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BOND BEHAVIOUR AND DEBONDING FAILURES

IN CFRP-STRENGTHENED STEEL MEMBERS

NANGALLAGE DILUM FERNANDO

Ph.D

The Hong Kong Polytechnic University

2010

lbsys

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This thesis in electronic version is provided to the Library by the author. In the case where its contents is different from the printed version, the printed version shall prevail.

The Hong Kong Polytechnic University

Department of Civil and Structural Engineering

BOND BEHAVIOUR AND DEBONDING

FAILURES IN CFRP-STRENGTHENED STEEL

MEMBERS

By

NANGALLAGE DILUM FERNANDO

BEng

A Thesis Submitted in Partial Fulfilment of the Requirements for

the Degree of Doctor of Philosophy

August 2010

I

CERTIFICATE OF ORIGINALITY

I hereby declare that this thesis is my own work and that, to the best of my

knowledge and belief, it reproduces no material previously published or written, nor

material that has been accepted for the award of any other degree or diploma, except

for where due acknowledge has been made in the text.

(Signed)

Nangallage Dilum FERNANDO

(Name of student)

II

ABSTRACT

Strengthening of steel structures with adhesively bonded carbon fibre reinforced

polymer (CFRP) plates (or laminates) has attracted much recent research attention.

In the strengthening of steel structures, CFRP is preferred to glass FRP (GFRP) due

to the much higher elastic modulus of the former. Existing studies have revealed

that debonding of the CFRP plate from the steel substrate is one of the main failure

modes in CFRP-strengthened steel structures. This thesis presents a series of

experimental and theoretical studies aimed at the development of a good

understanding of the mechanisms of and reliable theoretical models for debonding

failures in CFRP-strengthened steel structures.

Debonding failures between steel and CFRP may occur in the following modes: (a)

within the adhesive (cohesion failure); (b) at the bi-material interfaces between the

adhesive and the adherends (adhesion failure); (c) a combination of adhesion failure

and cohesion failure. Among these failure modes, cohesion failure in the adhesive is

the preferred mode of debonding failure at CFRP-to-steel interfaces as for such

debonding failure, the design theory can be established based on the properties of

the adhesive. A systematic experimental study is first presented in this thesis to

examine the effects of steel surface preparation and adhesive properties on the

adhesion strength between steel and adhesive. The test results show that the

adhesive bonding capability of a steel surface can be characterised using three key

surface parameters and that adhesion failure can be avoided if the steel surface is

grit-blasted prior to bonding.

Following an experimental study with sophisticated instrumentation which

confirmed the suitability of the single-shear pull-off test method for studying the

behaviour of CFRP-to-steel interfaces subjected to pure shear loading, the full-

range behaviour of CFRP-to-steel interfaces was then investigated through a series

of tests using this test setup. The focus of these tests was on the interfacial

behaviour when governed by cohesion failure. The parameters examined include

the material properties and the thickness of the adhesive layer and the axial rigidity

III

of the CFRP plate. The test results demonstrated that the bond strength of such

bonded joints depends significantly on the interfacial fracture energy among other

factors. Non-linear adhesives with a lower elastic modulus but a larger strain

capacity are shown to lead to a much higher interfacial fracture energy than linear

adhesives with a similar or even a higher tensile strength. The bond-slip curve is

shown to have an approximately triangular shape for a linear adhesive but to have a

trapezoidal shape for a non-linear adhesive.

Based on the experimental observations and results from single-shear pull-off tests,

bond-slip models were developed for CFRP-to-steel interfaces with a linear

adhesive and those with a non-linear adhesive respectively. The bond-slip models

include an explicit formula which predicts the interfacial fracture energy from the

properties of the adhesive. Analytical solutions were also developed for predicting

the full-range bond behaviour and the bond strength of CFRP-to-steel bonded joints,

with the definition of the effective bond length addressed as an important issue.

By making use of the bond-slip model for linear adhesives developed in the present

work, finite element modelling was conducted to simulate debonding failures in

steel beams flexurally-strengthened with CFRP. In the FE model, the bond-slip

model was employed with a mixed-mode cohesive law which considers the effect of

interaction between mode I loading and mode II loading on damage propagation

within the adhesive. Predictions from the FE model are shown to compare well with

existing test results. The proposed FE model represents a significant advancement

in the modelling of debonding failures in CFRP-strengthened steel structures.

The last part of the thesis extends the capability of FE analysis to the prediction of

debonding failures in the more complex problem of rectangular steel tubes with

CFRP plates bonded on the webs subjected to an end bearing load. A series of tests

is first presented, in which the effects of adhesive types and web slenderness on the

effectiveness of CFRP strengthening were examined. The failure of such members

is normally controlled by the debonding of the CFRP plates, so the properties of the

adhesive used are shown to be very important. The test results show that an

adhesive with a larger strain energy (e.g. a softer nonlinear adhesive) leads to a

larger load-carrying capacity for a strengthened rectangular hollow section (RHS)

IV

steel tubes. A FE model is next presented, in which the effect of interaction between

mode I loading and mode II loading on damage propagation within the adhesive is

duly considered. This FE model is shown to closely predict the experimental

behaviour of these CFRP-strengthened tubes.

V

LIST OF PUBLICATIONS

Refereed Journal Papers: 1. Fernando, D., Yu, T., Teng, J.G. and Zhao, X.L. (2009). "CFRP

strengthening of rectangular steel tubes subjected to end bearing loads:

Effect of adhesive properties and finite element modelling", Thin-Walled

Structures, 47(10), 1020-1028.

Conference Papers: 1. Fernando, N.D, Teng, J.G., Yu, T. and Zhao, X.L. (2007), “Finite element

modelling of CFRP-strengthened rectangular steel tubes subjected to end

bearing loads”, Proceedings of the 1st Asia-Pacific Conference on FRP in

Structures (APFIS 2007), December 12-14,Hong Kong.

2. Fernando, D., Yu, T., Teng, J.G. and Zhao X.L. (2008), “CFRP

strengthening of rectangular steel tubes subjected to end bearing loads:

effect of adhesive properties”, Proceedings of the Fourth International

Conference on FRP Composites in Civil Engineering (CICE2008), July 22-

24, Zurich, Switzerland.

3. Teng, J.G., Yu, T. and Fernando, D. (2009), “FRP composites in steel

structures”, Proceedings of the Third International Forum on Advances in

Structural Engineering, November 13-14, Shanghai, China.

4. Teng, J.G., Fernando, D., Yu, T. and

5. Fernando, D., Yu, T., Teng, J.G. and Zhao, X.L. (2010). "Experimental

behaviour of CFRP-to-steel bonded interfaces", Proceedings of the 11th

International Symposium of Structural Engineering, December 18-20,

Guang Zhou, China.

Zhao, X.L. (2010), “Preparation of

steel surfaces for adhesive bonding”, CICE 2010 - The 5th International

Conference on FRP Composites in Civil Engineering”, September 27-29,

2010 Beijing, China.

VI

ACKNOWLEDGEMENTS

I would first like to thank my supervisor, Professor Jin-Guang Teng, for all his

patience and guidance. I feel privileged to have learned under his supervision. He

has given me many opportunities for which I am very grateful.

I would also like to thank my co-supervisor, Dr. Tao YU, for his valuable guidance

and friendship. I am grateful to him for making his time freely available for me, and

his valuable advices that helped ensure the successful completion of this thesis. He

has also been a good friend to me and offered me help in many ways, for which I

am very grateful.

Thanks are also due to my second co-supervisor, Professor Xiao-Ling Zhao of

Monash University, Australia, who gave me much help in securing this opportunity

to study at The Hong Kong Polytechnic University. I also thank him for his many

advices and support during my PhD study.

I humbly thank all my colleagues at The Hong Kong Polytechnic University, Drs

Lei ZHANG, Guangming CHEN, Owen ROSENBOOM, and Wallace LAI and as

well as Messrs Yueming HU, Shishun ZHANG and Qiongguan XIAO among many

others for all their help and friendship.

My heartfelt gratitude also goes to all the laboratory technicians at The Hong Kong

Polytechnic University, especially Mr King Hei WONG, for fabricating the test rigs

and for helping me with various technical difficulties I faced during my

experimental work.

I would like to thank Dr Ann Schumacher for her valuable guidance during my stay

at the Swiss Federal Laboratories for Materials Testing and Research (EMPA).

Thanks also go to Professors Hamid Rabinovitch and Masoud Motavalli, Dr

Dimosthenis Rizos, Mr Christoph Czaderski and all the laboratory technicians at

EMPA for valuable advices and support.

VII

I would also like to thank my family, my mother Thilaka, sister Nadee, brother in-

law Ramesh, little Gabby and especially my wife Emma Yun ZHOU, for their

understanding and patience over the years. Last, but certainly not least, I would like

to thank my friends, both old and new: to the old friends for keeping in touch with

me and believing in me and to the new friends I have made in Hong Kong for

making this city a second home.

VIII

TABLE OF CONTENTS CERTIFICATE OF ORIGINALITY ................................................................. I

ABSTRACT .................................................................................................. II

LIST OF PUBLICATIONS ............................................................................ V

AKNOWLEDGEMENTS .............................................................................. VI

TABLE OF CONTENTS ............................................................................ VIII

LIST OF FIGURES ....................................................................................XIV

LIST OF TABLES ......................................................................................XXI

NOTATION.............................................................................................. XXIII

CHAPTER 1: INTRODUCTION .................................................................. 1

1.1 BACKGROUND .................. .................................................................. 1

1.2 EFFECTIVE USE OF FRP WITH STEEL............................................... 2

1.3 OBJECTIVES AND SCOPE .................................................................. 3

REFERENCES.......................... .................................................................. 8

CHAPTER 2: LITERATURE REVIEW ....................................................... 12

2.1 INTRODUCTION ................. ................................................................ 12

2.2 BOND BEHAVIOUR BETWEEN FRP AND STEEL ............................. 12

2.2.1 General .................. ................................................................ 12

2.2.2 Adhesion Failure.... ................................................................ 14

2.2.3 Bond Behaviour ..... ................................................................ 17

2.2.3.1 Bond strength ........................................................... 18

2.2.3.2 Bond-slip relationship ............................................... 20

2.3 FLEXURAL STRENGTHENING OF STEEL BEAMS ............................ 22

2.3.1 Plate End Debonding.............................................................. 23

2.3.2 Intermediate Debonding ......................................................... 24

2.4 FATIGUE STRENGTHENING .............................................................. 25

2.5 STRENGTHENING OF STEEL STRUCTURES AGAINST LOCAL

BUCKLING .......................... ................................................................ 27

2.5.1 Buckling Induced by High Local Stresses ............................... 27

2.5.2 Buckling Induced by Other Loads ........................................... 27

IX

2.6 CONCLUSIONS .................. ................................................................ 28

REFERENCES .......................... ................................................................ 31

CHAPTER 3: PREPARATION AND CHARACTERIZATION OF STEEL SURFACES FOR ADHESIVE BONDING ................ 42

3.1 INTRODUCTION ................ ................................................................ 42

3.2 ADHESION MECHANISMS ................................................................ 43

3.2.1 Physical Bonding.......................................................................43

3.2.2 Chemical Bonding.....................................................................44

3.2.3 Mechanical Interlocking.............................................................44

3.3 ISSUES IN SURFACE PREPARATION .............................................. 45

3.4 SURFACE CHARACTERIZATION……….……… ………………………46

3.4.1 Surface Energy.........................................................................46

3.4.2 Surface Chemical Composition .............................................. 48

3.4.3 Surface Roughness ................................................................ 48

3.5 EXPERIMENTAL PROGRAMME AND PROCEDURES...................... 50

3.6 RESULTS AND DISCUSSIONS .......................................................... 52

3.6.1 Surface Characteristics........................................................... 52

3.6.1.1 Surface roughness & topography .............................. 52

3.6.1.2 Surface chemical composition................................... 54

3.6.1.3 Surface energy .......................................................... 54

3.6.1.4 Inter-relationship between surface characteristics .... 56

3.6.2 Adhesion Strength . ................................................................ 57

3.7 CONCLUSIONS .................. ................................................................ 60

REFERENCES.......................... ................................................................ 62

CHAPTER 4: VALIDITY OF SINGLE-SHEAR PULL-OFF TESTS FOR SHEAR BOND BEHAVIOUR STUDIES ...................... 79

4.1 INTRODUCTION ................. ................................................................ 79

4.2 EXPERIMENTAL PROGRAMME ......................................................... 82

4.2.1 Specimen Preparation and Test Set-up .................................. 82

4.2.2. The Aramis Measurement System ........................................ 83

4.3 RESULTS AND DISCUSSIONS .......................................................... 85

4.4 FINITE ELEMENT MODEL . ................................................................ 88

X

4.4.1 Mesh Sensitivity..... ................................................................ 89

4.4.2 FE Investigation of Damage Initiation ..................................... 90

4.5 CONCLUSIONS .................. ................................................................ 93

REFERENCES.......................... ................................................................ 95

CHAPTER 5: EXPERIMENTAL BEHAVIOUR ON CFRP-TO-STEEL BONDED JOINTS .............................................................. 121

5.1 INTRODUCTION ................. .............................................................. 121

5.2 TEST PROGRAMME .......... .............................................................. 122

5.2.1 Test Method and Set-up ....................................................... 122

5.2.2 Specimen Details... .............................................................. 122

5.2.3 Instrumentation and Loading Procedure ............................... 124

5.3 TEST RESULTS AND DISCUSSIONS .............................................. 125

5.3.1 General .................. ............................................................. .125

5.3.2 Load-Displacement Behaviour .............................................. 126

5.3.3 Axial Strain Distribution along the FRP Plate........................ 128

5.3.4 Bond-Slip Behaviour ............................................................. 129

5.3.5 Bond Strength ........ .............................................................. 132

5.3.6 Interfacial Shear Stress Distributions .................................... 133

5.3.7 Effect of Adhesive Thickness ................................................ 134

5.3.8 Effect of Plate Axial Rigidity .................................................. 135

5.4 CONCLUSIONS .................. .............................................................. 135

REFERENCES.......................... .............................................................. 137

APPENDIX 5.1: ADDITIONAL FIGURES ……… ................................... 163

CHAPTER 6: THEORETICAL MODEL FOR FULL-RANGE BEHAVIOUR OF CFRP-TO-STEEL BONDED JOINTS..... 180

6.1 INTRODUCTION ................. .............................................................. 180

6.2 INTERFACIAL FRACTURE ENERGY UNDER MODE II LOADING .. 181

6.3 BOND-SLIP MODELS FOR CFRP-TO-STEEL BONDED

INTERFACES ..................... .............................................................. 183

6.3.1 Linear Adhesives ... .............................................................. 183

6.3.1.1 Accurate model ....................................................... 184

6.3.1.2 Bi-linear model ........................................................ 185

XI

6.3.2 Non-Linear Adhesives .......................................................... 186

6.4 FULL-RANGE BEHAVIOUR OF CFRP-TO-STEEL BONDED

JOINTS ............................... .............................................................. 188

6.4.1 Governing Equations ............................................................ 188

6.4.2. Analytical Solution for Linear Adhesives .............................. 191

6.4.3. Analytical Solution for Non-Linear Adhesives ...................... 191

6.4.3.1 Elastic stage ........................................................... 192

6.4.3.2 Elastic-plastic stage ................................................ 194

6.4.3.3 Elastic-plastic-softening stage ................................ 197

6.4.3.4 Elastic-plastic-softening-debonding stage .............. 201

6.4.3.5 Plastic-softening-debonding stage .......................... 202

6.4.3.6 Softening-debonding stage ..................................... 203

6.4.4 Comparison between Analytical Solution and

Experimental Results .......................................................... 203

6.4.4.1 Load-displacement curves ...................................... 203

6.4.4.2 Interfacial shear stress distributions ........................ 204

6.4.5 Effect of the Shape of the Bond-Slip Model .......................... 205

6.5 BOND STRENGTH MODEL .............................................................. 206

6.6 CONCLUSIONS .................. .............................................................. 207

REFERENCES.......................... .............................................................. 209

CHAPTER 7: FINITE ELEMENT MODELLING OF DEBONDING FAILURES IN STEEL BEAMS FLEXURALLY-STRENGTHENED WITH CFRP.......................................... 227

7.1 INTRODUCTION ................. .............................................................. 227

7.2 MODELLING OF CFRP-TO-STEEL INTERFACES ........................... 228

7.2.1 General .................. .............................................................. 228

7.2.2 Coupled Cohesive Zone Model ............................................ 230

7.2.2.1 Bond-slip model ...................................................... 230

7.2.2.2 Bond-separation model ........................................... 230

7.2.2.3 Mixed-mode cohesive law ....................................... 231

7.2.2.4 Implementation of the coupled cohesive zone

model in ABAQUS .................................................. 235

7.3 FE MODELLING OF CFRP-STRENGTHENED STEEL I-BEAMS ..... 235

XII

7.3.1 General .................. ............................................................. .235

7.3.2 Beam Tests Conducted by Deng and Lee (2007) ................. 236

7.3.3 FE Models ............. .............................................................. 236

7.3.4 Results and Discussions....................................................... 239

7.3.4.1 Specimen S300 (control beam) .............................. 239

7.3.4.2 Specimen S303 ...................................................... 239

7.3.4.3 Specimen S304 ...................................................... 243

7.3.4.4 Specimen S310 ...................................................... 243

7.3.4.5 Possible failure modes of CFRP-strengthened

steel beams ............................................................ 244

7.4 CONCLUSIONS .................. .............................................................. 244

REFERENCES.......................... .............................................................. 246

APPENDIX 7.1: FE MODELLING OF STEEL I-BEAM UNDER

FLEXURAL LOADING .................................................... 267

CHAPTER 8: CFRP STRENGTHENING OF RECTANGULAR STEEL TUBES SUBJECTED TO AN END BEARING LOAD ........ 279

8.1 INTRODUCTION ................................................................................ 279 8.2 END BEARING TESTS ....... .............................................................. 280

8.2.1 Test Specimens ..... .............................................................. 280

8.2.2 Material Properties ............................................................. .281

8.2.3 Preparation of Specimens ................................................... .282

8.2.4 Test Set-up and Instrumentation .......................................... 282

8.2.5 Results and Discussions ...................................................... 283

8.2.5.1 Series I-the effect of adhesive type ......................... 283

8.2.5.2 Series II- effect of web depth-to-thickness ratio ...... 286

8.3 FINITE ELEMENT MODELLING ........................................................ 288

8.3.1 Model Description .. .............................................................. 288

8.3.2 Mesh Convergence Study .................................................... 289

8.3.3 Results and Discussions ...................................................... 290

8.4 DESIGN MODELS .............. .............................................................. 293

8.4.1 Existing Work ........ ............................................................. .293

8.4.1.1 The web buckling mode of bare steel tubes............ 293

XIII

8.4.1.2 The web yielding mode of bare steel tubes............. 295

8.4.2 Proposed Model .... .............................................................. 296

8.4.2.1 Web buckling capacity ............................................ 297

8.4.2.2 Web yielding capacity ............................................. 298

8.5 CONCLUSIONS .................. .............................................................. 300

REFERENCES.......................... .............................................................. 303

APPENDIX 8.1: NUMERICAL MODELLING PROCEDURE FOR

COLD-FORMED STEEL RHS TUBES UNDER AN

END BEARING LOAD ................................................ 322

CHAPTER 9: CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH ........................................................ 333

9.1 INTRODUCTION ................. .............................................................. 333

9.2 TREATMENT OF STEEL SURFACES FOR EFFECTIVE

ADHESIVE BONDING ...... .............................................................. 333

9.3 BOND BEHAVIOUR OF CFRP-TO-STEEL BONDED JOINTS ........ .335

9.3.1 Test Method .......... .............................................................. 335

9.3.2 Experimental Behaviour of CFRP-to-Steel Bonded Joints ... 336

9.3.3 Bond-Slip Model .... .............................................................. 337

9.3.4 Analytical Solution for the Full-Range Behaviour of CFRP-

to-Steel Bonded Joints .......................................................... 338

9.3.5 Bond Strength Model ............................................................ 339

9.4 FINITE ELEMENT MODELLING OF DEBONDING FAILURES ......... 339

9.4.1 Modelling of CFRP-to-Steel Interface ................................... 339

9.4.2 Debonding Failures in Steel Beams Flexurally-

Strengthened with CFRP .................................................... 339

9.4.3 Debonding Failures in CFRP-Strengthened RHS Tubes

Subjected to an End Bearing Load ..................................... 340

9.5 FUTURE REASEARCH ..... .............................................................. 342

REFERENCES.......................... .............................................................. 343

XIV

List of Figures

Chapter 1 Figure 1.1 Typical FRP and mild steel stress-strain curves ................................... 11

Figure 1.2 Various failure modes in a CFRP-to-steel bonded joint ....................... 11

Chapter 2 Figure 2.1 Debonding failure modes in a CFRP-plated steel beam ....................... 39

Figure 2.2 Bi-linear bond-slip model ................................................................... 39

Figure 2.3 Stress-strain responses of adhesives..................................................... 40

Figure 2.4 End details of an adhesively-bonded joint............................................ 40

Figure 2.5 Strengthening for high local stresses (Zhao et al. 2006); Type 1-

bare tubes, Types 2 to 6-CFRP-strengthened tubes ............................. 41

Chapter 3 Figure 3.1 Surface energy components acting on a liquid droplet ......................... 69

Figure 3.2 Box counting method for evaluating the fractal dimension .................. 69

Figure 3.3 Stress-strain curves of adhesives ......................................................... 70

Figure 3.4 Tensile butt-joint specimen: (a) Dimensions; and (b) Test set-up ......... 70

Figure 3.5 Single-lap shear specimen: (a) Plan; (b) Elevation; and (c) Test set-

up ...................................................................................................... 71

Figure 3.6 Surface images from SEM/EDX analysis for different surface

types .................................................................................................. 72

Figure 3.7 Roughness parameter and fractal dimension for different surface

types .................................................................................................. 73

Figure 3.8 Chemical compositions of different surface types ................................ 73

Figure 3.9 Surface energies of different surface types .......................................... 74

Figure 3.10 Effect of average surface roughness on surface energy ...................... 74

Figure 3.11 Effect of surface topography on surface energy ................................. 74

Figure 3.12 Failed surfaces of tensile butt-joint test specimens ............................. 75

Figure 3.13 Failed surfaces of single-lap shear test specimens .............................. 76

Figure 3.14 Effect of fractal dimension on tensile butt-joint strength .................... 77

Figure 3.15 Effect of fractal dimension on single-lap shear joint strength ............. 77

XV

Figure 3.16 Effect of surface energy on tensile butt-joint strength ........................ 78

Figure 3.17 Effect of surface energy on single-lap shear joint strength ................. 78

Chapter 4 Figure 4.1 Single-shear pull-off test set-up ........................................................... 98

Figure 4.2 Support system for thickness control of the adhesive layer .................. 99

Figure 4.3 Support and loading .......................................................................... 100

Figure 4.4 Measurement window of the Aramis system...................................... 101

Figure 4.5 Failed specimen ................................................................................ 102

Figure 4.6 Experimental load-displacement curve from a single-shear pull-off

test ................................................................................................... 102

Figure 4.7 Strain distributions along the top of the CFRP plate at different

load levels ....................................................................................... 103

Figure 4.8 Failure process: major principal strain plots from Aramis (red

colour-high strain/cracks to blue colour-low strain) .......................... 104

Figure 4.9 Crack path plot based on the major principal strain pattern at 15kN ... 105

Figure 4.10 Strain-load curves for selected points .............................................. 106

Figure 4.11 Strain distributions along section A-A ............................................. 107

Figure 4.12 Details of the FE model ................................................................... 108

Figure 4.13 Interfacial shear and peeling stress distributions along the PA

interface ........................................................................................... 110

Figure 4.14 Interfacial shear and peeling stress distributions along the SA

interface ........................................................................................... 112

Figure 4.15 Interfacial shear and peeling stress distributions along the MA

plane ................................................................................................ 114

Figure 4.16 Shear stress distributions across the adhesive layer at the loaded

end ................................................................................................... 115

Figure 4.17 Peeling stress distributions across the adhesive thickness at the

loaded end ....................................................................................... 115

Figure 4.18 Fillet details at joint end .................................................................. 116

Figure 4.19 Axial and vertical displacement at the top surface of CFRP:

comparison between the FE model and the Aramis data ................... 117

Figure 4.20 Strain distributions along the top surface of CFRP from Aramis,

strain gauges and the FE model ........................................................ 118

XVI

Figure 4.21 Stress distributions along section A-A from the FE model with a

1.5mm radius fillet ........................................................................... 119

Figure 4.22 Major principal strain directions at 24kN ......................................... 119

Figure 4.23 Mechanism of failure away from the loaded end .............................. 120

Chapter 5 Figure 5.1 Single-shear pull-off test specimen and instrumentation .................... 144

Figure 5.2 Test rig .............................................................................................. 145

Figure 5.3 Failed specimens ............................................................................... 148

Figure 5.4 Load-displacement curves ................................................................. 151

Figure 5.5 Comparison of displacements obtained from LVDT and strain

gauge readings ................................................................................. 151

Figure 5.6 Strain distributions in specimen A-NM-T1-I: (a) Variation with

load level; (b) Variation with propagation of debonding ................... 152

Figure 5.7 Strain distributions in specimen C-NM-T1-I: (a) Variation with

load level; (b) Variation with propagation of debonding ................... 153

Figure 5.8 Experimental bond-slip curves for specimens failing in cohesion

failure .............................................................................................. 158

Figure 5.9 Idealized bond-slip curves ................................................................. 159

Figure 5.10 Comparison between experimental and predicted bond strengths ..... 160

Figure 5.11 Interfacial shear stress distributions of A-NM-T1-I at different

stages of deformation ....................................................................... 161

Figure 5.12 Interfacial shear stress distributions of C-NM-T1-I at different

stages of deformation ....................................................................... 162

Appendix 5.1 Figure A5.1 Strain distributions with (a) increasing load level (P/Pu); (b)

damage propagation for A-NM-T1-II specimen ............................... 163

Figure A5.2 Strain distributions with increasing load level (P/Pu) B-NM-T1-I

specimen .......................................................................................... 164

Figure A5.3 Strain distributions with increasing load level (P/Pu) B-NM-T1-

II specimen ...................................................................................... 164

Figure A5.4 Strain distributions with (a) increasing load level (P/Pu); (b)

damage propagation for C-NM-T1-II specimen................................ 165

XVII


damage propagation for D-NM-T1-I specimen ................................. 166


damage propagation for D-NM-T1-II specimen ............................... 167


damage propagation for A-NM-T1.5 specimen ................................ 168


damage propagation for A-NM-T2 specimen ................................... 169


damage propagation for A-NM-T3 specimen ................................... 170

Figure A5.10 Strain distributions with increasing load level (P/Pu) for C-NM-

T3 specimen .................................................................................... 171

Figure A5.11 Strain distributions with increasing load level (P/Pu for C-NM-

T2 specimen .................................................................................... 171


damage propagation for A-MM-T1 specimen................................... 172


damage propagation for A-HM-T1 specimen ................................... 173

Figure A5.14 Strain distributions with increasing load level (P/Pu) for A-ST-

T1 specimen .................................................................................... 174


damage propagation for C-MM-T1 specimen ................................... 175

Figure A5.16 Strain distributions with increasing load level (P/Pu) for C-HM-

T1 specimen .................................................................................... 175

Figure A5.17 Experimental bond-slip curves for specimens in series-I ............... 177

Figure A5.18 Experimental bond-slip curves for specimens in series-II .............. 178

Figure A5.19 Experimental bond-slip curves for specimens in series-III ............ 179

Chapter 6 Figure 6.1 Predicted versus experimental values of interfacial fracture energy

.................................................................................................. 212

Figure 6.2 Variation of experimental interfacial fracture energy fG with the

square of strain energy (adhesives A and C) ..................................... 213

fG

XVIII

Figure 6.3 Variation of experimental interfacial fracture energy fG with the

square root of adhesive thickness ..................................................... 213

Figure 6.4 Predicted versus experimental values of peak bond shear stress ........ 214

Figure 6.5 Predicted versus experimental slips at peak bond shear stress for

linear adhesives ............................................................................... 214

Figure 6.6 Predicted versus experimental bond-slip curves for linear

adhesives ......................................................................................... 216

Figure 6.7 Predicted versus experimental bond-slip curves for non-linear

adhesives (only applicable for adhesive C) ....................................... 217

Figure 6.8 Single-shear pull-off test of a CFRP-to-steel bonded joint ................. 218

Figure 6.9 Horizontal equilibrium of a bonded joint ........................................... 219

Figure 6.10 Local bond-slip model for non-linear adhesives ............................... 219

Figure 6.11 Interfacial shear stress distribution and propagation of debonding

for a larger bond length (a) elastic stress state; (b) initiation of

plastic state at x=L, point A in Figure 6.12; (c) elastic-plastic

stress state; (d) initiation of softening at x=L, point B in Figure

6.12; (e) elastic-plastic-softening state; (f) initiation of debonding

at x=L, point C in Figure 6.12; (g) elastic-plastic-softening-

debonding state; (h) initiation of plastic state at x=0; (i) initiation

of softening at x=0, point F in Figure 6.12; (j) linear unloading ........ 220

Figure 6.12 Typical theoretical full-range load-displacement curve for CFRP-

to-steel bonded joints with a non-linear adhesive ............................. 221

Figure 6.13 Predicted versus experimental load-displacement curves ................. 222

Figure 6.14 Predicted versus experimental interfacial shear stress distributions

for points shown in Figure 5.10a for specimen A-NM-T1 ................ 223

Figure 6.15 Predicted versus experimental interfacial shear stress distributions

for points shown in Figure 5.11a for specimen C-NM-T1 ................ 224

Figure 6.16 Effect of the shape of the bond-slip model on load-displacement

behaviour ......................................................................................... 225

Figure 6.17 Predicted versus experimental bond strengths .................................. 226

Chapter 7 Figure 7.1 Traction-separation curve .................................................................. 251

XIX

Figure 7.2 Linear damage evolution under mixed-mode loading ........................ 251

Figure 7.3 Details of test specimens of Deng and Lee (2007) ............................. 252

Figure 7.4 Stress-strain curve of steel used in FE simulation .............................. 253

Figure 7.5 Bond-slip model for Mode II loading used in FE simulation .............. 253

Figure 7.6 Bond-separation models for Mode I loading used in FE simulation .. 254

Figure 7.7 Load-displacement curves of a bare steel I beam ............................... 254

Figure 7.8 Deformed shape of S303-1-212 at failure ......................................... 255

Figure 7.9 Load-deflection curves for specimen S303 ........................................ 255

Figure 7.10 Normalized interfacial stresses at the plate end for specimen S303 .. 256

Figure 7.11 Longitudinal shear stresses in the adhesive from S303-1-212 .......... 256

Figure 7.12 Interfacial stress distributions along section X-X from model

S303-1-212 ...................................................................................... 258

Figure 7.13 Interfacial stress-strain behaviour at the plate end from model

S303-1-212 ...................................................................................... 259

Figure 7.14 Deformed shape of model S304-1-212 at failure .............................. 259

Figure 7.15 Load-deflection curves of specimens S304 and S310 ....................... 260

Figure 7.16 Deformed shape of model S310-1-212 at failure .............................. 260

Figure 7.17 Longitudinal shear stresses in the adhesive from model S310-1-

212 .................................................................................................. 262

Figure 7.18 Interfacial stress distributions along section Y-Y from model

S310-1-212 ...................................................................................... 263

Figure 7.19 Damage propagation in the adhesive layer in model S310-1-212-

P ...................................................................................................... 264

Figure 7.20 Load-deflection curve from model S310-1-212-P ............................ 264

Figure 7.21 Interfacial stress distributions along section Z-Z from model

S310-1-212-P................................................................................... 266

Appendix 7.1 Figure A7.1 Details of the specimen tested by Linghoff et al. (2009).................. 274

Figure A7.2 Different stress-strain curves used in FE models ............................. 275

Figure A7.3 Results of mesh convergence study................................................. 275

Figure A7.4 Effect of stress-strain curve on load-displacement behaviour .......... 276

Figure A7.5 Imperfection shapes ........................................................................ 276

Figure A7.6 Effect of imperfections on load-displacement behaviour ................ 277

XX

Figure A7.7 Residual stresses in a steel I-beam (Pi and Trahair 1994) ................ 277

Figure A7.8 Effect of residual stresses on load-displacement behaviour ............. 278

Figure A7.9 Comparison of load-strain behaviour .............................................. 278

Chapter 8 Figure 8.1 Bare and CFRP-strengthened RHS tubes ........................................... 309

Figure 8.2 Schematic views of the test set-up .................................................... 309

Figure 8.3 Specimens after testing ...................................................................... 310

Figure 8.4 Load-deflection curves of bare and CFRP-strengthened steel tubes ... 311

Figure 8.5 Increase in ultimate load vs. web depth-to-thickness ratio.................. 312

Figure 8.6 FE model (mesh not shown for clarity) .............................................. 312

Figure 8.7 Mesh details ...................................................................................... 313

Figure 8.8 Comparison of load-deflection curves from FE analysis and

experiments ..................................................................................... 314

Figure 8.9 FE interfacial stress distributions along the vertical section (Figure

8.6) in Specimen S30-A .................................................................. 316

Figure 8.10 FE interfacial stress distributions along the vertical section

(Figure 8.6) in specimen S330-A .................................................... 317

Figure 8.11 Debonding propagation in specimen S30-A (only the adhesive

layer is shown) ................................................................................. 319

Figure 8.12 Deformed shapes of strengthened tubes ........................................... 320

Figure 8.13 Composite section ........................................................................... 320

Figure 8.14 Mechanism models for web yielding failure .................................... 321

Appendix 8.1

Figure A8.1 Corner properties extended beyond each end of the curved

portion ............................................................................................. 330

Figure A8.2 Buckling modes; (a) First buckling mode; (b) Second buckling

mode; (c) Third buckling mode ........................................................ 330

Figure A8.3 Idealized weld-induced residual stress distribution of the weld

face on RHS..................................................................................... 331

Figure A8.4 Deformed shapes of the RHS tube .................................................. 332

XXI

List of Tables

Chapter 1

Table 1.1 Properties of Sika carbon fibre sheets* and CFRP plates....................... 10

Chapter 3

Table 3.1 Material properties of adhesives .......................................................... 65

Table 3.2 Grit composition as supplied by the manufacturer ................................ 65

Table 3.3 Roughness of different surface types ................................................... 65

Table 3.4 Chemical compositions of different surface types ................................. 66

Table 3.5 Contact angles and surface energies of different specimens .................. 66

Table 3.6 Ultimate loads of tensile butt-joint specimens (kN) ............................... 67

Table 3.7 Failure modes of tensile butt-joint specimens ....................................... 67

Table 3.8 Ultimate loads of single-lap shear specimens (kN) ................................ 68

Table 3.9 Failure modes of single-lap shear specimens......................................... 68

Chapter 4

Table 4.1 Material properties of steel, CFRP and adhesive ................................... 97

Chapter 5

Table 5.1 Specimen details ................................................................................. 139

Table 5.2 Ultimate loads and failure modes ........................................................ 140

Table 5.3 Key parameters for the experimental bond-slip curves ........................ 142

Table 5.4 Comparison of experimental and predicted bond strengths.................. 143

Chapter 6

Table 6.1 Predicted bond strengths versus experimental bond strengths ............. 210

Chapter 7

Table 7.1 Details of the test beams and the FE models ....................................... 250

Table 7.2 Key parameters for traction-separation models ................................... 250

Table 7.3 Experimental and FE results ............................................................... 250

XXII

Chapter 8

Table 8.1 Specimen details ................................................................................. 305

Table 8.2 Material properties of CFRP and steel ............................................... 305

Table 8.3 Results of end bearing tests on CFRP-strengthened RHS tubes ........... 306

Table 8.4 Traction-separation parameters for different adhesives ....................... 307

Table 8.5 Experimental ultimate loads versus predicted ultimate loads based

on the perfect bond assumption ........................................................ 307

Appendix 8.1

Table A8.1 Results of mesh convergence study for the corner ............................ 328

Table A8.2 Results of mesh convergence study for the flats ............................... 328

Table A8.3 Results of mesh convergence study for the bearing plate .................. 329

XXIII

NOTATION

da = Maximum length of the plastic region of a bonded joint

ua = Length of the plastic region at the beginning of the plastic-softening-debonding region

pA = Horizontal cross sectional area of the CFRP plate

wA = Horizontal cross sectional area of the steel RHS web

db = Length of the softening region at the beginning of debonding

pb = Plate width

stb = Width of the steel substrate

ub = Length of the softening region at the beginning of the softening-

debonding stage D

= Damage parameter of a cohesive zone model fD = Fractal dimension

E = Tensile elastic modulus

aE = Tensile elastic modulus of an adhesive

pE = Tensile elastic modulus of a plate

stE = Tensile elastic modulus of steel

aG = Shear modulus of an adhesive

fG = Interfacial fracture energy

nG = Work done in normal direction

s tG and G = Work done in shear direction

IG = Interfacial fracture energy required to cause failure for pure mode I

loading

IIG = Interfacial fracture energy required to cause failure for pure mode

II loading ek = Effective length factor for RHS tubes

nnK = Elastic stiffness in peeling direction

ssK and ttK = Elastic stiffness in shear direction L

= Length eL = Effective bond length of a bonded joint

,e eL = Effective bond length during the elastic stage of a bonded joint

2,eL = Effective bond length during the elastic-plastic stage of a bonded joint

P = Applied load

1,maxP = Predicted ultimate load at the end of elastic stage of a bonded joint

2,maxP = Predicted ultimate load at the end of elastic-plastic stage of a

bonded joint pP = Predicted ultimate load of the CFRP-strengthened RHS tube

uP = Ultimate load/ bond strength

,expuP = Experimental bond strength

XXIV

u FEP − = Ultimate load from FE analysis

,u predictP = Predicted bond strength of a bonded joint R = Tensile strain energy

aR = Average roughness

bbR = Web buckling capacity of a RHS tube maxbbR

= The web buckling capacity of a CFRP-strengthened RHS tube with perfect bonding between CFRP and steel

byR = Web yielding capacity of a RHS tube maxbyR

= The web yielding capacity of a CFRP-strengthened RHS tube with perfect bonding

qR = Root mean square roughness

extr = External corner radius of a RHS tube

0T = Initial thickness of adhesive layer

at = Thickness of the adhesive

nt = Normal traction

pt = Thickness of the plate

stt = Thickness of the steel plate

st and tt = Shear tractions

pu = Displacement of the CFRP plate

stu = Displacement of the steel plate

aW = Work of adhesion

cW = Work of cohesion

bα = Section constant in determining the web buckling load cα = Member slenderness reduction factor for column buckling

β = Web depth-to-thickness ratio Sγ =Total surface energy

SVγ = Surface energies at the solid/vapour interface

SLγ = Surface energies at the solid/liquid interface

LVγ = Surface energies at the liquid/vapour interface pxyγ = Polar energy component of x/y interface surface energy dxyγ = Dispersive energy component of x/y interface surface energy

∆ = Slip/ displacement u∆ = Displacement at the ultimate load

u FE−∆ = Displacement at the ultimate load from FE analysis δ = Slip/ separation

1δ = Slip/separation at peak bond stress

2δ = Slip at the beginning of softening

fδ = Slip/separation at complete failure

mδ = Effective displacement

XXV

fmδ = Effective displacement at complete failure 0mδ = Effective displacement at damage initiation maxmδ = Maximum effective displacement

nδ = Normal separation 1nδ = Separation at peak bond normal stress f

nδ = Separation at complete failure

sδ and tδ = Shear slip 1 1s tandδ δ = Slip at peak bond shear stress f f

s tandδ δ = Slip at complete failure

nε = Strain in normal direction

sε and tε = Strain in shear direction

uε = Ultimate strain

yε = Strain at yield θ = Contact angle

nλ = Web slenderness of RHS tubes

0.2σ = 0.2% proof stress

pσ = Axial stress in CFRP plate

rcσ = Compressive residual stresses

rtσ = Tensile residual stresses

stσ = Axial stress in steel plate

uσ = Ultimate strength

yσ = Yield strength

maxσ = Tensile strength/ peak bond normal stress τ = Shear stress

maxτ = Peak bond shear stress

bφ and bψ = Debonding reduction factors to account for debonding failures in

CFRP-strengthened steel RHS tubes under an end bearing load

1

CHAPTER 1 INTRODUCTION

1.1 BACKGROUND Fibre-reinforced polymer (FRP) composites are formed by embedding continuous

fibres in a polymeric resin matrix which binds the fibres together. The commonly used

fibres are carbon, glass and aramid fibres while the commonly used resins are epoxy,

polyester and vinylester resins. FRP composites have a high strength-to-weight ratio;

for example, carbon FRP (CFRP) has a strength that can be up to 10 times the strength

of mild steel (Figure 1.1) and is thus much less in weight compared to mild steel for the

same tensile capacity. FRP composites also possess excellent corrosion resistance.

These properties have made FRP composites a very attractive material in structural

engineering applications. Adding to these superior properties, ease of handling and

application (by the adhesive bonding technique) has opened up many opportunities for

FRP composites in the retrofit of existing structures as well as in the construction of

new structures. A useful general background on the composition of FRP materials and

their mechanical properties can be found in Holloway and Head (2001), Bank (2006),

ACI-440 (2007) and Hollaway and Teng (2008).

Use of FRP composites with concrete allows the concrete which is strong in

compression and weak in tension to benefit from the superior tensile properties of FRP,

creating a constructive combination. Thus the use of FRP in concrete structures has

gained the spotlight in existing research on FRP composites in civil engineering

(Hollaway and Leeming 1999; Teng et al. 2002; Bank 2006; Hollaway and Teng 2008).

Recently the use of FRP composites in combination with steel has received much

research interest.

2

1.2 EFFECTIVE USE OF FRP WITH STEEL Unlike concrete, steel, which also possesses a high elastic modulus and a high strength,

demands more innovative applications to gain the advantages of superior FRP

properties. FRP composites have many advantages over other conventional

strengthening materials such as steel. A much higher strength-to-weight ratio which

FRP possesses over steel, makes FRP a much easier material to handle and transport, so

FRP is advantageous in many aspects such as speed of construction and reduced

disturbance to the use of the structure, therefore minimizing economic losses due to the

suspension of services. The raw materials of FRP can be supplied in the forms of dry

fibre/fabric sheets and impregnating resins for the in-situ formation of FRP via the so-

called wet lay-up process, which allows the use of FRP on irregular and curved

surfaces where application of steel plates may be impossible or highly challenging.

Confinement of steel/concrete-filled steel tubes against tube local buckling failure (Tani

et al. 2000; Teng and Hu 2004; Xiao 2004; Xiao et al. 2005; Batikha et al. 2009) is an

attractive use of FRP where the shape flexibility of FRP has made the application

possible.

The FRP strengthening method by adhesive bonding has become attractive especially in

the strengthening of fatigue-sensitive structures. Conventional methods such as welding

steel plates suffer from welding-induced residual stresses which can weaken the fatigue

performance. Steel plates also can be adhesively bonded, but a steel plate with the same

tensile capacity as an FRP plate, has a much higher bending stiffness, which thus leads to

much higher peeling stresses at the interface between the steel plate and the steel

substrate; such peeling stresses are a main cause of debonding failure and need to be

minimised in strengthening structures with a bonded plate. Moreover, the need of

machinery and equipment to handle heavy steel plates and the need for temporary work to

hold the steel plate in-place make steel plates much less attractive than FRP composites.

3

Both CFRP and glass FRP (GFRP) materials have been used in strengthening of steel

structures. Other FRP materials such as aramid FRP (AFRP) can also be used to

strengthen steel structures. CFRP, with its superior elastic modulus, is more attractive than

GFRP when strength enhancement of the structure is of concern. CFRP can be in the

forms of fibre sheets (plus an epoxy resin for the wet lay-up formation of CFRP plates)

and pultruded plates. Properties of carbon fibre sheets and CFRP plates supplied by SIKA

are given in Table 1.1 to illustrate the properties of CFRP. When ductility enhancement is

of main concern, GFRP, which is more economical and offer a higher strain capacity, can

be more attractive. This thesis is explicitly concerned only with CFRP strengthening, but

many of the observations and conclusions are equally applicable to steel structures

strengthened with other FRP materials.

1.3 OBJECTIVES AND SCOPE

While extensive research has been conducted on the strengthening of concrete and

masonry structures using FRP composites, the potential of externally bonded FRP

composites in strengthening steel structures has been explored only to a very limited

extent (Hollaway and Cadei 2002; Zhao and Zhang 2007). Available studies (e.g.

Miller. et al. 2001; Sen et al. 2001; El Damatty et al. 2003; Jones and Civjan 2003;

Sebastian 2003; Tavakkolizadeh and Saadatmanesh 2003a; Tavakkolizadeh and

Saadatmanesh 2003b; Fawzia et al. 2007) have been mainly concerned with the

demonstration of the effectiveness of the FRP strengthening technique for steel

structures. However, many aspects are yet to be investigated, particularly the interfacial

behaviour of CFRP-to-steel bonded joints. A good understanding of the interfacial

behaviour of CFRP-to-steel bonded joints provides the key knowledge for designing

CFRP-to-steel interfaces against various debonding failure modes (Figure 1.2) which is

a critical issue in strengthening steel structures using CFRP.

Against this background, the present thesis presents investigations into the fundamental

issues relating to the bond-behaviour of CFRP-to-steel interfaces. The systematic

investigations presented in this thesis provide sound knowledge based on proper

4

preparation methods for CFRP-to-steel interfaces, bond behaviour and modelling of

CFRP-to-steel interfaces, possible applications of CFRP strengthening systems to

enhance the performance of steel structures; methods of applying the fundamental

concepts concerning the behaviour of CFRP-to-steel interfaces to model and predict the

behaviour of CFRP-strengthened steel structures are also examined. A combined

experimental, analytical and numerical approach was employed in the present PhD

research project. The topics covered in this thesis are summarized as follows.

Chapter 2 presents an extensive literature review of topics related to the present thesis.

Firstly, different possible debonding failure modes of CFRP-to-steel bonded joints are

introduced. Among these debonding failure modes, adhesion failure, which depends

strongly on the surface preparation methods for the adherends, is discussed. The

methods available for surface preparation and also the methods available to ensure the

surface quality are also examined. As research on the bond behaviour of CFRP-to-steel

interfaces is at a preliminary stage, a review of existing knowledge on FRP-to-concrete

and metal-to-metal bonded joints is also presented, focusing on concepts which are

common to such bonded joints and CFRP-to-steel bonded joints. Thereafter, a critical

review of the existing knowledge on bond behaviour of CFRP-to-steel bonded joints is

made. Finally, existing studies on possible strengthening applications, namely flexural

strengthening, strengthening against high local stresses and fatigue strengthening are

critically reviewed.

Chapter 3 presents a detailed study on different surface preparation methods for mild

steel for adhesive bonding, namely solvent-cleaning, solvent-cleaning followed by

hand-grinding, and solvent-cleaning followed by grit-blasting, on surface

characteristics and on adhesion strength. In grit-blasting, in order to obtain different

surface features, three different grit sizes were used to produce 3 different surface

types. Measurements of surface roughness, surface energy and surface chemical

composition were taken. The representation of surface topography using fractal

dimensions over surface roughness measurements is also discussed. The effect of

different surface types on adhesion strength was investigated using tensile butt-joint

5

tests and single-lap shear tests for four different commercially available structural

adhesives. It is clearly shown that the physical-chemical changes introduced by

different surface preparation methods can significantly influence the surface

characteristics and hence the adhesion strength. A standard method for steel surface

preparation to enhance adhesion strength as well as a method to assess the quality of

steel surfaces for adhesive bonding is proposed.

Chapter 4 presents a study aimed at investigating the suitability of a single-shear pull-

off test set-up to obtain bond-slip relationships and to study the full-range behaviour of

CFRP-to-steel bonded joints. In order to obtain shear bond-slip curves (or referred to

simply as “bond-slip curves”), the interface in a single-shear pull-off test should be

subjected to pure mode II loading (i.e. direct shear). The deformation and the fracture

of bonded joints were experimentally captured using an optical measurement system.

By comparing the deformation with a linear elastic finite element (FE) analysis, the

influence of different interfacial stress components on damage initiation and

propagation is discussed. The effect of an adhesive fillet at the joint end on interfacial

stresses is also discussed. This study provides the first ever experimental evidence to

support the use a single-shear pull-off test to obtain bond-slip curves under pure mode

II loading.

Chapter 5 presents a carefully planned series of single-shear pull-off tests to investigate

the full-range behaviour of CFRP-to-steel bonded joints. The experimental work

presented in this chapter fulfils the research need to understand the full-range behaviour

of CFRP-to-steel bonded joints which is essential knowledge for design against various

debonding failure modes. The effects of different adhesive mechanical properties,

adhesive layer thickness and plate axial rigidity on bond behaviour are investigated.

The effect of adhesive mechanical properties such as adhesive elastic modulus,

adhesive strength and tensile fracture energy as well as the adhesive layer thickness on

debonding failure modes, bond strength, load-displacement behaviour and stress

distributions along the bond length were experimentally investigated and are discussed

in this chapter. The bond-slip behaviour of the interface was derived experimentally for

6

each specimen that failed in cohesion failure using the strain distribution of the CFRP

plate. Bond-slip curves for both linear and non-linear adhesives are presented. Finally,

through the use of interfacial shear stress distributions obtained from strain readings of

the CFRP plate, the full-range behaviour of CFRP-to-steel bonded joints is examined.

Chapter 6 presents an analytical model for the prediction of bond strengths, bond-slip

behaviour, full-range bond behaviour and effective bond lengths. It therefore provides a

sound theoretical basis for the design of CFRP-to-steel bonded joints. Based on the

existing knowledge on FRP-to-concrete bonded joints, applicability of existing models

to predict the bond strength, bond-slip behaviour and full-range behaviour is discussed.

The dependency of the bond strength on the interfacial fracture energy is clearly

shown. An explicit formula to predict the interfacial fracture energy based on the

adhesive tensile strain energy and thickness is proposed. This formula provides a

method to predict the bond strength from commonly available CFRP plate and adhesive

properties. The applicability of existing bond-slip models for FRP-to-steel bonded

interfaces to the present CFRP-to-steel bonded joints is assessed. Different bond-slip

models are proposed to predict the bond-slip behaviour of linear and non-linear

adhesives. For linear adhesives, two different bond-slip models are proposed: (a) an

accurate model; and (b) a bi-linear model which is computationally simple and

provides a useful tool in predicting bond strengths. Finally, based on the idealized

bond-slip model for non-linear adhesives, a closed-form solution to predict the full-

range behaviour of CFRP-to-steel bonded joints is presented. Although this solution is

intended for CFRP-to-steel bonded joints, it is also applicable to any other similar

bonded joints (i.e. composed of a thin plate bonded to a substrate) which has a similar

bond-slip curve. The analytical model is also used to predict load-displacement

behaviour as well as interfacial stress distributions for comparison with experimental

results.

Chapter 7 explores the application of knowledge gained from the study presented in

Chapter 6, particularly bond-slip models for linear adhesives, in FE modelling to

predict debonding failure modes of steel beams flexurally-strengthened with CFRP.

7

Debonding failure modes are common failure modes in steel beams flexurally-

strengthened with CFRP, but so far no method exists which can accurately predict the

debonding failures in such beams. A bond-slip model was implemented in the FE code

ABAQUS using an appropriate cohesive law. The cohesive law adopted is presented

and discussed. The applicability of this law to mixed mode debonding failure is also

discussed. Detailed FE models of flexurally-strengthened steel beams for both

intermediate debonding failures and plate end debonding failures are presented. The

predictions of plate end debonding failures are compared with the existing

experimental results. A discussion of the effects of different interfacial stress

components, namely peeling stresses and shear stresses, on different debonding failure

modes is given.

Chapter 8 examines a possible strengthening application of CFRP, namely CFRP

strengthening of rectangular steel tubes subjected to an end bearing load. As failure of

such a strengthened tube generally occurs by debonding of the CFRP plates from the

steel tube, the effectiveness of this strengthening method depends significantly on the

properties of the adhesive. In addition, the effectiveness of the strengthening method

depends on the web depth-to-thickness ratio. Results of an experimental study aimed at

clarifying the effects of adhesive properties and the web depth-to-thickness ratio on the

failure mode and the load-carrying capacity are presented. Besides the experimental

study, this chapter also presents results from an FE study aimed at investigating the

applicability of the bond-slip model to predict the debonding failure of CFRP-

strengthened rectangular steel tubes. The effect of peeling stresses on debonding failure

is also presented.

Chapter 9 presents the conclusions drawn from the previous chapters and outlines the

areas in need of future work.

8

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9

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Xiao, Y., He, W. and Choi, K. (2005). "Confined concrete-filled tubular columns",

Journal of Structural Engineering, 131(3), 488-497.

Zhao, X.L. and Zhang, L. (2007). "State-of-the-art review on FRP strengthened steel

structures", Engineering Structures, 29(8), 1808-1823.

10

Table 1.1 Properties of Sika carbon fibre sheets* and CFRP plates #

Product

Elastic

modulus

(GPa)

Tensile

strength

(MPa)

Ultimate

strain (%)

Sika Wrap 200C* 230 3900 1.5

Sika Wrap 201C* 230 4900 2.1

Sika Wrap 300C Hi Mod NW* 640 2600 0.4

Sika CarboDur S# 165 2800 1.70

Sika CarboDur M# 210 2400 1.20

Sika CarboDur H# 300 1300 0.45

Extracted from manufacturer’s product data sheet

11

0.0 0.5 1.0 1.5 2.0 2.5 3.00

500

1000

1500

2000

2500

3000

Mild steel

GFRP

Stre

ss (M

Pa)

Strain (%)

CFRP

Figure 1.1 Typical FRP and mild steel stress-strain curves

Figure 1.2 Various failure modes in a CFRP-to-steel bonded joint

Interlaminar failure of CFRP- CFRP failure

Steel

Adhesive

CFRP

CFRP-adhesive interface debonding- adhesion failure

Adhesive failure- cohesion failure

Steel-adhesive interface debonding- adhesion failure

CFRP Rupture

12

CHAPTER 2 LITERATURE REVIEW

2.1 INTRODUCTION

This chapter presents a review on existing knowledge of CFRP-strengthened steel

structures where the performance of the strengthening system relies on the stress

transfer function of the interface between CFRP and steel. Although the present

thesis is limited to CFRP-strengthened steel structures, where necessary and

appropriate, existing studies on the behaviour of FRP-to-concrete and steel-to-steel

bonded joints are also reviewed considering the common concepts between these

bonded joints and CFRP-to-steel bonded joints.

The first part of the chapter gives a brief description of different categories of

CFRP-to-steel bonded joints. The effect of surface preparation of the adherends for

adhesive bonding is discussed. Particular attention is given to the characterization of

surfaces and the influence of surface preparation methods on surface characteristics.

To make the importance of surface preparation in adhesive bonding very clear,

existing studies on the behaviour of CFRP-to-steel bonded joints are next reviewed.

Considering the commonality in behaviour between FRP-to-concrete bonded joints,

metal-to-metal bonded joints, and CFRP-to-steel bonded joints, a thorough review

of existing knowledge of the two former types of bonded joints is also presented.

Following the discussion of bond behaviour, studies on CFRP-strengthened steel

structures are also discussed. Issues related to the flexural strengthening of steel

beams, CFRP strengthening against buckling, CFRP strengthening against high

local stresses as well as fatigue strengthening are presented and discussed.

2.2 BOND BEHAVIOUR BETWEEN FRP AND STEEL

2.2.1 General

Similar to the structural use of FRP in concrete structures, the structural use of FRP

with steel can be classified into two categories: (a) bond-critical applications where

13

the interfacial shear stress transfer function of the adhesive layer that bonds the steel

and the FRP together is crucial to the performance of the structure; and (b)

contact-critical applications where the FRP and the steel need to remain in contact

for effective interfacial normal stress transfer which is crucial to ensure the

effectiveness of the FRP reinforcement. The use of FRP in the strengthening of steel

structures provides good examples for both categories: externally bonded FRP

reinforcement for the flexural strengthening of steel beams falls into the first

category, while confinement of concrete-filled steel tubular members with FRP

jackets belongs to the second category.

In all bond-critical applications, the interfacial behaviour between FRP and steel is

of critical importance in determining when failure occurs and how effectively the

FRP is utilised. Usually in FRP-strengthened concrete structures, interfacial failure

generally occurs within the concrete substrate a few millimetres from the

concrete/adhesive interface. However due to a much higher tensile strength of the

steel than that of adhesive, failure in steel substrate cannot occur. As a result, for

FRP-strengthened steel structures, interfacial failure can only occur within the

adhesive layer (i.e. cohesion failure) or at the material interfaces (adhesion failure)

between the steel and the adhesive (referred to as the “steel/adhesive interface”

hereafter) or between the adhesive and the FRP (referred to as the “FRP/adhesive

interface” hereafter). Due to this difference design theories developed for

FRP-strengthened concrete structures cannot be directly applied to

FRP-strengthened steel structures.

If adhesion failure controls the strength of FRP-strengthened steel structures, then

the interfacial bond strength depends on how the steel surface and the FRP surface

are treated as well as the bond capability of the adhesive. As adhesion failure

depends on surface treatment and the degree of surface treatment, especially to the

steel substrate, is difficult to control on site, the development of a design theory

becomes much more involved. This important issue has not been given adequate

attention in previous research and is one of the issues addressed in the present

thesis.

14

2.2.2 Adhesion Failure

In an FRP-to-steel bonded joint, adhesion failure may occur at the steel/adhesive

interface or at the FRP /adhesive interface. When the FRP is formed and applied to

the structure via the wet lay-up process on site, adhesion failure at the FRP/steel

interface has been seldom observed (Hollaway and Cadei 2002). When a pultruded

FRP plate/strip is used, a peel-ply needs to be removed prior to bonding to ensure a

clean and fresh FRP surface for bonding (Hollaway and Cadei 2002); if such a peel

ply does not exist, the surface needs to be to abraded and then cleaned before

bonding (Hollaway and Cadei 2002; El Damatty et al. 2003). Such preparation

techniques can greatly reduce the risk of adhesion failure at the FRP/adhesive

interface (Holloway and Cadei 2002). However, failure at the steel/adhesive

interface has been observed much more frequently, so improving the steel surface

for adhesive bonding has received much research interest (Mays and Huthcinson

1992; McKnight et al. 1994; Harris and Beevers 1999; Baldan 2004; Schnerch et al.

2007).

The adhesion strength at the steel/adhesive interface results from both chemical

bonding and mechanical bonding between the two adherends (Mays and Huthcinson

1992; Packham 2003; Baldan 2004). The first and necessary condition to form a

good bond between adhesive and steel is that the adhesive must be in intimate

contact with the steel surface. This requires a sufficiently low viscosity of the

adhesive so that it can easily flow over the steel surface and fill the pores (Rosen

1993). However, even with a low viscosity adhesive, if the steel surface is

contaminated, the adhesive will first come in contact with the weak contaminant

layer, thus forming a weak bond (Baldan 2004). Therefore, cleaning of the steel

surface prior to bonding is necessary. For the spreading of the adhesive (wetting) on

the steel surface to occur, the steel surface should have a much larger surface

energy than that of the adhesive which in addition should have a low viscosity

(Harris and Beevers 1999; Baldan 2004). When the adhesive and the steel surface

come into contact, chemical bonds will form. The formation of the chemical bonds

mainly depends on the chemical composition of the steel surface and the adhesive,

so the selection of a chemically compatible adhesive is necessary (Baldan 2004).

15

While the major part of the adhesion strength between two adherends generally

depends on chemical bonding, mechanical bonding can also make a significant

contribution to the adhesion strength (Baldan 2004). When pores exist on the

surface, the adhesive will flow into these pores and act as a mechanical interlock

when hardened. Therefore mechanical bonding depends on the adhesive properties

as well as the roughness and topography of the steel surface (Gent and Lai 1995;

Packham 2003; Baldan 2004). Roughening the surface can significantly enhance

mechanical bonding (Gent and Lai 1995; Packham 2003), but it may also reduce the

level of contact between the two adherends (Tamai and Aratani 1972; Hitchcock et

al. 1981). Therefore, the three main properties of a steel surface, namely, surface

energy, surface chemical composition, and surface roughness & topography, are

often used as the key indicators to characterize a steel surface for adhesive

bonding (Gent and Lin 1990; Harris and Beevers 1999; Amada and Satoh 2000;

Lavaste et al. 2000).

The most popular approaches for cleaning a steel surface include solvent-cleaning

and mechanical abrasion through grit-blasting or using other tools (e.g. wire brushes,

abrasive pads and wheels, and needle guns) (Hollaway and Cadei 2002; Baldan

2004). Solvent-cleaning removes grease and other contaminants from the surface

and is a necessary first step in preparing a steel surface for adhesive bonding

(Hollaway and Cadei 2002; Schnerch et al. 2007). However solvent-cleaning alone

does not change the steel surface properties, so it alone only has a limited effect on

the adhesion strength (Harris and Beevers 1999). In solvent-cleaning, it is important

to use a volatile solvent (e.g. acetone) so that the amount of contaminants and their

negative effects on the adhesion strength is minimized (Mays and Huthcinson

1992; Hollaway and Teng 2008).

Mechanical abrasion roughens the surface and removes the weak surface layer (e.g.

oxide layer), thus providing a chemically active rough surface for adhesive bonding

(Harris and Beevers 1999; Baldan 2004). The available methods of mechanical

abrasion include grinding using abrasion pads and wire brushes and grit-blasting,

with grit-blasting being the most effective (Sykes 1982; Harris and Beevers 1999;

Hollaway and Cadei 2002; Schnerch 2005). Grit-blasting has been found to increase

the surface energy and the surface roughness (Harris and Beevers 1999), thus

16

promoting adhesion. Therefore, grit-blasting is recommended by some existing

guidelines (Cadei et al. 2004; Schnerch et al. 2007).

Grit-blasting introduces grit residue to the surface, thus altering the chemical

composition of the surface (Gettings and Kinloch 1977; Harris and Beevers 1999).

Therefore, it is important to select a grit type which is chemically compatible with

the adhesive. Even though the size of the grit used in grit-blasting may have a

significant effect on surface characteristics, the experimental study carried out by

Harris and Beevers (1999) revealed that within the range of grit sizes examined in

their study (i.e. 0.062mm and 0.25mm), the effect of grit size on the adhesion

strength is limited. Grit-blasting also introduces abrasive dust on the surface which

can have a negative effect on adhesive bonding (Hollaway and Cadei 2002).

Therefore, it is important to clean the surface again after grit-blasting. Hollaway and

Cadei (2002) suggested to remove the fine dust by dry-wiping or using a vacuum

head instead of by solvent-cleaning as they believed that solvent-cleaning could

only partially remove the dust and might redistribute the remaining dust on the

surface. El Damatty et al. (2003) however showed that with the use of a large

amount of solvent (to washout the dust and to avoid their re-depositing after the

solvent has evaporated), the dust could be completely removed and a clean surface

could be produced.

After surface treatment, the adhesive/primer should be applied as soon as possible

to avoid any contamination to the surface or formation of a weak oxide layer (Allan

et al. 1988). Cadei et al. (2004) recommended that the period between grit-blasting

and adhesive/primer application should not exceed two hours, while Schnerch et al.

(2007) suggested a more practical maximum period of twenty-four hours for the

adhesive application.

Besides following an appropriate surface treatment procedure, it is important to

characterize the surface to evaluate whether it is good enough for the development

of strong adhesion. To the best knowledge of the author, there is no established

method for the evaluation of surface quality for adhesive bonding. Hence

characterizing the surface for adhesive bonding is given a significant amount of

attention in this thesis.

17

2.2.3 Bond Behaviour

Similar to concrete structures externally bonded with FRP, interfacial failure

(debonding) in FRP-strengthened steel structures can occur either as (1) debonding

initiating away from the FRP plate ends (i.e. intermediate debonding) or (2)

debonding initiating from an FRP plate end (i.e. plate end debonding) (Figure 2.1).

In the former, failure is induced by high interfacial shear stresses due to either the

presence of a defect (e.g. crack) or yielding of the steel substrate (Sallam et al. 2006;

Silvestre et al. 2008), whereas in latter failure is induced by high interfacial peeling

stresses as well as interfacial shear stresses near the ends of the FRP plate ( Zhao et

al. 2006; Deng and Lee 2007a; Harries et al. 2009). Intermediate debonding has

been observed in FRP-strengthened steel beams (Sallam et al. 2006) and steel

sections strengthened with FRP against local buckling (Silvestre et al. 2008), while

plate end debonding has been observed in flexurally-strengthened steel beams

(Deng and Lee 2007a) and steel sections strengthened against end bearing loads

(Zhao et al. 2006) or other loads inducing local buckling (Harries et al. 2009).

The extensive research on FRP-strengthened concrete structures (Teng et al. 2002a;

Teng et al. 2002b; Teng et al. 2003a; Teng et al. 2003b; Yao et al. 2005a; Yao et al.

2005b; Yao and Teng 2007) has proven that in order to understand and model

debonding failures, the behaviour of simple bonded joints (Yao et al. 2005a; Zhao

and Zhang 2007) needs to be well understood first. The behaviour of simple

single-lap FRP-to-steel bonded joints, where interfacial shear stresses are dominant,

can give valuable insight into the behaviour of FRP-to-steel bonded interfaces in a

beam where intermediate debonding is critical as intermediate debonding is

dominated by interfacial shear stresses. Moreover, a thorough understanding of the

simple FRP-to-steel bonded joint is the first step towards understanding the more

complex behaviour of FRP-to-steel interfaces subjected to combined interfacial

shear and peeling stresses.

In FRP-to-concrete bonded joints, failure occurs within the concrete adjacent to the

concrete/adhesive interface. However, in FRP-to-steel bonded joints, failure in the

steel substrate is impossible. Therefore, provided adhesion failure at the

steel/adhesive interface or the FRP/adhesive interface is avoided, failure of

18

FRP-to-steel bonded joints usually occurs within the adhesive (i.e. cohesion failure).

Despite this difference, the generic concepts (e.g. the interfacial fracture energy)

well established for FRP-to-concrete bonded joints are also applicable to

FRP-to-steel bonded joints. Therefore as a first step in understanding the behaviour

of FRP-to-steel bonded joints, a review of the existing knowledge on

FRP-to-concrete bonded joints is necessary. In addition, the existing literature on

steel-to-steel bonded joints, which have similar interfacial failure modes to

FRP-to-steel bonded joints, is also reviewed below together with the limited

available studies on FRP-to-steel bonded joints ( Miller. et al. 2001; El Damatty and

Abushagur 2003; Sebastian 2003; Nozaka et al. 2005a; Nozaka et al. 2005b; Xia

and Teng 2005; Colombi and Poggi 2006b; Fawzia et al. 2007).

Different test methods for bonded joints have been used by different researchers

(Zhao and Zhang 2007), including double-lap shear tests ( Miller. et al. 2001;

Colombi and Poggi 2006b), beam tests (Nozaka et al. 2005b), shear-lap shear tests

under compression (El Damatty and Abushagur 2003) and single-lap pull-off tests

(Xia and Teng 2005). Despites the different methods used, most studies have been

focused on the ultimate load (i.e. the bond strength) and the bond-slip relationship

which are the two most important aspects of bond behaviour.

2.2.3.1 Bond strength

The bond strength is the ultimate tensile force that can be resisted by the FRP plate

in a bonded joint test before the FRP plate debonds from the substrate (Hollaway

and Teng 2008). Several experimental studies on FRP-to-steel bonded joints

(Nozaka et al. 2005b; Xia and Teng 2005; Fawzia et al. 2007) have revealed that the

bond strength does not always increase with the bond length. When the bond length

reaches a threshold value, any further increase in the bond length does not lead to a

further increase in the bond strength. Similar observations were made in

FRP-to-concrete bonded joint tests (Chen and Teng 2001; Yuan et al. 2004; Yao et

al. 2005a; Yao and Teng 2007). The bond length where no further increase in the

load will results is commonly referred to as the effective bond length (Le) (Chen and

Teng 2001).

19

Prediction of the bond strength is an essential task in designing of FRP-to-steel

bonded joints. The existing approaches consists of (1) strength-based approaches

(Nozaka et al. 2005b; Schnerch et al. 2007; Bocciarelli 2009) which assume the

bond strength is reached when the maximum stress/strain developed in the adhesive

reaches its corresponding strength; and (2) fracture mechanics-based approaches

(Bocciarelli et al. 2007; Bocciarelli et al. 2009b) which are similar to those for the

bond strength of FRP-to-concrete bonded joints (Yuan and Wu 1999; Chen and

Teng 2001) where the bond strength is related to the interfacial fracture energy.

Strength-based approaches have also been adopted in steel-to-steel bonded joints

(Volkersen 1938; Adams and Peppiatt 1974; Hart-Smith 1981). The failure criteria

of the adhesive used in these studies include maximum shear stress criterion

(Volkersen 1938), maximum principal stress criterion (Adams and Peppiatt 1974)

and maximum shear strain criterion (Hart-Smith 1981). In such strength-based

approaches, failure is assumed when the respective strength is reached, i.e. ultimate

load of the bonded joint is reached when the first crack occurs in the adhesive.

However, the existing study on FRP-to-concrete bonded joints under axial loading

have shown that the bonded joints with bond length larger than the Le, does not

necessarily fail when the respective strength is achieved (Yuan et al. 2004). Such

behaviour cannot be explained by using strength-based approaches. Nevertheless,

strength-based approaches can still give good predictions for bonded joints with

shorter bond lengths and if the complete failure of the bonded joint occurs as soon

as the first crack in the adhesive appears.

For the strength-based approaches to be used in predicting bond strength, an

accurate prediction of the interfacial stress and/or strain distribution is essential.

This important issue has attracted much research interest (Volkersen 1938; Goland

and Reissner 1944; Adams and Peppiatt 1973; Adams 1981; Rabinovitch and

Frostig 2000; Shen et al. 2001; Smith and Teng 2001; Teng et al. 2002b; Yang and

Ye 2010; Zhang and Teng 2010). These studies consist of analytical studies

(Volkersen 1938; Goland and Reissner 1944; Adams and Peppiatt 1973;

Rabinovitch and Frostig 2000; Shen et al. 2001; Smith and Teng 2001; Yang and

Ye 2010) as well as finite element (FE) studies (Adams 1981; Teng et al. 2002b;

Zhang and Teng 2010). However, the accuracy of such analysis depends on the

20

accuracy of the assumptions made in deriving the solutions. These include ignoring

peeling stresses assuming the effect of peeling stresses are negligible (Volkersen

1938), the assumption of a constant stress state over the thickness of the adhesive

(Rabinovitch and Frostig 2000; Smith and Teng 2001), and the idealization of the

edge shape of the FRP plate end as a square end (Harrison and Harrison 1972).

Depending on the joint configuration and the loading condition, these assumptions

may deviate significantly from the reality resulting in significant errors. A thorough

review of interfacial stress analysis can be found in Zhang and Teng (2010). The

existing studies on FRP-to-concrete bonded joints have shown that the fracture

mechanics-based approaches are superior to strength-based approaches in predicting

the bond strength of FRP-to-concrete bonded joints and steel-to-concrete bonded

joints (Yuan and Wu 1999; Chen and Teng 2001). The fracture mechanics-based

methods shows that the bond strength depends significantly on the interfacial

fracture energy instead of the strength of the adhesive. These approaches also

explain the existence of an effective bond length which has also been observed in

FRP-to-steel bonded joint tests (Nozaka et al. 2005b; Xia and Teng 2005).

Xia and Teng (2005) recently conducted a series of single-shear pull-off tests

aiming to understand the full-range behaviour of FRP-to-steel bonded joints. Their

test results verified the applicability of fracture mechanics-based approach to

predict the bond strength of FRP-to-steel bonded joints. However the effect of

adhesive material and geometrical (i.e. thickness) properties on the bond-slip

behaviour, thus on interfacial fracture energy was not considered.

2.2.3.2 Bond-slip relationship

The existing research on FRP-to-concrete bonded interfaces has shown the

importance of an accurate bond-slip model in understanding and modelling the

behaviour of FRP-strengthened concrete structures (Lu et al. 2005; Yao et al.

2005a). Similarly, an accurate bond-slip model is of fundamental importance to the

understanding and modelling of the behaviour of FRP-strengthened steel structures.

A bond-slip model describes the relationship between the local interfacial shear

stress and the relative slip between the two adherends. Hence, a bond-slip model

describes the behaviour of the bonded interface under mode-II (i.e. shear) loading.

21

In obtaining the bond-slip relationship experimentally, care should be taken to

select a test set-up which satisfies the pure mode-II loading condition. However,

due to the plate end peeling stresses, a pure mode-II loading condition may be

difficult to achieve using any of the existing bond test set-ups. To study the

bond-slip behaviour of FRP-to-concrete bonded joints, the so-called near-end

supported single-shear pull-off test is probably the most suitable (Yao et al. 2005a)

and was also used in a recent study on the full-range behaviour of FRP-to-steel

bonded joints (Xia and Teng 2005). Even though it has been argued that the effect

of peeling stresses is limited to a small region at the plate end and thus does not

affect the overall behaviour (Yao et al. 2005a), no experimental or numerical

verification of pure shear loading in such bond tests has been made.

For FRP-to-concrete bonded joints, (Lu et al. 2005) conducted a thorough review of

bond-slip models and proposed three two-branch bond-slip models, each containing

an ascending branch and a descending branch; they differ from each other in the

shape of the bond slip model and the associated level of accuracy. The simplest

version of these bond-slip models is a bi-linear bond-slip model with sufficient

accuracy (Figure 2.2). The key parameters of the bi-linear bond-slip model are the

maximum local bond stress maxτ and the corresponding slip 1δ , the slip when the

local bond stress reduces to zero fδ , and the interfacial fracture energy fG which

is equal to the area of the region enclosed by the bond-slip curve and the horizontal

axis. For FRP-to-concrete bonded joints, these parameters are generally related to

the tensile strength of concrete as the concrete is usually the weak link of the joint.

Therefore the expressions developed for these parameters are not directly applicable

to FRP-to-steel bonded joints where the adhesive layer is usually the weak link. Xia

and Teng (2005) showed that a bi-linear bond-slip model can also be used for

CFRP-to-steel bonded joints with the bond-slip parameters defined using adhesive

properties. This observation is believed to be valid only for the brittle adhesives

used in their study which had an approximately linear-elastic curve until the

attainment of brittle tensile failure. Since some of the adhesives available in the

market show significant non-linear stress-strain behaviour (Figure 2.3) and lead to

superior bond performance for metal-to-metal bonded joints (Hart-smith 1981), this

22

observation is unlikely to be valid for them. The effect of adhesive material

properties on bond-slip behaviour need further research.

2.3 FLEXURAL STRENGTHENING OF STEEL BEAMS

Similar to an RC beam, steel beams and steel-concrete composite beams can be

strengthened by bonding an FRP (generally CFRP) plate to its soffit (Miller. et al.

2001; Tavakkolizadeh and Saadatmanesh 2003c; Al-Saidy et al. 2004; Nozaka et al.

2005b; Colombi and Poggi 2006a; Lenwari et al. 2006; Sallam et al. 2006; Deng and

Lee 2007a; Schnerch and Rizkalla 2008; Shaat and Fam 2008; Fam et al. 2009;

Linghoff et al. 2009). The FRP plate not only enhances the ultimate flexural capacity

of the beam but also delays the yielding of the beam by increasing its flexural

stiffness (especially when high modulus CFRP is used) and thus reducing the strain

developed in the steel (Sen et al. 2001; Tavakkolizadeh and Saadatmanesh 2003b;

Colombi and Poggi 2006a; Schnerch and Rizkalla 2008). A number of failure modes

are possible in these beams: (a) in-plane bending failure (Linghoff et al. 2009); (b)

lateral buckling (Sallam et al. 2006); (c) plate end debonding (Deng and Lee 2007a);

and (d) intermediate debonding due to yielding and the opening-up of a crack

(Sallam et al. 2006). Additional but less likely failure modes include: (e) local

buckling of the compression flange; and (f) local buckling of the web.

Of these failure modes, the in-plane flexural capacity of an FRP-plated steel beam can

be easily determined, provided debonding does not become critical and hence the

plane section assumption can still be used (Moy 2001; Cadei et al. 2004). Many of the

existing analytical studies on FRP-strengthened steel beams used this simple

assumption (Moy 2001; Cadei et al. 2004; Colombi and Poggi 2006a; Fam et al. 2009;

Linghoff et al. 2009). However, in contrast to this assumption, debonding failures

have been observed in some existing experimental studies (e.g. Sallam et al. 2006;

Deng and Lee 2007a). Therefore, accounting for such debonding failures in

FRP-strengthened steel beams is necessary and has attracted considerable research

interest (e.g. Moy 2001; Cadei et al. 2004; Lenwari et al. 2006; Schnerch et al. 2006).

23

2.3.1 Plate End Debonding

Of the two debonding failure modes, plate end debonding has received more

attention (Sen et al. 2001; Deng and Lee 2007a; Schnerch et al. 2007). Plate end

debonding of FRP-plated steel beams occurs due to high localized interfacial

peeling stresses and shear stresses near the plate end. These localized interfacial

stresses depend on the plate end bending moment and shear force as well as the

geometry of the plate end. Several methods have been suggested to reduce the risk

of plate end debonding, including (a) moving the plate end away from high bending

regions (i.e. placing the plate end close to the adjacent support in a simply

supported beam) (Deng and Lee 2007a), (b) reducing plate end stress concentrations

by providing a spew fillet of excess adhesive, (c) tapering the edge of the adherend

(Hart-Smith 1981), and (d) using a softer adhesive at the plate end (Fitton and

Broughton 2005). All these methods can be effective to a certain extent in reducing

plate end stress concentrations, thus delaying or suppressing plate end debonding

failure. In addition, the use of a combination of some of these methods such as

providing a spew fillet of excess adhesive and reverse tapering of the plate near the

plate end has been suggested (Schnerch et al. 2007). Where possible providing

clamps or other types of mechanical anchors to avoid plate end failure due to high

peeling stresses are advisable (Sen et al. 2001).

A number of attempts have been made to accurately predict interfacial stresses in a

plated beam, including both analytical solutions (Rabinovitch and Frostig 2000;

Smith and Teng 2001; Colombi and Poggi 2006a; Stratford and Cadei 2006; Yang

and Ye 2010) and numerical studies (Teng et al. 2002b; Colombi and Poggi 2006a;

Linghoff and Al-Emrani 2010; Zhang and Teng 2010). However, these studies have

been based on different simplifying assumptions and their accuracy may be limited

due to the assumptions adopted (Zhang and Teng 2010). A comparison of different

modelling approaches has recently been presented by Zhang and Teng (2010),

which illustrates clearly how each assumption affects the predicted interfacial

stresses. Most of these studies are for plate ends with a sharp edge (Figure 2.4a).

Due to the numerical singularity near the edge, the stresses there approach infinity

(Teng et al. 2002b). The sharp edge is just a theoretical phenomenon and does not

normally exist in a real bonded joint. In a real bonded joint, it is very likely that a

24

fillet of excess adhesive exists near each plate end (Figure 2.4b). Mylonas (1954)

used photo-elastic techniques to investigate the stresses induced at the end of an

adhesive layer for a number of adhesive edge shapes and showed that the position

of the maximum stress depends on the edge shape. FE modelling has also shown

that the existence of an adhesive fillet significantly reduces plate end stress

concentration (Adams and Peppiatt 1974; Teng et al. 2002b; Zhang and Teng 2010).

In most of the existing studies on interfacial stresses, the adhesive layer was

assumed to be linear-elastic (Colombi and Poggi 2006a; Linghoff and Al-Emrani

2010). Such interfacial stress analysis can be used to predict the interfacial stress

distribution near the plate end and how this is affected by various factors (e.g. the

FRP plate rigidity, and the thickness and material properties of adhesive), and thus

is useful for understanding the mechanism of plate end debonding. However, such

elastic analysis cannot be used to predict the full-range behaviour or the ultimate

load at debonding, and is in serious error when used for beams strengthened using

non-linear adhesives. Despite this weakness, some attempts (Lenwari et al. 2006;

Schnerch et al. 2007) have been made to predict plate end debonding by simply

assuming that plate end debonding occurs when the maximum interfacial stresses

found from an elastic analysis reach their corresponding limiting stresses (i.e.

material strengths). These approaches may underestimate the ultimate load at plate

end debonding. To accurately predict plate end debonding, the non-linear and

damage behaviour of the interface in both the normal (or peeling) direction (i.e.

under mode I loading) and the shear direction (i.e. under mode II loading) and their

interaction should be appropriately considered.

2.3.2 Intermediate Debonding

Another possible debonding failure mode in FRP-plated steel beams is intermediate

debonding which can initiate due to either the presence of a defect (e.g. crack) or

local yielding of steel (Sallam et al. 2006). Intermediate debonding thus initiates in a

region where the FRP is highly stressed and moves towards the plate ends where the

stress in the FRP plate is lower. Different from plate end debonding, where

debonding normally propagates from a plate end to a higher bending region and thus

is a rather brittle process, intermediate debonding can be more ductile. Most of the

25

existing analytical models for FRP-plated steel beams do not consider intermediate

debonding, and much less research is available on intermediate debonding in

FRP-plated steel beams (Sallam et al. 2006). However, this kind of debonding is

regarded to be similar to intermediate-crack debonding (IC debonding) in

FRP-plated concrete beams (Teng et al. 2003b), in the sense that both initiates

where the substrate is locally damaged/weakened and the interface is consequently

subjected to high interfacial shear stresses. Therefore, it can be expected that the

intermediate debonding strength depends strongly on the interfacial shear fracture

energy obtained from simple bonded joint tests (e.g. from single-shear pull-off

tests). More research to gain a fuller understanding of intermediate debonding is

urgently needed.

2.4 FATIGUE STRENGTHENING

One of the most important aspects of FRP strengthening of steel structures is the

capability of the method to improve their fatigue resistance (Bassetti et al. 2000a;

Bassetti et al. 2000b; Colombi et al. 2003b; Dawood et al. 2007; Liu 2009a; Liu

2009b). Fatigue strengthening studies have been carried out on beams

(Tavakkolizadeh and Saadatmanesh 2003a; Deng and Lee 2007b; Shaat and Fam

2008), steel plates (Colombi et al. 2003a; Bocciarelli et al. 2009a; Liu 2009a; Liu

2009b), steel rods (Jones and Civjan 2003) and joints (Nakamura et al. 2009).

Depending on the particular fatigue strengthening problem being considered,

different measures need to be considered to achieve optimized performance. In the

strengthening of joints, the maximum possible length of the FRP plate may be

limited whereas in a girder a much longer FRP plate can be used. In the case where

the bond length is restricted, an adhesive with a lower effective length (Le) may be

preferred. Liu et al. (2009a, b) showed that the fatigue life increases with increases

in the bond length until Le is reached, but further increases in bond length cannot

significantly affect the fatigue life.

In the fatigue strengthening of cracked steel members, the purpose of strengthening

is to reduce the crack tip stress intensity (Colombi et al. 2003a; Taljsten et al. 2009).

It has been shown (Nakamura et al. 2009; Liu et al. 2009a, b) that the stress

26

intensity at the crack tip can be reduced by using a stiffer CFRP plate (i.e. by

increasing the thickness of the FRP plate or using higher modulus FRP) and as a

result, the post-crack fatigue life of cracked steel plates can be increased. However,

increasing the stiffness of the FRP, especially in unsymmetrical strengthening

systems such as single-side composite patching, can introduce significant bending

resulting in premature debonding (Tsouvalis et al. 2009). If this debonding is brittle,

then the effect will be catastrophic. Even if the debonding process is gradual, as

debonding occurs near the crack, a localised stiffness reduction in the debonded

region will occur, resulting in an increased stress intensity at the crack tip (Colombi

et al. 2003b), thus further increasing the rate of damage. Several methods of

analysis exist for the prediction of the stress intensity of a crack tip in a

strengthened system for a particular loading range (Colombi et al. 2003a; Liu et a.

2009a; Tsouvalis et al. 2009). Therefore, when deciding on a strengthening system,

it is advisable to carry out a preliminary analysis to examine the effects of different

adhesive properties and FRP properties on the crack tip stress intensity to optimise

performance.

By pre-stressing the bonded FRP reinforcement, compressive stresses can be

introduced in the steel substrate so that crack closure can be achieved, resulting in

much better fatigue performance. The influence of the pre-tensioning level on the

fatigue crack growth rate has been studied both experimentally and numerically

(Colombi et al. 2003a, b; Taljsten et al. 2009). By evaluating the stress intensity at

the crack tip of the strengthened system, the pre-tensioning force needed to stop

fatigue crack growth can be predicted (Taljsten et al. 2009).

The level of pre-tensioning that can be applied to an FRP strengthening system

depends on the static and fatigue strength of the bonded joint, so a good

understanding of the behaviour of bonded joints under fatigue cyclic loading is

required. In many studies, debonding of the FRP plate was observed (Deng and Lee

2007; Shaat and Fam 2008; Bocciarelli et al. 2009; Liu 2009a) during fatigue cyclic

loading, demonstrating the critical nature of the FRP-to-steel bonded interface.

Debonding of the FRP plate has been shown to have a significant influence on the

crack growth rate (Colombi et al. 2003a; Shaat and Fam 2008). More research is

therefore needed to understand the bond behaviour of FRP-to-steel bonded

27

interfaces under fatigue cyclic loading and how it affects the effectiveness of FRP

fatigue strengthening.

2.5 STRENGTHENING OF STEEL STRUCTURES AGAINST LOCAL BUCKLING

2.5.1 Buckling Induced by High Local Stresses

In practice, high stresses in a local zone often arise as a result of concentrated loads

and the need to introduce discrete supports, openings and other local features. Under

local high compressive stresses, local buckling is likely to control the wall thickness

of a thin-walled steel structure. Such local buckling can be easily prevented by

bonding FRP patches. Local high tensile stresses can also be dealt with in the same

way.

A practically important problem is the web crippling failure of thin-walled sections

under a bearing force (Zhao et al. 2006). Zhao et al. (2006) found from their

experimental study that bonded CFRP offers an effective solution to this problem

(Figure 2.5). Their strengthened specimens failed by debonding of CFRP plates, so a

better understanding of the mechanisms behind debonding of such strengthened

structures is needed. Furthermore, the effects of parameters such as adhesive material

properties and web slenderness of the section should be properly investigated

2.5.2 Buckling Induced by Other Loads

FRP, especially CFRP, has also been used to strengthen other thin-walled steel

structures against local buckling, including steel square columns (Shaat and Fam

2009), lipped channel steel columns (Silvestre et al. 2009), and steel welded T-section

compression members (Harries et al. 2009) subjected to axial compression. The FRP

strengthening method has been shown to be very effective (Harries et al. 2009) in

delaying local buckling and thus enhancing the strength of thin-walled steel structures,

especially for those with a slender section. While crushing of the FRP plate has been

observed in some experiments (Shaat and Fam 2009), debonding has been found to

be the most likely failure mode in such strengthened structures (Harries et al. 2009;

28

Shaat and Fam 2009; Silvestre et al. 2009). More research is therefore needed on the

debonding process so that a method for accurate prediction of the performance of

such strengthened structure can be developed.

2.6 CONCLUSIONS

The chapter has presented an in-depth review of the existing research on several

issues of importance in the strengthening of steel structures using bonded CFRP

plates. Research needs have been identified as a result of this review as detailed

below.

This chapter first presented a detailed review of the existing work on CFRP-to-steel

bonded joints. This review has indicated that although the effectiveness of CFRP

strengthening of steel structures has been demonstrated, there is a lack of

knowledge about the bond behaviour of CFRP-to-steel bonded joints. There is

therefore a need for more research into the bond behaviour of CFRP-to-steel bonded

interfaces to lay a solid foundation for the development of methods for the design of

CFRP plates bonded to steel members against various debonding failure modes. The

key issues that need further research include the effect of steel surface preparation

on bond behaviour, ways for the quantification of steel surface quality, the

bond-slip behaviour between CFRP and steel, and the full-range behaviour of

CFRP-to-steel bonded joints.

It has been well established that a steel beam can be strengthened by bonding a

CFRP plate to its tension face. The CFRP plate not only enhances the ultimate

flexural capacity of the beam but also delays the yielding of the beam by increasing

its flexural stiffness. Such CFRP-strengthened steel beams may fail by debonding;

the modes of debonding include intermediate debonding and plate end debonding.

Intermediate debonding is due to high interfacial shear stresses in a local

defective/damaged/yielded zone in the substrate while plate end debonding is due to

high local interfacial peeling stresses and shear stresses near a plate end. No reliable

theoretical method has been found which is capable of accurate predictions of such

debonding failures. To accurately predict plate end debonding failures, the

non-linear behaviour of the interface between CFRP and steel in both the normal (or

29

peeling) direction (i.e. under mode I loading) and the shear direction (i.e. under

mode II loading) as well as their interaction should be appropriately considered.

Accurate predictions of intermediate debonding require only the accurate simulation

of interfacial behaviour under mode II loading.

Existing studies have demonstrated that CFRP strengthening is effective in

enhancing the fatigue performance of steel beams, particularly when the CFRP plate

is pre-tensioned. By pre-stressing the bonded CFRP reinforcement, compressive

stresses can be introduced in the steel substrate so that crack closure can be

achieved, leading to much better fatigue performance. Much more research is

needed on the fatigue performance of CFRP-strengthened steel members, especially

to clarify the effect of debonding propagation on fatigue resistance under fatigue

cyclic loading.

CFRP has also been shown to be effective in the strengthening of thin-walled steel

structures against local buckling failures. In particular, existing experimental results

have shown that bonded CFRP reinforcement can be an effective solution to the web

crippling failure of thin-walled tubular members under an end bearing load. The

strengthened tube generally fails by debonding of the bonded CFRP plates. Therefore,

a better understanding of the mechanism behind the debonding failure of such

strengthened tubular members is needed.

This PhD thesis deals with all issues outlined above except the fatigue strengthening

aspect, due to the limited length of a PhD research programme. More specifically,

the present PhD research programme, as detailed in the subsequent chapters, has

been conducted with the following three major objectives:

(1) To examine the effects of surface preparation using different methods on

the adhesive bonding capability of steel surfaces and to develop a reliable

method for the quantification of steel surface quality after surface

preparation;

(2) To study the effects of adhesive mechanical properties as well as the

geometrical properties of bonded joints on the bond strength and the

full-range behaviour of CFRP-to-steel bonded joints.

30

(3) To gain better understanding of the mechanisms behind debonding failures of

CFRP-strengthened steel structures and to develop an accurate method for the

modelling of debonding debonding failures in CFRP-strengthened steel

structures.

31

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Zhao, X.L., Fernando, D. and Al-Mahaidi, R. (2006). "CFRP strengthened RHS

subjected to transverse end bearing force", Engineering Structures, 28(11),

1555-1565.

Zhao, X. L. and Zhang, L. (2007). "State-of-the-art review on FRP strengthened

steel structures", Engineering Structures, 29(8), 1808-1823.

39

Figure 2.1 Debonding failure modes in a CFRP-plated steel beam

Figure 2.2 Bi-linear bond-slip model

Intermediate debonding

Beam

CFRP plate Adhesive Plate end debonding

τ

1δ fδ δ

maxτ

40

Figure 2.3 Stress-strain responses of adhesives

(a) Sharp edge

(b) With a corner adhesive fillet

Figure 2.4 End details of an adhesively-bonded joint

Linear

Non-linear

Elasto-plastic

Strain

Stress

CFRP plate

Adhesive

Steel/ concrete

Sharp corner

CFRP plate

Adhesive

Steel/ concrete

Adhesive fillet

41

Figure 2.5 Strengthening for high local stresses (Zhao et al. 2006); Type 1- bare

tubes, Types 2 to 6-CFRP-strengthened tubes

42

CHAPTER 3 PREPARATION AND CHARACTERIZATION OF STEEL SURFACES FOR ADHESIVE BONDING

3.1 INTRODUCTION When steel structures are strengthened with adhesively bonded FRP laminates,

debonding failure between the steel and the FRP may occur in the following modes:

(a) within the adhesive (cohesion failure); (b) at the physical interfaces between the

adhesive and the adherends (adhesion failure); and (c) a combination of adhesion

failure and cohesion failure. If adhesion failure controls the strength of FRP-

strengthened steel structures, then the interfacial bond strength depends on how the

steel surface and the FRP surface are treated as well as the bond capability of the

adhesive. As adhesion failure depends on surface treatment while the degree of

surface treatment, especially to the steel substrate, is difficult to control precisely on

site, the development of a design theory becomes much more involved if adhesion

failure is critical. This important issue has not previously been given adequate

attention.

For an FRP-to-steel bonded interface, adhesion failure is much more likely to occur

at the steel/adhesive interface than at the FRP/adhesive interface. In the published

literature, the treatment and characterization of steel surfaces has received

significant research attention (Mays and Huthcinson 1992; Harris and Beevers 1999;

Baldan 2004). The most popular methods for steel surface treatment include

solvent-cleaning and mechanical abrasion through grit-blasting or using other tools

(e.g. sand papers, wire brushes, abrasive pads and wheels, and needle guns)

(Hollaway and Cadei 2002; Baldan 2004). Solvent-cleaning removes contaminants

on the surface (e.g. grease, oil and water) but does not change the surface properties.

Mechanical abrasion aims to roughen the surface and to remove the weak surface

layer (e.g. oxide layer) which is chemically inactive (Harris and Beevers 1999;

Baldan 2004). Among various mechanical abrasion approaches, grit-blasting

appears to be the most effective (Harris and Beevers 1999; Hollaway and Cadei

43

2002; Schnerch et al. 2007) and is recommended by existing guidelines (Cadei et al.

2004; Schnerch et al. 2007).

To better understand the effect of a particular surface treatment procedure, it is also

important to characterize the surface to evaluate its bonding capability. A steel

surface is often characterized by its three main properties (Gent and Lin 1990;

Harris and Beevers 1999; Amada and Satoh 2000; Lavaste et al. 2000): surface

energy, surface chemical composition and surface roughness & topography. All

three properties significantly affect the adhesion strength.

While many studies (Gent and Lin 1990; Mays and Huthcinson 1992; Baldan 2004)

exist on the surface preparation of various materials (e.g. steel, aluminium and

ceramic) for adhesive bonding, research focusing on the effects of surface

preparation methods and adhesive properties on the adhesion strength between steel

and adhesive is rather limited. This chapter therefore presents a systematic

experimental study to correct this deficiency within the context of FRP

strengthening of steel structures.

3.2 ADHESION MECHANISMS

In reaching an optimum surface condition for adhesive bonding, it is necessary to

first understand all the different possible bonding mechanisms, one or more of

which may be present at any given instant. Detailed discussions of interfacial forces

and adhesion mechanisms can be found in the published literature (Mays and

Huthcinson 1992; Adams et al. 1997; Baldan 2004; Packham 2005) where the main

mechanisms are identified as follows: (a) physical bonding, (b) chemical bonding,

and (c) mechanical interlocking. These mechanisms are particularly useful in

explaining certain phenomena associated with adhesive bonding and are briefly

discussed below.

3.2.1 Physical Bonding

Physical bonding contains two types of bonding: adsorption and electrostatic

attraction. The adsorption theory considers that the adhesive and the substrate are in

44

intimate molecular contact, and weak secondary or van der Waal’s forces operate

between them. This theory in return states that for bonding to be successful, an

adhesive must wet the surface to be bonded (adherend) (Flinn 1995). The theory of

electrostatic attraction claims that adhesion is due to the forces of attraction

occurring between the adhesive and the adherend surface arising from the transfer

of electrons between them, resulting in the formation of a double layer of electrical

charge at the interface (Mays and Huthcinson 1992). However, these attractions are

very unlikely to make a significant contribution to the final bond strength of the

interface (Baldan 2004).

3.2.2 Chemical Bonding

Chemical bonding refers to covalent or ionic bonds formed across the interface

between the adhesive and the adherend. These are strong primary forces and make a

significant contribution to the final bond strength (Adams et al. 1997; Baldan 2004).

Surface treatments often produce surfaces with different chemical compositions and

oxide stoichiometries. These morphological changes influence the nature of

chemical bonds.

3.2.3 Mechanical Interlocking

If the surface is rough and thus contains crevices and pores, adhesive in a liquid

form will penetrate into these crevices and pores. When the adhesive in these

crevices and pores get hardened (solidified) mechanical interlocking with the

surface layer is created, providing a mechanical bond. Good mechanical

interlocking requires irregularities of the substrate surface to be present, which is

the reason for the roughening of a substrate surface prior to bonding. Simple

mechanical interlocking between two surfaces can lead to a considerable degree of

bonding. However, the strength of mechanical bonding is lower than that of

chemical bonding (Chawla 1998). The strength of an interface with mechanical

bonding only is unlikely to be very high in transverse tension, but can allow

effective stress transfer when loads are applied parallel to the interface (Chawla

1998).

45

3.3 ISSUES IN SURFACE PREPARATION

In simple terms, it can be concluded that adhesion mainly results from mechanical

bonding between the adhesive and the adherend as well as chemical bonding (either

primary covalent bonds or polar secondary forces) between the two. The latter

(chemical bonding) is believed to be more important although mechanical bonding

also plays an important role (Mays and Huthcinson 1992; Hollaway and Cadei 2002;

Baldan 2004). To promote mechanical bonding, adherend surfaces are often

roughened before bonding, but such roughening may sometimes give

counterproductive results. It is possible for air bubbles to be trapped at the bottom

of crevices and these bubbles can act as stress concentrators to promote failure in a

rigid adhesive (Baldan 2004).

The bonding mechanisms discussed above emphasize the requirement of surface

preparation to enhance the formation of chemical bonds and mechanical bonds

between the adherend and the adhesive. Most surface treatment methods involve

cleaning, followed by removal of weak layers and then re-cleaning (Mays and

Huthcinson 1992; Hollaway and Teng 2008). Degreasing to remove oil, grease and

most potential contaminants is the necessary first step in the preparation of an

adherend surface. A volatile solvent such as acetone should always be used as

otherwise residues may result from a weak surface layer (Mays and Huthcinson

1992; Hollaway and Teng 2008). For metallic substrates, alkaline cleaners and/or

detergent solutions are often advised after solvent treatments to remove dirt and

inorganic solids (Mays and Huthcinson 1992; Schnerch et al. 2006; Hollaway and

Teng 2008).

Mechanical treatments are used primarily to produce a clean macroscopically rough

surface and to remove some of the existing oxide layer (Molitor et al. 2001; Baldan

2004). The combination of a clean, fresh adherend surface with significant macro-

roughness improves the initial dry strength of the adhesive/adherend interface

(Kinloch 1983). Among the mechanical treatment methods available, grit-blasting

has been the favourite (Sykes 1982; Adams et al. 1997; Hollaway and Cadei 2002;

Schnerch et al. 2007; Schnerch et al. 2006; Hollaway and Teng 2008). Parker (1994)

showed that for fibre-reinforced composite joints, those that were grit-blasted had

46

higher peel strengths than those which were hand-ground. A grit-blasting procedure

using angular grit removes the inactive oxide and hydroxide layers by cutting and

deformation of the base material. However, there is still considerable usage of hand-

grinding in the preparation of steel surfaces in the FRP strengthening of steel

structures.

Following grit-blasting the surface may be contaminated with fine abrasive dust.

Hollaway and Cadei (2002) suggested to remove the fine dust by dry-wiping or by

using a vacuum head instead of solvent-cleaning as solvent-cleaning will only

partially remove the dust and may redistribute the remaining dust on the entire

surface. El Damatty et al. (2003) however showed that with the use of a large

amount of solvent (enough to wash out the dust and to avoid the re-deposition of

dust as solvent evaporates), the dust can be completely removed and a clean surface

can be produced.

3.4 SURFACE CHARACTERIZATION

In studying the adhesion strength and the effectiveness of surface preparation

methods, it is important to understand how the adhesion strength is affected by the

three main surface characteristics which are changed by surface preparation: surface

energy, surface chemical composition, and surface roughness & topography. These

three characteristics are often used to characterize surfaces (Gent and Lin 1990;

Harris and Beevers 1999; Amada and Satoh 2000; Lavaste et al. 2000).

3.4.1 Surface Energy

The first and necessary condition of forming a successful bond is that the adhesive

must be in intimate contact with the adherend surface. This requires that the

adhesive wets the surface first. In general, the basic condition for wetting to occur is

that the adherend surface should possess more surface energy than the adhesive.

An adhesive is generally applied as a liquid and its angle of contact “θ ” with the

solid surface is related to the surface energies by Young’s equation (Packham 2005);

47

θγγγ cosLVSLSV += (3.1)

where SVγ , SLγ , and LVγ are surface energies at the solid/vapour (i.e. steel/vapour),

solid/liquid (i.e. steel/adhesive) and liquid/vapour (i.e. adhesive/vapour) interfaces

respectively (Figure 3.1). Thus for wetting to occur, SVγ should be greater than the

right hand side of Eqn 3.1.

For the failure of adhesive to occur, new surfaces should be formed, thus

appropriate surface energies (i.e the surface energies of the newly formed surfaces,

which can both be the adhesive surfaces or the adhesive surface and the adherend

surface) should be provided (Packham 2005). The surface energy term may be the

work of adhesion (Wa) or the work of cohesion (Wc

) depending on whether the

failure is adhesive or cohesive. Therefore, if bonded surfaces containing higher

energy a higher adhesion strength should be achieved.

The surface energy of steel (solid), SVγ , can be obtained by measuring the static

contact angle of a liquid droplet on the steel surface. By using 2 different liquids

whose surface energies LVγ are known and measuring the static contact angles “θ ”

of those two liquids with the steel surface, the surface energy of steel (solid), SVγ ,

can be obtained using Young’s equation (Eqn 3.1) combined with the geometric

mean equation given by Packham (2005) as follows:

( ) ( ) ( )1 1

2 21 cos 2 d d p pLV LV SV LV SVγ θ γ γ γ γ + = +

(3.2)

p d

SV SV SVγ γ γ= + (3.3)

where the superscripts d and p represent the dispersive and polar energy

components.

48

3.4.2 Surface Chemical Composition

Chemical bonds are formed between the chemical groups on the adhesive surface

and the compatible chemical groups on the adherend surface. The adhesion strength

of a bonded joint depends largely on chemical bonding and thus the number and

type of chemical bonds formed. Often on metal surfaces, weak and chemically

inactive oxide layers can be found, and it is common to remove these weak surface

layers before bonding (Baldan 2004). The process of removing these weak surface

layers often changes the surface chemical composition. In particular, grit-blasting

may introduce grit residues onto the adherend surface which might have a

significant effect on surface energy and adhesion (Harris and Beevers 1999).

3.4.3 Surface Roughness

The roughness of a surface can affect its adhesion strength in many different ways

(Packham 2003). For a moderately rough surface, an increase in surface area may

well lead to a proportionate increase in adhesion, as long as the roughness does not

reduce contact between the surfaces (Gent and Lai 1995; Packham 2003). Through

comparison between adhesion to smooth steel and adhesion to grit-blasted steel,

Gent and Lai (1995) reported increases in peel energy by a factor of 2 to 3, which

they attributed to an increase in surface area. By contrast, some researchers have

shown that within certain limits, roughening a substrate usually causes its

wettability to decrease (Tamai and Aratani 1972; Hitchcock et al. 1981), which can

be explained by noting that peaks, ridges and asperities form barriers which restrict

the spreading of droplets and reduce wettability. Properly roughened surfaces also

affect the joint strength by enhancing mechanical bonding.

The roughness of a surface is commonly represented by the following roughness

parameters (Harris and Beevers 1999; Shahid and Hashim 2002): the average

roughness aR , which is the arithmetic average of the absolute vertical deviation

values ( iy ) of the roughness profile from the mean line (Eqn 3.4) and the root mean

square roughness qR , which is the root mean square value of iy (Eqn 3.5).

49

1

1 n

a ii

R yn =

= ∑ (3.4)

2

1

1 n

q ii

R yn =

= ∑ (3.5)

Some researchers have argued that the roughness parameters given above can only

represent deviations from the mean value but cannot accurately capture the surface

profile/topography. Therefore for accurate representation of a surface profile/

topography, the fractal dimension should be used (Amada and Satoh 2000;

Packham 2003).

Fractal geometry can be used to analyze irregular or fractional shapes. A detailed

discussion of the concepts of fractals can be found in many publications

(Mecholsky et al. 1989; Lu and Hellawell 1995; Amada and Satoh 2000; Packham

2003). Accordingly, only the determination of the fractal dimension for a surface

profile is briefly explained below.

Consider an element of size (area) s on a fractal surface. Let N be the number of

elements required to form the surface. Then the fractal dimension Df

is defined as

(Amada and Satoh 2000; Packham 2003);

( )log .log2

fDN s s C= − + (3.6)

where C is a constant. If the element is represented by a rectangular box with height

(h.x) and width (w.x) with an aspect ratio of h/w (Figure 3.2), Eqn 3.6 can be

reproduced as [known as “the box counting method”, (Amada and Satoh 2000)],

( ) 'log .logfN x D x C= − + (3.7)

where C` is a constant. Now by changing the value of x, one can obtain the

corresponding N(x) values and plot logN versus logx. If this curve is linear, it can be

50

concluded that this profile has fractal characteristics and the slope of the curve, Df

is the fractal dimension.

3.5 EXPERIMENTAL PROGRAMME AND PROCEDURES

Tensile butt-joints tests and single-lap shear tests were carried out using mild steel

specimens. Four commonly available structural adhesives were used in both tensile

butt-joint tests and single-lap shear tests. Coupon tests were conducted to obtain the

tensile properties of the four adhesives used in this study and also for a fifth

adhesive (FYFE Tyfo) which was used in the study presented in Chapter 8. Five

coupons were tested for each adhesive. The key results averaged from the five

coupon tests for each adhesive are given in Table 3.1 and typical stress-strain curves

of these adhesives are shown in Figure 3.3. It is evident from Table 3.1 that the five

adhesives cover a wide range of elastic modulus (from 1.75 GPa to 11.25 GPa) and

ultimate tensile strain (from 0.003 to 0.0289).

Five different surface preparation (or pre-treatment) methods were employed in this

study to investigate the effect of surface preparation on bond strength. These five

surface preparation methods include: (1) solvent-cleaning; (2) hand-grinding after

solvent-cleaning; and (3)-(5) grit-blasting after solvent-cleaning using 0.5mm

angular alumina grit, 0.25mm angular alumina grit and 0.125mm angular alumina

grit respectively. The 0.5mm and 0.125mm grits were the so-called white alumina

grits and the 0.25mm grit was the so-called brown alumina grit. The chemical

compositions of the three different grits, as specified by the manufacturer, are

shown in Table 3.2. The main content of both types of grits is Al2O3 but the latter

has a larger percentage of SiO2

. Hand-grinding was carried out using a silicon

carbide 100Cw abrasive paper.

In all the specimens, the adhesive thickness was carefully controlled at 1mm by

using 1mm diameter steel bearings (3 in each), considering that a 1mm thick

adhesive layer is typical of CFRP-to-steel bonded joints. Three specimens for each

unique combination were tested, resulting in 60 tensile butt-joint tests and 60

single-lap shear tests. The tensile butt joints were made of two 25mm diameter mild

steel rods bonded together on the circular ends (ASTM C633 2001) (Figure 3.4).

51

The single-lap shear specimens were made from 80*25*2mm steel coupons with a

25*12.5mm bond area (Figure 3.5) (ASTM D3 165 2000). In grit-blasting, special

care was taken to control the blasting angle at approx 75o

; a pressure of 0.4MPa

with a stand-off distance of 100mm was used. After grit-blasting/hand-grinding, the

surface was dry-wiped using a vacuum to remove any surface dust. Adhesive

bonding was carried out within 24 hours of the grit-blasting/hand-grinding

operation to minimize any contamination. All the specimens were cured for 14 days

after adhesive bonding before testing. Testing was carried out using a 50kN

capacity testing machine at a displacement rate of 1.2mm/ min.

In addition to the tensile butt-joint specimens and the single-lap shear specimens,

three small rectangular specimens were prepared using each of the five surface

preparation methods for surface characterization.

The surface chemical composition was measured using a SEM (Scanning Electron

Microscopy)/EDX (Energy Dispersive X-ray) analyzing system. Three specimens

of each surface type were tested, and three readings for each specimen at three

different locations on the surface were taken. Chemical composition measurements

were carried out before surface energy measurements as the liquid used in surface

energy measurements may contaminate the surface. All the measurements were

completed within 24 hours of the grit-blasting time to minimize any surface

contamination.

Surface roughness was measured using a profilometer with a travel distance of 4mm.

For each specimen, six measurements, including three measurements at different

locations in each of the two perpendicular directions, were made. aR and qR were

then obtained from the profilometer readings for each curve and the average reading

of the six measurements was taken as the final value of the specimen.

Each profile obtained from the profilometer was divided into 5 segments, resulting

in a total of 30 segments for each specimen. The box counting method described in

previous section was then used to obtain the fractal dimensions for each segment.

The average value was taken as the fractal dimension of the surface of the specimen.

52

Static contact angles were found using the video contact angle measurement method.

A video contact angle (VCA) analyzer was used to register the angles on both sides

of a droplet without moving the substrate. Measurements were realized using de-

ionized water and formamide. The surface energy values for these liquids are well

established and can be found in many publications (Clint and Wicks 2001; Harris

and Beevers 1999; Rance 1982). Surface energy values of different mild steel

surfaces were then calculated in terms of polar and dispersive components using

Eqn 3.2.

3.6 RESULTS AND DISCUSSIONS

3.6.1 Surface Characteristics

3.6.1.1 Surface roughness & topography

The direct effect of surface preparation was observed in surface profiles; images of

surface profiles obtained using different surface preparation methods are shown in

Figure 3.6. A visual inspection of these surface profiles shows that the grit-blasted

surfaces have pore patterns that are much more densely distributed than the solvent-

cleaned and the hand-ground surfaces (Figure 3.6). The hand-ground surface shows

a scratchy finish, but distributed patterns of pores are not seen (Figure 3.6b). It

should be noted that even on the solvent-cleaned surface, some scratchy patterns

can be observed (Figure 3.6a). The surfaces were initially machined at the time of

preparation and kept for a few weeks before being used in these experiments.

Therefore these scratchy patterns observed in the solvent-cleaned surface are a

result of the machined surface and are different from what are observed on the

hand-ground surface. Among the grit-blasted surfaces shown in Figure 3.6, the

surface prepared with the 0.125mm grit shows a denser distribution of pore patterns

than the surfaces prepared with the 0.25mm and 0.5mm grits. However, between the

0.5mm and 0.25mm grit-blasted surfaces, a clear visual difference is difficult to

observe.

53

Table 3.3 shows the values of Ra, Rq and Df for different surface types. The

solvent- cleaned surfaces gave the lowest values for all three parameters. It is seen

that the roughness parameters (i.e. Ra and Rq) increase with the grit size (Figure 3.7,

where each point in Figure 3.7 represents the average value obtained from 3

specimens subjected for the same surface type). The roughness parameters of hand-

ground surfaces are seen to be higher than those of the grit-blasted surfaces. These

roughness measurements are capable of giving an indication about the deviation of

the surface from the mean surface but are incapable of representing surface

topography accurately. From the images of the surfaces and comparing the values

obtained for Ra, it is clear that Ra is not a good measure of surface topography

(Amada and Satoh 2000; Packham 2003). In the case of hand-ground surfaces, the

Ra

value obtained can be rather deceiving.

The same profile readings used in calculating the Ra and Rq

values were used for

surface fractal analysis. The box counting method was adopted to obtain the fractal

dimension and a larger value for the fractal dimension generally means a rougher

topography (Amada and Satoh 2000). Amada and Satoh (2000) showed that to

obtain reasonable results, the aspect ratio (h/w) should lie in the range of 1 to 10.

Therefore, an aspect ratio of 5 was selected in this study. Keeping the aspect ratio

the same and changing the size of the rectangular box, a curve between log(N) and

log(x) (see Eqn 3.7) was obtained. 10 different locations (i.e. 5 different segments

each from two profilometer readings of each specimen) of each surface were used

to evaluate the fractal dimension values, and the average value of these 10 readings

is taken as the fractal dimension value of the surface. For all the surfaces, a linear

relationship was observed confirming the fractal characteristics of these surfaces.

The fractal dimension values of the hand-ground surfaces were found to be lower

than those of the grit-blasted surfaces. In addition, the fractal dimension value tends

to decrease with an increase in grit size (Figure 3.7). An inspection of the images of

surface profiles obtained from SEM/EDX analysis (Figure 3.6) and comparing them

with their fractal dimension values (Figure 3.7) indicate that the fractal dimension is

a more reasonable indicator of the surface topography than the surface roughness

parameters. With an increase in grit size, the fractal dimension value decreases,

indicating the ability of finer grits to give a rougher surface profile/topography.

54

3.6.1.2 Surface chemical composition

Surface treatment can change the chemical composition of a surface by removing

the weak surface layer (e.g. the oxide layer) and/or by introducing grit or other

residues to the surface. Table 3.4 shows the atomic percentages of various foreign

atoms (i.e. atoms other than C and Fe) for the five surface preparation methods

examined in this study. In addition, Figure 3.8 shows the average values of the

atomic percentages of various foreign atoms from three nominally identical

specimens for each surface preparation method. Before surface pre-treatment, the

specimens used in the present experiments were found to have visible oil particles

which may have been derived from the machining process. Cleaning using acetone

was found to be effective in removing these oil particles, and the SEM/EDX results

showed that no such contaminants existed on the solvent-cleaned surfaces (Table

3.4). Compared with method (1) (i.e. solvent-cleaning), method (2) (i.e. hand-

grinding) led to a smaller oxygen percentage but introduced additional aluminium

atoms (Figure 3.8). This is believed to be due to the partial removal of the weak

oxide layer and the introduction of Al2O3 residues from the sand paper used for

hand-grinding. Similarly, grit-blasting introduced a large amount of Al2O3 residues

and/or SiO2 residues (Figure 3.8) although it was expected to be more effective in

removing the weak oxide layer. The amount of grit residues was found to be much

more than that introduced by the hand-grinding process (Figure 3.8), as a high

pressure was used in the grit-blasting process which pressed more grit deeply into

the surface. It can also be noted that when finer grits were used, a larger amount of

grit residues was introduced (Table 3.4). The obvious higher silicon percentage for

method (4) (i.e. grit-blasting with 0.25 mm grit) was due to the use of brown

alumina grit instead of white alumina grit which was used in the other two grit-

blasting methods; the former had a larger percentage of SiO2

(Table3.2).

3.6.1.3 Surface energy

The measured contact angles and the calculated surface energies for different

specimens are shown in Table 3.5. A good correlation between results of specimens

of the same surface type is observed except for hand-ground specimens. Of the

hand-ground specimens, specimen III had polar and dispersive energy components

55

which are significantly different from those of the other two specimens. It should be

noted that certain localized chemical or topographical hysteresis (i.e. chemical

concentrations resulting from embedded grit particles and topographical

concentrations such as peaks and ridges) can affect surface energy readings, so the

different surface energy readings for this particular specimen may have occurred

due to localized chemical or topographical hysteresis. Figure 3.9 shows the average

surface energy calculated from the measured contact angles.

The surface energies discussed here are all energies per unit area. However in the

case of a rough surface, it is more appropriate to use the true surface area instead of

the nominal surface area. If the surface is not very rough, this may be done by using

the simple Wenzel roughness factor (Wenzel 1936) defined below:

0

Ar A= (3.8)

where A is the true surface area and A0

is the nominal surface area. For simple real

surfaces, the roughness factor can be calculated from simple direct measurements.

The corrected area can then be used to evaluate the surface energy. However in the

present study, the corrected surface energy values were found to show a similar

trend as the nominal surface energy values (r for surfaces prepared using methods

(1)-(5) are 1.005, 1.01, 1.01, 1.03 and 1.037 respectively), so this correction was

found not to have any significant effect and was subsequently ignored. Harris and

Beevers (1999) reported similar observations.

The grit-blasted surfaces showed higher surface energy values than the hand-ground

or the solvent-cleaned surfaces. It can also be seen that with an increase in the grit

size, the total surface energy tends to reduce (Figure 3.9). When the contact angle

technique is used, surface energy is calculated as two parts; i.e. polar energy and

dispersive energy. Therefore the value of surface energy is reported in this thesis as

polar energy and dispersive energy components. However, as far as the adhesion

strength is concerned, only the total energy is relevant.

56

3.6.1.4 Inter-relationship between surface characteristics

It should be noted that it is very difficult, if not impossible to change the topography

of a surface without altering its chemical nature in some way (Harris and Beevers

1999; Packham 2003). The measured values of different specimens of the same

surface type except for hand-ground surfaces demonstrate good consistency

between surface energy, surface topography and surface chemical composition

values (Tables 3.3-5). This observation illustrates the ability of a particular surface

preparation method to reproduce a similar surface.

Harris and Beevers (1999) have shown that with an increase in the Ra value, the

surface energy value reduces; in other words, surfaces grit-blasted with larger grit

sizes show lower surface energy values. A similar trend can be observed from the

tests of the present study (Table 3.5 and Figure 3.9). A comparison of the fractal

dimension values of different surface types with their corresponding surface energy

values indicates a much better correlation than that for Ra

(Figures 3.10 and 11). An

increase in surface energy can be observed with an increase in the fractal dimension,

indicating the significant effect of surface profile on surface energy.

Past research has also shown that grit residues (SiO2 and Al2O3) contain much

higher polar energy components than dispersive energy components (Adams et al.

1997). This conclusion is seen to be also true for the grit-blasted surfaces of the

present study (Table 3.5), but the hand-ground surfaces which had a lower

percentage of grit residues showed a much higher polar energy component than the

0.5 mm grit-blasted surfaces. Therefore, a general conclusion on the effect of grit

residues on the polar energy component cannot be reached. It should be noted that

the bond strength depends mainly on the total energy, not the two individual

components. These components, however, have greater implications to bond

durability (Kinloch 1983; Harris and Beevers 1999). Harris and Beevers (1999)

observed that surfaces produced with a coarser grit had better durability properties.

Kinloch (1983) suggested that bonds with higher polar energy surfaces are more

sensitive to displacements caused by diffused water. Therefore, surfaces with a

higher polar surface energy (e.g. surfaces grit-blasted with a finer grit) are expected

57

to exhibit more rapid degradations (Harris and Beevers 1999). More research in this

area is needed for a better understanding.

Harris and Beevers (1999) discussed the question of whether changes in surface

energy observed in their experiments (the trends observed are similar to those of the

present work) were simply geometric effects of the surface or consequences of other

physico-chemical changes. Based on an investigation carried out using the adjusted

contact angles using Wenzel’s roughness factor and re-calculated surface energies

using adjusted contact angles, Harris and Beevers (1999) concluded that changes in

surface energy may be attributable to changes in surface chemical composition.

This observation was indeed supported by their results of chemical composition as

an increase in the polar energy component was found to correlate with an increase

in the amount of grit residues (such as Na, Mg, Al, Si). Unfortunately, Harris and

Beevers (1999) did not carry out any fractal analysis of the surface, which provides

a better representation of surface topography; as a result, any correlation between

surface energy and surface topography was unrevealed. In addition, although it can

be generally concluded that an increase in the amount of grit residues leads to an

increase in polar energy, the quantitative effect of the grit residues on surface

energy is difficult to evaluate. Therefore, the effect of surface topography on

surface energy is uncertain but cannot be ruled out. Based on the above discussions,

it is reasonable to conclude the three surface characteristics are inter-related and all

of them have a significant effect on adhesion strength.

3.6.2 Adhesion Strength

Table 3.6 presents the ultimate loads of all butt-joint specimens and Table 3.7 gives

their corresponding failure modes. The failed specimens are shown in Figure 3.12.

The results of the single-lap shear specimens are summarized in Table 3.8 and the

corresponding failure modes are given in Table 3.9. The failed single-lap shear

specimens are shown in Figure 3.13. It is clear that pure adhesion failure occurred

in most solvent-cleaned specimens, but such failure can be avoided if the steel

surface is grit-blasted prior to bonding. The ultimate loads of hand-ground

58

specimens are generally higher than those of corresponding solvent-cleaned

specimens, but are lower than those of the corresponding grit-blasted specimens.

Almost all hand-ground specimens and some grit-blasted specimens suffered a

combined adhesion and cohesion failure. The ultimate load of this combined failure

mode is expected to depend on both the adhesion strength between steel and

adhesive and the cohesion strength of the adhesive. All grit-blasted specimens of

the single-lap shear test series with Sika 330 or Araldite 2015 as the bonding

adhesive failed in the combined failure mode and the average ultimate load from

three nominally identical specimens was the smallest when the largest grit (i.e. 0.5

mm) was used. The use of the 0.25 mm and 0.125 mm grits, however, led to similar

ultimate loads. This observation indicates the importance of using sufficiently fine

grits in grit-blasting.

The nature of crack propagation (i.e. whether a smooth crack surface or a rough

crack surface requiring changes of the angle of crack front and thus more energy)

and the relative dominance of adhesion failure versus cohesion failure affect the

bond strength. The variations in bond strength among different specimens with the

same failure mode are attributed to these factors. However as no measurements

were taken to quantify the effects of these parameters, a clear quantitative analysis

of these variations cannot be undertaken.

Examined together with Figures 3.7 and 3.9, Tables 3.6 and 3.8 reveal that the

adhesion strength generally increases with the fractal dimension and the surface

energy until the two reach certain values (1.47 for the fractal dimension and 54.54

mJ/m2 for the surface energy in the present study) (also represented in Figures 3.14-

3.17). This is easy to understand as an increase in the fractal dimension leads to

stronger mechanical bonding while an increase in the surface energy generally

enhances the wettability of the surface which in turn enhances bonding. However

some researchers (Tamai and Aratani 1972; Hitchcock et al. 1981) argued that an

overly rough surface (i.e. an overly high fractal dimension) may also have negative

effects on bonding capability as it may restrict the spreading of the adhesive over

the surface. This explains the similar ultimate loads of grit-blasted specimens using

the 0.125 mm grit and the 0.25 mm grit, which may be the result of the two

59

counteracting effects of an increased fractal dimension. Therefore, based on the

above observations/arguments and the results of the present study, it is

recommended that in practical applications, surface preparation should aim to

achieve a surface topography similar to that achieved by the 0.25mm or 0.125mm

grit (i.e. 1.49 1.47fD≥ ≥ ). For the two adhesives of Sika 30 and Araldite 420, the

grit-blasted surfaces failed in the cohesion failure mode and the joint strength

cannot be explained by referring to the adhesion strength. Nevertheless, as for Sika

30 and Araldite 420 adhesives, adhesion strength is greater than the cohesion

strength, it can be concluded that if the surface topography is defined by

1.49 1.47fD≥ ≥ (provided the surface energy and the chemical composition are

similar), adhesion failure can be avoided and the recommendation of

1.49 1.47fD≥ ≥ is still valid.

To form a successful bonded joint, the prerequisite is that the adhesive must be in

intimate contact with the adherend surface. This requires first that the adhesive wets

the surface. To ensure wetting, the adherend surface must have a higher surface

energy than the adhesive. In other words, a low contact angle, meaning good

wettability, is a necessary but not sufficient condition for strong bonding. It has

been shown that if excellent wettability can be achieved, a weak Van der Waals

type low energy bond can be developed (Chawla 1998).

The measured surface energy values (Table 3.5) of different specimens of the same

surface type except for hand-ground surfaces are found to be consistent.

Nevertheless, for hand-ground surfaces, roughness and surface energy readings do

not always correlate well with each other. The tensile butt-joint tests showed that

the surface energy values of the grit-blasted surfaces were high enough to achieve

cohesion failure. However, a comparison of results of single-shear lap tests for Sika

330 with those for Araldite 2015 indicates that at a surface energy value above

about 50 mJ/m2, the adhesion strength has reached a plateau (Figures 3.16-17). The

breakage of two attached surfaces requires the surface energies of the two surfaces

to be provided through external actions. Therefore, the adhesion strength is

expected to increase with the surface energy of the adherend (Levine et al. 1964).

However, it was also shown that overly rough surfaces (i.e. with an overly high

60

fractal dimension) can have negative effects on adhesion strength (Tamai and

Aratani 1972; Hitchcock et al. 1981). Therefore, even though the surface energy

increases with the fractal dimension, overly rough surfaces may not result in a

higher adhesion strength.

It should also be noted that some previous studies (e.g. Adams et al. 1997) have

shown that the chemical composition of a surface can affect the adhesion strength,

but among the cases examined in the present study, this effect is not clearly seen.

Further studies are needed if the chemical composition of a surface is significantly

different from those examined in this study.

The SEM/EDX results of the test specimens show clearly that grit-blasting

introduces grit residues onto the surface, and the amount of grit residues introduced

tends to decrease with the grit size. However no significant effect of grit residues on

the adhesion strength has been observed. As the amount and nature of grit residues

depend on the type of grit used, it is important to select a grit type which is

chemically compatible with the adhesive to be used. Usually alumina grit is

chemically compatible with adhesives commonly used to bond FRP systems to steel

structures for strengthening purposes.

Tables 3.6 and 3.8 also show that the ultimate loads for different adhesives are quite

different, even for the same surface preparation method. In particular, Table 3.6

shows that Araldite 420 led to a much larger adhesion strength than the other three

adhesives, indicating the excellent bonding capability of this adhesive. The

differences in adhesion strength among the four adhesives are believed to depend

significantly on their different chemical compositions among other factors; more in-

depth investigations into this particular aspect are beyond the scope of this thesis.

3.7 CONCLUSIONS

This chapter has presented a systematic experimental study aimed at clarifying the

effects of steel surface preparation methods and adhesive properties on the adhesion

strength. Five surface preparation methods and four commonly available adhesives

were examined in this study, using two types of tests, namely, tensile butt-joint tests

61

and single-lap shear tests. The test results have shown that the grit-blasting method

resulted in significantly higher adhesion strengths over the other two methods (i.e.

solvent-cleaning as well as hand-grinding after solvent-cleaning). With the

adhesives used in the present study, it has been demonstrated that adhesion failure

can be avoided if the steel surface is grit-blasted prior to bonding.

Grit-blasting introduces grit residues onto the steel surface. Hence, when selecting a

grit type, care should be taken to ensure its chemical compatibility with the

adhesive to be used. Alumina grit which is compatible with adhesives commonly

used in the CFRP strengthening of steel structures is recommended. The grit size

has been shown to have no significant effect on the adhesion strength for the

selected adhesives. 0.25 mm angular alumina grit is recommended based on the

present experimental results.

Based on the values obtained for surface characteristics in the present study, the

following procedure is proposed for the assessment of a grit-blasted steel surface for

adhesive bonding:

• The surface energy of the steel surface should be measured using a video

contact angle measurement device and its value should exceed 50 mJ/m2

• The profile of a grit-blasted surface should be measured using a surface

profilometer and its surface topography should be characterized using the

fractal dimension. The same methods as described in this chapter may be

used in making these measurements, in which case the fractal dimension D

to

ensure that adhesive bonding is maximized;

f

1.49 1.47fD≥ ≥

should lie within the range of .

It has been revealed that a proper grit-blasting procedure using the same grit type

and size leads to similar post-treatment adherend surfaces. Measurement of the

chemical composition of a treated surface can be difficult, but such measurement

may not be necessary as the same chemical composition can be assumed for

surfaces grit-blasted using the same type and size of grit.

62

REFERENCES Adams, R.D., Comyn, J. and Wake, W.C. (1997). Structural Adhesive Joints in

Engineering, Chapman and Hall, London, UK.

Amada, S. and Satoh, A. (2000). "Fractal analysis of surfaces roughened by grit

blasting", Journal of Adhesion Science and Technology, 14(1), 27-41.

ASTM C633-2001 (2001). Standard Test Method for Adhesion or Cohesion

Strength of Thermal Spray Coatings.

ASTM D3165-2000 (2000). Standard Test Method for Strength Properties of

Adhesives in Shear by Tension Loading of Single-Lap-Joint Laminated

Assemblies.

Baldan, A. (2004). "Adhesively-bonded joints and repairs in metallic alloys,

polymers and composite materials: Adhesives, adhesion theories and surface

pretreatment", Journal of Materials Science, 39(1), 1-49.

Cadei, J.M.C., Stratford, T.J., Hollaway, L.C. and Duckett, W.G. (2004).

Strengthening Metallic Structures Using Externally Bonded Fibre-

Reinforced Polymers, C595, CIRIA, London.

Chawla, K.K. (1998). Composite Materials:Science and Engineering, Springer.

Clint, J.H. and Wicks, A.C. (2001). "Adhesion under water: surface energy

considerations", International Journal of Adhesion and Adhesives, 21(4),

267-273.


analytical investigation of steel beams rehabilitated using GFRP sheets",

Steel & Composite Structures, 3(6), 421-438.

Flinn, R. A. and Trojan, P.K. (1995). Engineering Materials and Their Applications,

John Wiley and Sons.

Gent, A.N. and Lai, S.M. (1995). "Adhesion and autohesion of rubber compounds-

Effect of surface-roughness", Rubber Chemistry and Technology, 68(1), 13-

25.

Gent, A.N. and Lin, C.W. (1990). "Model studies of the effect of surface-roughness

and mechanical interlocking on adhesion", Journal of Adhesion, 32(2-3),

113-125.

Harris, A.F. and Beevers, A. (1999). "The effects of grit-blasting on surface

properties for adhesion", International Journal of Adhesion and Adhesives,

19(6), 445-452.

63

Hitchcock, S.J., Carroll, N.T. and Nicholas, M.G. (1981). "Some effects of substrate

roughness on wettability", Journal of Materials Science, 16(3), 714-732.

Hollaway, L.C. and Cadei, J. (2002). "Progress in the technique of upgrading

metallic structures with advanced polymer composites", Progress in

Structural Engineering and Materials, 4(2), 131 - 148.




Kinloch, A.J. (1983). Durability of Structural Adhesives, Applied Science, London,

UK.

Lavaste, V., Watts, J.F., Chehimi, M.M. and Lowe, C. (2000). "Surface

characterisation of components used in coil coating primers", International

Journal of Adhesion and Adhesives, 20(1), 1-10.

Levine, M., Ilkka, G. and Weiss, P. (1964). "Relation of critical surface tension of

polymers to adhesion", Journal of Polymer Science Part B-Polymer Letters,

2(9Pb), 915-919.

Lu, S.Z. and Hellawell, A. (1995). "Using fractal analysis to describe irregular

microstructures", JOM-Journal of the Minerals, Metals & Materials Society,

47(12), 14-17.

Mays, G.C. and Hutchinson, A.R. (1992). Adhesives in Civil Engineering,

Cambridge University Press, Cambridge.

Mecholsky, J.J., Passoja, D.E. and Feinbergringel, K.S. (1989). "Quantitative-

analysis of brittle-fracture surfaces using fractal geometry", Journal of the

American Ceramic Society, 72(1), 60-65.

Molitor, P., Barron, V. and Young, T. (2001). "Surface treatment of titanium for

adhesive bonding to polymer composites: a review", International Journal

of Adhesion and Adhesives, 21(2), 129-136.

Packham, D.E. (2003). "Surface energy, surface topography and adhesion",


Packham, D.E. (2005). Hand Book of Adhesion, John Wiley and Sons, London, UK.

Parker, B.M. (1994). "Adhesive bonding of fiber-reinforced composites",


64

Rance, D.G. (1982). "Thermodynamics of weting: From its molecular basis to

technological application", Surface Analysis and Pretreatment of Plastics

and Metals, D. M. Brewis, ed., Applied Science Publishers, London.




Schnerch, D., Dawood, M., Rizkalla, S., Sumner, E. and Stanford, K. (2006). "Bond

behavior of CFRP strengthened steel structures", Advances in Structural


Shahid, M. and Hashim, S. A. (2002). "Effect of surface roughness on the strength

of cleavage joints", International Journal of Adhesion and Adhesives, 22(3),

235-244.

Sykes, J.M. (1982). Surface Analysis and Pretreatment of Plastics and Metals,

Applied Science Publishers Ltd, Essex, England.

Tamai, Y. and Aratani, K. (1972). "Experimental study of relation between contact

angle and surface-roughness", Journal of Physical Chemistry, 76(22), 3267-

3271.

Wenzel, R.N. (1936). "Resistance of solid surfaces to wetting by water", Industrial

and Engineering Chemistry, 28, 988-994.

65

Table 3.1 Material properties of adhesives

Adhesive Modulus of elasticity, Ea

Ultimate stress, σ (MPa)

max Ultimate strain, ε(MPa)

FYFE-Tyfo

u

3975 40.7 0.0111 Sika 30 11250 22.3 0.0030 Sika 330 4820 31.3 0.0075

Araldite 2015 1750 14.7 0.0151 Araldite 420 1828 21.5 0.0289 Table 3.2 Grit composition as supplied by the manufacturer

Description Composition by weight (%)

Al2O SiO3 Fe2 2O TiO3 CaO 2 MgO Na2 KO 2Brown alumina

O 95.20 1.10 0.20 3.10 0.05 0.35 0.01 0.00

White alumina 99.50 0.10 0.05 0.00 0.02 0.00 0.32 0.01 Table 3.3 Roughness of different surface types

Parameter Specimen

Surface type

Solvent-cleaned

Hand-ground

Grit-blasted 0.125mm

grit 0.25mm

grit 0.5mm

grit

RI

a 1.316 2.872 1.997 2.155 2.654

II 1.310 2.766 1.848 2.252 2.570 III 1.409 5.428 2.073 1.944 2.622

RI

q 1.658 3.648 2.538 2.800 3.319

II 1.555 3.697 2.381 2.758 3.243 III 1.783 6.549 2.572 2.638 3.254

DI

f 1.281 1.328 1.482 1.459 1.419

II 1.299 1.315 1.504 1.474 1.413 III 1.249 1.289 1.491 1.469 1.423

66

Table 3.4 Chemical compositions of different surface types

Surface type Specimen Chemical components, Atomic (%) C O Al Si Fe

Solvent-cleaned I 42.82 7.82 0.08 0.59 48.68 II 35.90 8.69 0.00 0.58 54.83 III 38.55 8.14 0.00 0.57 52.74

Hand-ground I 15.82 5.63 1.55 0.57 76.42 II 16.60 5.88 1.57 0.54 75.41 III 16.11 5.77 1.57 0.56 75.99

Grit-blasted- 0.125mm grit

I 8.27 30.57 9.88 3.43 47.85 II 9.56 27.50 8.53 3.07 51.34 III 6.88 30.08 9.36 3.88 49.81


I 8.28 30.39 0.00 11.56 49.77 II 8.94 28.74 0.00 10.96 51.36 III 8.91 26.62 0.11 9.89 54.47


I 7.80 23.38 5.19 4.51 59.12 II 8.36 23.40 5.21 4.73 58.30 III 7.80 23.38 5.19 4.51 59.12

Table 3.5 Contact angles and surface energies of different specimens

Surface type Specimen

Contact angle Polar energy,

γsp (mJ/m2

Dispersive energy,

γ)

sD (mJ/m2

Total energy,

γ)

s (mJ/m2

Average total

energy, γ) s

(mJ/m2

De-ionized water

)

Formamide

Solvent-cleaned

I 74.0 49.3 7.45 33.29 40.74 39.52 II 69.5 51.3 12.81 25.53 38.33

III 69.5 49.5 11.88 27.60 39.48

Hand-ground

I 60.5 52.0 24.70 16.27 40.97 43.67 II 54.0 46.5 29.78 16.25 46.03

III 76.5 63.5 7.45 36.55 44.00 Grit-blasted-

0.125mm grit

I 38.0 11.0 32.46 27.31 59.76 59.49 II 39.0 10.5 31.20 28.20 59.41

III 39.5 9.5 30.44 28.87 59.31


I 47.0 23.8 25.74 28.65 54.39 54.55 II 47.5 18.8 23.39 32.09 55.49

III 50.0 23.3 21.96 31.80 53.76


I 62.8 31.5 11.04 39.49 50.53 50.27 II 61.0 31.8 12.87 37.07 49.94

III 60.0 30.8 13.54 36.80 50.34

67

Table 3.6 Ultimate loads of tensile butt-joint specimens (kN)

Adhesive Specimen Solvent-cleaned

Hand-ground


grit 0.25mm

grit 0.5mm

grit

Sika 30 I 0.9 9.3 12.1 11.3 12.0 II 1.5 10.1 12.5 11.4 11.2 III 2.1 9.8 12.3 12.3 14.3

Sika 330 I 2.6 11.2 14.7 13.3 14.0 II 3.4 11.4 15.8 12.8 14.6 III 3.1 10.7 17.8 12.4 16.0

Araldite 2015 I 3.9 9.6 12.1 10.8 12.7 II 3.5 12.4 12.6 10.9 13.2 III 3.2 11.1 11.6 12.9 12.6

Araldite 420 I 9.6 12.2 21.0 17.4 18.4 II 11.6 16.0 21.7 17.9 19.7 III 9.9 12.2 21.6 16.7 17.9

Table 3.7 Failure modes of tensile butt-joint specimens


Hand-ground


grit 0.25mm

grit 0.5mm

grit

Sika 30 I A A+C C C C II A A+C C C C III A A+C C C C

Sika 330 I A A+C C C C II A A+C C C C III A A+C C C C

Araldite 2015 I A A+C C A+C C II A A+C C A+C C III A A+C C C C

Araldite 420 I A A+C C C C II A A+C C C C III A A C C C

68

Table 3.8 Ultimate loads of single-lap shear specimens (kN)


Hand-ground


grit 0.25mm

grit 0.5mm

grit

Sika 30 I 2.91 3.31 4.43 4.97 4.08 II 2.81 3.87 4.44 4.32 4.43 III 2.38 3.39 4.81 4.76 5.08

Sika 330 I 3.66 4.72 5.74 6.09 5.48 II 3.88 4.73 5.60 5.46 5.30 III 3.45 4.93 5.70 5.47 5.79

Araldite 2015

I 2.86 2.73 4.09 4.37 3.54 II 1.88 2.48 3.82 4.04 3.77 III 2.85 2.89 4.13 4.04 3.50

Araldite 420 I 3.67 5.23 5.62 5.70 5.42 II 3.04 5.30 6.65 5.15 5.40 III 3.56 5.11 5.39 6.01 5.45

Table 3.9 Failure modes of single-lap shear specimens


Hand-ground


grit 0.25mm

grit 0.5mm

grit

Sika 30 I A+C A+C C C C II A A+C C C C III A A+C C C C

Sika 330 I A A+C A+C A+C A+C II A A+C A+C A+C A+C III A A+C A+C A+C A+C

Araldite 2015

I A+C A+C A+C A+C A+C II A A+C A+C A+C A+C III A+C A+C A+C A+C A+C

Araldite 420 I A A+C C C A+C II A+C A+C C C C III A A+C C C A+C

69

Figure 3.1 Surface energy components acting on a liquid droplet

Figure 3.2 Box counting method for evaluating the fractal dimension

Young’s equation

γSV = γSL + γLV cos θ γSV

Vapour γLV

γSL

Liquid

Solid

θ

70

Figure 3.3 Stress-strain curves of adhesives

Figure 3.4 Tensile butt-joint specimen: (a) Dimensions; and (b) Test set-up

0

5

10

15

20

25

30

35

40

45

0 0.005 0.01 0.015 0.02 0.025Strain

Stre

ss (M

Pa)

Sika 30

Sika 330

FYFE-Tyfo

Araldite 420

Araldite 2015

12.5

mm

Steel rod

Steel rod

adhesive

1mm

52

.5m

m 10

5mm

25mm dia (a) (b)

71

Figure 3.5 Single-lap shear specimen: (a) Plan; (b) Elevation; and (c) Test set-up

25mm

(a)

2.5m

m

12.5

mm

2mm

65m

m

80m

m

5mm

2mm

(b) (c)

72

(a) Solvent-cleaned surface

(b) Hand-ground surface

(c) Grit-blasted surface-0.125mm grit

(d) Grit-blasted surface-0.25mm grit

(e) Grit-blasted surface-0.5mm grit

Figure 3.6 Surface images from SEM/EDX analysis for different surface types

73

Figure 3.7 Roughness parameter and fractal dimension for different surface types

Figure 3.8 Chemical compositions of different surface types

Solvent-cleaned

Hand-ground

Grit-blasted-

0.125mmgrit

Grit-blasted-0.25mm

grit

Grit-blasted-0.5mm

grit

1.25

1.3

1.35

1.4

1.45

1.5

1.55

00.5

11.5

22.5

33.5

44.5

5

Frac

tal d

imen

sion

, D

f

Rou

ghne

ss,

Ra,

q(µ

m)

Surface type

Ra

Rq

Df

0

5

10

15

20

25

30

35

Solvent-cleaned

Hand-ground Grit-blasted 0.5mm grit

Grit-blasted 0.25mm grit


Atom

ic %

Surface type

Oxygen- OAluminium-AlSilican- Si

74

Figure 3.9 Surface energies of different surface types

Figure 3.10 Effect of average surface roughness on surface energy

Figure 3.11 Effect of surface topography on surface energy

0

10

20

30

40

50

60

70

Solvent-cleaned

Hand-ground Grit-blasted 0.5mm grit



Surfa

ce e

nerg

y (m

J/m

2 )

Surface type

Polar energy

Dispersive energy

0

10

20

30

40

50

60

70

1.34 1.97 2.12 2.62 3.69

Surfa

ce e

nerg

y (m

J/m

2 )

Average roughness, Ra (µm)

Polar energy

Dispersive energy

0

10

20

30

40

50

60

70

1.28 1.31 1.42 1.47 1.49

Surf

ace

ener

gy (m

J/m

2 )

Surface fractal dimension, Df

Polar energy

Dispersive energy

75

Solvent-cleaned Hand-ground Grit-blasted-

0.125mm Grit-blasted-


0.5mm (a) Sika 30




0.5mm (b) Sika 330




0.5mm (c) Araldite 2015




0.5mm (d) Araldite 420

Figure 3.12 Failed surfaces of tensile butt-joint test specimens

76




0.5mm (a) Sika 30




0.5mm (b) Sika 330




0.5mm (c) Araldite 2015




0.5mm (d) Araldite 420

Figure 3.13 Failed surfaces of single-lap shear test specimens

77

Figure 3.14 Effect of fractal dimension on tensile butt-joint strength

Figure 3.15 Effect of fractal dimension on single-lap shear joint strength

0

5

10

15

20

25

1.25 1.3 1.35 1.4 1.45 1.5 1.55

Aver

age

ultim

ate

load

(kN

)

Fractal dimension, Df

Sika 30Sika 330Araldite 2015Araldite 420

0

1

2

3

4

5

6

7

1.25 1.3 1.35 1.4 1.45 1.5 1.55

Aver

age

ultim

ate

load

(kN

)

Fractal dimension, Df


78

Figure 3.16 Effect of surface energy on tensile butt-joint strength

Figure 3.17 Effect of surface energy on single-lap shear joint strength

0

5

10

15

20

25

39.52 43.67 50.27 54.55 59.49

Surface energy, mJ/m2

Ave

rage

ulti

mat

e lo

ad (k

N)


0

1

2

3

4

5

6

7

39.52 43.67 50.27 54.55 59.49

Surface energy, mJ/m2

Ave

rage

ulti

mat

e lo

ad (k

N)


79

CHAPTER 4 VALIDITY OF SINGLE-SHEAR PULL-OFF TESTS FOR

SHEAR BOND BEHAVIOUR STUDIES

4.1 INTRODUCTION

In CFRP-strengthened steel structures, the bond behaviour between CFRP and steel is

of great importance in understanding and modelling debonding failures. Usually the

performance of a CFRP-to-steel bonded interface is much weaker under interfacial

peeling (or normal) stresses than under interfacial shear stresses, so the design of

CFRP-to-steel bonded interfaces should aim at stress transfer mainly through shear,

with the effect of peeling stresses minimised (Adams et al. 1997; Hart-Smith 1981).

Nevertheless, peeling stresses cannot be completely avoided in CFRP-to-steel bonded

joints.

In flexurally-strengthened steel beams, it has been shown that at the joint ends (or plate

ends) where the FRP plate is terminated, high peeling stresses exist and contribute to

premature debonding failure (Deng and Lee 2007). Simple closed-form analytical

solutions for these interfacial stresses have been developed based on the assumptions of

constant peeling and shear stresses across the adhesive layer thickness (Smith and Teng

2001; Stratford and Cadei 2006). These approximate analytical solutions are in

relatively simple closed-form expressions. However, the simplicity of these solutions

results in the prediction that the maximum shear stress occurs at the end of the adhesive

layer (i.e. at the plate end), which violates the stress free boundary condition there. In

addition, of the three possible interfacial stress components (in a 2D plane) [namely

shear stresses, peeling stresses, and longitudinal normal stresses (referred to as the

longitudinal stress hereafter for brevity)], only the peeling and the shear stresses are

considered in such solutions. The predicted interfacial shear and peeling stresses of

such analytical solutions are similar to those at the mid-thickness plane of the adhesive

layer from a rigorous finite element (FE) analysis using plane stress elements (Teng et

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al. 2002; Starford and Cadei 2006; Zhang and Teng 2010), but variations of these

stresses across the adhesive layer thickness or the zero shear stress condition at the end

of the adhesive layer cannot be captured by them.

Rigorous FE studies using plane stress elements have shown that interfacial stresses

vary across the adhesive layer thickness and become larger for locations closer to the

bi-material interfaces between the adhesive and the two adherends (Teng et al. 2002;

Zhang and Teng 2010). Higher-order stress analysis models have also been developed

(Rabinovitch and Frostig 2001a; Shen et al. 2001; Yang et al. 2004) and some have

included longitudinal stresses in the adhesive layer (Shen et al. 2001; Yang et al. 2004).

These higher-order models provide more rigorous interfacial stress solutions but lack

the simplicity associated with the simple analytical models (Smith and Teng 2001).

Differences in interfacial stresses predicted by the above-discussed analytical solutions

lie in the different assumptions employed. For example, Smith and Teng’s (2001)

solution assumes constant shear stresses and peeling stresses across the adhesive layer

thickness and neglects longitudinal stresses; Rabinovitch and Frostig’s (2001a) solution

assumes constant shear stresses and linearly-varying peeling stresses across the

thickness of the adhesive layer and neglects longitudinal stresses; and Yang et al.

(2004) assumes linearly varying longitudinal stresses across the thickness of the

adhesive layer. These assumptions affect the predicted interfacial stress distributions

and therefore the accuracy of these solutions is limited by the accuracy of the

assumptions made (Zhang and Teng 2010). The recent study by Zhang and Teng

(2010) has clearly illustrated the effects of these different assumptions on interfacial

stress predictions using FE models. It has been shown by Zhang and Teng (2010) that

all the above analytical solutions lie between the simple analytical solution based on

the assumptions of constant shear stresses across the adhesive layer thickness and

negligible peeling stresses and a full 2D FE model where all three components (i.e. the

beam, the adhesive layer and the plate) are represented using plane stress elements

(which is the most accurate FE model possible with a 2D treatment) (Zhang and Teng

2010). However, to the best knowledge of the authors, no rigorous experimental

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verification of such interfacial stress solutions has been made due to difficulties in

making reliable measurements of rapid stress variations in a tiny region.

In the numerical analysis of interfacial stresses at joint ends, some researchers

modelled a joint end as a square end (i.e. a sharp end with the end edge being

perpendicular to the interface). As a result, a severe stress singularity exists at the plate

end and the stresses, particularly their peak values, predicted by such analysis are

sensitive to mesh refinement and are thus non-objective. In real joints, the end shape is

unlikely to be square and a spew fillet generally exists. It has been shown that plate end

peeling and shear stresses reduce significantly with the existence of a spew fillet

(Rabinovitch and Frostig 2001b; Teng et al. 2002).

In the flexural strengthening of beams by bonding an FRP plate to its tension face, plate

end interfacial stresses become less critical when the plate end is located far away from

the high bending moment region. To avoid plate end debonding due to high peeling

stresses, it is advisable to use some forms of mechanical anchors near the plate end

and/or fine details such as reverse tapering of the plate end and providing a spew fillet

at the plate end (Schnerch et al. 2007). Another mode of debonding which can occur in

FRP-strengthened steel structures is intermediate debonding which occurs within the

bonded region away from the plate ends; this mode of debonding is governed by

interfacial shear stresses (Sallam et al. 2006). In FRP-strengthened steel structures,

intermediate debonding can occur due to steel yielding (Bocciarelli et al. 2007) or

defects such as corrosion or fatigue cracks. Therefore, it is evident that in order to

understand and design bonded interfaces, a good understanding of interfacial stresses in

bonded joints and how bonded joints perform under pure shear stresses as well as

combined shear and peeling stresses is needed. The stress state in an adhesively bonded

joint, especially in the high stress concentration zones, can be highly complicated.

Therefore, as a first step towards understanding the behaviour of bonded joints, it is

valuable and necessary to first understand the behaviour of bonded joints under pure

mode-I and mode-II loadings.

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Bond-slip models (Lu et al. 2005) are commonly used to model the interfacial shear

behaviour of FRP-to-concrete bonded joints. A bond-slip model treats interfacial

damage and fracture as a process of shear sliding between two surfaces resisted by

interfacial cohesive tractions which are functions of the sliding (mode II) displacement.

As a result, when such a bond-slip model (in mode II) is used to characterise interfacial

debonding, the bonded joint is assumed to be under pure shear loading. Thus in

obtaining shear bond-slip data, the selected test-set up should satisfy the assumption of

pure shear loading, implying that the interfacial behaviour is dominated by interfacial

shear stresses.

Different test methods for bonded joints have been used by different researchers (Zhao

and Zhang 2007). A detailed description of these test methods can be found in Zhao

and Zhang (2007) and is therefore not given here. To study the shear bond behaviour of

FRP-to-concrete bonded joints, the so-called near end supported single-shear pull-off

test is probably the most suitable (Yao et al. 2005) and was also used in the first ever

study on the full-range behaviour of FRP-to-steel bonded joints (Xia and Teng 2005).

Even in a single-shear pull-off test, significant peeling stresses exist at the loaded end

of the plate (Chen et al. 2001). These peeling stresses have raised some concern over

the validity of the single-shear pull-off test as a test method for obtaining shear bond-

slip data. Against this background, this chapter presents a detailed study aimed at

experimentally and numerically verifying the suitability of the single-shear pull-off test

for determining the shear bond-slip behaviour of the interface. The effects of element

size and the presence of a adhesive fillet on plate end stress concentrations in a linear

elastic FE model are also discussed.

4.2 EXPERIMENTAL PROGRAMME

4.2.1 Specimen Preparation and Test Set-up

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Only a single specimen was prepared and tested in the present study. A typical single-

shear pull-off test set-up is shown in Figure 4.1. The commercially available Aramis

(2006) optical measurement system was used to capture the deformations at the loaded

end. Details of this measurement system are given in the next paragraph. Due to the

limitations of the measurement system, it was necessary to have a large enough

measurement area. Therefore, to enable more accurate measurement of deformations

within the adhesive layer, a relatively large adhesive layer thickness of 5.1 mm was

used. The support system shown in Figure 4.2 was used to obtain a uniform adhesive

thickness layer throughout the bond length. To obtain a better measurement field, one

end of the bonded joint was made flush with one face of the steel block (Figure 4.1b).

In such a set-up, when the horizontal loading is applied on the CFRP plate, bending of

the plate can be expected. To restrain this bending action, two lateral supports were

provided, one near the loaded end and another at the far end as shown in Figure 4.3. A

Sika Carbodur normal-modulus CFRP plate of 1.2 mm in thickness and 25 mm in

width was used in the test. The Sika 30 adhesive was selected for bonding given its

high viscosity which is desirable for forming such a thick adhesive layer. The material

properties of the CFRP plate and the adhesive are given in Table 4.1. The bonding

surface of the CFRP plate was lightly abraded with a sand paper and then cleaned with

Acetone prior to bonding. The steel surface was first cleaned with Acetone and then

grit-blasted and vacuumed-cleaned prior to bonding to ensure proper adhesion. Special

care was taken to remove any excess adhesive from the joint and to make the loaded

end of the adhesive layer as sharp as possible.

4.2.2 The Aramis Measurement System

Aramis, a commercially available non-contact optical 3D deformation measurement

system, was used to record the deformation of the joint during the experiment. By

recording a series of images through a set of digital cameras during the experiment and

then using the image correlation technique, Aramis calculates the relative deformations

to obtain deformation patterns relative to the unloaded state. A detailed description of

the Aramis measurement system can be found in its Users’ Manual (Aramis 2006) and

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is not discussed in detail here. Only some key points related to the measurement set-up

of the present experiment are discussed below.

In such an experiment, as failure is expected to occur within the adhesive layer in the

vicinity of the loaded end, detailed monitoring of this area is important. It is therefore

desirable to concentrate measurement points within this area. However, the Aramis

system available had a limitation of a minimum window size of 30 mm x 30 mm.

Consequently, this measurement field was selected, which resulted in approximately 25

measurement points in a row across the thickness of the adhesive layer, and

approximately 150 such rows along the longitudinal direction. To improve the

measurement quality, a high-contrast stochastic pattern (Figure 4.4) was sprayed on the

selected measurement field using an air brush. Furthermore, in such a small

measurement field, measurements are sensitive to temperature changes as well as light

changes. Hence, calibration was carried out immediately before starting the

experiment. The temperature was recorded during the experimental process to ensure

that no significant changes occurred. Shades were used to ensure that constant lighting

was provided to the specimen during calibration and during the loading process. The

Aramis software was used to process and analyse the recorded data. This software

allowed the user to calculate deformations in the measurement field as well as the

strains (Aramis 2006). Images were recorded at 1 kN intervals until 16 kN and then at

0.5 kN intervals until failure. The last image was recorded after the failure of the

specimen. A typical image recorded by Aramis of the present test specimen is shown in

Figure 4.4.

Strain gauges were also installed on the top surface of the CFRP plate at 20 mm

intervals (Figure 4.1b). Loading was applied using a hydraulic jack. Initially readings

were taken at 1 kN intervals. As the load reached 16kN (i.e. when the load-

displacement curve became non-linear), readings were taken at 0.5 kN intervals.

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4.3 RESULTS AND DISCUSSIONS

The failed specimen is shown in Figure 4.5. Failure initially involved loss of cohesion

and then changed into interlaminar failure of the CFRP plate at a small distance from

the loaded end, resulting in a brittle failure process. In the region where pure cohesion

failure occurred, a smooth crack surface (i.e. a knife-cut surface) parallel to the CFRP

plate was observed. Even in the region where combined cohesion and interlaminar

failure occurred, a relatively smooth crack surface was observed. At the loaded end, a

wedge of adhesive was observed and was detached from the CFRP plate (Figure 4.5). It

was unclear whether this wedge was initially attached to the CFRP plate and then

detached after complete failure as a result of the CFRP plate hammering onto the steel

block or was already detached prior to complete failure. A similar wedge was observed

by Xia and Teng (2005) in their single-shear pull-off tests on CFRP-to-steel bonded

joints. In their tests, it was reported that this wedge was attached to the CFRP plate.

The experimental load-displacement curve is shown in Figure 4.6. The displacement in

Figure 4.6 is the displacement of the loaded end which was calculated from the strain

gauge readings. Initially, the curve is linear. At around 15 kN (point A), the curve starts

to become non-linear and reaches its maximum load at 24.1kN (point B) before

forming a small plateau until the full detachment of the plate at point C. It can be noted

that at point A, a sudden jump in the displacement occurs. As the displacement was

calculated from strain gauge readings, it can be deduced that at this load level, a sudden

jump in the strain readings also occurred. Such a jump in strain readings is an

indication of the initiation of a debonding crack within the adhesive layer. It can also be

deduced that as the crack initiated, which led to a sudden reduction in the bond

resistance provided to the CFRP plate near the loaded end and thus a sudden increase in

the strains in the CFRP plate.

The strain distributions along the top surface of the CFRP plate are shown in Figure 4.7

for different load levels. At the load level of 15kN, a noticeable reduction in the strain

gradient between the first two strain gauge readings can be observed. At the load level

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of 21 kN, the strain gradient between the first two strain gauge readings is seen be

small. At the load level of 24.1 kN with a displacement of 0. 15 mm, the strain reading

of the first gauge becomes smaller than that of the second gauge. The joint then

continued to deform with the load remaining the same and when the displacement

reached 0.165 mm, the strain gauges readings in the third and fourth gauges further

increased and failure was imminent.

The strain gradient represents the average interfacial shear stress within the length

between two strain gauges (Pham and Al-Mahaidi 2007). A reduction of the strain

gradient represents softening of the adhesive layer and a zero strain gradient means that

no interfacial shear stress is transferred and the bondline is completely damaged.

However, these strain measurements can only reflect the accumulated effect of

interfacial shear stresses and any variation of shear stresses across the adhesive layer

thickness or the existence of peeling stresses are not reflected by them. Therefore, for a

more accurate understanding of the damage initiation and propagation process, the

strains within the adhesive layer need to be analyzed. Nevertheless, at the load level of

24.1 kN, the increases in the strain gauge readings along the length of the CFRP plate,

coupled with the strain readings of first two strain gauges being unchanged (Figure

4.7), is a clear indication of damage propagation along the bond length.

The Aramis readings of the major principal strain for load levels ranging from 14 kN to

24.1 kN are shown in Figure 4.8, illustrating the gradual development of cracks. It is

quite obvious from these readings that cracks initiated long before the load level of

24.1 kN and gradually propagated near the CFRP/adhesive interface, resulting in the

eventual full detachment of the CFRP plate. At about 14kN, the major principal strain

readings near the CFRP/adhesive interface are seen to be higher than those within the

adhesive layer but away from the CFRP/adhesive interface (Figure 4.8a). As the load

increased further, the strains near the CFRP/adhesive interface increased significantly

and at about 16kN, cracks already started to appear near the CFRP/adhesive interface

(Figure 4.8c). With further increases in the applied load, these cracks grew into deep

diagonal cracks (Figures 4.8c-f), and more and more cracks near the CFRP/adhesive

87

interface started to appear further away from the loaded end. At the load level of 22kN,

the full formation of a deep crack parallel to the CFRP/adhesive interface and further

propagation of the deep diagonal cracks near the loaded end were observed (Figure

4.8k). As the load continued to increase, further propagation of the deep parallel crack

and the diagonal cracks were observed. As the deep parallel crack propagated away

from the plate end, the number of diagonal cracks away from the plate end became

smaller (Figure 4.8k). The deep diagonal cracks propagated towards the loaded end. At

the load level of 24.1kN, complete debonding failure occurred (Figure 4.8l). From the

final crack pattern, it can be seen that towards the loaded end, the crack path followed

the deep diagonal cracks and away from the loaded end, the crack path was smooth and

followed the deep parallel crack.

In order to identify the crack initiation location and the corresponding load level,

several points inside the adhesive layer were selected for detailed examination. In the

coordinate system shown in Figure 4.9, the x axis goes to the right along the

CFRP/adhesive bi-material interface from the edge line of the adhesive layer while the

y axis goes upwards from the CFRP/adhesive bi-material interface. Careful inspections

of major principal strain patterns at load levels from 12 kN to 15kN showed that point

D with x = 7.5 mm and y = -0.25 mm had the highest initial stress concentration and is

on the crack surface (Figure 4.9). Therefore, several points, namely point D (7.5 mm, -

0.25 mm), point E (6 mm, -0.25 mm), point F (4.5 mm, -0.25 mm), Point G (1.5 mm, -

0.25 mm) and point H (0.2 mm, -0.25 mm) were selected and their shear and peeling

strains are shown against the applied load in Figure 4.10. It can be observed that at

point D, the shear and peeling strains became non-linear with the applied load when the

load reached 15kN. After this load level, the strain increase at this point became much

faster. These results agree well with the initiation of nonlinearity observed in the load-

displacement curve (point A at 15 kN). It is thus evident that failure occurred at point

D. To highlight this observation, the strain distributions of section A-A (at y = -0.25

mm) at 15 kN and 24 kN are given in Figure 4.11. It is obvious that at point D, as the

load exceeded 15kN, the peeling, shear and longitudinal stresses all became much

higher than values at other points of this plane. As point D had the highest strains at

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15kN and these strains started to become non-linear with the applied load at 15kN, it

can be concluded that point D was the crack initiation point and cracking started at the

load level of 15kN.

4.4 FINITE ELEMENT MODEL The strain values obtained from the Aramis measurement system include a great deal of

noise. It is therefore difficult to use these strain values to carry out an accurate

assessment of the stress state in the adhesive layer and to identify the critical stress

components. Consequently, a FE model was developed to obtain accurate stress data

for the adhesive layer at the initiation of damage.

The single-shear pull-off test was modelled using ABAQUS (ABAQUS 2004) to

predict interfacial stresses. A 2D model was adopted. 2D plane stress elements were

used to model the CFRP plate, the adhesive and the steel substrate (Teng et al. 2002;

Zhang and Teng 2010). Perfect bond was assumed at the steel/adhesive and

FRP/adhesive bi-material interfaces. All three materials were assumed to be linear

elastic, with the values of elastic modulus being those given in Table 4.1 and Poisson’s

ratio being 0.3. The actual dimensions of the specimen were used in the FE model, but

for the mesh convergence study a thinner adhesive layer of 1 mm was used. The mesh

convergence study presented below was originally carried out to find the interfacial

stresses in a single-shear pull-off test for the design of the experiment discussed earlier

in the paper. The specimen used in the mesh convergence study differs from the actual

test specimen only in that the adhesive layer thickness was 1 mm, a value which is

typical of real situations (e.g. Schnerch et al. 2007). The results of this mesh

convergence study are however applicable, at least qualitatively, to any adhesive layer

thickness. The tensile loading of the CFRP plate was effected by imposing axial

displacements. The restraints imposed on the steel substrate are as shown in Figure

4.12a, which represents closely the actual support conditions of the present experiment.

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4.4.1 Mesh Sensitivity

Initially, the end of the adhesive layer was modelled as a square end (Figure 4.12b). As

a result, numerical singularity points exists at the joint end at both the FRP/adhesive

(PA) interface and the steel/adhesive (SA) interface; the strength of singularity of the

PA interface is greater than that of the SA interface due to the geometry (Teng et al.

2002). The first part of the FE investigation presented herein is focussed on the mesh

sensitivity of the interfacial stresses in the vicinity of the loaded plate end. As very

small element sizes were expected to be explored, only a 1mm thick adhesive layer was

considered to reduce the computational effort of the mesh convergence study. All the

other dimensions were kept unchanged during the process. The element sizes examined

are 0.25mm, 0.1mm, 0.05mm, 0.01mm and 0.0025mm, resulting in 4, 10, 20, 100 and

400 elements respectively across the thickness of the adhesive layer.

The results of the mesh convergence study are shown in Figures 4.13-15 for the PA

interface, the SA interface, and the mid-adhesive plane (MA plane) respectively. The

peeling stress at the PA interface is seen to be tensile at the very end of the joint and

becomes compressive within a small distance (0.2mm) and then reduces to small values

at around 2 mm from the loaded end (Figure 4.13a). For both the SA interface and the

MA plane, the peeling stress is compressive near the loaded end (Figures 4.14a and

4.15a). At around 2.5mm from the loaded end, the peeling stresses becomes tensile, but

the magnitude is now negligible. For both the PA and SA interfaces, the peeling stress

and the shear stress grow exponentially with the reducing size of elements (or the

increasing number of elements) (Figures 4.13 and 4.14). However, for the MA plane,

the peeling stress does not change as the element size is reduced to very small values.

The shear stress of the MA plane is non-zero for a coarser mesh (element sizes of

0.25mm and 0.1mm) but becomes almost zero for an element size less than 0.05mm

(Figure 4.15d). For all three planes, the dependency of both the shear and the peeling

stresses on the element size is limited to a small region of around 1mm from the loaded

end (Figures 4.13a, 4.14a and 4.15a).

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The stress variations through the thickness of the adhesive layer at the loaded end are

shown in Figure 4.16 for the shear stress and in Figure 4.17 for the peeling stress. It

should be noted that these values were from the integration points, so the shear stress

values at the end are not exactly zero. It can be seen from Figure 4.15 that the shear

stress is almost zero except near the PA interface and the SA interface for element sizes

less than 0.05mm. Large values of the shear stress are seen near the PA interface and

the SA interface owing to stress singularity. As the element size reduces, the region

where non-zero shear stresses exist also reduces. The peeling stress tends to vary

almost linearly through the adhesive layer thickness except near the PA and the SA

interfaces (Figure 4.17). Near the PA and the SA interfaces, the peeling stress grows

exponentially with a reducing element size and the peeling stress at the PA interface

grows much faster than that at the SA interface, showing the higher strength of

singularity at the PA interface.

The above discussions indicate that it is impossible to achieve converged results for

interfacial stresses near the plate end due to the presence of stress singularity points.

Therefore, the values obtained from such an analysis for plate end interfacial stresses in

the close vicinity of the plate end (e.g. within the 0.1mm region from the plate end)

may not be reliable. However, except for this small region, the predicted interfacial

stresses are converged results and are accurate. As an element size of 0.05mm (20

elements across the adhesive layer thickness) leads to converged results except for the

very end of the adhesive joint, this element size was adopted in subsequent FE

analyses.

4.4.2 FE Investigation of Damage Initiation

For the numerical results presented hereafter, the adhesive layer thickness of the FE

model was modified to 5.1mm to simulate the experimental specimen described earlier

in the chapter. A close examination of the experimental specimen indicated that despite

all the efforts to make the joint edge as square as possible, a small adhesive fillet still

existed (Figure 4.18a). Previous studies of bonded joints (Rabinovitch and Frostig

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2001b; Teng et al. 2002) have shown that the existence of an adhesive fillet at the plate

end can significantly reduce the interfacial stresses near the plate end. With the

existence of the small adhesive spew fillet as shown in Figure 4.18a, the strength of

singularity at the plate end of the PA interface is significantly reduced. Therefore the

peeling stress at the PA interface can also be significantly reduced (Rabinovitch and

Frostig 2001b; Teng et al. 2002). Consequently, to accurately simulate the experimental

specimen, the FE model was also modified to include this spew fillet (Figure 4.18b).

The axial displacements of the top surface of the CFRP plate obtained from the FE

model at different load levels are compared with the test data obtained from Aramis in

Figure 4.19a, while Figure 4.19b shows a comparison for the vertical displacements of

the top surface of the CFRP plate. These comparisons demonstrate a reasonable

agreement between results from the two approaches, thus confirming the suitability of

the FE model for the bonded joint in the linear elastic range. Comparisons of the

longitudinal strain values obtained from the strain gauges, the Aramis system and the

FE model for the top surface of the CFRP plate are shown in Figure 4.20. It can be seen

that the strains from the three different sources are in very close agreement, further

confirming the accuracy of the FE model in the linear elastic range.

The interfacial stresses at the load level of 15kN on the A-A plane (Figure 4.9) are

shown in Figure 4.21. The crack initiation point (point D) which was identified from

the experimental measurements lies close to the horizontal location where the

interfacial shear stress is at its maximum, and at this point the interfacial peeling stress

is negligible. The major principal stress is also seen to be the highest close to the crack

initiation point (Figure 4.21). In addition, it can be seen that the major principal stress

is much greater than the shear or peeling stress, so it can be expected that failure is due

to the major principal stress. It is evident from the FE results that the peeling stress has

a negligible contribution to crack initiation which is governed by the major principal

stress. The two main stress components which contribute to the principal stresses at

point D are the shear stress and the longitudinal stress. On the load-displacement curve,

the crack initiation point is shown as point A (Figure 4.6). It can be seen that after this

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point, the load-displacement curve becomes non-linear but the load keeps increasing. It

is evident from Figure 4.8 that after crack initiation with further load increases,

cracking started to propagate diagonally towards the loaded end and parallel to the PA

interface towards the unloaded end. When the diagonal crack near the loaded end was

fully formed, no further material exists between the loaded end and the crack tip (i.e.

the crack front away from the loaded end) to resist the longitudinal stresses. Therefore,

as the diagonal cracks propagated, longitudinal stresses near the plate end would

diminish. Therefore when diagonal cracks were fully formed, further crack propagation

would be governed by shear stresses.

To further highlight the shear-dominant process of crack propagation, the major

principal strain directions of the adhesive and the adherends obtained from the Aramis

measurement system at the load level of 24 kN are presented in Figure 4.22. At this

stage, from the major principal strain pattern shown in Figure 4.8k, a deep crack

parallel to the CFRP/adhesive interface is seen to propagate away from the loaded end

and the diagonal cracks are seen to be smaller away from the loaded end. The major

principal strain directions away from the plate end and close to the CFRP/adhesive

interface as well as most parts of the adhesive layer are seen to be inclined at

approximately 45o, indicating that these are shear cracks (Figure 4.22). As these

diagonal cracks were formed, the formation of small cantilever columns resulted

(Figure 4.23) (Lu et al. 2005). Eventually, shear failure at the bottom of the small

cantilever columns will occur close to the CFRP/adhesive interface (see final failure

surface in Figure 4.23). Accordingly, relatively smooth failure surfaces result (Figure

4.23). A numerical model of FRP-to-concrete bonded joints using a meso-scale FE

model (Lu et al. 2005) has shown a similar crack pattern and explained clearly the

mechanism of failure which agrees with the current FE results. However, in FRP-to-

concrete bonded joints, due to the shear retention capability of concrete, deeper cracks

occur, so a smooth crack surface as observed in CFRP-to-steel bonded joints does not

result.

93

The current experimental results clearly show that damage initiation in the adhesive

layer occurred at a load level of 15kN which is much lower than the bond strength (i.e.

the ultimate load) of 24.1kN. Furthermore, this damage initiation was due to interfacial

shear and longitudinal stresses. However, with further damage propagation, the damage

became shear-dominated. It can thus be concluded that as the maximum load is

reached, peeling stresses and longitudinal stresses become negligible and the damage is

governed by the interfacial shear stresses. Hence, except for the small region at the

loaded end, when the load reaches its maximum, the behaviour of the single-shear pull-

off test is governed by mode-II fracture. Provided a sufficiently long bond length exists

for stable crack propagation, the mode-II behaviour of an FRP-to-steel bonded joint can

be studied effectively using the single-shear pull-off test set-up.

4.5 CONCLUSIONS

This chapter has presented the results of a combined experimental and numerical study

to examine the suitability of using the single-shear pull-off test set-up to obtain the

shear bond-slip behaviour of CFRP-to-steel bonded interfaces. In evaluating this bond-

slip behaviour, the test set-up needs to satisfy the condition that the bonded interface is

subjected to pure mode-II loading. The existence of plate end peeling stresses in such

bonded joints (Chen et al. 2001) has however cast some doubt on the validity of this

method for shear bond behaviour studies.

The experimental results presented in this chapter have provided the evidence that

provided a long enough bond length exists, the failure process of a single-shear pull-off

test is predominantly governed by pure mode-II loading of the bonded interface (i.e. the

adhesive layer) after the initial stage of crack propagation. Therefore, the single-shear

pull-off test is a suitable method for evaluating the shear bond-slip behaviour.

Results from linear elastic FE analyses have also been presented to examine the effects

of different stress components on fracture initiation. It was explained using FE results

that if the plate end is modelled as a square (i.e. sharp) end, convergence of predicted

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stresses at the plate end with reductions in element size cannot be achieved due to the

existence of stress singularity points. Therefore the numerical values obtained for the

very end of the plate are on-objective. It was also shown that with the existence of a

small adhesive fillet at the plate end, the peeling stress is reduced significantly.

The FE results have been shown to compare well with the experimental measurements

obtained from the Aramis system within the linear elastic range of behaviour, which

confirms the accuracy of the 2D FE model. The results also showed that cracking

initiated due to combined shear and longitudinal stresses, with the effect of peeling

stresses being negligible.

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Engineering, Chapman and Hall, London, UK.

Aramis. (2006). Aramis User's Manual. GOM Optical Measuring Techniques.

Bocciarelli, M., Colombi, P., Fava, G. and Poggi, C. (2007). "Interaction of interface

delamination and plasticity in tensile steel members reinforced by CFRP

plates", International Journal of Fracture, 146(1-2), 79-92.

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96





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97

Table 4.1 Material properties of steel, CFRP and adhesive

Material

Modulus of

elasticity, E

(MPa)

Ultimate stress, σu

(MPa)

Ultimate strain,

εu

Steel 210000#

CFRP 165000* 2800# 0.017#

Adhesive (Sika

30) 11250* 22.3* 0.0030*

#- Manufacturer data; *- measured values

98

(a) Elevation

(b) Experimental set up

Figure 4.1 Single-shear pull-off test set-up

Adhesive

Steel block

Support block

Grip

Rollers

Adjustable support

Clamps SA interface Loaded end

550mm

110mm

Front Support

PA interface CFRP top surface

CFRP plate, 1.2mm thick

Far end Mid-surface (MA plane)

Strain gauges on the top of the CFRP plate CFRP plate

Steel block

CFRP plate

flush with the

side of the steel

block

99

(a) Elevation

(b) Section X-X

Figure 4.2 Support system for thickness control of the adhesive layer

CFRP plate

Steel block

Heavy steel plate

Support blocks for the heavy steel plate, 6.3mm high

Adhesive layer, 5.1mm thick

X

X

Steel block

CFRP plate

Heavy steel plate

Support blocks for the heavy steel plate

Adhesive layer

100

Figure 4.3 Support and loading

Front support

Load grip

Clamp support at the far end

Lateral supports

Digital Cameras

Lighting

101

Figure 4.4 Measurement window of the Aramis system

102

Figure 4.5 Failed specimen

Figure 4.6 Experimental load-displacement curve from a single-shear pull-off test

0

5

10

15

20

25

30

0 0.05 0.1 0.15 0.2

Displacement (mm)

Load (kN)

Point A

Point B

Point C

CFRP plate

Diagonal crack at the loaded end

Cohesion Failure

Combined cohesion and CFRP interlaminar failure

Adhesive wedge detached from the CFRP plate

103

(24.1 kN-1: at a displacement of 0.15 mm; 24.1 kN-2: at a displacement of 0.165 mm)

Figure 4.7 Strain distributions along the top of the CFRP plate at different load levels

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150Distance from the mid section (mm)

Stra

in (%

)

9kN12kN15kN18kN21kN24.1kN-124.1kN-2

104

Figure 4.8 Failure process: major principal strain plots from Aramis (red colour-high

strain/cracks to blue colour-low strain)

(a)14kN (b)15kN (c)16kN

(d)17kN (e)18kN (f)19kN

(g)20kN (h)21kN (i)22kN

(j)23kN (k)24kN (l)24.1kN

post failure

High strain near CFRP/adhesive interface

Cracks start to appear near CFRP/adhesive interface

Deep diagonal cracks

Crack propagation parallel to CFRP/adhesive interface

105

Figure 4.9 Crack path plot based on the major principal strain pattern at 15kN

Crack surface

X=0

Y=0

+

-

+

A A

Point D

- +

Crack Path

106

(a) Peeling strain vs. load

(b) Shear strain vs. load

Figure 4.10 Strain-load curves for selected points

-0.50

0.51

1.52

2.53

3.54

4.5

0 5 10 15 20 25 30Load (kN)

Pee

ling

Stra

in (%

)Point DPoint EPoint FPoint GPoint H

-0.50

0.51

1.52

2.53

3.54

4.55

0 5 10 15 20 25 30Load (kN)

She

ar S

train

(%) Point D

Point EPoint FPoint GPoint H

107

(a) at 15kN

(b) 24kN

Figure 4.11 Strain distributions along section A-A

Point D

Point D

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 5 10 15 20 25Stra

in (%

)

Distance from the loaded end (mm)

Longitudinal strain

Peeling strain

Shear strain

Point D

Point D-5

-4

-3

-2

-1

0

1

2

3

4

5

0 5 10 15 20 25


Stra

in (%

)

Longitudinal strain

Peeling strain

Shear strain

108

(a) Dimensions, support and loading conditions of FE model

(b) Loaded end details of the FE model (for clarity not all lines of the mesh of the

adhesive layer are shown)

Figure 4.12 Details of the FE model

CFRP plate

Adhesive 5.1mm

Steel

1.2mm

X

50mm 450mm 100m

Front support- Ux=0

Base support at the bottom of the steel block, Uy=0

Support on the steel block at the far end, Uy=0

110 mm

Y

Vertical support at the loading point, Uy=0

Load applied to the CFRP plate

109

(a) Interfacial peeling stress distributions along the PA interface

(b) Interfacial peeling stress distributions along the PA interface near the loaded

end

-50

0

50

100

150

200

250

0 2 4 6 8 10


Pee

ling

stre

ss (

Mpa

)PA-0.25mmPA-0.1mmPA-0.05mmPA-0.01mmPA-0.0025mm

-50

0

50

100

150

200

250

0 0.02 0.04 0.06 0.08 0.1


Pee

ling

stre

ss (M

pa)

PA-0.25mmPA-0.1mmPA-0.05mmPA-0.01mmPA-0.0025mm

110

(c) Interfacial shear stress distributions along the PA interface

(d) Interfacial shear stress distribution along the PA interface near the loaded end

Figure 4.13 Interfacial shear and peeling stress distributions along the PA interface

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10Distance from the plate end (mm)

She

ar s

tress

(Mpa

)PA-0.25mmPA-0.1mmPA-0.05mmPA-0.01mmPA-0.0025mm

0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3 0.4 0.5 0.6Distance from the plate end (mm)

She

ar s

tress

(Mpa

)

PA-0.25mmPA-0.1mmPA-0.05mmPA-0.01mmPA-0.0025mm

111

(a) Interfacial peeling stress distributions along the SA interface

(b) Interfacial peeling stress distributions along the SA interface near the loaded end

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

0 2 4 6 8 10


Pee

ling

stre

ss (M

pa)

SA-0.25mmSA-0.1mmSA-0.05mmSA-0.01mmSA-0.0025mm

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

0 0.1 0.2 0.3 0.4 0.5 0.6


Pee

ling

stre

ss (M

pa)


112

(c) Interfacial shear stress distributions along the SA interface

(d) Interfacial shear stress distributions along the SA interface near the loaded end

Figure 4.14 Interfacial shear and peeling stress distributions along the SA interface

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10Distance from the loaded end (mm)

She

ar s

tress

(Mpa

)SA-0.25mmSA-0.1mmSA-0.05mmSA-0.01mmSA-0.0025mm

0

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1 1.2Distance from the loaded end (mm)

She

ar s

tress

(Mpa

)


113

(a) Interfacial peeling stress distributions along the MA plane

(b) Interfacial peeling stress distributions along the MA plane near the loaded end

-25

-20

-15

-10

-5

0

5

0 2 4 6 8 10

Pee

ling

stre

ss (M

pa)


MA-0.25mmMA-0.1mmMA-0.05mmMA-0.01mmMA-0.0025mm

-25

-20

-15

-10

-5

0

5

0 0.5 1 1.5 2 2.5 3

Pee

ling

stre

ss (M

pa)



114

(c) Interfacial shear stress distributions along the MA plane

(d) Interfacial shear stress distributions along the MA plane near the loaded end

Figure 4.15 Interfacial shear and peeling stress distributions along the MA plane

-5

0

5

10

15

20

25

0 2 4 6 8 10

She

ar s

tress

(Mpa

)



-5

0

5

10

15

20

25

0 0.5 1 1.5 2

She

ar s

tress

(Mpa

)



115

Figure 4.16 Shear stress distributions across the adhesive layer at the loaded end

Figure 4.17 Peeling stress distributions across the adhesive thickness at the loaded

end

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-80 -60 -40 -20 0Shear stress (Mpa)

Adhe

sive

heig

ht (m

m)

0.25mm

0.1mm

0.05mm

0.01mm

0.0025mm

stresses through adhesive thickness at the loaded end

0mm

1mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-200 -100 0 100 200 300Peeling stress (Mpa)

Adhe

sive

hei

ght (

mm

)

0.25mm0.1mm0.05mm0.01mm0.0025mm

stresses through adhesive thickness at the loaded end

0mm

1mm

116

(a) 1.5mm radius fillet at the joint end in the experiment specimen

(b) Modelling of the joint end fillet (for clarity not all the lines in the mesh of the

adhesive layer are shown)

Figure 4.18 Fillet details at joint end

1.5mm radius fillet

Steel

Adhesive

CFRP

1.5mm radius fillet Steel

Adhesive

CFRP

117

(a) Axial displacements

(b) Vertical displacements

Figure 4.19 Axial and vertical displacement at the top surface of CFRP:

comparison between the FE model and the Aramis data

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0-1 4 9 14 19


Axi

al d

ispl

acem

ent (

mm

)

Aramis-7kN

FE-7kN

Aramis -9kN

FE-9kN

Aramis-15kN

FE-15kN

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

-1 4 9 14 19 24


Ver

tical

dis

plac

emen

t (m

m)

Aramis-7kN

FE-7kN

Aramis-9kN

FE-9kN

Aramis-15kN

FE-15kN

118

(a) 9kN

(b) 15kN

Figure 4.20 Strain distributions along the top surface of CFRP from Aramis, strain

gauges and the FE model

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-5 5 15 25 35


Axi

al s

train

(%)

Aramis-9kN

Strain guage-9kN

FE-9kN

-0.2

0

0.2

0.4

0.6

0.8

1

-5 5 15 25 35


Axi

al s

train

(%)

Aramis-15kN

Strain guage-15kN

FE-15kN

119

Figure 4.21 Stress distributions along section A-A from the FE model with a

1.5mm radius fillet

Figure 4.22 Major principal strain directions at 24kN

Point D

Point D

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20 25

Stre

ss (M

Pa)


Major principal stress

Shear stress

Longitudinal stress

Peeling stress

Approx. 450 inclination; major principal strain direction

120

Figure 4.23 Mechanism of failure away from the loaded end

Applied load, P CFRP/adhesive interface

Cracks in adhesive near CFRP/adhesive interface, inclined at approximately 45o

Final failure surface in adhesive layer; parallel to the CFRP/adhesive interface

Meso-scale cantilever columns

121

CHAPTER 5 EXPERIMENTAL BEHAVIOUR ON CFRP-TO-STEEL

BONDED JOINTS

5.1 INTRODUCTION

As reviewed in Chapter 2, existing studies revealed that debonding of the FRP plate

from the steel substrate is one of the main failure modes in CFRP-strengthened steel

structures. In order to understand and model debonding failures, the behaviour of

simple FRP-to-steel bonded joints needs to be well understood first (Teng et al.

2009).

While extensive research has been conducted on FRP-to-concrete bonded joints

(Chen and Teng 2001; Yuan et al. 2004), existing studies on FRP-to-steel bonded

joints are rather limited (Xia and Teng 2005; Zhao and Zhang 2007; Teng et al.

2009). The critical difference between FRP-to-concrete and FRP-to-steel bonded

joints is that the concrete is usually the weak link in the former but in the latter, the

adhesive is the weak link, provided that adhesion failure at the steel/adhesive

interface and the FRP/adhesive interface is avoided by careful selection of the

adhesive and appropriate surface preparation of the steel and the FRP (Teng et al.

2009).

Different test methods for bonded joints have been used by different researchers

(Yao et al. 2005; Zhao and Zhang 2007). A detailed description of these test

methods can be found in these references and is thus not given here. To study the

behaviour of FRP-to-concrete bonded joints, the so-called near-end supported

single-shear pull-off test is probably the most suitable (Yao et al. 2005) and was

also used in the only existing study on the full-range behaviour of CFRP-to-steel

bonded joints (Xia and Teng 2005). Xia and Teng’s (2005) test results

demonstrated that the generic concepts such as the interfacial fracture energy and

the effective bond length (i.e. Le) (Chen and Teng 2001) well established for FRP-

to-concrete bonded joints are still applicable to FRP-to-steel bonded joints.

However, their study was limited to adhesives with linear elastic behaviour (i.e.

122

linear adhesives) and a large number of the test specimens failed by interlaminar

failure of the FRP plate which did not reflect the interfacial behaviour of the bonded

joints. This chapter presents a more comprehensive experimental study into the full-

range behaviour of CFRP-to-steel bonded joints, where both linear adhesives and

non-linear adhesives were examined.

5.2 TEST PROGRAMME

5.2.1 Test Method and Set-up

It has been concluded from the results presented in Chapter 4 that the near-end

supported single-shear pull-off test is suitable for studying the shear bond behaviour

(e.g. the bond strength and bond-slip behaviour) of FRP-to-steel bonded joints. This

test method was adopted in the present study. The test set-up (Figure 5.1) is similar

to that used in Xia and Teng (2005) and included a thick steel plate (thickness=30

mm, length=450 mm) with its bottom edges welded to a support block, and an FRP

plate bonded to the top surface and loaded at one end (Figure 5.2). The load was

applied to the FRP plate through a grip sitting on a set of rollers which was fixed on

an adjustable support (Figure 5.2); before each test, the height of the support was

carefully adjusted and a laser positioning device was used to make sure that the load

was horizontally applied.

5.2.2 Specimen Details

The main parameters affecting the behaviour of an FRP-to-concrete bonded joint

have been identified to be the concrete strength, the bond length, the FRP plate axial

stiffness, the FRP-to-concrete width ratio, the adhesive stiffness and the adhesive

strength (Chen and Teng 2001; Lu et al. 2005). In an FRP-to-steel bonded joint, the

adhesive is normally the weak link and failure is unlikely to occur within the steel

substrate. Therefore, the steel strength was not considered to be an important

parameter. Based on the same reason and given the fact that the FRP plate and the

adhesive layer normally have the same width, the FRP-to-steel or the FRP-to-

adhesive width ratio was also not considered as a significant parameter. The

investigation of the full-range behaviour of bonded joints generally requires a bond

123

length larger than the effective bond length Le

. In the present study, the bond length

was not taken as a variable to be examined; sufficiently large bond lengths were

selected according to existing test results (Xia and Teng 2005) and were adjusted

during the experimental programme according to new test observations. Given the

above considerations, the parameters examined in the present study include the

mechanical properties and thickness of the adhesive and the axial stiffness of the

FRP plate.

A total of eighteen single-shear pull-off tests were conducted in three series (i.e.

Series I to III). Series I was designed to investigate the effect of adhesive properties

and included eight specimens covering four different adhesives (i.e. adhesives A to

D, representing Sika 30, Sika 330, Araldite 2015 and Araldite 420 respectively);

two identical specimens were prepared for each adhesive. The material properties of

the four adhesives are summarized in Table 3.1. It is evident from Table 3.1 that the

four adhesives cover a wide range of elastic modulus (from 1.75 to 11.25 GPa) and

tensile strength (from 14.73 to 31.28 MPa); they also cover both linear adhesives

(adhesives A and B) and non-linear adhesives (adhesives C and D) (Figure 3.3). All

the specimens in Series I had the same normal modulus (NM) CFRP plate (elastic

modulus = 150 GPa; thickness = 1.2 mm) and the same adhesive thickness of 1 mm.

After the tests of Series I, two adhesives (i.e. adhesives A and C) were selected for

further investigation in the other two series of tests. Series II was designed to

investigate the effect of adhesive thickness and included five specimens for the two

selected adhesives; three adhesive thicknesses (i.e. 1.5 mm, 2 mm and 3 mm) were

adopted for adhesive A while two adhesive thicknesses (i.e. 2 mm and 3 mm) were

adopted for adhesive C. All the specimens in Series II had the same NM CFRP plate

as that used in Series I so that they can be compared with the four specimens in

Series I with adhesive A or C as the bonding adhesive and an adhesive thickness of

1 mm. Series III was designed to investigate the effect of the axial stiffness of FRP

plate and included five specimens for the two selected adhesives; two FRP plates

[i.e. medium modulus (MM) CFRP plate (elastic modulus = 235 GPa; thickness

=1.4 mm) and high modulus (HM) CFRP plate (elastic modulus = 340 GPa;

thickness =1.4 mm)] were tested for each of the two adhesives and one additional

test was conducted for adhesive A where a steel plate (elastic modulus = 200 GPa;

thickness =6.0 mm) was used instead of an FRP plate. All the specimens in Series

124

III had the same adhesive thickness of 1 mm so that they can be compared with the

four specimens in Series I with adhesive A or C as the bonding adhesive and an NM

CFRP plate. For all the specimens in Series I, the bond length was chosen to be 300

mm which is significantly higher than the effective bond length (i.e. Le, around 150

mm) found by Xia and Teng (2005) for the adhesives they tested. The higher bond

length was used as it was expected that the non-linear adhesives used in the present

study would lead to a longer Le

. After the tests of Series I, the bond length was

adjusted to be 380 mm for specimens using adhesive C but was kept at 300 mm for

the other specimens. Other details of the test specimens are summarized in Table

5.1.

In the preparation of specimens, the top surface of the steel plate was solvent-wiped,

grit-blasted using 0.25 mm angular grit, and then further cleaned using a vacuum

head, based on the study presented in Chapter 3. After surface preparation, the FRP

plate was adhesively bonded to the surface within 12 hours. All the specimens were

cured for 14 days before testing.

Each specimen is given a name, which starts with a letter to represent the adhesive

type (i.e. adhesives A to D), followed by a two-letter abbreviation to represent the

plate type (i.e. NM, MM, HM or ST representing a normal-modulus, medium-

modulus, or high-modulus CFRP plate or a steel plate). This is then followed by a

letter “T” and a number to represent the design/nominal thickness of the adhesive

layer (i.e. 1, 1.5, 2 or 3); the actual thicknesses achieved in the tests were slightly

different as precise thickness control during specimen preparation was difficult. For

the specimens in Series I, an additional roman number I or II appears at the end of

the name to differentiate the two nominally identical specimens.

5.2.3 Instrumentation and Loading Procedure

A number of strain gauges were attached on the top surface of the FRP plate at

intervals of 20 mm except the first two strain gauges (counted from the left end of

the steel substrate plate). The first strain gauge was at 5 mm from while the second

strain gauge at 20 mm from the left end of the steel substrate plate (Figure 5.1b).

125

Two LVDTs were used to measure the displacements at the loaded end and the free

end of the FRP plate respectively. Loading was applied using a hydraulic jack,

initially at load increments of about 1 kN, and then at duly adjusted displacement

increments after the load-displacement curve became non-linear.

5.3 TEST RESULTS AND DISCUSSIONS

5.3.1 General

Table 5.2 summarizes the ultimate loads for all the specimens and their

corresponding failure modes, while the specimens after tests are shown in Figure

5.3. Results from Series I show that the four specimens with adhesive A or adhesive

C basically failed in the cohesion failure mode (i.e. failure within the adhesive)

while those with adhesive B failed due to the interlaminar failure of the CFRP plate.

The two specimens with adhesive D failed in a combined failure mode where both

cohesion failure and CFRP interlaminar failure occurred, with cohesion failure

being dominant for specimen D-NM-T1-I while CFRP interlaminar failure being

more pronounced for specimen D-NM-T1-II. Given the above observations,

adhesive A and adhesive C were selected for the other two series of tests as the

present study is focused on investigating the interfacial behaviour of the bonded

joints governed by adhesive properties. With the use of these two selected adhesives,

most of the specimens in Series II and III failed in the cohesion failure mode except

three specimens which either had a large adhesive thickness (i.e. the C-NM-T2 and

C-NM-T3 specimens, failing by the interlaminar failure of CFRP) or a very stiff

CFRP plate (i.e. specimen C-HM-T1, failing by the rupture of CFRP).

It should be noted that even for the specimens failing basically in the cohesion

failure mode, localized CFRP interlaminar failure was found within a small region

near the free end of the bonded joints (Figure 5.3) where high normal (or peeling)

stresses are expected to exist. Except for specimen A-ST-T1, the failure of these

specimens all started with an initial crack which was close to the loaded end and

propagated gradually towards the free end. The failure process was rather gradual

and ductile before a sudden load drop occurred when the crack tip reached the free

126

end of CFRP or when brittle CFRP interlaminar failure close to the free end

occurred. Similar to the observations described in Chapter 4, a small wedge of

adhesive near the loaded end of CFRP was pulled off for all these specimens except

specimen A-ST-T1. For specimen A-ST-T1 where a thick steel plate with a high

bending stiffness was used, the failure was very sudden and brittle, which is

believed to be due to the combination of high normal stresses and shear stresses

developed in the adhesive layer.

All the four specimens failing by the interlaminar failure of CFRP showed a very

brittle behaviour. It should be noted that although their failure was all controlled by

the interlaminar strength of CFRP, the ultimate loads of the four specimens are

quite different, and are all lower than those of specimen C-NM-T1-I and II where

no failure in the CFRP plate was found, indicating the considerable effect of the

mechanical properties and thickness of adhesive on the stress state in the CFRP

plate for such bonded joint tests. Compared with adhesive C, adhesive B had a

larger elastic modulus and thus led to more pronounced local bending near the

loaded end of the CFRP plate, which caused the interlaminar failure at a much

smaller load. Similarly, the increase of thickness of the adhesive also led to larger

bending stresses in the CFRP plate and made interlaminar failure more likely to

occur.

Specimens D-NM-T1-I and II failed in a combined failure mode (i.e. combined

CFRP interlaminar failure and cohesion failure), and their failure processes were

ductile with gradual crack propagation from the loaded end to the free end of CFRP.

Specimen C-HM-T1 failed by the rupture of the CFRP plate when the tensile

strength of CFRP was reached and the failure was rather brittle.

5.3.2 Load-Displacement Behaviour

The load-displacement curves of all the specimens are shown in Figure 5.4. The

displacements shown in Figure 5.4 were calculated from readings of the strain

gauges attached on the CFRP plate instead of the LVDT readings at the loaded end

of the CFRP plate, as the latter were complicated by measurement noise. A typical

127

comparison between the two ways of obtaining displacements is shown in Figure

5.5, which illustrates that the displacements calculated from strain readings

basically agree well with the LVDT readings except for those at the final stage of

the experiments when significant slips occurred at the free end of the plate; such

slips could not be reflected by the CFRP strains.

Figure 5.4 shows that the curves of all the specimens failing by cohesion failure

have a long plateau because of the use of a large bond length (i.e. 300 mm or 380

mm), except for specimens A-ST-T1 and A-HM-T1. The failure of specimen A-ST-

T1 was induced by the combination of high normal stresses and shear stresses and

was thus brittle as discussed earlier. The failure of specimen A-HM-T1 was also

ductile but it showed some hardening instead of a long plateau. Different from other

specimens failing in the adhesive where the crack propagation was always close to

the CFRP surface, during the test of specimen A-HM-T1, it was found that the

crack first propagated close to the mid-surface of the adhesive layer and then moved

to be close to the CFRP surface. This may be due to the existence of some defects

(e.g. bubbles) in specimen A-HM-T1 which weakened the mid-surface of the

adhesive layer and made the specimen enter the plastic stage earlier. The two

specimens (i.e. specimens D-NM-T1-I and II) failing by the combined failure mode

also have similar load-displacement curves.

By contrast, the interlaminar failure of CFRP was rather brittle. The load-

displacement curves of the four specimens (i.e. specimens B-NM-T1-I, II, C-NM-

T2, C-NM-T3) with this failure mode are relatively short without a plateau.

Specimen C-HM-T1 failed by the rupture of the CFRP plate and the failure process

was also brittle as can be seen from the load-displacement curve.

Figure 5.4a also shows that the specimen with a stiffer adhesive (i.e. adhesive with

a larger elastic modulus) had a larger initial stiffness. An increase in the CFRP axial

stiffness generally leads to an increase in the initial stiffness, but an increase in the

adhesive thickness leads to a decrease in the initial stiffness (Figure 5.4). It is also

seen that the load-displacement curve becomes non-linear at a very early stage of

loading for all the specimens, and the nonlinearity is more pronounced for

128

specimens with a non-linear adhesive (i.e. adhesives C and D) and specimens with a

larger adhesive thickness.

Discussions in the following sections are focused on the specimens failing by

cohesion failure which is the focus of the present study, with reference to other

specimens only when necessary.

5.3.3 Axial Strain Distribution along the CFRP Plate

The axial strain distributions along the CFRP plate are shown in Figures 5.6 and 5.7

for two specimens with adhesive A (i.e. specimen A-NM-T1-I) and adhesive C (i.e.

specimen C-NM-T1-I) respectively. The axial strain values are readings from the

strain gauges attached on the upper surface of the CFRP plate (see Section 5.2.3 for

details) except for the strains at the loaded end, which were calculated from the

applied load and the properties of the CFRP plate. The axial strain distributions for

other specimens are similar and are provided in Appendix 5.1.

For the specimen with adhesive A, Figure 5.6a shows that significant CFRP strains

developed only within a small region close to the loaded end before the ultimate

load (Pu

) was reached. After that, the maximum CFRP strain remained nearly

constant but the region where this maximum CFRP strain was reached kept

expanding (Figure 5.6b), illustrating the process of debonding (i.e. shear stress

equal to zero) from the loaded end to the free end of CFRP. It is also seen that as

debonding propagates, the strain distributions beyond the debonded region are

similar (Figure 5.6b), indicating similar shear stress distributions within these

regions.

Compared with the specimen with adhesive A, in the specimen with adhesive C,

significant CFRP strains developed within a much larger region at the ultimate load

(Pu) (Figure 5.7a), but the development of CFRP strains after that is similar (Figure

5.7b). At the later stage of debonding propagation, significant CFRP strains and

shear stresses are developed close to the free end (Figure 5.7b), leading to

significant slips within this region.

129

It may also be concluded from Figures 5.6 and 5.7 that with a softer non-linear

adhesive (i.e. adhesive C), a much larger length of CFRP plate can be mobilized (i.e.

significant CFRP strains are developed), leading to a much larger ultimate load. It is

also implied that the effective bond length is larger when a soft non-linear adhesive

is used instead of a stiff linear adhesive.

5.3.4 Bond-Slip Behaviour

The interfacial shear behaviour of a bonded joint is often characterized by the so-

called bond-slip curve which depicts the relationship between the local interfacial

shear stress and the relative slip between the two adherends. In a single-shear pull-

off test, the interfacial shear stress and the slip can be found from readings of the

strain gauges attached on the CFRP plate using the following equations (Pham and

Al-Mahaidi 2005):

( )( )

1

2 1

i ii p p

i i

E tL Lε ε

τ +

+

−=

− (5.1)

( ) ( ) ( ) ( )1 1 21 2 1

2 4 2

ni i i i

i i i i ii i

L L L Lε ε ε ε

δ + + ++ + +

=

+ += − + −∑ (5.2)

where iε is the reading of the ith strain gauge counted from the loaded end of the

CFRP plate; n is the number of strain gauges on the CFRP plate within the bond

length; Li is the distance of the ith strain gauge from the loaded end of the CFRP

plate, with L0 pE= 0; and pt are the elastic modulus and thickness of the CFRP

plate respectively; 2

iτ and 2

iδ are the shear stress and slip at the middle point

between the ith strain gauge and the i+1th

strain gauge.

Figure 5.8 shows the bond-slip curves obtained using Eqns 5.1 and 5.2 for all the

specimens failing by cohesion failure. For the other specimens where the failure

was at least partially within the CFRP plate, the bond-slip curves obtained using

130

Eqns 5.1 and 5.2 are not governed purely by the adhesive; these curves are not

further discussed in the following sections but are provided in Appendix 5.1. In

Figure 5.8, several curves were obtained for each specimen using readings from the

strain gauges at different locations. The readings of the first strain gauge (i.e.

located at 5 mm from the loaded end) were not used in producing the bond-slip

curves as the stress state close to the loaded end was complicated by significant

interfacial normal stresses (see Chapter 4 for details). It is evident from Figure 5.8

that for the same specimen, the bond-slip curves obtained at different locations are

similar.

Figure 5.8 also shows that the bond-slip curves for adhesive A (a linear adhesive)

are quite different from those for adhesive C (a non-linear adhesive): the former

have an approximately bi-linear shape (i.e. an ascending branch followed by a

descending branch) but the latter have an approximately trapezoidal shape with an

obvious plateau (i.e. an ascending branch followed by a plateau and then a

descending branch). This is different from FRP-to-concrete bonded joints where the

bond-slip curve always has an approximately bi-linear shape because of the brittle

nature of concrete. It is also implied that different forms of bond-slip models should

be developed for CFRP-to-steel bonded joints with different adhesives.

For adhesive A (a linear adhesive), the bond-slip curves may be approximated by a

bi-linear curve as shown in Figure 5.9a. The main parameters characterizing the

curve are the maximum shear stress experienced by the interface maxτ (referred to as

the peak bond shear stress hereafter) and the corresponding slip 1δ , and the slip fδ

at which failure occurs (i.e. when the bond shear stress becomes zero). Table 5.3

summarizes the three key parameters extracted from the experimental bond-slip

curves for all the specimens with adhesive A and failing by cohesion failure. For

each of these specimens, maxτ and 1δ were averaged from the peak shear stresses

and the corresponding slips of several bond-slip curves obtained at different

locations (Figure 5.8); fδ was also obtained from several bond-slip curves for

different locations (Figure 5.8), and was calculated from the corresponding maxτ and

131

fG by assuming that max12f fG τ δ= . Apparently, the fδ values obtained in this way

are only an approximation of the experimental values.

For adhesive C, the bond-slip curves can be approximated by a trapezoidal curve as

shown in Figure 5.9b. The main parameters characterizing a trapezoidal bond-slip

curve include maxτ , the slip 1δ ) at which the plateau starts, the slip 2δ at which the

plateau ends and the descending branch starts, and the slip fδ at which the bond is

completely damaged. These key parameters were also extracted from the

experimental bond-slip curves and are summarized in Table 5.3 for all the

specimens with adhesive C and failing by cohesion failure. As the direct extraction

of these parameters from the results in Figure 5.8 is difficult, an experimental bond-

slip curve was first converted into an idealized trapezoidal curve by assuming that

the following four characteristics of the original and the converted curves are the

same: (1) the area under the curve ( fG ); (2) the initial slope of the curve; (3) the

slope of the descending branch of the curve (4) the slip where the bond shear stress

becomes zero (or a very small value) ( fδ ). The four parameters (i.e. maxτ , 1δ , 2δ and

fδ ) were then averaged from the idealized trapezoidal bond-slip curves at different

locations for each specimen.

Table 5.3 shows that the peak shear bond stress maxτ is similar for different

specimens with the same adhesive, even when these specimens were composed of

quite different CFRP plates and/or different thicknesses of adhesive. Examined

together with Table 3.1, it can be seen that the peak shear bond stress is close to but

slightly smaller than the tensile strength of the adhesive when cohesion failure

controls the debonding process. Table 5.3 shows that the other key parameters of

the bond-slip curve also depend significantly on the adhesive used.

132

5.3.5 Bond Strength

Within the context of studies on FRP-to-concrete and CFRP-to-steel bonded joints,

the term “bond strength” is commonly used to refer to the ultimate tensile force (i.e.

ultimate load) that can be resisted by the CFRP plate before the CFRP plate

debonds from the substrate (Hollaway and Teng 2008). The bond strengths of all

the specimens failing by cohesion failure (i.e. debonding) are summarized in Table

5.4. Other specimens failed at least partially by the material failure of the CFRP

plate (i.e. interlaminar failure or CFRP rupture), so their ultimate loads are not taken

as the bond strengths and are not discussed here.

It is evident from Table 5.4 that different adhesives led to quite different ultimate

loads of the bonded joints. Table 5.3 shows that the specimens with adhesive A

have a higher peak shear bond stress (also a higher adhesive tensile strength, see

Table 3.1) than adhesive C, but a much lower bond strength. The bond strength has

been found to depend significantly on the interfacial fracture energy Gf (i.e. the area

under a bond-slip curve) for FRP-to-concrete bonded joints (Lu et al. 2005; Yuan et

al. 2004; Xia and Teng 2005) and CFRP-to-steel bonded joints with a linear

adhesive (Xia and Teng 2005), so the interfacial fracture energy values extracted

from the experimental bond-slip curves are also summarized in Table 5.4 for

clarification. The dependency of bond strength on Gf

is also clearly seen for the

results from the present study for both linear and non-linear adhesives (Table 5.4).

With these observations, the experimental bond strengths are further compared with

the predictions of the following well-known equation (Taljsten 1997; Chen and

Teng 2001; Wu et al. 2002; Yuan et al. 2004) for FRP-to-concrete bonded joints

with an infinite bond length and with a plate equal in width to the concrete substrate

block (see Table 5.4 and Figure 5.10):

2u p p p fP b E t G= (5.3)

where pb is the plate width, pE is the elastic modulus of the CFRP plate, pt is the

thickness of the CFRP plate and fG is the interfacial fracture energy. In the

133

comparison, the experimental interfacial fracture energy values as summarized in

Table 5.3 are used. It is clear from Table 5.4 and Figure 5.10 that Eqn 5.3 can

provide accurate predictions for the bond strength, given that the interfacial fracture

energy used is accurate.

5.3.6 Interfacial Shear Stress Distributions

Figures 5.11 and 5.12 show the interfacial shear stress distributions along the CFRP

plate at different stages of loading/deformation for a specimen with adhesive A (i.e.

specimen A-NM-T1-I) and a specimen with adhesive C (i.e. Specimen C-NM-T1-I)

respectively. The interfacial shear stress distributions for other specimens are

similar. Again, the interfacial shear stresses were obtained from the axial strains of

the CFRP plate using Eqn 5.1.

Figure 5.11 shows that the development of shear stresses in the specimen with

adhesive A (a linear adhesive) includes three distinctive stages: (1) initial stage

(points A and B) when the shear stress is the largest at or very close to the loaded

plate end and reduces gradually towards the other end of the plate; (2) softening

stage (point C) when the shear stress near the loaded end starts to decrease after it

has reached its maximum value (i.e. the loaded end is on the descending branch of

the bond-slip curve); the load resisted by the bonded joint continues to increase in

this stage but the load-displacement curve becomes non-linear; (3) debonding stage

(points D to G) after the shear stress at the loaded end has reduced to zero, the peak

shear stress moves gradually towards the free end; the load is almost constant

during this stage. This observed process is similar to that observed by Xia and Teng

(2005) as the adhesives used by them were also linear adhesives.

Figure 5.12 shows that when a non-linear adhesive is used, the shear stress

distributions are quite different. At many loading/deformation levels, a certain

length of the bonded interface is subjected to similar shear stresses which are

approximately equal to the peak shear bond stress. In particular, after the shear

stress at the loaded end has reached its peak value, this stress value is maintained

and a stress plateau develops as the load increases until a certain load level at which

the loaded end enters the softening state and the constant stress region has been

134

fully developed. This behaviour of a bonded interface with a non-linear adhesive

reflects an approximately trapezoidal bond-slip curve for adhesive C as discussed in

Section 5.3.4. When the interfacial stress at the loaded end reaches zero, the stress

plateau starts to move gradually from the loaded end to the free end until point H of

the load-displacement curve is reached (Figure 5.12). At point H, localized CFRP

interlaminar failure occurred as discussed earlier (see Section 5.3.1) and the

calculated maximum shear stress is slightly higher than in the previous stages

(Figure 5.12).

For both linear and non-linear adhesives, Figures 5.11 and 12 show that significant

shear stresses are developed only within a limited region of the bonded interface at

any instance. After the shear stress at the loaded end has reduced to zero, this high-

stress region starts to move gradually towards the free end but the size of the high-

stress region remains almost constant. As the tensile force that the CFRP plate can

take relies on the shear stress transfer across the bonded interface, this observation

clearly explains the existence of an effective bond length, beyond which any further

increase in the bond length does not lead to a further increase in the bond strength

but leads to an increase in the ductility of failure process.

5.3.7 Effect of Adhesive Thickness

Table 5.3 shows that for adhesive A, the bond strength increases when the adhesive

thickness increases from 1 mm to 2 mm, but the adhesive thickness of 3 mm leads

to a considerably lower bond strength than an adhesive thickness of 2 mm. The

interfacial fracture energy also shows the same trend (Table 5.3). The specimen

presented in Chapter 4 was also bonded with adhesive A (thickness =5.1 mm) and

had a CFRP plate with similar mechanical properties (thickness = 1.2 mm; elastic

modulus =165 GPa), so its bond strength is also included here for comparison.

Considering that the width of the CFRP plate (i.e. 25 mm) is half of that used in the

specimens presented in this chapter, its bond strength (i.e. 24.1kN) needs to be

doubled for comparison with the results shown in Table 5.3. The comparison

indicates that the adhesive thickness of 5.1 mm leads to a significantly larger bond

strength than the smaller thicknesses. It may therefore be concluded that the bond

strength generally increases with the adhesive thickness, as found by Yuan and Xu

135

(2008) from their analytical study. The unexpected low bond strength for the

specimen with an adhesive thickness of 3 mm could be due to some unexpected

local defects in this specimen. Further research is needed to confirm this conclusion.

Table 5.3 also shows that the slip at the peak shear bond stress 1δ generally

increases with the adhesive thickness (except for the specimen with a 3 mm thick

adhesive layer).

For adhesive C, the two specimens in Series II with a thickness larger than 1 mm

both failed by the interlaminar failure of the CFRP plate, at a smaller bond strength.

An FE analysis not presented here showed that a larger adhesive thickness leads to

more pronounced local bending near the loaded end of the CFRP plate so that the

plate become more susceptible to interlaminar failure.

5.3.8 Effect of Plate Axial Rigidity

It is evident from Table 5.2 that the bond strength of a CFRP-to-steel bonded joint

increases with the plate axial rigidity, provided that failure occurs within the

adhesive (i.e. cohesion failure). This phenomenon is similar to that of FRP-to-

concrete bonded joints (Chen and Teng 2001). Although different CFRP plates led

to different bond strengths (i.e. ultimate loads) of the bonded joints, they had little

effect on the bond-slip curves of the bonded interfaces, as shown in Figure 5.8 and

Table 5.3.

5.4 CONCLUSIONS

This chapter has presented a systematic experimental study on the full-range

behaviour of CFRP-to-steel interfaces through the testing of a series of single-lap

bonded joints. The parameters examined include the mechanical properties and

thickness of the adhesive and the axial rigidity of the CFRP plate. The test results

and the discussions presented in this chapter allow the following conclusions to be

drawn:

(1) The bond strength (i.e. ultimate load) of such bonded joints depends strongly on

the interfacial fracture energy among other factors;

136

(2) Non-linear adhesives with a lower elastic modulus but a larger strain capacity

lead to a much higher interfacial fracture energy than linear adhesives with a

similar or even a higher tensile strength;

(3) The bond-slip curve has an approximately triangular shape for a linear adhesive

but has a trapezoidal shape for a non-linear adhesive, indicating the necessity of

developing different forms of bond-slip models for different adhesives;

(4) The bond-slip curve is independent of the rigidity of the CFRP plate;

(5) There exists an effective bond length in such bonded joints, beyond which any

further increase in the bond length does not lead to a further increase in the

bond strength but does lead to an increase in ductility;

(6) The bond strength increases with both the adhesive thickness and the CFRP

plate rigidity, provided that cohesion failure is the controlling failure mode; and

(7) As the adhesive thickness or CFRP plate rigidity increases, the failure mode is

likely to change from cohesion failure to the material failure of CFRP.

137

REFERENCES Chen, J.F. and Teng, J.G. (2001). "Anchorage strength models for FRP and steel

plates bonded to concrete", Journal of Structural Engineering, 127(7), 784-

791.






Pham, H.B. and Al-Mahaidi, R. (2007). "Modelling of CFRP-concrete shear-lap

tests", Construction and Building Materials, 21(4), 727-735.

Taljsten, B. (1997). "Defining anchor lengths of steel and CFRP plates bonded to

concrete", International Journal of Adhesion and Adhesives, 17(4), 319-327.

Teng, J.G., Yu, T. and Fernando, D. (2009), “FRP composites in steel structures”,

Proceedings of the Third International Forum on Advances in Structural

Engineering, Shanghai, China.

Wu, Z.S., Yuan, H. and Niu, H.D. (2002). "Stress transfer and fracture propagation

in different kinds of adhesive joints", Journal of Engineering Mechanics-

ASCE, 128(5), 562-573.

Xia. S.H. and Teng, J.G. (2005). "Behavior of FRP-to-steel bond joints",


2005), Hong Kong, China.

Yao, J., Teng, J.G. and Chen, J.F. (2005a). "Experimental study on FRP-to-concrete


Yao, J., Teng, J.G. and Lam, L. (2005b). "Experimental study on intermediate crack

debonding in FRP-strengthened RC flexural members", Advances in




553-565.

Yuan, H. and Xu, Y. (2008). "Computational fracture mechanics assessment of

adhesive joints", Computational Materials Science, 43(1), 146-156.

138

Zhao, X.L. and Zhang, L. (2007). "State-of-the-art review on FRP strengthened

steel structures", Engineering Structures, 29(8), 1808-1823.

139

Table 5.1 Specimen details

Series Specimen Adhesive type

Tensile strength

of the adhesive,

σmax

Elastic modulus of

the adhesive, E

(MPa) a

Adhesive

thickness, t

(GPa) a

Plate elastic

modulus, E

(mm) p

Plate width,

b(GPa)

p

Plate

thickness, t (mm)

pBond length,

L (mm)

(mm)

I

A-NM-T1-I Sika 30 22.34 11.25 1.07 150 50 1.2 300

A-NM-T1-II Sika 30 22.34 11.25 1.03 150 50 1.2 300

B-NM-T1-I Sika 330 31.28 4.82 1.02 150 50 1.2 300

B-NM-T1-II Sika 330 31.28 4.82 1.04 150 50 1.2 300

C-NM-T1-I Araldite 2015 14.73 1.75 0.99 150 50 1.2 300

C-NM-T1-II Araldite 2015 14.73 1.75 1.02 150 50 1.2 300

D-NM-T1-I Araldite 420 21.46 1.83 1.01 150 50 1.2 300

D-NM-T1-II Araldite 420 21.46 1.83 1.03 150 50 1.2 300

II

A-NM-T1.5 Sika 30 22.34 11.25 1.53 150 50 1.2 300

A-NM-T2 Sika30 22.34 11.25 2.06 150 50 1.2 300

A-NM-T3 Sika30 22.34 11.25 3.04 150 50 1.2 300

C-NM-T2 Araldite 2015 14.73 1.75 2.03 150 50 1.2 380

C-NM-T3 Araldite 2015 14.73 1.75 3.04 150 50 1.2 380

III

A-MM-T1 Sika 30 22.34 11.25 1.01 235 50 1.4 300

A-HM-T1 Sika 30 22.34 11.25 1.20 340 50 1.4 300

A-ST-T1 Sika 30 22.34 11.25 1.02 200 50 6.0 300

C-MM-T1 Araldite 2015 14.73 1.75 1.04 235 50 1.4 380

C-HM-T1 Araldite 2015 14.73 1.75 1.02 340 50 1.4 380

140

Table 5.2 Ultimate loads and failure modes

a. Series I: Effect of the adhesive type

Series I

Specimen Adhesive type

Tensile strength

of the adhesive,

σmax

Elastic

modulus of

the adhesive,

E (MPa)

a

Ultimate load,

P

(GPa) u, exp

Failure

mode (kN)

A-NM-T1-I Sika 30 22.34 11.25 30.75 C

A-NM-T1-II Sika 30 22.34 11.25 31.212 C

B-NM-T1-I Sika 330 31.28 4.82 67.76 I

B-NM-T1-II Sika 330 31.28 4.82 62.49 I

C-NM-T1-I Araldite 2015 14.73 1.75 112.87 C

C-NM-T1-II Araldite 2015 14.73 1.75 113.81 C

D-NM-T1-I Araldite 420 21.46 1.83 106.42 C+I

D-NM-T1-II Araldite 420 21.46 1.83 113.62 C+I

b. Series II: Effect of the adhesive layer thickness

Series II*

Specimen Adhesive type

Adhesive

thickness, ta Ultimate load,

(mm) Pu, exp

Failure mode (kN)

A-NM-T1-I Sika 30 1.07 30.75 C

A-NM-T1-II Sika 30 1.03 31.21 C

A-NM-T1.5 Sika 30 1.53 35.20 C

A-NM-T2 Sika30 2.06 40.00 C

A-NM-T3 Sika30 3.04 33.80 C

C-NM-T1-I Araldite 2015 0.99 112.87 C

C-NM-T1-II Araldite 2015 1.02 113.81 C

C-NM-T2 Araldite 2015 2.03 107.20 I

C-NM-T3 Araldite 2015 3.04 109.20 I

141

c. Series III: Effect of the plate axial rigidity

Series III*

Specimen Adhesive

type

Plate

elastic

modulus,

Ep

Plate

thickness,

t(GPa)

p

Plate axial

rigidity,

E(mm)

ptp bp

Ultimate

load,

(kN) Pu, exp

Failure

mode (kN)

A-NM-T1-I Sika 30 150 1.2 9000 30.75 C

A-NM-T1-II Sika 30 150 1.2 9000 31.21 C

A-MM-T1 Sika 32 235 1.4 16450 46.90 C

A-HM-T1 Sika 30 340 1.4 23800 63.80 C

A-ST-T1 Sika 30 200 6.0 60000 74.80 C

C-NM-T1-I Araldite 2015 150 1.2 9000 112.87 C

C-NM-T1-II Araldite 2015 150 1.2 9000 113.81 C

C-MM-T1 Araldite 2015 235 1.4 16450 130.50 C

C-HM-T1 Araldite 2015 340 1.4 23800 84.80 R

C-cohesion failure

I- interlaminar failure of CFRP plate

R- rupture of CFRP plate

* Four specimens of Series I are also treated as part of this series for ease of

presentation.

142

Table 5.3 Key parameters for the experimental bond-slip curves

Series I Specimen Failure

mode

Peak bond

shear

stress, τmax δ

(MPa)

1 δ (mm) 2 δ (mm) f

Interfacial

fracture energy,

G

(mm)

f #

I

(N/mm)

A-NM-T1-I C 17.79 0.046 N/A 0.119 1.06

A-NM-T1-II C 18.52 0.047 N/A 0.144 1.11

C-NM-T1-I C 14.10 0.080 0.780 1.050 12.34

C-NM-T1-II C 14.20 0.080 0.800 1.080 12.78

II

A-NM-T1.5 C 19.81 0.058 N/A 0.129 1.27

A-NM-T2 C 20.59 0.064 N/A 0.150 1.54

A-NM-T3 C 17.96 0.061 N/A 0.124 1.11

III

A-MM-T1 C 18.57 0.047 N/A 0.114 1.06

A-HM-T1 C 18.82 0.044 N/A 0.139 1.31

C-MM-T1 C 14.60 0.085 0.820 0.980 12.52

C-cohesion failure #

fG = area under an experimental bond-slip curve

143

Table 5.4 Comparison of experimental and predicted bond strengths

Series I Specimen

number Adhesive type

Plate elastic

modulus, EpPlate width,

b

(GPa) p

Plate

thickness, t (mm)

p

Interfacial

fracture

energy, G

(mm) f

P

(N/mm)

(kN) u,exp P

(kN) u,predict

Pu,predict/P

I

u,exp

A-NM-T1-I Sika 30 150 50 1.2 1.06 30.75 30.83 1.00

A-NM-T1-II Sika 30 150 50 1.2 1.11 31.21 31.57 1.01

C-NM-T1-I Araldite 2015 150 50 1.2 12.34 112.87 105.37 0.93

C-NM-T1-II Araldite 2015 150 50 1.2 12.78 113.81 107.25 0.94

II

A-NM-T1.5 Sika 30 150 50 1.2 1.27 35.20 33.87 0.96

A-NM-T2 Sika30 150 50 1.2 1.54 40.00 37.26 0.93

A-NM-T3 Sika30 150 50 1.2 1.11 33.80 31.60 0.93

III

A-MM-T1 Sika 30 235 50 1.4 1.06 46.90 41.69 0.89

A-HM-T1 Sika 30 340 50 1.4 1.31 63.80 55.82 0.87

C-MM-T1 Araldite 2015 235 50 1.4 12.52 130.50 143.51 1.10

144

(a) Specimen

(b) Instrumentation

Figure 5.1 Single-shear pull-off test specimen and instrumentation

CFRP plate Free end

Lcfrp

Lsteel

Steel substrate plate h

ta

50mm

x Adhesive

Loaded end

Strain gauges at 20mm cc

LVDT

LVDT

5mm

20mm Steel substrate plate

(Distance to the centre of the first strain gauge from the loaded end)

145

(a) Elevation

(b) Test specimen during testing

Figure 5.2 Test rig

LVDT at the loaded end

CFRP plate

Clamps

Grip

CFRP plate

Bearings

Adhesive

Steel plate

Bottom edge of the steel substrate plate welded to the support block

Support block

Grip

Rollers

Adjustable support

Clamps

146

(a) Failed specimens of Series I

D-NM-T1-I; Failure mode: C+I D-NM-T1-II; Failure mode: C+I

C-NM-T1-I; Failure mode: C C-NM-T1-II; Failure mode: C

B-NM-T1-I: Failure mode: I

B-NM-T1-II; Failure mode: I

A-NM-T1-I: Failure mode: C A-NM-T1-II; Failure mode: C

147

(b) Failed specimens of Series II

A-NM-T1.5; Failure mode: C A-NM-T2; Failure mode: C

A-NM-T3; Failure mode: C

C-NM-T2; Failure mode: I C-NM-T3; Failure mode: I

148

(c) Failed specimens of Series III

Figure 5.3 Failed specimens

A-HM-T1; Failure mode: C A-MM-T1; Failure mode: C

C-HM-T1; Failure mode: R C-MM-T1; Failure mode: C

149

(a) Series I: effect of adhesive type

(b) Series II: effect of adhesive layer thickness (specimens with adhesive A)

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5 3

Load

(kN

)

Displacement (mm)

A-NM-T1-I

A-NM-T1-II

B-NM-T1-I

B-NM-T1-II

C-NM-T1-I

C-NM-T1-II

D-NM-T1-I

D-NM-T1-II

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1 1.2

Load

(kN

)

Displacement (mm)

A-NM-T1-I

A-NM-T1-II

A-NM-T1.5

A-NM-T2

A-NM-T3

150

(c) Series II: effect of adhesive layer thickness (specimens with adhesive C)

(d) Series III: effect of plate axial rigidity (specimens with adhesive A)

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5 3

Load

(kN

)

Displacement (mm)

C-NM-T1-I

C-NM-T1-II

C-NM-T2

C-NM-T3

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2

Load

(kN

)

Displacement (mm)

A-NM-T1-I

A-NM-T1-II

A-MM-T1

A-HM-T1

A-ST-T1

A

151

(e) Series III: effect of plate axial rigidity (specimens with adhesive C)

Figure 5.4 Load-displacement curves

Figure 5.5 Comparison of displacements obtained from LVDT and strain gauge

readings

0

20

40

60

80

100

120

140

0 0.5 1 1.5 2 2.5 3

Load

(kN

)

Displacement (mm)

C-NM-T1-I

C-NM-T1-II

C-MM-T1

C-HM-T1

0

20

40

60

80

100

120

-0.05 0.45 0.95 1.45 1.95 2.45 2.95

Load

(kN

)

Displacement (mm)

From strain readings: C-NM-T1-I

From LVDT readings: C-NM-T1-I

From strain readings: A-NM-T1-I

From LVDT readings: A-NM-T1-I

152

(a) When the applied load uP P≤

(b) When the applied load uP P=

Figure 5.6 Strain distributions in specimen A-NM-T1-I: (a) Variation with load level;

(b) Variation with propagation of debonding

0

500

1000

1500

2000

2500

3000

3500

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


0.25

0.57

0.89

0.96

0.98

0.99

1

0

500

1000

1500

2000

2500

3000

3500

4000

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

Debonding propagation

153



Figure 5.7 Strain distributions in specimen C-NM-T1-I: (a) Variation with load level;

(b) Variation with propagation of debonding

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


0.20.560.850.920.950.991

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


Debonding propagation

Load level P/Pu=

154

(a)A-NM-T1-I

(b)A-NM-T1-II

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

30mm50mm70mm110mm130mm150mm170mm190mm210mm230mm

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

30mm50mm70mm150mm170mm190mm230mm

155

(c) C-NM-T1-I

(d) C-NM-T1-II

0

2

4

6

8

10

12

14

16

18

20

0 0.2 0.4 0.6 0.8 1 1.2Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)


0

2

4

6

8

10

12

14

16

18

20

0 0.2 0.4 0.6 0.8 1 1.2Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

20mm40mm60mm80mm100mm120mm

156

(e) A-NM-T1.5

(f) A-NM-T2

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa) 30mm

50mm70mm90mm110mm150mm170mm190mm210mm

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)


157

(g) A-NM-T3

(h) A-MM-T1

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)


0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

30mm50mm70mm90mm150mm170mm190mm210mm230mm

158

(i) A-HM-T1

(j) C-MM-T1

Figure 5.8 Experimental bond-slip curves for specimens failing in cohesion

failure

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2 0.25 0.3Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

30mm50mm70mm90mm110mm130mm150mm190mm210mm

02468

101214161820

0 0.2 0.4 0.6 0.8 1 1.2Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

20mm40mm60mm80mm100mm

159

(a) Linear adhesives

(b) Non-linear adhesives

Figure 5.9 Idealized bond-slip curves

τ

1δ fδ δ

maxτ

2δ

τ

1δ fδ δ

maxτ

160

Figure 5.10 Comparison between experimental and predicted bond strengths

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

Pre

dict

ed b

ond

stre

ngth

, Pu,

pre

dict

(kN

)

Experimental bond strength, Pu, exp (kN)

2u p p p fP b E t G=

161

(a) Points on the load-displacement curve

(b) Interfacial shear stress distributions

Figure 5.11 Interfacial shear stress distributions of A-NM-T1-I at different stages of

deformation

0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8 1Displacement (mm)

Load

(kN

)

0

5

10

15

20

25

30

0 50 100 150 200 250 300Distance from the loaded end (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

ABCDEFG

A

B

C

D E F G

162

(a) Points on the load-displacement curve

(b) Interfacial shear stress distributions

Figure 5.12 Interfacial shear stress distributions of C-NM-T1-I at different stage of

deformation

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5 3Displacement (mm)

Load

(kN

)

-5

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350


Inte

rfaci

al s

hear

stre

ss (M

Pa)

ABCDEFGH

A

B

C

D

E F G H

163

APPENDIX 5.1 ADDITIONAL FIGURES



Figure A5.1 Strain distributions with (a) increasing load level (P/Pu

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 50 100 150 200 250 300

CFR

P p

late

axi

al S

train

s (µε)


0.25

0.57

0.88

0.94

0.98

1

); (b) damage

propagation for A-NM-T1-II specimen

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

164

Figure A5.2 Strain distributions with increasing load level (P/Pu

) B-NM-T1-I

specimen


) B-NM-T1-II

specimen

0

1000

2000

3000

4000

5000

6000

7000

8000

0 50 100 150 200 250 300

CFR

P p

late

axi

al S

train

s (µε)


0.22

0.45

0.72

0.88

0.97

1

0

1000

2000

3000

4000

5000

6000

7000

8000

0 50 100 150 200 250 300

CFR

P p

late

axi

al S

train

s (µε)


0.24

0.55

0.76

0.89

0.97

1

Load level P/Pu=

Load level P/Pu=

165




0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al S

train

s (µε)


0.22

0.54

0.83

0.91

0.97

1

); (b) damage

propagation for C-NM-T1-II specimen

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

166




); (b) damage

propagation for D-NM-T1-I specimen

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al S

train

s (µε)


0.21

0.50

0.78

0.90

0.98

1

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

167




0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al S

train

s (µε)


0.20

0.50

0.79

0.90

0.98

1

); (b) damage

propagation for D-NM-T1-II specimen

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

168




0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.20

0.50

0.79

0.90

0.98

1

); (b) damage

propagation for A-NM-T1.5 specimen

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 100 200 300 400

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

169




0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.21

0.50

0.78

0.89

0.98

1

); (b) damage

propagation for A-NM-T2 specimen

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 100 200 300 400

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

170

(a) When the applied load uP P=



0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.20

0.50

0.78

0.89

0.98

1

); (b) damage

propagation for A-NM-T3 specimen

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

171


) for C-NM-T3

specimen


0

2000

4000

6000

8000

10000

12000

14000

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.20

0.50

0.78

0.89

0.98

1

for C-NM-T2

specimen

0

2000

4000

6000

8000

10000

12000

14000

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.20

0.50

0.78

0.89

0.98

1

Load level P/Pu=

Load level P/Pu=

172




0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.20

0.50

0.78

0.89

0.98

1

); (b) damage

propagation for A-MM-T1 specimen

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

173




0

200

400

600

800

1000

1200

1400

1600

1800

0 50 100 150 200 250 300

CFR

P p

late

axi

al S

train

s (µε)


0.21

0.50

0.78

0.87

0.98

1

); (b) damage

propagation for A-HM-T1 specimen

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 50 100 150 200 250 300

CFR

P p

late

axi

al s

train

( µε

)


Load level P/Pu=

174


) for A-ST-T1

specimen


0

200

400

600

800

1000

1200

1400

1600

1800

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.21

0.50

0.78

0.87

0.98

1

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.21

0.50

0.78

0.87

0.98

1

Load level P/Pu=

Load level P/Pu=

175



); (b) damage

propagation for C-MM-T1 specimen


) for C-HM-T1

specimen

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 100 200 300 400

CFR

P p

late

axi

al s

train

( µε

)


0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400

CFR

P p

late

axi

al S

train

s (µε)


0.21

0.50

0.78

0.87

0.98

1

Load level P/Pu=

176

(a) B-NM-T1-I

(b) B-NM-T1-II

0

5

10

15

20

25

30

35

0 0.05 0.1 0.15 0.2

Inte

rfaci

al s

hear

stre

ss (M

Pa)

Slip (mm)

12.25mm

30mm

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2

Inte

rfaci

al s

hear

stre

ss (M

Pa)

Slip (mm)

12.25mm

30mm

177

(c) D-NM-T1-I

(d) D-NM-T1-II

Figure A5.17 Experimental bond-slip curves for specimens in series-I

0

2

4

6

8

10

12

14

16

18

20

0 0.2 0.4 0.6 0.8 1 1.2Slip (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)


02468

101214161820

0 0.2 0.4 0.6 0.8 1 1.2

Inte

rfaci

al s

hear

stre

ss (M

Pa)

Slip (mm)


178

(a) C-NM-T2

(b) C-NM-T3

Figure A5.18 Experimental bond-slip curves for specimens in series-II

02468

101214161820

0 0.2 0.4 0.6 0.8 1 1.2

Inte

rfaci

al s

hear

stre

ss (M

Pa)

Slip (mm)

30mm50mm70mm90mm110mm

02468

101214161820

0 0.2 0.4 0.6 0.8 1 1.2

Inte

rfaci

al s

hear

stre

ss (M

Pa)

Slip (mm)


179

Figure A5.19 Experimental bond-slip curves for specimens in series-III

02468

101214161820

0 0.2 0.4 0.6 0.8 1 1.2

Inte

rfaci

al s

hear

stre

ss (M

Pa)

Slip (mm)

30mm50mm70mm90mm

180

CHAPTER 6 THEORETICAL MODEL FOR FULL-RANGE

BEHAVIOUR OF CFRP-TO-STEEL BONDED JOINTS

6.1 INTRODUCTION Chapter 5 has presented a comprehensive experimental study on the behaviour of

CFRP-to-steel bonded joints and examined the effect of several parameters including

the material properties and the thickness of the adhesive and the axial stiffness of the

CFRP plate. This chapter is concerned with the modelling of the behaviour of such

bonded joints, based on the experimental study presented in Chapter 5.

A bond-slip model depicts the relationship between the bond shear stress and the

relative slip between the two adherends bonded together. An accurate bond-slip

model for the CFRP-to-steel interface is of fundamental importance to the accurate

modelling and hence understanding of debonding failures in CFRP-strengthened

steel structures. A number of bond-slip models have been developed for

FRP-to-concrete interfaces (Lu et al. 2005), but only one bond-slip model exists for

CFRP-to-steel interfaces. This existing model was proposed by Xia and Teng (2005)

based on their limited results of bonded joint tests formed with linear adhesives. This

model therefore needs to be further examined with the new test results presented in

Chapter 5 for CFRP-to-steel interfaces with linear adhesives, and is apparently

unsuitable for interfaces formed using non-linear adhesives, as discussed in Chapter

5.

In this chapter, two new bond-slip models are first established for linear adhesives

and non-linear adhesives respectively based on the new test results and those of Xia

and Teng (2005). By making use of a bond-slip model for the interface, the entire

debonding propagation process of a bonded joint can be predicted, as illustrated by

Yuan et al. (2004) for FRP-to-concrete bonded joints. This chapter presents a

theoretical model (an analytical solution) for predicting the entire debonding

propagation process (i.e. full-range behaviour) of CFRP-to-steel bonded joints,

181

employing the new bond-slip models proposed in this chapter. Expressions for the

interfacial shear stress (i.e. bond shear stress) distribution and the load-displacement

response are derived for different loading stages, following the approach of Yuan et

al. (2004).

It has been shown in Chapter 5 that the simple bond strength model of Eqn 5.3

originally derived based on a fracture mechanics approach for FRP-to-concrete

bonded joints also works well for CFRP-to-steel bonded joints with an infinite (or a

sufficiently large) bond length, given that the interfacial fracture energy to be used in

this equation is accurate. In this chapter, this bond strength model is further examined

in the process of developing the analytical solution for the full-range behaviour of

bonded joints employing the newly proposed bond-slip models. An equation is also

proposed for the definition of the effective bond length.

6.2 INTERFACIAL FRACTURE ENERGY UNDER MODE II LOADING

The interfacial fracture energy fG is an essential parameter in determining both the

bond-slip behaviour of an interface and the bond strength of a bonded joint (Eqn 5.3).

Therefore, it is necessary to develop a model which can predict the interfacial

fracture energy of CFRP-to-steel bonded joints from the basic properties of the joints

(e.g. geometrical and material properties of the adhesive layer). Among the existing

studies, Xia and Teng (2005) has proposed the only equation for predicting fG of

CFRP-to-steel interfaces based on their experimental study using linear adhesives.

The equation proposed by Xia and Teng (2005) is given below:

0.56

0.27max62f aa

G tG

σ =

(N/mm2.mm) (6.1)

where aG and at are the shear modulus and thickness of the adhesive layer

respectively.

In Figure 6.1, the predictions of Eqn 6.1 are compared with the test results given in

Chapter 5 and those of Xia and Teng (2005). It is evident from Figure 6.1 that

182

although Eqn 6.1 provides reasonable predictions for linear adhesives, it

underestimates the interfacial fracture energy of non-linear adhesives.

The test results presented in Chapter 5 showed that non-linear adhesives with a

lower elastic modulus but a larger strain capacity can lead to a much higher

interfacial fracture energy than linear adhesives with a similar or even a higher

tensile strength. Further examination of the test data (Figure 6.2) indicates that the

interfacial facture energy is proportional to the square of the tensile strain energy of

the adhesive. Chapter 5 also showed that fG increases with the adhesive

thickness, and it is further shown in Figure 6.3 that fG is approximately

proportional to the square root of the adhesive thickness. Based on the above

observations, the following best-fit equation is proposed to predict fG based on

the test results presented in Chapter 5:

0.5 2628f aG t R= (N/mm2.mm) (6.2)

where at is the adhesive thickness in mm and R is the tensile strain energy of the

adhesive which is equal to the area under the uni-axial tensile stress (in MPa)-strain

curve.

In Figure 6.1, the predictions of Eqn 6.2 are compared with the test results from

Chapter 5 and Xia and Teng (2005). In Xia and Teng (2005), the interfacial fracture

energy values are not reported, so they were calculated from the corresponding

bond strengths, making use of Eqn 5.3. For the adhesives used in Xia and Teng

(2005) whose tensile stress-strain curve is not provided, it was assumed to be a

linear-elastic material and the strain energy was taken to be 2max 2 aEσ , with aE

being the elastic modulus of the adhesive. It is evident from Figure 6.1 that Eqn 6.2

provides accurate predictions of all the available test results (mean value of

predicted fG /experimental fG = 0.95, coefficient of variation = 15.1%). Even

when only linear adhesives are considered, Eqn 6.2 is seen to be superior to (the

mean value of predicted fG /experimental fG = 0.93, coefficient of variation =

183

10.7% ) Eqn 6.1 proposed by Xia and Teng (2005) (mean value of predicted fG

/experimental fG = 1.08, coefficient of variation = 13.1%). However, as the Eqn

6.2 was obtained using limited available data, when more experimental data become

available, Eqn 6.2 may be re-calibrated to increase the accuracy of predictions

(mainly by adjusting the constant, i.e. 628).

6.3 BOND-SLIP MODELS FOR CFRP-TO-STEEL BONDED INTERFACES

6.3.1 Linear Adhesives

Chapter 5 has shown that the bond-slip curves of CFRP-to-steel interfaces with a

linear adhesive (e.g. adhesive A in Chapter 5) have an approximately bi-linear

shape, containing an ascending branch and a descending branch. Further

examination of the bond-slip curves (see Figure 5.8) revealed that: (1) the initial

stiffness of the bond–slip curve is significantly larger than the secant stiffness at the

peak point; and (2) the slope of the descending branch decreases with increases in

the slip. The above observations suggest that the shape of the bond-slip curve for a

CFRP-to-steel interface is very similar to that of an FRP-to-concrete interface (Lu et

al. 2005). Therefore, the general forms of bond-slip models for the latter may be

used for the former, but the key parameters (e.g. maxτ , 1δ and fG ) need to be

defined differently based on test data of CFRP-to-steel bonded joints.

For FRP-to-concrete interfaces, the most accurate bond-slip models appear to be

those proposed by Lu et al. (2005) (Yao et al. 2005). In the present study, two of the

models proposed by Lu et al. (2005) are revised for use with CFRP-to-steel

interfaces, namely, the simplified model (called “the accurate model” in the present

study) which captures the above mentioned characteristics of a non-linear bond-slip

curve and the idealized bi-linear model (Lu et al. 2005). It should be noted that Lu

et al. (2005) also proposed a more sophisticated model referred to by them as “the

precise bond-slip model” based on their meso-scale finite element model, but a

number of the parameters of the precise model are dependent on the

three-dimensional constitutive behaviour of concrete which is different from that of

an adhesive, so this complex model is not further considered in the present study. It

184

should also be noted that Xia and Teng (2005) also proposed a bi-linear bond-slip

model for CFRP-to-steel interfaces. The bi-linear model proposed in the present

study is different from and superior to Xia and Teng’s (2005) model in that the

expressions for the key parameters are more accurate, as explained below.

6.3.1.1 Accurate model

The simplified model proposed by Lu et al. (2005) takes the following form:

max 11

ifδτ τ δ δδ

= ≤ (6.3a)

max 11

exp 1 ifδτ τ α δ δδ

= − − >

(6.3b)

max 1

max 1

33 2fG

τ δατ δ

=−

(6.3c)

where τ is the bond shear stress and δ is the slip. The expressions proposed by

Lu et al. (2005) for maxτ , 1δ and fG are not given here as these expressions are

not applicable to CFRP-to-steel interfaces, due to the significant differences

between CFRP-to-steel bonded joints and FRP-to-concrete bonded joints as

discussed earlier.

In the proposed model, Eqn 6.2 is adopted for fG . For both linear adhesives and

non-linear adhesives, the peak bond shear stress maxτ was found to be independent

of the adhesive thickness and the axial stiffness of the FRP plate (see Chapter 5).

Therefore, the following best-fit equation is proposed based on the test data

summarized in Table 5.3:

max max0.9τ σ= (6.4)

185

Chapter 5 showed that the slip at peak bond shear stress 1δ generally decreases

with the thickness of the adhesive layer. For CFRP-to-steel bonded joints with a

linear adhesive, it is reasonable to expect that 1δ is related to the stiffness of the

adhesive layer and the peak bond shear stress maxτ . Based on this consideration, the

following best-fit equation was obtained from the test data summarized in Table

5.3:

0.65

1 max0.3 a

a

tG

δ σ

=

(6.5)

It should be noted that Eqn 6.4 is applicable to both linear adhesives and non-linear

adhesives, but Eqn 6.5 is only applicable to linear adhesives. Comparisons between

the predictions of Eqns 6.4 and 6.5 and the test results are shown in Figures 6.4 and

6.5 respectively. It should also be noted that Xia and Teng (2005) did not report the

experimental peak bond shear stress or the corresponding slip for their specimens,

so only the data from Chapter 5 (Table 5.3) were used in the development of Eqns

6.4 and 6.5.

To summarize, the proposed accurate bond-slip model for CFRP-to-steel interfaces

with a linear adhesive includes Eqns 6.3a-c from Lu et al. (2005) and Eqns 6.2, 6.4

and 6.5 proposed in this section. The predictions of the proposed accurate bond-slip

model are compared with the experimental bond-slip curves in Figure 6.6, and a

very close agreement can be seen.

6.3.1.2 Bi-linear model

A bi-linear bond-slip model (Lu et al. 2005) can be expressed as:

max 11

ifδτ τ δ δδ

= ≤ (6.6a)

max 11

ff

f

ifδ δ

τ τ δ δ δδ δ

−= < ≤

− (6.6b)

186

0 fifτ δ δ= > (6.6c)

max

2 ff

Gδ

τ= (6.6d)

It is easy to note that there are three independent parameters in defining the bi-linear

bond-slip model. Given that Eqns 6.2, 6.4 and 6.5 are used to define fG , maxτ and

1δ respectively, the bond-slip curve can be uniquely determined by Eqns 6.6a-d.

The proposed bi-linear bond-slip model therefore includes Eqns 6.2 and 6.4-6.6.

The predictions of the proposed bi-linear bond-slip model are also compared with

the experimental bond-slip curves in Figure 6.6. It is evident that the predictions

generally agree well with the experimental curves, despite their underestimation of

the initial stiffness. The underestimation is due to the fact that in the bi-linear

bond-slip model, the ascending branch has a constant slope determined by the

secant stiffness of the experimental curve (Eqn 6.6a).

6.3.2 Non-Linear Adhesives

The available experimental results for CFRP-to-steel bonded joints with a

non-linear adhesive are very limited: only three such bonded joints with one single

type of adhesive were tested in the study presented in Chapter 5; all of them failed

in the cohesion failure mode. These limited test results, however, clearly showed

that the bond-slip curves of these interfaces have an approximately trapezoidal

shape which is quite different from those of the CFRP-to-steel interfaces with a

linear adhesive. In this section, a preliminary bond-slip model is proposed based on

the limited test results. Apparently, further development and verification of the

model is needed in the future.

The proposed model, predicting a trapezoidal curve, can be expressed in the

following expressions:

187

max 11

ifδτ τ δ δδ

= ≤ (6.7a)

max 1 2ifτ τ δ δ δ= < ≤ (6.7b)

max 22

ff

f

ifδ δ

τ τ δ δ δδ δ

−= < ≤

− (6.7c)

0 fifτ δ δ= > (6.7d)

As discussed earlier, Eqn 6.2 for fG and Eqn 6.4 for maxτ are also applicable to

non-linear adhesives. Therefore, only two additional independent parameters need

to be defined for the trapezoidal bond-slip model. A review of the test data in Table

5.3 leads to the following two equations:

1 0.081δ = (mm) (6.7e)

2 0.80δ = (mm) (6.7f)

With Eqns 6.2, 6.4 and 6.7 a-f, fδ can be determined by the following equation:

1max 2

2max

22f

f

G δτ δδ δ

τ

− − = + (6.7g)

It should be noted that in Eqns 6.7e and f, 1δ and 2δ are taken as constants because

of the limited test data which is from three bonded joint tests with the same type and

thickness of adhesive. It can however be expected that 1δ and 2δ should vary with

the properties of the adhesive layer (e.g. the stiffness and strength of the adhesive).

188

Therefore, further research is needed to develop equations for 1δ and 2δ that are

related to the mechanical properties of the adhesive.

Predictions from this trapezoidal model are in close agreement with the

experimental results as shown in Figure 6.7. This is no surprise as the same test data

are used to determine the parameters of the bond-slip curve.

6.4 FULL-RANGE BEHAVIOUR OF CFRP-TO-STEEL BONDED JOINTS

An experimental investigation into the full-range behaviour of CFRP-to-steel

bonded joints was presented in Chapter 5. Yuan et al. (2004) presented an analytical

solution for the entire debonding propagation process (i.e. the full-range behaviour)

for FRP-to-concrete bonded joints based on a bi-linear bond-slip model. Their

analytical solution can be directly used to predict the full-range behaviour of

CFRP-to-steel bonded joints with linear adhesives provided the expressions for the

three key parameters (i.e. maxτ , 1δ and fG ) are replaced with expressions for

CFRP-to-steel bonded interfaces. This section therefore focuses on the development

of an analytical solution for CFRP-to-steel bonded joints with a non-linear adhesive,

where a trapezoidal bond-slip model is used.

6.4.1 Governing Equations

The analytical solution to be presented in this section is for a typical single-shear

pull-off test of CFRP-to-steel bonded joint (see Figure 6.8). The thickness and the

width of all the three components (i.e. CFRP, adhesive and steel) are constant along

the length. The width and thickness of the CFRP plate are denoted by pb and pt

respectively, and those of the steel plate denoted by stb and stt respectively. The

width of the adhesive layer is taken to be equal to pb and the thickness of the

adhesive layer is denoted by at . The bond length of the plate (referred to as “the

bond length” hereafter) is denoted by L . The elastic moduli of the CFRP plate and

the substrate steel plate are denoted by pE and stE respectively.

189

Based on the test observations presented in Chapter 4, it is assumed that the

adhesive layer is subjected only to shear deformation. It is further assumed that both

adherends (i.e. the CFRP plate and the steel substrate plate) are subjected to

uniformly-distributed axial stresses and the adhesive layer is subjected only to shear

stresses which are constant over the thickness. With these assumptions, the

following fundamental equations can be derived (Wu et al. 2002; Yuan et al. 2004)

based on force equilibrium considerations (Figure 6.9):

0p

p

ddx tσ τ

− = (6.8a)

0p p p st st stt b t bσ σ+ = (6.8b)

τ is the shear stress in the adhesive layer (i.e. interfacial shear stress), pσ is the

axial stress in the CFRP plate and stσ is the axial stress in the steel plate.

Considering that the two adherends (i.e. CFRP and steel) both behave

linear-elastically and the interfacial shear stress is a function of the interfacial slip (

δ ), the constitutive equations can be expressed as

( )fτ δ= (6.8c)

pp p

duE

dxσ = (6.8d)

stst st

duEdx

σ = (6.8e)

where pu and stu are the displacements of the CFRP plate and the steel plate

respectively. The interfacial slip δ can then be defined as

p stu uδ = − (6.8f)

190

From Eqns 6.8b, d and e, the following equation can be obtained:

0p stp p p st st st

du duE t b E t bdx dx

+ = (6.8g)

Differentiating Eqn 6.8f with respect to x yields the following:

p stdu duddx dx dxδ

= − (6.8h)

Substituting Eqn 6.8g into Eqn 6.8h yields the following:

p p p p p

st st st

du E t b duddx dx E t b dxδ

= + (6.8i)

Differentiating Eqn 6.8i with respect to x yields the following:

22

2 2

1p pp p

p p st st st

d u bd E tdx dx E t E t b

δ = +

(6.8j)

Differentiating Eqn 6.8d with respect to x yields the following:

2

2p p

p

d d uE

dx dxσ

= (6.8k)

By defining a parameter λ as

2

2 max 12

p

f p p st st st

bG E t E t b

τλ

= +

(6.8l)

the following equation can be obtained by substituting Eqns 6.8c, j, k and l into Eqn

6.8a:

191

( )2

22 2

max

20fGd f

dxδ λ δ

τ− = (6.8m)

where maxτ is the peak bond shear stress and fG is the interfacial fracture

energy.

Eqn 6.8m is the governing differential equation of the bonded joint shown in Figure

6.8, and can be solved if the bond-slip model which relate the interfacial shear stress

to the slip is defined.

6.4.2 Analytical Solution for Linear Adhesives

As discussed earlier, the analytical solution developed by Yuan et al. (2004) can be

easily revised for CFRP-to-steel bonded joints with linear adhesives, because of

their use of a bi-linear bond-slip model. Yuan et al.’s (2004) solution includes

expressions for different loading stages (i.e. elastic stage, elastic-softening stage,

elastic-softening-debonding stage, and softening-debonding stage). In the next

section, an analytical solution is presented for CFRP-to-steel bonded joints with a

non-linear adhesive, employing a trapezoidal bond-slip model (Figure 6.10). As a

trapezoidal bond-slip model can be reduced to a bi-linear model by taking 1 2δ δ= ,

the analytical solution developed in the next section is also applicable to linear

adhesives. Therefore, the analytical solution for CFRP-to-steel bonded joints with a

linear adhesive is not given separately here.

6.4.3 Analytical Solution for Non-Linear Adhesives

The trapezoidal bond-slip model proposed in the present study (i.e. Eqns 7a-d) is

employed in developing the analytical solution for CFRP-to-steel bonded joints

with a non-linear adhesive. With this bond-slip model, Eqn 6.8m can be solved to

find the interfacial shear stress distribution and the load-displacement behaviour.

With reference to the experimental full-range behaviour explained in Chapter 5, the

solution is presented for the following loading stages: (1) elastic stage; (2)

elastic-plastic stage; (3) elastic-plastic-softening stage; (4)

192

elastic-plastic-softening-debonding stage; (5) plastic-softening-debonding stage;

and (6) softening-debonding stage, as illustrated in Figure 6.11. It should be noted

that the six loading stages all exist only for bonded joints with a sufficiently large

bond length.

6.4.3.1 Elastic stage

In the initial stage of loading, the bonded joint is subjected to a small load and the

entire length of the interface is in the elastic range with maxτ τ≤ (Figure 6.11 a).

The following equation can be obtained by substituting Eqn 6.7a into Eqn 6.8m:

2

2 max2 2

max 1

20fGd

dxτ δδ λ

τ δ− = (6.9a)

Taking

2 21

max 1

2 fGλ λ

τ δ= (6.9b)

Eqn 6.9a can be rewritten as

2

212 0d

dxδ λ δ− = (6.9c)

From Eqns 6.8d and i it is easy to arrive at

2max max

2 21 12p

f p p

d dG t dx t dxτ τδ δσ

λ δ λ= = (6.9d)

The boundary conditions for the elastic stage are: (1) at x = 0, 0pσ = ; and (2) at x

= L, pp p

Pb t

σ = , where P is the applied load. Solving Eqn 6.9c with these boundary

193

conditions, the following expressions for the interfacial slip, the interfacial shear

stress and the plate axial stress can be found:

( )( )

11 1

max 1

coshsinhp

xPb L

λδ λδτ λ

= (6.9e)

( )( )

11

1

coshsinhp

xPb L

λλτλ

= (6.9f)

( )( )

1

1

sinhsinhp

p p

xPb t L

λσ

λ= (6.9g)

During this stage of loading, the interfacial shear stress distribution is shown in

Figure 6.11a. Taking the slip at the plate end (i.e. x = L) as ∆ , the following

load-displacement relationship can be obtained from Eqn 6.9e:

( )max1

1 1

tanhpbP L

τλ

λ δ∆

= (6.9h)

The elastic stage depicted by Eqn 6.9 is shown as segment OA of the

load-displacement curve (Figure 6.12). The length of the interface that is mobilized

to resist the applied load is generally referred to as the effective bond length. The

effective bond length ,e eL is defined here as the bond length over which the shear

stresses offer a total resistance which is at least 97% of the applied load for a joint

with an infinite bond length. With this definition,

( )1 ,tanh e eLλ =0.97 (6.9i)

The effective bond length during the elastic stage is thus given by:

,1

2e eL

λ= (6.9j)

194

The end of the elastic stage is when the interfacial shear stress at the plate end (x=L)

reaches maxτ at a slip of 1δ . By substituting 1δ∆ = into Eqn 6.9h, the maximum

load at the end of the elastic stage (or at the beginning of the elastic-plastic stage)

can be found as

( )max1,max 1

1

tanhpbP L

τλ

λ= (6.9k)

6.4.3.2 Elastic-plastic stage

After the interfacial shear stress at the plate end (x = L) reaches maxτ ( 1δ∆ = )

(point A in Figure 6.12), the joint enters the elastic-plastic stage where the

interfacial shear stress over a certain length is constant and is equal to the peak bond

shear stress. This stage is illustrated in Figure 6.11c. In this stage, part of the

CFRP-to-steel bonded interface is in the plastic state (i.e. State II, see Figure 6.11)

while the rest remains in the elastic state (i.e. State I, see Figure 6.11). The load

continues to increase as the length of the plastic region a increases.

Substituting Eqn 6.7a (i.e. for 10 δ δ≤ ≤ ) into Eqn 6.8m yields:

2

212 0d

dxδ λ δ− = (6.10a)

By making use of the following boundary conditions: (1) at x = 0, 0pσ = ; and (2)

at x = L-a, 1δ δ= , the following solution for the elastic region can be found:

( )( )( )

11

1

coshcosh

xL aλ

δ δλ

=−

(6.10b)

( )( )( )

1max

1

coshcosh

xL aλ

τ τλ

=−

(6.10c)

195

( )( )( )

1max

1 1

sinhcoshp

p

xt L a

λτσλ λ

=−

(6.10d)

Substituting Eqn 6.7b (i.e. for 1 2δ δ δ≤ ≤ ) into Eqn 6.8m yields

2

21 12 0d

dxδ λ δ− = (6.10e)

By making use of the following boundary conditions: (1) at x = L-a,

( )( )max1

1

tanhpp

L atτσ λ

λ= − ; and (2) at x = L-a, 1δ δ= , the solution for the plastic

region can be obtained as

( )( ) ( ) ( ) ( ) ( )( )221 12 2 21 1

1 1 1 1 21 1 1

tanh tanh12 2

L a L a L aL ax L a x

λ λλ δδ λ δ λ δλ λ λ

− − −−= + − − + + −

(6.10f)

maxτ τ= (6.10g)

( )( ) ( )1max

1

tanhp

p

L ax L a

tλτσλ

−= + − −

(6.10h)

Considering that at x = L, pp p

Pb t

σ = , the applied load P for a given length of

plastic region a can be obtained as

( )( )maxmax 1

1

tanhp pP ab b L aττ λλ

= + − (6.10i)

The displacement at x = L for a given length of plastic region a is given by

( )( )2

21 11 1 1 1tanh

2a a L aλ δ δ λ δ λ∆ = + + − (6.10j)

196

The distribution of the interfacial shear stress during this stage is illustrated in

Figure 6.11c. Segment AB of the load-displacement curve (Figure 6.12) represents

this stage. For an infinite bond length, the maximum load at this stage is reached

when at x=L, δ reaches 2δ . At this moment, from Eqn 6.10f the following

equation can be obtained:

( )( ) ( ) ( ) ( ) ( )( )221 12 2 21 1

2 1 1 1 1 21 1 1

tanh tanh12 2

L a L a L aL aL L a L

λ λλ δδ λ δ λ δλ λ λ

− − −−= + − − + + −

(6.10k)

which yields

( )( ) 2 1 11

1 1

tanh2aL a

aδ δ λλλ δ

−− = − (6.10l)

Substituting Eqn 6.10l into 6.10i yields

2 12,max max 2

1 12paP b

aδ δτλ δ

−= +

(6.10m)

Considering that at the maximum value of P, the derivative of P with respect to a is

zero, the maximum length of the plastic region can be found as

2 12

1 12da δ δλ δ−

= (6.10n)

Substituting Eqn 6.10n into 6.10m yields

2 12,max max 2

1 1

1 22 2pP b δ δτ

λ δ− = +

(6.10o)

197

With the same definition for the effective bond length as described earlier, the

effective bond length at the end of this stage can be found from Eqn 6.10l and m as

( ) ( ) ( )( ) ( ) ( )

221 1 2 1 1 1

2, 221 1 1 2 1 1 1

2 0.97 2 0.9710.97 ln2 2 0.97 2 0.97

d de d

d d

a aL a

a aλ δ δ δ λ δ

λ λ δ δ δ λ δ

+ − −= +

− − + (6.10p)

6.4.3.3 Elastic-plastic-softening stage

Once the slip at the plate end (x = L) reaches 2δ , softening of the adhesive initiates,

and the joint enters the elastic-plastic-softening stage. In this stage, one part of the

interface is in the softening state (i.e. state III, see Figure 6.11), another part of the

interface is in the plastic state (i.e. state II) while the rest is in the elastic state (i.e.

state I) (Figure 6.11e). The load continues to increase as the length of the softening

region b increases. This stage is shown as segment BC of the load-displacement

curve in Figure 6.12.

Substituting Eqn 6.7a (i.e. for 10 δ δ≤ ≤ ) into Eqn 6.8m yields:

2

212 0d

dxδ λ δ− = (6.11a)

Using the two boundary conditions of (1) at x=0, 0pσ = ; and (2) at dx L a b= − −

, 1δ δ= , solving Eqn 6.11a yields the following equation for the elastic region:

( )( )( )

11

1

coshcosh d

xL a b

λδ δ

λ=

− − (6.11b)

( )( )( )

1max

1

coshcosh d

xL a b

λτ τ

λ=

− − (6.11c)

( )( )( )

1max

1 1

sinhcoshp

p d

xt L a b

λτσλ λ

=− −

(6.11d)

198

Substituting Eqn 6.7b (i.e. for 1 2δ δ δ≤ ≤ ) into Eqn 6.8m yields

2

21 12 0d

dxδ λ δ− = (6.11e)

Using the boundary conditions of (1) at dx L a b= − − ,

( )( )max1

1

tanhp dp

L a btτσ λ

λ= − − ; and (2) dx L a b= − − , 1δ δ= , solving Eqn 6.11e

yields the following equations for the plastic region:

( )( ) ( )

( ) ( ) ( )( )

212 21 1

1 11

212

1 1 21 1

tanh2

tanh12

dd

d dd

L a bx L a b x

L a b L a bL a b

λλ δδ λ δλ

λλ δ

λ λ

− −= + − − −

− − − −− −

+ + −

(6.11f)

maxτ τ= (6.11g)

( )( ) ( )1max

1

tanh dp d

p

L a bx L a b

tλτσ

λ

− −= + − − −

(6.11h)

Similarly, substituting Eqn 6.7c (i.e. for 2 fδ δ δ≤ ≤ ) into Eqn 6.8m yields

2

2 22 22 0f

ddx

δ λ δ λ δ− + = (6.11i)

where

( )2 22

max 2

2 f

f

Gλ λ

τ δ δ=

− (6.11j)

199

Using the boundary conditions of (1) at x L b= − ,

( )( )1

1

tanh dfp d

p

L a ba

tλτ

σλ

− −= +

; and (2) x L b= − , 2δ δ= solving Eqn 6.11i

yields the following equations for the softening region:

( )( )( ) ( )( ) ( ) ( )( )1 11 1 2 2 2

2

tanh sin cosf d d fL a b a L b x L b xλ δδ δ λ λ λ δ δ λλ

= − − − + − − + − − −

(6.11k)

( )( )( ) ( )( ) ( ) ( )( )max 1 11 1 2 2 2

2 2

tanh sin cosd d ff

L a b a L b x L b xτ λ δτ λ λ λ δ δ λδ δ λ

= − − + − − + − − − −

(6.11l)

( )( )( ) ( )( ) ( ) ( )( )max 2 1 11 1 2 2 22

1 1 2

tanh cos sinp d d fp

L a b a L b x L b xt

τ λ λ δσ λ λ λ δ δ λ

δ λ λ

= − − + − − − − − −

(6.11m)

Considering that at x=L, pp p

Pb t

σ = , the applied load P for a given length of the

softening region b can be obtained from Eqn 6.11m as

( )( )( ) ( ) ( ) ( )max 2 1 11 1 2 2 22

1 1 2

tanh cos sinpd d f

bP L a b a b b

τ λ λ δ λ λ λ δ δ λδ λ λ

= − − + + −

(6.11n)

The displacement at x=L for a given length of the softening region b is given by

( )( )( ) ( ) ( ) ( )1 11 1 2 2 2

2

tanh sin cosf d d fL a b a b bλ δδ λ λ λ δ δ λλ

∆ = + − − + − − (6.11o)

The distribution of the interfacial shear stress during this stage is illustrated in

Figure 6.11e. Segment BC of the load-displacement curve (Figure 6.12) represents

this stage. For an infinite bond length, the bond strength of the bonded joint is

reached when at x=L, δ reaches fδ . At this moment, the following equation can

be obtained from Eqn 6.11k:

200

( )( )( ) ( ) ( ) ( )1 11 1 2 2 2

2

tanh sin cos 0d d fL a b a b bλ δ λ λ λ δ δ λλ

− − + − − = (6.11p)

Eqn 6.11p can be further written as

( )( ) ( ) ( )21 1 2 2

1 1

tanh cotd d fL a b a bλλ λ δ δ λλ δ

− − + = − (6.11q)

Substituting Eqn 6.11q into 6.11n yields

( )( )

2max 22

1 1 2sinfp

u

bP

bδ δτ λ

δ λ λ

−= (6.11r)

In general, b can only be found from Eqn 6.11q by iteration. However, for bonded

joints with an infinite bond length, the bond strength expressed by Eqn 6.11r

converges to:

max pu

bP

τλ

= (6.11s)

Therefore, the effective bond length eL defined in the same manner as in Eqn

6.10p can be deduced from Eqns 6.11q and r as

1

1 1ln1e d e

CL a bCλ

+= + +

− (6.11t)

where

( ) ( )22 2 1

1 1

cotf e dC b aλ δ δ λ λλ δ

= − − (6.11u)

201

( )222

2 1 1

1 arcsin0.97e fb λ λ δ δ

λ δ λ

= −

(6.11v)

6.4.3.4 Elastic-plastic-softening-debonding stage

Once the slip at the plate end (x=L) reaches fδ (where the interfacial shear stress

reaches zero), debonding initiates and the joint enters the

elastic-plastic-softening-debonding stage (Figure 6.11f). At the beginning of the

stage, the length of the softening region for joints with an infinite bond length can

be found from Eqn 6.11q as

( )( )

2 2

2 1 1 1

1 arctan1

fd

d

ba

δ δ λ

λ λ δ λ

−=

+ (6.12a)

In this stage, no further increase in the load occurs. The interfacial shear stress

distribution profile shown in Figure 6.11f keeps moving towards the free end in this

stage. This stage is shown as segment CDE of the load-displacement curve in

Figure 6.12, where point D represents a state when the right tip of the interfacial

shear stress distribution profile reaches the free end (i.e. when the slip at the free

end of the joint starts to be nonzero). Four possible stress states exist in this stage,

namely, states I, II and III introduced earlier and state IV representing the

zero-stress state (i.e. debonded state). Taking the length of the debonded region as

d, Eqn 6.11m is still valid if L is replaced by ( )L d− . The load-displacement

relationship in this stage can then be written as

( )( )( ) ( )

( ) ( )

1 11 1 2

max 2 22

1 12 2

tanh cos

sin

d dp

f d

L a b d a bbP

b

λ δ λ λ λτ λ λδ λ

δ δ λ

− − − + =

+ −

(6.12b)

1 1

maxf

P dλ δδτ

∆ = + (6.12c)

202

Considering that at x=L-d the interfacial shear stress is zero, Eqn 6.11l can be

rewritten as the following equation by replacing L with ( )L d− :

( )( )( ) ( ) ( ) ( )1 11 1 2 2 2

2

tanh sin cos 0d d f dL a b d a b bλ δλ λ λ δ δ λ

λ− − − + − − = (6.12d)

Eqn 6.12b can then be further simplified to

( )( )

2max 22

1 1 2sinfp

d

bP

bδ δτ λ

δ λ λ

−= (6.12e)

At the end of this stage, the plastic-softening-debonding region starts when

d uL d b a− − = . At this moment, Eqn 6.12d yields

( ) ( )22 22

1 1

cotu f da bλ δ δ λλ δ

= − (6.12f)

6.4.3.5 Plastic-softening-debonding stage

Considering that at the plastic-softening-debonding stage, L-d=bd+a, the

load-displacement relationship in this state can be obtained using Eqn 6.12b as

( ) ( ) ( )2

max 2 1 12 2 22

1 1 2

cos sinpd f d

b aP b bτ λ λ δ λ δ δ λ

δ λ λ

= + −

(6.13g)

and

1 1

max

( )f dP L a bλ δδτ

∆ = + − − (6.13h)

This stage is represented by segment EF of the load-displacement curve (Figure

6.12). At the end of this stage, the free end (x=0) enters the softening state (Figure

6.11i).

203

6.4.3.6 Softening-debonding stage

During the softening-debonding stage, solving Eqn 6.11i with the boundary

conditions of (1) at 0x = , 0pσ = ; and (2) at x b= , 0τ = , fδ δ= , pp p

Pb t

σ =

yields:

22ub b πλ

= = (6.13i)

( )2

1 12

2 max

cosfp

P xbλ δδ δ λ

λ τ= − for 0 ux b≤ ≤ (6.13j)

It is evident from Eqn 6.13i that during this stage the length of the softening region

remains constant (Figure 6.11j). The maximum interfacial shear stress at x=0

reduces with the load. The displacement at the loaded end can be found directly as

1 1

max

( )f uP L bλ δδτ

∆ = + − (6.13k)

Eqn 6.13k suggests that the displacement reduces linearly with the load in this stage

(i.e. segment FG of Figure 6.12).

It should be noted that although the solution presented in this section is for

CFRP-to-steel bonded joints, it is applicable to similar bonded joints with a thin

plate bonded to steel and governed by a trapezoidal bond-slip model.

6.4.4 Comparison between Analytical Solution and Experimental Results

6.4.4.1 Load-displacement curves

204

By making use of the analytical solution presented above and the bond-slip models

presented in Section 6.3 (i.e. the bi-linear model for linear adhesives and the

trapezoidal model for non-linear adhesives), the load-displacement curves can be

easily obtained for the specimens presented in Chapter 5. The analytical predictions

are compared with the test results in Figure 6.13 for specimen A-NM-T1 and

specimen C-NM-T1 (see Chapter 5 for the specimen details), while the comparisons

for other specimens are similar. Figure 6.13b shows that the prediction agrees well

with the experimental curve except that the latter terminates earlier as in the final

stage of the test the failure of the bonded joint changed from cohesion failure to

brittle interlaminar failure of FRP (see Chapter 5). Figure 6.13a shows that the

analytical solution predicts the plateau of the experimental curve closely, but

underestimates its initial slope. This underestimation is believed to be at least

partially due to the use of a smaller initial stiffness in the idealized bi-linear model,

as explained earlier (see Figure 6.6). In addition, the analytical solution can predict

a descending branch of the load-displacement curve for the

plastic-softening-debonding stage and the softening–debonding stage, which is

difficult to be obtain from the experiments.

6.4.4.2 Interfacial shear stress distributions

The analytical solution is also able to predict the interfacial shear stress distributions

at different stages of loading. The predictions are compared with the experimental

results for specimen A-NM-T1-I with a linear adhesive and for specimen

C-NM-T1-I with a non-linear adhesive in Figures 6.14 and 6.15 respectively.

Figures 6.14 and 6.15 show that the analytical solution can generally provide

accurate predictions of the interfacial shear stress distributions at distinct

loading/deformation states as discussed in Section 5.3.6. It can also be noted that

there are significant differences between the predictions and the test results for the

interfacial shear stress close to the loaded end. This is believed to be at least

partially due to the complicated stress state (i.e. both the interfacial normal stress

and the interfacial shear stress are significant) near the loaded end because of the

pronounced local bending in that region (see Chapter 4).

205

6.4.5 Effect of the Shape of the Bond-Slip Model

It is clear from Eqn 5.3 that the shape of the bond-slip curve does not affect the

bond strength as long as the fG is the same. However, the shape of the bond-slip

curve can have a significant influence on the load-displacement curve of a bonded

joint. To further investigate this issue, three bond-slip models (i.e. models 1, 2 and 3

in Figure 6.16a) with the same fG but different shapes were employed in the

analytical solution developed in Section 6.5.3 to obtain three different

load-displacement curves. As shown in Figure 6.16a, model 1 is a trapezoidal

model, while models 2 and 3 are bi-linear models. The initial stiffnesses of models

1 and 2 are the same and are both 0.125 times that of model 3. The

load-displacement curves obtained based the three different bond-slip models are

compared in Figure 6.16b. The curves for models 1 and 2 show the same initial

stiffness but the stiffness of the curve for model 2 reduces significantly and

becomes significantly smaller than that for model 1 as the load approaches the

ultimate load. This stiffness difference is due to the difference between models 1

and 2 after the peak bond shear stress is reached: after reaching the peak bond shear

stress, the interfacial shear stress decreases significantly (i.e. in the softening stage)

according to model 2, but the interfacial shear stress remains constant for a certain

period according to model 1. In addition, it can be seen that the displacement at

which the bond strength is reached is larger for model 2 than for model 1. As

explained earlier (see Section 6.4.3), the bond strength is reached when debonding

initiates at the loaded end (i.e. when the interfacial shear stress at the loaded end

becomes zero and the slip there becomes fδ ). Figure 6.16a shows that fδ is

larger in model 2 than in model 1, which thus leads to a larger displacement

according to model 2 when the bond strength is reached. On the other hand, models

2 and 3 have the same fδ , so the curves for these two models reach the bond

strength at the same displacement. The higher initial stiffness of model 3 leads to a

larger initial slope of the load-displacement curve. As expected, all the three

bond-slip models lead to the same bond strength because they have the same fG .

206

6.5 BOND STRENGTH MODEL

According to the analytical solution given in Section 6.4.3, if the bond length is

larger than the eL defined by Eqn 6.11t, the bond strength (or the ultimate load)

uP can be predicted by Eqn 6.11s. Substituting Eqn 6.8l into 6.11s yields the

following equation:

max

2max 1

2

pu

p

f p p st st st

bPb

G E t E t b

τ

τ=

+

(6.14)

Considering that the axial stiffness of the steel substrate plate is much larger than

the axial stiffness of the CFRP plate, it is reasonable to assume 0p p p

st st st

b E tE t b

= . Eqn

6.14 can then be simplified to

2u p f p pP b G E t= (6.15)

which is exactly the same as Eqn 5.3. In Eqn 6.15, fG can be found from Eqn 6.2.

The bond strength predicted using Eqn 6.15 and Eqn 6.2 are compared with the

experimental results in Table 6.1 and Figure 6.17. The predicted bond strengths

using Xia and Teng’s (2005) model are also summarized in Table 6.1 and Figure

6.17. It can be seen that proposed model provides accurate predictions for the bond

strength of CFRP-to-steel bonded joints, including both those with a linear adhesive

and those with a non-linear adhesive. Xia and Teng’s (2005) model significantly

underestimates the bond strength of CFRP-to-steel bond joints with a non-linear

adhesive. Again, the good performance of Eqn 6.15 is no surprise as the expression

for fG (i.e. Eqn 6.2) are based on the same test results.

207

6.6 CONCLUSIONS

This chapter has presented an analytical study to develop bond-slip models for

CFRP-to-steel bonded interfaces and to predict the full-range bond behaviour of

CFRP-to-steel bonded joints. Bonded joints with a linear adhesive and those with a

non-linear adhesive have both been examined.

An equation which predicts the interfacial fracture energy from the properties of the

adhesive has been proposed. This equation approximates the existing test results

closely. The interfacial fracture energy is a key parameter in determining both the

bond-slip behaviour and the bond strength (i.e. ultimate load) of a bonded joint.

Two bond-slip models for CFRP-to-steel bonded interfaces with a linear adhesive

have been presented. These two models were revised from similar models proposed

by Lu et al. (2005) for FRP-to-concrete bonded interfaces, but takes into account

the unique properties of CFRP-to-steel bonded interfaces. The key parameters

include the interfacial fracture energy, the peak bond shear stress and the

corresponding slip. Both models have both been shown to represent the test results

closely.

A preliminary bond-slip model has also been proposed for CFRP-to-steel bonded

joints with a non-linear adhesive based on the limited test results presented in

Chapter 5. While the model needs to be further developed/verified when new test

data are available, it is believed that the trapezoidal shape adopted in this model

captures well the characteristics of such bonded joints.

Employing a trapezoidal bond-slip model (with a triangular model as a special

case), an analytical solution was also developed for predicting the full-range bond

behaviour of CFRP-to-steel bonded joints with a non-linear adhesive, following the

approach of Yuan et al. (2004). The analytical solution provides closed-form

expressions for the interfacial shear stress distributions and the load-displacement

208

behaviour at different loading stages of the bonded joints. The analytical solution

has been shown to represent the test results closely.

As part of the analytical solution, a bond strength model was also presented,

including an expression for the definition of the effective bond length. As expected,

the bond strength model provides accurate predictions for bonded joints with either

a linear adhesive or a non-linear adhesive.

209

REFERENCES



Wu, Z.S., Yuan, H. and Niu, H.D. (2002). "Stress transfer and fracture propagation

in different kinds of adhesive joints", Journal of Engineering Mechanics,

128(5), 562-573.

Xia, S.H. and Teng, J.G. (2005). "Behavior of FRP-to-steel bond joints",


2005), Hong Kong, China.

Yao, J., Teng, J.G. and Chen, J.F. (2005). "Experimental study on FRP-to-concrete

bonded joints", Composites Part B:Engineering, 36(2), 99-113.



553-565.

210

Table 6.1 Predicted bond strengths versus experimental bond strengths

Specimen

Adhesive properties

Adhesive thickness,

ta (mm)

CFRP plate elastic

modulus, EP (GPa)

CFRP plate thickness, tP

(mm)

Experimental bond

strength, Pu,exp (kN)

Predicted bond strength, Pu,predict (kN)

Pu,predict/Pu,exp

Elastic modulus, Ea

(MPa)

Tensile strength,

σmax (MPa)

Strain energy, R

(MPa mm/mm)

Xia and Teng (2005)

Proposed Xia and

Teng (2005) Proposed

A-NM-T1-I 11250 22.34 0.0405 1.07 150 1.2 30.75 38.33 30.98 1.25 1.01

A-NM-T1-II 11250 22.34 0.0405 1.03 150 1.2 31.21 38.14 30.69 1.22 0.98

A-MM-T1 11250 22.34 0.0405 1.00 235 1.4 46.90 51.42 41.29 1.10 0.88

A-HM-T1 11250 22.34 0.0405 1.20 340 1.4 63.80 63.31 51.85 0.99 0.81

A-NM-T1.5 11250 22.34 0.0405 1.53 150 1.2 35.20 40.23 33.88 1.14 0.96

A-NM-T2 11250 22.34 0.0405 2.06 150 1.2 40.00 41.88 36.49 1.05 0.91

A-NM-T3 11250 22.34 0.0405 3.04 150 1.2 33.80 44.14 40.22 1.31 1.19

C-NM-T1-I 1750 14.73 0.1475 0.99 150 1.2 112.87 57.20 110.59 0.51 0.98

211

C-NM-T1-II 1750 14.73 0.1475 1.02 150 1.2 113.81 57.43 111.41 0.50 0.98

C-MM-T1 1750 14.73 0.1475 1.04 235 1.4 130.50 77.85 151.36 0.60 1.16

A1# 4013 22.53 0.0632* 1.07 165 1.2 60.50 54.82 50.72 0.91 0.84

A2# 4013 22.53 0.0632* 1.98 165 1.2 61.70 59.57 59.15 0.97 0.96

B1# 10793 20.48 0.0405 0.83 165 1.2 39.40 38.32 30.45 0.97 0.77

B2a# 10793 20.48 0.0405 1.90 165 1.2 42.20 42.89 37.51 1.02 0.89

B2b# 10793 20.48 0.0405 1.76 165 1.2 38.80 42.45 36.80 1.09 0.95

Mean 0.97 0.95

Coefficient of Variation 25.2% 10.5%

#- Experiments reported in Xia and Teng (2005), * Calculated using 2max 2 aEσ

212

Figure 6.1 Predicted versus experimental values of interfacial fracture energy fG

0

2

4

6

8

10

12

14

0 5 10 15

Experimental Gf (N/mm2.mm)

Pre

dict

ed G

f (N

/mm

2 .mm

)Xia and Teng (2005)

Proposed

Linear adhesives

Non-linear

adhesives

213

Figure 6.2 Variation of experimental interfacial fracture energy fG with the square

of strain energy (adhesives A and C)

Figure 6.3 Variation of experimental interfacial fracture energy fG with the square

root of adhesive thickness

0

2

4

6

8

10

12

14

0 0.005 0.01 0.015 0.02 0.025

Inte

rfaci

al fr

actu

re e

nerg

y (N

/mm

2 .mm

)

(Strain energy, R)2

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60

Inte

rfaci

al fr

actu

re e

nerg

y (N

/mm

2 .mm

)

Sqrt (thickness, mm)

214

Figure 6.4 Predicted versus experimental values of the peak bond shear stress

Figure 6.5 Predicted versus experimental slips at peak bond shear stress for linear adhesives

R² = 0.857

10

12

14

16

18

20

22

24

26

28

30

10 12 14 16 18 20 22 24 26 28 30

Pre

dict

ed τ m

ax(M

Pa)

Experimental τmax (MPa)

Linear adhesives

Non-linear adhesives

R² = 0.7877

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Pre

dict

ed δ 1

(mm

)

Experimental δ1 (mm)

Linear adhesives

215

(a) A-NM-T1

(b) A-NM-T1.5

216

(c) A-NM-T2

(d) A-MM-T1

Figure 6.6 Predicted versus experimental bond-slip curves for linear adhesives

217

Figure 6.7 Predicted versus experimental bond-slip curves for non-linear adhesives (only applicable to adhesive C)

218

(a) Elevation

(b) Plan

Figure 6.8 Single-shear pull-off test of a CFRP-to-steel bonded joint

Steel substrate plate

bst

L

CFRP plate bp

CFRP plate

P

P

x

tst

Steel plate

ta

Adhesive

tp

219

Figure 6.9 Horizontal equilibrium of a bonded joint

Figure 6.10 Local bond-slip model for non-linear adhesives

δf δ1 δ2

τmax

σp+dσp

σst+dσst

Plate

steel

σp

σst

τ τ

220

Figure 6.11 Interfacial shear stress distributions for a long bonded joint: (a) elastic stress state; (b) initiation of plastic state at x=L, point A in Figure 6.12; (c)

(a)

maxτ τ<I

I

(b)

maxτ τ=

(c)

maxτ τ= I II

a

maxτ τ=(d)

I II

a=ad (e)

b

I II

a=ad

maxτ

III

I II

a=ad

maxτ

III

b=bd

(f)

III II

a=au b=bd

d

(g) I

maxτ

III II

a b=bd maxτ

d

(h)

(i)

IV

IV

III

b=bu d

maxτ

III

maxτ τ<

bu d

IV

IV (j)

x

221

elastic-plastic stress state; (d) initiation of softening at x=L, point B in Figure 6.12; (e) elastic-plastic-softening state; (f) initiation of debonding at x=L, point C in Figure

6.12; (g) elastic-plastic-softening-debonding state; (h) initiation of plastic state at x=0; (i) initiation of softening at x=0, point F in Figure 6.12; (j) linear unloading

Figure 6.12 Typical theoretical full-range load-displacement curve for CFRP-to-steel bonded joints with a non-linear adhesive

δf

P

∆ O

A

B

C D

E

G

F

222

(a) A-NM-T1

(b) C-NM-T1

Figure 6.13 Predicted versus experimental load-displacement curves

0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8 1Displacement (mm)

Load

(kN

)

Experimental

Analytical (Yuan et al. 2004)

0

20

40

60

80

100

120

0 1 2 3 4 5

Load

(kN

)

Displacement (mm)

Experimental

Analytical (present)

223

(a) Points A, B and C of Figure 5.10a

(b) Points D,E, F and G of Figure 5.10a

Figure 6.14 Predicted versus experimental interfacial shear stress distributions for points shown in Figure 5.10a for specimen A-NM-T1

0

5

10

15

20

25

30

0 100 200 300

Inte

rfaci

al s

hear

stre

ss (M

Pa)


A-Experimental

A-Analytical

B-Experimental

B-Analytical

C-Experimental

C-Analytical

02468

101214161820

0 100 200 300 400

Inte

rfaci

al s

hear

stre

ss (M

Pa)


D-Experimental

D-Analytical

E-Experimental

E-Analytical

F-Experimental

F-Analytical

G-Experimental

G-Analytical

224

(a) Points A,B, C and D of Figure 5.11a

(c) Points E,F, G and H of Figure 5.11a

Figure 6.15 Predicted versus experimental interfacial shear stress distributions for points shown in Figure 5.11a for specimen C-NM-T1

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400Distance from the loaded end (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa) A-Experimental

A-AnalyticalB-ExperimentalB-AnalyticalC-ExperimentalC-AnalyticalD-ExperimentalD-Analytical

0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400Distance from the loaded end (mm)

Inte

rfaci

al s

hear

stre

ss (M

Pa)

E-ExperimentalE-AnalyticalF-ExperimentalF-AnalyticalG-ExperimentalG-AnalyticalH-ExperimentalH-Analytical

225

(a) Bond-slip models used for comparison

(b) Load-displacement curves from the analytical model

Figure 6.16 Effect of shape of the bond-slip model on load-displacement behaviour

02468

10121416

0 0.5 1 1.5 2

Bon

d sh

ear s

tress

(MP

a)

Slip (mm)

Model-1

Model-2

Model-3

0

20

40

60

80

100

120

0 1 2 3 4 5Displacement (mm)

Load

(kN

)

Model-1

Model-2

Model-3

226

Figure 6.17 Predicted versus experimental bond strengths

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

20.00 70.00 120.00

Pre

dict

ed b

ond

stre

ngth

, Pu,

pred

ict(

kN)

Experimental bond strength, Pu,exp (kN)

Xia and Teng (2005)

Proposed

227

CHAPTER 7 FINITE ELEMENT MODELLING OF DEBONDING

FAILURES IN STEEL BEAMS FLEXURALLY-STRENGTHENED WITH CFRP

7.1 INTRODUCTION

Many studies have recently been conducted on steel beams or steel-concrete

composite beams (referred to collectively as “steel beams” hereafter for simplicity)

strengthened by bonding an FRP (generally CFRP) plate to the soffit

(Tavakkolizadeh and Saadatmanesh 2003; Miller. et al. 2001; Al-Saidy et al. 2004;

Nozaka et al. 2005; Colombi and Poggi 2006; Lenwari et al. 2006; Sallam et al.

2006; Schnerch and Rizkalla 2008; Shaat and Fam 2008; Fam et al. 2009; Linghoff

et al. 2009). CFRP strengthening can enhance both the yield strength and the load-

carrying capacity of the beam (Schnerch et al. 2007). The load-carrying capacity of

CFRP-strengthened beams may be governed by one or a combination of the many

possible failure modes, which include: (a) in-plane bending failure; (b) lateral

buckling; (c) debonding at the plate ends; and (d) yielding-induced debonding away

from the plate ends. Additional but less likely failure modes include: (e) local

buckling of the compression flange; and (f) local buckling of the web.

A number of theoretical studies (Al-Saidy et al. 2004; Deng et al. 2004; Colombi and

Poggi 2006; Lenwari et al. 2006; Deng and Lee 2007; Schnerch et al. 2007; Fam et

al. 2009; Linghoff and Al-Emrani 2009) have also been conducted on CFRP-

strengthened steel beams. Despite these studies, no theoretical model has been

developed that is capable of accurate prediction of failures governed by debonding of

the CFRP plate. Debonding of the CFRP plate, however, has been found to be very

common in such beams (Sen et al. 2001; Tavakkolizadeh and Saadatmanesh 2003;

Nozaka et al. 2005; Colombi and Poggi 2006; Sallam et al. 2006; Deng and Lee

2007; Shaat and Fam 2008; Linghoff et al. 2009). In a CFRP-strengthened steel

beam failing by debonding of the CFRP plate, the load-carrying capacity depends on

228

the contribution of the CFRP at the time of debonding, which in turn depends on the

interfacial stress transfer function of the adhesive layer. Therefore, an accurate

simulation of the bond behaviour of CFRP-to-steel interfaces is of particular

importance in the theoretical modelling of debonding failures.

Against this background, this chapter presents a finite element (FE) model for CFRP-

strengthened steel beams, with a particular emphasis on the accurate modelling of the

bond behaviour and debonding failure in such beams.

7.2 MODELLING OF CFRP-TO-STEEL INTERFACES

7.2.1 General

Debonding in a CFRP-strengthened steel beam may occur at the CFRP plate ends (i.e.

plate-end debonding) or away from the plate ends (i.e. intermediate debonding).

Intermediate debonding initiates from either the presence of a defect (e.g. a crack)

or yielding of the steel substrate (Sallam et al. 2006) where the FRP plate is highly

stressed, and propagates towards a plate end where the stress in the FRP plate is

normally lower. Very limited research is available on intermediate debonding in

CFRP-strengthened steel beams and no theoretical modelling exists so far.

However, this kind of debonding is regarded to be similar to intermediate-crack

induced debonding (IC debonding) in an FRP-plated concrete beam (Teng et al.

2003), in the sense that both initiates where the FRP is highly stressed and both are

dominated by interfacial shear stresses. Therefore, accurate simulation of

intermediate debonding requires an appropriate model for the non-linear and

damage behaviour of the interface in the shear direction (i.e. under mode II

loading). Apparently, the bond-slip models developed in Chapter 6 are very suitable

for such purposes.

Compared to intermediate debonding, the modelling of plate end debonding is more

involved as it is governed by both interfacial shear stresses and interfacial normal

stresses (Sen et al. 2001; Deng et al. 2004; Schnerch et al. 2007). Therefore, the

effect of interaction between mode I loading and mode II loading on damage

initiation and propagation within the adhesive layer needs to be appropriately

229

addressed. A number of theoretical studies (e.g. Lenwari et al. 2006; Schnerch et al.

2007) have been conducted on plate-end debonding, but they have generally

assumed that the adhesive layer is linear-elastic and that plate end debonding occurs

when the maximum interfacial stresses found from an elastic analysis reach their

limiting values (i.e. strength-based approach). These theoretical analyses have

generally significantly underestimated the performance of the strengthened beam, as

the bond strength depends on the fracture energy instead of the strength of the

adhesive (see Chapter 5). No existing studies have taken into account the damage

behaviour of adhesive in the simulation of CFRP-strengthened steel beams.

The above discussions suggest that the successful prediction of debonding failures

in CFRP-strengthened steel beams requires a model for the CFRP-to-steel interface

which has the following characteristics: (1) it accurately predicts the nonlinear and

damage behaviour of the interface subjected to pure mode I loading and pure mode

II loading; (2) it appropriately accounts for the effect of interaction between mode I

loading and mode II loading on the damage propagation along the interface. For (1),

an accurate bond-slip model (e.g. such as those presented in Chapter 6) can be

employed to predict the full-range interfacial behaviour under pure mode II loading;

similarly, the full-range interfacial behaviour under pure mode I loading can be

depicted by a bond-separation model (de Moura and Chousal 2006; Yuan and Xu

2008), where the area under the bond-separation curve represents the fracture

energy under mode I loading. For (2), the so-called mixed-mode cohesive law needs

to be involved. Among the existing modelling techniques, coupled cohesive zone

models appear to be the most suitable ones which may possess both of the two

required characteristics. Cohesive zone models have been used for simulating the

fracture of ductile and brittle solids (De Lorenzis and Zavarise 2009), the

delamination of composites (Sorensen 2002; Sorensen and Jacobsen 2003; Li et al.

2005; Li et al. 2006) and the behaviour of adhesively bonded joints (Goncalves et

al. 2003; Liljedahl et al. 2006). Bocciarelli et al. (2007) presented the only existing

finite element model for CFRP-to-steel bonded joints with a cohesion zone model

and showed good predictions for results from double-shear lap tests, but the

cohesion zone model used by them only considered interfacial behaviour under pure

mode II loading. In the following section, a coupled cohesive zone model is

proposed for CFRP-to-steel interfaces, which consists of all the three important

230

components, namely, the bond-slip model for mode II loading, the bond-separation

model for mode I loading, and a mixed-mode cohesive law. It should be noted that

the model presented in the following section is for linear adhesives only, but the

general concepts of the model are extendable to non-linear adhesives.

7.2.2 Coupled Cohesive Zone Model

7.2.2.1 Bond-slip model

The bi-linear bond-slip model proposed in Chapter 6 (i.e. Eqns 6.2 and 6.4-6.6) has

been shown to provide accurate predictions of the bond behaviour of CFRP-to-steel

bonded joints subjected to mode II loading, and is thus adopted here. This model

includes an explicit formula (Eqn 6.2) which accurately predicts the mode II

interfacial fracture energy of CFRP-to-steel interfaces from the geometrical and

material properties of the adhesive layer.

7.2.2.2 Bond-separation model

It is common to obtain the bond-separation model and the mode I fracture energy

using double cantilever beam tests (DCB) (Pardoen et al. 2005; de Moura and

Chousal 2006). In the absence of these test data, for linear adhesives a close

approximation of the bond-separation behaviour can be made using the tensile

stress-strain data of the adhesive (Campilho et al. 2008). The peak stress of the

bond-separation model can be assumed to be the same as the tensile strength of the

adhesive and the separation at complete failure fδ can be taken as the product of

the tensile strain at complete failure and the adhesive thickness (Campilho et al.

2008). In the present study, the tensile stress-strain behaviour of the adhesive was

used to define the bond-separation model, following the approach suggested by

Campilho et al. (2008).

231

7.2.2.3 Mixed-mode cohesive law

While uncoupled cohesive zone models assume the cohesive laws in the normal

direction and the tangential (shear) direction are independent of each other, coupled

cohesive zone models adopt mixed-mode cohesive laws which account for the

interaction between mode I loading and mode II loading. Some mixed-mode

cohesive laws assume the same fracture energy for both loading modes, but this

assumption may lead to significant errors as extensive experimental results have

indicated that the fracture energy in mode II loading is often much larger than that

in mode I loading (Hogberg 2006). Therefore, in the present study, a mixed-mode

law which accounts for different fracture energies in different loading modes is

adopted, following Xu and Needleman (1993) and Hogberg (2006).

The mixed-mode cohesive law adopted in the present study considers all the three

components of bond stresses (i.e. interfacial stresses) and deformations, namely,

those normal to the interface (i.e. the normal component), and those along the

interface (i.e. the two shear components). For ease of discussion, hereafter bond

stresses are referred to collectively as tractions while interfacial deformations (i.e.

displacements) are referred to collectively as separations. The three components of

the traction vector are thus the normal traction and the two shear tractions, which

are denoted by nt , st and tt respectively. Similarly, the corresponding separations

are denoted by nδ , sδ and tδ respectively. With the thickness of the cohesive

element taken as the original thickness 0T , it is easy to write:

0

nn T

δε = ; 0

ss T

δε = and 0

tt T

δε = (7.1)

where nε , sε and tε are strains in the normal and the two shear directions

respectively.

Elastic behaviour

It is assumed that the interface behaves linear-elastically until the initiation of

damage (Goncalves et al. 2003; de Moura and Chousal 2006; De Lorenzis and

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Zavarise 2009). The interfacial behaviour before damage initiation can thus be

represented by

0 00 00 0

n nn n

s ss s

t tt t

t Kt Kt K

δδδ

=

(7.2)

where nnK , ssK , ttK are the elastic stiffnesses of the normal and the two shear

directions respectively. It is obvious that nnK should be equal to the initial slope of

the bond-separation model for mode I loading and is given by

0

ann

EKT

= (7.3)

ssK and ttK are assumed to be the same, and should be equal to the initial slope of

the bond-slip model presented earlier for mode II loading. Based on Eqn 6.5, it is

easy to write

0.65

0

3 ass tt

GK KT

= =

(7.4)

Eqn 7.4 suggests that ssK and ttK depend on the shear modulus aG of the adhesive.

Therefore, the elastic stiffness in the two shear directions and that in the normal

direction are inter-related through the Poisson’s ratio.

Damage behaviour

As explained in Chapter 6, under pure mode II loading, damage of the interface

initiates when the shear stress reaches the peak bond shear stress. Similarly, under

pure mode I loading, damage initiates when the normal stress reaches the peak bond

normal stress. Under mixed-mode loading, a strength criterion needs to be adopted

to define the initiation of damage, considering the interaction between mode I and

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mode II loading. Following existing studies (Cui et al. 1992; Da’vila and Johnson

1993; Mohammadi et al. 1998; Camanho and Matthews 1999; Camanho et al. 2003),

the following quadratic strength criterion is adopted in the present study:

2 2 2

max max max

1n s tt t tσ τ τ

+ + =

(7.5)

where maxσ is the tensile strength of the adhesive, and maxτ is the bond shear

strength (i.e. the peak bond shear stress); the symbol represents the Macaulay

bracket which is used to signify that compressive stresses do not initiate damage (i.e.

nt is negative and thus nt is equal to zero). Based on Eqn 7.5, the damage

initiation point can be determined when the mode-mix ratio (i.e. a ratio representing

the relative magnitude of each mode) is known.

After damage initiation, a scalar damage variable D is introduced. D is equal to zero

at the initiation of damage and is equal to one at complete failure. The interfacial

behaviour can then represented by the following equation:

( )( )

( )

*1 0 0

0 1 0

0 0 1

nnn n

s ss s

t ttt

D Ktt D Kt D K

δδδ

− = − −

(7.6)

where * means that if nt is compressive, D* is equal to zero.

The complete failure of the interface, when D is equal to one, is defined based on

the fracture energy. While a few other criteria for the definition of complete failure

are available [e.g. the quadratic criteria or the BK criteria proposed by Benzeggagh

and Kenane (1996)], the linear criterion is adopted in the present study due to its

simplicity and good performance for adhesive joints (Reeder and Crews 1990;

Camanho et al. 2003; Xie et al. 2005). The linear criterion is expressed by:

234

*

1n s t

I II II

G G GG G G

+ + = (7.7)

where , ,n s tG G G are the works done by the traction and its conjugate displacement

in the normal and the two shear directions, respectively (Figure 7.1). IG and IIG

represent the interfacial fracture energy required to cause failure when subjected to

pure mode I loading and pure mode II loading respectively. It is evident that Eqn

7.7 allows the use of different interfacial fracture energy values for mode I loading

and mode II loading.

To describe the evolution of damage, the definition of effective displacement mδ is

introduced as follows:

2 2 2m n s tδ δ δ δ= + + (7.8)

With this definition, the displacement at complete failure fmδ can be found using

Eqn 7.7 for a certain mode-mix ratio. The damage variable D is then defined by the

following equation assuming linear softening of the interface (Camanho et al. 2003):

( )( )

max 0

max 0

fm m m

fm m m

Dδ δ δ

δ δ δ

−=

− (7.9)

where 0mδ is the effective displacement at the initiation of damage and max

mδ is the

maximum value of the effective displacement attained in the loading process

(Figure 7.2).

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7.2.2.4 Implementation of the coupled cohesive zone model in ABAQUS

The coupled cohesive zone model presented above was implemented in the

commercial FE program ABAQUS (ABAQUS 2004) for the present FE modelling

work. The cohesive elements provided by ABAQUS were adopted and their

constitutive behaviour was defined by the mixed-mode cohesive law. The elastic

behaviour was defined using the command *elastic, type=traction. The damage

initiation behaviour was defined using the command *damage initiation,

criterion=QUADS. The damage evolution behaviour was defined using the

command *damage evolution, type=ENERGY, mixed mode behaviour=power law,

power=1. Other parameters required for the FE model were obtained using the

bond-slip model for mode II loading and the bond-separation model for mode I

loading (see the descriptions earlier in this section).

7.3 FE MODELLING OF CFRP-STRENGTHENED STEEL I-BEAMS

7.3.1 General

In this section, an FE study is presented for CFRP-strengthened steel I beams, in

which the coupled cohesive zone model presented in Section 7.2 for CFRP-to-steel

interfaces was employed. FE models were developed for four beams tested by Deng

and Lee (2007), and were verified using the test results. Deng and Lee’s (2007)

experiments were selected for simulation among many other experimental studies

(e.g. Tavakkolizadeh and Saadatmanesh 2003; Nozaka et al. 2005; Colombi and

Poggi 2006; Sallam et al. 2006; Shaat and Fam 2008; Linghoff et al. 2009), because

in Deng and Lee’s (2007) study: (1) debonding failures controlled by cohesion

failure occurred; (2) experimental load-displacement curves were reported; (3)

different failure modes (e.g. plate-end debonding and compression flange buckling)

were observed due to the use of CFRP plates with different lengths. These

characteristics make Deng and Lee’s (2007) experiments the most suitable for

verifying the proposed FE approach, especially in terms of the behaviour of CFRP-

to-steel interfaces.

236

7.3.2 Beam Tests Conducted by Deng and Lee (2007)

Deng and Lee (2007) carried out a series of experiments on CFRP-strengthened

steel I beams. Four of the beams tested by Deng and Lee’s (2007) were selected for

FE modelling, including one control beam without CFRP strengthening, and three

beams strengthened with CFRP plates of three different lengths (i.e. 300 mm, 400

mm, and 1000 mm) respectively. The four specimens are referred to as specimens

S300, S303, S304 and S310 respectively, where the last two numbers represent the

length of the CFRP plate and the first number “3” indicates that the specimens were

subjected to three-point bending. All the steel beams had a length of 1.2 m (with a

clear span between the supports being 1.1m) and a cross-section of type

127x76UB13; the dimensions of the steel beams are shown in Figure 7.3. Grade

275 steel was used, which means that the steel had a nominal yield strength of 275

MPa (with the actual yield strength often being larger than 275 MPa) and a tensile

elastic modulus of 205 GPa. The CFRP plates used all had a thickness of 3 mm, a

width of 76 mm, and an elastic modulus in the fibre direction of 212 GPa. To avoid

premature flange buckling and web crushing, two 4 mm thick steel plate stiffeners

were welded to each beam at the mid-span, one on each side of the web. For beams

with a short CFRP plate (i.e. 300 mm or 400 mm), plate end debonding of the

CFRP plate was observed. However, when a longer CFRP plate (i.e. 1000 mm) was

used, failure was controlled by the buckling of the compression flange of the steel

section, which was the same as the failure mode of the control beam (i.e. specimen

S300). The details of the specimens are summarized in Table 7.1.

7.3.3 FE Models

FE models were developed for the four beams, with the exact dimensions and

support conditions (i.e. simply-supported boundary conditions) as given in Figure

7.3 and Table 7.1. The general purpose shell element S4R with reduced integration

was adopted for both the steel section and the CFRP plate, while the adhesive layer

was modelled using the cohesive element COHD8 provided by ABAQUS. The two

full-depth stiffeners were provided on the two sides of the web in the mid-span

region, and the three sides of each stiffener were tied to the top flange, the bottom

flange and the web of the cross section respectively. Similarly, the top surface and

237

the bottom surface of the adhesive layer were tied to the bottom surface of the steel

beam and the top surface of the CFRP plate respectively. Based on a mesh

convergence study, 2.5 mm x 2.5 mm elements were selected for the steel section

and the CFRP plate, while 2.5 mm x 2.5 mm x 1 mm (with 1 mm being in the

thickness direction) elements were selected for the adhesive layer. In all the FE

simulations, the analysis was terminated soon after the ultimate load had been

reached.

The well-known J2 flow theory was employed to model the plastic behaviour of the

steel. As the experimental stress-strain curve of the steel was not given, a tri-linear

(i.e. elastic-plastic-hardening) stress-strain model (Bayfield et al. 2005) as given in

Figure 7.4 was adopted. The yield strength was selected to be 330MPa by a trial-

and-error process to match the linear portion of the experimental load-displacement

curve of specimen S300. The tensile ultimate stress of steel was taken as 430MPa

following BS EN 10025-1 (2004). The use of such an idealized stress-strain curve

for the steel is believed to be the best pragmatic solution possible in the absence of

the experimental stress-strain curve and has only minor effects on the predictions

for the steel beam, as shown in Appendix 7.1.

The CFRP plate was treated as an orthotropic material in the FE model. In the fibre

direction, the elastic modulus (i.e. E3) provided by Deng and Lee (2007) was

adopted (i.e. 212 GPa based on a nominal thickness of 3mm). The elastic modulus

in the other two directions (i.e. E1, E2), the Poisson’s ratios and the shear moduli

were assumed the following values respectively based on the values reported in

Deng et al. (2004): E1=E2=10GPa, ν12=0.3, ν13=ν23=0.0058, G12=3.7GPa and

G13=G23=26.5 GPa.

The coupled cohesive zone model presented in Section 7.2 was adopted to model

the constitutive behaviour of the adhesive layer. In Deng and Lee (2007), the tensile

strength (29.7MPa), the tensile elastic modulus (8GPa) and the shear modulus

(2.6GPa) are provided for the adhesive. As the tensile stress-strain curve and the

corresponding strain energy are not provided, the strain energy was calculated by

assuming a bi-linear stress-strain curve with the slope of the ascending branch being

238

equal to the elastic modulus (i.e. 8GPa), the peak stress being equal to the tensile

strength (i.e. 29.7MPa) and the ultimate strain (i.e. the strain at the zero stress point

on the descending branch) being equal to 4% which is the value provided by the

manufacturer (Deng and Lee 2007). Considering the fact that the adhesive used in

Deng and Lee (2007) (i.e. Sika 31) is basically a linear adhesive, the above

assumption is believed to lead to a very close approximation of the strain energy.

With the parameters provided in Deng and Lee (2007) and the calculated strain

energy, the bond-slip model for mode II loading can be determined using Eqns

6.6a-d provided in Chapter 6, and the so-obtained bond-slip model is shown in

Figure 7.5. The bond-separation model for mode I loading can also be determined

using the assumed bi-linear stress-strain curve; the so-obtained bond-separation

model is shown in Figure 7.6 as model 1. Besides model 1 whose mode I fracture

energy is 0.059 N/mm, another bond-separation model (i.e. model 2, see Figure 7.6)

was also used, whose mode I fracture energy (i.e. 0.11 N/mm) is twice the elastic

energy of model 1. The use of two different bond-separation models for mode I

loading was to explore the possible effect of mode I fracture energy on damage

propagation in the adhesive layer. The parameters for the bond-slip model (for

mode II loading) and the bond-separation model (for mode I loading) are

summarized in Table 7.2.

As the failure of specimens S300 and S310 was controlled by compression flange

buckling, their behaviour may be affected by the second mode of imperfection

shown in Figure A7.5 (see Appendix 7.1). However, no measured imperfections are

reported in Deng and Lee (2007). In the FE model, a mode II imperfection with a

magnitude of 1.3 mm was selected by a trial-and-error process to match the ultimate

load of the control beam (i.e. specimen S300). The residual stresses shown in Figure

A7.7 (see Appendix 7.1) were included in the FE model using the command

*INITIAL CONDITIONS, TYPE=STRESS provided in ABAQUS. It should be

noted that although the imperfection and the residual stresses adopted in the FE

models may not be exactly the same as those in the tests, their effects on the

predictions are very limited: the imperfections have little effect on the load-

displacement curve before the ultimate load which is controlled by the bulking of

the steel section, and the residual stresses only have some effects on the slope of the

curve close to the yield load (see Appendix 7.1).

239

7.3.4 Results and Discussions

7.3.4.1 Specimen S300 (control beam)

The FE result is compared with the experimental load-displacement curve of the

control beam (i.e. specimen S300) in Figure 7.7. As explained earlier, both the

stress-strain curve and the imperfections of the steel section adopted in the FE

model were obtained through a trial-and-error process, to match the experimental

load-displacement curve of specimen S300. With these input parameters, the FE

result is seen to agree well with the test result (Figure 7.7). The small difference

between the two curves in Figure 7.7 after the initial linear portion is believed to be

due to the use of an idealized tri-linear stress-strain curve and the assumed

imperfections and residual stresses (see Appendix 7.1 for more discussions), which

may be slightly different from the experimental values. Nevertheless, the agreement

shown in Figure 7.7 is regarded to be sufficiently close. The material and geometric

properties adopted in the FE model are thus believed to reflect well the

experimental values, and any errors arising from these inputs are believed to have

negligible effects on the bond behaviour of the CFRP-to-steel interface.

7.3.4.2 Specimen S303

Two FE models were developed for specimen S303 tested by Deng and Lee (2007)

and they differ in the bond-separation model for mode I loading used (Figure 7.6).

These two FE models are referred to as models S303-1-212 and S303-2-212

respectively, where the number “1” and “2” in the middle represents whether model

1 or model 2 was adopted for bond-separation behaviour under mode I loading, and

the last three numbers “212” mean that the elastic modulus of the CFRP plate in the

fibre direction was 212GPa in the FE models (i.e. the same as the experimental

value). The same naming method is also adopted in this chapter for the other FE

models. Besides the two FE models, an additional FE model was also created, with

all the details being the same as model S303-1-212 except that the model adopted

an elastic modulus of 330GPa for the CFRP plate in the fibre direction. This

additional model was created to investigate the effect of the axial stiffness of the

CFRP plate, and is accordingly referred to as model S303-1-330.

240

In Deng and Lee’s (2007) tests, specimen S303 was found to fail by the plate end

debonding of the CFRP plate. The same failure mode was also predicted by all the

three FE models introduced above. The failure mode obtained from FE model

S303-1-212 is shown in Figure 7.8 while those for the other two FE models are

similar.

The load-deflection curves obtained from these FE models are compared with the

experimental curve in Figure 7.9, while other key results are summarized in Table

7.3. Figure 7.9 shows that models S330-1-212 and S303-2-212 predict very similar

load-deflection curves, despite the use of different bond-separation models. The

curve predicted by model S303-1-330 is slightly higher than the other two after the

initial linear portion because of the use of a stiffer CFRP plate, but ends at a lower

ultimate load. It is also shown that the curves predicted by models S303-1-212 and

S303-2-212, where the CFRP properties adopted is the same as that in the test

specimen, are very close to the experimental curve except that they both predicted a

higher ultimate load (Figure 7.9).

To further examine the FE results, two key points are marked on each of the

predicted load-displacement curves in Figure 7.9: (1) the point when damage

initiates in the adhesive layer (i.e. the interfacial stresses start to decrease with the

bond displacements); (2) the point when debonding initiates (i.e. when complete

damage occurs at a certain location and the interfacial stresses there reduce to zero).

The predicted loads at the damage initiation point are seen to be significantly lower

than the ultimate load achieved in the test (Figure 7.9). Considering that the damage

initiates when the strength of the adhesive is reached, this observation further

demonstrates that the strength-based approach [e.g. those adopted by Lenwari et al.

(2006) and Schnerch et al. (2007)] can significantly underestimate the load at plate-

end debonding, as found by Colombi and Poggi (2006). It is also interesting to note

that the predicted loads by models S303-1-212 and S303-2-212 at the debonding

initiation point (i.e. 118.3kN and 121.9kN) are both very close to the experimental

ultimate load (i.e. 120kN); the corresponding displacements predicted by the two

models (i.e. 5.08mm and 5.78mm) are also close to the experimental displacement

at the ultimate load (i.e. 5.12mm). This observation suggests that if failure of the

241

strengthened beam is assumed to occur at the debonding initiation point in the FE

models, these models can closely predict both the ultimate load and the load-

displacement curve before the ultimate load. Such an assumption is regarded to be

reasonable as after the initiation of debonding at the CFRP plate end, sudden energy

release can be expected as the debonding propagation is a dynamic process driven

by both the interfacial normal stresses and the interfacial shear stresses. In this

process, idealistic debonding propagation predicted in a static analysis (i.e. the part

after the debonding initiation point on the predicted load-displacement curve)

cannot occur; sudden debonding propagation is likely to happen instead which

means no further load increases can be recorded in the test.

The interfacial normal and longitudinal shear stresses at the plate end (i.e. 150mm

from the mid span) from the three models (i.e. S303-1-212, S303-2-212 and S303-

1-330) are shown in Figure 7.10. The magnitudes of the transverse shear stress are

very small, so they are not shown in this figure. It is clear that damage initiates at a

load of 83kN in models S303-1-212 and S303-2-212, but initiates at a smaller load

(i.e. 71kN) in model S303-1-330. At the damage initiation point, the normalized

normal stress (i.e. normalized by the tensile strength) and the normalized shear

stress (i.e. normalized by the peak bond shear stress) are similar in models S303-1-

212 and S303-2-212, but the latter is higher than the former in model S303-1-330,

indicating a stiffer CFRP plate leads to larger normal stresses. In addition, the load

at the debonding initiation point is smaller in model S303-1-330 (i.e. 115kN) than

in the other two models (i.e. around 120kN), suggesting that steel beams

strengthened with a stiffer CFRP plate are likely to fail at a smaller load due to

earlier plate end debonding.

The interfacial stress distributions along the adhesive layer in model S303-1-212 are

shown in Figure 7.11 for different load levels, while the interfacial stress

distributions along the mid-width of the adhesive layer - (i.e. section X-X in Figure

7.11a) are shown in Figure 7.12. The interfacial stress distributions in the other two

models are similar and are thus not provided here. Damage is seen to initiate at the

two plate ends and propagates towards the mid-span (Figure 7.11). Initially, both

the normal stress and the longitudinal shear stress at the plate ends are shown to be

high. While significant normal stresses are limited to a very small region near each

242

plate end, longitudinal shear stresses decrease only gradually from the plate ends to

the mid-span. After the initiation of damage at the plate end, both the interfacial

normal stress and the longitudinal shear stress at the very end of the plate decrease,

but the shear stress in the region nearby starts to increase (Figures 7.12b-c). This is

further highlighted in Figure 7.13, which compares the normalized normal stress-

normal strain curves and the normalized shear stress-shear strain curves for the

adhesive at the end of the plate (i.e. 150 mm from the mid-span) and those for the

adhesive at 2.5 mm away from the plate end (i.e. 147.5 mm from the mid-span).

Figure 7.13 also shows that the maximum normal stress and the maximum

longitudinal shear stress are equally high at the very end of the plate, but the former

is significantly lower than the latter at a location 2.5 mm away from the plate end,

suggesting that the significant effect of the normal stress on damage propagation of

the interface is limited only to a small region close to the plate end.

It is also interesting to note that although quite different bond-separation models for

mode I loading were employed, the predictions of models S303-1-212 and S303-2-

212 are very similar (Figure 7.9). The predictions are exactly the same before the

initiation of damage at the plate end (Figure 7.10). After damage initiation, the

interfacial stresses in model S303-1-212 are seen to decrease slightly more rapidly

with the load than those in model S303-2-212, as the mode I interfacial fracture

energy adopted in the former is smaller which leads to a smaller total interfacial

fracture energy at failure. However, as the mode II fracture energy (i.e. 1.59 N/mm)

in both models is much larger than the mode I fracture energy (i.e. 0.059 N/mm for

model S303-1-212 and 0.11 N/mm for model S303-2-212), the use of a larger mode

I fracture energy in model S303-2-212 has only a small effect on the total fracture

energy at failure for mixed-mode loading. This explains the very similar predictions

of the two models. It should be noted that for linear adhesives commonly used in

CFRP-to-steel bonded joints, the mode II fracture energy is often much larger than

the mode I fracture energy (Hogberg 2006), so the debonding of such joints under

mixed-mode loading is often governed by the mode II fracture energy. This also

suggests that the method adopted in the present study for estimating mode I fracture

energy (i.e. the method used for bond-separation model 1 in Figure 7.6) can work

well for common linear adhesives.

243


In Deng and Lee (2007), specimen S304 is reported to have failed by the plate end

debonding of the CFRP plate. The same failure mode was also predicted by model

S304-1-212. The deformed shape at failure obtained from model S304-1-212 is

shown in Figure 7.14. The load-deflection curve predicted by model S304-1-212 is

compared with the experimental results in Figure 7.15, where the damage initiation

point and the debonding initiation point are also indicated on the FE curve. Figure

7.15 again suggests that if failure is assumed to occur at the debonding initiation

point in the FE model, both the ultimate load and the load-displacement curve

before the ultimate load can be accurately predicted.


In Deng and Lee (2007), specimen S310 is reported to fail by the buckling of the

compression flange of the steel section. The same failure mode was also predicted

by model S310-1-212. The deformed shape at failure obtained from model S310-1-

212 is shown in Figure 7.16. The load-deflection curve predicted by model S310-1-

212 is seen to compare very well with the experimental results (Figure 7.15).

The longitudinal shear stress patterns of the adhesive layer at different load levels

are shown in Figure 7.17, while the interfacial stress distributions along section Y-Y

at different load levels are shown in Figure 7.18. Before the load reaches 102kN,

both the normal stress and the longitudinal shear stress are relatively low, and the

maximum interfacial stresses occur at the plate end (Figure 7.18a). As the load

increases, the longitudinal shear stress at the mid-span becomes higher than those at

the plate ends (Figure 7.18b). At the ultimate load, softening in the region close to

the mid-span has already begun (Figure 7.18c), but no debonding occurs before the

buckling of the compression flange.

To further examine the possibility of intermediate debonding in this beam, another

FE model was developed, where all the details are exactly the same as model S310-

1-212 except that an additional 6mm thick steel plate with the same properties as

the steel section was added (using tied nodes in the FE model) to the top flange of

244

the steel section, so that the buckling of the top flange can be delayed. This FE

model is referred to as S310-1-212-P where “P” means that an additional plate was

used. As expected, the failure mode predicted by model S310-1-212-P is the

intermediate debonding of the CFRP plate initiating from near the mid-span (Figure

7.19c). The load-deflection curve predicted by S310-1-212-P is shown in Figure

7.20. The longitudinal shear stress patterns of the adhesive layer at different load

levels are shown in Figure 7.19, while Figure 7.21 shows the interfacial stress

distributions along section Z-Z (Figure 7.19a) at different load levels. The

interfacial stress distributions in model S310-1-212-P at low load levels are similar

to those in model S310-1-212. However, as the load increases, a large increase in

the longitudinal shear stress at the mid-span is seen, which also means a higher

contribution of the CFRP plate. At the ultimate load, the longitudinal shear stress

near the mid-span is seen to have dropped significantly (Figure 7.21c).

7.3.4.5 Possible failure modes of CFRP-strengthened steel beams

The discussions above verifies that the proposed FE approach can provide very

accurate predictions for CFRP-strengthened steel beams failing in different failure

modes, in terms of both the ultimate load and the load-displacement curve.

In CFRP-strengthened steel beams, the contribution of the CFRP plate relies on the

stress transfer mechanism of the adhesive layer, so the ultimate load of such beams

is often governed by the failure of the adhesive layer. When a short CFRP plate is

used, the interfacial stresses (i.e. both the normal stress and the shear stress) at the

plate end are large, and the failure is often governed by plate end debonding. When

a longer CFRP plate is used, the interfacial stresses at the plate end are smaller and

the critical region of the adhesive layer may move to the mid-span region. In this

case, the failure mode changes from plate end debonding to intermediate debonding

or the buckling of the compression flange of the steel section.

7.4 CONCLUSIONS

This chapter has presented an FE study aimed at the accurate simulation of

debonding failures in steel beams flexurally-strengthened with CFRP. In the FE

245

model, the bi-linear bond-slip model developed in Chapter 6 for linear adhesives is

employed with a mixed-mode cohesive law which considers the effect of interaction

between mode I loading and mode II loading on damage propagation within the

adhesive. Damage initiation is defined using a quadratic strength criterion, and

damage evolution is defined using a linear fracture energy-based criterion, both of

which take account of mixed-mode loading. The proposed FE approach represents a

significant advancement in the modelling of debonding failures in CFRP-

strengthened steel structures.

Predictions from the FE model were found to compare well with the test results

reported by Deng and Lee (2007) for the strengthened beams failing by either the

plate-end debonding of the CFRP plate or the compression flange buckling of the

steel section. It was also concluded from the study that when a static FE analysis is

conducted, the ultimate load of a beam failing by the plate end debonding should be

taken as the load at which debonding initiates at the plate end.

Using the proposed FE approach, the behaviour of CFRP-strengthened steel beams

was examined and it was found that: (1) the use of a stiffer CFRP plate may lead to

a lower ultimate load because of plate end debonding may occur earlier; (2) the

plate end debonding is more likely to occur when a short CFRP plate is used, and

the failure mode may change to intermediate debonding or other failures modes

such as compression flange buckling if a longer plate is used.

246



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250

Table 7.1 Details of the test beams and the FE models

Specimen/ Model name

Length of CFRP

plate, mm

Elastic modulus of CFRP, GPa

Thickness of CFRP plate, mm

Mode I behaviour

Compression flange

strengthening S303* 300 212 3 N/A No S304* 400 212 3 N/A No S310* 1000 212 3 N/A No

S303-1-212# 300 212 3 model 1 No S303-2-212# 300 212 3 model 2 No S303-1-330# 300 330 3 model 1 No S304-1-212# 400 212 3 model 1 No S310-1-212# 1000 212 3 model 1 No

S310-1-212-P# 1000 212 3 model 1 6 mm steel plate *Test beams (Deng and Lee 2007) # FE models

Table 7.2 Key parameters for traction-separation models

Loading mode Peak bond stress (MPa)

Displacement at peak bond stress,

δ1 (mm)

Interfacial fracture energy,

Gf (N/mm) Mode I (model 1) 29.70 0.0037 0.0594 Mode I (model 2) 29.7 0.0037 0.11

Mode II 26.73 0.0018 1.59

Table 7.3 Experimental and FE results

FE model

Experimental results FE results

Ultimate load, Pu

(kN)

Deflection at ultimate

load, ∆u (mm)

Ultimate load, Pu-FE

(kN)

Deflection at ultimate load, ∆u-FE

(mm)

Load at debonding initiation, Pd-FE (kN)

Deflection at

debonding initiation, ∆p-FE (mm)

S300* 122.60 20.70 119.76 20.97 N/A N/A S303-1-212# 120.00 5.12 124.66 7.05 118.30 5.08 S303-2-212# 120.00 5.12 125.10 7.07 121.90 5.78 S303-1-330# N/A N/A 122.99 6.17 115.00 4.60 S304-1-212# 135.00 7.00 135.74 11.04 132.00 8.00 S310-1-212* 159.50 20.10 158.17 20.84 N/A N/A

S310-1-212-P^ N/A N/A 188.05 27.31 188.05 27.31 * = compression flange buckling, # = plate end debonding, ^ = intermediate debonding

251

Figure 7.1 Traction-separation curve

Figure 7.2 Linear damage evolution under mixed-mode loading

0mδ f

mδ

cmG

Traction

Separation

1nδ , 1

sδ , 1tδ f

nδ , fsδ , f

tδ

Traction

Separation

σmax, τmax

Knn, Kss, Ktt (1-D)K

GI-Gn, GII-Gs, GII-Gf

Gn,Gs,Gt

maxmδ

nδ , sδ , tδ

252

(a) Test set-up

(b) Cross-section of CFRP-strengthened specimen

Figure 7.3 Details of test specimens of Deng and Lee (2007)

4mm

7.6mm

127mm

76mm

76mm

LCFRP

1100mm

127x76UB13 steel I beam

3mm thick CFRP plate 1mm thick adhesive layer

253

Figure 7.4 Stress-strain curve of steel used in FE simulation

Figure 7.5 Bond-slip model for Mode II loading used in FE simulation

050

100150200250300350400450500

0 0.01 0.02 0.03 0.04 0.05

Stre

ss (M

Pa)

Strain

0

5

10

15

20

25

30

0 0.05 0.1 0.15

Bon

d sh

ear s

tress

(MP

a)

Slip (mm)

Mode II

254

Figure 7.6 Bond-separation models for Mode I loading used in FE simulation

Figure 7.7 Load-displacement curves of a bare steel I beam

0

5

10

15

20

25

30

35

0 0.002 0.004 0.006 0.008

Bon

d no

rmal

stre

ss (M

Pa)

Separation (mm)

Mode I- model 1

Mode I- model 2

0

20

40

60

80

100

120

140

0 10 20 30

Load

(kN

)

Mid-span deflection (mm)

S300- Experimental (Deng and Lee 2007)S300- FE

255

Figure 7.8 Deformed shape of S303-1-212 at failure

Figure 7.9 Load-deflection curves for specimen S303

0102030405060708090

100110120130

0 2 4 6 8 10 12Mid-span deflection (mm)

Load

(kN

)

S303-Experimental

S303-1-212

S303-2-212

S303-1-330

damage initiation of S303-1-330

damage initiation of S303-1-212 and S330-2-212

debonding initiation of S303-1-330



Adhesive layer

Plate end debonding

Dark blue color: zero stress region Red color: high stress region

(Deng and Lee 2007)

256

Figure 7.10 Normalized interfacial stresses at the plate end for specimen S303

(a) 92.6 kN

(b) 118.3 kN

Red colour: high positive stress region

Green colour: low stress region

Blue colour: high negative stress region

Figure 7.11 Longitudinal shear stresses in the adhesive from S303-1-212

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100 120 140

Nor

mal

ized

stre

ss

Load (kN)

Longitudinal shear-S303-1-212

Normal- S303-1-212


Normal- S303-2-212


Normal- S303-1-330

Debonding initiation

Debonding initiation X

X

76mm

300mm

257

(a) 71kN

(b) 92.6kN

-0.2-0.1

00.10.20.30.40.50.60.7

-200 -100 0 100 200Nor

mal

ized

stre

ss (M

Pa)

Distance from the mid span (mm)

Normal stress

Longitudinal shear stress

Transverse shear stress

-0.2-0.1

00.10.20.30.40.50.60.70.8

-200 -100 0 100 200

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



258

(c) 107 kN

(d) 118.3kN

Figure 7.12 Interfacial stress distributions along section x-x from model S303-1-

212

-0.2

0

0.2

0.4

0.6

0.8

1

-200 -100 0 100 200

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



-0.2

0

0.2

0.4

0.6

0.8

1

-200 -100 0 100 200

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



259

Figure 7.13 Interfacial stress-strain behaviour at the plate end from model S303-1-

212

Figure 7.14 Deformed shape of model S304-1-212 at failure

00.10.20.30.40.50.60.70.80.9

0 0.05 0.1 0.15

Nor

mal

ized

stre

ss

Strain

Normal stress-150mm from the mid-spanLongitudinal shear stress-150mm from the mid-spanNormal stress-147.5mm from the mid-spanLongituninal shear stress-147.5mm from the mid-span

Adhesive layer

Dark blue color: zero stress region Red color: high stress region

Plate end debonding

260

Figure 7.15 Load-deflection curves of specimens S304 and S310

Figure 7.16 Deformed shape of model S310-1-212 at failure

020406080

100120140160180

0 10 20 30

Load

(kN

)


S304- Experimental (Deng and Lee 2007)S310- Experimental (Deng and Lee 2007)S304-1-212

S310-1-212

Compression flange buckling

damage initiation of S304-1-212


261

(a) 102kN

(b) 140.5kN

(c) 159.7kN (peak load)

Y

Y

Softening at the mid region

High shear stress

76mm

1000mm

262

Red colour: high positive stress region

Green colour: low stress region

Blue colour: high negative stress region

Figure 7.17 Longitudinal shear stresses in the adhesive from model S310-1-212

(a) 102kN

(b) 140.5kN

-0.2-0.15-0.1

-0.050

0.050.1

0.150.2

0.25

-500 0 500

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-500 -300 -100 100 300 500

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



263


Figure 7.18 Interfacial stress distributions along section Y-Y from model S310-1-

212

(a) 33.7kN

(b) 159.5kN

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

-500 -300 -100 100 300 500

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



Z

Z

High longitudinal shear stresses

76mm

1000mm

264


(d) 186.7kN (post peak curve)

Red colour: high stress region

Green colour: intermediate stress region

Blue colour: low stress region

Figure 7.19 Damage propagation in the adhesive layer in model S310-1-212-P

Figure 7.20 Load-deflection curve from model S310-1-212-P

020406080

100120140160180200

0 10 20 30 40Mid-span deflection (mm)

Load

(kN

)

S310-1-212-P

damage initiation

debonding initiation

Debonding initiation

Debonding

265

(a) 176.8kN

(b) 184.8kN

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-500 -300 -100 100 300 500

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



-0.6-0.4-0.2

00.20.40.60.8

11.2

-500 -300 -100 100 300 500

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



266


(d) 186.7kN (a peak-peak state)

Figure 7.21 Interfacial stress distributions along section Z-Z from model S310-1-

212-P

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

-500 -300 -100 100 300 500

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

-500 -300 -100 100 300 500

Nor

mal

ized

stre

ss (M

Pa)


Normal stress



267

APPENDIX 7.1

FE MODELLING OF STEEL I-BEAM UNDER FLEXURAL LOADING

A7.1 INTRODUCTION

This appendix is concerned with the FE modelling of steel I beams subjected to

flexural loading. The work presented in this appendix serves as a basis for and

supplements the FE study presented in the main body of the chapter.

As discussed earlier, while the experimental study presented in Deng and Lee (2007)

is the most suitable among the existing studies for the verification of the proposed

FE approach, some basic information of the test specimens is not available in the

paper, including the stress-strain curve of the steel as well as imperfections and

residual stresses in the steel section. For the present study, the information was

either indirectly obtained from the reported load-displacement curve of the control

beam or based on a certain assumption (see Section 7.3). Apparently, the so-

obtained information is unlikely to be exactly the same as that in the actual

experiments. Therefore, in the FE simulation presented in this appendix, particular

emphasis was placed on the possible effects of the various assumptions on the FE

predictions for steel-I beams.

FE models were developed for a bare steel I-beam tested by Linghoff et al. (2009).

This beam test was selected as more details (e.g. the stress-strain curve of the steel,

load-strain curve of the beam) were provided, so that the FE model can be verified

with more confidence.

A7.1 BEAM TESTED BY LINGHOFF ET AL. (2009)

The selected steel beam tested by Linghoff et al. (2009) was constructed of a

standard HEA 180 profile and was subjected to four-point bending. The dimensions

of the cross-section and the test set-up are shown in Figure A7.1. The net span of

the beam was 1800 mm and simply-supported boundary conditions were provided.

To prevent local buckling of the web, full-depth 4 mm thick stiffeners were

268

provided on each side of the web at all support and loading points. To prevent

lateral buckling of the beam, lateral supports were provided at the mid-span (Figure

A7.1a). The experimental stress-strain curve of the steel was provided by Linghoff

et al. (2009) and is reproduced in Figure A7.2.

A7.2 FE MODELS FOR STEEL I BEAM

The FE simulations were conducted using the commercial FE program ABAQUS

(ABAQUS 2004). The exact dimensions and boundary conditions of the beam as

shown in Figure A7.1 were used in the FE models. The web stiffeners were

provided on each side of the web at the loading and support points; in the FE model,

three sides of each stiffener were tied to the top flange, the bottom flange and the

web of the cross section respectively. The general purpose shell element S4R with

reduced integration was adopted for the steel section, with nine integration points

through the thickness. Both material nonlinearity and geometric nonlinearity were

considered in the FE models. Vertical displacements were applied on the top flange

of the steel section at the two loading points.

The FE models developed include a reference model and a few other models; the

differences between the reference model and the other models lie in the following

parameters they adopted: (1) stress-strain curve of steel; (2) imperfections of the

steel section; and (3) residual stresses of the steel section. In the reference model,

the following were adopted for these three key parameters: (1) the experimental

stress-strain curve of steel provided by Linghoff et al. (2009); (2) no imperfections;

(3) the residual stress distribution adopted by Pi and Trahair (1994) (see section

A7.2.4 below for details).

A7.2.1 Mesh Convergence Study

A mesh convergence study was conducted, arriving at an appropriate mesh for the

subsequent finite element modelling work presented in this appendix. A commonly-

used approach for mesh convergence studies is to find a mesh which provides

almost the same results as those from a further refined mesh. It was found by trying

several different meshes (i.e. 5 mm x15 mm, 3 mm x 10 mm, 2.5 mm x 5 mm and

269

2.5 mm x 2.5 mm, where the first number is the size in the longitudinal direction

and the second number is the size in the transverse direction) that the element size

of 2.5 mm x 2.5 mm was fine enough (see Figure A7.3). Therefore, the element size

of 2.5 mm x 2.5 mm was adopted in the subsequent FE modelling work.

A7.2.2 Material Modelling

The accurate modelling of the constitutive behaviour of steel is very important for

the success of the FE model. Steel is normally regarded as an elastic-plastic material,

and the well-known J2

flow theory is often employed to model its plastic behaviour.

The key parameters determining the elastic-plastic behaviour are found from a

uniaxial stress-strain curve, which provides the elastic modulus, the yield strength

and the hardening parameter of steel. In the absence of an experimental stress-strain

curve, the uniaxial stress-strain behaviour of steel is normally approximated by an

idealized stress-strain model, among which the bi-linear (i.e. elastic-perfectly plastic)

model and the tri-linear (i.e. elastic-plastic-hardening) model are simple and

commonly used (Lay and Smith 1965; Pi and Trahair 1994; Bayfield and

Dhanalakshmi 2002; Byfield et al. 2005).

In this section, the effect of using different stress-strain curves for steel on FE

predictions is examined. Three stress-strain curves were considered in the present

study (i.e. the experimental stress-strain curve and the curves defined by the two

idealized stress-strain models) and they are shown in Figure A7.2. The bi-linear

stress-strain curve has the same initial slope (i.e. elastic modulus of steel) and yield

strength as the experimental curve. The tri-linear stress-strain curve also has the

same initial slope and yield strength; the plastic plateau of the curve ends at a strain

of 6εy with εy

being the yield strain and the hardening portion of the curve has a

slope of 2700MPa, following the recommendations of Bayfield et al. (2005).

Figure A7.4 shows a comparison of the predictions of the reference model and the

two other FE models. The two other FE models are exactly the same as the

reference model except for the stress-strain curve adopted for steel; the bi-linear

stress-strain curve and the tri-linear curve introduced above were used in these two

270

FE models respectively. As expected, the three predicted curves are exactly the

same before steel yielding, but after that small differences can be seen. The small

differences are due to the use of different stress-strain curves for steel (Figure A7.2):

in the experimental stress-strain curve, strain hardening occurs immediately after

the yield point, but strain hardening is not considered in the bi-linear model and is

assumed to occur only after a certain plastic strain in the tri-linear model. Figure

A7.4 also shows that the use of the tri-linear stress-strain curve, which takes into

account strain hardening, leads to results closer to that of the reference model. It

may therefore be concluded that in the absence of experimental stress-strain curve

for steel, the tri-linear stress-strain model (Bayfield et al. 2005) should be adopted

for a close approximation.

A7.2.3 Effect of Imperfections

The imperfections of a steel beam may affect its load-carrying capacity, especially

when the failure is controlled by the lateral buckling of the beam or by the local

buckling of the steel section. In the present study, three different modes of

imperfections provided in AS4100 (1998) were considered; the shapes and

magnitudes of these imperfections are shown in Figure A7.5. The present study only

considers imperfections which are constant along the length of the steel beam; this

consideration is regarded to be reasonable for steel beams with only local buckling

being a concern (i.e. overall bulking is unlikely to occur).

Three additional FE models were developed, which are exactly the same as the

reference FE model except that they adopted the three different modes of

imperfections (see Figure A7. 5) respectively. In Figure A7.6, the predictions of the

three additional FE models are compared with those of the reference model. It is

evident from Figure A7.6 that when the mode I or the mode III imperfections are

used, the predictions are almost the same as the FE model with no imperfections (i.e.

the reference model). By contrast, the mode II imperfections are shown to lead to

failure at a significantly smaller deflection due to the buckling of the compression

flange (Figure A7.6) but have only a limited effect on the load-carrying capacity.

271

A7.2.4 Effect of Residual Stresses

Residual stresses may also affect the load-displacement behaviour of steel beams. In

the present study, the residual stress distributions suggested by Pi and Trahair

(1994) were considered. The residual stresses distributions, as shown in Figure A7.7,

satisfy bending equilibrium requirements, so they are not expected to have any

effect on the load carrying capacity if the failure is by pure in-plane inelastic

bending. The residual stresses were incorporated into the FE model, by defining the

initial condition using the command *INITIAL CONDITIONS, TYPE=STRESS

provided in ABAQUS. In Figure A7.8, the predictions of the reference FE model

are compared with those of another FE model with all the details being the same as

the reference model except that no residual stresses were included. It is evident that

the inclusion of residual stresses does not affect the ultimate load of the beam, but

have some effects on the slope of the curve close to the yield load.

The predictions of the two models (i.e. the reference FE model and the model with

no residual stresses included) are compared with the experimental load-strain curves

in Figure A7.9, and a close agreement can be seen.

A7.3 CONCLUSIONS

This appendix has presented an FE study aimed at the accurate simulation of the

behaviour of steel I-beams under flexural loading. The key parameters examined in

the study include the material stress-strain behaviour, imperfections and residual

stresses of the steel section. The FE model proposed has been shown to provide

very close predictions of the test results. Results from the FE study allow the

following conclusions to be drawn:

(1) In the absence of an experimental stress-strain curve of steel, the tri-linear

stress-strain model proposed by Byfield et al. (2005) provides closer predictions

than the simple bi-linear stress-strain model.

(2) The mode II imperfections (Figure A7.5) have a significant effect on the

deflection at which compression flange buckling occurs, while the mode I and the

272

mode III imperfections have no obvious effects on the load-displacement behaviour

of the steel beam.

(3) The residual stresses have no effect on the ultimate load-carrying capacity of the

beam, but have some effects on the slope of the curve close to the yield load.

While the conclusions above are obtained from the FE modelling of a typical steel-I

beam, they are believed to be applicable to other similar beams with similar

boundary conditions and a similar failure mode (i.e. yielding followed by

compression flange buckling).

273

REFERENCES ABAQUS (2004). ABAQUS, ABAQUS Inc., Rising Sun Mills, 166 Valley Street,

Providence, RI 02909-2499, USA.

AS 4100 (1998). Steel Structures, Standards Australia, NSW 2142, Australia.

Byfield, M.P., Davies, J.M. and Dhanalakshmi, M. (2005). "Calculation of the

strain hardening behavior of steel structures based on mill tests", Journal of

Constructional Steel Research, Vol. 61, 133-150.

Byfield, M.P. and Dhanalakshmi, M. (2002). "Analysis of strain hardening in steel

beams using mill tests", Proceedings of the Third International Conference

on Advances in Steel Structures, Hong Kong SAR, China PRC. December.

139-146.

Deng, J. and Lee, M.M.K. (2007). "Behaviour under static loading of metallic

beams reinforced with a bonded CFRP plate", Composite Structures, 78(2),

232-242.

Lay, G. and Smith, R.D. (1965). "Role of strain hardening in plastic design",

Journal of Structural Division, ST3, 25-43.



Pi, Y.L. and Trahair, N.S. (1994). "Inelastic bending and torsion of steel I-bems",

Journal of Structural Engineering, 120(12), 3397-3417.

274

(a) Test set-up

(b) Cross-section of HEA 180

Figure A7.1 Details of the specimen tested by Linghoff et al. (2009)

6mm

9.5mm

171mm

180mm

Lateral supports

1800mm

110mm 110mm

HEA180 steel I-beam

275

Figure A7.2 Different stress-strain curves used in FE models

Figure A7.3 Results of mesh convergence study

0

50

100

150

200

250

300

350

400

450

0 0.01 0.02 0.03 0.04

Stre

ss (M

Pa)

Strain, ε

Bi-linear stress-strain curve

Tri-linear stress-strain curve

Experimental stress-strain curve

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Load

(kN

)


5mm*15mm

3mm*10mm

2.5mm*5mm

2.5mm*2.5mm

276

Figure A7.4 Effect of stress-strain curve on load-displacement behaviour

Figure A7.5 Imperfection shapes

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Load

(kN

)


FE-reference curve

FE-bi-linear stress-strain curve

FE-tri-linear stress-strain curve

1.8mm

3mm 3mm

3mm 3mm

3mm

(a) mode I (b) mode II (c) mode III

277

Figure A7.6 Effect of imperfections on load-displacement behaviour

Figure A7.7 Residual stresses in a steel I-beam (Pi and Trahair 1994)

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Load

(kN

)


FE-reference

FE- Mode I imperfections

FE- Mode II imperfections

FE- Mode III imperfections

h/2

σrc σrt

σrt

σrc σrc

σrc σrc σrc

σrt

σrt

h/4

h/4

σrc=0.35σy σrt=0.5σy

278

Figure A7.8 Effect of residual stresses on load-displacement behaviour

Figure A7.9 Comparison of load-strain behaviour

0

50

100

150

200

250

300

0 10 20 30

Load

(kN

)


FE-reference

FE-no residual stress

0

50

100

150

200

250

300

0 5000 10000 15000

Load

(kN

)

Strain at the mid-span on tension flange (µε)

Experimental

FE-reference

FE-no residual stress

279

CHAPTER 8 CFRP STRENGTHENING OF RECTANGULAR STEEL

TUBES SUBJECTED TO AN END BEARING LOAD

8.1 INTRODUCTION

Web crippling under transverse bearing is a common failure mode of thin-walled steel

or aluminium sections and has been studied by many researchers (e.g. Packer 1984;

Packer 1987; Zhao and Hancock 1992; Zhao and Hancock 1995; Zhou and Young

2006; Zhou and Young 2007). Zhao et al. (2006) recently explored the use of bonded

CFRP plates to enhance the transverse end bearing capacity of steel rectangular hollow

section (RHS) tubes through a series of tests. These tests showed that bonded CFRP

plates provide an effective means of enhancing the end bearing capacity of RHS tubes.

These tests also revealed that debonding of the CFRP plates from the steel substrate is a

common phenomenon in such CFRP-strengthened RHS tubes.

Debonding failure is always a concern for hybrid structures where two or more

materials are bonded together using adhesives. From the studies presented in the

preceding chapters, it is clear that interfacial stresses in the adhesive layer govern the

debonding failure mode. Furthermore, the effects of peeling and shear interfacial

stresses are different in different joint configurations.

The first part of this chapter presents results from an experimental study on steel RHS

tubes subjected to end bearing loads to clarify the effect of adhesive properties on their

failure mode and their load-carrying capacity as well as the effect of the web depth-to-

thickness ratio on their load-carrying capacity. The second part of the chapter presents

a finite element (FE) model to predict the debonding behaviour of CFRP-strengthened

RHS tubes under end bearing loads. Results from this FE study explain reasonably well

the experimental behaviour of the tubes strengthened with linear adhesives. To the best

280

knowledge of the author, no previous FE study on this debonding failure mode has

been attempted. Finally, a design model is presented to predict the load-carrying

capacity of CFRP-strengthened RHS tubes considering the effect of deboning failure.

The proposed model serves as a preliminary model which can be refined in the future

for the prediction of the load-carrying capacity of CFRP-strengthened RHS tubes.

8.2 END BEARING TESTS

8.2.1 Test Specimens

An experimental study on CFRP-strengthened steel RHS tubes was carried out in two

series. Series I was designed to investigate the effect of the adhesive type on the load-

carrying capacity, while Series II was designed to examine the effect of the web depth-

to-thickness ratio on the load-carrying capacity. The web depth-to-thickness ratio β is

defined as ( )2 extd rt

− , where d is the external depth of the section , extr is the

external corner radius, and t is the thickness of the web (Figure 8.1a).

In Series I, sixteen specimens were tested. These specimens included one bare RHS

tube as the reference specimen (Figure 8.1a) (as the bare steel tube was cut from the

same tube as CFRP-strengthened specimens, testing only one bare tube as the control

specimen is believed to be reasonable) and fifteen CFRP-strengthened RHS tubes

(Figure 8.1b); five different adhesives were used to bond the CFRP plates to the steel

tube (the CFRP plates were placed with fibres in the vertical direction) and three

identical specimens were made using each adhesive. The five adhesives are commonly

available in the market and were chosen to cover a wide range of adhesive material

properties. For all the Series I specimens, 100-50-2 RHS tubes (i.e. 100 mm in external

height, 50 mm in external width and 2 mm in tube wall thickness) were used.

In Series II, twelve specimens were tested. These specimens included four specimens

made from each of the three different tube sections (125-75-3, 100-50-3 and 75-25-3

281

respectively); one of the four specimens was a bare RHS tube as a reference specimen

but the other three nominally identical specimens were CFRP-strengthened RHS tubes

(Figure 8.1b). The two series of tests combined cover four different web depth-to-

thickness ratios. For all the specimens in Series II, the Araldite 2015 adhesive was used

based on the test results of Series I.

For ease of reference, the name of each specimen starts with an abbreviation to

represent the adhesive type (FYFE for FYFE Tyfo, S30 for Sika 30, S330 for Sika 330,

A2015 for Araldite 2015 and A420 for Araldite 420), followed by a letter from “A” to

“D” to represent the section type (A for 100-50-2, “B” for 125-75-3, “C” for 100-50-3

and D for 75-25-3) and followed by a Roman number to differentiate the three

nominally identical specimens with the same adhesive and section.

For each of the CFRP-strengthened RHS tubes, CFRP plates were bonded to the outer

surfaces of the two webs, as shown in Figure 8.1b. This strengthening scheme was

found by Zhao et al. (2006) to be highly effective. All specimens of the same

configuration were made from the same steel tube and the same high-modulus CFRP

with unidirectional fibres. The CFRP plates were cut to have a height equal to that of

the web (i.e. d-2rext) and to be 50 mm in width; two such plates were bonded to each

web side but for ease of reference the two plates together are referred to as a single

plate of 100 mm in width hereafter; they were also treated as a single plate in the

subsequent FE study considering the presence of adhesive joining the two plates

together. The specimen details are summarized in Table 8.1.

8.2.2 Material Properties

The properties of the steel and the CFRP are given in Table 8.2. The material properties

of the CFRP are those in the direction of fibres supplied by the manufacturer. The

material properties of the steel were found from tensile coupon tests; for section A

(100-50-2), coupons cut from both the flat regions and the corners of the steel tube (see

Figure 8.1c) were tested as their properties were expected to be different and were used

282

in FE modelling. However, only coupons cut from the flat regions were tested for other

RHS tubes (B-D). These specimens, with a nonlinear adhesive, were not included in FE

modelling. For web crippling capacity calculations, material properties of the flats are

sufficient. Tensile coupon tests were also conducted to obtain the tensile properties of

the five adhesives used in this study. Five coupons were tested for each adhesive. The

key results averaged from the five coupon tests for each adhesive are given in Table 3.1

(Chapter 3) and the typical stress-strain curves of these adhesives are shown in Figure

3.3 (Chapter 3). It is evident from Table 3.1 that the five adhesives cover a wide range

of elastic moduli (from 1.75 GPa to 11.25 GPa) and ultimate tensile strains (from 0.003

to 0.0289).

8.2.3 Preparation of Specimens

At the time this experimental study was conducted, the study presented in Chapter 3

was still in progress. Therefore, the following procedure was adopted in preparing the

CFRP-strengthened specimens based on the guidelines proposed by Schnerch et al.

(2007). The outer web surfaces of a steel tube were first cleaned with acetone and then

grit-blasted using 0.5 mm angular grit. The CFRP plates were then bonded to the

prepared surfaces within 24 hours. Before the bonding of CFRP plates, their surfaces

were also cleaned with acetone and roughened using a sand paper. The adhesive layer

was designed to be 1 mm thick and this thickness was closely controlled using glass

spacers except when adhesive FYFE Tyfo was used. For the latter, a uniform thickness

was difficult to achieve despite the use of glass spacers because of the low viscosity of

the adhesive. This poorer control of the adhesive thickness was expected to lead to

inferior bond performance.

8.2.4 Test Set-up and Instrumentation

The specimen was seated on a fixed steel base plate during the test, and the load was

applied through a bearing plate with a semi-circular block on the top. The semi-circular

block was used to ensure the constant direction and location of the applied load. A

283

schematic view of the test set-up is shown in Figure 8.2. Two LVDTs on each side of

the specimen (Figure 8.2) were used to measure the deflections. All the end bearing

tests were conducted using a 2000kN capacity Forney universal testing machine

(testing was carried out using the 300kN loading range with 0.5kN accuracy) with load

control at a loading rate of approximately 2kN per minute.


8.2.5.1 Series I-the effect of adhesive type

The failed specimens of Series I are shown in Figure 8.3a and the key test results are

summarized in Table 8.3, where the deflections were averaged from the readings of

four LVDTs. Except for the specimens with Araldite 420, failure occurred by the

debonding of the CFRP plates followed by web buckling; a number of different

debonding failure modes were observed. Adhesion failure at the steel/adhesive

interface occurred in specimens bonded with the FYFE Tyfo adhesive, cohesion failure

occurred in specimens with Sika 30, while combined adhesion (at the steel/adhesive

interface) and cohesion failure was found in specimens with Sika 330 and Araldite

2015. Specimens with Araldite 420 failed by the interlaminar failure of CFRP plates

(simply referred to as “CFRP failure” hereafter) again followed by web buckling.

Typical load-deflection curves are shown in Figure 8.4a. It is evident from Figure 8.4a

that all the CFRP-strengthened RHS tubes had almost the same initial stiffness despite

the use of different adhesives and this initial stiffness is much higher than that of the

bare RHS tube. These results indicate that the different adhesives were all able to

mobilize the contribution of the CFRP plates in the initial stage of loading and their

different elastic moduli had little effect on the overall stiffness of the strengthened

specimens.

Debonding of the CFRP plates always initiated from one of the plate ends (i.e. either

the top or the bottom end), but the propagation of debonding differed for different

284

adhesives. In specimens S30-A and S330-A, debonding propagated gradually towards

the mid-height of the web after the appearance of the first crack at a plate end; the load

kept increasing during this process (Figure 8.4). By contrast, in specimens A2015-A,

debonding was more localized near a plate end and its propagation was rapid; the load

dropped immediately after cracking was noted near a plate end (Figure 8.4a).

Formation of plastic hinges always followed debonding and these plastic hinges were

always located at the end of the debonded region. The lateral deflection of the web

increased rapidly after first cracking as a result of the loss of the resistance offered by

the CFRP plate against web buckling. The initial cracking at a plate end is believed to

be caused by high interfacial stresses (i.e. shear and peeling stresses) developed in this

region; the FE results presented in the next section demonstrate these interfacial stress

concentrations (Figures 8.9 and 8.10). For specimens S30-A and S330-A where the

first crack happened at a relatively low load level, an increasing load could be resisted

without web buckling following initial cracking so the debonding process was gradual.

For specimens A2015-A, the web was unable to resist the applied load after initial

cracking so debonding was sudden and the load dropped immediately.

Table 8.3 and Figures 8.3a and 8.4a show that the adhesive properties significantly

affected the behaviour of CFRP-strengthened RHS tubes subjected to an end bearing

load. Obviously, the failure modes of the specimens depended significantly on the

adhesion strength and the cohesion strength of the FRP-to-steel bonded joints (and thus

the properties of the adhesive) and the interlaminar strength of the CFRP plates which

is a material property of CFRP. It is easy to understand why specimens A420-A with

CFRP failure had the highest peak load among all the specimens as the stresses

developed in the CFRP plates were the highest in specimens A420-A. For specimens

S30-A, the cohesion strength was lower than the adhesion strength (cohesion failure,

see Table 8.3), but for specimens S330-A and A2015-A, the adhesion strength and the

cohesion strength were almost the same (combined adhesion and cohesion failure, see

Table 8.3). The load required to cause debonding failure was less than that to cause

CFRP failure for specimens with these three adhesives. For specimens FYFE-A,

adhesion failure occurred but this may be attributed to poor bonding caused by the low

285

viscosity of the adhesive, as explained earlier. It is thus difficult to draw firm

conclusions for this adhesive. For the three specimens of the same adhesive, some

significant variations in the peak load may be noted (Table 8.3) and the specimen with

a lower peak load was found to fail in a more unsymmetrical manner than other

specimens.

Although specimens S330-A and specimens A2015-A failed in the same mode (i.e.

combined adhesion and cohesion failure), their peak loads are significantly different

(Table 8.3 and Figure 8.4a). Specimens S330-A achieved a 48% peak load

enhancement on average over that of the bare RHS tube while the corresponding value

for specimens A2015-A is 103%. The elastic modulus and tensile strength of Sika 330

(specimen S330-A) are, however, much higher than those of Araldite 2015 (specimen

A2015-A) (see Table 3.1). Araldite 2015 is superior to Sika 330 only in the tensile

strain energy. The tensile strain energy of the former (=0.148) is approximately 39%

higher than the latter (=0.106). The results presented in Chapter 5 show that maximum

bond strength largely depends on the interfacial fracture energy. The FE results

presented in the next section show that significant peeling stresses exist at the plate

ends (Figures 8.9 and 8.10) which are believed to be the main cause of debonding

failure. A higher tensile strain energy provide higher resistance against the peeling

stresses before debonding failure occurs, leading to a higher ultimate load.

Indeed, Araldite 420 (specimen A420-A) which has the largest tensile strain energy

(=0.433) led to the highest peak load, indicating that the peak load of a CFRP-

strengthened RHS tube depends much more on the tensile strain energy than the tensile

strength of the adhesive. The interfacial stresses near the plate ends are expected to

increase with the elastic modulus of the adhesive. This increase of interfacial stresses

with the elastic modulus of the adhesive has been revealed by previous researchers

(Smith and Teng 2001; Smith and Teng 2002) for FRP-to-concrete bonded joints. In

addition, the nonlinear stress-strain behaviour of Araldite 2015 and Araldite 420 means

that significant stress redistributions near the plate ends are possible. The better

286

performance delivered by Araldite 2015 and Araldite 420 is believed to be the result of

these two factors.

It should be noted that Araldite 420 was also used in Zhao et al.’s tests (Zhao et al.

2006), but a different failure mode was observed. In their tests, combined adhesion and

cohesion failure occurred instead of CFRP failure found in the present tests. This

difference in failure mode is believed to be at least partially due to the different surface

preparation methods employed in the two studies. Instead of grit blasting, the steel

surfaces were hand-ground in Zhao et al’s study (Zhao et al. 2006), which is expected

to have resulted in inferior adhesion.

8.2.5.2 Series II- effect of web depth-to-thickness ratio

The experimental study (Section 8.2.5.1) on the effect of adhesive properties showed

that both Araldite adhesives (i.e. Araldite 2015 and Araldite 420) led to much higher

ultimate loads than the other adhesives investigated (Figure 8.4a). The reason for these

high ultimate loads is the ability of these adhesives to redistribute the high stresses near

the plate end and their high fracture energies in mode I and mode II. Since there is no

significant difference between the ultimate loads of the specimens made using these

two Araldite adhesives, Araldite 2015 is more attractive than Araldite 420 as the latter

has a lower viscosity and may thus be difficult to use on inclined surfaces. Therefore,

Araldite 2015 was used in all the specimens of Series II.

The failed CFRP-strengthened specimens of Series II are shown in Figure 8.3b while

the load-displacement curves for both the bare tubes and the CFRP-strengthened

specimens are shown in Figure 8.4b. For all the CFRP-strengthened specimens,

debonding occurred as combined adhesion and cohesion failure (Table 8.3). It was

difficult to ascertain by a post-test inspection whether debonding followed by web

buckling or web yielding was the failure mode (Figure 8.3b). For the bare tube

specimens, sections A and B showed web buckling failure and sections C and D

showed web yielding failure. For all the strengthened specimens, an increase in the

287

ultimate load is observed (Table 8.3). The load-carrying capacity of section A2015-A is

lower than the yield capacity of the bare section, thus the failure mode of section

A2015-A can be taken as debonding followed by web buckling. However, for all the

other strengthened sections, the load-carrying capacity is higher than the web yielding

or the buckling capacity of the bare section, thus it is difficult to conclude which failure

mode governed the strength.

Nevertheless, debonding of the CFRP plates always initiated from one of the plate ends,

and the formation of plastic hinges always followed debonding and was always located

at the end of the debonded region (Figure 8.3b). Except for section D, the location of

the plastic hinge on each web was close to the top corner (Figure 8.3b). In section D,

debonding propagated farther away from the top corner and the plastic hinge was closer

to the mid height of the web.

The effectiveness of CFRP strengthening in increasing the load-carrying capacity

depends on the failure mode of the bare steel tube (i.e. web buckling or web yielding)

(Figure 8.5). The strengthening provided against web buckling and web yielding can be

quite different and the strength enhancement depends on many factors among which

the web depth-to-thickness ratio plays a significant role. For strengthened tubes which

had a common failure mode in bare steel tubes, the effectiveness of strengthening

increases as the web depth-to-thickness ratio increases (Figure 8.5). Except for section

B specimens, debonding initiation in the specimens bonded with Araldite 2015 was

observed very close to the ultimate load. For the A2015-B specimens, early debonding

initiation was observed, but after the initiation of debonding, further increases in the

load were possible with these specimens. Plate end stress concentrations in the

strengthened specimens obviously depend on the lateral displacements of the web and

thus the web depth-to-thickness ratio. As a result, debonding initiation also depends on

this ratio. As debonding reduces the effectiveness of strengthening, the load-carrying

capacity of the strengthened tube also depends on this ratio.

288

8.3 FINITE ELEMENT MODELLING

8.3.1 Model Description

The finite element (FE) model was built using the commercially available software

package ABAQUS (Abaqus 2004). Because of the symmetric nature of the problem,

only half of the section was modelled, with appropriately defined symmetric boundary

conditions. The general purpose shell element S4R with reduced integration was used

to model the steel tube. Only the specimens with linear adhesives (i.e. Sika 30 and Sika

330) were modelled and therefore the steel tube modelled was that of section A. The

purpose of this FE study was to investigate the application of a bond-slip model in

predicting the debonding failure of CFRP-strengthened RHS steel tubes under an end

bearing load. A bi-linear bond-slip behaviour was assumed, which is suitable for only

for linear adhesives.

The base plate (Figure 8.6) was modelled as a fixed rigid body. The “surface to surface

contact” option provided in ABAQUS was employed for modelling the interaction

between the base plate and the steel tube. The “small sliding” option was adopted so

that the nodes on the slave surface (defined as the bottom corner region of the tube in

the present study) interacted appropriately with the same local area of the master

surface (defined as the top surface of the base plate), even when the surfaces underwent

large rotations. The “hard contact” option was used for the normal direction while a

friction coefficient of 0.45 (Oberg et al. 2000) was adopted to define the interaction in

the tangential directions.

The bearing plate (Figure 8.6) was modelled using the 8-node continuum element

C3D8. The interaction between the bearing plate and the steel tube was modelled in the

same manner as that for the base plate and the steel tube. The bottom surface of the

bearing plate was defined as the master surface and the top corner region of the steel

tube was defined as the slave surface. In the FE model, loading was applied at the top

four corners of the bearing plate by prescribing vertical displacements.

289

The measured material properties given in Table 8.2 (section A) were used for the steel

tube. The flat regions and the corner regions are illustrated in Figure 8.1(c). The

Poisson’s ratio was taken to be 0.3. The engineering stresses and strains were

transferred to the true stresses and true plastic strains to define the plastic part of the

steel behaviour.

More details of the FE modelling procedure of bare steel tubes subjected to an end

bearing load including the constitutive modelling of steel, the contact behaviour and the

selection of element type and size are given in Appendix 8.1.

The CFRP plates were treated as an orthotropic material. The elastic modulus in the

fibre direction (E3) was 300 GPa based on a nominal thickness of 1.4 mm according to

the manufacturer’s data while the elastic moduli of the other two directions (E1,E2), the

Poisson’s ratios and the shear moduli were assumed the following values based on the

results of (Deng et al. 2004): E1=E2=10 GPa, ν12=0.3, ν13=ν23=0.0058, G12=3.7 GPa

and G13=G23

=26.5 GPa. The CFRP plates were modelled using the general purpose

shell element S4R with reduced integration.

The adhesive layer was modelled using 3D cohesive elements COH3D8. The adhesive

surfaces were connected to the CFRP plate and the RHS web using tie constraints. The

cohesive law described in Section 7.2 (Chapter 7) was adopted to represent the

constitutive behaviour of the adhesive layer. The mode I fracture energy was assumed

to be equal to the tensile strain energy. The traction-separation behaviour was assumed

to be bi-linear for the adhesives in both mode I and mode II. The parameters of the

traction-separation curves used in FE modelling are summarized in Table 8.4. The

parameters for the mode II bond-slip curve were deduced from the bi-linear bond-slip

model presented in Chapter 6 (i.e. Eqns 6.2 and 6.4-6.6).

8.3.2 Mesh Convergence Study

290

A mesh convergence study was conducted, arriving at an appropriate mesh for the finite

element model adopted in the present study; more details of the mesh convergence

study of the bare steel tube are provided in Appendix 8.1. This mesh, as shown in

Figure 8.7, was found by testing several different meshes to be fine enough in the sense

further mesh refinement led to insignificant changes in the predicted ultimate load. 10

elements were selected to model each corner based on results obtained from the use of

2,4,6,8,9,10 and 11 elements; 200 elements were used over the height of the web based

on the results obtained from the use of 100, 150, 200, 250 elements.


The predicted load-deflection curves are compared with the experimental curves in

Figure 8.8. The FE model provides accurate predictions for the bare steel tube (Figure

8.8a).The post-failure branch of the predicted curve has a larger slope than the

experimental curve, which is attributed to the rotational restraint provided by the

loading head to the semi-circular loading block during the experiment; due to this

restraint, the semi-circular block in the laboratory test did not rotate as much about the

front edge of the steel tube as it did in the FE model. In addition, as the peak load is

reached, gradual slippage of the semi-circular block along the top flange was observed.

This gradual slippage of the semi-circular block means that the measured vertical

displacement was lower than the actual displacement of the top corner at the loaded end.

If no such discrepancy exists in experimental loading condition, a much better

agreement in the post-failure load-displacement branch can be achieved [see Fernando

et al. (2010) for further details].

The predicted ultimate loads for specimens S30-A and S330-A are in excellent

agreement with the experimental results (Figures 8.8b and c). However for the S330-A

specimens, some discrepancy is seen in the load-displacement behaviour close to the

ultimate load (Figure 8.8c). The FE model predicts much stiffer behaviour prior to the

ultimate load compared to the much longer stage of stiffness reduction prior to failure

observed in the experimental results. In the experiments it was observed that in the

291

S330-A specimens, crack initiation at a plate end occurred before the ultimate load was

reached (Figure 8.8c). In the experiments, debonding was a more dynamic process

compared to the much more gradual debonding propagation predicted by the FE model

which treated the process as a static problem. Due to the dynamic nature of debonding

cracking, deboning propagated farther than was possible without the dynamic effect,

leading to a greater reduction in the resistance/stiffness provided by the CFRP to the

web against lateral deformation. Therefore, the difference in stiffness reduction before

the ultimate between the experimental results and the FE results is due to dynamic

effect in the experiments which are not included in the FE model.

Typical predicted distributions of stresses in the adhesive layer over the height of the

adhesive layer (vertical section in Figure 8.6) are shown in Figure 8.9 for an S30-A

specimen and in Figure 8.10 for an S330-A specimen. In these figures negative peeling

stresses are compressive and the stress values are normalized values; the normal

stresses are normalized with respect to the tensile strength of the adhesive while the

shear stresses are normalized with respect to the shear strength of the adhesive found

from Eqn 6.4. The transverse shear stresses act along the fibre direction of the CFRP

plate (i.e. in the vertical direction) while the longitudinal shear stresses are

perpendicular to the fibre direction (i.e. in the horizontal direction).

As expected, there are local stress concentrations near the two plate ends (Figures 8.9

and 10). Figure 8.9a shows that for specimen S30-A at the 10kN load level, the peeling

stress in the vicinity of the plate end reaches around 90% of the adhesive tensile

strength, whereas the shear stress reaches only 42% of the adhesive shear strength.

Therefore, it is clear that the peeling stress is dominant in this type of bonded joints. As

debonding initiates, the interfacial stresses at the plate end region become zero (Figures

8.9b and c) and near the crack tip, the peeling stress continues to be dominant (Figures

8.9b and c). As debonding of the plate propagates, the resistance provided by the CFRP

plate to the rotation of the web is reduced and more rotation of the web can be expected,

which leads to increases in peeling stresses. This process keeps increasing peeling

stresses near the crack tip to drive the propagation of debonding. It is clear that this

292

debonding process is essentially governed by the interfacial peeling stress. The

debonding process of specimen S30-A shown in Figure 8.11 clearly shows the

initiation of debonding near the loaded end. It can also be seen that the high interfacial

stresses are concentrated initially at the plate ends, but as debonding propagates, these

high stresses move to the tip of the debonding crack.

Although peeling stresses also governed the behaviour of specimen S330-A, the

debonding process is slightly different. As the debonding initiates, the stresses at the

very ends of the plate reduce to zero in specimen S30-A (Figure 8.9b). However in

specimen S330-A, compressive peeling stresses exist at the plate end and debonding

initiates at a very small distance away from the plate ends (Figures 8.10 b and c). This

behaviour is believed to be caused by the reduced plate end stress concentrations due to

a lower elastic modulus of the Sika 330 adhesive. However, irrespective of the

difference in elastic modulus, the dominance of the peeling stress over the shear stress

is still clearly seen. In steel beams flexurally-strengthened with CFRP, significant

peeling stresses near the plate ends were found to lead to damage initiation (Figure

7.12). However it was also shown that as debonding initiates, peeling stresses become

much less important (Figure 7.12d). The FE results presented in this section for CFRP-

strengthened RHS steel tubes under an end bearing load show a different response. For

these members, interfacial peeling stresses are dominant not only at debonding

initiation and but also during the propagation of debonding (Figures 8.9 and 8.10). This

observation indicates that the mechanisms of damage initiation and propagation depend

on the type of bonded joints. The accuracy of such a FE model, where peeling stresses

are dominant, is highly dependent on the accuracy of the bond-separation behaviour

adopted for mode I loading. Hence more experimental results for the mode-I behaviour

of such bonded joints is needed to obtain a fuller understanding of the problem.

The deformed shapes of the specimens at failure predicted by the FE model are shown

in Figure 8.12. It is clear from Figure 8.12b that the failure mode of specimen S330-A

is localized at the top end of the RHS while the failure mode of specimen S30-A

involves overall lateral deformation of the web (Figure 8.12a). The experimental load-

293

displacement curves of the S330-A specimens (Figure 8.8b) indicate that around 18kN,

some load drops exist. Experimental observations indicated that this behaviour was due

to debonding occurring in the plate end regions. With the debonding in these regions,

sudden releases of the stresses and reductions in the resistance offered to the web

against rotation result, increasing the deformations of the web and reducing the web

stiffness. In the FE model, the process of debonding was predicted to be much more

gradual, leading to a higher stiffness in the load-displacement curve before the ultimate

load. In the S30-A specimens, no such load drops are seen in the experimental load-

displacement curves. It can be concluded that overall, the present FE model predicts the

load-displacement behaviour and the failure mode closely.

8.4 DESIGN MODELS

8.4.1 Existing Work

The only existing method for calculating the load-carrying capacity of CFRP-

strengthened RHS tubes subjected to an end bearing load was proposed by Zhao et al.

(2006). Their semi-empirical equations were based on experimental conducted on

specimens bonded using Araldite 420. In their model, two failure modes are identified

in terms of the bare steel tube (i.e. without CFRP strengthening): web buckling and

web yielding. The model of Zhao et al. (2006) is briefly presented below.

8.4.1.1 The web buckling mode of bare steel tubes

In Zhao et al.’s (2006) model, if the failure mode of the bare steel tube is web buckling,

the failure mode of the CFRP-strengthened RHS tube is assumed to remain as web

buckling or to be changed to web yielding (similar to the web yielding failure mode of

the bare steel tube). Therefore the ultimate load of a CFRP-strengthened RHS tube

where the failure mode of the bare RHS tube is web buckling is given as;

{ }min ,p bb byP R R= (8.1)

294

where pP is the predicted ultimate load of the CFRP-strengthened RHS tube, bbR is the

web buckling capacity and byR is the web yielding capacity. The formulas for bbR and

byR in AS4100 (1998) are adopted for Eqn 8.1 with some modifications to include the

strengthening effect of the bonded CFRP plates. These formulas are summarized below:

2bb b y cR b tσ α= (8.2)

2by b y pR b tσ α= (8.3)

0.5 1.5b extb N d r= + + (8.4)

In the above equations, N is the bearing width, extr is the external corner radius, t is the

thickness of the web, d is the height of the section and yσ is the yield strength of steel.

cα is the member slenderness reduction factor determined from AS4100 (1998) for

column buckling with a section constant 0.5bα = and a modified slenderness:

12250

yn ek

σλ β= (8.5)

( )22p s sk kα = + − (8.6)

2 1exts

rkt

= − (8.7)

The effective length factor ek is taken as 1.1 for bare RHS tubes (AS4100 1998; Zhao

and Hancock 1995). To account for the restraint provided by the CFRP it was

suggested to use 0.8 for ek (Zhao et al. 2006).

295

8.4.1.2 The web yielding mode of bare steel tubes

If web yielding is the failure mode for the bare RHS tube, the failure mode of the

CFRP- strengthened RHS tube is assumed to remain as web yielding. Therefore,

p byP R= (8.8)

Considering that the CFRP plate continue to take additional stresses when the steel has

already entered the strain hardening stage, the ultimate tensile stress of steel ( uσ )

should replace yσ . Therefore byR can be calculated as

2by b u pR b tσ α= (8.9)

where bb is given in Eqn 8.4 and the pα is taken as 0.32.

The current experimental results of Series II show that the assumption made for Eqn

8.1 is invalid. The failure mode of the bare RHS tube of section B was web buckling,

and the web yielding capacity of the bare RHS tube of section B was 50.3kN.

Therefore according to Eqn 8.1, the load-carrying capacity of the A2015-B specimens

cannot exceed 50.3kN. However, the experimental results show that the load-carrying

capacity of the A2015-B specimens is 56.2 kN on average with the A2015-B-II

specimen reaching an ultimate load of 61.6 kN (Table 8.3). Indeed, if the CFRP can

provide resistance to web yielding in a CFRP-strengthened RHS tube when the failure

mode of the bare RHS tube is web yielding, it should also be able to provide resistance

to web yielding in a CFRP-strengthened RHS tube when the failure mode of the bare

RHS tube is web buckling. In addition, the effective length factor ek depends on the

end restraints provided to the straight portion of the web. As CFRP strengthening is

limited to the straight portion of the web (i.e. 2 extd r− ), it will not have any effect on

the end restraints to the web. Furthermore, the effect of debonding, which is dependent

296

on the web slenderness as well as the adhesive type, has not been considered in this

strength model. To conclude, the applicability of Zhao et al.’s (2006) model is limited

to situations where a similar adhesive type is used and a similar type of failure mode

(i.e. debonding due to adhesion failure) controls the strength.

8.4.2 Proposed Model

From the experimental observations, it can be concluded that:

• Debonding has a significant influence on the strength enhancement;

• Debonding depends largely on the mechanical properties of the adhesive;

• Debonding also depends on the slenderness of the web; and

• CFRP strengthening increases both the web yielding and the web buckling

capacities

It is clear that any model for the prediction of the strength of such a strengthened

system should include a term to account for adhesive mechanical properties and a term

to account for the web slenderness which in return accounts for debonding. The FE

results presented previously have illustrated the mechanism of debonding in a CFRP-

strengthened RHS tube when a linear adhesive is used. If both the web slenderness and

a non-linear adhesive are considered, the problem becomes much more complicated

and more research is needed before a reliable design model may be proposed. If

however a perfect bond is assumed between the CFRP plates and the steel tube, the

problem becomes much less complicated. Therefore, as a first step, the strength

enhancement of CFRP-strengthened RHS tubes is first predicted with the assumption

of a perfect bond between CFRP and steel. This model can then be modified to account

for the effect of debonding. The load-carrying capacity of a CFRP-strengthened RHS

tube can be written as

{ }min ,d dp bb byP R R= (8.10)

297

where dbbR is the web buckling capacity of a CFRP-strengthened RHS tube with the

effect of debonding considered, and dbyR is the web yielding capacity of a CFRP-

strengthened RHS tube with the effect of debonding considered.

8.4.2.1 Web buckling capacity

The web buckling capacity maxbbR of a CFRP-strengthened RHS tube with perfect

bonding between CFRP and steel can be as calculated using Eqn 8.2, with bb being the

same as given by Eqn 8.4 and cα being the member slenderness reduction factor

determined from AS4100 (1998) for column buckling with a section constant 0.5bα =

and a modified slenderness parameter given by

250y

n elkr

σλ β =

(8.11)

Here, ek is taken to be the same as that for a bare RHS steel tube (i.e. 1.1) and r is

taken as the radius of gyration of the composite section (Figure 8.13) (the adhesive

layer which has negligible influence and is thus not considered) and is given as

t

t

IrA

= (8.12)

where

pt w p

s

EA A A

E= + (8.13)

pt w p

s

EI I I

E= + (8.14)

298

where wA and sE are the horizontal cross sectional area of the web and the elastic

modulus of steel respectively; pA and pE are the horizontal cross sectional area and the

elastic modulus of the CFRP plate respectively; and wI and pI are the moment of inertia

of the steel web and the CFRP plate taken about the mid-surface of the original web (i.e.

the axis of load transfer).

To consider the effect of debonding, the web buckling capacity of a CFRP-

strengthened RHS tube can be written as

maxd

bb b b bbR Rφ ψ= (8.15)

where 1bφ ≤ and 1bψ ≤ are the debonding reduction factors, which are functions of the

adhesive mechanical properties (i.e. tensile strength and elastic modulus) and the β

ratio respectively.

8.4.2.2 Web yielding capacity

The web yielding capacity of bare RHS tubes can be calculated based on the

mechanism model proposed by Zhao and Hancock (1995) (also in AS4100 1998). The

mechanism method considers the formation of six plastic hinges, two in each flange

and one in each web (Figure 8.14a). However with the presence of a CFRP plate on

each web, the weakest points are moved to the CFRP plate termination points, which

are also at the ends of the straight portion of the web. Therefore the mechanism shown

in Figure 8.14a can be expected to change to the mechanism shown in Figure 8.14b.

Since the CFRP plates can take additional stresses after the yielding steel and well into

the strain hardening stage of steel, the ultimate tensile stress ( uσ ) is proposed to replace

yσ in the evaluation of the web yielding capacity. Therefore, for CFRP-strengthened

RHS tubes, the upper bound value for the web yielding capacity can be calculated

assuming perfect bonding between CFRP and steel and the mechanism shown in Figure

299

8.14b. The yielding capacity from this mechanism model can be written as (for the

derivations, readers are referred to Zhao 1992);

max 2by b u pR b tσ α= . (8.16)

( ) ( )2 22

0.5 0.251 1 1 1sp pm pm

s D D

kk k k

α α α

= + − + − −

(8.17)

1 0.5pm

s Dk kα = + (8.18)

2 extD

rdkt t

= − (8.19)

and sk is given by Eqn 8.7. To account for the effect of debonding, two reduction

factors 1yφ ≤ and 1yψ ≤ can now be considered. These reduction factors are functions

of the adhesive mechanical properties (i.e. tensile strength and elastic modulus) and the

β ratio respectively. The lower bound value of the web yielding capacity of a CFRP-

strengthened RHS tube is the web yielding capacity of the bare RHS tube. The web

yielding capacity of a CFRP-strengthened RHS tube can be written as

( )maxmax ,dby by y y byR R Rφ ψ= (8.20)

where byR is the web yielding capacity of bare RHS tube calculated according to

AS4100 (1998).

The predicted ultimate loads for the CFRP-strengthened RHS tubes assuming perfect

debonding are compared with the experimental results in Table 8.5. The existing test

data are not sufficient to determine the values for the two reduction factors to account

300

for the effect of debonding. More research is thus needed to calibrate the model to

account for debonding. The increase in the buckling load of the perfectly-bonded

composite section is much higher than the increase in the web yielding capacity.

However, considering that specimens FYFE-A, S30-A, S330-A and A2015-A failed by

web buckling (as the yield capacity of the bare RHS tube is higher than the failure load

of the CFRP-strengthened RHS tube, it is certain that web buckling was the governing

failure mode), the effect of debonding on the web buckling capacity is much higher

than the effect of debonding on the web yielding capacity. For section D, the calculated

web yielding capacity of the bare steel tube (which was the governing failure mode) is

much lower than the experimental result. This specimen showed considerable strain

hardening behaviour, which is unusual for such cold formed sections. Therefore the

underestimation of the calculated web yielding capacity is believed due to this material

behaviour.

Also, cold-formed sections usually show enhanced material properties in corner regions

due to cold work of the cold forming process (Hancock 1988). Therefore, if plastic

hinges are formed in corner regions, the properties of the corner material properties

should be used instead of the material properties of the flats. However, for the current

series of tests, the hinges were formed at locations far enough from the corner regions

(i.e. more than a 2t distance away) and the use of the material properties of the flats is

more reasonable.

The above proposed model can serve as a first step in the development a sophisticated

design model for CFRP-strengthened CFRP RHS tubes. More research is needed on the

effects of adhesive properties and web slenderness to improve the accuracy of proposed

model.

8.5 CONCLUSIONS

This chapter has presented the results of an experimental study into the end bearing

behaviour of CFRP-strengthened RHS tubes. In the test programme, five different

301

commercially available adhesives were used to bond CFRP plates to RHS tubes of four

different sections. The test results showed that the adhesive properties have a strong

effect on the behaviour of such CFRP-strengthened RHS tubes. Four different

interfacial failure modes were observed in the tests: (1) adhesion failure; (2) cohesion

failure; (3) combined adhesion and cohesion failure; (4) interlaminar failure of CFRP

plates. These tests also revealed that for two adhesives of similar tensile strengths, the

adhesive with a larger ultimate tensile strain leads to a greater peak load. Among the

adhesives examined in this study, the two Araldite adhesives (Araldite 2015 and

Araldite 420) showed the best performance in terms of the ultimate load enhancement.

The test results of different RHS tubes strengthened with CFRP plates using Araldite

2015 showed that effectiveness of the strengthening system also depends on the

slenderness of the web. For sections with a slender web, a greater increase in load can

be achieved using the same CFRP plates. The increase in strength depends also on the

failure mode of the bare RHS tube which can be either web buckling or web yielding.

Nevertheless, the experimental results clearly showed that CFRP strengthening can

enhance both the web buckling and web yielding load-carrying capacities.

This chapter has also presented a finite element (FE) model for predicting the

behaviour of CFRP-strengthened RHS steel tubes subjected to an end bearing loads in

which debonding between CFRP and steel was modelled using the cohesive zone

model for the adhesive layer. The cohesive law adopted for modelling the adhesive

layer is based on a bi-linear traction-separation model, which is applicable only to

specimens with a linear adhesive. The FE results showed that debonding in these

strengthened RHS tubes was governed by the peeling stress. The excellent agreement

between the experimental and FE results validates the FE model and confirms the

usefulness of the traction-separation model in modelling debonding failures of CFRP-

strengthened metallic structures. More work is needed to implement a traction-

separation model for non-linear adhesives in the FE model.

302

A design model to predict the load-carrying capacity of CFRP-strengthened RHS tubes

was also proposed. The formulation of the design formula was based on the assumption

of a perfect bond between CFRP and steel. To account for debonding, two reduction

factors were introduced and these factors depend on the adhesive mechanical properties

and the web slenderness. Unfortunately, the existing experimental results are

insufficient for the calibration of these reduction factors. Nevertheless, the proposed

design model serves as the first step in developing a reliable design model for the load-

carrying capacity of CFRP-strengthened RHS tubes subjected to an end bearing load

with the effect of debonding duly considered.

303

REFERENCES

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AS 4100 (1998). Steel Structures, Standards Australia, NSW 2142, Australia.

Deng, J., Lee, M.M.K. and Moy, S.S.J. (2004). "Stress analysis of steel beams

reinforced with a bonded CFRP plate", Composite Structures, 65(2), 205-215.

Fernando, N.D., Teng, J.G., Yu, T. and Zhao, X.L. (2010). "Numerical modeling of

cold-formed stainless steel RHS under end bearing loads, In preperation.

Hancock, G.J. (1988). Design of Cold-Formed Steel Structures (To Australian

Standards AS1538-1988), Australian Institute of Steel Construction, Sydney,

Australia.

Oberg, E., Jones, F.D., Horton, H.L. and Ryffell, H.H. (2000). Machinery’s Handbook,

Industrial Press, 200 Madison Avenue, New York, USA

Packer, J.A. (1984). "Web crippling of rectangular hollow sections", Journal of

Structural Engineering, 110(10), 2357- 2373.

Packer, J.A. (1987). "Review of American RHS web crippling provisions", Journal of



guidelines for strengthening of steel bridges with FRP materials", Construction


Smith, S.T. and Teng, J.G. (2001). "Interfacial stresses in plated beams", Engineering

Structures, 23(7), 857-871.

Smith, S.T. and Teng, J.G. (2002). "FRP-strengthened RC beams. I: Review of

debonding strength models", Engineering Structures, 24(4), 385-395.

Zhao, X.L. (1992). The Behavior of Cold-Formed RHS Beams Under Combined

Actions, PhD Thesis, The University Sydney, Sydney, Australia.

Zhao, X.L., Fernando, D. and Al-Mahaidi, R. (2006). "CFRP strengthened RHS

subjected to transverse end bearing force", Engineering Structures, 28(11),

1555-1565.

304

Zhao, X.L. and Hancock, G.J. (1992). "Square and rectangular hollow sections

subjected to combined actions", Journal of Structural Engineering, 118(3), 648-

668.

Zhao, X.L. and Hancock, G.J. (1995). "Square and rectangular hollow sections under

transverse end-bearing force", Journal of Structural Engineering, 121(9), 1323-

1329.

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crippling", Journal of Structural Engineering, 132(1), 134-144.

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305

Table 8.1 Specimen details

Series Section Adhesive RHS tube Bearing

length (mm)

CFRP plate Height, d

(mm) Width, b

(mm) Thickness,

t (mm) Length, L

(mm) Height, d

(mm) Thickness,

t (mm) Length, L

(mm)

I 100-50-2 (A)

FYFE-Tyfo

99.8 50.1 1.78 202 50 92 1.4 100 Sika 30

Sika 330 Araldite 2015 Araldite 420

II 125-75-3 (B)

Araldite 2015 125.0 75.1 2.67 239 50 115 1.4 100

100-50-3 (C) 99.9 50.1 2.63 201 50 90 1.4 100 75-25-3 (D) 74.8 24.9 2.62 165 50 65 1.4 100

Table 8.2 Material properties of CFRP and steel

Section E, (GPa) σ0.2, (MPa)

σu (MPa)

A Flats 192 322 370

Corners 198 390 450 B Flats 199 317 402 C Flats 211 285 380 D Flats 209 286 439

CFRP 300 N/A 1300

306

Table 8.3 Results of end bearing tests on CFRP-strengthened RHS tubes

Series Adhesive/ Section Specimen Failure mode# Peak load,

Pu-exp, (kN) Deflection at peak load, ∆u-exp, (mm) Pu-exp/P* ∆u-exp/∆* Average

Pu-exp/P* Average ∆u-exp/∆*

I

FYFE Tyfo FYFE-A-I A 20.69 2.02 1.09 1.11

1.15 0.80 FYFE-A-II A 21.88 0.49 1.15 0.27 FYFE-A-III A 22.76 1.88 1.20 1.03

Sika 30 S30-A-I C 26.91 0.79 1.42 0.43

1.43 0.52 S30-A-II C 26.21 1.19 1.38 0.65 S30-A-III C 28.05 0.87 1.48 0.48

Sika 330 S330-A-I A+C 28.98 1.33 1.53 0.73

1.48 0.67 S330-A-II A+C 27.14 1.19 1.43 0.65 S330-A-III A+C 27.82 1.13 1.47 0.62

Araldite 2015 A2015-A-I A+ C 41.23 1.36 2.17 0.74

2.03 0.70 A2015-A-II A+ C 38.64 1.28 2.04 0.70 A2015-A-III A+C 35.64 1.19 1.88 0.65

Araldite 420 A420-A-I I 42.77 1.53 2.26 0.84

2.37 0.85 A420-A-II I 44.84 1.89 2.36 1.04 A420-A-III I 47.37 1.22 2.50 0.67

II

B A2015-B-I A+C 54.50 2.63 1.15 1.01

1.19 0.81 A2015-B-II A+C 61.60 1.73 1.30 0.66 A2015-B-III A+C 52.60 1.94 1.11 0.74

C A2015-C-I A+C 62.70 1.76 1.48 0.68

1.44 0.74 A2015-C-II A+C 59.10 2.13 1.40 0.82 A2015-C-III A+C 61.00 1.88 1.44 0.72

D A2015-D-I A+C 75.60 1.39 1.27 1.39

1.30 1.28 A2015-D-II A+C 78.40 0.99 1.31 0.99 A2015-D-III A+C 78.40 1.45 1.31 1.46

* P = ultimate web crippling load of the bare steel tube, ∆ = deflection at the peak load of the bare steel tube # A = Adhesion failure; C = Cohesion failure; A+C= combined adhesion and cohesion failure; I = Interlaminar failure of CFRP plates

307

Table 8.4 Traction-separation parameters for different adhesives

Adhesive Mode

Peak bond normal

stress, maxσ /Peak

bond shear stress,

maxτ (MPa)

Separation/Slip

at peak bond

stress 1δ (mm)

Interfacial fracture

energy, Gf (N/mm)

Sika 30 I 22.34 0.0020 0.041

II 20.11 0.0013 1.031

Sika 330 I 31.28 0.0065 0.106

II 28.15 0.0705 7.056

Table 8.5 Experimental ultimate loads versus predicted ultimate loads based on

the perfect bond assumption

Specimen

Average experimental ultimate load,

Pu-exp (kN)

Predicted load of bare RHS tube (AS4100 1998)

Predicted load of CFRP-strengthened RHS tube

(perfect bond) Web buckling capacity, bbR

(kN)

Web yielding capacity, byR

(kN)

Web buckling capacity,

maxbbR (kN)

Web yielding capacity,

maxbyR (kN)

Bare-A 18.96 23.31 43.23 NA NA Bare-B 47.30 42.16 50.31 NA NA Bare-C 42.30 53.81 40.02 NA NA Bare-D 59.70 74.46 35.84 NA NA

FYFE-A 21.78 23.31 43.23 103.79 52.22 S30-A 27.06 23.31 43.23 103.79 52.22

S330-A 27.98 23.31 43.23 103.79 52.22 A2015-A 38.50 23.31 43.23 103.79 52.22 A420-A 44.99 23.31 43.23 103.79 52.22 A2015-B 56.23 42.16 50.31 142.54 68.72 A2015-C 60.93 53.81 40.02 133.00 58.69 A2015-D 77.47 74.46 35.84 131.59 61.79

308

(a) Bare RHS tube

(b) CFRP-strengthened RHS tube

Figure 8.1 Bare and CFRP-strengthened RHS tubes

L

RHS CFRP plates

d-2rext

RHS

t rext d

L

b

309

(c) Section nomenclature

Figure 8.1 Bare and CFRP-strengthened RHS tubes (Cont’d)

(a) Side view (b) Front view Figure 8.2 Schematic views of the test set-up

Mid-width of the top flange

Mid-width of the

bottom flange

Loading Ram

Transducer

Semi-Circular Block

Bearing Plate

Test Specimen

Semi-Circular Block

Bearing Plate

Test Specimen

Loading Ram

310

(i) Adhesive

FYFE (ii) Adhesive

S30 (iii) Adhesive

S330

(iv) Adhesive A2015

(v) Adhesive A420

(a) Series I

(i) Section-A (ii) Section-B (iii) Section-C (iv) Section-D

(b) Series II

Figure 8.3 Specimens after testing

311

(a) Series I

(b) Series II

Figure 8.4 Load-deflection curves of bare and CFRP-strengthened steel tubes

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6 7 8Deflection (mm)

Load

(kN

)

Bare tube-A-Experimental

FIFE-A-III-Experimental-Adhesionfailure

S30-A-III-Experimental-Cohesionfailure

S330-A-III-Experimental-Combinedadhesion cohesion failure

A2015-A-II-Experimental-Combinedadhesion cohesion failure

A420-A-III-Experimental-CFRP failure

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5 6 7 8Deflection (mm)

Load

(kN

)


Bare tube-B-Experimental

Bare tube-C-Experimental

Bare tube-D-Experimental

A2015-A-II-Experimental-Combinedadhesion cohesion failure

A2015-B-I-Experimental-Combinedadhesion cohesion failure

A2015-C-I-Experimental-Combinedadhesion cohesion failure

A2015-D-II-Experimental-Combinedadhesion cohesion failure

312

Figure 8.5 Increase in ultimate load vs. web depth-to-thickness ratio

Figure 8.6 FE model (mesh not shown for clarity)

0.00

0.50

1.00

1.50

2.00

2.50

20 30 40 50 60

Pcf

rp/P

β

Governing failure- web buckling

Governing failure- web yielding

Bearing plate

RHS tube

Base plate

CFRP plate Vertical section, 2mm from the loaded end

Loaded end

Horizontal section, 3mm from the top end

Top end

313

Figure 8.7 Mesh details

(a) Bare steel tube-A

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6 7 8Deflection (mm)

Load

(kN

)


Bare tube-A-FE

Corner region, 10 elements

Finer mesh on the web near the corner region (10 elements at 0.2mm element size)

200 elements for the rest of the web height

314

(b) Sika 30 adhesive

(c) Sika 330 adhesive

Figure 8.8 Comparison of load-deflection curves from FE analysis and experiments

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8Deflection (mm)

Load

(kN

)S30-A-I-Experimental

S30-A-II-Experimental

S30-A-III-Experimental

S30-A-FE

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8Deflection (mm)

Load

(kN

)

S330-A-I-Experimental

S330-A-II-Experimental

S330-A-III-Experimental

S330-A-FE

315

(a) 10kN

(b) 18kN

-0.6-0.4-0.2

00.20.40.60.8

11.2

0 50 100

Distance from the top of the bond region (mm)

Nor

mal

ized

stre

ss

Peeling stress

Transverseshear stressLongitudinalshear stress

-0.6-0.4-0.2

00.20.40.60.8

1

0 50 100


Nor

mal

ized

stre

ss PeelingstressTransverseshear stressLongitudinalshear stress

316

(c) 28.7kN (ultimate load)

Figure 8.9 FE interfacial stress distributions along the vertical section (Figure 8.6) in

Specimen S30-A

(a) 10kN

-0.6-0.4-0.2

00.20.40.60.8

11.2

0 20 40 60 80 100


Nor

mal

ized

stre

ss Peeling stress

Transverseshear stressLongitudinalshear stress

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 50 100


Nor

mal

ized

stre

ss

PeelingstressTransverseshear stressLongitudinalshear stress

317

(b) 18kN


Figure 8.10 FE interfacial stress distributions along the vertical section (Figure 8.6) in specimen S330-A

-0.4-0.2

00.20.40.60.8

1

0 50 100


Nor

mal

ized

stre

ss


-0.4-0.2

00.20.40.60.8

1

0 50 100


Nor

mal

ized

stre

ss


318

(a) 10kN

(b) 18kN

Maximum stress

Maximum stress

Softening region

Softening region

319


(d) 26.6kN (post ultimate load)

Figure 8.11 Debonding propagation in specimen S30-A (only the adhesive layer is shown)

Maximum stress

Debonded region

Debonded region

Maximum stress

Debonded region

Debonded region

320

(a) Specimen S30-A (b) Specimen S330-A

Figure 8.12 Deformed shapes of strengthened tubes

Figure 8.13 Composite section

CFRP plate Adhesive

Centre line of the web

Steel web

321

(a) Mechanism model for bare RHS tubes with web yielding failure

(b) Mechanism model for CFRP-strengthened RHS tubes with web yielding failure

Figure 8.14 Mechanism models for web yielding failure

maxbyR /2 max

byR /2

1 2 3 4

5 6

Plastic hinge

Rby/2 Rby/2

Plastic hinge

1 2

6

4 3

5

Rby/2 Rby/2

322

APPENDIX 8.1

NUMERICAL MODELING PROCEDURE FOR COLD-FORMED STEEL RHS TUBES UNDER AN END BEARING

LOAD

A8.1 INTRODUCTION

A brief description is given in Section 8.3 of the FE modeling procedure for cold-formed

steel RHS tubes under an end bearing load. This appendix provides a more detailed

description of the modeling procedure for bare steel RHS tubes. The details provided here

include a mesh convergence study and the modeling of material behavior, corner strength

enhancement, load transmission, geometric imperfections and residual stresses. These

issues are discussed below with reference to section A (100-50-2) whose dimensions are

given in Table 8.1.

A8.2 MODELLING OF MATERIAL BEHAVIOUR

For the development of an accurate FE model, the representation of the material

characteristics plays a key role. In the present study, different stress-strain curves

obtained from tensile coupon tests for the flat portions (i.e. flats) and the corners were

used in the FE model; the properties obtained from tensile coupon tests are summarized

in Table 8.2. ABAQUS requires the material behaviour to be specified by means of a

multi-linear stress-strain curve. The initial part of the curve represents the elastic part up

to the proportional limit stress with the measured Young’s modulus; the Poisson’s ratio

was taken as 0.3. The second part of the curve was defined in terms of the true stress and

the logarithmic plastic strain, using the *PLASTIC command.

323

A8.3 MESH CONVERGENCE

To achieve accurate results, it is important to employ a suitably-refined finite element

mesh for an FE model. A finer mesh generally provides more accurate predictions but at

the same time leads to a greater computational task. It is a common practice to perform a

mesh convergence study to determine a suitable mesh for a particular problem that

ensures accuracy of results without requiring an excessive computational effort.

A convergence study was first carried out to find the best mesh density for the corner

region. The element size was kept constant for the flat regions of the section and for the

bearing plate while the number of elements for each corner was varied. The results of the

convergence study for the corner mesh are given in Table A8.1. Based on these results

and striking a balance between accuracy and computational time, 10 elements were

selected to model each corner.

Following the establishment of the corner mesh density, the number of elements for the

flats was varied to find a suitable mesh density for the flats while keeping the number of

elements for each corner (10 elements) and for the bearing plate unchanged. The results

are given in Table A8.2.

With the use of 10 elements at each corner, a mesh convergence study was carried out by

varying the element size for the bearing plate for two element sizes for the flats (i.e. 2

mm x 2 mm and 6 mm x 6 mm). The results are shown in Table A8.3, which indicates

that varying the element size for the bearing plate had little effect on the predicted

ultimate load. However it should be noted that this element size did affect the

convergence of analysis. In fact, in such a situation, divergence may arise from a mesh

mismatch between the two contact surfaces (i.e. the bearing plate and the steel tube in the

present problem). Given this consideration, the final mesh adopted included 6 mm x 6

mm elements for the flats, 6 mm x 6 mm elements for the bearing plate and 10 elements

for each corner. The corner elements had an aspect ratio of 1:0.13.

324

A8.4 EXTENDED CORNER REGIONS

Existing research showed that the enhancement of mechanical properties of steel at

corners due to the cold-forming process is not limited to corner regions (i.e. curved

portions) only; the effect can extend to the nearby regions (Karren 1967). For cold-

formed carbon steel, this effect of cold-forming was found to extend beyond each corner

to a distance approximately equal to the wall thickness t on each side of the corner

(Karren 1967). Therefore in the FE model, the corner material properties were employed

for an extended region of t on each side of the corner (Figure A8.1). This corner property

enhancement may have a significant effect on the FE results.

A8.5 LOAD AND BOUNDARY CONDITIONS

In simulating an end bearing test on an RHS tube, it is very important to use the correct

boundary conditions in the FE model. Because of the symmetry of the problem, only half

of the section was modelled, with symmetry conditions appropriately enforced. The

vertical and longitudinal translations of the corner edge (i.e. the point of transition

between the flat and the curved portions) of the bottom flange were fixed, but it was

allowed to experience rotations and transverse translations. These restraints to the bottom

are believed to closely represent the test condition.

A study carried out by Fernando et al. (2010) on the FE modelling of cold-formed

stainless steel RHS tubes under an end bearing load has shown that in order to accurately

model the loading process, the load application should be simulated using a bearing plate

which is imposed with displacement increments. This method was adopted in the present

study. The modelling of the bearing plate is explained in Section 8.3.1.

325

A8.6 IMPERFECTIONS

The study carried out by Fernando et al. (2010) showed that when the imperfection shape

is that of the first eigenmode (the critical buckling mode) (Figure A8.2 shows the first

three eigenmodes referred to as buckling modes 1, 2 and 3), the load-carrying capacity

keeps reducing with increases in the imperfection amplitude. However, when the

imperfection is in the shapes of buckling modes 2 and 3, the load-carrying capacity varies

little as the imperfection amplitude increases. Based on the study by Fernando et al.

(2010), the imperfection adopted in the present study had the shape of the first eigenmode.

Based on the recommendation of Fernando et al. (2010), the amplitude of the

imperfection was found from

tcr

= σσω 2.0

0 023.0

(A8.1)

where 2.0σ is the 0.2% proof stress, crσ is the critical buckling stress of a simply-

supported plate and t is the plate thickness. Equation A8.1 was initially proposed by

Gardner and Nethercot (2004).

A8.7 RESIDUAL STRESSES

As the stress-strain data obtained from coupon tests already include the effect of

deformation-induced residual stresses in an approximate manner, only residual stresses

induced by welding were considered. The simple residual stress pattern given in Figure

A8.3 (Young 1974) was adopted in the FE model, based on the recommendation of

Fernando et al. (2010). The residual stresses were incorporated in to the FE model by

using the command *INITIAL CONDITIONS, TYPE=STRESS.

A comparison of the load-displacement curves from the FE model and the experimental

curve for section A (100-50-2) is shown in Figure 8.8a and the deformed shapes at failure

are compared in Figure A8.4. Reasonable agreement is seen.

326

A8.8 PROPOSED PROCEDURE FOR THE FE MODELLING OF COLD-FORMED STEEL RHS TUBES UNDER AN END BEARING LOAD

Based on the above discussion and the study conducted by Fernando et al. (2010), the

following procedure for the accurate modelling of cold-formed steel RHS tubes subjected

to an end bearing load was adopted in the present FE study:

(a) 10 general-purpose shell elements (S4R) were employed to model each corner

region; 6 mm x 6 mm elements were employed for the flats as well as the bearing

plate.

(b) The bearing plate was included in the FE model to simulate the loading condition in

a realistic manner; the contact condition between the bearing plate and the RHS top

flange was defined using the small sliding contact option with the normal hard

contact property and using the penalty friction formulation to represent the tangential

behaviour.

(c) The enhancement of corner material properties was incorporated into the FE model.

Furthermore, the same enhancement was used for an extended region of t on each

end of the corner beyond the curved corner portion, where t is the thickness of the

tube wall.

(d) The initial geometric imperfection was assumed to be in the shape of the first

eigenmode and to be a bow-out imperfection (Figure A8.2a), with its magnitude

found form Eqn. A8.1.

(e) Since the material properties were found by testing coupons cut from the finished

cold-formed section, residual stresses due to cold bending was be ignored. Thermal

residual stresses due to welding was included using the simple model proposed

described by Young (1974).

327



Fernando, N.D., Teng, J.G., Yu, T. and Zhao, X.L. (2010). "Numerical modeling of cold-

formed stainless steel RHS tubes under an end bearing load", (in preparation).

Gardner, L. and Nethercot, D.A. (2004). "Numerical modeling of stainless steel structural

components - A consistent approach", Journal of Structural Engineering, 130(10),

1586-1601.

Karren, K.W. (1967). "Material property models for analysis of cold-formed steel

members", Journal of the Structural Division, ASCE, 93,401-32.

Young, B.W. (1974). "Effect of process efficiency on calculation of weld shrinkage

forces", Proceedings of the Institution of Civil Engineers Part 2-Research and

Theory, 57(DEC), 685-692.

328

Table A8.1 Results of mesh convergence study for the corner

Number of elements for the corner

Ultimate load Load, kN

% difference from the load

of the previous mesh

2 16.60 Not Applicable 4 18.32 10.35 6 18.70 2.06 8 18.72 0.13 9 18.78 0.32

10 18.83 0.27 11 18.85 0.10

Table A8.2 Results of mesh convergence study for the flats

Element size for the flats, mm*mm

Ultimate load Load, kN

% difference from the load of

the previous mesh

10*10 19.50 Not Applicable 8*8 19.08 2.21 6*6 18.83 1.29 4*4 18.72 0.56 2*2 19.00 -1.46 1*1 18.91 0.46

329

Table A8.3 Results of mesh convergence study for the bearing plate

Element size for the flats, mm*mm

Element size for the bearing plate, mm*mm Ultimate load, kN

6*6

2*2 18.61 3*3 18.71 4*4 18.80 5*5 18.86 6*6 18.90

2*2

2*2 18.78 3*3 18.86 4*4 18.93 5*5 18.98 6*6 19.00

330

Figure A8.1 Corner properties extended beyond each end of the curved portion

(a) (b) (c)

Figure A8.2 Buckling modes; (a) First buckling mode; (b) Second buckling mode; (c)

Third buckling mode

t

t

ω0 ω0 ω0

331

0.2tenσ

After Young (1974)

Figure A8.3 Idealized weld-induced residual stress distribution of the weld face on RHS

0.2tenσ

0.2tenσ

comrσ

c c

b/2

b

t

Tension

Compression Compression

332

(a) Deformed shape of the FE model

(b) Deformed shape of the test specimen

Figure A8.4. Deformed shapes of the RHS tube

333

CHAPTER 9 CONCLUSIONS AND RECOMMENDATIONS FOR

FUTURE RESEARCH

9.1 INTRODUCTION

Strengthening of steel structures with adhesively-bonded carbon fibre reinforced

polymer (CFRP) plates (or laminates) has received extensive research attention over

the past few years. Existing studies have revealed that debonding of the CFRP plate

from the steel substrate is one of the main failure modes in such CFRP-strengthened

steel structures. Against this background, this thesis has presented a series of

experimental and theoretical studies aimed at the development of a good understanding

of the mechanisms of and reliable theoretical models for debonding failures in CFRP-

strengthened steel structures. This chapter summarizes the main findings of the present

PhD project and the recommendations for future research.

9.2 TREATMENT OF STEEL SURFACES FOR EFFECTIVE ADHESIVE BONDING

Debonding failure between steel and CFRP may occur in the following modes: (a)

within the adhesive (cohesion failure); (b) at the bi-material interfaces between the

adhesive and the adherends (adhesion failure); (c) a combination of adhesion failure

and cohesion failure. Among these failure modes, cohesion failure in the adhesive is

the preferred mode of debonding failure at CFRP-to-steel interfaces as for such

debonding failure, the design theory can be established based on the properties of the

adhesive. A systematic experimental study has therefore been presented in this thesis to

examine the effects of steel surface preparation and adhesive properties on the adhesion

strength between steel and adhesive, and to explore the possibility of avoiding adhesion

failure by appropriate treatment of the steel surface. The study was focused on the steel

surface but not the CFRP surface as adhesion failure at the CFRP/adhesive interface

334

can generally be avoided through the use of a peel-ply which is removed prior to

bonding to ensure a clean and fresh FRP surface for bonding (Hollaway and Cadei

2002) or by abrading and cleaning the FRP surface before bonding.

Five surface preparation methods were examined in the study, including: (1) solvent-

cleaning; (2) hand-grinding after solvent-cleaning; and (3)-(5) grit-blasting after

solvent-cleaning using 0.5 mm angular alumina grit, 0.25 mm angular alumina grit and

0.125 mm angular alumina grit respectively. Four different adhesives covering a wide

range of mechanical properties (e.g. elastic modulus and ultimate strain) were also

examined. Two types of tests were used, namely, tensile butt-joint tests and single-lap

shear tests.

To characterize the surface, the VCA (video contact angle) device was employed to

measure the contact angle measurements from which the surface energy was evaluated,

the SEM/EDX (scanning electron microscopy/energy dispersive x-ray) system was

used to measure the surface chemical composition, while a profilometer was used to

measure the surface roughness and topography.

The test results have shown that the grit-blasting method results in significantly higher

adhesion strengths over the other two methods (i.e. solvent-cleaning and hand-grinding

after solvent-cleaning). For all the adhesives tested, both tensile butt-joint tests and

shear-lap shear tests revealed that it is possible to avoid pure adhesion failure if the

steel surface is appropriately treated. It was also suggested that, for adhesive bonding,

the steel surface should be solvent-cleaned, grit-blasted using angular grit, and then

further cleaned using a vacuum head.

Grit-blasting introduces grit residues to the steel surface, so the chemical composition

of the grit used should be compatible with the adhesive to be used. Alumina grit which

is compatible with adhesives commonly used in the CFRP strengthening of steel

structures is recommended. The grit size has been shown to have no significant effect

335

on the adhesion strength for the selected adhesives, and 0.25 mm angular grit is

recommended based on the present experimental results.

The surface preparation process introduces physico-chemical changes to the steel

surface, including the topography, the surface energy and the chemical composition of

the surface. Even though a quantitative relationship between the surface characteristics

and the adhesion strength is difficult to achieve, based on the results in the present

study, the following procedure is proposed for the assessment of a grit-blasted steel

surface for adhesive bonding:

• The surface energy of the steel surface should be measured using a video

contact angle measurement device and its value should exceed 50 mJ/m2;

• The profile of a grit-blasted surface should be measured using a surface

profilometer and its surface topography should be characterized using the

fractal dimension. The fractal dimension Df should lie within the range of

1.49 1.47fD≥ ≥ .

It has also been revealed that a proper grit-blasting procedure using the same grit type

and size leads to similar surface characteristics. Measurement of the chemical

composition of a treated surface can be difficult, but such measurement may not be

necessary as the same chemical composition can be assumed for surfaces grit-blasted

using the same type and size of grit.

9.3 BOND BEHAVIOUR OF CFRP-TO-STEEL BONDED JOINTS

9.3.1 Test Method

In most CFRP-strengthened structures, complex stress states exist in the adhesive layer

between CFRP and steel. In order to understand and model the interface behaviour

under these complex stress states, the first necessary step is to understand the behaviour

under pure mode II (i.e. pure shear) loading. A bond-slip relationship can be effectively

336

used to represent interfacial behaviour under mode II loading. In obtaining bond-slip

relationships experimentally, the test set-up should thus satisfy the pure mode II

loading condition. The single-shear pull-off test was commonly used to quantify bond-

slip behaviour and to study the full-range behaviour of FRP-to-concrete bonded joints.

However, the existence of plate end normal (or peeling) stresses in such bonded joints

has raised some concern over the validity of the single-shear pull-off test as a test

method for obtaining shear bond-slip data. Against this background, a detailed study

has been presented, aimed at experimentally and numerically verifying the suitability of

the single-shear pull-off test for determining the shear bond-slip behaviour of the

interface.

The experimental results showed that, even though the initiation of failure is affected

by both the interfacial shear stresses and the longitudinal normal stresses within the

adhesive layer, the failure process of a single-shear pull-off tests is predominantly

governed by pure mode II loading of the bonded interface after the initial stage of crack

propagation, provided that a long enough bond-length exists. Therefore, the single-

shear pull-off test is a suitable method for evaluating the shear bond-slip behaviour.

Results from linear elastic FE analyses have also been presented and these results

showed that, if the plate end is modelled as a square end, convergence of predicted

stresses at the plate end with reductions in element size cannot be achieved due to the

existence of stress singularity points. Furthermore, it has been shown that with the

existence of a small adhesive fillet at the plate end, the normal stress is reduced

significantly. The FE results also showed that cracking initiated due to combined

interfacial shear and longitudinal normal stresses, with the effect of normal stresses

being negligible.

9.3.2 Experimental Behaviour of CFRP-to-Steel Bonded Joints

Following the study which confirmed the suitability of the single-shear pull-off test

method for studying the behaviour of CFRP-to-steel interfaces subjected to pure shear

337

loading, the full-range behaviour of CFRP-to-steel interfaces was then investigated

through a series of tests using this test set-up. The parameters examined include the

material properties and the thickness of the adhesive and the axial rigidity of the CFRP

plate.

The test results showed that the bond strength (i.e. ultimate load) of such bonded joints

depends strongly on the interfacial fracture energy among other factors. Non-linear

adhesives with a lower elastic modulus but a larger strain capacity were seen to lead to

a much higher interfacial fracture energy than linear adhesives with a similar or even a

higher tensile strength. The bond-slip curve has an approximately triangular shape (i.e.

bi-linear) for a linear adhesive but has a trapezoidal shape for a non-linear adhesive,

indicating the necessity of developing different forms of bond-slip models for different

adhesives. The bond-slip curve is independent of the rigidity of the FRP plate.

The test results also confirmed that there exists an effective bond length in such bonded

joints, beyond which any further increase in the bond length does not lead to a further

increase in the bond strength but does lead to an increase in ductility. The bond strength

was found to increase with both the adhesive thickness and the FRP plate axial rigidity,

provided that cohesion failure is the controlling failure mode.

9.3.3 Bond-Slip Model

Based on the observations from the experimental study, two bond-slip models were

developed for linear adhesives. The two bond-slip models were revised from similar

models proposed by Lu et al. (2005) for FRP-to-concrete bonded joints, but taking due

account of the unique characteristics of CFRP-to-steel bonded joints. The key

parameters of the two models include the interfacial fracture energy ( fG ), peak bond

shear stress ( maxτ ) and the corresponding slip ( 1δ ).The two bond-slip models both

compared well with the test results.

338

An explicit formula was also developed for the accurate prediction of the interfacial

fracture energy from the adhesive properties. This formula is applicable to both linear

and non-linear adhesives. In addition, an explicit formula was also proposed to predict

the peak bond shear stress using the tensile strength of the adhesive; this formula is also

applicable to both linear and non-linear adhesives. For bonded joints with a linear

adhesive, the slip at peak bond shear stress 1δ was found to depend on both the maxτ

and the stiffness of the adhesive layer, so an explicit formula was proposed for 1δ ,

taking into account this observation.

For CFRP-to-steel bonded joints with a non-linear adhesive, a preliminary trapezoidal

bond-slip model was proposed, which is composed of a linear ascending branch, a

constant stress branch and a linear descending branch. While the model needs to be

further developed/verified when new test data are available, it is believed that the

trapezoidal shape adopted in this model captures well the characteristics of such

bonded joints.

9.3.4 Analytical Solution for the Full-Range Behaviour of CFRP-to-Steel

Bonded Joints

Employing a trapezoidal bond-slip model (with a triangular model as a special case), an

analytical solution was also developed for predicting the full-range bond behavior of

CFRP-to-steel bonded joints with a non-linear adhesive, following the approach of

Yuan et al. (2004). The analytical solution provides closed-form expressions for the

interfacial shear stress distribution, the effective bond length and the load-displacement

behaviour at different loading stages of the bonded joints. The analytical solution has

been shown to represent the test results closely.

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9.3.5 Bond Strength Model

As part of the analytical solution, a bond strength model was also presented, including

an expression for the definition of the effective bond length. As expected, the bond

strength model provides accurate predictions for bonded joints with either a linear

adhesive or a non-linear adhesive.

9.4 FINITE ELEMENT MODELLING OF DEBONDING FAILURES

9.4.1 Modelling of CFRP-to-Steel Interface

By making use of the bond-slip model for linear adhesives developed in the present

work, a coupled cohesive zone model was proposed for modeling the CFRP-to-steel

interface. In this cohesive zone model, the bond-slip model is employed with a mixed-

mode cohesive law which considers the effect of interaction bweteen mode I loading

and mode II loading on damage prapogation within the adhesive. Damage initiation is

defined using a quadratic strength criterion, and damage evolution is defined using a

linear fracture energy-based criterion, both of which take account of mixed-mode

loading. The proposed approach represents a significant advancement in the modelling

of debonding failures in CFRP-strengthened steel structures.

9.4.2 Debonding Failures in Steel Beams Flexurally-Strengthened with CFRP

Debonding of the CFRP plate, including both plate end debonding and intermediate

debonding, has been commonly observed in CFRP-strengthened steel beams, but no

theoretical model has been developed that is capable of accurate prediction of such

debonding failures. An FE study was therefore conducted in the present PhD project to

correct this deficiency of existing knowledge, using the coupled cohesive zone model

discussed above for CFRP-to-steel interfaces.

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FE models were developed for three CFRP-strengthened steel beams tested by Deng

and Lee (2007), which failed by plate end debonding or compression flange buckling.

Two additional FE models were also developed to investigate the effect of the CFRP

plate stiffness and to explore the possibility of intermediate debonding in such beams.

Predictions from the FE models were found to compare well with the test results

reported by Deng and Lee (2007) for the strengthened beams failing by either plate-end

debonding of the CFRP plate or compression flange buckling of the steel section. It

was also concluded from the study that when a static FE analysis is conducted, the

ultimate load of a beam failing by plate end debonding should be taken as the load at

which debonding initiates at the plate end.

Using the proposed FE approach, the behaviour of CFRP-strengthened steel beams was

examined and it was found that: (1) the use of a stiffer CFRP plate may lead to a lower

ultimate load due to plate end debonding; (2) plate end debonding is more likely to

occur when a short CFRP plate is used, and the failure mode may change to

intermediate debonding or other failures modes such as compression flange buckling if

a longer plate is used.

9.4.3 Debonding Failures in CFRP-Strengthened RHS Tubes Subjected to an

End Bearing Load

The FE approach proposed for CFRP-to-steel interfaces in flexurally-strengthened steel

beams has also been extended to the prediction of debonding failures in the more

complex problem of rectangular steel tubes with CFRP plates bonded on the webs and

subjected to an end bearing load.

A series of tests was first presented, in which the effects of adhesive types and web

slenderness on the effectiveness of CFRP strengthening were examined. The failure of

such members was found to be normally controlled by the debonding of the CFRP

plates, so the properties of the adhesive used were shown to be very important. Four

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different failure modes were observed in the tests: (1) adhesion failure; (2) cohesion

failure; (3) combined adhesion and cohesion failure; (4) interlaminar failure of CFRP

plates. The test results showed that an adhesive with a larger strain energy (e.g. a softer

non-linear adhesive) leads to a larger load-carrying capacity for a strengthened RHS.

The test results of different RHS tubes strengthened with CFRP plates using Araldite

2015 showed that the effectiveness of the strengthening system also depends on the

slenderness of the web. For sections with a slender web, a greater increase in load can

be achieved using the same CFRP plates. The increase in strength depends also on the

failure mode of the bare RHS tube which can be either web buckling or web yielding.

Nevertheless, the experimental results clearly showed that CFRP strengthening can

enhance both the web buckling and web yielding load-carrying capacities.

An FE study was next presented to predict the behaviour of CFRP-strengthened

rectangular steel tubes under an end bearing load, employing the coupled cohesive zone

model proposed earlier in the present PhD project. The proposed FE model was shown

to closely predict the experimental behaviour of these CFRP-strengthened tubes. The

FE results also showed that debonding in such tubes is governed by interfacial normal

stresses.

A design model to predict the load-carrying capacity of CFRP-strengthened RHS tubes

was also proposed. The formulation of the design formula was based on the assumption

of a perfect bond between CFRP and steel. To account for debonding, two reduction

factors were introduced and these factors depend on the adhesive mechanical properties

and the web slenderness. Unfortunately, the existing experimental results were

insufficient for the calibration of these reduction factors. Nevertheless, the proposed

design model serves as the first step in developing a reliable design model for the load-

carrying capacity of CFRP-strengthened RHS tubes subjected to an end bearing load

with the effect of debonding duly considered.

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9.5 FUTURE RESEARCH

Although a trapezoidal bond-slip model has been proposed for non-linear adhesives in

the present PhD project, this model has been based on the test results of bonded joints

with one single non-linear adhesive (i.e. Araldite 2015) and a single adhesive layer

thickness. Some of the key parameters in this model (i.e. 1δ and 2δ ) have been taken as

constants because of the limited test data. Additional tests are thus required to enable

the further development of this bond-slip model, with the establishment of more

rational and accurate expressions for the key parameters (e.g. 1δ and 2δ ) being an

important task.

The FE modelling of debonding failures in CFRP-strengthened steel structures

presented in this thesis has also been limited to members bonded with linear adhesives.

Further research is therefore needed to develop an approach for the accurate prediction

of debonding failures involving CFRP-to-steel interfaces with a non-linear adhesive.

Apparently, a mixed-mode cohesive law which considers the effect of interaction

bweteen mode I loading and mode II loading on damage prapogation within the non-

linear adhesive should be adopted in such a FE simulation and the bond-slip model

proposed in the present PhD project, with appropriate extensions, may be adopted as an

important component.

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REFERENCES Deng, J. and Lee, M.M.K. (2007). "Behaviour under static loading of metallic beams

reinforced with a bonded CFRP plate", Composite Structures, 78(2), 232-242.

Lu, X. Z., Teng, J. G., Ye, L. P., and Jiang, J. J. (2005). "Bond-slip models for FRP

sheets/plates bonded to concrete." Engineering Structures, 27(6), 920-937.

Yuan, H., Teng, J. G., Seracino, R., Wu, Z. S., and Yao, J. (2004). "Full-range behavior

of FRP-to-concrete bonded joints." Engineering Structures, 26(5), 553-565.

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