FATIGUE BEHAVIOR IN HYGROTHERMALLY DEGRADED TOUGHENED … · Fatigue Behavior in Hygrothermally...

FATIGUE BEHAVIOR IN HYGROTHERMALLY DEGRADED TOUGHENED EPOXY ADHESIVES

by

Naresh Varma Datla

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Mechanical and Industrial Engineering University of Toronto

© Copyright by Naresh Varma Datla, 2011

ii

Fatigue Behavior in Hygrothermally Degraded Toughened Epoxy

Adhesives

Naresh Varma Datla

Doctor of Philosophy

Department of Mechanical and Industrial Engineering

University of Toronto

2011

Abstract

A method to measure the mixed-mode fatigue behavior of environmentally degraded

adhesive joints was developed. Firstly, the absorption and desorption of water in two different

rubber-toughened epoxy adhesives was measured gravimetrically. The water absorption in both

adhesives showed anomalous behavior that was fitted to a new “sequential dual Fickian” (SDF)

model. The water desorption in both adhesives was modelled accurately using Fick’s law, and

there was a significant difference in the amount of retained water after drying in the two

adhesives.

The effects of long-term aging were studied using open-faced specimens made with two

different rubber-toughened epoxy adhesives. The contrasting results illustrated the effects of

environmental degradation on the matrix and toughener. Furthermore, the differences in the

degradation behavior of both adhesives, combined with gravimetric and dynamic mechanical

thermal analysis (DMTA) results, were used to illustrate the role of retained water in degrading

the toughening mechanisms. The measured fatigue results invalidated the environmental index

(EI) hypothesis for fatigue behavior, at least for the relatively short aging times studied here.

Compared with aging under constant humidity, the fatigue performance of joints was found to be

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superior after aging in a cyclic salt-spray environment due to the lower water concentrations in

the adhesive.

The effects of test environment humidity and temperature on the fatigue behavior were

also studied using closed, un-aged specimens. Both individual and combined effects of

temperature and humidity on fatigue behavior were studied. In elevated temperature and

humidity environment, joint performance at higher crack growth rates was degraded solely due

to the effect of the increased temperature, whereas fatigue performance at low crack growth rates

degraded predominantly because of elevated moisture.

Finally, to generalise the techniques developed to automotive aluminum sheets, a

reinforced specimen was developed that avoids yielding of thin aluminum sheet adherends while

loading. Fatigue testing with these reinforced specimens revealed that the fatigue behavior was

sensitive to the loading phase angle and the orientation of rolling lines on the sheet. These

reinforced specimens were also used to study the effects of long-term aging and the effects of

test environment.

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Acknowledgments

First of all, I would like to express my sincere gratitude to my doctoral supervisors, Prof.

Jan K. Spelt and Prof. Marcello Papini, for providing the opportunity to pursue my doctoral

dissertation and for their continuous guidance and encouragement during this research. I am

fortunate to have had spend the past few years learning from them about science and life.

I would like to thank Dr. Allan Hull at Engineering Materials Research for patiently

helping me setting up and performing fatigue experiments. The fruitful discussion with him and

his valuable suggestions have helped my work.

I would also like to extend my gratitude to my committee members Prof. Chul B. Park,

Prof. F. Ben Amara, Prof. Craig A. Steeves for their valuable comments and suggestions.

I am grateful for the financial support from General Motors of Canada, Centres of

Excellence and Natural Sciences and Engineering Research Council. My special thanks to

researchers at General Motors Dr. Jessica Schroeder, Dr. Douglas Faulkner, Dr. Blair Carlson

and Dr. John Ulicny for providing technical information and valuable suggestions during the

progress meetings and regular communications.

I would like to thank my lab mates for always being helpful and creating an enjoyable

work place. My special thanks are to Amir Ameli and Shahrokh Azari for their collaboration in

setting up the experiments.

I am indebted to my parents, Rama Raju and Vijaya Lakshmi, and my brother, Suresh, for

their constant source of motivation and encouragement in fulfilling my aspirations. I dedicate

my thesis to my parents.

Most of all, I would like to thank my wife, Kanthi. Her endless support, love, and

happiness gave me the strength to successfully pursue my research. I owe my future success to

you.

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Table of Contents

Acknowledgments .......................................................................................................................... iv

Table of Contents ............................................................................................................................ v

List of Tables ................................................................................................................................. ix

List of Figures ............................................................................................................................... xii

List of Appendices ...................................................................................................................... xxii

Chapter 1 Introduction .................................................................................................................... 1

1.1 Background and motivation ................................................................................................ 1

1.2 Objectives ........................................................................................................................... 2

1.3 Overview of thesis .............................................................................................................. 2

Chapter 2 Modified DCB and CLS Specimens for Mixed-mode Fatigue Testing of

Adhesively Bonded Thin Sheets ................................................................................................ 6

2.1 Introduction .......................................................................................................................... 6

2.2 Experiments .......................................................................................................................... 7

2.2.1 Reinforced sheet specimen ........................................................................................ 7

2.2.2 Fatigue tests ............................................................................................................. 10

2.3 Results and discussion........................................................................................................ 12

2.3.1 Effect of reinforcing adhesive .................................................................................. 12

2.3.2 Effect of phase angle and sheet rolling-line orientation .......................................... 17

2.3.3 Effect of test environment ........................................................................................ 23

2.4 Conclusions ........................................................................................................................ 25

Appendix 2A Adhesive stresses for unequal adherends [7] .................................................... 26

Appendix 2B Comparison of G calculated using FE and analytical model ............................ 30

2.5 References .......................................................................................................................... 32

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Chapter 3 Hygrothermal properties of highly toughened epoxy adhesives .................................. 34

3.1 Introduction ........................................................................................................................ 34

3.2 Mathematics of diffusion models ....................................................................................... 35

3.2.1. Dual Fickian model ................................................................................................. 36

3.2.2 Langmuir model ....................................................................................................... 39

3.2.3 Fickian model in desorption ..................................................................................... 40

3.3 Experimental procedure ..................................................................................................... 41

3.4 Results and discussion ................................................................................................ 42

3.4.1 Moisture absorption ................................................................................................. 42

3.4.2 Moisture desorption ................................................................................................. 60

3.4.3 XPS analysis ............................................................................................................ 65

3.5 Conclusions ........................................................................................................................ 66

3.6 References .......................................................................................................................... 68

Chapter 4 The Effects of Test Temperature and Humidity on the Mixed-mode Fatigue

Behavior of a Toughened Adhesive Aluminum Joint .............................................................. 70

4.1 Introduction ........................................................................................................................ 70

4.2 Experiments ........................................................................................................................ 71

4.2.1 Specimen preparation ............................................................................................... 71

4.2.2. Fatigue tests ............................................................................................................ 72

4.3 Results and Discussion ....................................................................................................... 75

4.3.1. Effect of temperature .............................................................................................. 75

4.3.2 Effect of humidity level ........................................................................................... 87

4.3.3 Combined effect of higher temperature and humidity ............................................. 96

4.4 Conclusions ........................................................................................................................ 99

4.5 References ........................................................................................................................ 101

Chapter 5 Mixed-mode fatigue behavior of degraded toughened epoxy adhesive joints ........... 104

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5.1 Introduction ...................................................................................................................... 104

5.2 Experiments ...................................................................................................................... 105

5.2.1 Specimen preparation ............................................................................................. 105

5.2.2 Aging conditions .................................................................................................... 108

5.2.3 Gravimetric measurements .................................................................................... 109

5.2.4 Fatigue tests ........................................................................................................... 109

5.2.5 Measurement of residual adhesive thickness ......................................................... 110

5.3 Results and discussion...................................................................................................... 110

5.3.1 Moisture diffusion .................................................................................................. 110

5.3.2 Fresh open-faced specimens .................................................................................. 113

5.3.3 Aging of joints in constant humidity environments ............................................... 115

5.3.4 Aging of joints in cyclic environment ................................................................... 123

5.4 Conclusions ...................................................................................................................... 127

Appendix 5A Moisture diffusion ........................................................................................... 129

5.5 References ........................................................................................................................ 131

Chapter 6 Effects of aging on the fatigue behavior of two toughened epoxy adhesives ............ 133

6.1 Introduction ...................................................................................................................... 133

6.2 Experimental .................................................................................................................... 134

6.2.1 Open-faced specimen preparation .......................................................................... 134

6.2.2 Aging and test conditions ....................................................................................... 137

6.2.3 Fatigue testing procedures and environment ......................................................... 137

6.2.4 Adhesive rubber tougheners .................................................................................. 138

6.2.5 DMTA .................................................................................................................... 140

6.3 Results and Discussion ..................................................................................................... 140

6.3.1 Gravimetric analysis .............................................................................................. 140

6.3.2 DMTA .................................................................................................................... 142

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6.3.3 Fatigue behavior of joints with adhesive 1 ............................................................ 148

6.3.4 Fatigue behavior of joints with adhesive 2 ............................................................ 166

6.4 Conclusions ...................................................................................................................... 169

6.5 References ........................................................................................................................ 171

Chapter 7 Conclusions and Recommendations ........................................................................... 173

7.1 Conclusions ...................................................................................................................... 173

7.1.1 Fresh adhesive joints .............................................................................................. 173

7.1.2 Water diffusion in toughened epoxy adhesives ..................................................... 173

7.1.3 Effects of test environment .................................................................................... 174

7.1.4 Effects of long-term aging environments .............................................................. 175

7.2 Future work ...................................................................................................................... 177

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List of Tables

Chapter 2

Table 2. 1 Mechanical properties of adhesive and adherends at room temperature. ..................... 8

Table 2. 2 Strain energy release rate and phase angle calculated using finite element model for

laminate adherend and equivalent stiffness adherend specimens. A 600 N load

applied to both adherends for ADCB specimen with crack length of 60 mm. .......... 16

Table 2. 3 G and Ψ obtained from finite element model by changing E of reinforcing adhesive.

A 500 N load was applied to both adherends of the ADCB specimen with crack

length of 60 mm. Sheet thickness was 2 mm and other properties as per Table 2.1. 16

Table 2. 4 G and Ψ obtained from finite element model for different sheet thicknesses. A 500 N

load was applied to both adherends of the ADCB specimen with crack length of 60

mm. ............................................................................................................................ 16

Table 2. 5 Elemental composition (atomic %) of failure surface compared with bare pretreated

sheet and bulk adhesive using XPS analysis. ............................................................. 19

Table 2. 6 Average surface roughness, Ra, measured on the sheet side of the fracture surface

along and across the length of the specimen. Average and standard deviation of

readings from 3 different locations in the threshold region. ...................................... 20

Chapter 3

Table 3. 1 Mechanical and physical properties of adhesives 1 and 2 at room temperature as

supplied by the manufacturers. .................................................................................. 42

Table 3. 2 Different exposure conditions for adhesives 1 and 2 and saturated salt solutions used

to achieve different levels of RH. .............................................................................. 42

Table 3. 3 SDF model parameters obtained by curve fitting the experimental gravimetric results

at different combinations of temperature and RH for adhesive 1. M1∞ values obtained

x

from PDF model are also given. Each data point is given as an average of three

values obtained from the repetitions. SD shows the standard deviation. .................. 47

Table 3. 4 Langmuir model parameters obtained by curve fitting to the experimental gravimetric

results at different combinations of temperature and RH for adhesive system 1. Each

data point is given as an average of three values obtained from the repetitions. SD

shows the standard deviation. .................................................................................... 48

Table 3. 5 SDF model parameters obtained by curve fitting to the experimental gravimetric

results at different combinations of temperature and RH for adhesive 2. M1∞ values

obtained from PDF model are also given. Each data point is an average of three

values obtained from the repetitions. SD shows the standard deviation. .................. 51


results at different combinations of temperature and RH for adhesive 2. Each data

point is an average of three values obtained from the repetitions. SD shows the

standard deviation. ..................................................................................................... 51

Table 3. 7 Percentage of oxygen atoms associated with different chemical bonds with their

binding energy for fresh, saturated wet and dried samples of adhesives 1 and 2. Each

data point is an average of three repetitions. .............................................................. 66

Chapter 4

Table 4. 1 Temperature and humidity conditions used in fatigue experiments. Number of

thresholds reached and ADCB specimens tested. ...................................................... 73

Table 4. 2 Mechanical properties of adhesive at room temperature as provided by the

manufacturer and of adherends taken from ref. [17,18]............................................. 75

Chapter 5

Table 5. 1 Stages of the cyclic aging environment. Salt spray was applied in the ambient stage

four times for 30 s each. ........................................................................................... 107

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Table 5. 2 SDF model parameters of the adhesive for both humid environments studied. Each

data point is the average of three repetitions, where SD indicates the standard

deviation. .................................................................................................................. 107

Table 5. 3 SDF model parameters of the adhesive immersed in salt water and deionised water.

Each data point is the average of three repetitions, where SD indicates the standard

deviation. .................................................................................................................. 113

Table 5. 4 Moisture diffusion parameters of the adhesive used in the finite element model. Data

is from [17]. .............................................................................................................. 126

Table 5. 5 Moisture concentration (mass of water per unit mass of adhesive) profile at the

adherend-adhesive interface of the open-faced specimen exposed to the cyclic

environment. ............................................................................................................ 127

Chapter 6

Table 6. 1 SDF diffusion model parameters (Eqs. (1) and (2)) of the adhesives for the various

humid environments studied (data from [22]). Each data point is the average of three

repetitions, where SD indicates the standard deviation. .......................................... 136

Table 6. 2 Conditioning environments and the corresponding fractional water uptake (Mt), glass

transition temperature (Tg), and storage modulus at room temperature (ERT) of fresh,

wet, and dry samples of both adhesives. Percentage change in Tg and ERT values

from the fresh sample values of the corresponding adhesive were also included. .. 145

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List of Figures

Chapter 2

Figure 2. 1 Configuration of (a) ADCB and (b) CLS specimens (dimensions in mm, not to

scale). The reinforcing bar (A) was 12.7 mm thick AA6061-T6. The reinforcing

adhesive (B) was 0.4 mm thick, the pretreated sheet (C) was 2 mm thick, and the

primary adhesive (D) was 0.4 mm thick. The second adherend (E) was a 25.4 mm

thick AA6061-T6 bar for the ADCB, and a 12.7 mm thick AA6061-T6 bar for the

CLS specimens. Width of specimens was 19.05 mm. The clip gauge locations on

both geometries are shown. .......................................................................................... 9

Figure 2. 2 Cracked adhesive sandwich with both axial load and moment acting on adherends. 10

Figure 2. 3 Measured Gth for ADCB specimens made with either 2 mm reinforced sheet or 14.9

mm thick bar. Both sheet and bar were of P2-etched AA6061-T6. Three repetitions

in each case, with Gth for each specimen shown above the columns. ........................ 14

Figure 2. 4 Comparison of the measured fatigue crack growth with and without reinforcing

adhesive layer for the same specimens as Fig. 2.3. .................................................... 14

Figure 2. 5 (a) Typical mesh used for the finite element analysis of the reinforced specimen. (b)

Enlarged view of mesh in primary and reinforcing adhesive layer. (c) Enlarged view

of mesh at crack tip where collapsed quarter point singular elements were used. .... 15

Figure 2. 6 Gth values in RD environment for laminated ADCB (phase angle 13) and CLS

(phase angle 50) specimens. Sheet rolling lines either parallel to crack growth

direction (longitudinal) or perpendicular to it (transverse). Three repeats were done

in each case with the threshold values shown above the columns. ............................ 19

Figure 2. 7 Comparison of crack growth rates for laminated ADCB and CLS specimens having

different orientations of the rolling lines on the sheet. Each data series represents a

single specimen from the 3 that were tested. Arrows indicate thresholds and

maximum G reached during the tests. ........................................................................ 20

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Figure 2. 8 Failure surfaces of specimens in threshold region: (a) laminated ADCB-longitudinal

rolling lines, (b) laminated ADCB-transverse rolling lines, (c) laminated CLS-

longitudinal rolling lines, (d) laminated CLS-transverse rolling lines, and (e)

laminated ADCB tested in hot-wet environment with longitudinal rolling lines. In

each figure, A is the laminated adherend, B is the second adherend. Load shedding

occurred in region I to decrease the crack speed, while crack growth was accelerating

away from the threshold in region II. ......................................................................... 22

Figure 2. 9 Gth in different test environments for laminated ADCB specimens. ......................... 24

Figure 2. 10 Comparison of fatigue crack growth when tested in room temperature dry (RD) and

hot-wet environments. The bottom arrow indicates the threshold of a sample

specimen and the top arrow indicates the final Gmax reached. ................................... 24

Figure 2. 11 Beam-on-elastic-foundation model. ........................................................................ 29

Figure 2. 12 G calculated using FE model and analytical model for an ADCB specimen at

different crack lengths. A 600 N load was applied to both adherends of the ADCB

specimen as shown in Fig. 2.1(a). .............................................................................. 30

Figure 2. 13 G calculated using FE model and analytical model for a CLS specimen at different

crack lengths. A 9,450 N axial load was applied to both loading pins as shown in

Fig. 2.1(b). .................................................................................................................. 31

Chapter 3

Figure 3. 1 Schematic illustration of the sequential dual Fickian (SDF) model. .......................... 38

Figure 3. 2 Measured fractional mass uptake versus square root of time and the least-squares fits

based on the SDF, Langmuir and PDF models at three RH levels for adhesive 1 at

20°C. Each data point is an average of three repetitions. ......................................... 44


based on the SDF, Langmuir and PDF models at five RH levels for adhesive 1 at


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based on the SDF, Langmuir and PDF models at three RH levels for adhesive 1 at



based on the SDF, Langmuir and PDF models at 95% RH and three different

temperatures for adhesive 2. Each data point is an average of three repetitions. ..... 50

Figure 3. 6 Variation of first diffusion coefficient, D1 with temperature for adhesives 1 and 2.

At each temperature, D1 was taken as the average obtained from different RH

conditions. Linear fit to the Arrhenius equation (Eq. (18)) with the slope equal to –

Q/R. ............................................................................................................................ 53

Figure 3. 7 Variation of the first and second saturated fractional mass uptake values, M1∞ and

M2∞ with temperature at 95%, 82% and 43% RH for adhesive 1. The lines are least

square fits. Each data point is an average of three repetitions. ................................. 55

Figure 3. 8 Variation of the transition time with temperature at 95% RH for both adhesives.

Each data point is an average of three values obtained from the repetitions. The lines

show least square regressions between td and exp(1/T) and the slopes of the lines give

the values of Q/R. ....................................................................................................... 57

Figure 3. 10 Variation of β and γ probabilities with temperature at 82% RH for adhesive 1. Each

data point is an average of three values obtained from the repetitions. The lines show

least square regressions between the probabilities and exp(1/T). .............................. 59

Figure 3. 11 Variation of β and γ probabilities with RH at temperatures of 40°C and 60°C for

adhesive 1. Each data point is an average of three values obtained from the

repetitions. The lines are only to guide the trends. ................................................... 59

Figure 3. 12 Fractional retained mass during drying versus square root of time, fitted with the

simple Fickian model for adhesive 1 initially saturated at 20°C and different RH.

Each data point is an average of three repetitions. ..................................................... 61

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Figure 3. 13 Fractional retained mass during drying versus square root of time, fitted with

simple Fickian models for adhesive 1 initially saturated at 40°C and different RH.

Each data point is an average of three repetitions. ..................................................... 61

Figure 3. 14 Fractional retained mass during drying versus square root of time and fitted simple

Fickian models for adhesive 1 initially saturated at 60°C and different RH. Each data

point is an average of three repetitions. ..................................................................... 62

Figure 3. 15 Fractional retained mass profile during drying versus square root of time and fitted

simple Fickian model for adhesive 2 initially saturated at 60°C-95%RH. Each data

point is an average of three repetitions. ..................................................................... 62

Figure 3. 16 Variation of minimum fractional retained water, Mr with the temperature of

absorption condition at different RH levels for adhesive 1. Each data point is an

average of three repetitions. The linear least square fits show the general trends. ... 63

Figure 3. 17 Variation of minimum fractional retained water, Mr with the RH of the absorption

condition at different temperatures for adhesive 1. Each data point is an average of

three repetitions. The linear least square fits show the general trends. ..................... 64

Figure 3. 18 Variation of minimum fractional retained water, Mr with the ambient water

concentration achieved during different exposure conditions for adhesive 1. Each

data point is an average of three repetitions. The linear least squares fit shows the

general trend. .............................................................................................................. 64

Figure 3. 19 Variation of minimum fractional retained water during the desorption process with

the saturated fractional mass uptake, M∞ for adhesive 1. Each data point is an

average of three repetitions. The linear least square fit shows the general trend...... 65

Chapter 4

Figure 4. 1 Configuration of ADCB specimen (dimensions in mm, not to scale). Width of

specimen was 19 mm. The clip gauge mounting location is also shown. ................. 72

Figure 4. 2 Configuration of reinforced ADCB specimen (dimensions in mm, not to scale). The

reinforcing bar (A) and second adherend (E) were 12.7 mm and 25.4 mm thick

xvi

AA6061-T6 bars, respectively. The reinforcing adhesive (B) and primary adhesive

(D) were 0.4 mm thick, and the pretreated sheet (C) was 2 mm thick. Width of

specimen was 19 mm. The clip gauge mounting location is also shown. ................. 72

Figure 4. 4 Effect of temperature on fatigue crack growth behavior of P2-etch pretreated ADCB

joints. Two of three experimental results shown for each temperature. ................... 78

Figure 4. 5 Effect of temperature on the fatigue crack growth behavior of P2-etch pretreated

ADCB joints. Each line is a linear regression fit of all the data points lying on the

Paris law (linear) region at a temperature, as show in Fig. 4.4. ................................. 79

Figure 4. 6 Failure surfaces on the thinner adherend of joints tested under dry conditions at

temperatures of (a) 20ºC, (b) 40ºC, and (c) 80ºC. In cases where a single specimen

was used to reach two thresholds, both threshold regions are indicated. ................... 80

Figure 4. 7 Typical profiles of fracture surfaces measured across the specimen width on the

more highly-strained adherend at G values of: (a) 750 and (b) 147 J/m2 for specimens

tested at 80ºC. The corresponding residual adhesive thickness values are given in

legend. 0 µm on vertical axis corresponds to interface between highly-strained

adherend and adhesive. .............................................................................................. 82

Figure 4. 8 Thickness of the remaining adhesive on the more highly-strained adherend as a

function of applied Gmax. ............................................................................................ 83

Figure 4. 9 Multi-linear model used for the adhesive at both room temperature (tensile test) and

at 80ºC (elastic modulus and proportionality limit reduced by 50% of room

temperature values). ................................................................................................... 85

Figure 4. 10 Effect of G on the (a) plastic zone thickness, and (b) plastic zone size, both at room

temperature and at 80ºC obtained using FE model for ADCB specimen. ................. 86

Figure 4. 11 Effect of RH on Gth for P2-etch pretreated ADCB joints tested at 40ºC. Given

values are average Gth (error bars indicate ± standard deviation). Numbers above

each data point indicate the number of thresholds reached and the number of

xvii

specimens tested, respectively; these two numbers are different in cases where a

single specimen was used to reach two thresholds. ................................................... 89

Figure 4. 12 Effect of RH on the fatigue crack growth behavior of P2-etch pretreated ADCB

joints tested at 40ºC. Each data series is from a single specimen. ............................ 89

Figure 4. 13 Moisture concentration versus distance ahead of crack tip for exposure to 40ºC-

95%RH environment at different crack growth rates. Crack tip radius assumed as 1

µm. ............................................................................................................................. 90

Figure 4. 14 Magnified image of a crack opening viewed from the side of the specimen showing

reflection from condensed water at the interface. Crack tip is to the right of the

image. ......................................................................................................................... 90

Figure 4. 15 Failure surface of the joints tested at 40ºC and under RH levels of (a) 0%, (b) 43%,

(c) 95% and (d) 100%. On each failure surface the threshold region is indicated. ... 92

Figure 4. 16 Magnified image of the failure surface on the highly-strained adherend at threshold

region for P2-etch pretreated joints tested under RH levels of (a) 95% and (b) 100%.

.................................................................................................................................... 93

Figure 4. 17 Negative ToF-SIMS spectra of the bare P2-etched aluminum and failure surface in

the mass/charge (m/z) ranges of (a) 0-200 m/z, and (b) 200-400 m/z. The failure

surface was from the P2-etch pretreated joint tested at 40C-100% RH in the

threshold region on the thin adherend side. ............................................................... 95

Figure 4. 18 Effect of test environment on the Gth of ADCB joints made with P2-etch and CC

pretreatments. Number above each data point indicates the number of specimens

tested in each case, and error bars indicate the standard deviation in each case.

Each specimen was used to reach a single threshold. ................................................ 97

Figure 4. 19 Effect of test environment on fatigue crack growth behavior of ADCB joints made

with P2-etch and CC pretreatments. Each data series represent a single specimen. . 98

xviii

Figure 4. 20 Negative ToF-SIMS spectra of the failure surface between (a) 0-200 m/z, and (b)

200-400 m/z. The failure surface was from the CC pretreated joint tested at 40C-

100% RH in the threshold region on the thin adherend side. .................................... 99

Chapter 5

Figure 5. 1 Open-faced specimen used for aging. The arrows indicate the direction of moisture

diffusion into the primary adhesive layer. ............................................................... 107

Figure 5. 2 Configuration of open-faced reinforced ADCB specimen after being closed

(dimensions in mm, not to scale). The thickness of primary, secondary, and

reinforcing adhesive layers are 0.4, 0.25, and 0.4 mm, respectively, and the thickness

of the sheet is 2 mm. Width of the specimen was 19 mm. The location of the clip

gauge is also shown. The upper adherend is the open-faced adherend shown in Fig.

5.1. ............................................................................................................................ 108


based on SDF model (Appendix) when immersed in salt water and deionised water at

(a) room temperature and (b) 40ºC. Each data point is an average of three

repetitions. The standard deviation in each case was approximately 2%. .............. 112

Figure 5. 4 Measured Gth of fresh closed and open-faced joints tested in a room temperature and

dry air environment. The 3 test repetitions are shown in each case, with Gth for each

specimen shown above the columns. ....................................................................... 114

Figure 5. 5 The measured fatigue crack growth rate curves of unaged closed and unaged open-

faced joints tested in a room temperature and dry air environment. ........................ 115

Figure 5. 6 Fatigue threshold vs. aging time for specimens aged under 40ºC-95% RH and

60ºC-95% RH environments. Trend lines show the exponential regression lines fit to

the data. Numbers next to each data point indicate the number of thresholds reached

and the number of specimens tested, respectively; these two numbers are different

cases where a single specimen was used to reach two thresholds. Error bars represent

the range of the measurements. ................................................................................ 116

xix

Figure 5. 7 Repetitions of the measured fatigue crack growth rate curves of specimens aged for

60 days at 40°C–95% RH and 60°C–95% RH. Two specimens aged at each

condition. .................................................................................................................. 118

Figure 5. 8 Measured fatigue crack growth rate curves of specimens aged at (a) 40°C–95% RH

and (b) 60°C–95% RH. Aging time in days is given in the legend. ....................... 119

Figure 5. 9 Effect of aging temperature on the crack growth rate curves for specimens aged for

(a) 1 week, (b) 2 weeks, (c) 1 month, and (d) 2 months. Each line is the least-squares

fit to the linear Paris region of the crack growth curves shown in Fig. 5.8. ............ 121

Figure 5. 10 Fracture surfaces on the more highly-strained (reinforced) adherend for: (a) unaged

joint, (b) 2 weeks aged at 60ºC – 95% RH, and (c) 4 months aged at 60ºC – 95% RH.

.................................................................................................................................. 122

Figure 5. 11 Thickness of the residual adhesive on the fracture surface of the more highly-

strained adherend as a function of crack growth rate for a fresh joint and a joint aged

for four months at 60ºC – 95% RH. ......................................................................... 123

Figure 5. 12 Fatigue threshold versus aging time for open-faced specimens aged in the cyclic

environment. Numbers next to each data point indicate the number of thresholds

reached and the number of specimens tested, respectively; these two numbers are

different cases where a single specimen was used to reach two thresholds. The error

bars show ± 1 standard deviation. ............................................................................ 125

Figure 5. 13 Crack growth rates versus applied Gmax for specimens aged in the cyclic

environment. Three specimens at each aging condition. ........................................ 126

Chapter 6


diffusion into the primary adhesive layer. The adherend is the thinner one in the

ADCB (Fig. 6.2) and was therefore subject to greater bending strain during fracture

testing. ...................................................................................................................... 136

xx

Figure 6. 3 FESEM micrograph that shows the rubber particles dispersed in the epoxy matrix for

(a) adhesive 1, and (b) adhesive 2. Approximate size of rubber particles is 1 µm and

0.2 µm for adhesives 1 and 2, respectively. ............................................................. 139

Figure 6. 4 Illustration of the sequential dual Fickian (SDF) model for water absorption and the

simple Fickian model for water desorption. ............................................................. 142

Figure 6. 5 Dynamic storage modulus (a) and loss modulus (b) as a function of temperature for

adhesive 1 measured using DMTA. Samples of adhesive as-cured, and tested after 5

days exposure to the 60C-95%RH environment without being dried (“wet” state)

and after drying to remove absorbed, unbound water (“dry” state). ........................ 146

Figure 6. 7 Fatigue threshold as a function of square root of aging time for adhesive 1 specimens

aged at 95% and 43% RH at temperatures of (a) 40ºC and (b) 60ºC. Trend lines are

the least-square fits of Eq. (3) to the measured data. Numbers next to each data point

indicate the number of thresholds reached and the number of specimens tested,

respectively; these two numbers are different in cases where more than one threshold

was reached using a single specimen. Error bars represent the range of the

measurements. .......................................................................................................... 150

Figure 6. 8 Gth,∞ values in different aging environments and the Gth of fresh specimens. Average

threshold values are shown above the columns and the error bars represent ±1

standard deviation. ................................................................................................... 151

Figure 6. 9 Least-squares fits of Eq. (3) for the data of Fig. 6.7 at 95% RH. ............................. 151

Figure 6. 10 Measured fatigue crack growth rate curves for adhesive 1 specimens aged at: (a)

40°C – 43% RH, (b) 40°C – 95% RH, (c) 60°C – 43% RH, and (d) 60°C – 95% RH.

Aging times in days are given in the legend. ........................................................... 155

Figure 6. 11 Variation of crack growth rate curves with aging time for adhesive 1 specimens

aged at: (a) 40°C–43% RH, (b) 40°C–95% RH, (c) 60°C–43% RH, and (d) 60°C–

95% RH. Each line is the least-squares fit to the linear Paris region of the crack

growth curves shown in Fig. 6.10. Aging times in days are given in the legend. .. 157

xxi

Figure 6. 12 Effect of aging environment on the crack growth rate curves for adhesive 1

specimens aged for: (a) 7, (b) 21, (c) 45, (d) 90, (e) 150, and (f) 240 days. Each line

is the least-squares fit to the linear Paris region of the crack growth curves shown in

Fig. 6.10. .................................................................................................................. 160

Figure 6. 13 Fracture surfaces on the more highly-strained (reinforced) adherend for adhesive 1

specimens that were: (a) unaged, (b) aged for 21 days at 40ºC – 95% RH, and (c)

aged for 150 days at 40ºC – 95% RH. In each case, the fatigue region is to the left of

the arrow showing where Gth occurred. After reaching Gth, specimens were

fractured, except for (c) where the fatigue process was repeated. ........................... 161

Figure 6. 15 Differences in the crack growth rates for adhesive 1 with similar EIT values that

were aged at different RH at aging temperatures of (a) 40ºC and (b) 60ºC. EIT values

of specimens are given in the legend (multiplied by 106 g/g.s). Each line is the least-

squares fit to the linear Paris region of the crack growth curves shown in Fig. 6.10.

.................................................................................................................................. 165

Figure 6. 16 Fatigue threshold vs. aging time for adhesive 2 specimens aged at 60ºC and 95%

RH. Numbers next to each data point indicate the number of thresholds reached and

the number of specimens tested, respectively. Error bars represent the range of the

measurements. .......................................................................................................... 167

Figure 6. 17 Measured fatigue crack growth rate curves for adhesive 2 specimens aged at 60°C–

95% RH. Aging time is given in the legend. .......................................................... 167

xxii

List of Appendices

Chapter 2

Appendix 2A Adhesive stresses for unequal adherends [7] ........................................................ 26

Appendix 2B Comparison of G calculated using FE and analytical model ................................ 30

Chapter 5

Appendix 5A Moisture diffusion ................................................................................................ 129

1

Chapter 1 Introduction

1.1 Background and motivation

Adhesively bonded joints offer many benefits over traditional bolted, welded and riveted

joints by their ability to join dissimilar materials, high strength to weight ratios, and improved

stress distribution within the joint. These benefits have led to increasing use of adhesives in

widespread applications, especially in automotive industry.

Presently the use of adhesives joints in the automotive industry is limited to non-critical

structures, and rarely used for highly-loaded structures. This limitation is due to the uncertainty

regarding long-term reliability, particularly after exposure to hot, wet environments and cyclic

loading. The strength of adhesive joints usually decreases in humid and high temperature

environments with prolonged exposure time. Moreover, joint strength is much lower under

cyclic loads compared to monotonic loading. Therefore, an understanding of degradation

mechanisms and the ability to predict long-term fatigue behavior is crucial to the design of

reliable automotive joints.

The fatigue behavior of aged adhesive joints is usually studied using actual “closed”

specimens. The limitations of these specimens are they take a long time to degrade due to the

length of the diffusion paths, and the degradation is non-uniform across the joint area, being

greatest at the exposed edges. This non-uniform degradation makes it difficult to associate a loss

of joint strength with a particular level of degradation. Recent studies have overcome this

limitation using “open-faced” specimens in which the adhesive is applied to only one adherend,

subject to environmental aging, and then bonded to a second adherend to make the final fracture

specimen. This reduces the water diffusion path to the thickness of the adhesive layer over the

entire joint area, thus producing a relatively uniform state of moisture concentration and

degradation in a relatively short period of time. Though open-faced specimens have been used

for fracture studies, their applicability to study fatigue behavior has not been examined.

2

1.2 Objectives

The objectives for this PhD research were:

(a) Develop a method to measure the fatigue threshold and the crack growth rates of

environmentally degraded adhesive joints. The method should minimize the time required to

characterize adhesive systems and be general enough to be applicable to automotive structures.

(b) Identify and explain the mechanisms of environmental degradation in toughened

epoxy adhesive joints.

(c) Asses the applicability of the “environmental index” (EI), defined as the integral of

water concentration over time, as a means of characterizing an aging history.

1.3 Overview of thesis

Two different proprietary, commercial DGEBA-based heat-cured rubber-toughened

structural epoxy adhesives were studied in this research.

Firstly, a reinforced specimen that voids yielding of the thin aluminum sheet adherend

was developed to measure the crack growth rates and the fatigue threshold of adhesive joints.

These reinforced specimens facilitated the characterization of automotive joints that are usually

made of thin sheet adherends. These reinforced specimens were used to study the effects of

loading phase angle and hot-wet test environments on the fatigue behavior of adhesive 1. The

effect of the sheet rolling-line orientation was also investigated. All the fatigue tests for this

research were done on load frames located at Engineering Materials Research, Downsview, ON.

The results and conclusions of this study are given in Chapter 2. This chapter has been published

in the International Journal of Adhesion and Adhesives and was presented in a conference as:

N.V. Datla, M. Papini, J.A. Schroeder, J.K. Spelt, Modified DCB and CLS specimens for mixed-

mode fatigue testing of adhesively bonded thin sheets, International Journal of Adhesion and

Adhesives, 30 (2010) 439-447.

N.V. Datla, M. Papini and J.K. Spelt, Fatigue tests of reinforced sheet specimen: Effects of

reinforcing adhesive layer, 32nd Annual Meeting of The Adhesion Society, Savannah, GA, USA,

Feb. 2009.

3

In Chapter 3 describes the water absorption and desorption properties of adhesive 1 and

adhesive 2 measured over a wide range of temperature and relative humidity. The data were

fitted to a new diffusion model in which Fick’s law was assumed to act in two sequential stages,

each with its own diffusion coefficient and saturated water concentration. This “sequential dual

Fickian” (SDF) model and a Langmuir-type diffusion model are both able to model the

absorption behaviour. The dependence of the SDF model parameters on temperature and RH

was investigated in detail. The two adhesives were selected to establish the generality of the

SDF model and because they demonstrated different fatigue durability behavior. These tests

have been done in collaboration with another Ph.D. student (A. Ameli) and the chapter has been

published in the Journal of Adhesion as:

A. Ameli, N.V. Datla, M. Papini, and J.K. Spelt, Hygrothermal properties of highly toughened

epoxy, Journal of Adhesion, 86 (2010) 698-725.

Chapter 4 describes the effects of test environment humidity and temperature on the

fatigue threshold and crack growth behavior of P2-etched and commercial coil-coated (CC)

aluminum adhesive joints under mixed-mode loading. The experiments isolated the effects of

pretreatment, temperature and humidity on both the fatigue threshold and the crack growth rates.

Finally, the combined effects of elevated temperature and humidity in hot-wet tests were

explained from this understanding of the individual effects of temperature and humidity.

Adhesive 1 was used in this study. This chapter has been accepted for publication in

Engineering Fracture Mechanics and was presented in a conference as:

N.V. Datla, M. Papini, J. Ulchni, B. Carlson and J.K. Spelt, The effects of test temperature and

humidity on the mixed-mode fatigue behaviour of a toughened adhesive aluminum joint,

Engineering Fracture Mechanics, 76 (2011) 1125-1139.

N.V. Datla, M. Papini and J.K. Spelt, Effect of humidity and temperature on the fatigue

behaviour of a toughened epoxy adhesive, 33rd Annual Meeting of The Adhesion Society,

Daytona Beach, FL, USA, Feb. 2010.

4

Open-faced specimens that accelerate the aging process by decreasing the water diffusion

path have been used in the work described in Chapters 4 and 5 to study the long-term fatigue

behaviour of adhesive joints. Chapter 4 investigates the effect of the aging environment on the

mixed-mode fatigue behavior of adhesive joints with coil-coated sheet adherends and adhesive 1.

The experiments illustrated the effects of aging time and temperature on both the fatigue

threshold and the crack growth rates. The experiments also compared the durability of joints

aged in constant humidity and cyclic environments. This chapter has been published in the

International Journal of Adhesion and Adhesives as:

N.V. Datla, M. Papini, J. Ulchni, B. Carlson and J.K. Spelt, Mixed-mode fatigue behavior of

degraded toughened epoxy adhesive joints, International Journal of Adhesion and Adhesives,

Vol. 31, pp. 88-96, 2011.

In Chapter 5, aged open-faced ADCB specimens made with adhesive 1 and adhesive 2

were subject to cyclic loading under mixed-mode conditions. The degradation of the fatigue

thresholds and crack growth rates were quite different, and illustrated the effects of

environmental degradation of the matrix and toughener as a function of aging time, temperature,

and relative humidity (RH) on both the fatigue threshold and crack growth rates. Differences in

the water absorption properties and dynamical mechanical thermal analysis (DMTA) of the two

adhesives were used to explain the differences in the fatigue degradation behavior. The data was

used to evaluate whether a unique degradation parameter exists that can combine the effects of

both exposure time and water concentration. This chapter is being prepared as a journal

publication and has been presented in a conference as:

N.V. Datla, M. Papini and J.K. Spelt, Effects of aging on the fatigue behavior of two toughened

epoxy adhesives, in preparation.

N.V. Datla, M. Papini and J.K. Spelt, Fatigue behavior of degraded adhesive joints measured

using open-faced specimens, 34th Annual Meeting of The Adhesion Society, Savannah, GA,

USA, Feb. 2011.

5

Finally, Chapter 7 lists the major conclusions of the research and recommends future

work.

6

Chapter 2 Modified DCB and CLS Specimens for Mixed-mode Fatigue

Testing of Adhesively Bonded Thin Sheets

2.1 Introduction

Aluminum and steel sheet is usually pretreated to improve the strength and durability of

adhesive bonds. In cases where the pretreatment is applied continuously to large coils of sheet

material by, for example roll or bar coating, the pretreatment cannot be reliably reproduced on

thicker plate or bars. Consequently, realistic fracture and fatigue test specimens must be made of

relatively thin sheet. This can greatly limit the maximum loads and strain energy release rates

that can be applied to the joint before the thin sheets yield. However, it is frequently desirable to

be able to assess the fracture, fatigue and durability of the pretreatment over a wider range of

strain energy release rates. This can facilitate comparison with data for other pretreatments as

well as simulating the loading conditions in practical joints, such as those in automobile and

truck frames that can be made of laminates of several thin sheets or sheets and thicker structural

members. In addition, the generation of mixed-mode loading conditions during fracture and

fatigue testing of adhesive joints often requires an asymmetric double cantilever beam specimen.

In this case, the requirement to use coil-coated thin sheet as the primary bonding surface

necessitates the lamination of the sheet to a stiffening member.

To overcome these limitations on the testing of thin sheet, Jethwa et al. [1] created a

mode I fracture specimen by laminating a thin sheet to a bar using a reinforcing adhesive, but

they found it difficult to avoid cracking in the reinforcing adhesive. They attributed this to

higher shear and out-of-plane tensile stresses in the reinforcing adhesive. The specimen was

then modified successfully by capturing the edges of the sheet within two wedge-shaped grooves

machined into the raised sides of the reinforcing bar. The sheet was then inserted lengthwise

into the grooves over top of the reinforcing adhesive which filled the gap between the sheet and

the steel bar. Although this prevented crack growth in the reinforcing adhesive layer, the

specimen is cumbersome to manufacture. Furthermore, the paper did not consider the possible

effect of the additional compliance introduced by the presence of the reinforcing adhesive layer

on the calculation of the strain energy release rate, (GI and GII are the mode I and

7

mode II strain energy release rates, respectively) and the phase angle, . In

the present study, reinforcement was used to study the mixed-mode fatigue behavior of joints

made with a highly-toughened epoxy adhesive and aluminum sheet that had been commercially

coil coated. Crack growth rates and threshold strain energy release rates, Gth, were measured in

dry and humid environments at several phase angles. The effect of the sheet rolling-line

orientation was also investigated.

2.2 Experiments

2.2.1 Reinforced sheet specimen

Asymmetric double cantilever beam (ADCB) and CLS specimens were made using

single-part, heat-cured rubber toughened adhesive and 2 mm thick AA5754-O aluminum sheet

with a commercial coil-coated pretreatment. The sheets were stiffened by laminating them to

AA6061-T6 aluminum bars using a “reinforcing adhesive” as illustrated in Fig. 2.1. The rolling

lines on the sheet gave an average roughness, Ra, of 0.21 μm parallel to the lines and 0.39 μm in

the transverse direction, measured using an optical profilometer (NANOVEA ST400, Micro

Photonics Inc. CA, USA).

A crack under mixed-mode loading tends to follow a path of maximum mode I, bringing

it closer to the more highly strained adherend [2]. Hence, the mixed-mode fatigue behavior is

most sensitive to the pretreatment on the more highly-strained adherend, which in the present

situation was the reinforced pretreated sheet. The opposing adherend was a bar of AA6061-T6

aluminum with the P2-etch pretreatment consisting of an aqueous solution of ferric sulfate and

sulfuric acid as prescribed in ASTM D2651 [3]. Table 2.1 lists the mechanical properties of the

adhesive, sheet and reinforcing aluminum bar obtained from manufacturer.

During the validation stage, some ADCB specimens were also made with 2 mm thick

AA6061-T6 sheets having the P2-etch pretreatment rather than the coil-coated AA5754-O.

8

Table 2. 1 Mechanical properties of adhesive and adherends at room temperature.

Adhesive AA5754-O AA6061-T6

Young’s Modulus (GPa) 1.96 68.9 68.9

Poisson ratio 0.45 0.33 0.33

Yield stress (MPa) 40 165 255

Prior to bonding, the pretreated sheet was wrapped with tissue paper, clamped between

the two bar adherends, and the sandwich was milled to a uniform width. The pretreated sheet

was then gently wiped with acetone using a cheese cloth. One surface of the sheet was bonded

to the AA6061-T6 bar using the reinforcing adhesive to form a “laminated adherend”, the other

surface of the sheet was bonded to the other AA6061-T6 bar using the “primary adhesive” (Fig.

2.1). The same adhesive was used as both the primary and reinforcing adhesives. A bond-line

thickness of 0.4 mm was achieved by placing piano wires in both the primary and reinforcing

adhesive layer. Both the primary and the reinforcing adhesive layers were cured in a single

curing cycle, by placing the assembly in an oven at 180°C for 30 min, as prescribed by the

adhesive manufacturer. The assembly was clamped using large binder clips (25.4 mm wide by

50.8 mm long, from ACCO Brands) that were centred directly over the spacing wires in the

primary and the reinforcing adhesive to avoid uneven clamping. Furthermore, since both the

primary and reinforcing adhesive were the same and had the same thickness and cure profile, the

residual stress was balanced on both sides of the sheet, thereby preventing bending of the sheet

during cure.

9

(a) ADCB

(b) CLS

Figure 2. 1 Configuration of (a) ADCB and (b) CLS specimens (dimensions in mm, not to

scale). The reinforcing bar (A) was 12.7 mm thick AA6061-T6. The reinforcing adhesive (B)

was 0.4 mm thick, the pretreated sheet (C) was 2 mm thick, and the primary adhesive (D) was

0.4 mm thick. The second adherend (E) was a 25.4 mm thick AA6061-T6 bar for the ADCB, and

a 12.7 mm thick AA6061-T6 bar for the CLS specimens. Width of specimens was 19.05 mm.

The clip gauge locations on both geometries are shown.

To ensure crack propagation in the primary adhesive, a 10 μm thick aluminum foil was

folded and placed in the primary adhesive to act as a form of precrack. The precrack length, a,

10

for the CLS specimens was of 30 mm from the start of the joint overlap, while that for the ADCB

specimens was 50 mm from the loading pins.

Need for reinforcement

The maximum strain energy release rate, Gmax, that can be applied before yielding a

mode-I DCB specimen made of 2 mm thick sheets of AA5754-O was estimated using [4]:

33

2

3

33

2

3

22

2

2

22

2

2

11

2

1

11

2

1

222222 IE

M

hE

P

IE

M

hE

P

IE

M

hE

PG

(1)

where Pi and Mi are the normal force and the moment, respectively, per unit width acting on the

ith cross-sectional centroid at the crack tip. Ii is the second moment of area per unit width, Ei is

the modulus of elasticity, and hi is the beam thickness. The subscripts 1 and 2 refer to the

adherends and subscript 3 refers to the compound beam to the right of the crack tip as shown in

Fig. 2.2. Using the mechanical properties of the sheet (Table 2.1), in this case the sheet would

begin to yield at Gmax=136 J/m2 which was only 3% of the critical strain energy release rate, Gc,

obtained in a fracture test with the same adhesive [5]. This greatly limited the range of fatigue

crack growth rates that could be studied without yielding the sheet adherends, necessitating the

need for reinforcement.

Figure 2. 2 Cracked adhesive sandwich with both axial load and moment acting on adherends.

2.2.2 Fatigue tests

Fatigue testing was performed with a servo-hydraulic load frame under force control

using a sinusoidal waveform at a frequency of 20 Hz. A constant load ratio (ratio of minimum to

11

maximum load, Pmin/Pmax) of 0.1 was used. The specimens were enclosed in a chamber to

control both temperature and humidity. The dry air condition (11% - 15% relative humidity,

RH) was achieved by placing desiccant inside the chamber, and the humid condition (100% RH)

was maintained by circulating air over a water surface in a duct using a fan.

The manually-controlled, discrete-step load shedding method was used to reach Gth,

which was defined as a crack growth rate of 10-6

mm/cycle [6]. The crack was initiated from the

foil precrack by applying a Gmax higher than the expected threshold and a crack in the primary

adhesive layer was then grown about 2 mm before manual load shedding was started. In each

load shedding step, both Pmax and Pmin were reduced by 5% to maintain a constant load ratio after

a crack growth of at least 0.5 mm. After the threshold was reached, cycling was continued with

constant Pmax and Pmin in order to obtain the crack growth rate as a function the applied G.

Because the crack length increased while the loads were held constant, this produced

accelerating crack growth.

Crack length measurements

The crack length was monitored using both optical and specimen compliance methods.

Optical measurements were performed using a CCD camera mounted on a motorized linear

stage. A telescopic lens attached to the camera allowed a field of view of 2 mm. To obtain clear

photographs of the crack, the specimen cycling was stopped and held at the mean load for 15 s

every 9,000 cycles. The specimen compliance was obtained from the relationship between the

crack opening and the applied force during the unloading portion of the loading cycle. A clip

gauge (Model 3541, Epsilon Technology Corp., Jackson, WY, USA) recorded the normal

opening at the loading points in the ADCB specimen and the normal opening at the precrack end

of overlap in the CLS specimens (Fig. 2.1).

A polynomial relationship between the optically observed crack length and the specimen

compliance was established according to ASTM E647 [6]. The crack length inferred from this

relationship was used in subsequent calculations of crack growth rate and G based on the

continuous clip gauge compliance data.

Strain energy release rate calculations

12

A beam-on-elastic-foundation model for unequal adherends [7] was used to calculate G

and Ψ for both ADCB and CLS specimens as described in Appendix A. The laminated adherend

was modeled as an aluminum bar of the same width and equivalent bending stiffness, calculated

using simple composite beam theory. This analytical model differed by less than 6% from a

finite element model in the prediction of G, (Appendix B). The phase angles for the ADCB and

CLS specimens were 13° and 51°, respectively, calculated using the beam-on-elastic-foundation

model [7]. Over the range of crack lengths and applied loads used in the experiments, there was

a negligible change in the phase angle for both specimen geometries as a crack grew; i.e.

increased by only 2° and 1° for ADCB and CLS specimens, respectively.

2.3 Results and discussion

2.3.1 Effect of reinforcing adhesive

The fatigue behavior of an ADCB specimen with a laminated adherend (Fig. 2.1(a)) was

compared with an equally stiff monolithic ADCB specimen; i.e. the laminated adherend in Fig.

2.1(a) was replaced with a monolithic AA6061-T6 aluminium bar having the same bending

stiffness, which was achieved by adjusting the bar thickness to 14.9 mm [8]. Since the adherend

stiffnesses of both specimens were nearly same, the phase angles were also very similar,

differing by less than 1°. Since it was not possible to apply the sheet coil-coated pretreatment on

the thick adherend, the P2-etch pretreatment was used on both the solid bar and on the 2 mm

thick AA6061-T6 sheet for this validation study.

Figure 2.3 shows that both the monolithic and the laminated specimen geometries had

essentially the same fatigue thresholds in a room temperature dry air (RD) environment; average

values of Gth were 157 and 165 J/m2, respectively (Gth defined as Gmax at threshold). Similarly,

Fig. 2.4 shows that the fatigue crack growth behaviour over a wide range of crack speeds was

indistinguishable between the reinforced specimens (average slope m=3.89±0.34 standard

deviation based on 3 specimens) or the monolithic ones (m=3.73±0.18). These differences in Gth

and crack growth rate between laminate and monolithic specimens were insignificant at the 95%

confidence level using the t-test.

A two-dimensional finite element analysis was used to examine the change in the stress

state at the crack tip due to the compliant reinforcing adhesive layer in the laminated and

13

monolithic specimen geometries described above. The two specimen geometries were modelled

using a total of 7158 8-node PLANE183 elements (ANSYS 12.0, Canonsburg, PA, USA).

Further refinement of the mesh did not change the calculated G by more than 0.1%, which

ensured that the results were independent of the mesh. The crack tip was assumed to be in the

middle of the primary adhesive layer and was modelled using collapsed quarter-point singular

elements (Fig. 2.5). The material properties of Table 2.1 were used for the model, and the G was

calculated using virtual crack extension method [9]. To calculate the phase angle, mixed-mode

stress intensity factors (SIF) were calculated using the displacement extrapolation method (using

KCALC in ANSYS). The G and the local phase angle were calculated at the crack tip under

loading conditions that produced a G close to the threshold value reached in the experiments.

The results shown in Table 2.2 confirmed that only a very small decrease in the local phase angle

was observed in the laminated adherend specimen. Similarly, the calculated G was essentially

unchanged by the presence of the reinforcing adhesive. It was thus concluded that the effect of

the compliant reinforcing adhesive layer on the stress state at the crack tip in the primary

adhesive was negligible. Therefore, the fatigue crack growth measured as a function of the strain

energy release rate and phase angle in a reinforced thin-sheet specimen is indeed a characteristic

of the sheet-adhesive system, being unaffected by the presence of the reinforcing adhesive and

adherend.

These results were generalized for reinforcing adhesives of different stiffness and for

sheets of various thickness using the above finite element model. Table 2.3 shows that the effect

of reinforcing adhesive tensile modulus, E, is small; e.g. decreasing E by a factor of 4, increased

G by only 6%. Similarly, decreasing the sheet thickness from 2 mm to 0.5 mm, changed G by

less than 1%. Therefore, the use of a laminated adherend to test thin sheet is applicable to a wide

range of sheet thicknesses and reinforcing adhesives.

14

Figure 2. 3 Measured Gth for ADCB specimens made with either 2 mm reinforced sheet or 14.9

mm thick bar. Both sheet and bar were of P2-etched AA6061-T6. Three repetitions in each

case, with Gth for each specimen shown above the columns.

Figure 2. 4 Comparison of the measured fatigue crack growth with and without reinforcing

adhesive layer for the same specimens as Fig. 2.3.

152 150160 155

184167

0

40

80

120

160

200

Reinforced sheet Bar adherend

Gth

, J/m

2

-8

-7

-6

-5

-4

-3

-2

2 2.2 2.4 2.6 2.8 3

Lo

g(d

a/d

N),

mm

/cycle

Log(Gmax), J/m2

Bar1

Bar2

Bar3

Sheet1

Sheet2

Sheet3

15

(a) (b)

(c)

Figure 2. 5 (a) Typical mesh used for the finite element analysis of the reinforced specimen. (b)

Enlarged view of mesh in primary and reinforcing adhesive layer. (c) Enlarged view of mesh at

crack tip where collapsed quarter point singular elements were used.

16

Table 2. 2 Strain energy release rate and phase angle calculated using finite element model for

laminate adherend and equivalent stiffness adherend specimens. A 600 N load applied to both

adherends for ADCB specimen with crack length of 60 mm.

Specimen Calculated

G (J/m2)

Phase angle

Ψ(°)

Laminate adherend 158 13.0

Equivalent stiffness adherend 158 13.3

Table 2. 3 G and Ψ obtained from finite element model by changing E of reinforcing adhesive.

A 500 N load was applied to both adherends of the ADCB specimen with crack length of 60 mm.

Sheet thickness was 2 mm and other properties as per Table 2.1.

Reinforcing adhesive

E (GPa) G (J/m

2) Ψ (°)

0.5 143.6 13.2

1.0 138.7 13.1

1.96 135.7 13.1

4.0 133.6 13.1

Table 2. 4 G and Ψ obtained from finite element model for different sheet thicknesses. A 500 N

load was applied to both adherends of the ADCB specimen with crack length of 60 mm.

Sheet thickness (mm) G (J/m2) Ψ (°)

0.5 136.8 13.0

1.0 136.1 13.0

2.0 135.7 13.1

4.0 136.8 13.5

17

2.3.2 Effect of phase angle and sheet rolling-line orientation

The laminated ADCB and CLS specimens (Fig. 2.1) prepared with the coil-coated

AA5754-O were bonded with the rolling lines oriented both along the length of the specimen

(longitudinal) and across the specimen (transverse). Figures 2.6 and 2.7 show Gth and the crack

growth rates of both specimens tested in the RD environment. For the sake of clarity, Fig. 2.7

shows only one test for each case. The Gth measured with the ADCB specimen was independent

of the rolling line orientation (t-test, 95% confidence level). The crack paths in these specimens

were cohesive, but close to the interface of the adhesive and coil-coated sheet (Figs. 2.8(a) and

2.8(b)). This visual observation was confirmed using x-ray photoelectron spectroscopy (XPS)

over a 400×400 µm scan area. Table 2.5 shows that the composition of the failure surface on the

pretreated sheet near the threshold was similar to that of the bulk adhesive and quite distinct from

that of the bare pretreated sheet.

Figures 2.8(a) and 2.8(b) also illustrate that the thickness of the remaining adhesive on

the surface of the sheet increased consistently as the applied G and the crack speed increased

(moving to the right from the threshold in Fig. 2.8). This tendency of the fatigue crack to

propagate closer to the midplane with increasing G was also reported by Azari et al. [13]. It is

hypothesized that as the applied G increases, the size of the damage zone ahead of the crack tip

also increases, causing the crack path to deflect away from the interface.

In contrast to the ADCB results, Fig. 2.6 shows that the CLS specimens with transverse

rolling lines had a significantly higher Gth than those with longitudinal rolling lines (t-test at 95%

confidence level). It is hypothesized that this was due to the higher phase angle of CLS

specimens which drove the crack closer to the interface. This change in Gth was consistent with

the failure surfaces which were cohesive for the transverse rolling line CLS specimens (higher

Gth) and interfacial for the longitudinal rolling line CLS specimens (lower Gth) (Figs. 2.8(c) and

2.8(d)). This change in the crack path as a function of the rolling line direction was reflected in

surface roughness measurements shown in Table 2.6, obtained using an optical profilometer on

the sheet side of the failure surface in the threshold region, both along and across the length of

the specimen. Each measurement was taken for a scan length of 5 mm. In the CLS specimen

with longitudinal rolling lines, the Ra values were close to the bare sheet values, indicating that

the failure was interfacial. However, in the CLS specimens with transverse rolling lines, Ra was

18

similar along and across the lines, and was different from the surface roughness of the bare sheet,

indicating that the crack path was cohesive.

Therefore, it was concluded that the fatigue behavior was sensitive to the surface

roughness introduced by the rolling lines only at higher phase angles (CLS specimens), where

the crack tends to grow closer to the sheet. This may be similar to the dependence of fatigue

behavior on adherend surface roughness observed with tubular single lap joints loaded with a

high degree of mode II, which would also drive the crack to the interface [10, 11].

Figure 2.6 shows that for both the longitudinal and transverse rolling line specimens, Gth

increased with phase angle, which is consistent with the general trend observed in the literature,

for toughened epoxy adhesives [12, 13]. This trend of increasing toughness with increasing

phase angle was also observed in fracture tests [5]. Gth increased only marginally with phase

angle for the longitudinal rolling line specimens, whereas the increase was greater for the

transverse rolling line specimens. It appears as if the increase in Gth with increasing phase angle

observed with the longitudinal rolling line specimens was relatively small because of the change

in failure locus from cohesive in the ADCB specimens to interfacial in the CLS specimens. The

larger increase in Gth observed in transverse rolling line specimens was simply due to the failure

locus remaining cohesive in both ADCB and CLS specimens.

Figure 2.7 shows that the crack growth rates at a phase angle of 13° (ADCB) were

essentially the same for specimens with longitudinal lines (average slope m=2.75±0.04 standard

deviation, based on 3 specimens) or transverse rolling lines (m=2.60±0.10), where crack path

moved closer to midplane of adhesive layer at higher crack growth rates (Fig. 2.8(a) and 2.8(b)).

However, at a phase angle of 50° (CLS), where the crack path remained closer to interface at all

crack growth rates (Fig. 2.8(c) and 2.8(d)), the crack growth rates were significantly lower for

the transverse (m=2.04±0.19) than for the longitudinal rolling line specimens (m=2.92±0.19) (t-

test, 95% confidence interval). This was expected given the similar trend seen with Gth.

Overall, the crack speed decreased as the phase angle increased from 13° (ADCB) to 50°

(CLS) for both orientations of rolling lines. This is consistent with the increased Gth seen with

increasing phase angle. It is also consistent with the increase in critical strain energy release rate

of fracture with increasing phase angle that is typical of epoxy adhesives [4, 5]. This trend of

decreasing crack speed with phase angle agrees with previous studies with rubber toughened

19

epoxies [12, 14], but is opposite to that reported with adhesives like modified methacrylate ester

and mineral filled epoxies [15, 16].

Figure 2. 6 Gth values in RD environment for laminated ADCB (phase angle 13) and CLS

(phase angle 50) specimens. Sheet rolling lines either parallel to crack growth direction

(longitudinal) or perpendicular to it (transverse). Three repeats were done in each case with the

threshold values shown above the columns.

Table 2. 5 Elemental composition (atomic %) of failure surface compared with bare pretreated

sheet and bulk adhesive using XPS analysis.

Pretreated sheet Adhesive Failure surface

C 29 68 72

O 43 23 23

Si 19 5.2 1.2

Ca 0.04 0.44 0.13

128 135158

277

142 150

185

284

166 169199

286

0

40

80

120

160

200

240

280

320

ADCB-L ADCB-T CLS-L CLS-T

Longitudinal Transverse

Gth

, J/m

2

20

Table 2. 6 Average surface roughness, Ra, measured on the sheet side of the fracture surface

along and across the length of the specimen. Average and standard deviation of readings from 3

different locations in the threshold region.

Along rolling lines (µm) Across rolling lines (µm)

Bare sheet 0.21±0.07 0.39±0.02

CLS-Longitudinal fracture surface 0.22±0.03 0.34±0.01

CLS-Transverse fracture surface 0.36±0.05 0.40±0.05

Figure 2. 7 Comparison of crack growth rates for laminated ADCB and CLS specimens having

different orientations of the rolling lines on the sheet. Each data series represents a single

specimen from the 3 that were tested. Arrows indicate thresholds and maximum G reached

during the tests.

-7

-6

-5

-4

-3

2 2.25 2.5 2.75 3

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

ADCB-L

ADCB-T

CLS-L

CLS-T185 135

142 286 J/m2

800 J/m2

21

(a)

(b)

(c)

22

(d)

(e)

Figure 2. 8 Failure surfaces of specimens in threshold region: (a) laminated ADCB-longitudinal

rolling lines, (b) laminated ADCB-transverse rolling lines, (c) laminated CLS-longitudinal

rolling lines, (d) laminated CLS-transverse rolling lines, and (e) laminated ADCB tested in hot-

wet environment with longitudinal rolling lines. In each figure, A is the laminated adherend, B is

the second adherend. Load shedding occurred in region I to decrease the crack speed, while

crack growth was accelerating away from the threshold in region II.

23

2.3.3 Effect of test environment

Figures 2.9 and 2.10 show Gth and crack growth rates for the coil-coated AA5754-O sheet

in laminated ADCB specimens tested in the RD and the hot-wet (40°C and 100% RH) test

environments, respectively. Gth decreased significantly in the hot-wet environment compared to

the RD environment (RD: 145 J/m2, hot-wet: 57 J/m

2; t-test, 95% confidence), and the crack path

became completely interfacial in the threshold region of the hot-wet test (Fig. 2.8(e)), whereas it

was cohesive in the dry test (Fig. 2.8(a)). This is similar to the observations in [17-20] made at

high humidity or water immersion environments. The darker area in the threshold region of Fig.

2.8(e) was likely the result of aluminum oxidation.

It was also observed in the hot-wet tests that after reaching the threshold there was a

distinctive lag in the resumption of crack growth as G was progressively increased; i.e. crack

growth did not begin again until Gmax was well above Gth. Crack growth resumed when Gmax

reached approximately 150 J/m2 compared to an average Gth of 58 J/m

2. This effect was not seen

in the dry environment. There are several possible explanations for this local increase in the

Gmax required for the resumption of crack growth: 1. Water diffusion into the adhesive ahead of

the threshold crack tip might have increased its toughness [21, 22]. 2. Absorbed water would

also decrease the modulus of the adhesive near the crack tip and promote crack tip blunting [21,

22]. 3. The aluminum oxide deposits behind the crack tip may have prevented complete crack

closure, thereby decreasing the effective stress intensity range during a loading cycle and

retarding crack growth [23]. Once crack growth resumed from the threshold, crack growth rates

in the HW environment were initially higher than those tested in the RD environment (Fig. 2.10),

showing the influence of moisture on fatigue behavior [17-20]. However, at higher crack growth

rates both environments produced a similar fatigue behavior; this effect was also observed in

[17]. This may be an indication that moisture diffusion was slower than these rates of crack

propagation and hence could not degrade the adhesive bond ahead of the crack tip.

24

Figure 2. 9 Gth in different test environments for laminated ADCB specimens.

Figure 2. 10 Comparison of fatigue crack growth when tested in room temperature dry (RD) and

hot-wet environments. The bottom arrow indicates the threshold of a sample specimen and the

top arrow indicates the final Gmax reached.

128

37

142

56

166

78

0

50

100

150

200

Room temp. & dry air Hot-wet

Gth

, J/m

2

-7

-6

-5

-4

-3

-2

2 2.25 2.5 2.75 3

Lo

g(d

a/d

N),

mm

/cycle

Log (Gmax), J/m2

RD1

RD2

RD3

HW1

HW2

HW3

142 J/m2

995 J/m2

25

2.4 Conclusions

A reinforced sheet specimen was used to study the fatigue behavior of thin sheet

adherends without yielding. It was concluded that the additional compliance of the reinforcing

adhesive layer had an insignificant effect on the stress state at the crack tip, and thus the strain

energy release rate and phase angle of loading. Therefore, the laminated sheet specimen can be

used to measure fatigue behavior that is characteristic of the adhesive-sheet system, being

unaffected by the reinforcement. This is useful in the fatigue testing of metal sheets that have

been coil coated with pretreatments that cannot be applied reliably on thicker material.

Fatigue experiments were conducted with ADCB (phase angle 13) and CLS (phase

angle 50) specimens made with reinforced aluminum sheet that had been pretreated using a

commercial coil-coating process. It was found that the fatigue threshold was sensitive to the

orientation of the rolling lines on the sheet at higher phase angles, being increased significantly

when the rolling lines were perpendicular to the direction of crack growth on the CLS specimens

(transverse to the specimen length). The fatigue crack growth rates were very similar for all

specimens except the CLS specimens having the transverse rolling lines, where they were lower.

These observations were related to the increasing proximity of the crack path to the sheet

interface as the phase angle increased.

Fatigue testing of the coil-coated sheet in a hot-wet environment significantly reduced the

threshold compared to testing in room temperature dry air. The crack path in the hot-wet

environment became fully interfacial, whereas it was cohesive in the dry case.

26

Appendix 2A Adhesive stresses for unequal adherends [7]

Using the virtual crack closure technique [25], GI and GII were calculated from

(A.1)

(A.2)

where Ea and Ga are the elastic and shear modulus of the adhesive, respectively, and 2t is the

bondline thickness. The normal and shear stresses, σ and τ, in the adhesive layer are governed

by the linear differential equations

(A.3)

(A.4)

where D1 and D2 are the flexural rigidity of adherends 1 and 2, respectively, and x is the distance

from crack tip. K1, K2 and K3 are defined by

(A.5)

(A.6)

(A.7)

27

The general solutions to Eqs. (A.3) and (A.4) contain 7 and 6 constants, but if the bonded

overlap is long, adhesive stress are bounded for large x, and the stresses can be approximated as

(A.8)

(A.9)

The coefficients A1-A3 are expressed in terms of the loads acting at using boundary

conditions (A.10)-(A.12) at .

(A.10)

(A.11)

(A.12)

where F, M and V are axial force, moment and shear force acting on the centre of each adherend

cross-section, and subscripts 1 and 2 represent upper and lower adherends respectively as shown

in Fig. 2.11. For ADCB specimens the reaction loads acting at crack tip are straight forward to

calculate, however for CLS specimens they are calculated using beam theory [14]. The system

of equations determining the Ai’s can be written in the matrix form , where

(A.13)

(A.14)

(A.15)

28

(A.16)

(A.17)

(A.18)

(A.19)

(A.20)

(A.21)

(A.22)

(A.23)

(A.24)

with the solution

(A.25)

29

(A.26)

(A.27)

The coefficients B1-B3 are calculating using the coefficients A1-A3 (Eqs. (A.25)-(A.27)) in

the relation:

(A.28)

which gives

(A.29)

(A.30)

(A.31)

Figure 2. 11 Beam-on-elastic-foundation model.

30

Appendix 2B Comparison of G calculated using FE and analytical

model

To gain confidence in the beam-on-elastic-foundation model used in this paper for the

calculation of G (Appendix A), a comparison was made with a finite element (FE) model. The

FE model used in Section 2.3.1 was used for this study. Figures 2.12 and 2.13 show the G

calculated using both models as a function of crack length for ADCB and CLS specimens. The

maximum difference was 3% and 6% for ADCB and CLS specimens, respectively. This

difference is acceptable, give that the typical scatter in experimental data was close to 10%.

Figure 2. 12 G calculated using FE model and analytical model for an ADCB specimen at

different crack lengths. A 600 N load was applied to both adherends of the ADCB specimen as

shown in Fig. 2.1(a).

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140

G (

J/m

2)

Crack length, a (mm)

FE model

Analytical model

31

Figure 2. 13 G calculated using FE model and analytical model for a CLS specimen at different

crack lengths. A 9,450 N axial load was applied to both loading pins as shown in Fig. 2.1(b).

0

100

200

300

400

0 20 40 60 80 100

G(J

/m2)

Crack length, a (mm)

FE model

Analytical model

32

2.5 References

1. J.K. Jethwa, A.J. Kinloch, G. Wallington, A new test method for determining the

adhesive fracture energy when bonding thin or coated substrates, J. Mat. Sci. Lett., 14(3)

(1995) 155-157.

2. J.W. Hutchinson, Z. Suo, Mixed-mode cracking in layered materials, Adv. Appl. Mech.,

29 (1992) 63-191.

3. ASTM, Standard guide for preparation of metal surfaces for adhesive bonding, D2651

(2001).

4. G. Fernlund, J.K. Spelt, Failure load prediction: I. Analytical method, Int. J. Adhes.

Adhes., 11(4) (1991) 213-220.

5. S. Azari, M. Eskandarian, M. Papini, J.A. Schroeder, D.L. Faulkner, J.K. Spelt, Fracture

load predictions and measurements for toughened-epoxy adhesive joints, Eng. Frac.

Mech., 76(13) (2009) 2039-2055.

6. ASTM, Standard test method for measurement of fatigue crack growth rates, E647

(2000).

7. G. Fernlund, Analysis and fracture load predictions of structural adhesive joints, PhD

Thesis, University of Toronto, Toronto, Canada (1994).

8. Y. Wyser, C. Pelletier, J. Lange, Predicting and determining bending stiffness of thin

films and laminates, Package Tech. Sci., 14(3) (2001) 97-108.

9. D.M. Parks, A stiffness derivative finite element technique for determination of crack tip

stress intensity factors, Int. J. Fract., 10(4) (1974) 487-502.

10. K.J. Wook, L.D. Gil, Effects of surface roughness and bond thickness on the fatigue life

of adhesively bonded tubular single lap joints, J. Adhes. Sci. Tech., 14(8) (2000) 1085-

1102.

11. K.K. Soo, K.W. Tae, L.D. Gil, J.E. Jin, Optimal tubular adhesive-bonded lap joint of the

carbon fiber epoxy composite shaft, Compos. Struct., 21(3) (1992) 163-176.

12. K. Okubo; H. Yoshimitsu, T. Fujii, Static and fatigue crack propagation of toughened

epoxy adhesives under mixed mode loading, Trans. Jpn. Soc. Mech. Eng. A, 67(661)

(2001) 1514-1519.

13. S. Azari, M. Papini, J.A. Schroeder, J.K. Spelt, The effect of mode ratio and bond

interface on the fatigue behavior of a highly-toughened epoxy, Eng. Fract. Mech. (2009),

doi: 10.1016/j.engfracmech.2009.09.011.

14. X.X. Xu, A.D. Crocombe, P.A. Smith, Mixed-mode fatigue and fracture behaviour of

joints bonded with either filled or filled and toughened adhesive, Int. J. of Fatig., 17(4)

(1995) 279-286.

15. A. Pirondi, G. Nicoletto, Mixed mode I/II fatigue crack growth in adhesive joints, Eng.

Fract. Mech., 73(16) (2006) 2557-2568.

33

16. M. Dessureault, J.K. Spelt, Observations of fatigue crack initiation and propagation in an

epoxy adhesive, Int. J. Aadhes. Adhes., 17(3) (1997) 183-199.

17. A.J. Kinloch, M.S.J. Little, J.F. Watts, The role of the interphase in the environmental

failure of adhesive joints, Acta. Mater., 48 (2000) 4543-4553.

18. J. Zhang, Fatigue crack propagation behavior of underfill materials in microelectronic

packaging. Mater. Sci. Eng. A, 314 (2001) 194-200.

19. M.L. Abel, A.N.N. Adams, A.J. Kinloch, S.J. Shaw, J.F. Watts, The effects of surface

pretreatment on the cyclic-fatigue characteristics of bonded aluminium-alloy joints, Int. J.

Adhes. Adhes., 26 (2006) 50-61.

20. K.A. Lubke, L.M. Butkus, W.S. Johnson, Effect of environment on fracture toughness

and debond growth of aluminum/FM®73/boron-epoxy adhesively bonded joints, J.

Comp. Tech. Res., 23(1) (2001) 42-49.

21. J.W. Wylde, J.K. Spelt, Measurement of adhesive fracture properties as. environmental

degradation, Int. J. Adhes. Adhes., 18(4) (1998) 237-246.

22. A.K. Moidu, A.N. Sinclair, J.K. Spelt, Adhesive joint durability assessed using open-

faced peel system, J. Adhes., 65 (1998) 239-257.

23. S. Suresh, G.F. Zamiski, R.O. Ritchie, Oxide-induced crack closure: An explanation for

near-threshold corrosion fatigue crack growth behavior, Metall. Mater. Trans. A, 12(8)

(1981) 1435-1443.

24. E.F. Rybicki, M.F. Kanninen, A finite element calculation of stress intensity factors by a

modified crack closure integral, Eng. Fract. Mech., 9 (1977) 931-938.

34

Chapter 3 Hygrothermal properties of highly toughened epoxy adhesives

3.1 Introduction

It is widely known that the water ingress plays a significant role in the progressive

degradation of the mechanical properties and hence the durability of epoxy adhesives. Many of

the diffusion models that have been proposed to explain hygrothermal effects in epoxies fall into

two categories. One is defined by the assumption that water diffuses into the epoxy and resides

in the free volume of the material. The other assumes that absorbed water molecules couple

strongly with certain hydrophilic functional groups such as hydroxyls in the epoxy resin.

However, some researchers have shown that both physical and chemical mechanisms may occur

simultaneously [1-4].

The simplest diffusion model is Fick’s law, which assumes that there are no interactions

between the absorbed water molecules and the polymer chains. Simple Fickian behavior is

observed in epoxies well above the glass transition temperature, Tg [5]. In many cases, however,

the simple Fickian model does not represent the absorption process and tends to overestimate

water concentration [1-3, 6-9]. Such cases are called non-Fickian or anomalous.

One class of diffusion models proposed for the anomalous behaviour of water diffusion

into epoxy adhesives is based on modifications to Fick’s law. For example, the dual Fickian

diffusion model assumes that the diffusion is Fickian, but occurs through two different

mechanisms acting in parallel with different diffusion properties [8-10]. The dual Fickian model

is hence the superposition of two single Fickian models. Fick’s law has also been generalized by

introducing time-varying diffusion coefficients [1,7] or time-varying boundary conditions [1,2].

In these models, the diffusion coefficient or boundary condition is assumed to take the form of a

Prony series which requires finding multiple coefficients and corresponding retardation times.

These models introduce many degrees of freedom to the problem and the solution can be

cumbersome and time-consuming.

Another class of anomalous diffusion models is based on a combination of physical

diffusion and chemical interactions. Several studies, partially reviewed in [11], have been made

to clarify the formation and existence of two different states of water molecules in epoxy, termed

35

free and bound. Carter and Kibler [12] suggested a Langmuir-type two-phase diffusion model

which assumes the existence of diffusing molecules in free and bound states. The Langmuir

model has been used with some success at times [1,6,12].

Unlike absorption, water desorption behavior is normally Fickian [8]. The absorbed

water in an epoxy cannot be completely removed in some cases and the existence of retained

water after drying at temperatures below Tg has been reported in the literature [13-16]. For

example, Moy and Karasz [16] investigated epoxy–water interaction by differential scanning

calorimetry (DSC), infrared spectroscopy (IR), nuclear magnetic resonance spectroscopy

(NMR), and water absorption/desorption gravimetric experiments using a tetraglycidyl 4 4

diaminodiphenyl methane/diaminodiphenylsulphone (TGDDM/DDS) resin system. They

observed a strong hysteresis related to the desorption process indicating retained amounts of

water that could only be removed by heating the epoxy to temperatures above 100°C. Zhou and

Lucas [14] showed that retained water after low-temperature desorption was related to the

amount of water molecules forming stronger bonds (i.e. multiple hydrogen bonds) with the

epoxy network.

The absorption and desorption of water in two different rubber-toughened epoxy

adhesives is measured gravimetrically over a relatively wide range of temperature and RH. The

data are fitted to a new diffusion model in which Fick’s law was assumed to act in two sequential

stages, each with its own diffusion coefficient and saturated water concentration. This

“sequential dual Fickian” (SDF) model and a Langmuir-type diffusion model are both able to

model the absorption behaviour. The dependence of the five SDF model parameters on

temperature and RH is investigated in detail. The two adhesives were selected to establish the

generality of the SDF model and because they demonstrated different fracture durability

behavior in a separate test program.

3.2 Mathematics of diffusion models

In this study, a newly developed type of dual Fickian model and a Langmuir-type model

were used to characterize the anomalous behaviour of water absorption in two rubber-toughened

epoxy adhesives, while a simple Fickian model was employed for the desorption modeling.

Based on the size and shape of the wafer samples and the experimental setup, the diffusion was

considered as one dimensional. The initial condition of absorption for both models was assumed

36

to be zero water concentration and the constant saturation concentration value was taken as the

boundary condition.

3.2.1. Dual Fickian model

In simple Fickian diffusion, it is assumed that the moisture flux is directly proportional to

the concentration gradient in a material. The one-dimensional differential equation of Fickian

diffusion, the boundary conditions and the initial condition for absorption to a plane sheet of

thickness 2h are given as follows:

0)0,(

),(

),(),(2

2

txC

CthxC

x

txCD

t

txC

(1)

where C(x,t) is the water concentration (% by mass) at any spatial coordinate x (m) and time

interval t (s), C∞ (%) is the saturated moisture concentration and D (m2/s) is the diffusion

coefficient. The solution to the partial differential equation in Eq. (1) is given by:

h

xn

h

tnD

nC

txC

n

n

2

)12(cos

4

)12(exp

12

)1(41

),(2

22

0

(2).

The fractional mass uptake, Mt (i.e. the total mass uptake of water at time t expressed as a

percentage of the initial mass of the sample) can be obtained by integrating Eq. (2) over the

spatial variable x:

2

22

022 4

)12(exp

)12(

181

h

tnD

nM

M

n

t

(3)

37

where M∞ is the saturated fractional mass uptake, i.e. the mass uptake at saturation expressed as a

percentage of the initial mass of the sample.

In the dual Fickian models present in the literature [8,9,17], two diffusion mechanisms

are considered to be working in parallel such that the fractional mass uptake increases

continuously until it reaches M∞. These models are called “parallel dual Fickian” (PDF). The

Langmuir-type model and the gravimetric results in this study however indicated that there was a

pseudo-equilibrium state at intermediate exposure times before reaching the final saturation

(Section 3.4). This has been modeled in the present work by assuming that the pseudo-

equilibrium corresponds to the completion of the first uptake mechanism and the start of the

second one. Based on this assumption, a new “sequential dual Fickian” (SDF) model was

developed in which the moisture concentration at any t and x is determined by:

22

222

0

12

221

0

2

)12(cos

4

)()12(exp

12

)1(41)(

2

)12(cos

4

)12(exp

12

)1(41),(

Ch

xn

h

ttnD

ntt

Ch

xn

h

tnD

ntxC

d

n

n

d

n

n

(4)

where C1∞ and C2∞ are the saturated concentrations of the first and second diffusion mechanisms

such that C1∞+C2∞=C∞, where C∞ is the total saturation concentration. D1 and D2 are the

diffusion coefficients of the first and second moisture uptake mechanisms, respectively. td is the

time at which the transition from the first diffusion mechanism to the second one occurs, and

φ(t) is the Heaviside step function defined as:

d

dd

tt

tttt

,1

,0)(

(5)

The Heaviside step function in the second part of the right hand side of Eq. (4) ensures

that the moisture concentration corresponding to the second mechanism is zero as long as the

exposure time is less than td. By integrating Eq. (4) over the spatial variable, the fractional mass

uptake, Mt for the SDF model at any time t is given by:

38

22

222

022

12

221

022

4

)()12(exp

)12(

181)(

4

)12(exp

)12(

181

Mh

ttnD

ntt

Mh

tnD

nM

d

n

d

n

t

(6)

where M1∞ and M2∞ correspond to the first and second uptakes, respectively and M1∞+M2∞=M∞

(Fig. 3.1). The fractional mass uptake at any time t, Mt was determined experimentally using

gravimetric measurements and its value is given by:

%100

i

itt

W

WWM

(7)

where Wi and Wt are the sample weights before any exposure and after an exposure time of t,

respectively. Thus the model has 5 parameters: D1, D2, C1∞, C2∞ and td. The present data were

used to identify the dependence of these parameters on temperature, T, and relative humidity,

RH, in order to make the model predictive for a range of environmental conditions.

Figure 3. 1 Schematic illustration of the sequential dual Fickian (SDF) model.

39

3.2.2 Langmuir model

Carter and Kibler proposed a Langmuir-type adsorption theory to model the anomalous

behaviour of moisture diffusion in polymers [12]. This model assumes the existence of diffusing

molecules in mobile and bound states, each with probabilities of interchanging their states.

Based on this model, for the one-dimensional case, the molecular number densities at exposure

time t and spatial coordinate x satisfy the coupled pair of equations:

t

n

t

n

x

nD bmm

L

2

2

(8)

bmb nnt

n

(9)

where DL is the diffusion coefficient, nm and nb represent the number of mobile and

bound water molecules per unit volume. γ and β are the probabilities per unit time (s-1

) that

mobile and bound molecules will change their respective states. Solving these equations with

the equivalent initial and boundary conditions as for the SDF model gives the number of

molecules at time t and position x. The total number of water molecules per unit volume in an

adhesive at time t, Nt is approximated by [6]:

for short exposure times: tN

Nt

2/3

4

(10)

for long exposure times: tt eN

N

1

(11)

where N∞ is the total number of water molecules per unit volume at saturation and κ is

defined as:

2

2

4h

DL

(12).

40

The total number of water molecules per unit volume at the pseudo-equilibrium state, Npe

may be obtained as [6]:

N

N pe

(13).

3.2.3 Fickian model in desorption

The desorption process was modeled using Fick’s law as:

CtxC

CthxC

x

txCD

t

txC

r

d

)0,(

),(

),(),(2

2

(14)

where Dd and Cr are the diffusion coefficient of the desorption process and the minimum

retained water concentration, respectively. The solution of this differential equation set for time t

and spatial coordinate x is:

h

xn

h

tnD

nCC

CtxC d

n

n

r

r

2

)12(cos

4

)12(exp

12

)1(4),(

2

22

0

(15).

The fractional retained mass of water in the adhesive sample in percentage at time t, ltM

can be obtained by integrating Eq. (15) over the spatial variable:

2

22

022 4

)12(exp

)12(

18

h

tnD

nMM

MM d

nr

rlt

(16)

where Mr is the minimum fractional retained water.

41

3.3 Experimental procedure

Two different proprietary, commercial DGEBA-based heat-cured rubber-toughened

structural epoxy adhesives were studied (Table 3.1). The recommended curing profiles were at

least 30 min at 180° C, monitored using a thermocouple embedded in the adhesive layer.

Adhesive wafers were cast between two aluminum plates coated with a

polytetrafluroethylene release agent. The wafer thickness of 0.8 mm was controlled using

spacing wires. After curing, the adhesive wafers were cut to approximately 40 x 40 mm ensuring

that the diffusion process was essentially one-dimensional in the thickness direction (the edge

surface area was less than 4% of the total). A sharp knife was used to prevent edge cracking.

XPS indicated some traces of release agent (fluorine) on the wafer surfaces; however, the

gravimetric results did not change when this was sanded off.

To remove any absorbed moisture, the wafers were kept in a vacuum oven containing

anhydrous calcium sulphate at 40°C for approximately 7 days. Mass uptake measurements were

made under different combinations of temperature and RH as given in Table 3.2 along with the

saturated salt solutions used to generate the atmospheres [18,19]. Table 3.2 also gives the

amount of water present per unit volume of atmosphere at each exposure condition [20]. Airtight

plastic containers were used as conditioning chambers within temperature-controlled ovens, and

the wafers were placed on a grating with point contacts. Absorption and desorption

measurements were repeated on three wafers at each exposure condition. Desorption was carried

out in a vacuum oven containing anhydrous calcium sulphate at 40°C for up to three months.

Some of the samples were analysed in fresh, saturated, and dried states using XPS to investigate

changes in the composition due to water ingress.

42

Table 3. 1 Mechanical and physical properties of adhesives 1 and 2 at room temperature as

supplied by the manufacturers.

Adhesive

Elastic

modulus,

E, MPa

Poisson's

ratio, ν

Tensile

strength,

σy, MPa

Glass

transition

Temp, Tg, °C

Cured

density

g/cm3

Adhesive 1 1.96 0.45 44.8 125 1.50

Adhesive 2 1.73 0.39 N/A 122 1.14

Table 3. 2 Different exposure conditions for adhesives 1 and 2 and saturated salt solutions used

to achieve different levels of RH.

RH

(%)

Salt

solution

Temperature (°C)

20 40 50 60

H2O

content

(g/m3)

Adh.

studied

H2O

content

(g/m3)

Adh.

studied

H2O

content

(g/m3)

Adh.

studied

H2O

content

(g/m3)

Adh.

studied

31 MgCl2 5.5 N/A 16.2 1 26.2 N/A 41.0 N/A

43 K2CO3 7.4 1 21.7 1 35.2 N/A 55.1 1

75 NaCl 12.9 N/A 37.9 1 61.4 N/A 96.1 N/A

82 KCl 14.1 1 41.5 1 & 2 67.1 1 105.1 1 & 2

95 K2SO4 16.3 1 & 2 48.0 1 & 2 77.8 1 121.7 1 & 2


3.4.1 Moisture absorption

Both the new sequential dual Fickian (SDF) and the Langmuir models were used to

characterize moisture diffusion into adhesives 1 and 2. It was assumed that the diffusion

coefficients D1 and D2 in the SDF model and DL for the Langmuir model were independent of

time. D1 was determined by assuming a linear relationship between normalized mass uptake,

Mt/M1∞ and t1/2

during the initial stages of absorption. This linear relationship was approximated

by [21]:

43

2/1

1

1

2

tD

hM

M t

(17).

It was assumed that the samples were fully saturated during the absorption period and the

total saturated fractional mass uptake, M∞ (=M1∞+M2∞) was determined from the gravimetric

data. The other three parameters of SDF model (M1∞, td and D2) were determined by curve

fitting. A nonlinear, least-squares optimization approach was developed using MATLAB

programming to find the best fit of Eq. (6) to the experimental data points. In the Langmuir

model, the diffusion coefficient, DL was assumed to be equivalent to D1 in the SDF model. The

probabilities β and γ were found by a least-square fitting of the analytical model to the

experimental data points. Following the formulation and procedure given in [8,9], the parallel

dual Fickian (PDF) model was also fitted to the experimental results using a least-squares

optimization approach in MATLAB to compare with the SDF and Langmuir models.

3.4.1.1 Fractional mass uptake profiles of adhesive 1

Figures 3.2-3.4 show the measured fractional mass uptake, Mt and the fitted SDF,

Langmuir and PDF models versus the square root of time (t1/2

) for adhesive system 1 at different

RH values for three temperatures. After the initial linear Fickian diffusion and the onset of a

plateau, a second mass increase was observed in most of the exposure conditions. The single-

stage Fickian model thus overestimated the experimental results, especially at high temperatures

and RH, and at intermediate times.

Tables 3.3 and 3.4 list the parameters of the SDF and Langmuir models, respectively, for

adhesive 1 under the different exposure conditions. At the lower temperatures and RH (40°C-

43%RH, 40°C-31%RH, 20°C-43%RH), the second diffusion mechanism disappeared and the

fractional mass uptake profiles followed a simple Fickian diffusion behaviour (D2=0, td=∞,

M2∞=0). In these cases, the pseudo-equilibrium and final equilibrium states of the Langmuir

model become coincident and there is no unique solution because any β with γ=0 satisfies the

model. Therefore, the Langmuir model was not used in these cases.

44

0

1

2

3

4

0 500 1000 1500 2000 2500 3000

Mt (%

)

t1/2(s1/2)

T=20°C

95%RH

82%RH

43%RH

SDF

Langmuir

PDF


based on the SDF, Langmuir and PDF models at three RH levels for adhesive 1 at 20°C. Each

data point is an average of three repetitions.

45

0

1

2

3

4

5

0 500 1000 1500 2000 2500 3000

Mt(%

)

t1/2 (s1/2)

T= 40°C

95%RH

82%RH

75%RH

43%RH

31%RH

SDF

Langmuir

PDF


based on the SDF, Langmuir and PDF models at five RH levels for adhesive 1 at 40°C. Each


46

0

1

2

3

4

5

6

7

0 500 1000 1500 2000 2500 3000

Mt(%

)

t1/2 (s1/2)

T=60°C

95%RH

82%RH

43%RH

SDF

Langmuir

PDF


based on the SDF, Langmuir and PDF models at three RH levels for adhesive 1 at 60°C. Each


47

Table 3. 3 SDF model parameters obtained by curve fitting the experimental gravimetric results

at different combinations of temperature and RH for adhesive 1. M1∞ values obtained from PDF

model are also given. Each data point is given as an average of three values obtained from the

repetitions. SD shows the standard deviation.

T

(°C)

RH

(%)

D1=DL±SD

(10-14

m2/s)

D2±SD

(10-14

m2/s)

M1∞±SD

(%)

(SDF)

M∞=N∞±SD

(%)

td1/2

(s1/2

)

M1∞

(%)

(PDF)

20

95 36±6 3.9±0.6 3.31±0.05 3.94±0.06 845 2.72

82 33±5 3.5±0.5 2.77±0.02 2.96±0.02 941 2.25

43 45±6 0.0 1.78±0.04 1.78±0.04 ∞ 1.78

40

95 134±17 3.8±0.7 3.36±0.09 4.78±0.15 536 2.80

82 142±6 3.3±0.4 2.71±0.04 3.55±0.06 524 2.34

75 159±25 3.6±0.6 2.21±0.05 2.79±0.06 521 1.97

43 113±11 0.0 1.65±0.04 1.65±0.04 ∞ 1.65

31 139±19 0.0 1.26±0.04 1.26±0.04 ∞ 1.26

50 95 207±9 4.5±0.7 3.59±0.08 6.67±0.17 427 3.11

82 222±12 3.6±0.4 2.71±0.02 3.69±0.04 416 2.28

60

95 314±25 8.6±0.9 3.73±0.11 6.98±0.18 329 2.59

82 294±28 4.9±0.7 2.75±0.05 4.02±0.08 308 2.39

43 271±24 4.3±0.8 1.38±0.03 1.62±0.04 924 2.72

48


results at different combinations of temperature and RH for adhesive system 1. Each data point

is given as an average of three values obtained from the repetitions. SD shows the standard

deviation.

T

(°C)

RH

(%)

β±SD

(10-7

/s)

γ±SD

(10-7

/s)

Npe

(%)

20 95 3.23±0.19 0.68±0.03 3.23±0.08

82 3.46±0.14 0.43±0.02 2.63±0.06

40

95 4.07±0.26 1.94±0.12 3.20±0.09

82 3.66±0.18 1.23±0.05 2.66±0.07

75 3.43±0.16 0.88±0.04 2.18±0.04

50 95 4.97±0.22 5.31±0.28 3.20±0.08

82 4.78±0.15 1.75±0.06 2.69±0.06

60

95 10.9±0.81 12.86±0.73 3.21±0.11

82 6.88±0.43 3.22±0.22 2.75±0.05

43 2.52±0.14 0.53±0.04 1.36±0.04

3.4.1.2 Fractional mass uptake profiles of adhesive 2

Figure 3.5 shows the experimental fractional mass uptake, Mt versus square root of time

(t1/2

) and the fitted SDF, Langmuir and PDF models at 20, 40 and 60°C and 95% RH for

adhesive 2. The corresponding parameters for both models are given in Tables 3.5 and 3.6.

The SDF model was able to characterize the anomalous diffusion behaviour of adhesives

1 and 2, showing a good agreement with the experimental results, the Langmuir model and the

PDF model. Using the Langmuir model provides a means to estimate the relative amounts of

bound and free water molecules in the adhesive. However, the probabilities β and γ have no

physical significance in the diffusion process and also must be adjusted for any new exposure

condition (Section 3.4.1.6). The SDF model divides the diffusion process into two separate

stages governed by Fick’s law, which has a physical significance. The predictions of the SDF

49

and PDF models were very similar, deviating the most at high RH and intermediate exposure

times close to td. The M1∞ values obtained from the SDF model agree well with the total number

of water molecules per unit volume in the pseudo-equilibrium state (Npe) of the Langmuir model

(average difference of 4%; see Section 3.4.1.5). This agreement adds physical significance to

M1∞ in the SDF model. The M1∞ values obtained from the PDF model were always lower than

the corresponding Npe values with an average difference of 15%. As will be discussed in Section

3.4.1.4, it is reasonable to assume that some of the water diffusion mechanisms occur after a

delay time (i.e. td), leading to the second stage of water uptake; therefore, the SDF model is

believed to represent a more realistic representation of water diffusion in the present adhesives.

Furthermore, it has been reported that in some cases the pseudo-equilibrium state (M1∞

occurring after td) for water absorption by DGEBA-based epoxies can be much longer than was

found with the present adhesives [8, 22]. Since the PDF model assumes that both of the

diffusion mechanisms start from the beginning of the absorption process, the predicted mass

uptake always increases with time and it is difficult to model such absorption behavior

accurately. To deal with this limitation, Mubashar et al. [8] used a “delayed SDF” model by

adding a power function to the SDF formulation. This delayed SDF model, however, adds three

more constants and so increases the degrees of freedom of the problem, making it more difficult

to develop the ability to predict how the model parameters vary with temperature and RH. As

with the original PDF model, there is no physical significance to the added power function. On

the other hand, by assuming two sequential water uptake stages, the SDF model provides a more

general water absorption model that relates to the physical significance of Fick’s law and the

Langmuir model.

In general, adhesive 2 appeared to be more resistant to water ingress than adhesive 1, and

all five SDF parameters (D1, D2, C1∞, C2∞, td) for adhesive 2 were always less than those for

adhesive 1 at the same exposure condition. The D1 and M∞ values of adhesive 2 were

approximately 28% and 26% lower than those of adhesive 1, respectively.

In order for the SDF and Langmuir models to be predictive beyond the ambient

conditions used in the experiments, it is necessary to identify the dependence of the model

parameters on temperature and RH. This is discussed in the following subsections. It is noted

that the present experiments did not investigate the possibility that the adhesive thickness

influences the diffusion properties as reported in [9]. However, such changes were reported to

50

be relatively small, being of the same order as the experimental scatter (e.g. Table 3.4).

Moreover, ref. [9] did not provide an explanation for the observed dependency on adhesive

thickness, and therefore the generality of this phenomenon remains unknown.

0

1

2

3

4

5

0 500 1000 1500 2000 2500

Mt(%

)

t1/2 (s1/2)

60°C

40°C

20°C

SDF

Langmuir

PDF


based on the SDF, Langmuir and PDF models at 95% RH and three different temperatures for

adhesive 2. Each data point is an average of three repetitions.

51

Table 3. 5 SDF model parameters obtained by curve fitting to the experimental gravimetric

results at different combinations of temperature and RH for adhesive 2. M1∞ values obtained

from PDF model are also given. Each data point is an average of three values obtained from the

repetitions. SD shows the standard deviation.

T

(°C)

RH

(%)

D1=DL±SD

(10-14

m2/s)

D2±SD

(10-14

m2/s)

M1∞±SD

(%)

(SDF)

M∞=N∞±SD

(%)

td1/2

(s1/2

)

M1∞

(%)

(PDF)

20 95 26±4 6.8±1.2 2.31±0.04 2.99±0.06 631 1.87

40 95 87±11 4.1±0.8 2.83±0.06 3.75±0.09 386 2.41

82 104±13 9.8±1.5 2.14±0.06 2.27±0.07 497 1.78

60 95 248±29 8.1±1.5 3.16±0.09 4.78±0.12 219 2.59

82 208±24 9.6±1.3 2.38±0.03 2.8±0.04 273 1.99


results at different combinations of temperature and RH for adhesive 2. Each data point is an

average of three values obtained from the repetitions. SD shows the standard deviation.

T

(°C)

RH

(%) β±SD

(10-7

/s)

γ±SD

(10-7

/s)

Npe±SD

(%)

20 95 10.88±0.73 5.8±0.34 2.06±0.04

40 95 10.64±0.84 4.7±0.29 2.58±0.08

82 12.5±0.87 1.1±0.06 2.08±0.07

60 95 22.3±1.38 12.9±0.69 3.10±0.10

82 24.2±1.82 0.5±0.03 2.32±0.06

3.4.1.3 The effect of temperature and RH on the diffusion coefficients

Analysis of variance showed that D1 for adhesive 1 was independent of RH at all

temperatures (95% confidence). Similarly, in the case of adhesive 2, a t-test showed that the

average values of D1 were independent of RH at all temperatures. The second diffusion

52

coefficient, D2 was always appreciably less than D1 for both adhesives (Tables 3.3 and 3.5).

Excluding the inexplicably high D2 value at the 60°C-95% RH condition for adhesive 1, and

unexpectedly low value at 40°C-95% RH condition for adhesive 2, analysis of variance revealed

that D2 could be assumed independent of temperature and RH (95% confidence) for both

adhesives. Since both points excluded were at 95% RH condition, the above conclusion appears

to be valid only at lower RH levels and not valid at relatively higher humidity level.

The Arrhenius rate equation was used to investigate the effect of temperature on D1:

RT

QDD exp01

(18)

where D0 and Q are the diffusion constant and activation energy, respectively. R is the universal

gas constant (0.00198 kcal K-1

mol-1

) and T is absolute temperature (K). Figure 3.6 shows D1

versus inverse temperature, 1/T on a logarithmic scale for both adhesives. At a given

temperature, D1 was taken as the average obtained from the different RH conditions, since it was

independent of RH as described above. Least squares regression showed that the D1 variation

with exp(1/T) was sufficiently linear in both adhesives during the first diffusion process to be

modeled using Eq. (18). The calculated activation energy of the first diffusion process was

essentially the same for adhesives 1 and 2; i.e. 10.2 and 10.6 kcal/mol, respectively.

By way of comparison, Atkins reported that the energy required for breaking the

hydrogen bonds present in liquid water (O-H…

O) ranges from 5 to 20 kcal/mol [23]. The

activation energy of the main-chain bonding of the epoxy network was reported to be 60-100

kcal/mol, and that of physical bonding (Van der Waals and/or dipole-dipole) is 0.5-2 kcal/mol

[14]. Zhou and Lucas also reported the activation energy of water diffusion in a DGEBA-based

epoxy to be 9.3 kcal/mol and attributed it to hydrogen bonding [14]. Therefore, the average

activation energy of approximately 10 kcal/mol for both adhesives falls within the range reported

for that of water diffusion in epoxy as well as the energy of hydrogen bonding given in the

literature.

Popineau et al. [6] studied the kinetics of absorbed water in epoxy and concluded that the

first diffusion mechanism corresponds to the diffusion of water molecules having strong

interactions with the epoxy, while the water molecules absorbed during the second diffusion

53

mechanism are relatively mobile. The second diffusion mechanism can then be related to a

physical phenomenon such as clustering, in which the water molecules fill the free volume of the

epoxy [9]. The water molecules within a cluster have no strong connections with the epoxy

backbone and are essentially free.

1 : y = 0.00017e-5157x

R² = 0.98

2 : y = 0.00020 e-5311x

R² = 0.99

10203040506070

1

10

100

0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035

Inverse Temperature (1/ K)

D1

(10

-12m

2/

s)

Temperature (°C)

Adhesive 1

Adhesive 2

Figure 3. 6 Variation of first diffusion coefficient, D1 with temperature for adhesives 1 and 2.

At each temperature, D1 was taken as the average obtained from different RH conditions. Linear

fit to the Arrhenius equation (Eq. (18)) with the slope equal to –Q/R.

3.4.1.4 The effect of temperature and RH on the saturated fractional mass

uptakes

As seen in Fig. 3.7, M1∞ increased significantly with RH, but it remained almost

independent of temperature. This indicates that temperature affected only the rate of the first

diffusion mechanism and not its saturation concentration value.

54

Figure 3.7 also shows that M2∞ increased with both temperature and RH, although

saturation in the second stage was not reached over the durations of the present experiments at

the lowest temperature and RH exposure conditions (20°C-43%RH, 40°C-43%RH).

The dependence of M2∞ on RH and temperature can be explained in terms of the

clustering of water molecules which is hypothesized to have occurred during the second uptake.

One of the main factors that can increase the potential sites for the clustering is volumetric

swelling of the adhesive due to water absorption, which will increase with both RH and

temperature. The swelling strain is negligible during the initial stage of exposure but starts to

increase (up to 10%) from medium exposure times [9,24,25]. It is then reasonable to assume that

the volumetric expansion caused by the diffusion of water into the adhesive does not act

immediately, which supports the assumption of a transition time td. The expansion causes the

enlargement of the potential clustering sites within the adhesive and water molecules can then

diffuse to fill these new voids.

An increase in the free volume for clustering and hence M2∞, can also occur because of

thermal expansion and osmotic pressure within water clusters, both of which will depend on

temperature and RH [26]. Osmotic pressure can be created by the diffusion of soluble

components such as fillers into water clusters [27], thereby expanding the epoxy network. The

water diffusion mechanism activated by osmotic pressure can then be assumed to start after the

formation of water clusters at a later time (td) instead of the beginning of the diffusion (t=0).

The osmotic expansion and its contribution to M2∞ will be proportional to the amount of

absorbed water which is a function of temperature and RH. The absence of second stage within

the period of the experiments at the lowest temperature and RH (20°C-43%RH, 40°C-43%RH)

can be attributed to the relatively slow rate of volumetric expansion.

55

0

1

2

3

4

0 10 20 30 40 50 60

M (%

)

Temperature (°C)

M1∞/95%RH

M2∞/95%RH

M1∞/82%RH

M2∞/82%RH

M1∞/43%RH

Figure 3. 7 Variation of the first and second saturated fractional mass uptake values, M1∞ and

M2∞ with temperature at 95%, 82% and 43% RH for adhesive 1. The lines are least square fits.

Each data point is an average of three repetitions.

3.4.1.5 The effect of temperature and RH on the transition time

As seen in Table 3.3, td remained mostly unchanged with RH at different temperatures for

adhesive 1, except for the 60°C-43%RH condition in which the transition time appeared to be

unexpectedly long. It varied slightly with RH for the conditions studied with adhesive 2 (Table

3.5). Noting that the first diffusion mechanism was shown to be a chemical interaction

(hydrogen bonding) which followed the Arrhenius rate equation, it is reasonable to assume that

the time required for the first process to be completed (td) depends on the rate of the process

(D1). If it is hypothesized that td has an inverse linear relationship with D1 as:

11 KDtd (19)

where K is a constant, then substituting D1 from Eq. (18) into Eq. (19) results in

56

RT

Qtt dd exp0

(20)

where td0=KD0 is a transition time constant. To examine this hypothesis, the activation energy of

the first diffusion mechanism, Q was calculated using Eq. (20) and the measured td. Figure 3.8

shows the variation of td with inverse temperature on a logarithmic scale at 95% RH for both

adhesives. Very similar results were observed at 82% RH for adhesive 1. A very good linear

least squares fit between td and exp(1/T) suggested that Eq. (19) was a valid assumption and

using these fits, Q for adhesives 1 and 2 was found to be 9.7 and 10.2 kcal/mol, respectively.

Using the results at 82% RH, Q for adhesive 1 was calculated to be 10.1 kcal/mol. These values

compare well with those calculated for D1 using the data of Fig. 3.6, differing by only 5% and

3%, respectively.

Furthermore, the fractional mass uptake at td, M1∞, agrees well with the pseudo-

equilibrium mass uptake, Npe of the Langmuir model at any exposure condition with an average

difference of about only 4% (Fig. 3.9). Therefore, td of the SDF model corresponds to the

pseudo-equilibrium state of the Langmuir model. These results lend confidence that td as the

time of saturation for the first diffusion mechanism was properly determined.

57

y = 0.043 e4907 x

R² = 0.99

y = 0.010 e5147 x

R² = 0.99

10203040506070

1

10

100

0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035

Inverse Temperature (1/ °K)

t d (

10 4

s)

Temperature (°C)

Adhesive 1

Adhesive 2

Figure 3. 8 Variation of the transition time with temperature at 95% RH for both adhesives.

Each data point is an average of three values obtained from the repetitions. The lines show least

square regressions between td and exp(1/T) and the slopes of the lines give the values of Q/R.

58

20°95%

40°95%

50°95%

60°95%

20°82%

40°82%

50°82%

60°82%

20°43%

40°43%

60°43%

0

1

2

3

4

M1∞

, Np

e(%

)

M1∞

Npe

Figure 3. 9 Comparison between the first saturated fractional mass uptake, M1∞ of the SDF

model and the pseudo-equilibrium mass uptake, Npe of the Langmuir model at different

combinations of temperature and RH. Each data point is an average of three values obtained

from the repetitions.

3.4.1.6 The effect of temperature and RH on the β and γ probabilities of

Langmuir model

Figure 3.10 shows the variation of β and γ with inverse temperature on a logarithmic

scale at 82% RH for adhesive 1. The fair linear fits indicate that both probabilities varied

approximately exponentially with T and followed the Arrhenius rate equation at a particular RH.

Similarly at 95% RH, both β and γ varied exponentially with T but with different rates. Figure

3.11 shows that β and γ also depended strongly on RH, especially at higher temperature. Hence,

although the form of the Langmuir model fits absorption data well, it does so with adjustable

parameters β and γ that are unknown functions of both temperature and RH. This limits the use

of the Langmuir model to environments where β and γ have been determined, and makes

interpolation and extrapolation to different environments uncertain.

59

R² = 0.76

R² = 0.99

10203040506070

0

1

10

0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035

Inverse Temperature (1/ K)

β,γ

(10

-7s

-1)

Temperature (°C)

β

γ

Figure 3. 10 Variation of β and γ probabilities with temperature at 82% RH for adhesive 1.

Each data point is an average of three values obtained from the repetitions. The lines show least

square regressions between the probabilities and exp(1/T).

0

3

6

9

12

15

0 20 40 60 80 100

β,γ

(10

-7s

-1)

RH (%)

β-60°C

γ-60°C

β-40°C

γ-40°C

Figure 3. 11 Variation of β and γ probabilities with RH at temperatures of 40°C and 60°C for

adhesive 1. Each data point is an average of three values obtained from the repetitions. The

lines are only to guide the trends.

60

3.4.2 Moisture desorption

After the absorption process, the samples were dried in a vacuum oven at 40°C to

measure the desorption profiles. The mass of samples decreased uniformly with drying time to

minimum fractional retained water, Mr (%) and remained unchanged, even after approximately 3

months. The simple Fickian model sufficiently characterized the desorption process in both

adhesives in terms of the desorption diffusion coefficient, Dd, the saturated fractional mass

uptake, M∞ and the minimum fractional retained water, Mr. Dd was determined in the same

manner as D1 using Eq. (17) and normalized mass loss profiles.

3.4.2.1 Fractional retained mass profiles of adhesives 1 and 2

Figures 3.12-3.14 show the experimentally measured fractional retained mass, versus

square root of time, t1/2

and Fickian fits for the wafers of adhesive 1 that had been exposed to

different RH at 20, 40 and 60°C. Figure 3.15 shows the same results for adhesive 2 with the

exposure condition of 60°C-95% RH. No second slope was observed during desorption and the

simple Fickian model adequately characterized the behaviour of both adhesives. The main

difference between the fractional retained mass profiles of the adhesives 1 and 2 was the

minimum fractional retained water, Mr; 1.4% and 0.16%, respectively, for the same M∞ of 4.8%.

The Mr value for adhesive 1 was approximately 30% of the corresponding M∞.

As mentioned previously, Marsh et al. [15] and Moy and Karasz [16] concluded that a

drying temperature above Tg was required to completely remove absorbed water from epoxy

resin. Zhou and Lucas [14] observed some retained water in both DGEBA and TGDDM based

epoxies after drying at temperatures up to 90°C, which was greater than Tg. They found that the

amount of retained water eventually reached zero, but the activation energy required for high-

temperature desorption was higher than that of low-temperature desorption. They concluded that

the water molecules retained after low-temperature desorption had multiple hydrogen bonds with

the epoxy network.

61

0

1

2

3

4

0 200 400 600 800 1000 1200

Mtl

(%)

t1/2 (s1/2)

20°C

95%RH

82%RH

43%RH

Figure 3. 12 Fractional retained mass during drying versus square root of time, fitted with the

simple Fickian model for adhesive 1 initially saturated at 20°C and different RH. Each data

point is an average of three repetitions.

0

1

2

3

4

5

0 200 400 600 800 1000 1200

Mtl

(%)

t1/2 (s1/2)

40°C

95%RH

82%RH

75%RH

43%RH

31%RH

Figure 3. 13 Fractional retained mass during drying versus square root of time, fitted with

simple Fickian models for adhesive 1 initially saturated at 40°C and different RH. Each data

point is an average of three repetitions.

62

0

1

2

3

4

5

6

7

0 200 400 600 800 1000 1200

Mtl

(%)

t1/2 (s1/2)

60°C

95%RH

82%RH

43%RH

Figure 3. 14 Fractional retained mass during drying versus square root of time and fitted simple

Fickian models for adhesive 1 initially saturated at 60°C and different RH. Each data point is an

average of three repetitions.

0

1

2

3

4

5

0 200 400 600 800 1000 1200 1400

Mtl

(%)

t1/2 (s1/2)

60°C - 95% RH

Figure 3. 15 Fractional retained mass profile during drying versus square root of time and fitted

simple Fickian model for adhesive 2 initially saturated at 60°C-95%RH. Each data point is an

average of three repetitions.

63

3.4.2.1 The effect of temperature and RH on the minimum fractional

retained water

Figures 3.16 and 3.17 show that Mr was proportional to the temperature and RH during

the absorption process for adhesive 1. At low temperature (20°C), Mr remained relatively

unchanged with RH (Fig. 3.17). Similarly, at low RH (43%), Mr was largely independent of T.

Figure 3.18 also shows that Mr increased linearly with the ambient water concentration during

absorption, regardless of temperature.

Figure 3.19 depicts the variation of minimum fractional retained water during the

desorption process, Mr with the saturated fractional mass uptake M∞ (M1∞+M2∞=M∞) which was

obtained at different combinations of temperature and RH. Mr increased linearly with M∞,

independent of the original exposure condition. This finding may be useful in predicting the

amount of retained water in the adhesive exposed to a varying environment.

0

0.5

1

1.5

2

0 10 20 30 40 50 60

Mr(%

)

Temperature (°C)

95%RH

82%RH

43%RH

Figure 3. 16 Variation of minimum fractional retained water, Mr with the temperature of

absorption condition at different RH levels for adhesive 1. Each data point is an average of three

repetitions. The linear least square fits show the general trends.

64

0

0.5

1

1.5

2

0 20 40 60 80 100

Mr(%

)

RH (%)

60°C

40°C

20°C

Figure 3. 17 Variation of minimum fractional retained water, Mr with the RH of the absorption

condition at different temperatures for adhesive 1. Each data point is an average of three

repetitions. The linear least square fits show the general trends.

0

0.5

1

1.5

2

0 25 50 75 100 125 150

Mr(%

)

Ambient water concentration (g/m3)

Figure 3. 18 Variation of minimum fractional retained water, Mr with the ambient water

concentration achieved during different exposure conditions for adhesive 1. Each data point is

an average of three repetitions. The linear least squares fit shows the general trend.

65

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5 6 7 8

Mr(%

)

M∞ (%)

Figure 3. 19 Variation of minimum fractional retained water during the desorption process with

the saturated fractional mass uptake, M∞ for adhesive 1. Each data point is an average of three

repetitions. The linear least square fit shows the general trend.

3.4.3 XPS analysis

The significant difference between Mr for these two adhesives was investigated using

XPS. Table 3.7 shows the percentage of oxygen atoms associated with different chemical bonds

(binding energies) for fresh (as-cured), saturated wet, and dried samples of adhesives 1 and 2.

The O1sB peak corresponded to a bond associated with water molecules since it was present in

the wet samples of both adhesives, but not in the fresh and dried samples of adhesive 2, nor was

it significant in the fresh adhesive 1. As seen in Table 3.7, the atomic percentage of O1sB was

10% in dried samples of adhesive 1 which qualitatively supports the gravimetric results

indicating that a considerable amount of absorbed water in the adhesive 1 could not be removed

during the drying process at 40°C.

66

Table 3. 7 Percentage of oxygen atoms associated with different chemical bonds with their

binding energy for fresh, saturated wet and dried samples of adhesives 1 and 2. Each data point

is an average of three repetitions.

Exposure

condition:

60°C-95% RH

O1s O1sA O1sB

Atomic

%

Binding

energy

(eV)

Atomic

%

Binding

energy

(eV)

Atomic

%

Binding

energy

(eV)

Adhesive 1

Fresh (Mt=0) 84 532.7 12 534.0 4 531.0

Wet

(Mt=M∞=6.98%) 67 532.6 15 533.6 18 531.5

Dry

(Mt=Mr=1.82%) 76 532.7 13 533.7 10 531.4

Adhesive 2

Fresh (Mt=0) 77 532.9 23 533.8 0 N/A

Wet

(Mt=M∞=4.78%) 62 532.8 15 533.8 23 531.6

Dry

(Mt=Mr=0.20%) 76 532.8 24 533.7 0 N/A

3.5 Conclusions

The water absorption and desorption of two different rubber-toughened epoxy adhesives

were characterized using gravimetric measurements. A newly developed sequential dual Fickian

(SDF) model was developed to fit the fractional mass uptake profiles and agreed well with the

Langmuir diffusion model. The diffusion mechanism in the first stage appeared to be influenced

by hydrogen bonding while the diffusion mechanism in the second stage was primarily physical

in nature. The diffusion coefficients in both stages were found to be largely independent of RH,

while the saturated fractional mass uptake values increased with RH. The diffusion coefficient

of the first stage and the saturated fractional mass uptake of the second stage were both functions

of temperature. These functional dependencies were described, making the SDF model

predictive over the ranges of temperature and RH that were investigated.

The desorption during drying in both adhesives was described well by Fick’s law. Both

gravimetric results and XPS revealed that there was a significant difference between the amounts

67

of minimum fractional retained water in the two adhesives after drying. The relatively large

amount of retained water in adhesive 1 was attributed to multiple hydrogen bonds between the

water molecules and the epoxy or other constituents such as the rubber toughener particles or the

filler. In a separate test program, it was found that these differences in water absorption-

desorption corresponded to marked differences in the degradation of fracture toughness in hot-

wet aging environments (to appear in a future publication).

The SDF model can be used to predict the water concentration distribution in adhesive

joints exposed to environments of changing temperature and RH under the assumption of

negligible interface diffusion.

68

3.6 References

1. LaPlante, G., Ouriadov, A.V., Lee-Sullivan, P., Balcom, B. J., J. Applied Polymer

Science 109, 1350-1359 (2008).

2. Fernandez-Garcia, M., Chiang, M.Y.M., J. Applied Polymer Science 84, 1581-1591

(2002).

3. Musto, P., Ragosta, G., Mascia, L., Chem. Mater. 12, 1331-1341 (2000).

4. Weir, M. D., Bastide, C., Sung, C. S. P., Macromolecules 34, 4923-4926 (2001).

5. Masaro, L., Zhu, X. X., Prog. Polym. Sci. 24, 731–775 (1999).

6. Popineau, S., Rondeau-Mouro, C., Sulpice-Gaillet, C., Shanahan, M. E. R., J. Polymer

46,,10733–10740 (2005).

7. Roy, S., Xu, W. X., Park, S. J., Liechti, K. M., J. Applied Mechanics 67, 391-396 (2000).

8. Mubashar, A., Ashcroft, I. A., Critchlow, G. W., Crocombe, A. D., Int. J. Adhesion

Adhesives 29, 751-760 (2009).

9. Loh, W. K., Crocombe, A. D., Abdel Wahab, M. M., Ashcroft, I. A., Int. J. Adhesion

Adhesives 25, 1–12 (2005).

10. Maggana, C., Pissis, P. J., Polym. Sci. Part B: Polym. Phys. 37,1165-1182 (1999).

11. Feng, J., Berger, K. R., Douglas, E. P., J. Mater. Sci. 39, 3413–3423 (2004).

12. Carter, H. G., Kibler, K. G., J. Compos. Mater. 12, 118–131 (1978).

13. Lin, Y. C., J. Polymer Research 13, 369-374 (2006).

14. Zhou, J., Lucas, J. P., J. Polymer 40, 5505–5512 (1999).

15. Marsh, L. L., Lasky, R., Seraphim, D. P., Springer, G. S., In: Springer G. S, editor

Environmental effects on composite materials (Technomic Publishing Co., Westport,

1988) p. 51.

16. Moy, P., Karasz, F. E., Polym. Eng. Sci. 20, 315-319 (1980).

17. Loh, W. K., Crocombe, A. D., Abdel Wahab, M. M., Ashcroft, I. A., J. Adhesion 79,

1135–1160 (2003).

18. Loh, W. K., Crocombe, A. D., Abdel Wahab, M. M., Ashcroft I. A., Eng. Frac. Mech.

69, 2113–2128 (2002).

19. Greenspan, L., J. Research National Bureau Standards A: Physics and Chemistry 81, 89-

96 (1977).

69

20. ASHRAE Handbook – Fundamentals, (American Society of Heating, Refrigerating and

Air-Conditioning Engineers, Inc., 2009) I-P Edition, pp: 1.1-1.20.

21. Wylde, J. W., Spelt, J. K., Int. J. Adhesion Adhesives 18, 237-246 (1998).

22. De Neve B, Shanahan M. E. R., Int J Adhesion Adhesives 12, 191–196 (1992).

23. Atkins, P. W., Quanta (Oxford University Press, New York, 1990) 2nd ed., p. 68.

24. El-Sa’ad, L., Darby, M. I., Yates, B., J. Mater. Sci. 24, 1653–1659 (1989).

25. Chang, T., Lai, Y. H., Shephard, N. E., Sproat, E. A., Dillard, D. A., J. Adhes 60, 153–

162 (1997).

26. Ivanova, K. I., Pethrick, R. A., Affrossman, S., J. Applied Polym. Sci. 82, 3468–3476

(2001).

27. Tu, Y., Spelt, J. K., J. Adhesion 72, 359-372 (2000).

70

Chapter 4 The Effects of Test Temperature and Humidity on the Mixed-

mode Fatigue Behavior of a Toughened Adhesive Aluminum Joint

4.1 Introduction

The fatigue performance of structural adhesive joints is known to degrade when tested in

environments of elevated temperature [1-3], high humidity [4-7], or combinations of these [8-

10]. Since this degradation happens in a relatively short period of time during the fatigue test

itself, such hot-wet fatigue tests have been proposed as a means of quickly assessing the long-

term degradation behavior of adhesive joints [7,9]. Briskham and Smith [9] compared the

relative durability of different surface pretreatments by cyclically loading aluminum-epoxy

single lap shear (SLS) joints under water and by tensile testing after aging. They observed that

certain joints degraded significantly while cyclically loaded under water, but did not show any

loss of tensile shear strength even after 1500 hr of aging.

Abel et al. [4] found that a critical humidity level exists below which the mode I fatigue

threshold behavior of epoxy-aluminum joints remained unaffected by the test environment;

however, the crack growth rates were not measured, and the tests were performed only at room

temperature. In contrast, Ritter et al. [11] observed that the crack growth rate of epoxy-glass

joints under mixed-mode loading was independent of the humidity level during the test.

Harris and Fay [2] found that the fatigue life of steel-epoxy SLS joints decreased as the

test temperature increased. A similar decrease in fatigue life with increasing temperature was

observed using plastic-plastic and metal-plastic SLS joints [10]. However, Ashcroft et al. [1, 3]

observed that the effect of temperature on fatigue threshold depended on the joint geometry for

composite double cantilever beam, single lap shear, and double lap shear joints. They attributed

this dependence to the accumulated creep that changes with the joint geometry for a given

temperature. The understanding of the mixed-mode fatigue behavior of adhesive joints in

environments of high temperature and humidity is limited, and further study is necessary to

predict the long-term behavior of adhesive systems. The present study investigated the effects of

the test environment on the mixed-mode fatigue behavior of joints made with aluminum and a

71

highly-toughened epoxy adhesive. The experiments isolated the effects of pretreatment,

temperature and humidity on both the fatigue threshold and crack growth rates.

4.2 Experiments

4.2.1 Specimen preparation

ADCB specimens (Fig. 4.1) were made with aluminum alloy AA6061-T6 adherends

bonded with a single-part, heat-cured toughened epoxy adhesive. These specimens produced a

phase angle, 18 , defined as III GGarctan , where GI and GII are the mode I and

mode II strain energy release rates, respectively. The purpose of choosing such a mixed-mode

specimen and loading configuration was to direct the crack path toward the interface of the

more highly-strained adherend, particularly at slow crack growth rates near the threshold

[13,14]. This created a test situation that provided a better evaluation of the interfacial bond

integrity than would a pure mode-I loading where the crack tends to follow an average path in

the mid-plane of the adhesive layer. The exact value of the phase angle (18) was arbitrary, the

only requirement being an appreciable amount of mode II in the loading. The adhesive was

cured using the recommended temperature profile of at least 30 min at 180ºC, monitored with

an embedded thermocouple. The thickness of the adhesive layer was 0.4 mm, controlled by

clamping the adherends against steel wires. A precrack was formed by placing a folded 10 µm

aluminum foil in the adhesive layer. Prior to bonding, the aluminum adherends were abraded

with an orbital sander using a silicon carbide nylon mesh abrasive pad that produced a surface

roughness, Ra=1.33 µm. The abraded aluminum adherends were then pretreated using the P2-

etch method [12] that involved acetone cleaning and etching with an aqueous solution of ferric

sulfate and sulfuric acid. After curing, any excess adhesive from both sides of the specimen

was removed using a belt sander with 120 grit sand paper and water as a coolant, followed by a

final stage of gentle hand sanding with a 600 grit sand paper to minimize mechanical damage.

A thin layer of diluted white paper correction fluid was applied to the bondline, in order to

facilitate observation of the crack tip during the fatigue testing.

In addition, reinforced ADCB specimens were prepared using 2 mm thick AA5754-O

aluminum sheets having a commercial coil-coated pretreatment. The objective was to study

the effect of pretreatment in resisting harsh environments under fatigue conditions. To achieve

72

a wide range of G levels while avoiding yielding of the relatively thin sheet adherends, the

reinforcement technique of ref. [8] was used, as illustrated in Fig. 4.2.

Figure 4. 1 Configuration of ADCB specimen (dimensions in mm, not to scale). Width of

specimen was 19 mm. The clip gauge mounting location is also shown.

Figure 4. 2 Configuration of reinforced ADCB specimen (dimensions in mm, not to scale). The

reinforcing bar (A) and second adherend (E) were 12.7 mm and 25.4 mm thick AA6061-T6 bars,

respectively. The reinforcing adhesive (B) and primary adhesive (D) were 0.4 mm thick, and the

pretreated sheet (C) was 2 mm thick. Width of specimen was 19 mm. The clip gauge mounting

location is also shown.

4.2.2. Fatigue tests

Fatigue testing was performed with a servo-hydraulic load frame under displacement

control using a sinusoidal waveform at a frequency of 20 Hz. A constant displacement ratio

73

(ratio of minimum to maximum displacement, δmin/δmax) of 0.1 was used. The typical δmax used

in these tests was approximately 1 mm. Since δmax and displacement ratio were fixed, testing

began with the application of the highest strain energy release rate, G, where the crack length

was the shortest, which then decreased as the crack grew under constant displacement until the

threshold crack growth rate (10-6

mm/cycle) was reached at the threshold strain energy release

rate, Gth. As indicated in Table 4.1, in some cases a single specimen was used to measure two

thresholds.

The primary purpose of using ADCB specimens, rather than a symmetric mode-I DCB

configuration, was to cause cracks to grow near the adherend interface of interest; i.e. the

reinforced sheet. In addition, it has been found that fatigue crack growth under mixed-mode

loading, by promoting such asymmetric crack growth within the bondline, provides a more

sensitive test of the interfacial bond strength than the mode-I DCB specimen, particularly at slow

crack growth rates near the threshold [13,14].

Table 4. 1 Temperature and humidity conditions used in fatigue experiments. Number of

thresholds reached and ADCB specimens tested.

T (ºC) RH (%) Substance placed in the chamber

Number of thresholds reached,

specimens tested

P2-etch pretreatment CC pretreatment

20 <10 Desiccant 3,3 3,3

40 <10 Desiccant 4,3 -

40 43 Saturated solution of K2CO3 3,2 -

40 95 Saturated solution of K2SO4 3,2 -

40 100 Distilled water 3,3 3,3

80 <10 Desiccant 3,2 -

Humidity and temperature control

The ADCB joints were enclosed in a chamber with a thermostatted resistive heating

element and a fan to maintain a constant temperature. The dry and humid conditions were

74

maintained by placing either desiccant or various saturated salt solutions in the chamber, as

indicated in Table 4.1. Each salt solution was at equilibrium at the desired relative humidity

(Table 4.1; [15,16]), and the fan ensured that the air was uniformly mixed. The humidity

levels were monitored during testing using a humidity probe (Vaisala HMT100, Vaisala Inc.,

Woburn, MA, USA).


Crack length was measured using the specimen compliance method which was calibrated

using optical measurements with a CCD camera mounted on a motorized linear stage. A

telescopic lens attached to the camera allowed a field of view of 2 mm. To obtain clear

photographs of the crack tip, the specimen cycling was stopped and held at the mean load for 15 s

every 9,000 cycles. Unlike fracture tests where the much greater applied strain energy release

rates create a relatively large damage zone of micro-cracks ahead of the macro-crack [17], in

fatigue tests these micro-cracks were absent and the crack tip was well defined by the macro-

crack. The specimen compliance was obtained from the relationship between the crack opening

and the applied force during the unloading portion of the loading cycle. A clip gauge (Model

3541, Epsilon Technology Corp., Jackson, WY, USA) recorded the normal opening at the loading

pins (Fig. 4.1 and 4.2). A polynomial relationship between the optically observed crack length and

the specimen compliance was established according to ASTM E647 [18]. The crack length

inferred from this relationship and the continuous clip gauge compliance data were used in

subsequent calculations of the crack growth rates and G. Azari et al. [14] used this same

procedure to measure crack lengths in fatigue tests with the same adhesive system used in this

study. They showed that the measured specimen compliance agreed well with that calculated

using analytical and the finite element analyses [14].


An analytical beam-on-elastic-foundation model for unequal adherends was used to

calculate G and Ψ from the measured force and crack length [8]. The G values from this

analytical model differed by less than 6% from those obtained using a finite element model that

assumed elastic properties for both the adhesive and adherends [8]. The average phase angles

calculated using the analytical model for ADCB (Fig. 4.1), and reinforced ADCB (Fig. 4.2)

75

specimens were 18° and 13º, respectively. These calculations were performed using the

mechanical properties of the adhesive provided by the manufacturer and of the adherends taken

from ref. [19,20], as given in Table 4.2. There was only a negligible change in Ψ as the crack

grew, e.g., for the ADCB specimens, Ψ increased by only 2° over crack lengths of 40 to 120 mm

[8]. Furthermore, a sensitivity analysis showed that an error in measuring the crack length by 1

mm, for crack lengths in the range of 40-120 mm, changed G by at most 4%, which can be

considered as negligible.

Table 4. 2 Mechanical properties of adhesive at room temperature as provided by the

manufacturer and of adherends taken from ref. [17,18].

Elastic modulus (GPa) Poisson ratio Yield stress (MPa)

Adhesive 1.5 0.45 44.8

AA6061-T6 [17] 68.9 0.33 255

AA5754-O [18] 68.9 0.33 165

4.3 Results and Discussion

4.3.1. Effect of temperature

To study the effect of the temperature on the fatigue behavior, fresh aluminum ADCB

joints were tested in a dry air environment at temperatures of 20º, 40º, and 80ºC, well below the

140ºC glass transition temperature of the adhesive. Figure 4.3 shows that the measured Gth for

these joints remained virtually constant; the small differences were not statistically significant (t-

test, 95% confidence).

Figures 4.4 and 4.5 show the da/dN vs. Gmax curves at these three temperatures. For each

temperature, a linear regression line was fit to all data points in the Paris (linear) region of the

curves. The slopes and 95% confidence intervals for these regression lines were: 20ºC:

4.120.15, 40ºC: 4.580.26, 80ºC: 5.250.25. Therefore, the increase in slope with temperature

was statistically significant at the 95% confidence level, indicating a faster crack growth for the

76

same applied Gmax as the temperature increased. The differences between the curves tended to

become slightly smaller at lower crack speeds, near the threshold.

As expected in these ADCB joints, the fatigue crack paths were always much closer to

the more highly-strained arm of the ADCB, since cracks tend to grow normal to the direction of

the maximum principal stress [21]. Figure 4.6 compares the fracture surfaces of the thinner arms

of the ADCB joints tested at various temperatures. The crack path remained cohesive in the

adhesive at all crack speeds and temperatures. However, the thickness of the residual adhesive

on the highly-strained adherend varied with the temperature and the crack length. The

dependence on crack length implies that the residual adhesive thickness on the thinner adherends

was directly proportional to the applied strain energy release rate and the crack growth rate.

Fatigue cycling may increase the crack tip temperature due to viscous dissipation,

although the effect is usually relatively small. For example, the maximum crack tip temperature

increased by less than 1°C in rubber-toughened epoxies tested at 1–100 Hz [22], and

approximately 10°C in nylon and polyester composites tested at 20 Hz in the Paris law crack

growth regime [23]. The increase in temperature of aluminum adhesive joints would be much

smaller due to the rapid heat dissipation provided by the adherends. Therefore, any effects of a

small increase in adhesive temperature due to viscous damping were ignored.

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77

Figure 4. 3 Effect of test temperature on the average Gth of P2-etch pretreated ADCB joints

tested under dry conditions. Numbers above each data point indicate the number of thresholds

reached and number of specimens tested, respectively; these two numbers are different in cases

where a single specimen was used to reach two thresholds. Error bars show ± standard

deviation.

0

50

100

150

200

0 20 40 60 80 100

Gth

(J/m

2)

Temperature (ºC)

3,34,3

3,2

78

Figure 4. 4 Effect of temperature on fatigue crack growth behavior of P2-etch pretreated ADCB

joints. Two of three experimental results shown for each temperature.

-7

-6

-5

-4

-3

-2

2 2.2 2.4 2.6 2.8 3 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

20ºC #1

20ºC #2

40ºC #1

40ºC #2

80ºC #1

80ºC #2

79

Figure 4. 5 Effect of temperature on the fatigue crack growth behavior of P2-etch pretreated

ADCB joints. Each line is a linear regression fit of all the data points lying on the Paris law

(linear) region at a temperature, as show in Fig. 4.4.

-7

-6

-5

-4

-3

-2

2 2.2 2.4 2.6 2.8 3 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

20ºC

40ºC

80ºC

80

Figure 4. 6 Failure surfaces on the thinner adherend of joints tested under dry conditions at

temperatures of (a) 20ºC, (b) 40ºC, and (c) 80ºC. In cases where a single specimen was used to

reach two thresholds, both threshold regions are indicated.

Residual adhesive thickness

To accurately define the crack path, the residual adhesive thickness was measured at

various crack lengths on the highly-strained adherend of the fractured specimen. To provide an

elevation datum corresponding to the interface, residual adhesive was removed from a narrow

region, about 2 mm wide, on both ends of the joint width using a solvent (mixture of methylene

chloride and methyl alcohol; Glue Buster, Kosmic Surf-Pro Inc., Saint Amable, Quebec). Then

using an optical profilometer (NANOVEA ST400, Micro Photonics Inc. CA, USA), a line scan

was made across the width of the joint with both ends on the datum regions, thereby giving the

thickness of the adhesive layer. Figure 4.7 shows typical failure surface profiles measured across

the specimen width on the more highly-strained adherend at G values of 750 J/m2 and 147 J/m

2

for a specimen tested at 80ºC. Figure 4.8 summarizes the measured residual adhesive

thicknesses changes with applied G for specimens tested at various test temperatures. At any test

temperature, the residual adhesive thickness decreased consistently as the applied G, and hence

81

the crack speed, decreased. This tendency of a crack to move closer to the interface under

mixed-mode loading as the crack speed decreases was also observed in refs. [8,13]. More

importantly, the residual adhesive thickness at any particular applied G increased with

temperature (Fig. 4.8). It was hypothesized that these differences in crack path can be explained

in terms of the effect of temperature on the size of the crack tip damage zone. However, the

actual damage zone size is difficult to predict since it consists of yielded adhesive, cavitation

voids and dispersed micro-cracks ahead of the continuous macro-crack. Therefore, as an

approximation it was assumed that the size of the damage zone would be proportional to the

plastic zone, and that a relative comparison of damage zone sizes under different loads and

conditions could be made in this manner. A similar approach of using plastic zone size was used

by Kinloch and Shaw [24] to explain the effects of temperature on the fracture toughness of a

toughened epoxy.

82

(a)

(b)

Figure 4. 7 Typical profiles of fracture surfaces measured across the specimen width on the

more highly-strained adherend at G values of: (a) 750 and (b) 147 J/m2 for specimens tested at

80ºC. The corresponding residual adhesive thickness values are given in legend. 0 µm on

vertical axis corresponds to interface between highly-strained adherend and adhesive.

0

100

200

300

400

0 4 8 12 16

He

igh

t (µ

m)

Length (mm)

Gmax=750 J/m2, tr=176 µm

0

100

200

300

400

0 4 8 12 16

He

igh

t (µ

m)

Length (mm)

Gmax=147 J/m2, tr=15 µm

83

Figure 4. 8 Thickness of the remaining adhesive on the more highly-strained adherend as a

function of applied Gmax.

Plastic zone size

In an unconstrained material the size of the plastic zone is directly proportional to the

elastic modulus and inversely proportional to the square of the yield stress [25], both of which

are known to decrease as temperature increases [1]. Furthermore, since the yield stress decreases

more rapidly than the elastic modulus [1], and the plastic zone size is more sensitive to yield

stress than elastic modulus, the size of the plastic zone is expected to increase with temperature.

An additional factor in adhesive joints is the constraint imposed by the adherends which can

affect the development of the plastic zone [26]. The changes in the size of the plastic zone with

temperature were studied using a two-dimensional finite element model.

The ADCB specimen was modelled with PLANE 183 elements (ANSYS 12.0,

Canonsburg, PA, USA). The crack tip was meshed using collapsed quarter-point singular

elements, and the crack plane in the adhesive layer was positioned according to the measured

crack paths (Fig. 4.8). The adhesive was modelled using a multi-linear stress-strain curve with

plane strain assumptions, while the adherends were modelled as a linear elastic material with

plane stress assumptions. Figure 4.9 shows the multi-linear stress-strain relations of the adhesive

at room temperature (obtained from tensile tests) and at 80ºC, based on the trend observed in [1],

0

50

100

150

200

0 200 400 600 800

Th

ickne

ss (

µm

)

Gmax (J/m2)

80ºC

40ºC

20ºC

84

whereby both elastic modulus and yield stress decrease by 50% of the room temperature values.

The size of plastic zone was defined as the area in which the von Mises stress was larger than the

adhesive proportional limit, consistent with recent work [26] which modeled the fatigue behavior

of toughened epoxies. Azari et al. [26] showed that the predicted area of the plastic zone using a

similar 2D FE model was on average 12% smaller than the predicted area in the middle of the

joint using a 3D FE model. This difference is acceptable for the purpose of qualitatively relating

the size of the plastic zone to the applied G; therefore, the 2D model was used in this study.

Figure 4.10(a) shows the effect of G on plastic zone thickness at both temperatures. The

plastic zone always extended to the more highly-strained adherend interface. Furthermore, the

plastic zone thickness was less than the bondline thickness for the range of G studied at room

temperature and for G up to 200 J/m2 at 80ºC; i.e. plastic zone was constrained only by the more

highly-strained adherend. However, for G above 200 J/m2 at 80ºC the plastic zone thickness

occupied the entire bondline and was constrained by both adherends. The observation that the

plastic zone at room temperature and at 80ºC was constrained only by the more highly-strained

adherend near Gth might explain the observed insensitivity of temperature on Gth. Figure 4.10(b)

shows that, as expected, the plastic zone size increased with temperature and applied G. It is

plausible to expect crack growth rates (which increase with G, Fig. 4.4) to be proportional to the

cross-sectional area of the plastic zone, since this is a reflection of the damage being done to the

crack tip adhesive by the loads. This trend is also consistent with the changes in the crack speed

shown in Fig. 4.4. Furthermore, if it is assumed that the crack path lies toward the center of the

plastic zone, the residual adhesive thickness on the more highly-strained adherend would be

expected to increase with temperature, which agrees with the observations made in Fig. 4.8.

Another factor that may have contributed to the increase in residual adhesive thickness

with temperature was the reduction in the phase angle associated with a decrease in the adhesive

modulus. The phase angle is known to decrease as the stiffness mismatch between the adhesive

and the adherend increases [27]. For example, a 50% reduction in the adhesive modulus would

decrease the phase angle in the aluminum ADCB joint by 2º. As the phase angle approaches 0º

(pure mode I), the crack path moves progressively toward the midplane of the joint, as expected

for this symmetric loading. This was illustrated in [13] using the same adhesive system, where it

was found that the thickness of the remaining adhesive decreased with increasing phase angle.

85

However, since the decrease in phase angle with temperature was small, phase change might not

be solely responsible for the observed change in crack path.

Figure 4. 9 Multi-linear model used for the adhesive at both room temperature (tensile test) and

at 80ºC (elastic modulus and proportionality limit reduced by 50% of room temperature values).

0

10

20

30

40

50

0 0.02 0.04 0.06 0.08 0.1

Tru

e s

tress, M

Pa

True strain, mm/mm

Room temperature

80ºC

86

(a)

(b)

Figure 4. 10 Effect of G on the (a) plastic zone thickness, and (b) plastic zone size, both at room

temperature and at 80ºC obtained using FE model for ADCB specimen.

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800

Pla

stic z

on

e t

hic

kne

ss, m

m

Gmax, J/m2

Room temperature

80ºC

0

0.25

0.5

0.75

0 200 400 600 800

Pla

stic z

on

e a

rea

, m

m2

Gmax, J/m2

Room temperature

80ºC

87

4.3.2 Effect of humidity level

Figure 4.11 shows the Gth of joints tested at 40ºC and the four levels of relative humidity.

Gth remained virtually unchanged at the lower humidities of 0%, 43% and 95% RH, but

decreased significantly at 100% RH, by approximately 50% of the undegraded threshold. The

corresponding crack growth rate curves for single representative specimens at each humidity

level are shown in Fig. 4.12. At relatively high crack growth rates, the curves were

indistinguishable. However, at lower crack growth rates approaching the threshold, the fatigue

performance at 100% RH was degraded appreciably. This behavior is consistent with the

explanation proposed in ref. [28], whereby the onset of degradation in fracture specimens was

related to the relative speed of moisture diffusion and crack advance. Figure 4.13 shows the

steady-state moisture concentration profile ahead of the crack tip for a crack moving at constant

crack growth rate exposed to 40ºC–95% RH environment, using the analytical diffusion relation

[29]:

D

vr

D

vrK

D

vr

D

vrK

C

C

s

2

cosexp

2

2

cosexp

2

00

0

0

(1)

where, C is the moisture concentration at a distance r ahead of the moving crack tip, r0 is the

crack tip radius (assumed as 1 µm), v is the crack speed, D is the diffusion coefficient, Cs is the

equilibrium moisture concentration at the crack tip, and K0 is the modified Bessel function of

second kind and order zero. The D and Cs values used for the adhesive were 1.34×10-12

m2/s and

3.34%, respectively, taken from ref. [30] where the hygrothermal properties were characterized

for the same adhesive used in this study. It can be seen from Fig. 4.13 that for crack growth rates

of 10-5

mm/cycle and above, the moisture diffusion ahead of the crack tip was less than about 10

µm, which was less than 10% of the plastic zone length at threshold. This was assumed to be a

negligible amount of water uptake which would not affect the properties of the crack tip region.

This explains the observed insensitivity of moisture to fatigue behavior at higher crack growth

rates.

88

The difference between the 100% RH experiments and those at lower RH may be due to

the presence of liquid water at the crack tip. This was investigated by applying a load to the

ADCB and photographing the crack tip immediately after the fatigue threshold was reached.

Figure 4.14 shows the presence of condensed water within the crack as a highly reflective band

behind the crack tip. Such moisture condensation was absent in joints tested at humidities below

saturation.

At elevated humidities, the presence of condensed water at a crack tip is usually

explained by capillary condensation, which is described by the Kelvin equation relating the

curvature of the liquid-air interface and the partial pressure of the water vapor [31]. The radius

of curvature increases exponentially as RH approaches the saturation level, thereby facilitating

condensation in ever wider cracks. Therefore, water condensation was observed in fatigue tests

at 100% RH, but not at 95% RH.

The condensed water at crack tip in 100% RH tests changes the exposure environment to

one similar to water immersion, which can significantly increase the saturated moisture

concentration in the adhesive. Gravimetric measurements using wafers of the adhesive (30 × 30

× 0.4 mm) showed that changing the exposure environment from 95% RH to water immersion

increased the saturated moisture concentration by 15% (i.e. from 4.75% at 95% RH to 5.47%

when immersed in water). The increased moisture concentration in the adhesive can also

increase the moisture available at the interface, thereby accelerating interfacial degradation. The

effects of the absorbed moisture were studied by observing the crack paths.

89

Figure 4. 11 Effect of RH on Gth for P2-etch pretreated ADCB joints tested at 40ºC. Given

values are average Gth (error bars indicate ± standard deviation). Numbers above each data point

indicate the number of thresholds reached and the number of specimens tested, respectively;

these two numbers are different in cases where a single specimen was used to reach two

thresholds.

Figure 4. 12 Effect of RH on the fatigue crack growth behavior of P2-etch pretreated ADCB

joints tested at 40ºC. Each data series is from a single specimen.

0

50

100

150

200

0 50 100

Gth

(J/m

2)

RH (%)

4, 33, 2

3, 2

3, 3

-7

-6

-5

-4

-3

-2

1.8 2.3 2.8 3.3

Lo

g (

da

/dN

)

Log Gmax (J/m2)

Dry

43% RH

95% RH

100% RH

90

Figure 4. 13 Moisture concentration versus distance ahead of crack tip for exposure to 40ºC-

95%RH environment at different crack growth rates. Crack tip radius assumed as 1 µm.

Figure 4. 14 Magnified image of a crack opening viewed from the side of the specimen showing

reflection from condensed water at the interface. Crack tip is to the right of the image.

0

0.2

0.4

0.6

0.8

1

0.000001 0.00001 0.0001 0.001

C/C

s

Distance ahead of crack tip (m)

10-7 mm/cycle

10-6 mm/cycle

10-5 mm/cycle

10-4 mm/cycle

91

Crack paths

Figure 4.15 compares the fracture surfaces of the thinner arms of the ADCB joints tested

under various humid environments. At higher crack speeds, the crack paths were very similar in

the four cases. Furthermore, as the crack speed decreased, in all cases the crack paths moved

closer to the more highly-strained adherend, a behavior that has also been reported under mixed-

mode loading in refs. [8,13,14]. At low crack growth rates near the threshold, this tendency may

have contributed to a marked change in the crack path of specimens tested at 100% RH

compared to those tested at the lower humidities. Near the threshold, the cracks became

interfacial in joints tested at 100% RH, but remained cohesive at the other humidities. This was

confirmed by looking at the failure surfaces in the threshold region using an optical microscope

for specimens tested at 95% RH and 100% RH, as shown in Fig. 4.16. The failure surface at

95%RH shows fragments of adhesive remaining on the adherend indicating a cohesive failure,

but at 100% RH no visible epoxy fragments were observed indicating an interfacial failure. This

was confirmed to be an interfacial failure by time-of-flight secondary ion mass spectrometry

(ToF-SIMS) analysis as explained in the next section.

92

Figure 4. 15 Failure surface of the joints tested at 40ºC and under RH levels of (a) 0%, (b) 43%,

(c) 95% and (d) 100%. On each failure surface the threshold region is indicated.

93

(a) (b)

Figure 4. 16 Magnified image of the failure surface on the highly-strained adherend at threshold

region for P2-etch pretreated joints tested under RH levels of (a) 95% and (b) 100%.

Failure surface analysis

Figure 4.17 compares the negative ToF-SIMS spectra of the bare P2-etched aluminum

and the adherend failure surface from the threshold region of a joint tested at 100% RH (as in

Fig. 4.15(d)). An increase in aluminum hydroxide species on the 100% RH specimen is evident

as an increase in the ratio of OH (m/z = 17 Da) to O (m/z = 16 Da); approximately 1.0 for the

bare P2-etch treated aluminum and 1.24 for the grey, threshold region of the failure surface.

This is also apparent in the increase of the heights of the peaks corresponding to the various

forms of hydrated Al2O3. The growth of hydrated aluminum oxides is associated with the

formation of a weaker interface [32], and would explain the poorer fatigue performance of

specimens tested at 100% RH.

Davis et al. [33] found that aluminum oxide hydration required an incubation time that

depended on the moisture concentration at the interface and the temperature. For example, the

incubation time varied from 3 min at 70ºC to 85 min at 40ºC for a bare FPL treated surface

94

subjected to water immersion [34]. The presence of water behind the crack tip might have

increased the moisture concentration just ahead of the crack tip beyond the critical level needed

to hydrate the oxide layer. This critical humidity level was found to be between 55-80% RH at

25ºC for cyclically loaded joints made from silane primed aluminum alloy bonded with epoxy

film [4]. In another study, Brewis et al. [35] found a critical moisture concentration in the

adhesive of 1.4% by quasi-static testing of aged single lap joints made from sandblasted

aluminum alloy bonded with an epoxide adhesive, and exposed to various humidities at 50ºC.

The present fatigue experiments showed a critical relative humidity at 40ºC of 100%,

corresponding to water condensation at the crack tip. Once a weak hydrate oxide layer was

formed by the condensed water (Fig. 4.17), the crack shifted to this weak oxide interface, leading

to a significant decrease in Gth.

At crack growth rates between the threshold and the linear Paris-law region, a distinct

horizontal inflection was observed in the crack growth rate curves of specimens tested at 100%

RH (Fig. 4.12). It was observed that this horizontal region of the curve corresponded to

interfacial failure, suggesting that the crack growth rate became independent of the applied G

once the crack path reached the interface. Michel et al. [36] observed a similar inflection in the

crack growth rate curve of several aluminum alloys tested in humid environments. They

explained that crack growth at such low applied G was solely due to fracture of the brittle oxide

layer at the crack tip, and not due to crack formation in the aluminum itself. Therefore, the crack

growth rate was proportional to the rate of formation of the oxide layer at the crack tip, which

depended on the environment and was independent of the applied G over a small range just

above the threshold (i.e. G over this range exceeded the critical value for the oxide film, but was

not high enough to cause crack growth in the alloy) [36]. It is believed that a similar mechanism

is responsible for the inflection in the present case for specimens tested at 100% RH (Fig. 4.12).

In the Paris law region, the crack path was near the interface but within the adhesive, so that

crack growth increment per cycle depended on the applied G. However, once the applied G was

low enough for the crack path to reach the interface, the crack growth rate was determined by the

rate at which the hydrated oxide layer formed ahead of the crack tip due to water diffusion. The

critical strain energy release rate for this hydrated oxide was smaller than the applied G over a

range just above the threshold, so that crack growth was independent of G, until it effectively

95

ceased at the threshold. When the applied G exceeded that of the inflection region, the crack

path moved out of the oxide layer and was governed by the fatigue properties of the adhesive.

(a)

(b)

Figure 4. 17 Negative ToF-SIMS spectra of the bare P2-etched aluminum and failure surface in

the mass/charge (m/z) ranges of (a) 0-200 m/z, and (b) 200-400 m/z. The failure surface was

from the P2-etch pretreated joint tested at 40C-100% RH in the threshold region on the thin

adherend side.

Fracture surface

P2-etched aluminum

Fracture surface

P2-etched aluminum

96

4.3.3 Combined effect of higher temperature and humidity

The combined effect of higher temperature and humidity is illustrated by comparing the

fatigue behavior of joints tested under hot-wet (40ºC and 100% RH) and room temperature dry

air (20ºC and <10% RH) environments. Figures 4.18 and 4.19 show that the Gth and crack

growth rate behavior measured in these environments with both P2-etched and coil coated (CC)

adherends was indistinguishable (t-test, 95% confidence). As was observed with P2-etch

pretreated joints, there was evidence of condensed water behind the crack tip leaving a dark grey

oxide layer on the failure surfaces of the CC pretreated joints in the hot-wet environment. This

grey region also showed hydrated aluminum oxides when analyzed using ToF-SIMS (Fig. 4.20).

The hot-wet environment affected the fatigue behavior in two ways: firstly, the fatigue

threshold was significantly decreased, and secondly, the crack growth curve shifted to the left,

indicating a higher crack speed in the hot-wet environment at a given Gmax. Both of these effects

can be explained from the understanding of the individual effects of temperature and humidity.

As was discussed earlier, at higher crack growth rates, moisture effects were negligible

because of the insufficient time for moisture to diffuse ahead of the crack tip. However,

increasing the temperature from 20ºC to 40ºC increased the size of the plastic zone which

increased the crack growth rate. Therefore, the increase in the crack speeds at higher G (higher

crack growth rates) was mainly due to the temperature increase. At lower crack growth rates, the

fatigue threshold was relatively insensitive to temperature (Fig. 4.3), and hence the poorer

fatigue behavior was due mostly to moisture condensing behind the crack tip at 100% RH and

weakening the interface.

97

Figure 4. 18 Effect of test environment on the Gth of ADCB joints made with P2-etch and CC

pretreatments. Number above each data point indicates the number of specimens tested in each

case, and error bars indicate the standard deviation in each case. Each specimen was used to

reach a single threshold.

0

40

80

120

160

200

240

RD Hot-wet

P2-etch CC

Gth

, J/m

2

3

3

33

98

Figure 4. 19 Effect of test environment on fatigue crack growth behavior of ADCB joints made

with P2-etch and CC pretreatments. Each data series represent a single specimen.

-7

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

log(d

a/d

N),

mm

/cycle

log (Gmax), J/m2

P2-etch RD

P2-etch hot-wet

CC RD

CC hot-wet

99

(a)

(b)

Figure 4. 20 Negative ToF-SIMS spectra of the failure surface between (a) 0-200 m/z, and (b)

200-400 m/z. The failure surface was from the CC pretreated joint tested at 40C-100% RH in

the threshold region on the thin adherend side.

4.4 Conclusions

The temperature and humidity of the test environment were found to have a significant

effect on the mixed-mode fatigue behavior of aluminum adhesive joints. Under dry conditions,

there was little change in the fatigue threshold over the temperature range 20-80ºC, but the crack

growth rate in the Paris law region increased significantly with increasing temperature, and the

crack path tended to move away from the interface. These observations were consistent with the

growth of the crack-tip plastic zone with increasing temperature, as predicted using finite

100

element modeling. A larger plastic zone would lead to greater damage accumulation, resulting in

increased crack growth rates and residual adhesive thickness.

Fatigue behavior was insensitive to ambient moisture at higher crack growth rates, but

became sensitive to the moisture level as crack growth rates neared the threshold where the

speed of moisture diffusion ahead of crack tip was greater than the crack growth rate. In

particular at 100% RH, the crack growth rate became independent of the applied strain energy

release rate, G, for a small range of G just above the threshold. This inflection in the curve of

crack growth rate vs. G may have been caused by the crack growth increment per cycle being

limited to the thickness of the hydrated oxide film forming at the crack tip between loading

cycles. This is analogous to the mechanism that has been proposed for a similar inflection

reported in the fatigue of aluminum alloys. As the humidity in the test environment reached the

saturation level, moisture condensed behind the crack tip. It is believed that this increased water

diffusion to the point where it exceeded a critical moisture level needed to hydrate the oxide

layer ahead of the crack tip. This hydration may then have caused a shift in crack path to the

interface and a decrease in Gth.

Finally, the combined effects of elevated temperature and humidity were explained from

this understanding of the individual effects of temperature and humidity. At higher crack growth

rates, the joint fatigue performance degraded solely due to the increased temperature, whereas at

low crack growth rates, fatigue performance degraded predominantly because of the elevated

moisture. These effects of a hot-wet testing environment on fatigue behavior were found to be

similar for both a P2-etch pretreatment and a commercial coil-coat pretreatment.

The present work addressed the effect of the immediate testing environment on the

fatigue behavior of these adhesive joints. The degradation produced by long-term exposure to

hot-wet conditions can have additional effects on fatigue. This has been examined recently using

an open-faced adhesive joint to accelerate aging with this same adhesive system [37].

101

4.5 References

1. Ashcroft IA, Shaw SJ. Mode I fracture of epoxy bonded composite joints 2. Fatigue

loading. Int J Adhes Adhes 2002;22:151-67.

2. Harris JA, Fay PA. Fatigue life evaluation of structural adhesives for automotive

applications. Int J Adhes Adhes 1992;12:9-18.

3. Ashcroft IA; Hughes DJ; Shaw SJ, Abdel Wahab M, Crocombe A. Effect of Temperature

on the Quasi-static Strength and Fatigue Resistance of Bonded Composite Double Lap

Joints. J Adhes 2001;75:61-88.

4. Abel ML, Adams ANN, Kinloch AJ, Shaw SJ, Watts JF. The effects of surface

pretreatment on the cyclic-fatigue characteristics of bonded aluminium-alloy joints. Int J

Adhes Adhes 2006;26:50-61.

5. Curley AJ, Hadavinia H, Kinloch AJ, Taylor AC. Predicting the service-life of

adhesively-bonded joints. Int J Fract 2000;103:41-69.

6. Kinloch AJ, Little MSJ, Watts JF. The role of the interphase in the environmental failure

of adhesive joints. Acta Mater 2000;48:4543-53.

7. Fernando M, Harjoprayitno WW, Kinloch AJ. A fracture mechanics study of the

influence of moisture on the fatigue behaviour of adhesively bonded aluminium-alloy

joints. Int J Adhes Adhes 1996;16:113-119.

8. Datla NV, Papini M, Schroeder JA, Spelt JK. Modified DCB specimen for mixed-mode

fatigue testing of adhesively bonded thin sheets. Int J Adhes Adhes 2010;30:439-47.

9. Briskham P, Smith G. Cyclic stress durability testing of lap shear joints exposed to hot-

wet conditions. Int J Adhes Adhes 2000;20:33-38.

10. Chen NNS, Niem PIF, Lee RC. Fatigue Behaviour of Adhesive Bonded Joints. J Adhes

1987; 21:115-28.

11. Ritter JE, Lardner TJ, Grayeski W, Prakash GC, Lawrence J. Fatigue crack propagation at polymer

adhesive interfaces. J Adhes 1997; 63:265-84.

12. ASTM D2651, Standard guide for metal surfaces for adhesive bonding. West

Conshohocken (PA): ASTM International; 2001.

102

13. Azari S, Papini M, Schroeder JA, Spelt JK. The effect of mode ratio and bond interface

on the fatigue behavior of a highly-toughened epoxy. Eng Fract Mech 2010; 77:395-414.

14. Azari S, Papini M, Schroeder JA, Spelt JK. Fatigue threshold behavior of adhesive joints.

Int J Adhes Adhes 2010;30:145-59.

15. ASTM E104, Standard practice for maintaining constant relative humidity by means of

aqueous solutions. Philadelphia (PA): ASTM International; 1985.

16. Greenspan L. Humidity fixed points of binary saturated aqueous solutions. J. Research

National Bureau Standards A: Physics and Chemistry 1977; 81:89–96.

17. Ameli A, Papini M, Schroeder JA, Spelt JK. Fracture R-curve characterization of

toughened epoxy adhesives. Eng Fract Mech 2010;77:521-34.

18. ASTM E647, Standard test method for measurement of fatigue crack growth rates. West


19. Aluminum standards and data, 2nd

edition, The Aluminium Association, Inc.,

Washington, DC (1982).

20. Li JX, Wen XY, Man CS, Zhai T. Fatigue of continuous cast AA5754 Al alloy sheet.

Mater Sci Eng 2007; 23:324-32.

21. Hutchinson JW, Suo Z. Mixed-mode cracking in layered materials. Adv Appl Mech

1992; 29:63-191.

22. Hwang JF, Manson JA, Hertzberg RW, Miller GA, Sperling LH, Fatigue crack

propagation of rubber-toughened epoxies, Polym Engng Sci 1989; 29:1477–1487.

23. Lang RW, Manson JA, Crack tip heating in short-fibre composites under fatigue loading

conditions, J Mater Sci 1987; 22:3576–3580.

24. Kinloch AJ, Shaw SJ. The fracture resistance of a toughened epoxy adhesive. J Adhes

1981;12:59-77.

25. Knot JF. Fundamentals of fracture mechanics. New York: John Wiley-Halsted Press;

1973.

26. Azari S, Papini M, Spelt JK. Effect of adhesive thickness on fatigue and fracture of

toughened epoxy joints-Part II. Analysis and finite element modeling. Eng Fract Mech

2011;78:138-52.

27. Suo Z, Hutchinson JW. Sandwich test specimens to measuring interface crack toughness.

Mater Sci Eng 1989; A107:135-43.

103

28. Kinloch AJ, Korenberg CF, Tan KT, Watts JF. Crack growth in structural adhesive joints

in aqueous environments. J Mater Sci 2007; 42:6353-70.

29. Kasul DB, Heldt LA. Embrittlement of B2 iron aluminide by water vapor and by

hydrogen. Metall Mater Trans A 1994; 25:1285-90.

30. Ameli A, Datla NV, Papini M, Spelt JK. Hygrothermal properties of highly toughened

epoxy adhesives. J Adhes 2010;86:698-725.

31. Crichton SN, Tomozawa M, Hyden JS, Suratwala TI, Campbell JH. Subcritical Crack

Growth in a Phosphate Laser Glass. J Am Ceram Soc 1999; 82:3097-104.

32. Venables JD. Adhesion and durability of metal-polymer bonds. J Mater Sci 1984;

19:2431-53.

33. Davis GD, Whisnant PL, Venables JD. Subadhesive hydration of aluminum adherends

and its detection by electrochemical impedance spectroscopy. J Adhes Sci Technol 1995;

9:433-42.

34. Davis GD, Krebs LA, Drzal T, Rich J, Askland P. Electrochemical sensors for

nondestructive evaluation of adhesive bonds. J Adhes 2000; 72:335-58.

35. Brewis DM, Comyn J, Raval AK, Kinloch AJ. The effect of humidity on the durability of

aluminium-epoxide joints. Int J Adhes Adhes 1990; 10:247-53.

36. Michel SA, Kieselbach R, Figliolino M. Environmental and frequency effects on fatigue

crack growth rate and paths in aluminium alloy. Fatig Fract Eng Mater Struct 2005;

28:205-14.

37. Datla NV, Ulicny J, Carlson B, Papini M, Spelt JK. Mixed-mode fatigue behavior of

degraded toughened epoxy adhesive joints. Int J Adhes Adhes 2011; 31:88–96.

104

Chapter 5 Mixed-mode fatigue behavior of degraded toughened epoxy

adhesive joints

5.1 Introduction

Moisture can degrade adhesive joints by damaging the adhesive-adherend interfacial

region or the adhesive itself. The effect of moisture on bulk epoxy adhesives depends on

whether the absorbed water molecules are in a free or bound state [1]. Free water molecules

plasticize and soften the adhesive, decreasing its glass transition temperature [2]; however, these

effects are reversible upon drying. Bound water molecules, on the other hand, introduce

irreversible damage to the adhesive by hydrolysis and chain scission [3]. Su et al. [4] studied the

fatigue degradation of steel double lap joints made from several different epoxy adhesives

subjected to different aging environments, and found that the adhesive that absorbed the most

moisture also degraded the most. Hence, it is important to characterize the moisture diffusion

behavior of an adhesive in order to understand its fatigue degradation behaviour.

The fatigue behaviour of fresh (undegraded) adhesive joints has been studied extensively

in ambient test environments [5,6] and aggressive test environments [7-9]; however, the fatigue

performance of aged adhesive joints is not well understood. Ferreira et al. [10] found that

increasing the temperature of the aging environment decreased the fatigue life of composite

adhesive lap joints, and related this behaviour to the increased creep deformation with

temperature. Lubke et al. [11] found that the fatigue behavior of epoxy-aluminum DCB joints

degraded more in a high-humidity aging environment than in a natural outdoor environment;

however, only mode I loading was considered. In contrast, Su et al. [4] found that the fatigue

life of epoxy-steel double lap joints was more or less the same in both outdoor and high-humidity

environments. In all these tests, the closed adhesive joints were first aged for relatively long

periods and then fatigue tested in an ambient environment.

Closed joints are usually used in degradation studies, although they take a long time to

degrade due to the length of the diffusion paths, and the degradation is non-uniform across the

joint area. This non-uniform degradation makes it difficult to associate a loss of joint strength

105

with a particular level of degradation. These limitations can be overcome using open-faced

specimens that reduce the length of diffusion path to the thickness of the adhesive layer, thus

producing a relatively uniform state of moisture concentration and degradation in a relatively

short period of time. Open-faced specimens have previously been used to study degradation

under quasi-static loading [12-16], and the present study extends their application to cyclic

loading.

This paper investigates the effect of the aging environment on the mixed-mode fatigue

behavior of open-faced joints made with aluminum alloy adherends and a highly-toughened

epoxy adhesive. The experiments illustrate the effects of aging time and temperature on both the

fatigue threshold and crack growth rates (CGR). The experiments also compare the durability of

joints aged in constant humidity and cyclic environments.

5.2 Experiments

5.2.1 Specimen preparation

Both open-faced and closed asymmetric double cantilever beam (ADCB) specimens were

made using a proprietary DGEBA-based, heat-cured, rubber-toughened structural epoxy

adhesive and AA5754-O aluminum sheet with a commercial coil-coated pretreatment. Since this

pretreatment could not be reliably reproduced on thicker bars, fatigue test specimens were made

with 2 mm thick sheets that had been commercially pretreated. To avoid yielding of these

relatively thin sheets while applying a wide range of strain energy release rates, G, the

reinforcement technique discussed in ref. [17] was used; i.e. the sheet was stiffened by bonding it

to an AA6061 aluminum bar using a “reinforcing” layer of adhesive.

Open-faced specimens

The fatigue behavior was studied in various environments using open-faced ADCB

specimens. On one side of the sheet, a 0.4 mm thick “primary” layer of adhesive was cast using

a backing plate coated with polytetrafluroethylene release agent, while the other side of the sheet

was reinforced by attaching it to a 12.7 mm thick P2-etched aluminum AA6061 bar using a 0.4

mm thick reinforcing layer of adhesive (Fig. 5.1). Since under mixed-mode loading the crack

path is close to the more highly-strained adherend [18], the reinforced pretreated sheet was used

106

only as one of the adherends and the other adherend was made from a thicker aluminum bar.

The desired bond-line thickness was achieved by placing 0.4 mm size piano wires in both the

primary and reinforcing adhesive layers. Since both the primary and reinforcing layers utilized

the same adhesive, both layers could be cured in a single step using the cure profile recommend

by the manufacturer; i.e., at least 30 min at 180ºC. The assembly was clamped using large

binder clips (25.4 mm wide by 50.8 mm long, from ACCO brands) that were centered directly

above the spacing wires in both adhesive layers to avoid an uneven bondline thickness. After

curing, the backing plate was removed and the open-faced specimens (Fig. 5.1) were exposed to

various environments for a range of times, as shown in Tables 5.1 and 5.2.

The present experiments focused on the effects of irreversible degradation by drying the

aged specimens in a vacuum oven containing anhydrous calcium sulphate at 40ºC for

approximately 7 days. This eliminated reversible effects such as plasticization by water

molecules [13]. After drying, the complete ADCB specimen (Fig. 5.2) was made by bonding the

primary adhesive layer of the open-faced specimen to a 25.4 mm thick P2-etched aluminum

AA6061 bar using a 0.25 mm thick “secondary” layer of adhesive (the P2 etch uses sulphuric

acid as described in [19]). The bondline thickness of the secondary layer was achieved by

placing 0.65 mm diameter (sum of primary and secondary layer thicknesses) piano wires

between the sheet and the second adherend in locations without adhesive. In order to improve

the bonding between the primary and secondary adhesive layers, the degraded primary layer was

sanded lightly with a 100 grit sand paper, wiped with acetone and then dried prior to the

application of the secondary adhesive. After the secondary cure, the excess adhesive on the sides

of the specimen was removed using a belt sander with a 120 grit sand paper and water as a

coolant, followed by hand sanding with a 600 grit sand paper. A thin layer of white paper

correction fluid diluted with hexane was then applied to enhance the observation of the crack tip

during the fatigue testing.

107


diffusion into the primary adhesive layer.

Table 5. 1 Stages of the cyclic aging environment. Salt spray was applied in the ambient stage

four times for 30 s each.

Aging Stage Temperature and Humidity Elapsed Time (h)

Ambient stage 25±3ºC, 45±10% RH 0-8

Humid stage 49±2ºC, 100% RH 8-16

Dry stage 60±2ºC, <30% RH 16-24

Table 5. 2 SDF model parameters of the adhesive for both humid environments studied. Each

data point is the average of three repetitions, where SD indicates the standard deviation.

Environment H2O content

(g/m3)

Absorption Desorption

D1±SD

(10-14

m2/s)

D2±SD

(10-14

m2/s)

M1∞±SD

(%)

M∞±SD

(%)

td1/2

(s1/2

)

Mr

(%)

40ºC and

95% RH 48.0 134±17 3.9±0.7 3.34±0.09 4.78±0.15 532 1.40

60ºC and

95% RH 121.7 314±25 8.9±0.9 3.68±0.11 6.98±0.18 315 1.72

Closed specimens

To investigate whether the presence of the secondary adhesive layer had any effect on the

fatigue behavior of the adhesive primary layer, fatigue tests were also carried out on closed

108

ADCB specimens made with a single 0.4 mm thick layer of adhesive between the sheet and

second adherend. This choice of bondline thickness was made following the work of Ameli et

al. [16], who found that the fracture toughness of double-layer joints depended on the thickness

of the primary layer of adhesive, but not on the combined thickness of the primary and secondary

layers. Therefore, the thickness of the adhesive layer in these closed specimens was chosen to be

equal to the thickness of the primary layer in the open-faced specimens. The configuration of

these closed specimens was the same as the open-faced specimens (Fig. 5.2), except for the

absence of the secondary adhesive layer.

Figure 5. 2 Configuration of open-faced reinforced ADCB specimen after being closed

(dimensions in mm, not to scale). The thickness of primary, secondary, and reinforcing adhesive

layers are 0.4, 0.25, and 0.4 mm, respectively, and the thickness of the sheet is 2 mm. Width of

the specimen was 19 mm. The location of the clip gauge is also shown. The upper adherend is

the open-faced adherend shown in Fig. 5.1.

5.2.2 Aging conditions

Open-faced specimens were exposed to either a constant or cyclic humidity environment.

Two different constant humidity environments were used: one at 40ºC and other at 60ºC, both at

95% relative humidity (RH). A constant RH was achieved by placing the specimens in air-tight

plastic containers that contained a saturated salt solution of K2SO4. To maintain a constant

temperature, the containers were placed in temperature controlled ovens.

109

For the cyclic environment, the conditions were varied between the ambient, humid, and

dry stages in a daily cycle as shown in Table 5.1. During the ambient temperature stage, the

specimens were exposed to a salt spray (salt fog) four times for 30 s each, as described in ref.

[20]. The salt solution used in the salt fog was composed of 0.9% NaCl, 0.1% CaCl2, and

0.075% NaHCO3 (percentages by weight).

5.2.3 Gravimetric measurements

The moisture uptake of the adhesive was characterized using gravimetric measurements

of two sets of three adhesive wafers (30×30×0.4 mm) immersed in either salt water or deionised

water. To ensure an initially dry state, the samples were kept in a vacuum oven at 40ºC for 7

days prior to immersion. The mass uptake was measured by weighing the wafers at fixed time

intervals, after removing them from the liquids and drying them with clean tissue paper.

5.2.4 Fatigue tests

Fatigue testing was performed with a servo-hydraulic load frame under displacement

control using a sinusoidal waveform at a frequency of 20 Hz. A constant displacement ratio (i.e.

ratio of minimum to maximum displacement, δmin/δmax) of 0.1 was used. The testing began with

the application of the highest strain energy release rate, G, which then decreased as the crack

grew under constant displacement until the threshold crack growth rate of 10-6

mm/cycle was

reached at the threshold strain energy release rate, Gth. The joints were enclosed in a chamber

containing desiccant to maintain a room temperature dry environment (<10% RH) while testing.


The crack length was measured using both optical and specimen compliance methods.



photographs of the crack tip, load cycling was stopped and held at the mean load for 15 s every

9,000 cycles. The specimen compliance was obtained from the relationship between the crack

opening and the applied force during the unloading portion of the loading cycle. A clip gauge

(model 3541, Epsilon Technology Corp., Jackson, WY, USA) recorded the opening

110

displacement at the loading pins (Fig. 5.2). For each specimen, a polynomial relationship

between the optically observed crack length and the specimen compliance was established

according to ASTM E647 [21]. Using this relationship, the crack length was inferred from the

continuous clip gauge compliance data, and used in all calculations of crack growth rate and G.


A beam-on-elastic-foundation model for unequal adherends was used to calculate G and

phase angle, Ψ (defined as III GGarctan , where GI and GII are the mode I and mode II

strain energy release rates, respectively), from the measured force and crack length [17]. The

average phase angle calculated using the model was 14° for the ADCB specimen, with only a

negligible change occurring as the crack grew. For example, Ψ increased by only 2° for an

increase in crack length from 40 to 120 mm [17]. The phase angle in the closed open-faced

joints was essentially the same as that in the closed joints that were made for comparison without

the secondary adhesive (difference of less than 0.5°).

5.2.5 Measurement of residual adhesive thickness

To define the crack path, the thickness of the residual adhesive on some of the fracture

surfaces was measured at various crack lengths on the more highly-strained adherend. The

elevation datum corresponding to the steel interface was established by removing residual

adhesive from a narrow region on both sides of the joint width using a solvent (mixture of

methylene chloride and methyl alcohol; Glue Buster, Kosmic Surf-Pro Inc., Saint Amable,

Quebec). An optical profilometer (NANOVEA ST400, Micro Photonics Inc. CA, USA) was

used to make a line scan across the width of the joint with both ends on the datum regions,

thereby giving the thickness of the residual adhesive layer.


5.3.1 Moisture diffusion

For constant humidity environments, the water absorption of the present adhesive was

previously found to be non-Fickian, with a pseudo-equilibrium state at intermediate exposure

times before reaching a final saturation state [22]. The water desorption, however, was found to

111

follow a simple Fickian trend [22]. The diffusion coefficient of the first stage and the saturated

were both functions of temperature. Desorption studies showed that even after prolonged drying

the adhesive retained a significant amount of water, and that the amount of retained water was

proportional to the fractional mass uptake at the end of the second stage. This absorption and

desorption behavior was characterized using a sequential dual Fickian (SDF) model [22], which

is described in Appendix 1.

Figure 5.3 shows the measured moisture mass uptake and the fitted SDF model versus the

square root of time for the adhesive wafers immersed in salt water and deionised water. Table

5.3 lists the SDF model parameters of the adhesive under both immersion conditions. At room

temperature, the second diffusion mechanism was absent and the moisture uptake followed a

simple Fickian behavior where both the second stage diffusion coefficient, D2, and fractional

mass uptake, M2, were equal to zero. Furthermore, insignificant differences in the fractional mass

uptake M1∞, and diffusion coefficient D1, of the first stage were observed between both

immersion environments (t-test, 95% confidence interval), indicating that the salt did not affect

the moisture diffusion behavior at room temperature.

At 40ºC the moisture uptake followed a non-Fickian behavior, as also seen in [22]. The

first stage of diffusion was similar for both immersion conditions (insignificant difference in M1∞

and D1, t-test 95% confidence), whereas in the second stage the saturated mass uptake was

significantly lower for the samples that were immersed in salt water than for those immersed in

deionised water. This is consistent with previous work which demonstrated that increases in the

concentration of the NaCl in a salt solution decreases the saturated water mass uptake into an

adhesive due to osmosis [23,24]. Since the effect of the salt was observed only in the second

stage of diffusion, this implies that the osmotic effects were predominant only during the second

stage. Furthermore, using the same adhesive used in this study, Ameli et al. [22] showed that the

diffusion mechanism in the first stage is governed by chemical interaction between the water

molecules and the epoxy matrix, whereas the diffusion mechanism in the second stage is

governed by relatively mobile water molecules in the adhesive. Therefore, it can be concluded

that the salt water environment produces an osmotic pressure that does not affect the chemical

interactions of the water molecules with the adhesive, but affects the diffusion kinetics of the

mobile water molecules in the epoxy during the second stage of absorption.

112

(a)

(b)


based on SDF model (Appendix) when immersed in salt water and deionised water at (a) room

temperature and (b) 40ºC. Each data point is an average of three repetitions. The standard

deviation in each case was approximately 2%.

0

1

2

3

4

5

0 500 1000 1500 2000 2500

Mt(%

)

t1/2 (s1/2)

Salt water

Deionised water

0

1

2

3

4

5

6

7

8

9

0 500 1000 1500 2000 2500

Mt(%

)

t1/2 (s1/2)

Salt water

Desionised water

113

Table 5. 3 SDF model parameters of the adhesive immersed in salt water and deionised water.

Each data point is the average of three repetitions, where SD indicates the standard deviation.

Temperature Solution D1±SD

(10-14

m2/s)

D2±SD

(10-14

m2/s)

M1∞±SD

(%)

M∞±SD

(%)

td1/2

(s1/2

)

20ºC Salt water 37.6±5 - 3.64±0.1 3.64±0.1 ∞

Deionised water 30.72 - 3.53±0.1 3.53±0.1 ∞

40ºC Salt water 150±11 16.66±5 4.22±0.2 6.26±0.1 580

Deionised water 136±30 16.45±4 4.06±0.1 5.46±0.1 580

5.3.2 Fresh open-faced specimens

To provide a baseline to which the effect of degradation can be compared, fatigue tests

were conducted on fresh open-faced specimens. For these specimens, the secondary layer of

adhesive of 0.25 mm thickness was applied and cured immediately after the primary layer was

cured. The measured fatigue threshold strain energy release rate, Gth, of these joints was 125±9

J/m2 (± standard deviation, 3 threshold measurements with each threshold from a single

specimen).

The primary difference between an open-faced joint that has been closed to form an

ADCB and a conventional closed joint is the presence of the secondary adhesive layer. This will

increase the local compliance slightly and introduce a second cure cycle to the primary adhesive

layer. To investigate these effects, the fatigue behavior of fresh open-faced joints was compared

to that of the conventional closed joints that were prepared with a 0.4 mm thick single layer of

adhesive. Figure 5.4 shows that the average Gth of the open-faced specimens was 9% lower than

that of the closed joints, but this difference was considered small although the t-test showed that

the difference was statistically significant at the 95% confidence level. Furthermore, Fig. 5.5

shows that the crack growth rate curves of both the closed and open-faced joints overlap,

indicating a similar fatigue crack growth behavior. In all tests using the ADCBs made from the

open-faced joints, the fatigue crack path was within the primary adhesive layer. Hence, it was

concluded that the presence of the secondary adhesive layer and the second cure cycle had an

insignificant effect on the fatigue behavior of the primary adhesive layer. This is consistent with

114

the fracture test results of Ameli et al. [16], who showed an insignificant effect of a second cure

cycle on the quasi-static critical strain energy release rate of conventional closed DCB joints

prepared with the same adhesive used in the present study.

Figure 5. 4 Measured Gth of fresh closed and open-faced joints tested in a room temperature and

dry air environment. The 3 test repetitions are shown in each case, with Gth for each specimen

shown above the columns.

117133

123141135

151

0

50

100

150

200

Open-faced Closed

Gth

, J/m

2

115

Figure 5. 5 The measured fatigue crack growth rate curves of unaged closed and unaged open-

faced joints tested in a room temperature and dry air environment.

5.3.3 Aging of joints in constant humidity environments

5.3.3.1 Effect of aging time and temperature on Gth

Figure 5.6 shows the variation of Gth with aging time for 95% RH at 40ºC and 60ºC, and

the average Gth of unaged open-faced joints. The curves are the least-squares power function fits

at each temperature. Two stages of degradation were observed in each environment. In the first

stage, the threshold for the joints aged at 60ºC decreased by 65% (125±9 to 43±6) and by a lesser

amount, 54% (125±9 to 58±4) for the joints aged at 40ºC. In the second stage, Gth remained

constant at a low value with further aging. Increasing aging temperature also increased the rate

at which the joints degraded and decreased the time to the onset of the second stage; i.e.

approximately after two weeks at 60ºC and after one month at 40ºC.

The quasi-static fracture toughness of the adhesive used in this study was found

previously to degrade in three stages [12]. Although these results were established with a

different pretreatment, since the crack path was cohesive in both the present study and that of ref.

-7

-6

-5

-4

-3

-2

1.8 2.2 2.6 3

Lo

g(d

a/d

N),

mm

/cycle

Log(Gmax), J/m2

Closed #1

Closed #2

Open face #1

Open face #2

Open face #3

116

[12], the effect of pretreatment should be negligible. In the quasi-static fracture study of ref.

[12], the first two stages of degradation were similar to those described above, but during the

third stage, after very long aging times, the critical quasi-static fracture toughness decreased

further. In the present study, it was not possible to determine whether a third stage of

degradation might exist for specimens aged over 6 months at 60ºC and 95% RH, because fatigue

cracks grew in the reinforcing adhesive layer rather than in the primary adhesive layer for these

long exposure times. This occurred because moisture diffused into the reinforcing layer from the

exposed sides of the open-faced joint, reaching moisture concentrations of 3.8% at centre and

6.98% at the edges of the reinforcing layer. This absorbed moisture was not completely

desorbed while drying the primary adhesive layer, and probably caused damaging internal

stresses to develop during the secondary cure cycle. Hence, the reinforcing layer was weaker

than the primary layer. This limitation could have been avoided by applying an additional sealant

to the sides of the open-faced specimens.

Figure 5. 6 Fatigue threshold vs. aging time for specimens aged under 40ºC-95% RH and

60ºC-95% RH environments. Trend lines show the exponential regression lines fit to the data.

Numbers next to each data point indicate the number of thresholds reached and the number of

y = 188.96x-0.292

R² = 0.8849

y = 90.93x-0.175

R² = 0.93260

25

50

75

100

125

150

0 30 60 90 120 150

Gth

, J/m

2

Aging time, days

40ºC, 95% RH

60ºC, 95% RH

1,12,2

2,2

2,1

1,1

3,3

4,3

3,3

3,3

117

specimens tested, respectively; these two numbers are different cases where a single specimen

was used to reach two thresholds. Error bars represent the range of the measurements.

5.3.3.2 Effect of aging time and temperature on crack growth behavior

Figure 5.7 shows the scatter in the crack growth rate curves of specimens aged for two

months at 40ºC and 60ºC. It can be seen that the scatter is comparable in both degraded and

fresh specimens (Fig. 5.5). Figure 5.8 shows the variation in the crack growth rate curves with

aging time at 40ºC and 60ºC, respectively. At shorter aging times (up to one month at 40ºC and

one week at 60ºC), insignificant differences were observed between the crack growth rate curves

of fresh and aged joints. However, as the aging time increased, the crack growth rates at a given

applied Gmax increased (i.e. the curves for the aged joints began to shift upward). This happened

sooner and to a large extent at 60ºC than at 40ºC, reflecting the accelerating effect of temperature

on fatigue degradation. This is illustrated further in Fig. 5.9, which shows that the differences in

the crack growth rates at the two aging temperatures were insignificant after the first week of

aging, and grew after that. For example, at an applied Gmax of 250 J/m2, the crack speeds were

0.4, 5.8, 8.5 and 7.9 times greater at 60ºC than at 40ºC for aging times of one week, two weeks,

one month and two months, respectively.

The threshold and crack growth rate behaviors were affected differently by degradation.

At 60ºC, Gth decreased to a saturated level after two weeks of aging, whereas the fatigue crack

growth rate continued to increase until after 4 months of aging. It is hypothesized that the

fatigue failure mechanisms near the threshold are different from those at higher crack growth

rates. Indeed, using a rubber toughened epoxy adhesive, Azimi et al. [25] showed that adhesive

toughening mechanisms were absent at crack growth rates close to the threshold, and that the

fatigue behavior was similar to an unmodified epoxy. Hence, it is likely that the continuing

increase in the crack growth rate with aging time was related to the loss of the toughening

mechanisms from the rubber particles, and the decrease in Gth was related to the degradation of

the epoxy matrix.

118

Figure 5. 7 Repetitions of the measured fatigue crack growth rate curves of specimens aged for

60 days at 40°C–95% RH and 60°C–95% RH. Two specimens aged at each condition.

(a)

-7

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

Lo

g(d

a/d

N),

mm

/cycle

Log(Gmax), J/m2

60ºC-95%RH #1

60ºC-95%RH #2

40ºC-95%RH #1

40ºC-95%RH #2

-7

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

Fresh

7 days

14 days

28 days

60 days

119

(b)

Figure 5. 8 Measured fatigue crack growth rate curves of specimens aged at (a) 40°C–95% RH

and (b) 60°C–95% RH. Aging time in days is given in the legend.

-7

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

Fresh

7 days

14 days

28 days

60 days

132 days

120

(a)

(b)

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

1 week

Fresh

40ºC - 95% RH

60ºC - 95% RH

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

2 weeks

Fresh

40ºC - 95% RH

60ºC - 95% RH

121

(c)

(d)

Figure 5. 9 Effect of aging temperature on the crack growth rate curves for specimens aged for

(a) 1 week, (b) 2 weeks, (c) 1 month, and (d) 2 months. Each line is the least-squares fit to the

linear Paris region of the crack growth curves shown in Fig. 5.8.

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

1 month

Fresh

40ºC - 95% RH

60ºC - 95% RH

-6

-5

-4

-3

-2

1.4 1.8 2.2 2.6 3

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

2 months

Fresh

40ºC - 95% RH

60ºC - 95% RH

122

5.3.3.3 Effect of aging time and temperature on crack path

Figure 5.10 shows that the crack paths in both the unaged and aged joints were cohesive

at all crack growth rates. Furthermore, the thickness of the residual adhesive on the more highly-

strained open-faced adherend decreased with decreasing crack growth rate (decreasing Gmax) in

all specimens (Fig. 5.11). In [17], a similar trend was explained in terms of the decreasing size

of the plastic zone at the tip of the crack as the applied G decreased. Assuming that the average

crack path tends toward the centre of the plastic zone, the residual adhesive thickness will also

decrease as the applied G decreases and the crack slows. Related to this argument, Fig. 5.11 also

shows that at a relatively high crack growth rates, the thickness of the residual adhesive

decreased with aging due to the lower associated G levels and the resulting smaller crack tip

plastic zones. The residual adhesive thickness in the threshold region did not change appreciably

with aging time.

Figure 5. 10 Fracture surfaces on the more highly-strained (reinforced) adherend for: (a) unaged

joint, (b) 2 weeks aged at 60ºC – 95% RH, and (c) 4 months aged at 60ºC – 95% RH.

123

Figure 5. 11 Thickness of the residual adhesive on the fracture surface of the more highly-

strained adherend as a function of crack growth rate for a fresh joint and a joint aged for four

months at 60ºC – 95% RH.

5.3.4 Aging of joints in cyclic environment

Figures 5.12 and 5.13 show the Gth and crack growth rate curves of open-faced joints

aged in the cyclic environment for two and four weeks, respectively. Statistically insignificant

differences were observed in Gth and the slope of the linear Paris regions of the fresh and aged

joints (t-test, 95% confidence), indicating that the joints were undegraded even after four weeks

of aging in the cyclic environment. In contrast, Figs. 5.6 and 5.8 show that, for the same aging

time, the joints degraded significantly in the constant humidity environments. For example, after

4 weeks of aging, Gth of the joints aged in the constant humidity environment decreased by 62%

(from 125±10 to 47 J/m2) at 60ºC – 95% RH and by 42% (from 125±10 to 72±4 J/m

2) at 40ºC –

95% RH, whereas Gth of the joints aged in the cyclic humidity environment increased slightly by

3% (from 125±9 to 128±11 J/m2). It was therefore hypothesized that the moisture concentration

in the specimens aged in the cyclic environment was below that in the specimens aged in the

0

20

40

60

80

-7 -6 -5 -4 -3 -2 -1

Th

ickne

ss, µ

m

Log(da/dN), mm/cycle

Fresh

4 months

124

constant humidity environments. To investigate this hypothesis, a two-dimensional finite

element model was used to estimate the moisture concentration in the adhesive for specimens

aged in the cyclic environment.

The cross-section (0.4×18 mm) of the adhesive layer was modeled using a total of 192 4-

node thermal PLANE55 elements (ANSYS 12.0, Canonsburg, PA, USA), used with a thermal –

diffusion analogy. The top surface and the sides of the adhesive were assumed to be at the

saturated moisture concentration, and moisture transfer was prevented on the bottom surface. To

simplify the model, water diffusion was approximated using Fick’s law rather than the more

accurate dual-Fickian mode. Table 5.4 shows the adhesive diffusion parameters that were used

for the different stages of the cyclic aging environment of Table 5.1. These diffusion parameters

were taken to be those measured in [22], for the same adhesive used in the present study. Mesh

refinement did not change the moisture concentration at the adhesive-adherend interface by more

than 0.1%.

Figure 5.14 shows the finite element model predictions of the moisture concentration

versus aging time at the adhesive-adherend interface, which is the locus of failure in the

threshold region. It can be seen that the moisture concentration at this interface reached a cyclic

equilibrium, varying between 2.2% and 4.3% after the third day of aging. These concentrations

were significantly below the saturated moisture concentrations of 4.8% and 7.0% at 40ºC and

60ºC aging environments, respectively. Moreover, these levels of water uptake would not

increase with longer exposure to the cyclic environment since drying and absorption reached a

cyclic equilibrium. This explains why the fatigue behavior of the joints aged in the cyclic

environment would be superior to that of joints aged in the constant humidity environments.

Moreover, the intermittent salt spray application did not appear to accelerate the degradation

process, probably because of the decreased saturated moisture concentration in the adhesive in

the presence of the salt solution. Finally, the thermal cycling aspect of this accelerated aging test

did not seem to produce any measureable effect.

125

Figure 5. 12 Fatigue threshold versus aging time for open-faced specimens aged in the cyclic

environment. Numbers next to each data point indicate the number of thresholds reached and the

number of specimens tested, respectively; these two numbers are different cases where a single

specimen was used to reach two thresholds. The error bars show ± 1 standard deviation.

0

40

80

120

160

0 7 14 21 28 35

Gth

(J/m

2)

Aging time (days)

3,23,3

3,3

126

Figure 5. 13 Crack growth rates versus applied Gmax for specimens aged in the cyclic

environment. Three specimens at each aging condition.

Table 5. 4 Moisture diffusion parameters of the adhesive used in the finite element model. Data

is from [17].

Aging Stage D (10-14

m2/s) M∞ (%)

Ambient stage 45 1.78

Humid stage 207 6.67

Dry stage 271 1.62

-7

-6

-5

-4

-3

-2

2 2.4 2.8 3.2

Lo

g(d

a/d

N),

mm

/cycle

Log(Gmax), J/m2

Fresh

14 days #1

14 days #2

14 days #3

28 days #1

28 days #2

28 days #3

127

Table 5. 5 Moisture concentration (mass of water per unit mass of adhesive) profile at the

adherend-adhesive interface of the open-faced specimen exposed to the cyclic environment.

5.4 Conclusions

The mixed-mode fatigue behavior of degraded toughened epoxy-aluminum adhesive

joints was studied using open-faced ADCB specimens. Both constant humidity environments

and cyclic environments were studied. In constant humidity environments, the fatigue threshold

and crack growth rate behavior were affected differently. The fatigue threshold strain energy

release rate, Gth, decreased from an undegraded value to a constant minimum value that did not

change even after prolonged aging. In contrast, the crack growth rates continued to increase with

aging time, showing no tendency to reach a limiting value. It was hypothesized that the

continuing increase in the crack growth rate with aging time was related to the loss of the rubber

toughening mechanism, and that the decrease in Gth was related to the degradation of the epoxy

matrix. Increasing the aging temperature accelerated the rate at which Gth decreased from its

initial value. The crack paths remained cohesive in the adhesive layer in all of the experiments,

with the residual adhesive thickness on the more highly-strained adherend decreasing as the

crack growth rate (or applied G) decreased.

0

1

2

3

4

5

0 5 10 15

C(%

)

Aging time (days)

128

For joints aged in the cyclically changing environment with intermittent salt spray,

neither Gth nor the crack growth rates degraded until after four weeks of aging. The superior

fatigue performance of these joints compared to joints aged in constant humidity environments

was due to the lower equilibrium water concentrations in the adhesive, which were modeled

using the finite element method. This was supported by moisture uptake measurements of the

adhesive in deionised and salt water environments which showed that the diffusion was simple

Fickian at room temperature and dual-Fickian at the higher temperatures. The salt spray

produced an osmotic pressure that affected the diffusion kinetics of the mobile water molecules

in the epoxy during absorption.

129

Appendix 5A Moisture diffusion

The sequential dual Fickian (SDF) model was used to determine the moisture

concentration at any time, t, and distance, x, from the boundary by [17]:

22

22

2

0

12

22

1

0

2

)12(cos

4

)()12(exp

12

)1(41)(

2

)12(cos

4

)12(exp

12

)1(41),(

Ch

xn

h

ttnD

ntt

Ch

xn

h

tnD

ntxC

d

n

n

d

n

n

(A.1)

where C1∞ and C2∞ are the saturated concentrations of the first and second diffusion mechanisms

such that C1∞+C2∞=C∞, where C∞ is the total saturation concentration. D1 and D2 are the

diffusion coefficients of the first and second moisture uptake mechanisms, respectively. td is the

time at which the transition from the first diffusion mechanism to the second one occurs, and

Φ(t) is the Heaviside step function which is equal to zero for negative values and equal to one for

positive values.

Integrating Eq. (A.1) over the spatial variable, the fractional mass uptake, Mt for the SDF

model at any time t is given by:

22

222

022

12

221

022

4

)()12(exp

)12(

181)(

4

)12(exp

)12(

181

Mh

ttnD

ntt

Mh

tnD

nM

d

n

d

n

t

(A.2)

where M1∞ and M2∞ correspond to the first and second uptakes, respectively and M1∞+M2∞=M∞.

The fractional mass uptake at any time t, Mt was determined experimentally using gravimetric

measurements according to:

%100

i

itt

W

WWM

(A.3)

130

where Wi and Wt are the sample weights before any exposure and after an exposure time of t,

respectively. The model has 5 parameters: D1, D2, C1∞, C2∞ and td. Further details on calculating

the model parameters are given in ref. [17].

131

5.5 References

1. G. LaPlante, A.V. Ouriadov, P. Lee-Sullivan, B.J. Balcom, Anomalous moisture

diffusion in an epoxy adhesive detected by magnetic resonance imaging, J. Appl. Polym.

Sci. 109 (2008) 1350-1359.

2. K.F. Lin, R.J. Yeh, Moisture absorption behavior of rubber-modified epoxy resins, J.

Appl. Polym. Sci. 86(2002) 3718–3724.

3. G. Xian, V.M. Karbhari, DMTA based investigation of hygrothermal ageing of an epoxy

system used in rehabilitation, J. Appl. Polym. Sci. 104 (2007) 1084–1094.

4. N. Su, R.I. Mackie, W.J. Harvey, The effects of aging and environment on the fatigue life

of adhesive joints, Int. J. Adhes. Adhes. 12 (1992) 85-93.

5. W.S. Johnson, S. Mall, A fracture mechanics approach for designing adhesively bonded

joints, in: W.S. Johnson (Ed.), Delamination and Debonding of Materials, ASTM STP

876, American Society for Testing and Materials, 1985, pp. 189-199.

6. S. Mall, W.S. Johnson, Characterization of mode I and mixed-mode failure of adhesive

bonds between composite adherends, in: J.M. Whitney (Ed.), Composite materials:

testing and design, ASTM STP 893, American Society for Testing and Materials, 1986,

pp. 322–34.

7. J.A. Harris, P.A. Fay, Fatigue life evaluation of structural adhesives for automotive

applications, Int J Adhes. Adhes., 12 (1992) 9-18.

8. M. Fernando, W.W. Harjoprayitno, A.J. Kinloch, A fracture mechanics study of the

influence of moisture on the fatigue behaviour of adhesively bonded aluminium-alloy

joints, Int. J. Adhes. Adhes., 16 (1996) 113-119.

9. P. Briskham, G. Smith, Cyclic stress durability testing of lap shear joints exposed to hot-

wet conditions, Int. J. Adhes. Adhes., 20 (2000) 33-38.

10. J.A.M. Ferreira, P.N. Reis, J.D.M. Costa, M.O.W. Richardson, Fatigue behaviour of

composite adhesive lap joints, Compos. Sci. Technol., 62 (2002) 1373-1379.

11. K.A. Lubke, L.M. Butkus, W.S. Johnson, Effect of environment on fracture toughness

and debond growth of aluminum/FM®73/boron-epoxy adhesively bonded joints, J.

Compos. Technol. Res. 23 (2001) 42–49.

12. A. Ameli, M. Papini, J.K. Spelt, Fracture R-curve of a toughened epoxy adhesive as a

function of irreversible degradation, Mater. Sci. Eng. A 527 (2010) 5105-5114.

13. J.W. Wylde, J.K. Spelt, Measurement of adhesive joint fracture properties as a function

of environmental degradation, Int. J. Adhes. Adhes. 17 (1998) 237-246.

14. A. Moidu, A.N. Sinclair, J.K. Spelt, Adhesive joint durability assessed using open-faced

peel specimens, J. Adhes. 65 (1998) 239-257.

15. W.K. Loh, A.D. Crocombe, M.M. Abdel Wahab, I.A. Ashcroft, Environmental

degradation of the interfacial fracture energy in an adhesively bonded joint, Eng. Frac.

Mech. 69 (2002) 2113–2128.

132

16. A. Ameli, M. Papini, J.K. Spelt, Hygrothermal degradation of two rubber-toughened

epoxy adhesives: Application of open-faced fracture tests, Int. J. Adhes. Adhes.

(submitted).

17. N.V. Datla, M. Papini, J.A. Schroeder, J.K. Spelt, Modified DCB and CLS specimens for

mixed-mode fatigue testing of adhesively bonded thin sheets, Int. J. Adhes. Adhes. 30

(2010) 439-447.

18. J.W. Hutchinson, Z. Suo, Mixed-mode cracking in layered materials, Adv. Appl. Mech.

29 (1992) 63–191.

19. ASTM D2651, Standard guide for metal surfaces for adhesive bonding. West


20. R.B. Rebak, L.F. Aprigliano, S. Daniel Day, J.C. Farmer, Salt fog testing iron-based

amorphous alloys, Mater. Res. Soc. Symp. Proc. 985 (2007).


(2000).

22. A. Ameli, N.V. Datla, M. Papini, J.K. Spelt, Hygrothermal properties of highly

toughened epoxy adhesives, J. Adhes. 86 (2010) 698-725.

23. R. Kahraman, M. Al-Harti, Moisture diffusion into aluminum powder-filled epoxy

adhesive in sodium chloride solutions, Int. J. Adhes. Adhes. 25 (2005) 337-341.

24. R.C.L. Tai, Z. Szklarska-Smialowska, Effect of fillers on the degradation of automotive

epoxy adhesives in aqueous solutions, J. Mat. Sci. 28 (1993) 6199-6204.

25. H.R. Azimi, R.A. Pearson, R.W. Hertzberg, Fatigue of rubber-modified epoxies: effect of

particle size and volume fraction, J. Mat. Sci. 31 (1996) 3777-3789.

133

Chapter 6 Effects of aging on the fatigue behavior of two toughened epoxy

adhesives

6.1 Introduction

Water can degrade adhesive joints by damaging the adhesive-adherend interfacial region

or the adhesive itself; therefore, degradation in an adhesive joint exposed to varying amounts of

water is closely related to the water absorption and desorption behavior of the adhesive [1-3].

Water absorption in rubber-toughened epoxy adhesives usually exhibits anomalous (non-

Fickian) behavior [4-6], whereas moisture desorption on drying follows Fick’s law [7]. Some

adhesives retain water after drying [8-10], because of the relatively strong bonds formed between

water molecules and the epoxy [9]. Water molecules in the bulk epoxy are either in a free or

bound state [11]. Free water molecules plasticize and soften the adhesive, decreasing its glass

transition temperature [12]; however, these effects are reversible upon drying. Bound water

molecules, on the other hand, introduce irreversible damage to the adhesive by hydrolysis and

chain scission [13].

Closed joints are usually used in degradation studies, although they take a long time to

degrade due to the length of the diffusion paths, and the degradation is non-uniform across the

joint area, being greatest at the exposed edges. This non-uniform degradation makes it difficult

to associate a loss of joint strength with a particular level of degradation. These limitations can

be overcome using open-faced specimens in which the adhesive is applied to only one adherend,

subject to environmental aging, and then bonded to a second adherend to make the final fracture

specimen [14-19]. This reduces the water diffusion path to the thickness of the adhesive layer

over the entire joint area, thus producing a relatively uniform state of moisture concentration and

degradation in a relatively short period of time. Since previous study [19] correlating the loss of

fatigue strength to a particular level of degradation was limited to the effects of aging

temperature, further study using open-faced specimens focusing on both effects of temperature

and relative humidity (RH) of aging environment is necessary to predict the long-term behavior

of adhesive systems.

134

Previous researchers [15, 18] have proposed that the degradation of the fracture

toughness of an adhesive joint aged at a given temperature is a function of the exposure index

(EI), defined as the time integral of the water concentration in the joint. This concept is

motivated by the desire to combine the effects of time and water concentration in a single

parameter which could be used to quantify the severity of the aging condition. In order for this

concept to be practically useful, the degradation should be uniquely related to EI such that a

given amount of degradation corresponds to a particular EI regardless of the exposure pathway;

i.e. long exposure to a low relative humidity (RH) environment should be equivalent to shorter

exposure to a high RH environment. This hypothesis has been confirmed for the degradation of

fracture toughness [15, 18] at relatively high EI values, but its validity has not been examined for

the degradation of the fatigue threshold and crack growth rates.

In the present work, aged open-faced ADCB specimens made with two different rubber-

toughened epoxy adhesives were subject to cyclic loading under mixed-mode conditions. The

degradation of the fatigue thresholds and crack growth rates were quite different, and illustrated

the effects of environmental degradation of the matrix and toughener as a function of aging time,

temperature, and RH on both the Gth and crack growth rates. A degradation model analogous to

Fick’s law was proposed to characterize the decrease in fatigue threshold with degradation that

was seen for adhesive 1. The EI hypothesis was also evaluated for fatigue threshold and crack

growth rates. Differences in the water absorption properties and glass transition temperatures of

the two adhesives were used to explain the differences in the degradation behavior.

6.2 Experimental

6.2.1 Open-faced specimen preparation

Open-faced ADCB specimens were prepared by casting a 0.4 mm thick “primary” layer

of adhesive on a 12.7 mm thick P2-etch treated AA6061 bar using a smooth backing plate coated

with polytetrafluroethylene release agent (Fig. 6.1). Adhesive 1 and adhesive 2 were used as the

primary adhesives for system 1 and system 2, respectively. The desired bondline thickness was

achieved by placing 0.4 mm diameter piano wires in the primary layer. The assembly was

clamped using large binder clips (25.4 mm wide by 50.8 mm long, ACCO, Booneville, MS,

135

USA) that were centered directly above the spacing wires. The assembly was then cured using

the cure profile (180C for at least 30 min for both adhesives) recommended by the adhesive

manufacturer. The backing plate was removed after curing and the open-faced specimens were

exposed to various environments for a range of times as shown in Table 6.1. Since the present

experiments focused on the effects of irreversible degradation, the aged specimens were dried in

a vacuum oven containing anhydrous calcium sulphate at 40ºC for approximately 7 days. This

drying procedure removed the absorbed moisture (unbound water molecules) thereby eliminating

the reversible effects such as plasticization by water molecules. After drying, the complete

ADCB specimen (Fig. 6.2) was made by bonding the primary adhesive layer of the open-faced

specimen to a 25.4 mm thick P2-etched aluminum AA6061-T6 bar using a 0.25 mm thick

“secondary” layer of adhesive. Adhesive 2 was used as the secondary layer for both adhesive

systems. The desired bondline thickness of the secondary layer was achieved by placing 0.65

mm diameter (combined thickness of primary and secondary layer) piano wires between both

adherends in locations without adhesive. To improve bonding between the primary and

secondary adhesive layers, the degraded primary layer was sanded lightly with a 100 grit sand

paper, wiped with acetone and then dried prior to the application of the secondary adhesive. The

assembly was given a secondary cure following the cure profile (180C for at least 30 min)

recommended by the adhesive manufacturer. After the secondary cure, the excess adhesive on

the sides of the specimen was removed using a belt sander with a 120 grit sand paper and water

as coolant, followed by hand sanding with a 600 grit sand paper.

136

Table 6. 1 SDF diffusion model parameters (Eqs. (1) and (2)) of the adhesives for the various

humid environments studied (data from [22]). Each data point is the average of three repetitions,

where SD indicates the standard deviation.

Environment

Absorption Desorption

D1 ±SD

(10-14

m2/s)

D2±SD

(10-14

m2/s)

M1∞±SD

(%)

M∞±SD

(%)

td1/2

(s1/2

)

Dd ± SD

(10-14

m2/s)

Mr

(%)

Adhesive 1

40ºC 43% RH 113±11 0.0 1.65±0.04 1.65±0.04 ∞ 242±19 0.86±0.04

40ºC 95% RH 134±17 3.8±0.7 3.36±0.09 4.78±0.15 536 214±22 1.40±0.09

60ºC 43% RH 271±24 4.3±0.8 1.38±0.03 1.62±0.04 924 186±18 0.98±0.03

60ºC 95% RH 314±25 8.6±0.9 3.73±0.11 6.98±0.18 329 172±22 1.76±0.11

Adhesive 2

60ºC 95% RH 248±29 8.1±1.5 3.16±0.09 4.78±0.12 219 143±13 0.16±0.03


diffusion into the primary adhesive layer. The adherend is the thinner one in the ADCB (Fig.

6.2) and was therefore subject to greater bending strain during fracture testing.

137

Figure 6. 2 Configuration of open-faced ADCB specimen after being closed (dimensions in mm,

not to scale). The thicknesses of the primary and secondary adhesive layers were 0.4 and 0.25

mm, respectively. Width of the specimen was 19 mm. The location of the clip gauge is also

shown. The upper adherend is the open-faced adherend shown in Fig. 6.1.

6.2.2 Aging and test conditions

As mentioned above, the open-faced specimens were exposed to environments

maintained at constant humidity and temperature (Table 6.1). A constant relative humidity (RH)

was achieved by placing the specimens in air-tight plastic containers above a saturated salt

solution. The containers were then placed in temperature controlled ovens for aging. These

procedures were identical to those followed in [19] which presented fatigue durability results for

adhesive 1 aged only at 95%RH.

6.2.3 Fatigue testing procedures and environment

Fatigue tests were performed with a servo-hydraulic load frame under displacement

control using a sinusoidal waveform with a frequency of 20 Hz. A constant displacement ratio

(i.e. ratio of minimum to maximum displacement, δmax/δmin) of 0.1 was used. The testing began

with the application of the highest strain energy release rate, G, which then decreased as the

crack grew under constant displacement until the threshold crack growth rate of 10-6 mm/cycle

was reached at the threshold strain energy release rate, Gth. During fatigue testing, the specimens

were enclosed in a chamber to ensure a room temperature, dry air (RD) condition (21±2°C and

<10% RH).

138

A phase angle = 18º was achieved when equal loads were applied to both adherends of

the ADCB [20]. The phase angle, , is defined as , where GI and GII are the

mode I and mode II strain energy release rates, respectively.

The crack length was measured using both optical and specimen compliance methods.



photographs of the location of the crack tip, the load cycling was stopped and held at the mean

load for 15 s every 9,000 cycles. The specimen compliance was obtained from the relationship

between the crack opening and the applied force during the unloading portion of the loading

cycle. A clip gauge (model 3541, Epsilon Technology Corp., Jackson, WY, USA) recorded the

opening displacement at the loading pins (Fig. 6.2). For each specimen, a polynomial

relationship between the optically observed crack length and the specimen compliance was

established according to ASTM E647 [21]. Using this relationship, the crack length was inferred

from the continuous clip gauge compliance data, and used in all calculations of crack growth rate

and G. A beam-on-elastic-foundation model for unequal adherends was used to calculate G and

Ψ from the measured force and crack length [20].

6.2.4 Adhesive rubber tougheners

A field emission scanning electron microscope (FESEM) was used to examine the rubber

toughener morphology of both adhesives. Bulk adhesive wafers were freeze-fractured in liquid

nitrogen to obtain a planar surface. These fractured surfaces were carbon coated and then

examined under the microscope. The micrographs shown in Fig. 6.3 indicate that the size of

rubber particles were approximately 1 µm and 0.2 µm for adhesives 1 and 2, respectively.

139

(a)

(b)

Figure 6. 3 FESEM micrograph that shows the rubber particles dispersed in the epoxy matrix for

(a) adhesive 1, and (b) adhesive 2. Approximate size of rubber particles is 1 µm and 0.2 µm for

adhesives 1 and 2, respectively.

140

6.2.5 DMTA

A dynamic mechanical thermal analyser (DMTA Q800, TA Instruments, New Castle,

DE, USA) was used to measure the dynamic mechanical properties of bulk samples of the two

adhesives in the fresh, wet, and dried states, as a function of temperature. Cast adhesive wafers

(10 mm × 20 mm × 0.8 mm thickness) of both adhesives were tested under a tensile strain of

0.1% using a frequency of 1 Hz at a temperature ramp of 10ºC/min between room temperature

(25ºC) and 190ºC. The Tg was taken as the temperature at which the loss modulus was

maximum. The wet samples were tested immediately after removal from the environment

chambers, and the dry samples were dried using the procedure explained above for the open-

faced specimens. The DMTA temperature scan was also repeated a second time, immediately

after the first scan, .for a few dry and wet samples of adhesive 1.

6.3 Results and Discussion

6.3.1 Gravimetric analysis

The water absorption of both adhesives was previously found to be non-Fickian, with a

pseudo-equilibrium state being reached at intermediate exposure times before ultimately

reaching a final saturation state; however, water desorption showed simple Fickian behavior

[22]. The absorption and desorption behaviors for both adhesives were modeled using a

sequential dual Fickian (SDF) model [22] and a simple Fickian model, respectively, as illustrated

in Fig. 6.4. The fractional mass uptake, Mt, at any time t, for the SDF model during absorption is

given by [22]:

22

22

2

022

12

22

1

022

4

)()12(exp

)12(

181)(

4

)12(exp

)12(

181

Mh

ttnD

ntt

Mh

tnD

nM

d

n

d

n

t

(1)

where M1∞ and M2∞ correspond to the fractional mass uptake in the first and second stages,

respectively, and M1∞+M2∞=M∞. D1 and D2 are the diffusion coefficients of the first and second

141

moisture uptake stages, respectively. td is the transition time between the two stages, and Φ(t-td)

is the Heaviside step function which is equal to zero for negative values of t-td and equal to one

otherwise.

During drying, the Fickian model gives Mt as:

r

d

n

rt MMh

tnD

nMM

2

22

022 4

)12(exp

)12(

18

(2)

where Mr is the minimum fractional retained water after drying, and Dd is the diffusion

coefficient of the desorption mechanism. Table 6.1 lists the absorption and desorption

parameters for the different exposure conditions for both adhesives as found in [22]. These

parameters were used to calculate the water concentrations at given degradation times in the aged

open-faced ADCB joints.

It is seen that D1 for both adhesives was largely independent of RH, but depended on

temperature (Table 6.1). Furthermore, M for both adhesives was a function of both temperature

and RH. Significant differences in water desorption behavior were observed between adhesive 1

and adhesive 2. A fraction of the absorbed water in adhesive 1 was retained even after prolonged

drying, whereas the absorbed water in adhesive 2 was almost completely eliminated by drying

(Table 6.1). This amount of retained moisture, Mr, for adhesive 1 was proportional to the

saturated water concentration, M∞, so that Mr increased as the temperature and RH of the

environment increased. Ameli et al. [22] used XPS to confirm that water molecules were present

in adhesive 1 after prolonged drying at 40ºC.

142

Figure 6. 4 Illustration of the sequential dual Fickian (SDF) model for water absorption and the

simple Fickian model for water desorption.

6.3.2 DMTA

Figures 6.5 and 6.6 show representative examples of the measured storage and loss

moduli as a function of temperature for fresh, wet, and dry samples of both adhesives obtained

using DMTA. Table 6.2 summarizes the conditioning history of the samples with the

corresponding fractional water uptake (Mt), glass transition temperature (Tg), and room

temperature storage modulus (ERT). The water absorption behavior in the chosen conditioning

environments was dual-Fickian (0 < td < ∞, see Table 6.1), except for the wet A1 sample where

the water absorption was simple Fickian (td = ∞ at 40ºC-43%RH environment, see Table 6.1).

The Tg of the wet samples of both adhesives was smaller than the Tg of the fresh samples

(Table 6.2), decreasing approximately 9º and 7ºC, respectively for adhesives 1 and 2, for each

1% increase in water concentration. These values agree well with the 8ºC drop in Tg per 1%

water concentration reported with a DGEBA epoxy resin [23]. As seen in Table 6.2, this

decrease in Tg was reversible for both adhesives, and drying restored Tg to the value of the fresh

143

samples of both adhesives, irrespective of the amount of retained water after drying. Noting that

the reversible decrease in Tg with absorbed water was due to plasticization from free water

molecules [24], it can be concluded that the retained water in adhesive 1 was not in a free state

and was bound strongly to the adhesive constituents since it did not affect Tg. This is consistent

with the conclusions reached in [18] for these same adhesives. To further test this conclusion, a

second DMTA temperature scan was performed immediately after the first, for few wet and dry

samples of adhesive 1. As observed in [9, 13], the high temperature of the DMTA scan

decreased the water concentrations in the samples. Gravimetric measurements before and after

the first scan showed that the retained water in the dry samples decreased from 1.68% to 1.28%,

and that, for the wet samples, there was a larger decrease from 4.68% to 1.71%. This loss of

water affected the Tg differently for the wet and dry samples. The Tg of the dry samples

remained almost constant (112ºC and 113ºC for the first and second scans, respectively)

indicating that retained water in dry samples had no plasticizing effect. In contrast, the Tg of the

wet samples significantly increased (75ºC in first scan to 111ºC in the second scan) indicating

that the water present in the wet samples had a plasticizing effect. These results support the

argument that the retained water after drying is in the bound state.

The data for the room temperature storage modulus, ERT, was used to understand the

effects of water on the modulus of the adhesive. Table 6.2 shows that the ERT of the adhesive 1

samples that had been wet and then dried increased as the amount of retained water after drying,

Mr, increased. As discussed above, since the retained water in adhesive 1 after drying was in a

bound state, it can be concluded that elastic modulus increased as the amount of bound water in

the adhesive increased. This increase in modulus with bound water can be explained as an

increased resistance to molecular mobility within the adhesive constituents as a result of the

formation of strong bonds with water molecules.

Table 6.2 also shows that ERT of the wet samples of both adhesives decreased below the

ERT of the fresh samples, except for the wet A1 sample, which was aged at a relatively low

temperature and RH (40ºC-43%RH) and therefore contained little water. This inconsistency in

the change in ERT of the wet samples compared with that in the dry samples of adhesive 1 is

expected, because water in wet samples exists in both the free and bound states, and each affects

the elastic modulus differently; i.e. water in the bound state was shown above to increase the

elastic modulus, while water in the free state is known to plasticize and decrease the elastic

144

modulus [25, 26]. Therefore, the ratio of bound to free water in the adhesive determines whether

ERT increases or decreases with water absorption; i.e. ERT increases when the ratio of bound to

free water is high where the increase in stiffness due to bound water dominates the decrease in

stiffness due to free water, and ERT decreases when the ratio is low. Since ERT increased above

the value of the fresh sample only for the wet A1 sample, the ratio of bound to free water is the

highest in this sample compared to other samples. Furthermore, since water absorption followed

a simple-Fickian relationship only for the wet A1 sample as a consequence of the relatively low

temperature and RH of the aging environment (40ºC-43%RH), and was dual-Fickian for all other

samples, it can be concluded that the ratio of bound to free water is highest for simple-Fickian

absorption and that the ratio was relatively low for dual-Fickian absorption when the aging

environment was at a higher temperature and RH.

It is noted that absorbed water decreased the Tg of the wet adhesive 2 sample (A2) well

below the temperature of the conditioning environment (60ºC); however, the Tg of the wet

adhesive 1 samples (A1, B1 and C1) remained well above the temperatures of the respective

conditioning environments (40ºC and 60ºC). The effects of aging these adhesives below or

above their Tg is discussed below.

145

Table 6. 2 Conditioning environments and the corresponding fractional water uptake (Mt), glass

transition temperature (Tg), and storage modulus at room temperature (ERT) of fresh, wet, and dry

samples of both adhesives. Percentage change in Tg and ERT values from the fresh sample values

of the corresponding adhesive were also included.

Sample Conditioning Mt

(%)

Tg

(ºC)

%

change

in Tg

ERT

(N/mm2)

%

change

in ERT

Adhesive 1

Fresh, A1 cured and dried 0 121 1402

Wet, A1 Saturated at 40ºC-43%RH 1.68 117 -3 1628 +16

Wet, B1 5 days aging at 60ºC-95%RH 4.54 75 -38 1126 -20

Wet, C1 7 days aging at 60ºC-95%RH 4.81 81 -33 1097 -22

Dry, A1 Saturated at 40ºC-43%RH and dried 0.86 124 +2 1575 +11

Dry, D1 Saturated at 60ºC-43%RH and dried 0.98 122 +1 1543 +10

Dry, C2 Saturated at 60ºC-95%RH and dried 1.76 121 0 1711 +22

Adhesive 2

Fresh, A2 Cured and dried 0 75 995

Wet, A2 7 days aging at 60ºC-95%RH 4.32 42 -44 770 -20

Dry, A2 7 days aging at 60ºC-95%RH and

dried 0.16 78 +4 1078 +7

146

(a)

(b)


adhesive 1 measured using DMTA. Samples of adhesive as-cured, and tested after 5 days

exposure to the 60C-95%RH environment without being dried (“wet” state) and after drying to

remove absorbed, unbound water (“dry” state).

0

400

800

1200

1600

2000

0 50 100 150 200

Sto

rage

mo

du

lus, M

Pa

Temperature, ºC

Adhesive 1

Fresh

60ºC 95% RH Wet

60ºC 95% RH Dry

0

20

40

60

80

100

120

140

0 50 100 150 200

Lo

ss m

od

ulu

s, M

Pa

Temperature, ºC

Adhesive 1Fresh

60ºC 95% RH Wet

60ºC 95% RH Dry

147

(a)

(b)


adhesive 2 measured using DMTA. Samples of adhesive as-cured, and tested after 7 days

exposure to the 60C-95% RH environment without being dried (“wet” state) and after drying to

remove absorbed unbound water (“dry” state).

0

200

400

600

800

1000

1200

0 50 100 150 200

Sto

rage

mo

du

lus, M

Pa

Temperature, ºC

Adhesive 2

Fresh

60ºC 95% RH Wet

60ºC 95% RH Dry

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200

Lo

ss m

od

ulu

s, M

Pa

Temperature, ºC

Adhesive 2

Fresh

60ºC 95% RH Wet

60ºC 95% RH Dry

148

6.3.3 Fatigue behavior of joints with adhesive 1

6.3.3.1 Effects of aging environment on the fatigue threshold

Figure 6.7 shows the variation of Gth with aging time under the two humidity levels at

40ºC and 60ºC, and the average Gth of an unaged (freshly bonded) closed specimen of adhesive

1. Two stages of degradation were observed in all aging environments. In the first stage, the

fatigue threshold decreased relatively quickly with aging time, but then Gth remained

approximately constant at a low value (Gth,) with further aging. A similar two-stage

degradation of the fatigue threshold was observed for joints with pretreated AA5754 adherends

bonded with adhesive 1 that were aged and tested under similar environments [19]. These

similarities were expected, because in both studies the crack path remained cohesive in the

adhesive layer; i.e. since the crack path was in the adhesive layer, the degradation in threshold

behavior was sensitive to the adhesive and was insensitive to the pretreatment.

It was hypothesized that the variation in threshold with time, Gth(t), could be modeled,

using a simple Fickian-type relation since it appeared to depend mostly on the amount of water

absorbed, or equivalently, on the amount of retained water. Therefore, following the form of Eq.

(2),

(3)

where Gth,fresh and Gth,∞ are the fatigue thresholds of the fresh joint and the joint after prolonged

aging, respectively. Ddeg is defined as a degradation coefficient reflecting the rate of

degradation. Treating Ddeg as an adjustable coefficient and minimizing the least-squares error

gave the solid curves in Fig. 6.7. In general, the agreement between the fitted curves and the

data was good, especially at 60ºC and at 95%RH. Under the driest conditions (40ºC-43%RH)

the fit was good at short and long times, but tended to overpredict the decrease in Gth, with aging

time at intermediate times. This supports the contention that the degradation of Gth, under hot-

wet aging tends to develop in proportion to the amount of absorbed water, or retained water in

the dry adhesive since they were related as discussed above (Table 6.1)

Figure 6.8 shows that Gth,, the stable value after relatively long exposure times, was

affected more by the RH than by the temperature of the aging environment; i.e. at each RH,

149

increasing the aging temperature from 40ºC to 60ºC had a statistically insignificant effect on

Gth,, whereas at each temperature, increasing RH from 43% to 95% decreased Gth, significantly

(t-test, 95% confidence level). This can be attributed to the much larger change in the amount of

water in the adhesive due to changes in RH than due to changes in temperature; i.e. Table 6.1

shows that M increased by 190% at 40ºC and 330% at 60ºC as the RH increased from 43% to

95%. In comparison, M increased by only 46% at 95% RH when the temperature increased

from 40ºC to 60ºC.

Figure 6.9 compares the variation in threshold with aging time for specimens aged at

95% RH and temperatures of 40ºC and 60ºC. Increasing the aging temperature increased the rate

at which the joints degraded and decreased the time to the onset of the steady-state stage; i.e. the

aging time required for Gth to decrease to 80% of the ultimate degradation was approximately 60

days at 60ºC and 87days at 40ºC.

(a)

0

25

50

75

100

125

150

175

200

0 5 10 15 20

Gth

(J/m

2)

t1/2 (Day1/2)

Fresh

40ºC 43% RH

40ºC 95% RH

40ºC

2,2

2,2

4,2

3,2

3,2

2,12,1

2,2

2,1

150

(b)

Figure 6. 7 Fatigue threshold as a function of square root of aging time for adhesive 1 specimens

aged at 95% and 43% RH at temperatures of (a) 40ºC and (b) 60ºC. Trend lines are the least-

square fits of Eq. (3) to the measured data. Numbers next to each data point indicate the number

of thresholds reached and the number of specimens tested, respectively; these two numbers are

different in cases where more than one threshold was reached using a single specimen. Error

bars represent the range of the measurements.

0

25

50

75

100

125

150

175

200

0 5 10 15 20

Gth

(J/m

2)

t1/2 (Day1/2)

Fresh

60ºC 43% RH

60ºC 95% RH

60ºC

3,22,1

2,1

2,12,1

3,22,2

2,2

2,1

151

Figure 6. 8 Gth,∞ values in different aging environments and the Gth of fresh specimens. Average

threshold values are shown above the columns and the error bars represent ±1 standard deviation.

Figure 6. 9 Least-squares fits of Eq. (3) for the data of Fig. 6.7 at 95% RH.

172

116

77

122

68

0

50

100

150

200

250 Adhesive 1

Gth

, J/m

2

0

25

50

75

100

125

150

175

200

0 5 10 15 20

Gth

(J/m

2)

t1/2 (Day1/2)

40ºC 95% RH

60ºC 95% RH

95% RH

152

6.3.3.2 Effects of aging environment on the crack growth rate behavior of adhesive 1

Figure 6.10 shows the variation of the adhesive 1 crack growth rate curves with aging

time for the various aging environments. Similar to threshold degradation, the crack growth

rates degraded in two stages, with rapidly increasing crack growth in the first few weeks of aging

followed by a stabilization where the crack growth rates remained largely unchanged with

further aging. This is illustrated in Fig. 6.11 which shows the best-fit lines to the Paris regions of

the curves of Fig. 6.10.

As expected, Fig. 6.12 shows that the crack growth rate curves for the different aging

environments became more widely separated as the aging time increased. Furthermore, as was

observed in threshold degradation, at longer aging times the crack growth rates were affected

more by RH than by the temperature of the aging environment. In other words, for the longer

aging times at each RH, increasing the aging temperature from 40ºC to 60ºC had an insignificant

effect on the crack growth rate (Figs. 6.12(e) and 6.12(f)).

The first stage of degradation ended sooner for the threshold than for the crack growth

rate; for example, for specimens aged at 60ºC and 95% RH the threshold stabilized after 48 days

(Fig. 6.10(b)) and after 90 days for the crack growth rate (Fig. 6.12(d)). These transition points

between the first and second stages of threshold degradation were defined as the minimum aging

times required to degrade Gth to 80% of the ultimate degradation measured at stabilization.

Similar differences between the degradation of the fatigue threshold and the crack growth rates

were observed in earlier work with joints made with pretreated AA5754 adherends bonded with

adhesive 1 [19].

It is hypothesized that this can be explained by differences in the fatigue failure

mechanisms near the threshold and at higher crack growth rates, which are related to differences

in the plastic zone size at the crack tip. Datla et al. [27] used finite element modeling of the

ADCB specimen ( =18º) used in this study to show that the thickness of the plastic zone of

adhesive 1 near the threshold at an applied Gmax=150 J/m2 was around 80 µm. This grew to

approximately 120 µm at Gmax =200 J/m2 at the start of the linear Paris region of the crack

growth rate curve. In comparison, Fig. 6.3(a) indicates that the rubber particle size in adhesive 1

was approximately 1 µm. Therefore, fatigue at the threshold will involve a smaller volume of

rubber particles and the behavior of the epoxy matrix will be relatively more important than at

153

higher crack growth rates. Since the degradation of Gth stabilizes sooner than the crack growth

rate, this hypothesis implies that the degradation of the cross-linked epoxy matrix stabilizes

before the degradation of the toughening associated with the rubber particles. Similarly using

the same adhesive system, Ameli et al. [18] concluded that the fracture toughness of epoxy

matrix degrades, but at longer aging times. Their conclusion was based on the observation that

initiation fracture toughness, which was governed by the matrix, decreased at very long aging

times; for example, specimens aged at 60ºC and 95% RH showed that initiation toughness values

decreased after 360 days of aging, while fatigue threshold decreased from the start of exposure).

This difference in the aging times required to observe degradation suggests that fatigue is more

sensitive to degradation than fracture.

This is similar to the concept proposed by Azimi et al. [28] who found that the fatigue

threshold of a rubber-toughened epoxy adhesive was the same as that of an untoughened epoxy,

suggesting that rubber toughening mechanisms were absent at these small crack growth rates

close to the threshold. They attributed this to the size of the plastic zone ahead of the crack tip

being smaller than the rubber particles, thereby minimizing their influence in crack propagation.

154

(a)

(b)

-7

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

s

Log (Gmax), J/m2

40ºC 43% RH

Fresh

7 days

20 days

42 days

60 days

90 days

153 days

251 days

-7

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

s

Log (Gmax), J/m2

40ºC 95% RHFresh

7 days

19 days

42 days

60 days

90 days

152 days

246 days

155

(c)

(d)

Figure 6. 10 Measured fatigue crack growth rate curves for adhesive 1 specimens aged at: (a)

40°C – 43% RH, (b) 40°C – 95% RH, (c) 60°C – 43% RH, and (d) 60°C – 95% RH. Aging

times in days are given in the legend.

-7

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

s

Log (Gmax), J/m2

60ºC 43% RH

Fresh

7 days

21 days

42 days

60 days

90 days

154 days

248 days

-7

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

s

Log (Gmax), J/m2

60ºC 95% RH

Fresh

7 days

20 days

48 days

90 days

149 days

231 days

156

(a)

(b)

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

40ºC - 43% RHFresh

7

20

42

60

90

153

251

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

40ºC - 95% RHFresh

7

19

42

60

90

152

246

157

(c)

(d)

Figure 6. 11 Variation of crack growth rate curves with aging time for adhesive 1 specimens

aged at: (a) 40°C–43% RH, (b) 40°C–95% RH, (c) 60°C–43% RH, and (d) 60°C–95% RH.

Each line is the least-squares fit to the linear Paris region of the crack growth curves shown in

Fig. 6.10. Aging times in days are given in the legend.

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

60ºC - 43% RHFresh

7

21

42

60

90

154

248

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

60ºC - 95% RH

Fresh

7

20

48

90

149

231

158

(a)

(b)

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

7 days

Fresh

40ºC 43%RH

40ºC 95%RH

60ºC 43%RH

60ºC 95%RH

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

21 days

Fresh

40ºC 43%RH

40ºC 95%RH

60ºC 43%RH

60ºC 95%RH

159

(c)

(d)

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

45 days

Fresh

40ºC 43%RH

40ºC 95%RH

60ºC 43%RH

60ºC 95%RH

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

90 days

Fresh

40ºC 43%RH

40ºC 95%RH

60ºC 43%RH

60ºC 95%RH

160

(e)

(f)

Figure 6. 12 Effect of aging environment on the crack growth rate curves for adhesive 1

specimens aged for: (a) 7, (b) 21, (c) 45, (d) 90, (e) 150, and (f) 240 days. Each line is the least-

squares fit to the linear Paris region of the crack growth curves shown in Fig. 6.10.

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

150 days

Fresh

40ºC 43%RH

40ºC 95%RH

60ºC 43%RH

60ºC 95%RH

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

240 days

Fresh

40ºC 43%RH

40ºC 95%RH

60ºC 43%RH

60ºC 95%RH

161

6.3.3.3 Effects of aging environment on the crack path of adhesive 1

Figure 6.13 shows that the crack paths in both the unaged and aged joints were cohesive

at all crack growth rates. Furthermore, the thickness of the residual adhesive on the more highly-

strained open-faced adherend decreased monotonically with decreasing crack growth rate

(decreasing Gmax) in all specimens. A similar trend has been explained in terms of the decreasing

size of the plastic zone at the tip of the crack as the applied G decreased [20]. This relation was

illustrated above for Gmax=150 J/m2 and 200 J/m

2. Assuming that the average crack path tends

toward the centre of the plastic zone, the residual adhesive thickness will decrease as the applied

G decreases and the crack slows. Figure 6.13 also shows that the aging time did not affect the

thickness of the residual adhesive.

Figure 6. 13 Fracture surfaces on the more highly-strained (reinforced) adherend for adhesive 1

specimens that were: (a) unaged, (b) aged for 21 days at 40ºC – 95% RH, and (c) aged for 150

days at 40ºC – 95% RH. In each case, the fatigue region is to the left of the arrow showing

where Gth occurred. After reaching Gth, specimens were fractured, except for (c) where the

fatigue process was repeated.

162

6.3.3.4 Exposure index (EI) behavior of adhesive 1

The analytical expression for EI during the absorption, the time integral of the water

concentration within the adhesive at a given spatial location x from the exposed surface as a

function of absorption time t in an open-faced specimen, based on the SDF model for water

absorption, is given by [18]:

(4)

where and are the water saturated concentrations of the first and second diffusion

mechanisms such that , where is the total saturation concentration.

Assuming a uniform distribution of water concentrations at saturation, and

. h is the thickness of the primary layer of adhesive. Since the absorbed water can also

degrade the adhesive during the drying period (7 days in vacuum oven), which sometimes is a

significant portion of the exposure time, the environmental exposure during desorption process,

EId was also considered [18]:

(5)

where is the retained water concentration, C is the water concentration before drying, and is

the drying time. Assuming a uniform distribution of water concentration after drying, .

The total exposure index, EIT from start of exposure to hot-wet environment to the end of the

drying period is thus

(6)

Figure 6.14 shows the variation in the average Gth with the total exposure index, EIT, for

joints aged using two different aging paths: 43% and 95% RH at temperature of 40ºC and 60ºC.

For both temperatures, at any particular EIT value the decrease in Gth was greater for specimens

163

aged at 95% RH than at 43% RH. For example, at an EIT of 25×106 g/g.s at 60ºC the Gth

decreased by 57% after exposure at 95% RH for 48 days (from 172±20 to 74 J/m2) and by 32%

for specimens aged at 43% RH for 154 days (from 172±20 to 117±7 J/m2). Furthermore, Fig.

6.15 shows significant differences in the crack growth rate curves for similar EIT values reached

using two different aging paths. For both temperatures, at any particular applied G the crack

growth rates were higher for specimens aged at 95% RH than at 43% RH, even though the EIT

values were quite similar. This indicates that degradation in the fatigue threshold and crack

growth rates was not path independent, thereby invalidating the EI hypothesis for both the

fatigue threshold and crack growth rates, at least for relatively small values of EIT <36×106 g/g.s.

A similar dependence on the path of the aging at lower EIT (less than 25×106 g/g.s) was

observed for fracture toughness using the same adhesive system (1) as in present study [29].

However, at higher EIT values (> 25×106 g/g.s) path independence was observed. Since the

maximum EIT reached at the lower humidity level in the present tests was 36×106 g/g.s, which is

relatively small, it is possible that path independence may exist at higher EIT values.

164

(a)

(b)

Figure 6. 14 Fatigue threshold vs. EIT for adhesive 1 specimens aged at 43% and 95% RH and

temperatures of (a) 40ºC and (b) 60ºC. Trend lines show the best-fit power law curves to the

data at 95% RH.

y = 200.56x-0.236

R² = 0.9219

0

25

50

75

100

125

150

175

200

0 50 100 150

Gth

, J/m

2

EIT,106 g/g.s

40ºC 43% RH

40ºC 95% RH

40ºC 95% RH

y = 176.55x-0.222

R² = 0.8104

0

25

50

75

100

125

150

0 50 100 150 200

Gth

, J/m

2

EIT, 106 g/g.s

60ºC 43% RH

60ºC 95% RH

60ºC 95% RH

165

(a)

(b)

Figure 6. 15 Differences in the crack growth rates for adhesive 1 with similar EIT values that

were aged at different RH at aging temperatures of (a) 40ºC and (b) 60ºC. EIT values of

specimens are given in the legend (multiplied by 106 g/g.s). Each line is the least-squares fit to

the linear Paris region of the crack growth curves shown in Fig. 6.10.

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

43% RH (13.3)

95% RH (15.1)

43% RH (35.6)

95% RH (34.6)

T = 40ºCT = 40ºC

-6

-5

-4

-3

-2

-1

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

43% RH (8.4)

95% RH (10.3)

43% RH (21.5)

95% RH (26.9)

T = 60ºCT = 60ºC

166

6.3.4 Fatigue behavior of joints with adhesive 2

Figure 6.16 shows the variation of Gth with aging time for specimens aged at 60ºC - 95%

RH, and the average Gth of unaged closed specimens. It can be seen that the threshold decreased

significantly by 36% (from 129±15 to 82±2 J/m2) after 2 months of aging, and by 43% (from

129±15 to 73±21 J/m2) after 6 months of aging. However, Fig. 6.17 shows insignificant changes

in crack growth rates with aging at relatively high crack growth rates, corresponding to G greater

than approximately 102.4 = 250 J/m2. In other words, the fatigue performance at loads above Gth

was undegraded even after 180 days of open-faced aging. This is in marked contrast to the

behavior of adhesive 1 which showed significant degradation of the threshold and the crack

growth rate from the onset of aging.

As with adhesive 1, Fig. 6.18 shows that the crack path in both unaged and aged joints

with adhesive 2 was cohesive at all crack growth rates. It was also observed that at high crack

growth rates the crack path was inconsistent for aged specimens; i.e. the crack path was in the

primary layer for some specimens (Fig. 6.18(b)) and in the secondary layer for the remaining

specimens (Fig. 6.18(c)). Furthermore, since the changes in the crack growth rate curves were

insignificant (see Fig. 6.17), this inconsistency in crack path was probably caused by the

approximately equal toughness of the aged (primary) and unaged (secondary) layers. Figures

6.18(b) and 6.18(c) also show that the crack path remained in the primary adhesive near the

interface of the more highly-strained adherend as the crack growth rate approached the threshold.

167

Figure 6. 16 Fatigue threshold vs. aging time for adhesive 2 specimens aged at 60ºC and 95%

RH. Numbers next to each data point indicate the number of thresholds reached and the number

of specimens tested, respectively. Error bars represent the range of the measurements.

Figure 6. 17 Measured fatigue crack growth rate curves for adhesive 2 specimens aged at 60°C–

95% RH. Aging time is given in the legend.

0

50

100

150

0 30 60 90 120 150 180

Gth

, J/m

2

Aging time, days

2,22,2

2,2

-7

-6

-5

-4

-3

1.6 2 2.4 2.8 3.2

Lo

g (

da

/dN

), m

m/c

ycle

Log (Gmax), J/m2

Fresh

60 days

180 days

168

Figure 6. 18 Fracture surfaces of adhesive 2 specimens on the more highly-strained adherend for

an unaged closed joint (A) and for two 180 days aged specimens at 60ºC – 95% RH with crack

path at higher crack growth rates in the primary layer (specimen B) and in the secondary layer

(specimen C). Crack growth from left to right corresponding to an applied G that decreased

from left to right toward the threshold. Specimens were fractured after reaching Gth.

6.3.4.1 Degradation mechanisms of adhesive 2

As discussed above, Figs. 6.16 and 6.17 show that aging of adhesive 2 caused Gth to

decrease significantly with aging time, but that crack growth rates were mostly unaffected by

aging. Following the reasoning used in Section 3.3.2 to explain the differences between the

threshold and crack propagation behaviors in adhesive 1, it is possible that the rubber toughening

mechanisms that were present at relatively high crack growth rates above threshold were absent

as the crack growth rates reached threshold.

A marked difference was observed between both adhesives in their degradation behavior

at crack growth rates above threshold: while adhesive 1 degraded with aging time adhesive 2 did

not degrade, even after prolonged aging. This difference in degradation combined with the key

169

observation that retained water in the form of bound water was present only in adhesive 1 and

not in adhesive 2, suggests that the bound water in adhesive 1 may have been responsible for

degradation at relatively high crack growth rates. Since rubber toughening mechanisms are

strongly affected by the adhesion between the rubber particles and the matrix [30-32], a possible

explanation for the degradation in adhesive 1 was that the retained bound water disrupted

chemical bonds between the rubber particles and the matrix by being bound at the rubber-matrix

interface. This hypothesis was supported by an earlier observation by Ameli et al.. [14] that

showed that the degraded fracture toughness of adhesive 1 decreased to a low value which was

approximately equal to the fracture toughness of an un-toughened epoxy. The negligible

retained water in adhesive 2 suggests that the chemical bonds at the rubber-matrix interface

could not have been disrupted in this way, thereby leaving the toughening mechanisms and

consequently the crack growth rates unaffected in adhesive 2. This is consistent with the work in

ref. [14] showing that the quasi-static fracture toughness of adhesive 2 remained unchanged

when aged under these same conditions.

It is interesting to note that aging was done at temperatures below the wet Tg for adhesive

1 and above the wet Tg for adhesive 2 (see Table 6.2). Further work is required to determine if

aging at temperatures above Tg, when the adhesive was in the rubbery state, had an effect on

degradation that was independent of the effect attributable to the absence of retained water in

adhesive 2.

6.4 Conclusions

Two rubber-toughened epoxy adhesives exhibited very different degradation behaviors

when aged in hot-wet environments. The reasons for these differences were investigated by

comparing the water absorption/desorption behavior and the results of dynamic mechanical

thermal analysis (DMTA). In adhesive 1 a significant amount of absorbed water was retained in

the adhesive even after prolonged drying, whereas in adhesive 2 the amount of retained water

was negligible. The DMTA results showed that retained water in adhesive 1 was bound to the

adhesive constituents and was not in a free state.

170

Aged open-faced ADCB specimens made with these adhesives were subject to cyclic

loading under mixed-mode conditions. The contrasting results illustrated the effects of

environmental degradation of the matrix and the rubber-toughening particles. The fatigue

threshold strain energy release rate, Gth, of adhesive 1 initially decreased with aging time until it

reached a constant minimum value for long times. Similarly, fatigue crack growth rates initially

increased with aging time until reaching a limiting upper value. However, Gth reached the

minimum value sooner than did the crack growth rate. In contrast, Gth of adhesive 2 decreased

significantly with aging time while the crack growth rates remained unchanged, even after

prolonged aging.

These differences in fatigue threshold and crack growth rate behavior were explained by

the changes in the size of the plastic zone at the crack tip as the applied loads changed. At

relatively high crack growth rates, rubber-toughening mechanisms were active because of the

relatively large plastic zone. These mechanisms were much less effective when the crack tip

plastic zones became smaller with the decreasing applied loads as the crack growth rates

approached the threshold. The differences in the effects of degradation between the two

adhesives at relatively high crack growth rates is believed to be primarily related to the amount

of retained, bound water. The experimental observations were consistent with the hypothesis

that bound water disrupted the rubber/matrix interface in adhesive 1, thereby degrading the

toughening mechanisms. Having no retained, bound water, adhesive 2 was unaffected by this

degradation.

The hypothesis that degradation can be correlated with the time integral of the water

concentration in the adhesive layer (the “exposure index”, EI) was evaluated using different

combinations of water concentration and exposure time that gave the same EI. For the range of

EI values that were investigated, it was found that such path independence did not exist. This

limits the applicability of the EI approach, at least for the relatively small EI values that were

studied.

171

6.5 References

1. M.A. Wahab, I.A. Ashcroft, A.D. Crocombe, S.J. Shaw, Diffusion of moisture in

adhesively bonded joints, J. Adhes.77(2001) 43–80.


diffusion in an epoxy adhesive detected by magnetic resonance imaging. J. Appl. Polym.

Sci. 109(2008) 1350–1359.

3. M. Fernandez-Garcia, M.Y.M. Chiang, Effect of hygrothermal aging history on sorption

process, swelling, and glass transition temperature in a particle-filled epoxy-based

adhesive, J. Appl. Polym. Sci. 84(2002) 1581–1591.

4. P. Musto, G. Ragosta, L. Mascia. Vibrational spectroscopy evidence for the dual nature

of water sorbed into epoxy resins, Chem. Mater. 12(2000) 1331–1341.

5. S. Roy, W.X. Xu, S.J. Park, K.M. Liechti, Anomalous moisture diffusion in viscoelastic

polymers: modeling and testing, J. Appl. Mech. 67(2000) 391–396.

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Chapter 7 Conclusions and Recommendations

7.1 Conclusions

7.1.1 Fresh adhesive joints

A reinforced sheet specimen was used to study the fatigue behavior of thin sheet

adherends without yielding. It was concluded that the additional compliance of the reinforcing

adhesive layer had an insignificant effect on the stress state at the crack tip, and thus the strain

energy release rate and phase angle of loading. Therefore, the laminated sheet specimen can be

used to measure fatigue behavior that is characteristic of the adhesive-sheet system, being

unaffected by the reinforcement. This is useful in the fatigue testing of metal sheets that have

been coil coated with pretreatments that cannot be applied reliably on thicker material.

Fatigue experiments were conducted with ADCB (phase angle 13) and CLS (phase

angle 50) specimens made with reinforced aluminum sheet that had been pretreated using a

commercial coil-coating process. It was found that the fatigue threshold was sensitive to the

orientation of the rolling lines on the sheet at higher phase angles, being increased significantly

when the rolling lines were perpendicular to the direction of crack growth on the CLS specimens

(transverse to the specimen length). The fatigue crack growth rates were very similar for all

specimens except the CLS specimens having the transverse rolling lines, where they were lower.

These observations were related to the increasing proximity of the crack path to the sheet

interface as the phase angle increased.

Fatigue testing of the coil-coated sheet in a hot-wet environment significantly reduced the

threshold compared to testing in room temperature dry air. The crack path in the hot-wet

environment became fully interfacial, whereas it was cohesive in the dry case.

7.1.2 Water diffusion in toughened epoxy adhesives

The water absorption and desorption of two different rubber-toughened epoxy adhesives

were characterized using gravimetric measurements. A newly developed sequential dual Fickian

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(SDF) model was developed to fit the fractional mass uptake profiles and agreed well with the

Langmuir diffusion model. The diffusion mechanism in the first stage appeared to be influenced

by hydrogen bonding while the diffusion mechanism in the second stage was primarily physical

in nature. The diffusion coefficients in both stages were found to be largely independent of RH,

while the saturated fractional mass uptake values increased with RH. The diffusion coefficient

of the first stage and the saturated fractional mass uptake of the second stage were both functions

of temperature. These functional dependencies were described, making the SDF model

predictive over the ranges of temperature and RH that were investigated.

The desorption during drying in both adhesives was described well by Fick’s law. Both

gravimetric results and XPS revealed that there was a significant difference between the amounts

of minimum fractional retained water in the two adhesives after drying. The relatively large

amount of retained water in adhesive 1 was attributed to multiple hydrogen bonds between the

water molecules and the epoxy or other constituents such as the rubber toughener particles or the

filler. In a separate test program, it was found that these differences in water absorption-

desorption corresponded to marked differences in the degradation of fracture toughness in hot-

wet aging environments (to appear in a future publication).

The SDF model can be used to predict the water concentration distribution in adhesive

joints exposed to environments of changing temperature and RH under the assumption of

negligible interface diffusion.

7.1.3 Effects of test environment

The temperature and humidity of the test environment were found to have a significant

effect on the mixed-mode fatigue behavior of aluminum adhesive joints. Under dry conditions,

there was little change in the fatigue threshold over the temperature range 20-80ºC, but the crack

growth rate in the Paris law region increased significantly with increasing temperature, and the

crack path tended to move away from the interface. These observations were consistent with the

growth of the crack-tip plastic zone with increasing temperature, as predicted using finite

element modeling. A larger plastic zone would lead to greater damage accumulation, resulting in

increased crack growth rates and residual adhesive thickness.

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Fatigue behavior was insensitive to ambient moisture at higher crack growth rates, but

became sensitive to the moisture level as crack growth rates neared the threshold where the

speed of moisture diffusion ahead of crack tip was greater than the crack growth rate. In

particular at 100% RH, the crack growth rate became independent of the applied strain energy

release rate, G, for a small range of G just above the threshold. This inflection in the curve of

crack growth rate vs. G may have been caused by the crack growth increment per cycle being

limited to the thickness of the hydrated oxide film forming at the crack tip between loading

cycles. This is analogous to the mechanism that has been proposed for a similar inflection

reported in the fatigue of aluminum alloys. As the humidity in the test environment reached the

saturation level, moisture condensed behind the crack tip. It is believed that this increased water

diffusion to the point where it exceeded a critical moisture level needed to hydrate the oxide

layer ahead of the crack tip. This hydration may then have caused a shift in crack path to the

interface and a decrease in Gth.

Finally, the combined effects of elevated temperature and humidity were explained from

this understanding of the individual effects of temperature and humidity. At higher crack growth

rates, the joint fatigue performance degraded solely due to the increased temperature, whereas at

low crack growth rates, fatigue performance degraded predominantly because of the elevated

moisture. These effects of a hot-wet testing environment on fatigue behavior were found to be

similar for both a P2-etch pretreatment and a commercial coil-coat pretreatment.

7.1.4 Effects of long-term aging environments

7.1.4.1 Adhesive system with CC aluminum sheet adherend

The mixed-mode fatigue behavior of degraded toughened epoxy-aluminum adhesive

joints was studied using open-faced ADCB specimens. Both constant humidity environments

and cyclic environments were studied. In constant humidity environments, the fatigue threshold

and crack growth rate behavior were affected differently. The fatigue threshold strain energy

release rate, Gth, decreased from an undegraded value to a constant minimum value that did not

change even after prolonged aging. In contrast, the crack growth rates continued to increase with

aging time, showing no tendency to reach a limiting value. It was hypothesized that the

continuing increase in the crack growth rate with aging time was related to the loss of the rubber

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toughening mechanism, and that the decrease in Gth was related to the degradation of the epoxy

matrix. Increasing the aging temperature accelerated the rate at which Gth decreased from its

initial value. The crack paths remained cohesive in the adhesive layer in all of the experiments,

with the residual adhesive thickness on the more highly-strained adherend decreasing as the

crack growth rate (or applied G) decreased.

For joints aged in the cyclically changing environment with intermittent salt spray,

neither Gth nor the crack growth rates degraded until after four weeks of aging. The superior

fatigue performance of these joints compared to joints aged in constant humidity environments

was due to the lower equilibrium water concentrations in the adhesive, which were modeled

using the finite element method. This was supported by moisture uptake measurements of the

adhesive in deionised and salt water environments which showed that the diffusion was simple

Fickian at room temperature and dual-Fickian at the higher temperatures. The salt spray

produced an osmotic pressure that affected the diffusion kinetics of the mobile water molecules

in the epoxy during absorption.

7.1.4.2 Adhesive system with P2-etched aluminum bar adherends

The mixed-mode fatigue beahvior of two toughened epoxy adhesives were studies using

open-faced ADCB specimens. The contrasting results illustrated the effects of environmental

degradation of the matrix and toughener. The fatigue threshold strain energy release rate, Gth,

and the crack growth rates of adhesive system 1 degraded in two stages: Gth initially decreased

with aging time until it reached a constant minimum value for long times. Similarly, fatigue

crack growth rates initially increased with aging time until reaching a limiting upper value.

However, Gth reached the minimum value sooner than did the crack growth rate. In contrast, the

Gth of adhesive system 2 decreased significantly with aging while the crack growth rates

remained unchanged even after prolonged aging. These differences in fatigue threshold and

crack growth rates behavior of both adhesives was explained by the rubber toughening

mechanisms that were present at relatively high crack growth rates above threshold and were

absent as the crack growth rates reached threshold.

Gravimetric measurements and dynamic mechanical thermal analysis (DMTA) illustrated

the differences in the two adhesives. In adhesive 1 a significant amount of absorbed water was

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retained in the adhesive even after prolonged aging, where as in adhesive 2 the amount of

retained water was negligible. The DMTA results showed that retained water in adhesive 1 was

bound strongly to the adhesive constituents and is not in a free state. From these observations,

the difference in the fatigue degradation behavior between the two adhesives at relatively high

crack growths was related to the bound water that disrupted the rubber/matrix interface in

adheisve1, and did not disrupt the the rubber/matrix interface in adhesive 2 due to negligible

amount of bound water. Another observation to explain the differences between both adhesives

was that aging decreased Tg below the aging temperature for adhesive 2, whereas Tg was well

above the aging temperature for adhesive 1. It was hypothesized that the aging of adhesive 2 at

temperatures above Tg did not degrade the toughening mechanism, but did produce degradation

of the epoxy matrix.

Evaluation of the degradation in fatigue threshold and crack growth rates with the

humidity-time exposure history (pathway) showed that degradation was path dependent, thereby

invalidating the EI hypothesis for the fatigue threshold and crack growth rates.

7.2 Future work

1. The current study used open-faced specimens to measure the degradation in fatigue

threshold and crack growth rates with aging. A natural extension of this study is to use

open-faced results to predict long-term fatigue behavior of closed joints.

2. Investigate the role of water plasticization on the degradation of aged joints. Such a

study combined with the present results on irreversible degradation (done by drying the

aged specimens before testing) will explain the degradation behaviour of wet, aged joints.

3. This study invalidated the EI hypothesis, at least for the extent of aging times studied in

this research. However, further study needs to be done to determine if this is true for

longer aging times, and to explore other degradation parameters that can characterize an

aging history and may be uniquely related to fatigue degradation.

4. Study degradation of galvanized steel adhesive joints using open-faced specimens.

5. This study showed the applicability of open-faced specimens to characterize degradation

behaviour of joints that failed cohesive in the adhesive layer. To generalise the

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applicability of open-faced specimens, further study needs to be done to characterize

adhesives systems that fail at the adhesive/adherend interface upon degradation.

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