solved for a interphase
thickness.

Obviously, the above solution is oversimpliﬁed because the diffusion coefﬁcient
drops out of the analysis. If Equation (6. 1) is recast in a form with the diffusion
coefﬁcient being a function of concentration of the curing agent, we arrive at the

following steady-state equation to describe the diffusion process:
=—5-(D(C)£) (6.9)
br Or

with the same boundary conditions as with Equation 6.7. If it is assumed that

D(C) ~ e‘c’m", Equation (6.9) can be solved by separation of variables to arrive at a
solution. However, again because of the nature of the boundary conditions, the solution
suggests that about 80% of the curing agent must be adsorbed onto the ﬁber surface to
arrive at the measured thermal response of the polymer in the interfacial region.
Equation (6.9) presents the best method, to attack this rather complicated problem. The
problem is difﬁcult because the boundary conditions are not clear cut. Obviously, the
diffusion coefﬁcient cannot be modeled as a function of concentration alone; a time factor
must also be included and a different functionality (other than exponential) must be used
to relate the diffusion coefﬁcient to the reacting properties of the matrix.

 

132

While sorption, drying and uptake data for various liquids into cured epoxy
networks are available in the literature [137 ,138], the author was not able to ﬁnd any
existing literature describing the change in the diffusion coefﬁcient with extent of cure,
concentration of curing agent or time of reaction. Once this relationship is
experimentally elucidated, Equation (6.9) can be used to arrive at a interphase thickness
by a numerical trial and error procedure of systematically varying the interphase
thickness until it matches the observed changes in the interfacial stoichiometry.

Another way this process can be visualized is by considering transient behavior.
Essentially we have the following situation (see Appendix B):

2
29:05.3 (6.10)
5‘ or"

with the following boundary conditions:
at t=0, all r, C=C.,.,=Chull
at t>0, r=rf, C=Ci
at t>0, r=ri, C=Cu
then the following small time solution [13] can be obtained:

_C-= _'_.m
can em4Dt) (6.11)

here t is time, D is the effective diffusion coefﬁcient (10“cm2lsec), and r is radial
distance outward from the ﬁber surface. To achieve C/CM~0.8, r can be estimated to
be very small (104 nm) at the time of gelation (at 70°C). However, this is a very
approximate solution and strictly holds only for very small times. It can therefore be
seen that it is difﬁcult to model the formation of an interphase region for an unsized AS4
ﬁber system beeause the system boundaries are difﬁcult to deﬁne. To arrive at a

133
accurate solution also requires a correlation between the diffusion coefﬁcient and

reacting parameters of the matrix which are not yet available.

6.5 CONCLUSIONS

The dependence of the ﬁber-matrix interfacial shear strength on temperature for
epoxy matrices reinforced with AS4 and AS4-C carbon ﬁbers was studied in this chapter.
The results indicate that the interfacial shear strength decreases with increasing
temperature because of the decreasing interphase modulus. At a temperature slightly
below the bulk T, of the matrix, a signiﬁeant decrease in the interfacial shear strength
was detected. This drop, seen in all the systems, is most likely related to the structure
of the polymer (and hence T, of the polymer) in the interphase region, whose
composition can be different than that of the bulk matrix and whose mechanical
properties control the level of ﬁber-matrix adhesion. Linear superposition was used to
reduce all of the thermoset data into one master curve making possible the prediction of
interfacial shear strength under any thermal conditions such as during temperature
excursions encountered by the composite material. Additionally, the AS4-C system has
been shown to exhibit a distinct decrease in interfacial shear strength at low temperatures
(i.e. low T,) indieating the formation of a low modulus interphase layer. A model
derived from ﬁrst principles has been proposed to explain the results. By making some
simplifying assumptions on the diffusive and reactive characteristics of the bulk matrix,
and by assuming steady-state behavior, an estimate is made on interphase properties and
thickness. This model has the advantage of providing a closed, analytical solution
relating concentration of curing agent at the interface to the reactive characteristics of the

matrix and to the diffusive characteristics of curing agent in epoxy.

 

In this chapter, a method will be outlined for the measurement of interfacial

transverse strength of single ﬁber microcomposites.

7.1 INTRODUCTION

In addition to the shear stresses, normal stresses are also important contributors to
the generation of defects during processing at the ﬁber-matrix interface. It is necessary
to lmow the value of these normal stresses and to be able to measure their magnitude
with changes in interphase and bulk composition. While various authors [102,139] have
presented 3-dimensional models and empirical relationships relating matrix properties to
compressive radial stresses, little or no experimental work has been done in an attempt
to elucidate the relationship between ﬁber-matrix interfacial transverse strength and
properties of the matrix. It will be shown in this chapter that new a single ﬁber

transverse strength technique can be used to qualitatively determine this quantity.

7.2 EXPERIMENTAL

As described in Chapter 2 (section 2.2.4), the experimental technique for the
determination of interfacial shear strength outlined previously in Chapter 2 has been
modiﬁed. Basically, these ”transverse" tests were performed by mounting the ﬁber of
interest transverse to the coupon axis. in the standard dogbone shaped mold described
earlier. The matrix was then poured in and cured. After appropriate curing, the edges
of the samples were polished to create a very smooth surface (using 100 grit sandpaper).
The specimens were then tested, using an optical microscope, under reﬂected light. By
focusing the light directly down onto the ﬁber, and by subjecting the matrix to increasing

134

135
strain (in this particular set-up a pneumatic controller was used so that the amount of load
applied can be directly measured), changes in the light pattern can be noticed when the
ﬁrst sign of debonding from the matrix under transverse loading occurs. By assuming
the ﬁber to be a rigid, cylindrical inclusion, and by knowing the applied load, the actual
load (at debonding) can be calculated using a stress concentration factor [45,140].
Because the moduli of the ﬁbers are large [1] in comparison to the modulus of the
matrix, the stress concentration factor has a constant value of approximately 1.8. Four
different types of ﬁber were tested in the standard mPDA/DGEBA matrix. AS4, AU4,
Kevlar and silicone-coated ﬁbers were used to vary the level of ﬁber matrix adhesion and
to subsequently investigate the transverse strength at the interface. A minimum of 35
samples were analyzed with each ﬁber/ matrix combination to ensure statistically

signiﬁcant transverse strengths.

7.3 RESULTS AND DISCUSSION

Table 7 .1 contains the actual transverse loads at debonding for all of the systems
studied. All transverse loads (at debonding) were calculated by multiplying the measured
load at debonding by an appropriate stress concentration factor as suggested by Chua et
al. [45]. For all the systems studied here, the stress concentration factor is about 1.8.
CarbonAS4ﬁbersweretestedinitiallyinamatrixofDGEBAresincuredwitha
stoichiometric amount of mPDA curing agent. Because of the relatively high interfacial
shear strength (Chapter 5) of A84 ﬁbers in this matrix, transverse debonding was
difﬁth to detect in all of the specimens tested (about 40 in all) until very high strains
were reached in the matrix. Frequently, no debonding was detected up to the point of
matrix failure. Since the specimens did not exhibit debonding up to the point of matrix
failure, a load at debonding of 20,300 psi was computed using the failure stress of the

136
matrix as an estimate for the lower limit for the load needed to transversely debond these
specimens.

In a further attempt to elucidate the transverse properties of AS4 ﬁbers, the AS4
ﬁbers were coated with a silicone-based release agent (by manually dipping the ﬁbers in
the chosen release agent; Silicone Z6020 release agent-Dow Coming) in an effort to
decrease the interfacial and therefore the transverse bond strength. Interfacial shear
strength (using the fragmentation test described in Chapter 5) measurements on the AS4-
silicone coated samples (with mPDA/DGEBA matrix) have shown a reduction in shear
strength of 65-70% . Figure 7.1 shows ”before” and ”after" photomicrographs
illustrating the debonding of these ﬁbers. The transverse strengths of these ﬁbers (about
35 tested in all) are shown in Table 7.1. The actual load at debonding is seen to be
about 7300 psi, a decrease of at least 60% when compared to the load at debonding for
"as-received” AS4 ﬁbers. This shows that the coating agent applied to the AS4 ﬁbers
has drastically decreased the transverse properties. An equally effective method for
elucidating the transverse interfacial properties of AS4 ﬁbers would be to embed the
ﬁbers in a more ductile matrix.

Kevlar 49 (polyaramid) ﬁbers were also analyzed using the same matrix and test.
These ﬁbers were seen to debond at very low loads. The results from Table 7.1 (for a
total of about 45 samples) indicate that the load at debonding for K-49 ﬁbers is about
5300 psi. This indicates a very weak interface when compared to AS4/epoxy interfaces.
Kalantar and Drzal [39] have shown that the interfacial shear strength of Kevlar ﬁbers
is about a third of AS4 ﬁbers. The results indicate that the K-49 ﬁbers debond at about
the same level as the weak-interfaced silicone based AS4 ﬁbers. Figure 7.2 shows
('before" and 'after") photomicrographs indicating the debonding that occurs for the
Kevlar-49 ﬁbers under transverse load. The failure mode is again seen to occur at the
interface between ﬁber and matrix as with the coated-AS4 ﬁbers in Figure 7.1.

137

    

Initial Light Pattern (ﬁber diameter~7 um)

 

‘ Transmitted Light Pattern at First Sign of Debonding

Figure 7.1: Transverse interfacial mode of failure for
Si Coated AS4 ﬁber in mPDA/DGEBA matrix

 

Initial Light Pattern (ﬁber diameter~ 12 p.111)

 

Transmitted Light Pattern at First Sign of Debonding

Figure 7 .2: Transverse interfacial mode of failure for
Kevlar ﬁber in mPDA/DGEBA matrix

139

Finally, AU4 carbon ﬁbers were also tested with same protocol. AU4 ﬁbers are
untreated carbon ﬁbers and have an interfacial shear strength lower than the AS4 ﬁbers
(but they exhibit a higher level of adhesion than do the Kevlar and Silicone-coated AS4
ﬁbers). The average values of transverse strengths for the AU4 ﬁbers (about 55
samples) is about 17.5 ksi.

In Table 7 .1 the matrix used was mPDA/DGEBA cured under the normal curing
conditions listed in Chapter 2. To convert from applied load at debonding (column 3 in
Table 7.1) to actual transverse stress at debonding (column 4 in Table 7.1), the applied
load was divided by the minimum cross sectional area of the specimen and then

multiplied by a stress concentration factor of 1.8. It can also be noted from Table 7 .1

      
 
   
  
    

STRESS AT

DEBONDING DEBONDING LOST DUE
(lbs) (ksi) TO MATRIX

FAILURE

AS4 65 > 130 > 21 95
AU4 40 100.4 17513.5 10
39.5 5.9;0.76 5

 

 

 

 

 

8.410.92

 

 

 

 

 

that the percentage of samples lost due to matrix failure is very high for systems with
strong interfaces and reduces as the interfacial shear strength decreases. All the data
from Table 7.1 are summarized in bar graph form in Figure 7.3.

INTERFACIAL

TRANSVERSE STRENGTH

(PSI)

140

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20000
[E3 ALL DATA WITH DGEBA RESJNJ

15000~
*1 I

10000~

5000~ ‘10 _
0 L

AS4 AU4 AS4 Kevlar

Si Coated

Figure 7 .3: Interfacial transverse strengths of carbon, Kevlar and
EﬁdxmmxbaubonfﬂxashrnﬂHJAleﬁﬂhknmnﬁx

141

7 .4 CONCLUSIONS

In this chapter, a single ﬁber method for determining the transverse interfacial
strength was developed. The results show that the transverse interfacial strength closely
follows changes in the interfacial shear strength. With the data shown in this Chapter,
it can generally be said that the transverse interfacial strength decreases as the interfacial
shear strength decreases. All other things being constant, a system with a high interfacial
shear strength would be expected to exhibit a high transverse interfacial strength.

CHAPTER 8

W
W

In this chapter, a brief study will be conducted on the variation of interfacial shear
strength with temperature in thermoplastic matrices. Using a polycarbonate matrix
reinforced with carbon-AS4 ﬁbers, the experimental protocol used in Chapter 6 will be
used to determine the inﬂuence of temperature on the measured interfacial shear strength.

8.1 INTRODUCTION

Thermoplastic matrices offer some unique advantages [141] over thermosetting resins
in certain applications. These include short molding cycle time, inﬁnite shelf life of
prepreg, recyclability and repairability, reduced handling problems, increased moisture
resistance and better fracture toughness. In general, thermosetting polymers adhere more
strongly to carbon ﬁbers than do thermoplastic polymers. Evidence for these differences
in adhesion is based primarily on scanning electron microscopy of failed carbon ﬁber
reinforced polymer composites [142]. The ﬁbers in the SEM micrographs of epoxy and
other thermosetting polymer composites are coated with the matrix polymer whereas in
similar SEM micrographs of thermoplastic matrix composites the ﬁbers appear to have
cleanly separated from the matrix [142,143]. Many authors have tried to use various
explanations to describe these photographic differences. Hunston et al. [144] and Parker
et al. [145] compared the interlaminar fracture energy as a function of the matrix fracture
energy and found that Carbon Fiber Reinforced Plastics did not ﬁt the general trend
exhibited by thermoset matrix composites. Bascom et al. [142,143] observed that these
differences in adhesion are not necessarily universal. They used SEM to show that
highly cross-linked epoxy and bisamelemimide matrices suggested interfacial failure.
They suggest that these observations may be due to limitations in the resolution of the

142

143

SEM or to micromechanical effects that focus failure into the interfacial region but not
actually at the interface. Bascom et al. [143] have done further experimentation on the
adhesion of three different carbon ﬁbers to epoxy polymers and to a variety of
thermoplastic polymers using the single ﬁber fragmentation test. They speculate on the
following reasons for the data revealing that all three ﬁbers (AS4, A81 and XAS)
exhibited strong adhesion to the thermoset epoxies, but only one (XAS) exhibited strong
adhesion to the thermoplastics: (1) formation of a weak boundary layer, (2) surface
roughness, (3) differing amounts of surface treatment and (4) ﬁber surface chemical
constitution.

In an attempt to illustrate how the interface between carbon AS4 ﬁber and
thermoplastic matrix behaves under ”typical” processing conditions, a brief study will be
conducted to study the alteration of interfacial shear strength with temperature using
carbon, AS4 ﬁbers embedded in a thermoplastic polycarbonate matrix. It will be seen
that the methodology developed in the previous chapters for determining interphase
formation from elevated temperature interfacial shear strength data of thermoset materials
can also be applied to thermoplastic matrices. Recently, Muzzy et al. [146] have also
used the changing viscosity (and modulus) to develop a model for describing the changes
that occur during the processing cycle of toughened therrnoplastics to predict changing
thermal and interfacial properties of the ﬁnal composite material.

8.2 EXPERIMENTAL

Carbon AS4 ﬁbers, described in detail in previous chapters were used as the
reinforcement in a thermoplastic polycarbonate matrix. The speciﬁc polycarbonate used
was Lexan 8050-MC112 (without anti-oxidant, obtained from Cadillac Plastics Co.—
Troy, MI) in the form of 2 mil thick sheets. The glass transition temperature of this
material was found to be about 145-150°C.

144

While the fragmentation test used to quantify the interfacial shear strength is the
same as that described in earlier chapters, the specimen preparation technique is quite
different with this thermoplastic. For these specimens, the single ﬁber microcomposite
specimens were processed in the following manner. Fibers were carefully aligned in
between two thin sheets of Lexan (used as received from supplier) before being enclosed
in a aluminum gasket. The sample was subsequently hot pressed at elevated temperature
and pressure with a hydraulic press to ensure consolidation of the thermoplastic matrix
around the ﬁbers. A careful study of previous work [147] was done to ensure the proper
processing conditions (temperature and pressure). The speciﬁc processing cycle used is
shown below in Table 8.1:

I 1 l 8 I' E . I E I I I .

 

Heat samples to 125°C at l atrn. and hold 1 hr.
Ramp to 240°C.

At 230°C, increase pressure to 7500 lbs.

Heat samples at 240°C for 40 min. at 7500 lbs.
Quench to room temperature at 7500 lbs.

At room temperature, release pressure.

$999!”!"2‘

Remove samples, and cutout specimens with
dogbone shaped punch and die.

In Table 8.1, before completing step #7 the samples are carefully examined under an
optical microscope and the regions with straight ﬁbers are identiﬁed before being
punched out. Further details on these fabrication procedures and techniques can be found
elsewhere [147].

145

8.3 RESULTS AND DISCUSSION

Interfacial shear strength measurements were made from room temperature up to
120°C using the specially designed cell discussed in Chapter 6. The critical length data
are summarized in Table 8.2 and the interfacial shear strengths are shown in Figure 8.1
as a function of test temperature. An average of eight samples were tested at each
temperature. It can be noted from Figure 8.1 that the interfacial shear strength at
ambient conditions is about 45 MPa. This level of adhesion is equivalent to the lower
modulus based thermoset matrices used earlier. As the test temperature is

1.": ' rte: 9121.11- 9'! o

 

 

 

 

 

 

 

-‘ .31 161.1 one) .14 s ' rig-1
I T a“; B“, (1.5., 1'

(°C) (nucrons) (mrcrons) (MPa)
I AMBIENT 3.5753 542.05 7.3;01 44.4 3.4
I 4511.3 2.8767 640.45 7.6;03 40312.8
' 651:2.0 2.8888 716.42 7.321301 36.5 3.7
8012.3 3.2323 713.45 7.7;03 36.7 _ 6.3
97:1:3.3 2.7876 845.68 7.3;02 31.3:t3.3
1153.5 _ _ 2.9993 867.45 7.4101 29.6:t4.5

 

 

 

 

increased, the interfacial shear strength is seen to decrease. In comparison to the
thermoset matrices studied in chapter 6, the decrease is seen to be more linear here with
no precipitous decrease seen (as with the thermoset matrices) as T, of the matrix is
approached. This linear decrease in interfacial shear strength with temperature for
thermoplastic systems has been noted earlier by Oshawa et al. [59]. This seems to be
indicative of a modulus effect on the interfacial shear strength. As the test temperature
is increased, the modulus of the matrix is decreasing thereby reducing the ability of the
matrix to transfer stress to the interface (Chapter 5). This type of decrease in interfacial

146

 

 

LO Lexan matrix/AS4 ﬂbeF]

 

 

 

#—

 

 

l. n
{/1
I e

AVERAGE INTERFACIAL
SHEAR STRENGTH (MPO)
3
L

(at

0

L
U97

 

 

 

 

I I ' I I I j I I I f I ' T ' I T I T I
20 :50 40 50 60 70 30 90 100 110 120
TEST TEMPERATURE (°C)

Figure 8.1: Interfacial shear strength as a function of test temperature
for thermoplastic Lexan matrix reinforced with carbon, AS4 ﬁbers

147

shear strength would be expected in this amorphous system since no curing agent is
present to diffuse into the interphase region in this matrix and the interphase properties
should be very similar to the bulk properties of the matrix itself.

The mode of failure for this particular thermoplastic system is shown in Figures 8.2-
8.6 for ﬁve differart temperatures varying from ambient temperature to 120°C. The
birefringent patterns are all seen to be diffuse indicative of weak adhesion at the interface
when compared to the thermoset systems studied earlier (see Figures 5 .2-5 .6). Also, as
expected, as the temperature is increased more interfacial damage (larger interfacial
cracks) as well as larger amounts of matrix damage is seen to occur. The debonding,
at all temperatures tested, is seen to take place interfacially. This is in good agreement
with previous work done by Waterbury et al. on a similar polycarbonate thermoplastic
system [34,147]. Bascom et al. [53,148] has also shown very similar birefringent
patterns for various different thermoplastic microcomposites.
8.4 CONCLUSIONS

In this chapter, the inﬂuence of temperature on the interfacial shear strength of a
thermoplastic (polycarbonate) matrix reinforced with carbon AS4 ﬁber was investigated.
It was shown that the modulus of the matrix controls the level of adhesion throughout the
temperature regime. Failure modes were indicative of interfacial mode of failure and a
weak level of interfacial adhesion. No deﬁnitive conclusions about the interphase
properties being signiﬁcantly different than the bulk could be made due to the inability
to conduct experiments above 120°C (since the T, of the material is about 150°C, further
experiments must be conducted closer to the bulk T, of the matrix to detect possible
differences in the mechanical and thermal properties of the polymer near the ﬁber/ matrix
interface).

148

 

Polarized Light Micrograph
(ﬁber diameter ~ 7 um)

 

Transmitted Light Micrograph

Figure 8.2: Interfacial failure mode for Lexan/AS4 at 25°C

 

Polarized Light Micrograph
(ﬁber diameter~7 11m)

 

Transmitted Light Micrograph

Figure 8.3: Interfacial failure mode for Lexan/AS4 at 45°C

150

 

 

Polarized Light Micrograph
(ﬁber diameter~7 11m)

 

Transmitted Light Micrograph

Figure 8.4: Interfacial failure mode for Lexan/AS4 at 65°C

151

 

Polarized Light Micrograph
(ﬁber diameter~7 um)

 

Transmitted Light Micrograph

Figure 8.5: Interfacial failure mode for Iexan/AS4 at 85°C

152

 

Polarized Light Micrograph
(ﬁber diameter~7 um)

 

Transmitted Light Micrograph

Figure 8.6: Interfacial failure mode for Lexan/AS4 at 120°C

CHAPTER 9
W

9.1 CONCLUSIONS

In this work, the effect of processing variables on the interfacial shear strength was
investigated for a typical thermoset epoxy/carbon ﬁber (mPDA/DGEBA/AS4) system.
The processing cycle was conveniently divided into three different regimes; a pre-gelation
regime, an ambient temperature regime, and an elevated temperature regime. In each
of the three different regimes, readily measurable properties of the matrix and interphase
were used to predict the interfacial shear strength. Predictive models were developed in
each of the different regimes.

In the pre-gel state, the kinetics of crosslinking and viscokinetic properties of the
reacting matrix were related to a interfacial pull-out strength measured with a gravimetric
apparatus. A modiﬁed WLF equation of state was used to model the changes in viscosity
and in pull-out strength as a function of extent of cure.

At ambient conditions, constant interfacial and matrix chemistry was used to
systematically vary the matrix properties from ductile, plastic to brittle, elastic in order
to simulate the actual processing cycle and to simulate thermoset versus thermoplastic
behavior. A single ﬁber fragmentation test was used to quantify the interfacial shear
strength. With all other parameters held constant, it was found that the interfacial shear
strength is sensitive to matrix modulus and decreases monotonically with decreasing
modulus of bulk matrix. A shear lag model was used to linearly model the changes in
interfacial shear strength as a function of matrix and ﬁber properties.

At elevated temperatures, a specially designed teﬂon cell was used to conduct the
interfacial (single ﬁber) shear strength measurements. The results conﬁrm the reduction

153

154

in interfacial shear strength with a reduction in matrix modulus as found at ambient
conditions. As the T, of the matrix is approached, a corresponding large decrease in
interfacial shear strength is noted. The different matrices (with constant interfacial
chemistry) used previously were used to generate a master curve to describe changes in
interfacial shear strength as a function of temperature. Additionally, epoxy sized ﬁbers
were used to study and model the formation of an interphase region by diffusion and
reaction of curing agent with the epoxy sizing creating an interphase with different
mechanicalpropertiesthanthebulkmatrix. Thesedataareusedtoarriveatan
interphase thickness and effective diffusion coefﬁcient in the interphase region.

Overall, a predictive methodology has been developed for describing changes in the
interfacial shear strength [149] throughout the proeessing cycle of the thermoset
composite. This methodology has the advantage of being able to predict the interfacial
(shear) properties by measuring fundamental properties of the reacting or reacted matrix.

9.2 RECOMMENDATIONS FOR FUTURE WORK

While most of the experimental work presented in this work is complete, the
modeling of the interphase formation presented in Chapter 6 is only a ﬁrst step. A more
complete knowledge of the formation of an interphase could lead to ”tailoring” of an
interphase for speciﬁc composite properties and performance. Future work should
include and address improvement of the model by determining the relationship between
diffusion coefﬁcient (of curing agent into epoxy resin) and extent of reaction. In other
words, the concentration proﬁle of curing agent (or of the epoxy resin) in the interphase
must be evaluated either analytically, experimentally or both. Efforts are already
underway to elucidate this relationship. Once this data is available, Equation (6.1) can
be used to arrive at a more complete ﬁnal solution. Additionally, alteration and
retardation of the kinetics and gelation characteristics of the matrix should allow for

155

transient behavior to be taken into account. The effect of stoichiometry on the kinetics
of the epoxy/amine reaction may also play an important role in the interphase region and
must be accounted for. Obviously, the modeling of interphase formation due to
migration and diffusion of curing agent is in its infancy stage and the model presented
in Chapter 6 should serve as a springboard for a more in-depth mathematical analysis.

Chapter 8 presents a very brief introduction to the effect of temperature on interfacial
behavior of a thermoplastic polycarbonate matrix ("Lexan") reinforced with carbon, AS4
ﬁber. With the advent of new thermoplastic materials capable of increased thermal
stability, a knowledge of how the interface changes with the processing of the
thermoplastic is paramount for a complete understanding of the ﬁnal thermoplastic
composite. While thermoplastic systems will pose unique characteristics (such as
crystallinity and transcrystallinity [150,151,152]-which when occurring in the interphase
region could lead to variations in the level of ﬁber-matrix adhesion; interfacial adhesion
could as well be affected by migration and segregation of low molecular weight
constituents from the bulk to the interface during processing) compared to thermoset
systems, the methodology used in this dissertation should serve as a starting point on the
determination of how processing parameters affect interfacial properties in thermoplastic

systems.

APPENDICES

APPENDIX A
W

In Chapter 3, isothermal kinetic data was used to describe the kinetics of crosslinking
of the mPDA/DGEBA system. Rigorous numerical regression techniques were employed
to arrive at the necessary parameters to describe the reaction kinetics (see Table 3.1).
In this section, ”peak” isothermal data will be used to arrive at similar kinetic parameters
as that shown in Table 3.1. The major advantage to this method, ﬁrst developed by
Kissinger et al. [71] for dynamic (different heating rates) DSC data and later used by
others for isothermal data, is that it only involves algebraic manipulation of the assumed
kinetic rate equation and peak reaction rate data at different temperatures. Kinetic data
must be collected at various isothermal temperatures and the time to reach the peak in
reaction rate and the extent of reaction at the peak is all that is required to complete the
analysis. It will be shown that, for this particular autocatalytic reaction, the two different
methods give rise to similar kinetic parameters.

The starting point for this analysis is the general assumed form of the kinetic reaction
rate expression (autocatalytic)

%=(k,+k,¢')(l-a)’ (A1)

from Equation Al it is evident that the reaction rate constant k, (at a given temperature)
can be obtained by plotting 0: vs. t and calculating the tangent (or initial slope) at t=0
and a=0. Thus, initially, when t=0 and a=0, Equation Al reduces to

156

157
._ dd A2
e-zcxwaw ( )

Equation A2 indicates that the kinetic rate constant k1 is readily determined directly from
isothermal reaction rate data. The maximum (or peak) of the reaction rate curve is
deﬁned by

2
12:0 (A3)
d1:

Applying this condition to the kinetic expression given by Equation Al gives

dda

Etz>=-nk.a-ar"-nk,a'a-a>'“+mk.<l-¢>'«"‘ (A4)

dividing through by (l- )"ar"H and setting the left hand side equal to zero (at a=a,) gives

0=-nlc,a,1"(l-a')"-nk,a,(l1)"):me (A5)
multiplying through by (1-a,) and multiplying the resulting expression by (- 1) gives

0=nk,a,‘"+nk,a,-mk,+mk,a, (A5)
rearranging gives
0=nk,a,""+k1(m ”Def-Mk, (A7)
as discussed in Chapter 3, the overall order of the reaction is assumed to be two so that
m+n =2 (A8)

if now the above equation is substituted into Equation A7 and manipulated for k, we

arrive at

158

‘2‘"“15” (A9)
III-2a,

 

h-

note here that m must be greater than 261, for this relation to hold mathematically; then,
solving Equation Al for m gives (where we deﬁne d: =da/dt)

 

at
4‘.
(l-a)'
1111—] (A10)
*2

111- Inc

ﬁnally, substitution of Equation A9 into A10 at the ”peak“ gives

ﬂ, - -
(l-agz" kl
(Z-MYQGI,” (Al 1)
Int-2a,

inc,

 

 

 

 

here the entire numerator falls into the ln bracket. With this analysis, Equations A2, A9
and All give the necessary parameters needed to deﬁne the kinetics of reaction. The
only data required are the 'peak' characteristics at various isothermal times.

Isothermal runs were made in-situ in the DSC at various temperatures and the time
toreachapeakinthereactionrateaswellasthereactionrateatpeakwere measured.
These data are summarized below in Table A1. The extent of reaction at peak can be
obtained from Figure 3.8 and is always around the gelation point (between 0.58 and 0.64
extent of conversion) for this particular system. The time to reach peak reaction rate (t,)
and the peak reaction rate itself (da/dt), listed in Table A1 can be plotted in Arrenhius
form [153] resulting in the relationships shown in Table A2.

159
Usage of Equations A2, A9 and All gives the kinetic parameters at the various
temperatures once a, and (da/dt), are known from Table A1. A comparison between the

 

 

 

 

 

 

 

 

 

 

 

 

I II E I’ E I I . .
(dirt/d1)n (min")
.00466
90 2.755 55.9 .0121”
100 2.681 36.3 .01650
110 2.611 19.8 .01910
120 2.545 10.3 .01167
130 2.481 6.80 .09590
140 2.421 2.80 .13333
I II 12. E I . I .

t,=6.96x107exp(6487f1), t, in min; T in °K
(da/dt),= 1 .93xlO’exp(-4l96/T), (da/dt), in min"; r in “K

 

more rigorous method presented and used in Chapter 3 and the approximate method used
in this chapter is given below in Table A3. It is seen from Table A3 that while the pre—
exponential factors vary somewhat, the activation energies are in good agreement using
either method. The kinetic exponents are also found to be in good agreement.

Thus, in this section, a rapid estimation technique is proposed for the determination
of the kinetic parameters of an autocatalytic reaction of epoxy cure. The method outlined
utilizes information from a single characteristic point, namely, the point at maximum rate
of cure. The proposed method is a slight modiﬁcation of the method presented initially

160

by Kissinger et al. [71] for determination of kinetic parameters using DSC data at
different heating rates (”dynamic" data). The proposed method yields results which are
in close agreement with the more rigorous numerical technique presented in Chapter 3.

It must be noted that for reaction temperatures below about 85 °C, the kinetics of this
particular reaction are adequately described by pseudo-ﬁrst order kinetics (i.e.
daldt=k(l—a); where 1n k=13.18-(‘7610/T) for k in sec" and T in “IQ and an
autocatalytic model is unnecessary.

 

 

k, = l.693x10°exp(-7034/T)
k¢=9505exp(-4l96/T)

'r in at and km in min"

1 m=-2.75x10”T+1.43 (T in °C, for T> 85°C)

 

MEIHQDJISEILHERE
k1=8.724x10’exp(-5700/'I')

k2=2.814x10‘exp(-4001/'I')

Tin°Kandkminmin4

APPENDIX B

1103.1011131 0;. 0111's 4 31d 0] 0 .108. b

Figure B1 below schematically represents the physical situation that exists when a
microdroplet (0.2 mm) is placed on a carbon ﬁber. Before the droplet gels, the liquid
(mPDA) curing agent diffuses out of the droplet leading to a uncured droplet as discussed

inChapter 4.

 

 

dFO

1W1

tension“!
M

 

 

 

it>0

 

1.:

 

 

 

 

 

 

Figure B1: Diffusion process in microdrop

An initial assumption is that the diffusion coefﬁcient, D, is constant and that there
is no gelation (reaction between curing agent and epoxy resin) from the interface out.
It can then be shown that a mass balance (on the curing agent) combined with Fick’s law
of diffusion gives [13] the following governing partial differential equation describing the
process:

161

— =D— (Bl)

Equation (B1) is subject to the following boundary conditions:
at t=0, all z, C=C.~C...
at t>0, z=0, C=Cu
at t>0, z=oo, C=C.=0

Here, C represents the curing agent concentration. The second boundary condition is
only an approximation as the interface is not continuously refreshed with curing agent.
However, for small times, it has been shown by Crank [136] that this approximation can
be used. The method of combination of variables, to transform the partial differential
equation (Bl) into an ordinary differential equation, is used to solve this problem. We
start by making the following deﬁnition of a dimensionless variable

 

Z
= (32)
(400"2
by using the chain rule of differentiation, we change Equation (Bl) to:
2
43(5) =D£(ﬂ)2 (BB)

d( d: 4? dz

then from appropriate differentiation of Equation (BZ) we have

 

163

 

J: t '3”
—=-z (B4)
at «a m)
and,
dc 2 -1
— = 4Dt (B5)
( dz) ( )
substitution of Equations (B4) and (BS) into (B3) gives the governing ordinary differential
equation:
2
.d_£ +2: £9. :0 (B6)
dc2 d6

In other words, the partial differential Equation (Bl) has been transformed into an
ordinary differential equation with the following boundary conditions:
at {=0, C =C...
at j’=oo, C=C..=0
The solution is now straightforward. One integration of Equation (B6) gives:

(37)

where a is an integration constant. A second integration and use of the above boundary

conditions gives:

c-cu,

a???“ “’8’

here erf is the error function whose values can be found in any standard mathematical
handbook. In our situation, C.~0, so that the ﬁnal solution becomes:

164

i=1 watt) (B9)

Chalk

By assuming a diffusion coefﬁcient of 107cm2/sec [93] for liquid mPDA diffusing
out of liquid epoxy resin, we can derive the time required to achieve a very low
concentration of mPDA curing agent at the interface (uncured droplet). The time
required to reach a 20% of bulk concentration at the interface for a 200 micron droplet
can be calculated to be 0.02 minutes. The experimental protocol for placing droplets on
the ﬁber is on the order of minutes so that diffusion of curing agent out of small droplets
is expected to occur.

For the more viscous J700 curing agent, the diffusion coefﬁcient is expected [13,93]
to be at least a magnitude of order lower (10"cm’lsec) than for the volatile mPDA curing
agent. For a 200 micron droplet, the time to reach a 20% concentration at the interface
canbecalculated tobe .45 minutes. Itcanbe seen that thetimerequired forthesame
amount of curing agent to diffuse out are an order of magnitude higher. The analysis
presented here thus validates and explains some of the curing observations made earlier
in Chapter 4 with these two different systems.

APPENDIX C
W

The physical situation of diffusion of curing agent is discussed in Chapter 6 and is
illustrated in Figure 6.5. An attempt is made here to derive a model to describe the
preferential diffusion of curing agent into the interphase region of thiclaress Ar. We start
by making the following assumptions to simplify the analysis:

1. Small thickness (slab geometry-1 dimensional)

2. First order reaction between epoxy and curing agent, mPDA
3. Constant, ”effective” diffusion coefﬁcient, D

4. No accumulation of curing agent in interphase (steady-state)

With these assumptions, the governing diffusion equation takes the form:

2
Dd—Cﬂ -kC(r) =0 (DI)
dr2

here C(r) is the concentration of curing agent in the interphase region, k is the pseudo
ﬁrst order rate constant (@ ~70°C) for the epoxy-amine reaction, D is the diffusion
coefﬁcient of curing agent into the epoxy-rich interphase, and r is the radial distance.
Equation (D1) is subject to the following boundary conditions:

at r=r,, C =C...

at r=r,, dC/dr=0
The ﬁrst boundary condition implies a bulk concentration (14.5 phr) of curing agent at
the boundary between interphase and bulk matrix. The second boundary condition is the
“no-slip” (no net-ﬂux) condition at the solid ﬁber surface. If we make the following
deﬁnition:

165

a2=.’£ (D2)
D
Equation (D1) becomes:
2
g—C-azcw (D3)
dl‘z
the general solution to Equation (D3) is [15,136]:
C =Cle "'+C2e" (D4)

here C, and C, are integration constants. The ﬁrst boundary condition inserted into
Equation (D4) gives:

Cm=Cle 1‘+C,e"‘ (135)
and the second boundary condition with Equation (D4) gives:

0=££=-aC,e ”Wage”? (D6)
dr

solving (D6) for the constant C, gives:
e"’
c1 =c,— (N)

ew’

and solving (D5) for the constant C, gives:
Substitution of Equation (D7) into (D8) and solving for C... gives:

 

167

 

 

_ ’0,
C=er C1‘
2 ,1
e
ar e"’ -ar
C = e ‘+C e ‘
ban: 2 2 _,,I

e

solving Equation (D9) for C, and rearrangement results in:

 

e
C =C
2 M e 4"") +e C(rff)

substitution of Equation (D10) into (D7) gives:

"I

 

e
C =C
1 Meow—r) +e coy-r.)

(D3)

(D9)

(1310)

(D11)

Equations (D10) and (D11) substituted into Equation (D4) gives us the ﬁnal analytical

solution:

C _ cw”) Haw")
CM cam-r) +¢ col-r)

 

 

(D12)

It is more convenient to make Equation (D12) non-dimensional. Thus we make the

following dimensionless deﬁnitions:

1b =a(r, -r})

and,

(D13)

(014)

168
with these deﬁnitions, it is easily shown that Equation (D12) reduces to the form shown
in Chapter 6:

C e «1")+e “1“.)

(D15)
cor, -¢

 

 

Chart

This completes the derivation of the model to describe diffusion into the interphase
region. Equation (D15) gives the curing agent concentration proﬁle in the interphase by
larowing the diffusion coefﬁcient, reaction rate constant and the radial position in the
interphase region. Some simplifying assumptions suggested by Theocaris et al. [133]
were used to derive this analytical solution. ,

In this model, there are two adjustable parameters only. While the reaction rate
constant was determined experimentally (from the data in Chapter 3, it can be shown that
the pseudo-ﬁrst order reaction rate constant at 70°C is approximately 1.58x104 see"), the
diffusion coefﬁcient, D, was obtained from the literature as discussed in Chapter 6.
Obviously, if the diffusion coefﬁcient is determined experimentally and known more
accurately and a more in-depth kinetic analysis is used, a correspondingly more accurate
solution can be obtained. Even though Equation (D15) predicts proper interphase
thickness based on inferred interfacial stoichiometry (for coated ﬁbers), a more realistic
model would also include the dependence of the diffusion coefﬁcient on extent of reaction
and concentration of curing agent as the epoxy-amine reaction proceeds. Separate
experiments must be conducted to ascertain these data. A more realistic approach could
also include the possibility of a moving interphase boundary by diffusion of polymer out
of the interphase into the bulk.

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10.

11.

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