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This is to certify that the
thesis entitled
EFFECT OF CROSSLINK DENSITY DISTRIBUTION ON MECHANICAL

RESPONSES OF PHYSICALLY AGED EPOXY GLASSES

presented by

Yitong Wang
has been accepted towards fulfillment

of the requirements for

Master's degree in Materials Science

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MSU In An Afflnnotivo Action/Equal Opportunlty Inctnulon
W

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EFFECT OF CROSSLINK DENSITY DISTRIBUTION ON MECHANICAL
RESPONSES OF PHYSICALLY AGED EPOXY GLASSES

By

Yitong Wang

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Materials Science and Mechanics

1995

ABSTRACT

EFFECT OF CROSSLINK DENSITY DISTRIBUTION ON MECHANICAL
RESPONSES OF PHYSICALLY AGED EPOXY GLASSES

By

Yitong Wang

A series of epoxy resin were crosslinked with diamine of known molecular weight
distribution to form network of control crosslink density distribution. The mechanical
properties such as, the fracture toughness, Kxc, creep compliance under small step stresses,
D(t), and small strain stress relaxation, E(t), of these networks were investigated as
function of time and temperature. In fracture experiment, it was found that one was able
to increase the KC with increases in molecular weight of diamine used. Interestingly, the
fracture toughness also increase with longer aging time for network containing high
fraction of longer molecular weight diamine. This is in contrast with observation of aging
efl‘ect on single component of polymeric glasses which the value of ch decreases with
longer aging time. The relaxation/retardation spectrum of this type of networks were
modified with the ratio of bimodal molecular weight distribution of curing agent used (i.e.
diamine). However, for all networks investigated here, the creep compliance curves and
stress relaxation curves at different aging time and aging temperature were able to be
superimposed and form master curves, thus demonstrating the applicability of the classical

time-aging time; time-temperature superposition principle to each these of networks.

ACKNOWLEDGMENTS

I would like to thank Dr. Andre Lee for his support and guidance in completing
this research. Without his ideas, encouragement, constant focusing of my research, and
patience this body of work would not have been completed. I would also like to thank to
my committee members Dr. Iwona Jasiuk and Dr. Dahsin Liu for their valuable

suggestions.

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER 1 INTRODUCTION

CHAPTER 2 FRACTURE

2.1

2.2

2.2.1

2.2.2

2.2.3

2.2.4

2.3

2.3.1

2.3.2

Introduction

Experimental Procedures

Materials and Sample Preparation

Sample CharaCterization

Physical Aging Condition and Fracture Experiment
Data Analysis Method

Results and Discussion

DSC Results

Fracture Experiment Results

iv

Page
vi

vii

ll
12

12

13

21

CHAPTER 3 VISCOELASTIC RESPONSES

3. 1 Introduction

3.2 Experimental Procedures

3.2.] Materials and Sample Preparation
3.2.2 Sample Characterization

3.2.3 Physical Aging Experiment
3.2.4 Data Analysis Method

3.3 Results and Discussion

3.3.1 DSC Results

3.3.2 Creep Compliance Test Results
3.3.2.1 Boltzmann Superposition
3.3.2.2 Aging Results

3.3.3 Stress Relaxation Results
3.3.3.1 Boltzmann Superposition

3.3.3.2 Aging Results

CHAPTER 4 CONCLUSIONS

REFERENCES

30

34

36

37

39

41

42

44

66

66

77

79

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

LIST OF TABLES

Samples for fracture tests

DSC Results for fracture tests specimens

Fracture toughness result

Samples for DGEBA/diamine networks

DSC results for the DGEBA/diamine networks

The KWW curve fitting parameters of creep compliance tests for Tg - T = 15° C
The KWW curve fitting parameters of creep compliance tests for Tg - T = 8 ° C
The KWW curve fitting parameters of creep compliance tests for Tg - T = 5 ° C

The KWW curve fitting parameters of stress relaxation tests for Tg - T = 15° C

vi

Figure 1.
Figure 2.
Figure 3.
Figure 4.

Figure 5.

Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

LIST OF FIGURES
Schematic architecture of the DGEBA/PPO networks
Schematic of enthalpy (volume) versus temperature
The molecular structure of DGEBA
The molecular structure of D230, D400 and D2000

Compact tension configuration and Schematic of the location of fracture
surface

A DSC curve for DGEBA+100%D23O

A DSC curve for DGEBA+99%D230+1%D2000

A DSC curve for DGEBA+98%D230+2%D2000

A DSC curve for DGEBA+95%D230+5%D2000

A DSC curve for DGEBA+98%D230+2%D400

A DSC curve for DGEBA+95%D230+5%D4OO

A DSC curve for DGEBA+90%D230+10%D4OO

Critical stress intensity factor Krc as a function of molar ratio of D2000

Load-displacement for DGEBA/D230 and DGEBA/D230/D2000 after 50
hours aging

Critical stress intensity factor ch as a function of aging time for
DGEBA/D230 and DGEBA/D230/D2000

Fracture surface of DGEBA+100%D230 aged for 50 hours

Fracture surface of DGEBA+98%D230+2%D2000 aged for 50 hours

vii

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Figure 23.

Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.

Figure 32.

Fracture surface of DGEBA+95%D230+5%D2000 aged for 50 hours

Schematic of volume-temperature plot show volume change from point A to
point B during aging

Schematic of the relative effects of aging on viscoelastic response at point A
and point B

Schematic of stress history where all probes are of equal magnitude

The response of DGEBA+1 00%D230 aged at 78.50 C for 24 hours to loading
followed by unloading

Creep compliance curves of DGEBA+1 00%D23O aged at 66.9:0.3° C for
various aging times

Creep compliance curves of DGEBA + 98%D230 + 2%D2000 aged at
61.1:03o C for various aging times

Creep compliance curves of DGEBA + 95%D230 + 5%D2000 aged at
49.6103o C for various aging times

Creep compliance curves of DGEBA + 95%D230 + 5%D2000 aged at
49.5:0.3° C for different stress histories

Creep compliance curves of DGEBA + 100%D230 aged at 75.2::O.30 C for
various aging times

Creep compliance curves of DGEBA + 98%D23O + 2%D2000 aged at
66.6103o C for various aging times

Creep compliance curves of DGEBA + 95%D230 + 5%D2000 aged at
58.0:030 C for various aging times

Creep compliance curves of DGEBA + 90%D230 + 10%D400 aged at
66.7:030 C for various aging times

Creep compliance curves of DGEBA + 100%D23O aged at 78.5:030 C for
various aging times

Creep compliance curves of DGEBA + 98%D230 + 2%D2000 aged at
71 3:03" C for various aging times

viii

Figure 33.

Figure 34.

Figure 35.

Figure 36.

Figure 37.

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Figure 42.

Figure 43.

Creep compliance curves of DGEBA + 95%D230 + 5%D2000 aged at
60.8:0.3° C for various aging times

Creep compliance curves of DGEBA+98%D230+2%D2000 at aging time of
60 min for various aging temperature

Creep compliance curves of DGEBA+95%D230+5%D2000 at aging time of
60 min for various aging temperature

Double logarithmic plot of aging time shift factor ate versus aging time for
creep compliance test at temperature Tg - 15° C

Double logarithmic plot of aging time shift factor a... versus aging time for
creep compliance test at temperature Tg - 8° C

Double logarithmic plot of aging time shift factor atc versus aging time for
creep compliance test at temperature Tg - 5° C

The response of DGEBA+98%D230+2%D2000 aged at 608° C for 4 hours to
loading followed by unloading

Stress relaxation curves of DGEBA+100%D23O aging at 67.9:0.3° C for a
period of time

Stress relaxation curves of DGEBA+98%D230+2%D2000 aging at 60.8
103° C for a period of time

Stress relaxation curves of DGEBA+95%D230+5%D2000 aging at 51.2
:0.3° C for a period of time

Stress relaxation curves of DGEBA+90%D230+10%D4OO aging at 61.0
:0.3° C for a period of time

Figure 44. Stress relaxation curves of DGEBA+95%D230+5%D2000 at aging time of

Figure 45.

Figure 46.

480 min for various aging temperature

Double logarithmic plot of aging time shift factor a1c versus aging time for
stress relaxation test at temperature Tg - 15° C

Logarithmic of temperature shift factor aT versus temperature difference T -
Tg for DGEBA+95%D230+5%D2000 at aging time 480 min

ix

CHAPTER 1 INTRODUCTION

In order to elucidate the effect of the molecular weight distribution between
crosslinks on the mechanical responses of epoxy networks, difimctional amine terminated
curing agent with the same composition but different molecular weight were mixed with
diepoxy to form networks of crosslink distribution. The diamines used in this study were
linear diamines of poly(propylene oxide) (PPO). As shown in Figure 1. the DGEBA is
connected with PPO chain to form varying crosslink density distribution. The DGEBA
regularly alternating blocks with diamines formed the crosslinked epoxy networks. The
term “alternating” refers to the connection between the long-chain and the short-chain
blocks [1].

Glassy polymers are prone to brittle fracture. To improve the fracture toughness,
one often incorporates a second rubber phase. This can be accomplished by either add in
second rubber phase or directed copolymerization of networks with soft segments (larger
distance between crosslink junctions). Although a lot of work have been studied with
rubber toughened system, relatively few studies involve copolymerization method. The
highly crosslinked thermoset polymer such as epoxy exhibits relatively low resistance to
crack propagation. To improve this, one often incorporates second rubbery phase. This
is accomplished either by adding a CTBN rubber - the true secondary phase or by
corporating into network with longer distance between crosslink junction. There is a

large number of studies which involve rubber toughened epoxy network, while relatively

 

 

 

 

 

Figure 1. Schematic architecture of the DGEBA/PPO networks

3

little has been done using copolymerization method. One of the copolymerization
methods incorporates diamines with longer molecular weight between crosslink junctions
through copolymerization.

In this study, I am particularly interested in the long term performance of these
networks. Physical aging is a phenomenon that has recently been shown to have a great
importance in considering the long term mechanical behavior of glassy polymers [2].
Physical aging is a result of slow continuation below the glass transition temperature, Tg,
of the glass formation process that begins at Tg. After the (kinetic) transition from
liquid-like to glass-like behavior, the material is in a non-equilibrium state and its
structure spontaneously evolves towards equilibrium [3,4]. Accompanying the change in
glassy structure is the change in the mechanical (viscoelastic) response of the glass [5-8].

As the polymer material is cooled through the glass transition, the molecules are
essentially “frozen” into a nonequilibrium state relative to the corresponding equilibrium
state extroplated from liquid state; see Figure 2. The glassy state is a unstable
thermodynamic state. Therefore, enthalpy and volume of this system spontaneously
evolved toward to equilibrium state. The molecular mobility below the glass transition,
although greatly reduced, remains finite, thus the physical and mechanical properties of
polymers will change with time [9]. Practical interest in the aging behavior of glassy
polymer has arisen due to the rather significant mechanical property changes which have
been observed to occur as a result of the approach toward the equilibrium state [10,11].
Typical of these changes are an increase in tensile and flexural yield stresses, a decrease

in impact strength, fracture energy, ultimate elongation, and creep rate, and a transition

 

glass ' liquid
I

   
 

 

 

 

TEMPERATURE

Figure 2. Schematic of enthalpy (volume) versus temperature plot. Arrow
showing enthalpy (volume) decrease represents normal isothermal response
of a glass after rapid cooling to a non-equilibrium state

5

from ductile behavior to brittle fracture [12-14]. Such studies have been performed in
order to develop a better understanding of the molecular origin of the physical properties
in polymers. From these studies, the mechanism of physical aging has been related to
molecular conformation, entanglement networks, and free volume [15-18]. Since the
behavior of epoxy glasses exhibits both viscous and elastic behavior, they are termed
viscoelastic. The examination of this behavior will determine how a polymer will
respond to a stress or strain over a long period time at temperature below its Tg. The
above factors will lead to an examination of creep compliance and stress relaxation
behavior of the epoxy glasses. In particular, how does the crosslink density distribution
on mechanical response affect the aging behavior of the epoxy glass? Therefore, fracture
and viscoelastic tests can be performed in order to identity the mechanical responses of
the epoxy glasses during physical aging. Fracture tests based on compact tension
specimen (CTS) and creep compliance and stress relaxation tests in uniaxial extension are

performed to characterize the mechanical responses during the aging process.

CHAPTER 2 FRACTURE

2.1 Introduction

Epoxy resins are some of the most commonly used therrnosetting polymers. The
use of polymer matrix fibrous composites in automotive, durable goods, and
infrastructure areas have been slowed by a certain lack of confidence in their durability,
reliability and, hence, their cost effectiveness. Among many desirable properties of these
networks are high modulus and good performance at elevated temperatures. However,
they exhibit poor fracture toughness and low resistance to crack growth [19, 20]. To
improve the toughness of glassy polymer, one can incorporate rubber domains into the
system. There are two general methods of adding this rubber domain. The first is
through blending an incompatible rubbery polymer with the matrix and the second is
through copolymerization [21].

The use of rubber particles in a brittle polymer has a major effect upon the
mechanical properties. The material will yield and then deform plastically before
fracture. Brittle network polymers such as epoxy can be toughened by the addition of a
rubbery particles. An example of this is the addition of 8.7% by weight of a carboxyl-
terminated poly(butadiene-co-acrylonitrile) (CTBN) rubber to the epoxy prepolymer and
curing agent. The rubber is first soluble in the prepolymer mixture but precipitates in the
form of particles as the resin increases in molar mass during curing. This volume of

precipitate is what controls the toughness of the material [21]. The rubber particles have

7

a Young’s modulus of about 3 orders of magnitude lower that of the glassy matrix. This
causes stress concentration at the equators of the particles during mechanical
deformation. Since rubber particle can undergo large elastic deformation, the stress
concentration can cause shear yielding or crazing around every particle and hence
throughout a large volume of material rather than just at the crack tip. The polymer is
toughened by the large amounts of energy absorbed during deformation.

Although the rubber toughening is the effective method to improve fracture
toughness of the polymers, in some application this phase separation may not be
desirable, as for example the phase separated material is often nontransparent [22]. As an
alternative approach to this goal, one incorporated diamines with longer molecular weight
between crosslink junctions through copolymerization. Although these methods of
toughness are not as effective in compared to rubber toughening, but sample remain
transparency, and one can achieve high fracture toughness. Since the chain length
between crosslink junctions is longer and therefore it takes longer to deformation. As
mentioned previously, I am interested in the long term performance of epoxy glasses, the
fracture toughness test used in this study was that of the compact tension specimen (CTS)
which was aged at 70° C with aging time range from 1 hour to 100 hours. The fracture
was occurred at room temperature immediately after aging condition. By comparing the
results of these tests, the effect of the crosslink density distribution on crosslinked epoxy

glasses due to physical aging was determined.

2.2 Experimental Procedures
2.2. 1. Materials and Sample Preparation

Diglycidyl ether of bisphenol A (DGEBA, DER 332, Dow Chemical, USA) was
chosen as the model epoxy monomer in this work. DGEBA is a difunctional epoxy, the

DER3 32 is typically used commercial epoxy resin.

0 CH3 0
/ \ I / \
CH.-CH-CH,-OHCo-CH,-CH-CH,
I
CH3

Figure 3. The molecular structure of DGEBA.

Jeffamine of different molecular weight was the curing agent. (Jeffamine is a
tradename of Texaco Chemical Company). Jeffamine D230 and D2000 were used in this
work. i The D-series amines are difunctional amines linked by poly(propylene oxide)
(PPO) chain. Where It is the average number of repeat units in the epoxy resin molecule.
(The number of n is taken from manufacture’s booklet).

CH3
HZN— Cil—CHZ ( O—CH2 —CH )n NHZ n _=. 2.6 for D230

CH3 n 5 33.1 for D2000

Figure 4. The molecular structure of D230 and D2000.

9

The DGEBA epoxide monomer was preheated at 60° C for 2 hours to melt any
crystals present before hand mixing with the amines until the mixture was clear. The
mole ratio of the DGEBA epoxide monomer and amine was that of the stoichiometric
ratio. The mixture was degassed for 20 min at room temperature to remove the bubbles,
then cast into a mould with dimensions of 8 x 4 x 0.25 inch (20.32 x 10.16 x 0.635 cm)
and cured at 100° C for 24 hours. The sample was then allowed to cool slowly in the
oven overnight to 23° C. Specimens conforming to ASTM D5045-91 geometry (3 = 0.35
inch (0.89 cm), B = 0.25 inch (0.64 cm) and W = 1.00 inch (2.54 cm) were machined
from the cast sheets (The dimensions are shown in Figure 5). The samples were kept in a
sealed desiccator until the experiments were performed.

All the samples were cured with stoichiometric amounts of reactants, i.e., one
mole of diamine to two moles of epoxy resin. The molar ratio of diepoxide to diamine
was kept in stoichemetric ratio, i.e. [E] : [H] = 1 : 1 (see Table l). The following is the
example calculation used to convert number fraction to weight fraction for DGEBA,
D230 and D2000.

DGEBA = ( 340 g / mol ) / 2 epoxy groups = 170 g / epoxy group (eg)
D230 = ( 230 g / mol )/4 amine groups = 57.5 ( g / eg)

D2000 = ( 2000 g / mol )/ 4 amine groups = 500 ( g / eg )

Example calculation: W

( 1 )‘(57.5g/eg)+170(g/eg)=227.5(g/eg)

Weight fraction of D230 = ( 57.5 g / eg ) / ( 227.5 g / eg ) = 0.2527

Weight fraction of DGEBA =( 170 g / eg ) / ( 227.5 g / eg ) = 0.7473

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) k W/4
J
/
i; 1 :i .6 W
.mfi W T __
{3— .6w
‘ B
a [re—v]
‘——>
k W #1»
b)
Fracture Direction
>
Precrack Zone
/ \
Load Direction Fracture Surface

Figure 5. a) Compact Tension Configuration
b) Schematic of the location of fracture surface

11

Table 1: Samples for fracture tests

 

 

 

 

Sample Molar ratio" of [E] : [1110230 : [Hlozooo
A : DGEBA+100%D230 1 : 1 :0
B: DGEBA+98%D230+2%D2000 1 : 0.98 : 0.02
C: DGEBA+95%D230+5%D2000 l : 0.95: 0.05

 

 

 

 

‘[E]: Epoxide monomer
[H]m30: Hydrogen contributed by D230
[Hiozoooi Hydrogen contributed by D2000

2.2.2. Sample Characterization

The TA Instruments Differential Scanning Calorimeter (Modulated DSC) 2920
applies an enthalpy-change method to determine the difference in energy flow into a
material as a function of temperature. These measurements are all taken in relationship to
a reference material under a controlled temperature program. The glass transition
temperature is where an amorphous solid becomes rubbery. The glass transition is
accompanied by a change in heat flow of the sample and therefore will be indicated on
the DSC curve.

The glass transition temperature, Tg , and the changes in heat capacity ACp at Tg
for the testing samples were determined by the MDSC. The temperature scale was
calibrated with the melting transition of indium. Temperature scans were performed at
5° C/min with modulated : 1° C every 60 seconds and was operated over a temperature
ranging from -60° C to +120° C. Tests were performed on 10 to 20 mg samples. The

heating scans were performed immediately after cooling samples which had been held at

12
120° C for 30 min to erase the thermal history. The Tg was taken by the inflection point,

the point on the curve with the steepest slope, which is considered the midpoint of the

step transition from glassy to the liquid state.

2.2.3. Physical Aging Condition and Fracture Experiment

All the specimens were first annealed at 102° C (20° C above Tg of
DGEBA/D230) for 30 minutes to remove all previous aging. Immediately after
annealing, all the specimens were put into the oven and held at 70° C for aging. The
aging time ranged from 1 to 100 hours. Immediately after aging treatment, the machine
notched specimens were precracked to approximately 0.2 inches. The precracking
procedure consisted of placing a razor blade dipped in liquid nitrogen and tapping it with
a hammer. The fracture measurements were then performed using a computer-controlled
screw-driven testing machine (Instron apparatus model 4206) at room temperature and at
crosshead speed of 10 min/min. A loading clevis suitable for testing compact tension
specimens is used to clip the test specimen. Both ends of the specimen are held in such a
clevis and loads are applied to the sample through the pins. An Olympus
reflected/transmitted light microscope with camera attachment was used to analyze of the

CTS fracture surface morphology.

2.2.4 Data Analysis Method

All the fracture toughness data were analyzed according to the concepts of linear

elastic fracture mechanics (LEFM) [23]. The critical stress intensity factor Krc, is also

13

called the fracture toughness because it characterizes the resistance of a material to crack
propagation. It is normally a function of the applied load, crack length and specimen
dimensions. According to ASTM D 5045-91 the following formulas were used to
calculate the Km factor.
KQ=(PQ /BW"2)f(X) (I)
where ( 0.2 < X < 0.8 ):
f(X) = [(2 + X)(O.886 + 4.64X - 13.32x2 + 14.72x3 — 5.6x4 )] / (1 - X)”2
P0 = the maximum tensile load
B = the thickness of the specimen
W = the width of the specimen
a = the initial crack length of the specimen

X=a/W

2.3 Results and Discussion
2.3.1 DSC Results

The DSC results for DGEBA/D230 and a blend containing 2% and 5% of D2000
are presented in Table 2 and Figure 6, Figure 8 and Figure 9. All the materials exhibit a
primary transition zone corresponding to the glass transition temperature (Tg). One can
see that as the amount of D2000 increase, the glass transition temperature (Tg) is
decreased, the heat capacity (Cp) at Tg is increased, the glass transition zone is
considerably broadened as increasing the amount of D2000. Because the Tg’s of the two

components (DGEBA/D230 is 82.89° C, and DGEBA/D2000 is -48° C) are not close, the

("/91

Heat Flown

14

 

    
 

 

 

 

Sample: DGEBA+100%D230 D S C File: C: 100360230005
Size: 12.5000 mg Operator: YTN
Method: MOO. RAMP -60 T0 140°C Run Date: 3-Jan-QS 17:32
Comment: MOD. RAMP AT 5°C/MIN. ~60°C TO 140°C '
0.00

-0.05-

J
-0.10-

76.60°C
82.89°ClI)

-0.15-

. 86.90°C
“0.20 1 I V r v r v y r I v r v 1 v

-60 -40 -20 O 20 40 60

0.05. “Ono '.. 1.539.
Temperature! (°C) '

Figure 6. A DSC curve for DGEBA + 100%D230

(N/gl

Heat Flow

15

 

 

 

 

Sample: DGEBA+9920230+1202000 D S C File: C: 1102000002
Size: 13.8000 mg Operator: YTN
Method: M00. RAMP -60 T0 120°C Run Date: d-Jan-QS 23:44
Comment: M00. RAMP AT 5°C/MIN. -60°C T0 120°C. SECOND RUN '
0.00
-0.05~
-O.10"
-o.15- 78.65°C(Il
‘ 83.50°C
-0.20 r I ' I f I r I ' I Y I ' I '
-60 -40 -2O 0 20 40 60

- OMOSC V11601A r4 129
Temperature! 1°C) ' n

Figure 7. A DSC curve for DGEBA + 99%D230 + 1% D2000

 

(H/gl

Heat Flow!

16

 

  
 
    

 

 

Sample: DGEBA+98%D230+2%D2000 D S C File: C: 2102000002
Size: 12.7000 mg Operator: YTN
Method: M00. RAMP -50 TO 120°C Run Date: d-dan-QS 21:17
Comment: MOO. RAMP AT 5°C/MIN. -60°C TO 120°C.SECONO RUN
0.00

-0.05-

,
-O.10—

. 66.30°C
-o.is« 74.7a°ctt)

‘ ao.13°c
‘0 . 20 V T ' fi f r r l v I v I v ,

-60 -40 -20 O 20 40 60

0«use V1160” TA 1120:
Temperature! 1°C) ' ns

Figure 8. A DSC curve for DGEBA + 98%D230 + 2%D2000

 

(w/g)

Heat Flows

17

 

  
 
 
  

 

 

 

Sample: DGEBA+95%D230+5%02000 - [3 E3 C: File: C:5%02000.002
Size: 11.3000 mg Operator: YIN
Method: MOO. RAMP -60 TO 120°C Run Date: 3-Jan-95 22:57
Comment: M00. RAMP AT 5°C/MIN, -60°C TO 120°C.SECON0 RUN ‘
0.00
-0.05-
—0.10-
53.53°C
-0.15—
65.35°C1I)
72.76°C
‘0.2O ' I ' I I I r I ' I ' h
-60 -40 -20 0 2O 40 60

Temperature! 1°C)

Figure 9. A DSC curve for DGEBA + 95%D230 + 5%D2000

o 100 ' 120
MOSC V1.1A TA Ins'

1N/g)

Heat Flow!

18

Sample: 0688A+9810230+210400 D S C Fi 1e: C: 220400.002
Size: 13.5000 mg Operator: YTH
Method: MOO. RAMP -60 T0 120°C Run Date: 10-Jan-95 02:23
Comment: M00. RAMP AT 5°C/MIN, -60°C TO 120°C SECOND RUN
0.00

 

-0.05-

-O.10‘

  
 
    

75.49°C

-O.15-
82.50°C1Il

87.0l°C

 

 

 

‘0.20 1 I ' I
-60~ -40 -20

I ' fi ' r v I v r f
20 40 60 80 MDSC ViloolA TA 13°
Temperature! 1°C) '

D.

Figure 10. A DSC curve for DGEBA + 98%D230 + 2%D400

(w/g)

Heat Flown

19

Sample: DGEBA+95%D230+5%D400 D S C File: C: 5310400002
Size: 12.9000 mg Operator: YTN
Method: MOD. RAMP -60 T0 120°C Run Date: IO-Jan-QS 04:46
Comment: M00. RAMP AT 5°C/MIN. -60°C T0 120°C SECOND RUN ‘
0.00

 

-0.05n

  
 
   
  

 

 

-o.1o-
‘ 71.40°c
-0'15‘ ' 7a.os°c111
‘ 81.85°C
-o.2o . . - , , r . . , . , . , - , .
—60 v-ao -2o 0 20 40 60

OMDSC VlloolA TA .1129
Temperature! 1°C) ' n

Figure 11. A DSC curve for DGEBA + 95%D230 + 5%D400

 

(N/g)

Heat Flown

20

 

     
 

 

 

Sample: 06EBA+9020230+10X0400 D S C File: C: 1020400002
Size: 12.1000 mg Operator: YTH
Method: M00. RAMP -60 T0 120°C Run Date: 10-Jan-95 20:43
Comment: MOD. RAMP AT 5°C/MIN, -60°C TO 120°C SECOND RUN
0.00
J
-0.05-
—0.10—
68.35°C
75.33°C(I)
-0.15d
79.91°C
-0.20 . I . I A . I . u . r’* #7444 - I . r
-60 -4O -2O 0 20 4O 60 80

MDSC ViloolA TA 1Iglo
Temperature! 1°C) '

Figure 12. A DSC curve for DGEBA + 90%D230 + 10%D400

 

21

temperature range of DSC curve is from -60° C to +120° C. Since there is only one glass

transition temperature for each specimen, the above observations indicated that no phase

separation has occurred when blending the small amount of D2000. It is apparent that the

epoxy network is still a single phase network. The components of each specimen are

compatible each other. But by adding the D2000, the glass transition zone is broader,

which indicates where the system has broadened crosslink distribution.

Table 2. DSC Results

 

 

 

 

 

Sample Tg (° C) ACp ( J / g / °C) Glass Transition Zone (° C)
A 82.89 0.1208 _ 10.30
B 74.78 0.1343 13.83
C 65.35 0.1370 19.23

 

 

 

 

2.3.2 Fracture Experiment Results

The fracture behavior of epoxy glass networks has been examined. The

calculated critical stress intensity factor KIC, determined from the load-displacement

curves according to eqn. (1) is reported in Table 3.

Table 3. Fracture toughness result, KIC (MPa mm)

 

KIC , at different aging time

 

Sample

1 hour

50 hours 100 hours

 

A: DGEBA +100%D230

0.84:0.08

0.92:0.09 0.96:0.08

 

B: DGEBA + 98%D230 + 2%D2000 1.1512010

1.15:0.07 1.14:0.12

 

 

C: DGEBA + 95%D230 + 5%D2000 1.27:0.11

 

 

1 6010.09 1 5610.09

 

 

 

 

22

The value of critical stress intensity factor ch is reported in Figure 13. as a
function of the molar ratio of D2000 in the blend after 1 hour physical aging. It will
noted that there is a significant increase in KIC with increasing D2000 content. It
demonstrated an correlation between Krc and the amount of D2000 in the blend. This
results are the same as a single phase homogeneous epoxy/polycarbonate network, i.e.,
the fi'acture toughness of this blend system increases marketly with increasing PC content
in the blend [24]. The toughening effect of D2000 is more dramatically evidenced on
Figure 14. The curve shown in Figure 14 is observed for the unmodified and D2000
modified epoxy resin after 50 hours aging. In curve A and B, the load rises linearly with
strain up to maximum value where the crack propagates instantaneously causing a rapid
drop in the load. The corresponding fracture surface exhibits a smooth and relatively
featureless surface which can be evidence of brittle failure in Figures 16 and 17. The
load-displacement curve shown in Figure 14C is representative of blend containing 5% of
D2000. The load increases linearly up to a critical value and then the crack propagates
intermittently in a stable manner until the stored elastic energy in the sample decreases to
such an extent that crack arrest is allowed. Upon reloading the sample the process of
crack-growth is iterated up to the complete failure of the sample. Examination of the
corresponding fracture surface show clear evidence of ductile failure in Figure 18.

The critical stress intensity factor ch as a function of aging time is reported in
Figure 15. During physical aging, the value of Km for the sample A and sample B didn’t
change very much, but sample C containing 5%D2000 had a significant increase with

increasing aging time and failed in a ductile manner. This ductile failure is important

23

 

p—g ,—
C»: A
r I

p.
N
I

p—s
O
O

V I

S:
to
A
' r

 

 

FRACTURE mam, K,c (MPa 1111/2)

 

 

0.8 L..i-.rii..ii..i .......
0.00 0.01 0.02 0.03 0.04 0.05 0.06

MOLAR RATIO OF D2000

Figure 13. Critical stress intensity factor ch as a function
of molar ratio of D2000 ( after 1 hour aging)

24

 

0.20

0.15 —

0.10 —

LOAD (KN)
;>

0.05 -

I l l 1 l l l I I J

 

 

 

 

 

 

0.00 J l l L 1 l
0.0 0.2 0.4 0.6 0.8 1.0

DISPLACEMENT (mm)

Figure14. Load-displacement curve (after 50 hours aging)
(A) DGEBA + 100%D230; (B) DGEBA + 98%D230
+ 2%D2000; (C) DGEBA + 95%D230 + 5%D2000

25

 

E...
a

H
O
65

 

A.

1.4

 

 

 

 

 

 

FRACTURE mucrmrss. KL. (MPa mm)

0.8...tL..1...L...i...1.-4
O 20 40 60 80 100120

AGING TIME (Hours)

Figure 15. Critical stress intensity factor Km as a function of
aging time (0) DGEBA + 100%D230; (O) DGEBA + 98%
D230 + 2%D2000; ( El )DGEBA + 955D230 + 5%D2000

26

 

Figure 16. Fracture surface of DGEBA + 100%D230
aged for 50 hours ( x 20 )

27

 

Figure 17. Fracture surface of DGEBA + 98%D230 + 2%D2000
aged for 50 hours ( x 20 )

28

 

Figure 18. Fracture surface of DGEBA + 95%D230 + 5%D2000
aged for 50 hours ( x 20 )

29

because its contradicts chacteristics of physical aging in amorphous materials defined by
Struik [9] that during the aging material becomes more and more glass-like and less
rubber-like. It becomes stiffer and more brittle.

The considerable increase in toughness found in epoxy/diamine can be ascribed to
an increase D2000 in the epoxy glasses network. Toughness depends on the distance
between crosslinking point in network. Increasing the length of the chain will toughen
the cured epoxy. Because the D2000 molecular segments are longer and more flexible
than D230, so the D2000 as hardener play a role in increasing the fracture toughness. On
a molecular level, physical aging is thought to accompany motion of the polymer chains
into a tighter packing density without crystallization [25]. When comparing the three
samples, after 1 hour aging, the sample B and sample C have a higher fracture toughness
than sample A due to its D2000 content. When the samples aged at 700 C, both sample A
and sample B are in glassy state (below their Tg), the fracture toughness didn’t change
during aging. But for sample C containing 5%D2000, since it is above its Tg for D2000,
would generally have a higher molecular mobility than that of the glass phase, which is
below Tg. The long and flexible D2000 chains congregate together, this cause the ductile

failure at longer aging time.

CHAPTER 3 VISCOELASTIC RESPONSES

3. 1 Introduction

A distinctive feature of the mechanical behavior of polymer is the way in which
their response to an applied stress or strain depends upon the rate or time period of
loading. This dependence upon rate and time is in marked contrast to the behavior of
elastic solids such as metals and ceramics which, at least at low strains, obey Hooke’s law
and the stress is proportional to the strain and independent of loading rate. On the other
hand the mechanical behavior of viscous liquids is time dependent. It is possible to
represent their behavior at low rates of strain by Newton’s law whereby the stress is
proportional to the strain rate and independent of the strain. The behavior of most
polymers can be thought of as being somewhere between that of elastic solid and viscous
liquids. Polymers are therefore termed viscoelastic as they display aspects of both
viscous and elastic types of behavior. This leads to a specific relationship between stress
and strain. When the strain is held constant and the stress decays slowly with time
whereas in an elastic solid it would remain constant, this behavior of a viscoelastic
material is referred as stress relaxation. If a constant stress is applied to the specimen at
zero time and the strain increases rapidly at first, showing down over longer time periods,
this is called creep.

In glass forming polymers, when sample is cooled fiom above glass transition, the
polymer materials are not in thermodynamic equilibrium state at temperature below the

30

 

ii

\‘is

ac

Vii

ll;

SITE

En.

an:

1.90.1

4. .
511.111:

31

glass transition, the gradual rearrangement of molecular chains will occurs [26, 27].
Volume relaxation studies reveal that below Tg the molecular mobility is not quite zero.
There is a slow and gradual approach to equilibrium. During this volume evolution the
viscoelastic behaviors of polymer materials also change [6]. Physical aging is the
change in viscoelastic properties accompanying the volume relaxation. Example of
schematic graph is shown in Figurel9 and Figure 20, where the volume change between
point A and point B, the viscoelastic response (creep compliance) will shift horizontally
along the time axis.

The viscoelastic response can generally be categorized as linear and nonlinear
viscoelastic depending on the type of loading. The Boltzmann superposition principle is
a comer-stone of the linear viscoelasticity. It allows the state of stress or strain in a
viscoelastic body to be determined from knowledge of its previous deformation history.
The basic assumption is that the responses can be determined from the algebraic sum of
strains/stress due to each stress/strain step, i.e., e(t) = 2 Ad, D(t-ti) and e(t) = 2 Ac,
E(t-ti), where e(t) and o(t) are the overall strain and stress from each increment; D(t-ti)
and E(t-ti) are creep compliance and stress relaxation modulus [21].

According to the time-aging time superposition principle, it is possible to predict
the long term properties of polymeric materials using short term tests. Creep compliance
and stress relaxation studies can be performed on polymer materials to help understand
the dependence of stress and strain upon aging time. The viscoelastic response of the
epoxy/diamine networks of different crosslink densities with homogeneous length was

studied by Lee and McKenna [5]. In their study, the crosslink density increase with

32

 

VOLUME

 

 

 

 

TEMPERATURE

Figure 19. Schematic of volume-temperature plot show volume
change from point A to point B during aging

 

 

 

 

U.)
D
Z
<
:3 A B
E ————>
O
O
p.
a
U
LOG CREEP TIME

Figure 20. Schematic of the relative effects of aging on
viscoelastic response at point A and point B

33

decrease the length between junctions, it was found that when the crosslink density
increases, the glass transition temperature (Tg) increase, but the ACp at Tg didn’t change,
the shape of the viscoelastic spectrum was also found to be independent of crosslink
density for the epoxy networks, and the master curves for different crosslink densities
could be superimposed onto a single curve consistent with a time - aging time -
temperature - crosslink density superposition principle. Below described work in which
the epoxy/diamine networks of different crosslink densities with bimodal length, its
network is a random network crosslinked by random junction points. Analysis the data
from the creep compliance under small step stress and the small strain stress relaxation
tests in simple extension for different aging times and temperatures will show the

relationship between the viscoelstic responses and the crosslink density distribution in

bimodal length network.

34

3.2 Experimental Procedures
3.2.1. Materials and Sample Preparation

Two types of epoxy specimens were studied; one contained a single diamine
(DGEBA/D230) and the other contained a mixture of two diamines
(DGEBA/D230/D2000 or D400). Diglycidyl ether of bisphenol A (DGEBA, DER 332,

Dow Chemical, USA) was chosen as the model epoxy monomer in this work.

0 CH, 0
/ \ | / \
CHz-CH-CHz-O‘@_C@O-CHz-CH-CHZ
1
CH,

Figure 3. The molecular structure of DGEBA.

Jeffamine of different molecular weight was the curing agent. (Jeffamine is a
tradenarne of Texaco Chemical Company). Jeffamine D230, D400, and D2000 were
used. The D-series amines are difunctional amines linked by poly(propylene oxide)
(PPO). Where n is the average number of repeat units in the epoxy resin molecule. (The

number of n is taken from manufacture booklet).

CH3 n s 2.6 for D230
HZN— CH—CHZ ( O—CHZ —CH )n NH2 n s 5.6 for D400
CH3 n E 33.1 for D2000

Figure 4. The molecular structure of D230, D400 and D2000.

35
The DGEBA epoxide monomer was preheated at 600 C for 2 hours to melt any

crystals present before hand mixing with the amines until the mixture was clear. The
mole ratio of the DGEBA epoxide monomer and hydrogen contributed by D230, D400
and D2000 was that of the stoichiometric ratio. The mixture was degassed for 20 min at
room temperature to remove the bubbles, then cast into a mould with dimensions of 6.5 x
0.75 x 0.15 inch (16.51 x 1.91 x 0.38 cm) and cure at 1000 C for 24 hours. The sample
was then allowed to cool slowly in the oven to 23° C overnight. Specimens conforming
to ASTM D638 geometry were machined from the cast sheets, milled into dumb-bell
shaped samples. The edges and surfaces of the samples were abraded with 600 grit SiC
paper to keep the samples parallel sided thickness, then kept in a sealed desiccator until
the experiments were performed.

The following is the calculation used to convert number fraction to weight
fraction for DGEBA, D230, D400, and D2000. All the samples were cured with
stoichiometric amounts of reactants, i.e., [E] : [H] = 1 : 1 ( See Table 4 ).

DGEBA = ( 340 g / mol ) / 2 epoxy groups = 170 g / epoxy group (eg)
D230=(230g/mol)/4aminegroups= 57.5(g/eg)
D400=(400g/mol)/4aminegroups=100(g/eg)
D2000=(2000g/mol)/4aminegroups=500(g/eg)

Example calculation: W
(0.05)*(500g/eg)+(0.95)*(57.5g/eg)+ l70(g/eg)=249.6(g/eg)
Weight fraction of D230 = ( 54.6 g / eg ) / ( 249.6 g / eg ) = 0.2188

Weight fraction of D2000 = ( 25.0 g / eg ) / ( 249.6 g / eg ) = 0.1002

 

 

 

 

 

In

La)

lam

36
Weight fraction of DGEBA = ( 170 g / eg ) / ( 249.6 g / eg ) = 0.6810

Table 4. Samples for DGEBA/diamine networks

 

 

 

 

 

 

 

 

 

Sample Molar ratio“ of [E] : [Hip2303 [Hlpzooommom

A: DGEBA + 100%D230 1 : 1 :0

B: DGEBA + 99%D230 + 1%D2000 1 : 0.99 : 0.01
C: DGEBA + 98%D230 + 2%D2000 l : 0.98 : 0.02
D: DGEBA + 95%D230 + 5%D2000 1 : 0.95 : 0.05
E: DGEBA + 98%D230 + 2%D400 1 : 0.98 : 0.02
F: DGEBA + 95%D230 + 5%D400 l : 0.95 : 0.05
G: DGEBA + 90%D230 + 10%D400 1 : 0.90 : 0.10

 

 

*[E]: Epoxide monomer
[Hlpzzoi Hydrogen contributed by D230
[I-I]D400: Hydrogen contributed by D400
[Hlpzoooi Hydrogen contributed by D2000

3.2.2. Sample Characterization

The TA Instruments Differential Scanning Calorimeter (Modulated DSC) 2920
applies an enthalpy-change method to determine the difference in energy flow into a
material as a function of temperature. These measurements are all taken in relationship to
a reference material under a controlled temperature program. The glass transition

temperature is where an amorphous solid becomes rubbery. The glass transition is

 

37

accompanied by a change in heat flow of the sample and therefore will be indicated on
the DSC curve.

The glass transition temperature, Tg , and the changes in heat capacity ACp at Tg
for the testing samples were determined by the MDSC. The temperature scale was
calibrated with the melting transition of indium. Temperature scans were performed at
5° C / min with modulated : 10 C every 60 seconds and was operated over a temperature
ranging from -60° C to +120° C. Tests were performed on 10 to 20 mg samples. The
heating scans were performed immediately after cooling samples which had been held at
1200 C for 30 min to erase the thermal history. The Tg was taken by the inflection point,
the point on the curve with the steepest slope, which is considered the midpoint of the

step transition from glassy to the liquid state.

3.2.3 Physical Aging Experiments

The aging behavior was probed using the uniaxial extension under creep
compliance and stress relaxation conditions. The mechanical tests were performed using
a computer-controlled servo-hydraulic testing machine (Instron model 1321) equipped
with an oven for temperature control. Measurements of the temperature between the top
and bottom of the samples showed that the gradient was less than 06° C. Oven stability
was better than 1 03° C during each experiment. The dumbbell-shaped specimens were
first annealed at 1020 C ( 20° C above Tg of DGEBA/D230 determined by the D. S. C.)
for 30 min to remove all previous aging, and then quickly placed in the testing machine

at the testing temperature (Tg - T = 15, 8, and 5° C) where the glass began to age.

38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E tc: loading time(sec)
E
m t,=9o 180 360 720
$5—
{-1
U)
Q
LL]
I—I
v—1
5

0 .

60 120 240 480
AGING TIME (min)
Figure 21. Schematic of stress history where all probes are of equal

magnitude

 

Succ
mil

deft

leng
W35
stre

rela

11151

U311

Gil

39

Successive deformations were applied at aging times, te , which approximately doubled
with each test, i.e. te = 60 min, 120 min, 240 min etc (see Figure 21). At each interval of
deformation, the ratio of the deformation duration time, t,, to aging time was 0.05. In the
creep compliance tests, the engineering stress applied to the samples were 1, 2.5, and 5
MP3 respectively. The strain was measured with an Instron extensometer attached to the
Spec imen. Because the specimens did not return to zero deformation as the applied stress
released, the residual strain was substracted from the total strain and the specimen gauge
1811 gth was corrected for each loading interval of the aging test. The creep compliance
was then calculated at e(t) / o, where e(t) is the corrected strain and o is the engineering
stress, determined from the original cross-sectional area of the specimen. In the stress
relaxation tests, the applied strain, a, in these tests was 0.1% and was measured with an
Instron extensometer. Successive deformations were applied at aging time, t,, which
approximately doubled with each test. At each internal of deformation, the ratio of
deforrnation duration time, ti, to aging time was 0.05. The stress, o(t), was measured

using a 20001b (900 kg) capacity load cell. Thus the stress relaxation modulus was E(t) =

e(t) / e: -

3.2.4. Data Analysis Method
The creep compliance curve was analysed using Kohlrausch-Williams-Watts
(KWW) type function [28,29]:

D(t)=D.{1+exp[(t/r>"1} <2)

 

 

sh

sup

W11.

‘tal

1111.

1151

40

where 2D0 is the zero-time compliance, t is a characteristic retardation time and the
exponent B characterize the shape parameter for the creep curve and the width of the
viscoelastic spectrum. To perform the superposition and a master curve, the value of Do
and [3 at various aging time and temperature must be same.
The stress relaxation curve at a given aging time was curve fitted with the KW
[28, 29] stretched exponential function:
E(t>=E.exp[-(t/r>“1 (3)
where E0 is the modulus at t = 0, t is a characteristic relaxation time and [3 describes the
shape of the relaxation curve and the width of the viscoelastic spectrum. To perform the
superposition and a master curve, the value of E0 and B at the various aging time and
temperature must be same.
The aging time shift factor a1c is defined in terms of the KW [28, 29] function as:
atc=T(tc)/T(tcr) (4)
where 1: ( t, ) is the value of 1: in equation (2, 3) at the aging time tc and T ( t") is its
value at the reference aging time.
The temperature shift factor a1 is defined in terms of the KWW [28, 29] function as:
aT=T(tc)/T(te) (5)
where r (te ) is the value of t in the equation (2, 3) at the aging temperature and 1: (tc ) is
its value at the reference temperature.
The aging process is conveniently characterized by the double-logarithmic shift
rate, [1, defined as (4):

|.1=dloga,,/dlogtc (6)

41

3.3 Results and Discussion
3.3.1 DSC Results

Table 5. DSC results for the DGEBA/diamine networks

 

 

 

 

 

 

 

 

 

Sample Tg (° C) ACp ( J / g/° C) Glass transition zone (° C)

DGEBA+100%D230 82.89 0.1208 10.30
DGEBA+99%D230+1%D2000 78.65 0.1325 13.45
DGEBA+98%D230+2%D2000 74.78 0.1343 13 .83
DGEBA+95%D230+5%D2000 65 .3 5 0.1370 19.23
DGEBA+98%D230+2%D400 82.50 0.1349 1 1.25
DGEBA+95%D230+5%D400 78.06 0.1360 1 1.52
DGEBA+90%D23 0+ 1 0%D400 75 .33 0. 1364 I 1 .56

 

 

 

 

In Table 5, the value of Tg and the change in heat capacity ACp at Tg as determined by
D. S. C. for all the epoxy networks were listed. One can see from the table that when
D400 or D2000 is added to D230, Tg decreased, the ACp at Tg increased by more than
10%. The glass transition zone, changed from rubber to glassy state, is broadened by
adding D2000, but it doesn’t change very much by adding D400. Since D2000 is long
chain diamine (compared to D230 and D400), when mixing D2000, the distance between
the crosslink point in the epoxy network is no longer same. The length between crosslink
junction networks are no longer homogeneous and the ACp increase during glass
transition with decreases Tg. From Figures 4-10., one can see that there is no phase

separation has occurred when mixing small amount of D400 and D2000, since there is

 

42

only one glass transition temperature for each specimen. It is important evidence that no
gross segregation occurs between these two diamine chains, otherwise one would detect
two distinct transitions. So the DGEBA/diamine networks are compatible and the
samples containing two diamines with a regularly alternating long and short diamine

chains are single-phase materials.

3.3.2 Creep Test Results
3.3.2.1 Boltzmann Superposition

The use of the Boltzmann superposition principle can be applied in the creep
compliance tests for all epoxy networks. In creep compliance tests, a stress of do is
applied at t = 0 and take off at t = ti (duration time). The strain due to loading, e], is given
by e, = do D(t) and that due to unloading is similarly e, = -do D(t - t,). The total strain
after time t ( > t, ), e(t) is given by e(t) = do D(t) - do D(t - ti). In this region e(t) is
decreasing and this process is known as recovery. If the recovered strain e3(t - t,) is
defined as the difference between the strain that would have occurred if the initial stress
had been maintained and the actual strain then e3(t - ti) = do D(t - t,), which is identical to
the creep strain expected for a stress of +do applied after a time t,. Therefore, if e, = e3(t
- ti) then the Boltzmann superposition applied and the test is in linear viscoelastic range.
If not, it is in nonlinear viscoelastic range. In this creep compliance tests, the e, at e3(t - ti)
for all tests. It proved that these creep compliance tests are in nonlinear viscoelastic

range. Figure 22. shows a example of these tests.

STRAIN

43

0.011

 

0.010 f
0.009
0.000 E ’ o
0.007 :- QA °’ ° ' ’°
0.000 E o D '
0.005

0.004 ’- ° ,1

 

0.003

 

0.002 ***** +~Leei
O 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

TIME (sec)

 

Figure 22. The response of DGEBA+100%D230 aged at 785° C for 24
hours to loading followed by unloading, illustrating the Boltzmann
superposition principle. (0) loading; (0) unloading; (A) extroplated
from loading curve

El]

111:

44
3.3.2.2 Aging Results

In Figures 23-25, it was shown the double-logarithmic plots of creep compliance
at the indicated aging times versus time for these epoxy networks at the 15° C below the
D. S. C. measured Tg of each sample. The value of the applied stress in these
experiments was 5 MPa. The KWW parameters for these data are tabulated in Table 6. It
is evident that creep compliance during this time period of the experiment increases with
sub Tg aging time, thus indicating an increase in the retardation times. This behavior
occurs due to the decrease in molecular mobility as free volume decreases during physical
aging. This reduced mobility causes molecular relaxations to become slower, thus
shifting the relaxation spectrum to longer times as the physical aging process proceeds
and the shorter time relaxations occur. Importantly, the values of Do and [3 do not vary
with aging time for any given epoxy networks. However, the values of the width of the
viscoelastic spectrum [3 and the ratardation time 1 decrease as D2000 increases. This
indicates that the D2000 content have a greater resistance to creep. Although time -
aging time superposition appears to be valid for these epoxy networks, time-crosslink
density superposition is not in this temperature range for these epoxy networks.

The above creep compliance tests were performed after 16 hours physical aging.
In Table 6 and Figure 26, it also showed that the aging time was 64 hours for
DGEBA+95%D230+5%D2000, the sample was different with the aging time for 16
hours, but the results were similar, it proved that the experiments were repeatable. The
experiment without intermittent stress was performed. The two curves were similar.

Therefore, the successive loading will not affect the results in small strain range.

45

 

 

 

 

A80
T .
53
a 6.0—
C
q...
x h-
; o o ' A ‘
o . [j I A ‘
E40- . D _ A ,
o 0 I A A
é a i E 3 ° ‘
' ° a ' 2 3 ‘
8 102’“ e i t
9..
a
O 2.0 . ......r . .......r r.r.....1.......i .
10"1 10° 101 102 103 104

TIME (SEC)

Figure 23. Creep compliance curves for DGEBA + 100%D230 quenched
from102° C (i.e. 20° C above Tg of DGEBA/0230) to 669° C and kept
at 66.9 1 03° C for a period of time. The applied engineering stress is
5 MPa; [3 is 0.2851 and Do is 1.3075 (x 1010 Pa"). The different curves
were measured at various aging time indicated: (0) 60 min; (0) 120
min; (I) 240 min; (A) 480 min; (A) 960 min

46

 

 

 

A15)-
"r" I
a .
D412 :-
Q )-
2: ’ A
- I
--i _
5|? 9 "' O . 0. A
.. o
m c
U L O o I
C o ’ A
6 — o 9 D 2
. o o 0 z
E o 6 E 2
O '- 0 . - A
o
0 t 9 9 g E A
9 i.
E i i ii. i
A A
U. 1 L1 114111 1 1 1111111 L 1 1 111111 1 1 1 11111] _L 1 1 11111

 

H00
""1

10° 101 102 103 10‘
TIME(SEC)

Figure 24. Creep compliance curves for DGEBA + 98%D230
+2%D2000 quenched from 102° 'C (i.e. 20° C above Tg of
DGEBA/D230) to 61.1° C and kept at 61.1 : 0.3° C for a period of
time. The applied engineering stress is 5 MPa; B is 0.2171 and D, is
1.6831 (x 10‘° Pa"). The different curves were measured at various
aging time indicated: (0) 60 min; (0) 120 min; (El) 240 min; (I) 480
min; (A) 960 min

47

 

 

 

A20
Tact
9‘16-
2 C
o, A‘
g12‘ 0"
V ’ .IA
3‘
8’ .Q:A
a
o .02‘
or ii ‘
1
fi 1 $51
g E
t.)

 

4T 1 1 1 111.11 1 L 1.11.11 1 r 1 111111 1 1 1111111 1 1 .11...
10'1 10° 101 102 10° 104
TIME (SEC)

Figure 25. Creep compliance curves for DGEBA+95%D230 +5%D2000
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 496° C
and kept at 49.6 : 0.3° C for a period of time. The applied engineering
stress is 5 MPa; B is 0.1769 and D. is 1.8827 ( x 10” Pa"). The different
curves were measured at various aging time indicated: (0) 60 min; ([1)
120 min; (II) 240 min; (A) 480 min; (A) 960 min

48

 

 

 

 

fir .
I . o
g - A
.. ‘2: s
E: 1 A
v-t ’ O
3.1 9 - A
E 1* °
A o

t A O
O A o
C.) A A 0
p. A 0 °
III-1 $ A 2 ° 0

0

g 4 1 11111111 A 1 1111111 1 1 llllLlL #1 1111111 1 1 111111

10'1 10° 10' 102 103 10‘

TIME (sac)

Figure 26. Creep compliance curves for DGEBA+95%D230+5%D2000
quenched from 1020 C (i.e. 200 C above Tg of DGEBA/D230) to 495° C
and kept at 49.5 3: 03° C for a period of time. The applied engineering
stress is 5 MPa. The different curves were measured at different stress
histories indicated: (0) without intermittent stress; (A) with intermittent
stress

49

Table 6. KWW curve fitting parameters for Tg-15° C; d is 5 MPa

 

 

Sample t (min) Do (x101U Pa") ‘t (s) B
DGEBA+100%D230 60 1 34 268.13 0.29
120 1.31 479.64 0.28
T* : 669° C 240 1.31 899.87 0.28
480 1.29 1591.01 0.28
960 1 27 2930.01 0.27
DGEBA+98%D230+2%02000 60 1.74 51.35 0.22
120 1.71 77.11 0.22
T“ :61.1° C 240 1.66 110.68 0.21
480 1.66 188.98 0.21
960 1.62 263.52 0.20
DGEBA+95%D230+5%02000 60 1.90 14.49 0.18
120 1.90 25.66 0.17
T“ : 49.6° C 240 1.87 36.44 0.17
480 1.86 52.72 0.17
960 1.87 84.48 0.17
DGEBA+95%D230+5%D2000" 60 2.13 18.83 0.18
120 2.09 26.54 0.17
T“ : 495° C 240 2.08 37.22 0.17
480 2.04 54.80 0.17
960 2.04 83.06 0.17
1920 2.02 123.31 0.16
3840 2.00 199.26 0.16
DGEBA+95%DZ30+5%02000*** 3840 1.90 211.09 0.17
DGEBA+98%D230+2%D400 60 1.48 107.58 0.27
120 1.47 240.55 0.28
T“ : 690° C 240 1.43 444.79 0.27
480 1.41 815.11 0.27
960 1.41 1512.51 0.27
DGEBA+90%D230+10%D400 60 1.49 332.16 0.26
120 1.46 573.45 0.26
T* : 60.3° C 240 1.45 1083.61 0.27
480 1.43 1870.44 0.26
960 1.41 3378.34 0.26

 

T* : aging temperature for each sample
** : different sample for longer aging time
*** : different sample without intermittent stress

50

In Figures 27-30, it was shown the double-logarithmic plots of creep compliance at
indicated aging time versus time for these epoxy networks, but the aging temperature is at
the 8° C below the D. S. C. measured Tg of each sample. The applied stress was 2.5
MPa. The KWW parameters for these datas are tabulated in Table 7. Again, it is
observed that the values of D0 and B do not vary with aging time for any given epoxy
networks. The time-aging time superposition appear to be valid for these epoxy
networks, but time-crosslink density superposition is not valid.

One also carried out experiment at the temperature closed to Tg ( Tg - T = 5° C)
and the applied stress is 1 MPa. The curves are plotted in Figures 31-33. The results of
KWW analysis are tabulated in Table 8. It is observed that the values of Do and B do not
vary with aging time for any given epoxy networks. In Figure 33, the creep curves are
plotted at increasing aging time for sample of DGEBA+95%D230+5%D2000 network at
5° C below the D. S. C. measured Tg. It is apparent from this curve that after
approximately 120 min of aging the creep curves no longer shift to longer time, i.e. aging
has ceased and equilibrium has been reached. It is indicated that the time dependent
creep compliance rises faster with a short aging time (i.e., has a higher creep rate). This
is a direct consequence of the increased molecular mobility with short aging time. Again,
time-aging time superposition was found to be valid, but time-crosslink density

superposition was not.

51

 

20
1‘ A
I
14 _ a 1
on
D- 00A
'-
00
81h o u A
A
E

fii
a A
388

4.:-
>
[I
>

g

 

 

2 1 1 1 11111] 1 1 111111l 1 1 111111! 1 1 1111111 L4 111
10"1 10° 101 102 103 104
TIME (SEC)

 

,CREEP COMPLIANCE (111010 Pa")

Figure 27. Creep compliance curves for DGEBA + 100%D23O quenched

fi'om 102° C (i.e. 20° C above Tg of DGEBA/D230) to 752° C and kept
at 75.2 -_|: 0.3° C for a period of time. The applied engineering stress is
2.5 MPa; B is 0.2508 and Do is 1.6986 ( x 10‘° Pa"). The different curves
were measured at various aging time indicated: (0) 60 min; (0) 120
min; (El) 240 min; (I) 480 min; (A) 960 min

52

 

 

 

 

:~ 30

I ..

d“; 23 - I A

S - A

O Q

317.- .9 A

a z .

fi 10 - g A

:1 i 4

g . 1 1

o a a

35 .9- 3% g

E 3? 1 11111111 1 1L11111l 1 1411111l 1 11111111 1 1111111

' 10‘1 10° 101 102 103 104

TIME (SEC)

Figure 28. Creep compliance curves for DGEBA+98%D23O +2%D2000
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 66.6° C
and kept at 66.6 : 0.3° C for a period of time. The applied engineering
stress is 2.5 MPa; B is 0.1968 and D0 is 1.5465 ( x 101° Pa"). The
different curves were measured at various aging time indicated: (0)
60 min; (0) 120 min; (Cl) 240 min; (I) 480 min; (A) 960 min

53

 

05
O

I I I‘T I I I I I IWITIIIITTIIIT'ITI'IIIIT

1%
03
m 9
DID.
DID

p..
\1
EIJID

I

I

till

I

 

 

1 1 1111ul 1 1 1111ul 1 1 11111d 1 1 L111”! 1 1 1111u
0"1 10° 101 102 103 10‘
TIME (SEC)

Figure 29. Creep compliance curves for DGEBA+95%D230+ 5%D2000
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 580° C
and kept at 58.0 : 0.3° C for a period of time. The applied engineering
stress is 2.5 MPa; B is 0.1583 and Do is 1.8983 (x 1010 Pa"). The
different curves were measured at various aging time indicated: (0)
60 min; (0) 120 min; ([3) 240 min; (I) 480 min; (A) 960 min

 

CREEP COMPLIANCE (x10lo Pa")

.403

54

 

 

 

 

{>121
a“: 1-
° 10? A
E I . ° '.
if", 8 L- o. D
" A
8 F 2 a '
3 ’ 9 . ' °
5 T 2 o g A
g " o g H a
o , . g g B a
% $.8lag
E
U 3 111111111 111.1111 111.111.11.1113411 11.1111
10"1 100 101 102 103 104
TIME (SEC)

Figure 30. Creep compliance curves for DGEBA+90%D230+10%D4OO
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 667° C
and kept at 66.7 1; 0.3° C for a period of time. The applied engineering
stress is 2.5 MPa; B is 0.2636 and D, is 1.7561 (x 10‘° Pa"). The
different curves were measured at various aging time indicated: (0) 60
min; (0) 120 min; (B) 240 min; (I) 480 min; (A) 960 min

55

 

 

 

 

T1021
“ 1-
D- : A00
2 _ .AAA
0 - DI 1‘ 0
s—i D A
N . o'l ‘ 0
V . D 2 0
C23 0 §
" 10'- ’ 1 °
: o 8 o
: O 3 °
_ g o o
E h :5 B B 8 '
O 0 o
o 1
Q_, L
EL]
133
g 100 4 1111111! 1 1 1111111 1 1 1111111 4 1 1111111 1 1 111111

10'1 10° 10' 102 103 104
TIME (SEC)

Figure 31. Creep compliance curves for DGEBA + 100%D230 quenched
from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 785° C and kept
at 78.5 1: 0.3° C for a period of time. The applied engineering stress is
1 MPa; B is 0.2099 and Do is 1.3472 ( x 1010 Pa“). The different
curves were measured at various aging time indicated: (0) 90 min; ([1)
180 min; (I) 360 min; (A) 720 min; (A) 1440 min; (0)2880 min

56

 

 

 

 

7103

I“ :

Q, 1

a 1-

O F A‘A 0°

3102? . 05.?) 0

L15 : 6 g o

O : g o

5 . g 3

:3 g g

E 1015” B 8 a S

8 36.9%

o. 1.

ES 1

g 100 1.1.1.111 1.1.11.1 . 1.1.11.1 1.11.1..1 1
10"1 10° 101 102 103 104

TIME (SEC)

Figure 32. Creep compliance curves for DGEBA+98%D230+2%D2000
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to
713° C and kept at 71.3 : 0.3° C for a period of time. The applied
engineering stress is 1 MPa; B is 0.1636 and D1, is 1.6736 ( x 1010 Pa").
The different curves were measured at various aging time indicated:
(0) 90 min; (0)180 min; (I) 360 min; (A) 720 min; (A) 1440 min; (0)
2880 min

57

 

 

 

 

:1" 103:
| .
C5 C
9.. .
a .
3 ‘9°
>4 102 :- AO
v : .6

1. DB
8 I 8’8

.. a B

r- a U a

D D

% 101.é—0I° D D
O
D h-
m .-
£13
a l
U 100 L 111L1111 1 1 L111111 1 1411111' J LUJUII J 1 111111

10" 10° 10' 102 103 104
TIME(SEC)

Figure 33. Creep compliance curves for DGEBA+95%D230+5%D2000
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to
608° C and kept at 60.8 3; 0.3° C for a period of time. The applied
engineering stress is 1 MPa; B is 0.1388 and D0 is 2.2504 ( x 1010 Pa").
The different curves were measured at various aging time indicated:
(0) 90 min; (Cl) 180 min; (I) 360 min; (A) 720 min; (A) 1440 min; (0)
2880 min

58

Table 7. KW curve fitting parameters for Tg - 8° C; o is 2.5MPa

 

 

Sample t (min) Do (x10"’ Par) 1: (s) B
DGEBA+100%D230 60 1 .67 26.43 0.26
120 1.66 34.19 0.25
T“ I 75.20 C 240 1.67 52.19 0.25
480 1.75 79.43 0.24
960 1.72 105.17 0.23
DGEBA+98%D230+2%D2000 60 1 .40 4.69 0.20
120 1.53 6.77 0.20
T" I 66.60 C 240 1.53 9.34 0.19
480 1.62 12.14 0.19
960 1.63 15.09 0.18
DGEBA+95%D230+5%D2000 60 1.81 0.56 0.15
120 1.93 0.89 0.16
T" I 58.00 C 240 1.89 0.94 0.15
480 1.89 1.12 0.15
960 1.94 1.24 0.15
DGEBA+90%D230+10%D400 60 1 .73 93 .42 0.25
120 1.78 157.86 0.26
T" : 67.80 C 240 1.73 243.82 0.26
480 1.75 439.01 0.26
960 1.76 698.38 0.26

 

T* : aging temperature for each sample

59

Table 8. KW curve fitting parameters for Tg - 5° C; o is 1 MPa

 

 

Sample t (min) D0 (x10lo Pa") 1: (s) B
DGEBA-1'1 00%D230 45 1.46 1.87 0.21
90 1.39 2.56 0.21
T* I 78.50 C 180 1.34 3.35 0.21
360 1.26 3.94 0.21
720 1.27 4.31 0.20
1440 1.34 5.08 0.19
DGEBA+98%D230+2%D2000 45 1.62 0.09 0.17
90 1.61 0.12 0.16
T“ I 71.30 C 180 1.64 0.14 0.16
360 1.66 0.16 0.16
720 1.74 0.18 0.15
1440 1.75 0.19 0.15
DGEBA+95%D230+5%D2000 45 2.02 0.08 0.14
90 2.16 0.10 0.14
T" 260.8OC 180 2.18 0.11 0.14
360 2.32 0.11 0.13
720 2.37 0.12 0.13
1440 2.42 0.12 0.13
DGEBA+90%D230+10%D400 45 2.22 1.75 0.21
90 2.15 3.79 0.21
T" I 67.80 C 180 2.21 3.87 0.20
360 2.32 5.25 0.21
720 2.15 6.18 0.19
1440 2.28 8.61 0.19

 

T“ : aging temperature for each sample

60

The time-temperature superposition principle was also investigated. Figures 34-
35 depict a series of creep compliance curve at a constant aging time (60 min) as a
function of temperature below Tg. A master curve can be obtained by simple horizontal
shifting of the curves along the time axis, the arrow points to the shifting direction. The
temperature shift factor, aT, can be obtained from equation 5.

In Figures 36-38, show the double logarithmic plot of a“, versus tc at different
values of Tg - T = 15, 8 and 5° C for these epoxy networks. There are two features of
interest in these figures. First, at each temperature range under the same applied stress,
the value of the shifi rate It decreases as the amount of D2000 increases. Secondly, at the
temperature approximately 5° C below Tg, these epoxy networks were able to age into
structural equilibrium, i.e. the value of atc become independent of aging time, where the
shift rate“ 11 ( the slope of the plot ) changes from a value near unity to virtually zero.
Again this corresponds to the point where aging has arrested and equilibrium has been

attained. This transition from aging to non - aging behavior is quite abrupt.

61

 

35
30 - A A
25 -
20 -
15 -

10* A o d3
. A OA

0

A o (a

5 1. A o °‘b
i 8 §o§o8<>8°§°9°°°°°

0

 

CREEP COMPLIANCE (1110‘0 Pa")

 

I 1111 l 1111 1 £111 l 111' I llll 1 ll

10" 10° 10I 102 103 10‘ 105

AGING TIME (ms)

Figure 34. Creep compliance curves for DGEBA + 98%D230 +
2%D2000 aging at variant temperature for 60min. The applied
engineering stress is 1 MPa. The curvatures of these curves were same,
the master curves resulting from a superposition by time shifi along the
axis, so the time - temperature superposition were applied. The
temperatures (° C): (A) 69.9; (0) 65.9; (D) 60.7 (the shifting reference
temperature)

62

 

 

 

 

50
L.
C" - D a
1m L
D— 40 ..
a 1-
S ; o ————> :1
>4
g t :1 c1
20 --
é __ c1 0
8 1 o o
c1 c1
_ I: o :1 o
E 10: D o °o;oc9°°o
L o 0 0 019
o $ g Goeoaogfldé
O l l LllllLL l _Llllllll _l_l lllllll l llllllLL A l lllllll L Llllll
10'1 10° 10' 102 1o3 10‘ 105

AGING TIME (Ins)

Figure 35. Creep compliance curves for DGEBA + 95%D230 +
5%D2000 aging at variant temperature for 60 min. The applied
engineering stress is] MPa. The curvatures of these curves were same,
the master curves resulting from a superposition by time shifi along the
axis, so the time-temperature superposition were applied. The
temperatures (° C): (D) 59.8; (0) 55.1; (A) 50.4 (the shifiing reference
temperature)

63

 

 

 

 

1.2
1.0 — o
b D
0.8 b O A
53 h D
an 0.6 - o A
.3 1 a
0.4 - A
B
0.2 -
0.0 1 1 1 1%141L 1 1 1_11111J 1 1 1 11111
- 10' 102 10’ 10‘

AGING TIME (min)

Figure 36. Double logarithmic plot of aging time shift factor a1,
versusaging time for all the sample at Tg - 15° C, the reference aging time
was chosen as 60 min for each sample. The applied stress is 5 MPa. (0)
DGEBA + 100°/11D230; (U) DGEBA + 98%D230 + 2%D2000; (A)
DGEBA + 95%D230 + 5%D2000

64

 

 

 

 

0.8
0.6 - °
1. D
3 O
G 7 CI
no 0.4 -
3 - A
~ 0 A
b A
0.2 —
P e
00 1 1 1 131111 1 1 1111111 1 1 111111
10l 102 103 10‘

AGING TIME (min)

Figure 37 . Double logarithmic plot of aging time shift factor a.. versus
aging time for all the sample at Tg - 8° C, the reference aging time was
chosen as 60 min for each sample. The applied stress is 2.5 MPa. (0)
DGEBA + 100%D230; (D) DGEBA + 98%D230 + 2%D2000; (A)
DGEBA + 95%D230 + 5%D2000

65

 

 

 

 

0.6
0.5 ~
I o
0.4 ~
G3 i o 0
w >
' o
3 0.21 o
' o
D A A
01 g A A
O , A
1
0.0 - --..‘fi~~1 - 4-4---1 A-
10‘ 10‘ 103 10‘

AGING TIME (min)

Figure 38. Double logarithmic plot of aging time shift factor a., versus
aging time for all the sample at Tg - 5° C, the reference aging time
was chosen as 60 min for each sample. The applied stress is 1 MPa.
(0) DGEBA + 100%D230; (Cl) DGEBA + 98%D230 + 2%D2000;
(A) DGEBA + 95%D230 + 5%D2000

66

3.3.3 Stress Relaxation Results
3.3.3.1 Boltzmann Superposition

It is possible to analyse stress relaxation in a similar way as using the Boltzmann
superposition principle in creep compliance tests. In this case it is necessary to define a
stress relaxation modulus E(t) which relates the time-dependent stress o(t) to the strain e
through the relationship o(t) = E(t) e. When a strain of eo is applied at time t = O and take
off at t = ti (duration time). The stress due to applied strain, 6,, is given by c, = e0 E(t)
and that due to releasing strain is similarly 0‘2 = -e() E(t - t,). The total stress after time t
( > t, ), o(t) is given by o(t) = eo E(t) - eo E(t - t,). In this region 0(t) is increasing and this
process is known as recovery. If the recovered stress 03 (t - t,) is defined as the
difference between the stress that would have occurred if the initial strain had been
maintained and the actual stress then is identical to the stress expected for a strain of eo
applied for a time ti. Therefore, if 0" = o3(t - t,), then the Boltzmann superposition
applied. The tests are in linear viscoelastic range. In this stress relaxation tests, all the
experimental datas obey this condition. Therefore, the stress relaxation tests are in linear

viscoelastic range. In Figure 39. show a example of these tests.

3.3.3.2 Aging Results
Figures 40-43 depict the family of stress ralaxation isotherms for the ralaxation
modulus, E(t), at Tg - T = 15° C, obtained for these epoxy networks at various aging

times, as indicated. The KWW parameters for these data are tabulated in Table 9. The

67

 

 

 

 

 

 

5 -
4
3
A D D D
a? 2 l m A A
2 A A
1 .
1 03 (t'ti)
Ow
. O
O
-1 r- 500 o
-2 -
- 0 A150 300 7450 2600 750 900 1050 1200 1350 1500

TIME (see)

Figure 39. The response of DGEBA + 98%D230 + 2%D2000 aged at
608° C for 4 hours to loading followed unloading, illustrating the
Boltzmann superposition principle. (U) loading; (A) unloading; (O)

extroplated from loading curve

 

68

 

 

 

 

4.5_
’1? :
953.833 8 8
V : 00:, q a 8 8 8 O
B ~ ' ‘3 g - a g 1.
533.0— 0 2 . A o
8 ’ 9 ' f: :3
2 :1 o
I o
52.3»- .°
g _, D I A 0
B11 1
o:
1.5 ' .1....1 11.1.1111 . 1.1.1.1 1.11.1.1 .1.
10‘1 10° 101 102 103 101
TIME (SEC)

Figure 40. Stress relaxation curves for DGEBA + 100%D230 quenched from
102° C (i.e. 20° C above Tg of DGEBA/D230) to 679° C and kept at 67.9 :1;
0.3° C for a period of time. The applied strain is 0.1%. The different curves
were measured at various aging time indicated: (0) 60 rrrin; (C1) 120 min;
(I) 240 min; (A) 480 min; (0) 960 nrin

69

 

 

 

 

4.0
’1?
On 0 o
830 9 2 o
_ 0 a I A 8 o o
m 0 0 a A
:3 _ o I A O
O D . A o
g __ . o I A O
Q . D - A o
g 20 ’— . D - A 0
Z ' . a I A 0
E . D I A
‘ o
0 :1
5:3
0:!
1.0 1 11111111 1 11111111 1 11111111 111111111 11111

10‘1 10° 101 102 103 104
TIME (SEC)

Figure 41. Stress relaxation curves for DGEBA + 98%D230 + 2%D2000
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 608° C
and kept at 60.8 : 0.3° C for a period of time. The applied strain is 0.1%.
The different curves were measured at various aging time indicated: (0) 60
min; ([1) 120 min; (I) 240 min; (A) 480 min; (0)960 min

70

 

 

 

 

3.5

2‘?

o 2.5 8

v 0

U) r a fig 3 a 9

D _ g 8

g . I 8

91.5 - 12 . 2

O a . O

2 " ' c1 2 0

Z ' 0 A o

E b . U. .4 Ao

g - o

m

D: ()5 1L .11....1 11.111111 .1 . 1....

10’1 10° 101 102 103 104

TIME (SEC)

Figure 42. Stress relaxation curves for DGEBA + 95%D230 + 5%D2000
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 512° C
and kept at 51.2 : 0.3° C for-a period of time. The applied strain is 0.1%.
The different curves were measured at various aging time indicated: (0) 60
min; ([1) 120 rrrin; (I) 240 min; (A) 480 min; (0) 960 nrin

71

 

4.0
A
D? AOA ‘3 0
V3 3 — o 0 I 0
{/3 ° 9 o I A 0
D O D I A 2 o
I-l . U .
:3 r c U I A 0
8 O U n A
2 D
O o
D A
E: n o
g b ° 0 I A o
L l 1 111111 1 l lllllll l llllllll l l l llllll 1 I [III

 

 

 

1.8
10"1 10° 101 102 1o3 104
TIME (SEC)

Figure 43. Stress relaxation curves for DGEBA + 90%D230 + 10%D400
quenched from 102° C (i.e. 20° C above Tg of DGEBA/D230) to 512° C
and kept at 51.2 _+_- O.3° C for a period of time. The applied strain is 0.1%.
The different curves were measured at various aging time indicated: (0) 60
min; (El) 120 min; (I) 240 min; (A) 480 min; (0)960 min

72

values of E0 and B do not vary with aging time for any given epoxy networks, these
relaxation curves can be shified along the time axis to form a single master curve. When
increasing the D2000 content, the width of the viscoelastic spectrum decreases and the
retardation spectrum also decrease. Although time-aging time superposition appears to
be valid for these epoxy networks, the time-crosslink density superposition is not in these
stress ralaxation tests.

The time-temperature superposition was also investigated. Figure 44 depicts a
series of stress relaxation curves at a constant aging time (480 min) as a function of
temperature below Tg. The master curve can be obtained by simple horizontal shifiing of
the curves along the time axis combined with small amount of vertical shifiing. The
arrow pointed to the shifting direction. The temperature shift factor, aT, can be obtained
from equation 5.

The double-logarithmic plot of aging time shift factor at, versus tc for these epoxy
networks at Tg - 15° C present in Figure 45, suggest that as the fraction of D2000 is
increased the rate of shifiing (the slope of the plot) decreases. As can be seen, there is no
significant difference between the responses in these two experiments. This demonstrates
that, in spite of the viscoelastic range, the response of the glass aging process has not
changed.

Figure 46 show log aT versus T - Tg at aging time 480 min for sample of
DGEBA+95%D230+5%D2000. The reference was chosen at a temperature
approximately 15° C below Tg. There are two regions of behavior. At lower value of T -

Tg there is a linear temperature dependence. For T - Tg = -10 to -15° C there is a rapid

73

 

35

A
8
of A A ABBOBDBQ’C‘bog
U 18 A D 0 Ub%
v A U %
A 0 Qb

cm A 0 ‘e
D A D Q
A 0.9 A c: m
:3 A 0 0A
8 A A
2 A A
.2. .1 —-— 1
F A A

01 4 LL11 1 1111 1 rtrl 1 till 1 1111 Lllll 1 LLJ

 

 

 

'10-1 10° 10' to2 10° 10‘ 105 10°

TIME (SEC)

Figure 44. Stress relaxation curves for DGEBA + 95%D230 + 5%D2000
quenched from 102° C to variant temperature for 480 min. The applied strain
is 0.2%. The curvatures of these curves were same, the master curves
resulting from a superposition by shifting the datas along the axis, so the time-
temperature superpositon were applied. The temperature (° C): (A) 55.2; (CI)
51.2; (0) 45.1 (the shifting reference temperature)

74

 

1.2

1.0 —

DO

0.8 _ 8

0.6 —-

Log ate

0.4 *-

 

 

 

00 1 111m111L 1 1 1111111 1 111111
. u

10I 102 103

AGING TIME (min)

Figure 45. Double logarithmic plot of aging time shift factor a... versus
aging time for Tg - 15° C, the reference aging time was chosen as 60
min for each sample. The applied strain is 0.1%. (O) DGEBA +
100%D230; (El) DGEBA + 98%D230 + 2%D2000; (A) DGEBA +
95%D230 + 5%D2000

10‘

75

 

 

 

 

2.0
:11;
-1.0 —
‘2'9-25 l ~2lo L —is 1 -i0 1

T—Tg(°C)

Figure 46. Log of temperature shifi factor a: versus temperature
difference T -Tg for DGEBA+95%D230+5%D2000 at aging time 480
min. For T -Tg = -10 to -15° C a; decreases rapidly; this is apparently a
transition region from linear dependence to a WLF type dependence on
temperature

76

decrease in shifi factor; this is apparently a transition region from the linear dependence
to a WLF [31] type dependence on temperature. This result is similar to the results

reported by Lee and McKenna [30] of a study on a sample of DGEBA+100%D230.

Table 9. KW curve fitting parameters for Tg - 15° C; a is 0.1%

 

 

Sample t (min) E(t) (GPa) r (s) B
DGEBA+100%D230 60 3.67 1346.04 0.34
120 3.68 2056.04 0.34
T“ : 67.9° C 240 3.77 4109.01 0.33
480 3.79 7644.05 0.34
960 3.80 13599.01 0.34
DGEBA+98%D230+2%D2000 60 3.43 347.01 0.23
120 3.37 683.44 0.24
T" : 60.80 C 240 3.27 1215.41 0.24
480 3.42 2139.61 0.24
960 3.56 3382.01 0.23
DGEBA+95%D230+5%D2000 60 2.91 l 18.04 0.21
120 2.82 227.38 0.21
T* : 51.2° C 240 2.86 329.88 0.21
480 2.89 545.09 0.21
960 2.89 857.62 0.21
DGEBA+90%D230+10%D400 6O 3 .52 1652.1 1 0.32
120 3.55 3272.31 0.31
T“ : 61.00 C 240 3.58 5338.61 0.32
480 3.66 1 1641.01 0.29
960 3.65 20570.01 0.30

 

T* : aging temperature for each sample

CHAPTER 4 CONCLUSIONS

The effect of crosslink density distribution on mechanical response of physically
aged epoxy glasses were investigated. The Differential Scanning Calorimeter (DSC)
results show that the glass transition is broadening with addition of D400 or D2000
content, in particular the glass transition temperature (Tg) decreases with increases of
D400 or D2000. But the epoxy networks are still a single phase system, and the value of
ACp at Tg increases in this random length network. These results are contradict with
previous study by Lee and McKenna [5] that the ACp at Tg no longer changes as
function of Tg in the homogeneous length network.

In fracture test, as expected, toughening is achieved for the DGEBA/D230/DZOOO
networks, it was found that the fracture toughness of this epoxy network increases
marketly with increasing D2000 content in this epoxy networks. The fracture toughness
also increases with longer aging time for network containing high fraction of longer
molecular weight diamine. This result is in contradiction with Struik’s [6] understanding
the ductile to brittle transition during physical aging. I believe, this is due to the high
mobility of D2000 fraction in this network for amorphous polymer. Therefore as the
network aged into equilibrium, the D2000 species congregate together, this causes the

ductile failure at longer aging time.

77

78

In viscoelastic response, the creep compliance curves and stress relaxation curves
at different aging time and aging temperature were able to be superimposed and form
master curves, thus demonstrating the applicability of the classical time - aging time;
time - temperature superposition principle to each these of networks. Although the time
- crosslink density superposition is not. Furthermore, it is possible to defrne a double
logarithmic aging rate, 11, which depends on the ratio of the bimodal molecular weight
distribution. The double-logarithmic shift rate 11 decreases as the D2000 content
increase. The aging process is slow down by containing the long chain D2000 which is
already in equilibrium state. As increasing the D2000 contents, the viscoelastic spectrum
is broadening, this is indicated by the width of the relaxation time [3 decreases at same
temperature range. This phenomenon is observed in both creep and stress relaxation

experiments.

10.

11.

12.

13.

14.

15.

16.

17.

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