PSZ 19 : 16 (Pind 1/97)
UNIVERSITI TEKNOLOGI MALAYSIA
BORANG PENGESAHAN STATUS TESIS
JUDUL: THE DEVELOPMENT OF MATHEMATICAL MODEL FOR
PREDICTING BONDING BEHAVIOUR OF CFRP PLATE-EPOXY-CONCRETE BONDED SYSTEM
SESI PENGAJIAN : 2006 / 2007 Saya, KHUSYAIRI BIN MOHAMED
( HURUF BESAR )
mengaku membenarkan tesis ( PSM / Sarjana / Doktor Falsafah )* ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut : 1. Tesis adalah hakmilik Universiti Teknologi Malaysia. 2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan pengajian
sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi
pengajian tinggi. 4. ** Sila tandakan ( √ ). SULIT (Mengandungi maklumat yang berdarjah keselamatan atau
kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972)
TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh
organisasi/badan di mana penyelidikan dijalankan)
TIDAK TERHAD Disahkan oleh ( TANDATANGAN PENULIS ) ( TANDATANGAN PENYELIA )
Tarikh : 6 MAY 2007 Tarikh : 6 MAY 2007
CATATAN * Potong yang tidak berkenaan.
** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai
SULIT atau TERHAD. *** Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan penyelidikan, atau Laporan Projek Sarjana Muda (PSM).
Alamat Tetap : KG. BUKIT TANAH, 16810 SELISING, PASIR PUTEH, KELANTAN
MR SHUKUR HAJI ABU HASSAN Nama Penyelia
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UTM(FKM)-1/02
Fakulti Kejuruteraan Mekanikal
Universiti Teknologi Malaysia
PENGESAHAN PENYEDIAAN SALINAN E-THESIS
Judul Tesis : THE DEVELOPMENT OF MATHEMATICAL MODEL FOR PREDICTING BONDING BEHAVIOUR OF CFRP PLATE-EPOXY-CONCRETE BONDED SYSTEMPENYERAP KEBISINGAN UNTUK SISTEM EKZOS
Ijazah : MECHANICAL ENGINEERING (PURE)
Fakulti : FACULTY OF MECHANICAL ENGINEERING
Sesi Pengajian : 2006 / 2007
Saya, KHUSYAIRI BIN MOHAMED
(HURUF BESAR)
No. Kad Pengenalan 830602-13-5547 mengaku telah menyediakan salinan e-thesis sama
seperti tesis asal yang telah diluluskan oleh panel pemeriksa dan mengikut panduan
Penyedian Tesis dan Disertasi Elektronik (TDE), Sekolah Pengajian Siswazah, Universiti
Teknologi Malaysia, Disember 2006.
(Tandatangan pelajar) (Tandatangan penyelia sebagai saksi)
Nota: Borang ini yang telah dilengkapi hendaklah dikemukakan kepada FKM bersama penyerahan CD.
Alamat Tetap :
KG. BUKIT TANAH, 16810 SELISING, PASIR PUTEH, KELANTAN. Tarikh: 6 MAY 2007
Nama : MR. SHUKUR HAJI ABU HASSAN Penyelia Fakulti : FACULTY OF MECHANICAL ENGINEERING Tarikh : 6 MAY 2007
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�I hereby declare that I have read the content of the thesis and in my opinion, the
content of the thesis have fulfilled the scope and quality for the purpose of achieving
the Degree of Bachelor of Engineering (Mechanical-Pure).�
Signature : �������������.
Supervisor : MR. SHUKUR HAJI ABU HASSAN
Date : 6 MAY 2007
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THE DEVELOPMENT OF MATHEMATICAL MODEL FOR PREDICTING
BONDING BEHAVIOUR OF CFRP PLATE-EPOXY-CONCRETE BONDED
SYSTEM
KHUSYAIRI BIN MOHAMED
A Dissertation Submitted to the Faculty of Mechanical Engineering in Partial
Fulfillment of the Requirement for The Award of the Degree of Bachelor of
Mechanical Engineering (Pure)
Faculty of Mechanical Engineering
Universiti Teknologi Malaysia
MAY 2007
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ii
�I hereby declare that this writing is my original work except for quotations and summaries,
each one of which I have clearly stated its source.�
Signature : ..................................................
Author�s Name : KHUSYAIRI BIN MOHAMED
Date : 6 MAY 2007
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iii
First of all, all the praises and thanks be to Allah S.W.T for His Love,
This thesis is dedicated to my family,
To my beloved parent, Mohamed b. Jusoh & Che Nab Bt. Awang,
Maslina Bt. Abu Bakar
And all my friends,
Thank you very much for your unstinting help and encouragement.
iv
ACKNOWLEDGEMENTS
In the name of Allah, the most Gracious and most Compassionate
Firstly, i want to to thank Allah Almighty for blessing me and giving me
strength to accomplish this thesis. I would like also to take this opportunity to gather
all my most sincere gratitude towards my gracious and benevolent supervisor, Mr.
Shukur Haji Abu Hassan for his proper guidance and generous assistance throughout
the accomplishment of the work contain in the thesis. I have benefitted through his
kind help, valueable suggestion and encouragement in completing my work and
compiling this thesis.
I would like to express my earnest appreciation and thanks to Mr. Ismail
Kamis for providing helpful and significant information when i needed him most.
Many thank to all of the technicians especially Mr. Rizal and Mr. Fadli for their
cooperation and assisting me in the various laboratory tasks.
Last but not least, to those who contribute towards the accomplishment of this
thesis especially Maslina, Bob, Matzul, Pokceq, Chuban, Shah, Adib and all my
family members, i offer my deepest and genuine gratefulness for their support,
opinion and suggestion.
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ABSTRACT
The double-lap joint CFRP plate-epoxy-concrete bonded system is
considered in this investigation. A simplified one dimensional model based on the
classical elasticity theory by Volkersen/ de Bruyne is presented. The shear
deformation in the adhesive, thickness of adherend and adhesive are assumed
constant along bond length. Adherends shear deformation and peeling effect are
neglected. The analytical solutions of shear stress in the adhesive is obtained and
almost agreed with experimental results studied by Shukur A.H. The influential
parameters on bond stress distribution are determined by the equation
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vi
ABSTRAK
Double-lap joint bagi CFRP-epoksi-konkrit dipertimbangkan di dalam kajian
ini. Model satu dimensi yang dipermudahkan berdasarkan teori elastik klasik oleh
Volkersen/ de Bruyne dipersembahkan. Perubahan bentuk daya ricih pada adhesive,
ketebalan adhesive dan juga adherend dianggap malar sepanjang bond length. Selain
itu, ubah bentuk ricih pada adherend dan juga efek kupasan adalah diabaikan.
Penyelesaian tegasan ricih secara analitikal yang diperolehi sangat hampir dengan
keputusan dari eksperimen yang dijalankan oleh Shukur A.H. Seterusnya, pengaruh
parameter-parameter terhadap taburan tegasan ricih ditentukan berdasarkan
penyelesaian analitikal tersebut.
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vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
TITLE PAGE i
DECLARATION OF ORIGINALITY ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xi
LIST OF FIGURES xii
LIST OF SYMBOLS xvi
LIST OF APPENDICES xvii
1 INTRODUCTION
1.1 Project background 1
1.2 Objective 2
1.3 Scope 2
2 LITERATURE REVIEW
2.1 The Technology and Application of
FRP or Steel Plate Bonded System in
Construction Industry 4
2.1.1 Definition of Durability 9
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viii
2.1.2 The Bond Durability of Steel Plate as
Externally Bonded System 9
2.1.3 The Bond Durability of FRP Plate as
Externally Bonded System 10
2.1.4 Factors Affecting Bond Strength 15
2.1.5 Factors Affecting Bond Durability 19
2.1.6 Failure Modes of FRP-Concrete Bonded
System 21
2.1.6.1 Failure at Interface 22
2.1.6.2 Adhesive Failure 23
2.1.6.3 Adherend Failure 23
2.2 Fibre Reinforced Polymer (FRP) Composites 24
2.3 Advanced FRP Composites Applied for Load
Bearing Structures 24
2.3.1 Carbon Fibre 26
2.3.2 The Pultrusion Process 27
2.3.3 FRP Pultruded Composites Plates 28
2.3.4 Durability of FRP Composites 29
2.4 Adhesive Bonding Technology 37
2.4.1 Adhesive Selection 38
2.4.2 Adhesive Mechanical Properties 39
2.4.3 Effects of Loading Configuration on
Adhesive Joint 40
2.4.4 Advantages and Limitations of
Adhesive Bonding 41
2.5 The Principles of Adhesive Bonding Technology
for Structural Applications 42
2.5.1 Factors Considered in Adhesive
Joint Design 43
2.5.2 Bond Mechanism 43
2.5.3 Joining Technique 44
ix
2.5.4 Joint Geometry Effect on Joint Strength 45
2.5.5 Elastic Properties and Deformation 47
2.6 Double Lap Joint 48
2.7 Surface Treatments 50
2.8 Adhesive Joint Design Principles 50
2.9 Failure Modes 52
2.10 Mathematical Model for Predicting Bond Stress
Behaviour 54
3 METHODOLOGY
3.1 The Parameters Effect 67
3.2 Bond Test for CFRP Plate-Epoxy-Concrete
Specimen 68
3.2.1 Experimental Details 68
3.2.2 Details of Test Materials 70
3.2.3 Determination of Bond Stress
Characteristics 71
3.3 Conclusion of Research Methodolgy 74
4 DEVELOPMENT OF MATHEMATICAL MODEL
4.1 Theoretical Analysis on Tension-Compression
CFRP Plate-Concrete Prism Bonded System 76
5 ANALYSIS AND DISCUSSION
5.1 Equation validation 85
5.2 Discussion of Equation Validation 89
5.3 Parametric study 90
5.3.1 The Effect of CFRP Plate Young�s
x
Modulus 92
5.3.2 The Effect of CFRP Plate Thickness 93
5.3.3 The Effect of Concrete Young�s Modulus 94
5.3.4 The Effect of Adhesive Shear Modulus 96
5.3.5 The Effect of Adhesive Thickness 97
5.3.6 The Effect of Bond Length 98
5.4 Conclusion of Parametric Study 99
6 CONCLUSION AND RECOMMENDATION
6.1 Conclusion 101
6.2 Suggestion for Future Study 103
REFERENCES 104
APPENDICES 110
xi
LIST OF TABLES
TABLE NO. TITLE PAGE
2.1 List of projects using CFRP for structures
rehabilitation in Malaysia since 2001 5
2.2 Experimental results of control and exposed
Beams 12
2.3 Properties of Selfix Carbofibe Pultruded CFRP Plates
System 25
2.4 Typical reinforcing unidirectional fibre properties 26
5.1 Material and physical properties of testing specimens 86
5.2 Three different parameter�s value 91
5.3 Influential parameters matrix 91
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xii
LIST OF FIGURES
FIGURE NO. TITLE PAGE
2.1 Steel plate member used for strengthening RC
Beam 7
2.2 FRP laminate system used for strengthening RC
Beam 8
2.3 Muar Bridge Beams strengthened with CFRP Sheet 9
2.4 Typical behaviour of load vs deflection for control
Beams 12
2.5 Typical behaviour of load vs defelection for exposure
beams under wet/dry cycles 13
2.6 Typical Load-Strain Bi-linear Curve for FRP
Sheet-Concrete Prism Bonded Specimen 17
2.7 Comparison of bond strength due to different
concrete surface preparation methods 18
2.8 Typical force transfer distributions for concrete mix
A: (a) control; (b) wet�dry; (c) freeze�thaw and
(d) dual. 20
2.9 Typical force transfer distributions for concrete
mix B: (a) control; (b) wet�dry; (c) freeze�thaw;and
(d) dual 20
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xiii
2.10 Progressive failure of CFRP plate externally bonded
to concrete due to vertical and horizontal concrete
crack openings near to loading point 21
2.11 (a)Cohesive failure 22
(b)Adhesive failure 23
(c)Adherend failure i.e. concrete shearing 24
2.12 The Pultrusion process in manufacturing FRP plate 27
2.13 Products produced by Pultrusion Process 28
2.14 CFRP Plate (black strip) externally bonded to tension
face of reinforced concrete beam 29
2.15 (a)The changes of width and thickness respectively of
T300/934 graphite/epoxy immersed in distilled water
at different temperatures 31
(b)The weight change of T300/934 graphite/epoxy
immersed in distilled water at different temperatures 31
2.15 Stress-life (S-N) data for pultruded composite coupons
tested in fatigue at room temperature using
environmental conditions A through to F 33
2.17 Flexural strength and modulus for 0 specimens of
pultruded composite coupons before and after
environmental aging 34
2.18 Flexural modulus for 90° specimens of pultruded
composite coupons before and after environmental
aging 34
2.19 Sorption behaviour of pultruded composite
coupons under various aging conditions. 35
2.20 Properties of as-delivered (control), fresh-water-aged
and salt-water-aged materials 36
2.21 S�N curves of the as-delivered (control), water-aged
and 3.5% salt-solution-aged materials 36
2.22 Typical brittle and ductile adhesive behaviour 39
xiv
2.23 Loading modes or type of stresses 40
2.24 Good wetting (A) Poor wetting (B) 44
2.25 Type of adhesive joints techniques for flat
Adherends 45
2.26 Areas of failure initiation and critical strength 46
2.27 A typical adhesive shear stress distribution in a lap
joint according to elastic-plastic model 46
2.28 (a) Deformation of rigid members and
(b) Deformation of elastic members 47
2.29 Double lap joint configuration specimen under
pull-push loads 48
2.30 Relative joint strength of various joint
configurations 51
2.31 The development of the damage process for out of
plane and cohesive failure modes 54
2.32 a): Specimen geometry and material parameters of
double-lap joint under pull-push loads 55
(b)Force analysis on elementary bar model 55
2.33 Two models of stress relationship 57
2.34 Bond slip model for pull � push joint 60
2.35 Equilibrium of the CFRP 61
2.36 Strain of the intervening materials of the bond
region 61
2.37 Loaded end slip vs. pullout force relationship 63
2.38 The free-body diagram of a single-lap joint. 64
2.39 The free-body diagram of a double-lap joint. 64
2.40 The shear stress obtained by Eqs. (11) and FEM
along the adhesive region for a single-lap joint 65
3.1 Instrumentation set-up onto CFRP Plate-epoxy-
concrete prism specimen for this study 69
3.2 Standard test rig used by Swamy et. al.
xv
for GFRP Plate-epoxy-concrete pull-out test 69
3.3 Arrangement of pull-out test rig onto CFRP Plate-
epoxy-concrete prism specimen 71
3.4 Elementary force analysis 72
4.1 Geometry and material parameters of the CFRP
plate-epoxy-concrete prism 76
4.2 Force analysis on elementary bar model 77
4. 3 Linear shear stress and strain distribution through the
thickness of adherends 78
5.1 Theoretical and experimental local bond stress for
BOSTUS specimens at 10 kN 86
5.2 Theoretical and experimental local bond stress for
BOSTUS specimens at 40 kN 87
5.3 Theoretical and experimental local bond stress for
BOSTUS specimens at 60 kN 88
5.4 Roughness and irregularities of concrete surface
profile 90
5.5 Local bond stress with different CFRP Young 93
5.6 Local bond stress with different CFRP thickness 94
5.7 Local bond stress with different concrete Young�s
modulus 95
5.8 Local bond stress with different adhesive shear
modulus 97
5.9 Local bond stress with different adhesive thickness 98
5.10 Local bond stress with different bond length 99
6.1 Exponential line of theoretical and experimental local
bond stress 102
xvi
LIST OF SYMBOLS
L - Length of overlap
E - Elastic modulus
T - Thickness
o - Outer adherend
i - Inner adherend
a - Adhesive
G - Shear modulus
T - Applied force per unit width (kN/m)
x - Distance from loaded end point
y - Local coordinates system with the origin at the top surface
- Shear strain
u - Displacement
- Longitudinal normal stress
cf - Concrete compressive strength
F - Force
A - Area
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xvii
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Data of theoretical and experimental local bond stress 110
B Data of parametric study 113
C Determine local bond stress from governing equation 116
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CHAPTER 1
INTRODUCTION
1.0 Project background
Joint which connects two components together is a common technology for
assembling structures, and is increasingly being used in aerospace and automotive
industries. Statistics shows that approximately 70% of the failure of structures is
initiated from joints [39].
Most of structures are formed by connecting different components through
the joints. In adhesive bonding, the load is transmitted from one adherend to another
adherend smoothly through the adhesive layer in the overlap region, which means the
adhesive serves as a medium for load transmission. In this study, the adherends are
the FRP plate and concrete, while the adhesive is epoxy.
Fiber reinforced polymer (FRP) arises as a strong alternative to replace steel
material. The advantages of this new material over traditional construction materials
are its low weight, high strength and greatly improved resistance against corrosion
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and durability. FRP is usually used to strengthen deteriorated reinforced concrete
structures.
Thus, to ensure the safety of that joint in structures, it is necessary to analyze
the stress distribution on the joint. The double�lap joint with the characteristics of
simplicity and efficiency has been used widely in many applications and becomes a
standard test specimen for determining the mechanical properties of adhesives beside
the single lap joint.
The major difference between adhesive bonding and mechanical fastener is
the bonded area. The area of adhesive bonding is larger than that of mechanical
fastener. The stress concentration is minimized due to the larger bonded area, and the
stress distributions become more uniformly in the overlap region
1.1 Objective
The objective of this study is to develop and produce a mathematical
governing equation that can be used to predict the local bond stress characteristics for
FRP plate-epoxy-concrete bonded system.
3
1.2 Scope
The scope of this study is to cover the literature review that relates to bonding
technology and existing bonding formulation. Then, a mathematical model of
bonding behaviour for CFRP plate-epoxy-concrete bonded system under pull-push
loading configuration will be developed. The results from the equation will be
analyze and discussed. Conclusion and suggestion for the future study also will be
included in the report writing.
CHAPTER 2
LITERATURE REVIEW
2.0 Introduction
In this chapter, the literature reviews were focused into technical aspects that
started from the structure strengthening applications and durability problems
identification, exposure site weathering characteristics, FRP composites technology
and applications, adhesive bonding technology, application and formulation and
finally focused into the development of test rigs for experimentation purposes that
have been developed and applied by past researchers. The important of focusing into
those aspects are the key elements to answer the study programme objectives.
2.1 The Technology and Application of FRP or Steel Plate Bonded System in
Construction Industry
The technique for strengthening structures such as reinforced concrete beam,
column and slab by method of bonding of FRP Plate or laminating of FRP sheet was
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5
slowly accepted by Malaysian authority for the past few years and the momentum
was kept moving positively. Table 2.1 shows list of selected projects that were
undertaken by FOSROC Sdn. Bhd. i.e. one of the leading company that deal with
strengthening works in Malaysia.
The technique was proven to be successful applied in most European
countries and in United States of America and has been referred as a technological
benchmark to be used in Malaysia. The main concept of applying this technique for
damaged or deteriorated structures is to strengthen and stiffen the stress-critical
areas. The advantages of using FRP composites for that kind of application compared
to the existing conventional technique that used of steel bars are FRP far less light
than steel and also extremely resistant to corrosion. Besides that FRP composite also
offers flexibility in site handling and flexibility in applying onto irregular structure
shapes.
Table 2.1: List of projects using CFRP for structures rehabilitation in Malaysia since
2001 (Source: FOSROC Sdn. Bhd.)
NO
PROJECT APPLICATION YEAR
1 Rehabilitation/Strengthening Works to Muar
Bridge At Muar, Johor.
(Fosroc SK-N200)
R.C.Beams 2001
2
Rehabilitation/Strengthening Works to Kuala
Besut Bridge At Terengganu.
(Fosroc SK-N200)
R.C.Beams &
Slabs
2001
3 Rehabilitation/Strengthening Works to Muar
Bridge, Johor. (Fosroc SK-N200)
R.C.Columns 2002
4 Strengthening Works to AIA Building At Jalan
Ampang, Kuala Lumpur.
(Fosroc SK-N300)
R.C.Beams 2002
6
5 Strengthening Works to Beams At Cyberia
Homes, Cyberjaya.
(Fosroc SK-N300)
R.C.Beams 2002
6
Rehabilitation/Strengthening Works to Kuala
Besut Bridge At Terengganu.
(Fosroc SK-N200)
R.C.Beams &
Slabs
2003
7 Rehabilitation/Strengthening Works to Chukai
Bridge, Terengganu.
(Fosroc SK-N200)
R.C.Beams 2003
8 Strengthening Works to R.C.Beams at Cyberjaya
For Kenwin Engineering Sdn Bhd, Cyberjaya.
(Fosroc SK-N300)
R.C.Beams 2003
9 Strengthening Works to Beams at Palace of
Justice, Putrajaya.
(Fosroc SK-N300)
R.C.Beams 2003
10
Rehabilitation/Strengthening Works to Dungun
Bridge At Terengganu.
(Fosroc SK-N200)
R.C.Beams 2003
11 Strengthening Works to Muar Bridge at Muar,
Johor.
(Fosroc SK-N200)
R.C.Columns 2005
12 Strengthening Works to �Projek Perumahan
Rakyat, Lembah Pantai, Kerinchi, Wilayah
Persekutuan.
(Fosroc SK-N300)
R.C. Slab and
Shearwall
2006
13 Strengthening Works to Tan Chong Showroom,
Kuala Lumpur.
(Fosroc SK-N200 & N-200)
R.C. Slab &
Beam
2006
The long-term durability of any construction materials is a key element in
order to ensure that the structure able to maintains its integrity and provides the
service according to its design throughout its service life. The deteriorated concrete
7
structures require repair and maintenance or sometimes need strengthening to extend
their service life. The development of epoxy material as an adhesive system since
1960s has shown a great opportunity for strengthening of existing reinforced
concrete structures by externally bonded steel plate technique. In the area of
strengthening deteriorated reinforced concrete members the steel plate-bonding
system has been widely used and proven to be the most successful externally repair
technique and Fig. 2.1 shows the application of steel plate bonded to the tension face
of reinforced concrete beam at site.
Fig. 2.1: Steel plate member used for strengthening RC beam [5]
From a survey conducted by McKenna and Erki [2], its shows that steel plate-
bonded system has been used since 1964, when malleable steel plate with an
adhesive bonded were applied to load bearing structures of apartment building, in
Durbain, South Africa. The same system was also applied for upgrading several
buildings in Switzerland in early 1970s, Tee-beam bridges in France in 1972 and
1974. The survey also reported that in Japan over 200 highway bridges have been
strengthened with steel plate bonded with epoxy together with anchorage bolted
system. Most of problems of the existing structures member are due to poor design,
inadequate of reinforcement, corrosion and creep. The survey also indicates that the
steel plates epoxy bonded system was quite successfully used to rehabilitate wide
range of structural problems for the last 30 over years.
8
However due to possible corrosion problem and handling aspect during
installation other techniques are being investigated. Nowadays, with the
advancement in the material technology an advanced composite materials or
technically known as Fibre Reinforced Polymer (FRP) shows a great opportunity to
be used for renewal programme in the construction industry in the rehabilitation
work throughout the world [3]. Fig. 2.2 shows the laminating technique of CFRP to
the reinforced concrete beam and Fig. 2.3 show the application of CFRP sheet for
rehabilitation to the damage bridge beams.
Fig. 2.2: FRP laminate system used for strengthening RC beam [6]
9
Fig. 2.3: Muar Bridge Beams strengthened with CFRP Sheet (Source: FOSROC
Sdn. Bhd.)
2.1.1 Definition of Durability
The durability of a material or a structure is defined as the ability to resist
cracking, oxidation, chemical degradation, delamination, wear, and/or the effects of
foreign object damage for a specified period of time, under the appropriate load
conditions, under specified environmental conditions [3,4].
2.1.2 The Bond Durability of Steel Plate as Externally Bonded System
In the area of steel plate bonding system numerous researches have been
carried out and the knowledge on the long-term performance of the system is well
10
established [1]. Results showed that maximum composite action could be achieved
by the adhesive bonded and together with significant improvement in performance in
terms of ultimate load, stiffness and crack control [7]. However, in the exposure test
that was carried out indicates that significant amount of corrosion of steel may take
place during exposure at site. A localized bond failure due to corrosion that resulting
loss in bond strength at the steel-epoxy interface was observed and the reduction of
the overall strength of the exposed beams was attributed to the corrosion [8]. Finally
it could be concluded that the use of externally bonded steel plate to rehabilitate
reinforced concrete structures have shown some disadvantages in handling at site and
also sensitive to an aggressive environment.
2.1.3 The Bond Durability of FRP Plate as Externally Bonded System
The FRP plate bonding system whether using CFRP or GFRP plate is seen to be
applicable as strengthening technique but several aspects of structural implications
and long-term behaviour and durability of the system need to be understood and
designed for before such techniques can be widely applied. In addition, the long-term
durability of the plate-adhesive and concrete-adhesive interface exposed to tropical
environment with heavy rain and sunshine throughout the year is the important factor
to determine the suitability of the FRP plate-bonded system to be used in this region.
Long-term durability is one of the most important properties of most polymeric
based adhesive bonds. Although it can be difficult to achieve in aggressive
environments, there are some methods to slow the degradation process. Material
selection, proper surface preparation and right joint design able to increased and
maintain the durability of joints. Such study is essential for any modification or
recommendation, if necessary, pertaining to the use of the FRP plate bonding system
in particular using the CFRP plate.
11
In contrast to steel, CFRP composite is seen to be more durable to most
aggressive environment which corrosion problem that facing by steel plate system
can be eliminated. However the CFRP plate-bonded system is relatively new
technology in the construction industry although the design concept is quite similar
to the steel plate bonding system. Therefore, there are still many areas of material
and structural implication arising from the use of CFRP plates-bonded system that
are not yet clear and need further research especially in durability aspects [21].
Furthermore, most of the studies have been conducted in Japan, Europe, Canada and
United States of America in which the weather pattern is different from tropical
environment. Research on the short-term structural performance of reinforced
concrete beams strengthened with CFRP plate bonded system that have been
conducted showed a significant improvement in the ultimate flexural capacity of the
beams [9]. Another testing programme on strengthening undamaged beams with FRP
plates demonstrated that bonded FRP plates improved the strength and stiffness of
reinforced concrete beams [10].
Many researches have been conducted on the flexural behaviour of reinforced
concrete beams strengthened on the tension face with either GFRP or CFRP plates
and fabric wet lay-up system. The findings showed that due to higher tensile strength
and higher modulus of elasticity of CFRP plate compared to GFRP plate, the overall
structural performance of reinforced concrete beams strengthened with CFRP plate is
better than GFRP plate. The typical failure mechanisms of the strengthened beams
are plate peeling or debonding close to the plate ends, flexural tensile cracks in
concrete with rupture of FRP plate and shear cracks in concrete starting from the
plate ends [11]. Due to the abrupt curtailment of the plate-adhesive system adjacent
to the support a high concentration of interface shear stress in the vicinity of the plate
occurred [12]. This may lead to abrupt and non-ductile failure of the member, which
is undesirable in the design. It can be seen that the bond between adhesive-FRP plate
and adhesive-concrete interface is of particular important for the member to develop
maximum flexural capacity and affect the long-term performance of the strengthened
member. Toutanji and Gomez [13] on their durability study of FRP composites
bonded to concrete beams had shows that exposure to salt water and dry condition at
35 °C under 90 % humidity under wet/dry cycles was exhibited less improvement in
12
term of ratio of ultimate load for both exposed and control specimens (Table 2.2).
The behaviour of beams strengthened with CFRP and GFRP sheet were shows by
Figs. 2.4 and 2.5. Their results show that debonding of FRP sheets from concrete
interface shows by all the FRP bonded beams.
Table 2.2: Experimental results of control and exposed beams [13]
Fig. 2.4: Typical behaviour of load vs deflection for control beams [13]
13
Fig. 2.5: Typical behaviour of load vs defelection for exposure beams under wet/dry
cycles [13]
A similar study also was conducted by Chajes [14] on durability of concrete
beams externally bonded with aramid, glass and carbon composites. The externally
bonded beam specimens were exposed to freeze thaw and calcium chloride solution
under wet/dry conditions. The results shows that the effects of aggressive
environments were degraded the FRP externally bonded beam strength
performances. The beams bonded with aramid and glass fibre system exhibited about
50 % reduction of strength due to both exposure conditions.
Experimental study conducted by Karbhari and Zhao [15] had shows that the
effects of exposure conditions onto composite and composite-concrete interfaces was
degraded due to moisture uptake. Their study involved the application of GFRP and
CFRP composites system that were externally bonded to the tension face of concrete
beam specimens. The specimens were exposed to fresh water, salt water, freeze-thaw
and under freezing temperature. The flexural load test results were indicates that the
14
degradation was occurred primarily at the interface level of FRP-concrete and FRP
itself due to changes composite stiffness caused by resin plasticization. They also
discovered that the moisture absorption rate was high in fresh water compared to
exposure to sea water.
On the other hand, not many studies have been conducted on the long-term
performance of reinforced concrete beams strengthen using FRP plate-bonded
system that exposed to natural weather. Thus, this area needs further investigation
especially with different exposure conditions. In relation to that, the long-term
durability of the FRP-plate bonded system exposed to different aggressive
environments need to be addressed especially exposure to tropical climate in which
at present the data are very limited or non-existence. In the plate bonding system
penetration of moisture may also occur through the resin via micro cracks, which can
leads to local debonding of the FRP plate [16]. Furthermore, most of the FRP
reinforcement that had been developed in temperate countries was tested for
durability under conditions simulating those countries. Since the tropical climate
experience abundant rain and sunshine throughout the year, therefore, it would be
essential to assess the long-term durability of the FRP plate-bonded system in this
region [17].
The environmental resistance of any bonded assembly FRP system depends
on the durability of the individual components materials, as well as on the bond
between them [22]. For example, in the use of FRP Plate as a material for external
strengthening of reinforced concrete structures, the individual components are the
reinforced concrete, the FRP and the adhesive. The long-tem integrity of bonded
joints implies both chemical and mechanical durability under varying temperature,
moisture and other environmental factors. Adhesive bonded joints with equivalent
bond strength values in short-term static tests may differ markedly with respect to the
durability.
15
The measured residual joint strength after environmental exposure is a
function of change in the cohesive properties of the adherend and in the adhesion
between the adhesives and the adherend. Therefore, joint durability demands a three-
fold consideration of the structural integrity of the cured adhesive, the adherends and
the environmental stability of the interface.
Adhesive bonded joints are generally attacked by exposure to moisture and
elevated temperature. In a well mode joint where a sound bond has been achieved,
the main effect will be on the adhesive layer. A small amount of moisture will
induces plasticization of the adhesive in a highly stressed regions may actually be
beneficial in reducing stress concentrations. However, a small reduction in joint
strength should normally be anticipated in relation to the effects of environmental
conditions on the adhesive itself.
2.1.4 Factors Affecting Bond Strength
The strength of the joint depends on the tensile yield strength (i.e. for ductile
materials), its modulus and thickness of the adherend as well as shear modulus and
the thickness of an adhesive. The adhesive layer must be as thin as possible to avoid
joint starvation and the shear modulus should be higher in order to provide joint
toughness (i.e. able to absorb or to resist stresses at the bond interface). The analysis
of bond durability strength can be related to the following parameters;
Type of adhesive
Different adhesive provides different bond strength, toughness and
durability level. The selection of the adhesive should be done
carefully based on the type of joint, strength needed, and the
materials to be bonded and working environments.
Bonded materials
16
The bonded materials (i.e. adherends) should be compatible as
possible to the adhesive. Each adherend has it own properties that
will provide different strength and durability level especially at the
bond adherend-adhesive interface.
Adherend preparation
Adherend preparation should follow the strict procedure to produce
good adhesion and absorption by chemical contact or by mechanical
interlocking mechanism between adherend and the adhesive.
Curing parameters (i.e. temperature and pressure)
The adhesive only will provide high bond strength if completely
cured. To reach this level, the bonding needs enough time for curing,
dry and a clean environment during preparation, suitable curing
temperature and pressure. Uncompleted curing process can weaken
the bond strength which finally caused slipping problems at
adhesive-adherend interfaces.
Adhesive thickness
The thickness of the adhesive should be controlled; not too thick or
less. Thick bond layer will create an unexpected force and moment.
Besides, it will risk a peel failure. The less thickness could cause
lower strength of bonding and easily fractured.
The study conducted by Horiguchi and Saeki [23] had shows that the shear
test method exhibit the lowest bond strength relative to compressive strength of the
concrete. The shear test method showed relatively low bond strength and less effect
toward the concrete compressive strength. The type of failure mode was dominated
by debonding between CFRP and concrete interface. However, they are not focusing
into depth the factors such as concrete surface preparation, local force distribution,
local strains and the durability aspects (long-term effect) in their study.
17
Toutanji and Ortiz [24], in their research finding has shown that the cracks
have occurred on the bonded FRP-concrete prism for all test specimens i.e. around
the specimen centre. The measured strains i.e. at the center of test specimen on FRP
sheets was gradually increased from the centre toward the outside i.e. due to
formation or development of cracks at concrete surface where the separation
occurred and slowly widen finally leads to the final concrete fracture. It shows that
final concrete fracture was occurred at FRP/Concrete interface. The concrete surface
preparation by water jet treatment on concrete surface has shown 50 % higher of load
up to failure compared to sanding method. They are also found that the high modulus
CFRP composite produced bond strength about 25 % higher than low modulus type.
Their finding also shows that the fibre stiffness and concrete surface treatment were
the main factors that contributing to specimen stiffness after first cracking as shown
in Figs. 2.6 and 2.7 respectively.
Fig. 2.6: Typical load-strain bi-linear curve for FRP sheet-concrete prism bonded
specimen [24]
18
Fig. 2.7: Comparison of bond strength due to different concrete surface preparation
methods [24]
Arden and Nanny [25] in their research finding have showed that the
reinforced concrete beam surface preparation by sandblasting method is slightly
improved their ultimate failure load and the beam stiffness compared to the tested
beam treated by sanding method. Its could be estimated that an increased of failure
load and deflection is about 20 kN (i.e. about 15%) and 5.5 mm (i.e. about 78.60%)
compared to both beams surface preparation methods. Depending failure at the
adhesive-concrete interface has occurred on each tested beam. The failure initially
started within the constant moment region which started by cracks development that
produced high stress level at bond interface at the higher load. This implies failure at
bond interface that finally propagated towards the sheet end. Their finding has also
includes that pre-cracked concrete beams surface treatments produced negligible
effects in the increment of the ultimate failure loads and the deflections.
19
2.1.5 Factors Affecting Bond Durability
One of the most important factors in bond durability is the environmental
stability factor occurs at adhesive-adherend interfaces. The changes in the adhesive
and the adherend mechanical or chemical properties can be the factors that allowed
for changes in adhesion properties. Therefore, bond surface conditions and pre-
treatments often represent the key to enhancing the bond durability. In FRP-concrete
bonded system for example, if the bond procedure is well followed, the surfaces of
both concrete and FRP materials are relatively stable; finally the durable bonds with
epoxy adhesives can be achieved. The substitution of FRP materials for steel in
strengthening reinforced concrete members is motivated by the assurance of superior
bond integrity.
The most outstanding durability study was conducted by Mukhopadhyaya
[21] onto GFRP-epoxy-concrete that were exposed to various aggressive conditions.
They used two different concrete mixed with compressive strength of 35 MPa and 50
MPa for mix A and B respectively. They were discovered that aggressive
environmental conditions, i.e. wet and dry cycles and freeze-thaw do create further
damage to the plate-concrete-adhesive interfaces. All the exposure specimens that
exposed to aggressive regimes showed higher dimensional changes and differential
movement between the plate and concrete compared to the control specimens. They
also had found that the exposure regime has a distinct and strong influence on the
nature of the bond transfer length (refer to Figs. 2.8 (a) to (d) and Figs. 2.9 (a) to (d).
The exposure regime not only increases the length over which the force is transferred
from the plate to the concrete, but it is also progressively increases the process of
debonding at the stressed end.
20
Fig. 2.8: Typical force transfer distributions for concrete mix A: (a) control; (b) wet�
dry; (c) freeze�thaw and (d) dual. [21]
Fig. 2.9: Typical force transfer distributions for concrete mix B: (a) control; (b)
wet�dry; (c) freeze�thaw;and (d) dual [21]
21
2.1.6 Failure Modes of FRP-Concrete Bonded System
Externally FRP bonded to concrete beams could fail in several ways when
loaded in bending. If both reinforcing steel and FRP cross sectional area fractions are
small, reinforcing steel yielding may be followed by rupture of FRP composite sheet
or plate. If the FRP cross sectional area fraction is high, failure is due to concrete
crushing while the steel may have yielded or not, depending in its cross sectional
area fraction. Debonding of FRP from concrete cover may occurs due to the
following phenomenon [18,19,20,26];
i. The sudden propagation of cracks in the adhesive-concrete interface
(i.e. due to brittleness of both materials).
ii. Peeling-off of the FRP sheet/plate due to opening caused by shear
cracks in the concrete (Fig. 2.10).
iii. Shear failure between concrete cover and FRP sheet layer and the
longitudinal reinforcement.
Fig. 2.10: Progressive failure of CFRP plate externally bonded to concrete due to
vertical and horizontal concrete crack openings near to loading point [26]
22
By referring to Mukhopadhyaya [21], the failure of FRP plate-adhesive-
concrete bonded that subjected to tension-compression loads could occur in three
different ways, namely; (a) cohesive failure in the adhesive layer, (b) adhesion
failure and (c) concrete shearing failure. Those types of failures are shown in Figs.
2.11 (a) to (c).
2.1.6.1 Failure at Interface
This may arise through failure of an interlayer between the substrate material
and adhesive (i.e. an oxide coating or primer layer) or through failure of the adhesive
bond surface. In practice, the interface is not perfectly flat and the surface
topography acts to create a layer where there is both adhesive and substrate present.
Fig. 2.11 (a): Cohesive failure
23
2.1.6.2 Adhesive Failure
Cohesive failure occurs through excessive strain with the adhesive material
and may occur anywhere within the adhesive layer. Stresses and strains peak at the
ends of the overlap and generally close to substrate.
Fig. 2.11 (b): Adhesive failure
2.1.6.2 Adherend Failure
This type of failure will arise through development of excessive strain within
the adherend material and it is more common to occur for brittle type materials. In
particular, joints made with adherends of FRP composite with concrete bonded with
toughened adhesive failed by adherend failure, usually by concrete shearing.
24
Fig. 2.11 (c): Adherend failure i.e. concrete shearing
2.2 Fibre Reinforced Polymer (FRP) Composites
Composite material can be defined as a material that consists of multiphase
material that exhibits a proportion of the properties of both constituent phases such
that a better combination of properties can be produced. Traditionally, a composite
material can be modeled as a material that consists of a matrix phase and a
reinforcement phase, with the overall quality and efficiency of the material being
primarily determined by the efficiency of the load transfer mechanisms. Advanced
composites materials is classified as a material that possess high strength, high
modulus to weight ratio and high fracture toughness whilst not exhibiting an increase
in weight [27].
2.3 Advanced FRP Composites Applied for Load Bearing Structures
Advanced Fibre Reinforced Polymer (FRP) composites have been
successfully used as an engineering structures or members for many years in the
25
aerospace, automotive, marine, chemical industries, etc. FRP composite is more
preferable than steel for such specific applications due to their durability aspects
when being subjected to extreme environment conditions such as exposure to
highly polluted or coastal area, high temperature fluctuation and high moisture
condition. FRP materials have characteristics that are different from most
conventional engineering material. For example, the characteristic of carbon
fibres are low bulk density, high tensile strength and modulus to weight ratios
and excellent fatigue behaviour, however, the variation in type of carbon and the
sheets or plates forming process have resulted different characteristic of
mechanical and physical performances.
The mechanical properties of three different types of CFRP plates that
produced through Pultrusion process which classified as an advanced composite
is shown in Table 2.4. The CFRP plates listed in Table 2.4 can be categorized in
three types; Type S referred as high tensile strength, Type M referred as high
strength with intermediate modulus and Type H known as high modulus
composite. In the application of strengthening steel structure, type M is most
preferred due to compatibility of elastic properties with mild steel material. The
three most popular reinforcing fibres system that has been classified as advanced
material is shown in Table 2.5.
Table 2.4: Properties of Selfix Carbofibe Pultruded CFRP Plates System (Source:
Exchem EPC Group Ltd., United Kingdom)
Plate
type
Ult. tensile strength
(average)
(MPa)
Tensile
modulus
(GPa)
Plate width
(mm)
Plate thickness
(mm)
S 2800 150 50/80/120 1.2/1.4
M 3200 200 50/80/120 1.2/1.4
H 1600 280 50/80/120 1.2/1.4
26
Table 2.5: Typical reinforcing unidirectional fibre properties [28]
Fibre Tensile
strength
(MPa)
Modulus of
elasticity
(GPa)
Elongation
(%)
Specific
density
Carbon: high
strength*
Carbon: high
modulus*
Carbon: ultra high
modulus**
4300-4900
2740-5490
2600-4020
230-240
294-329
540-640
1.9-2.1
0.7-1.9
0.4-0.8
1.8
1.78-
1.81
1.91-
2.12
Aramid: high
strength and high
modulus
3200-3600 124-130 2.4 1.44
Glass 2400-3500 70-85 3.5-4.7 2.6
2.3.1 Carbon Fibre
Carbon fibres are currently the predominant high strength to high modulus
fibres used in the manufacture of advanced polymer composites load bearing
structures such as for automotive driveshaft, bridge beam, wings skin for jet fighter
etc. The genesis of carbon fibre technology was the need to produce lightweight, stiff
and strong materials for the rapidly growing aerospace industry. Typical sizes of
carbon fibres are in between 6 ìm and 8 ìm in diameter and consist of small
crystallites of turbo static graphite i.e. one of the allotropic forms of carbon. The
carbon fibres are formed by treating organic fibres (precursors) with heat and tension
to form a highly ordered carbon structure. In standard graphite single crystals, the
carbon atoms exist as hexagonal arrays stacked in a regular ABAB sequence. The
atoms in each layer are held together by very strong covalent bonds, whereas the
27
layers are only connected by weak van der Waals forces, and hence graphite is
anisotropic. In turbo static graphite, the stacking sequence is highly irregular.
2.3.2 The Pultrusion Process
Pultrusion is a process that enables hybrid composite components in the
forms of rod, profile sections, and tubular sections to be manufactured in continuous
lengths [29]. The basic technique employed is to impregnate the reinforcing fibers, in
continuous form with resin matrix such as polyester or epoxy prior pulling the
impregnated fibres through a curing and post curing die zones which imparts the
desired shape to the composite. A diagrammatic representation of the process is
shown in Fig.2.12.
Fig. 2.12: The Pultrusion process in manufacturing FRP plate [29]
Pultrusion machine is capable in producing hundreds of metres of profile
section per hour under single operative control. A wide range of component shapes
can be manufactured by this process at a very competitive cost due to its highly
automated nature (Fig.2.12). Polyesters, vinylesters and epoxy resins are among the
principal matrix systems that have been used for the process coupled with carbon,
glass, aramid or hybrid of those reinforcement materials respectively.
28
Fig. 2.13: Products produced by Pultrusion Process (Source: Strongwell
Corporation, USA)
2.3.3 FRP Pultruded Composites Plates
One of the most important properties of FRP composites is the tensile
behaviour whereby the stiffness and strength of FRP composites can be varied in
magnitude and direction to meet the structural design requirements. From
experienced in the testing fields, it can be seen that the mechanical properties of FRP
under tensile load are greatly influences by fibre properties, fibre forms, fibre
volume fraction, fibre orientation, matrix properties and processing methods [30]. In
design practice, the reinforcing fibres are specifically oriented parallel to the applied
load in order to gain the maximum strength capacity of the fibres. The best example
is orthotropic pultruded CFRP plate that being used for upgrading the flexural
performances of reinforced concrete (Fig. 2.14) or steel structures.
29
Fig. 2.14: CFRP Plate (black strip) externally bonded to tension face of reinforced
concrete beam (Source: Behaviour of Beams Strengthened with CFRP Composite,
IRPA 72272, 1999-2001)
2.3.4 Durability of FRP Composites
More recently, the use of FRP composite materials was extended to be used
as primary structures in aircrafts, automotive applications and infrastructure such as
for rehabilitation or strengthening of steel or reinforced concrete bridges and
buildings. This fact brings the issue of durability which the long-term
experimentation results can be used to predict the long-term properties and residual
life, as a determinant factor in the success of the referred applications. FRP
composite materials find to be increased in infrastructure applications, where design
lives cycles are about ten times longer than those in aerospace, the issue of durability
becomes more critical and must seriously focused. The tolerance of composites to
damage induced by mechanical loading and moisture ingress is the most importance
factors should be considered in real life applications.
30
The studies conducted by previous known researchers that related to the
durability performances of FRP composites are the main focused in this following
literatures review. The review is to gain the knowledge that related to the study FRP
composite degradation effects from exposure to moisture environment conditions
(i.e. outdoor, fresh water and salt water). Referring to the study conducted by Zhou
and Lucas [31], onto the effects of unidirectional graphite/epoxy composite under
water environment at temperature of 45°C, 60°C, 75°C and 90°C that exposed for
more 8000 hours were revealed two important factors that are summarised as
follows;
i. Water sorption in graphite/epoxy (T300/934) material exhibited both
Fickian and non-Fickian diffusion behaviour. The materials obey the
Fickian diffusion behaviour at lower temperatures and non-Fickian
behaviour at higher temperatures. The non-Fickian behaviour was
resulted from chemical modification and physical damage to the epoxy
resin. Cracks, voids and surface peeling were observed clearly through
SEM and optical microscopy.
ii. Moisture-induced expansion of T300/934 composite was measured in
length (fibre direction), width and thickness directions. There was no
expansion due to water absorption was detected in the fibre direction
dimension. Significant dimensional changes resulting from moisture-
induced expansion were observed in the width and thickness directions
of the laminate. The thickness decreased of the specimen at high
temperature was associated with surface resin dissolution and peeling.
Those characteristics are shown in Figs. 2.23 (a), (b) and (c).
31
Fig. 2.15 (a) and (b): The changes of width and thickness respectively of T300/934
graphite/epoxy immersed in distilled water at different temperatures [31]
Fig. 2.15 (c): The weight change of T300/934 graphite/epoxy immersed in distilled
water at different temperatures. The solid lines represent theoretical Fickian diffusion
[31]
Amer [32], on their studies related to hydrothermal effect on single fibre
composite have revealed that the interfacial degradation mechanism due to
environmental exposure of graphite/epoxy was mechanical in nature. Matrix swelling
was the main factor that degraded the interfacial stresses which finally produced a
complex state of stress within the fibre-matrix interface. Their study also revealed
that the analysis done on the single fibre system able to predict the bulk composites
behaviour. This was confirmed by experimental and FEA on bulk composites with
volume fraction ranging from 63%� 71%.
(a (b)
32
The long term durability study conducted by Liaoa [33] onto pultruded glass-
fiber-reinforced vinyl ester composite coupons subjected to various environment
conditions to study the long-term durability for infrastructure applications. Several
groups of specimens were aged in water or in salt solutions containing mass fractions
of either 5% NaCl or 10% NaCl for up to 6570 hours. The control (as-received) and
aged specimens were cyclically tested in air or while immersed in water or in salt
solution. For specimens cyclically loaded at or above 45% of the average flexural
strength of the dry coupons, no substantial difference in fatigue life was observed
among all the specimen groups. For samples cyclically loaded at 30% of the dry
flexural strength, however, all specimens tested in air survived beyond 107 cycles
while all those tested in water environments did not. It is found that long-term
environmental fatigue behaviour is not controlled by the quantity of water absorbed;
rather, it is governed by a combination of both load and fluid environment. No
difference in fatigue life was found for specimens aged in different fluid
environments at room temperature prior to fatigue testing. Relative to these samples,
however, a significant difference was seen for specimens aged in water at 75°C for
2400 hours prior to cyclic test at load levels above 30% of the dry flexural strength
(Fig. 2.25). When tested at 30% of the dry flexural strength the differences were
within the experimental uncertainty. Microscopic examination of the fatigue
specimens revealed evidence of a degraded fiber/matrix interphase region in those
specimens where environmental exposure caused premature failure so this is
believed to be a controlling factor in the environmental performance of the glass
composite.
33
Fig. 2.16: Stress-life (S-N) data for pultruded composite coupons tested in fatigue at
room temperature using environmental conditions A through to F [33]
Liaoa [34], on their durability study of pultruded glass�fiber-reinforced vinyl
ester matrix composite coupons subjected to environmental aging in water or salt
solutions at room temperature (25°C) or in water at 75°C for various times. The
flexural properties (strength and modulus) were determined for bending
perpendicular to the 0 degree orientations for all aging conditions. In addition,
flexural properties in the 90 degree orientation and tensile properties in the 0 degree
orientation were also tested for the as-received specimens and the specimens exposed
to selected aging conditions. Both strengths and moduli were generally found to
decrease with environmental aging. A group of specimens were also aged in room
temperature water for 9120 h before being tested for failure in tension. The mean
tensile modulus after aging (14.4 GPa) is 23% lower than that before aging (18.6
GPa). The mean tensile strength after aging (227 MPa) dropped by 29% compared to
those without aging (160 MPa). The failure strain for the control and the aged
specimens are 2.1 and 1.4%, respectively.
In addition, examination of the failure surfaces and comparisons between the
strength of the 90 degree specimens suggested that degradation of the fiber/matrix
34
interphase region also occurred during the aging process. Their durability study
results were presented in the following respective graphs shows in Fig. 2.17 (a) and
(b), Fig. 2.18 and Fig. 2.19.
Fig. 2.17 (a) and (b): Flexural strength and modulus for 0 specimens of pultruded
composite coupons before and after environmental aging [34]
Fig. 2.18: Flexural modulus for 90° specimens of pultruded composite coupons
before and after environmental aging [34]
(a) (b)
35
Fig. 2.19: Sorption behaviour of pultruded composite coupons under various aging
conditions [34]
The study conducted by McBagonluri [35] on the effects of short-term cyclic
moisture aging on the strength and fatigue performance of a glass/vinyl ester
pultruded composite system exposed to fresh and salt water. They have found that
the quasi-static tensile strength was seen to reduce by 24% at a moisture
concentration of 1% by weight. This reduction in strength was not recoverable even
when the material was dried, suggesting that the exposure to moisture caused
permanent damage in the material system. Even though the fatigue damage process
of the control, fresh-water- and salt-water-saturated material was similar, the cyclic
moisture absorption�desorption experiments altered the fatigue performance of the
composite system tested. Their elastic properties and fatigue strength results are
shown in Fig. 2.20 and Fig. 2.21 respectively.
36
Fig. 2.20: Properties of as-delivered (control), fresh-water-aged and salt-water-aged
materials [35]
Fig. 2.21: S�N curves of the as-delivered (control), water-aged and 3.5% salt-
solution-aged materials [35]
Experimental study conducted by Gautier [36] has shown that glass fibre
reinforced polyester pultruded composites immersed in water at different
temperatures (ranging from 30°C to 100°C) were produced three types of damage:
osmotic cracking in the matrix, at the interphase and interfacial debonding. The
result shows that the matrix osmotic cracking is the factor for specimen weight loss.
The result also shows that the decreased of interlaminar shear strength (ILSS) is
caused mainly by interfacial debonding, induced by differential swelling, and by
osmotic cracking at the interphase but the matrix also contributes to the decrease.
They finally concluded that the composite life time is greatly dependent on the
ability of the matrix to microcrack under the service conditions.
37
2.4 Adhesive Bonding Technology
Adhesives have been successful used for a number of decades in joining most
of aircraft and automotive components. Nowadays, the adhesives had also successful
used in textile industry, medicine and construction industry. The adhesive bonded
joint offers or form a major proportion of modern aircraft and automotive
construction to reduce weight, mechanical stresses and production time. Adhesives
have significant advantages over other mechanical joints such as rivets, bolts and
screws which adhesive bonding technology has a great potential to avoid excessive
stresses concentration by spreading stresses over a larger area. This finally able to
permit thinner joining surfaces that very important in low-weight applications.
By referring to Eurocomp Design Code and Handbook [31], bonded joint can
be defined as where the materials (similar or dissimilar) bond surfaces are held
together (i.e. by mechanical or chemical mechanism) by means of structural
adhesive. In order to achieve their functions, the following conditions must be
reached;
i. The adhesive should not exceed an allowable shear stress. The
performances of the joint depend to the adjustment of the maximum
shear stresses to be less than the joint shear strength.
ii. The adhesive also not exceed an allowable tensile (peel stress).
iii. The adherend is not exceed the through thickness tensile stress allowable
iv. The adherend must not exceed the allowable in-plane shear stress.
In design practice, the in-plane shear stress will be by testing before put in
design analysis. Typically, one or more of the three conditions above will become
critical before in-plane shear stress limit in the adherends exceed.
38
2.4.1 Adhesive Selection
The selection for suitable adhesive depends on several important factors as
mentioned by Budinski [40]. Among the factors that need to be considered are as
follows;
i. Service temperature
ii. Chemical level
iii. Duration of application
iv. Adherend materials
There are a few groups of adhesives system can be considered for bonding
most of the structural parts, and they are as follows:
Epoxy: Two-part adhesive system that cured at room temperature based on
epoxy-polyamide which has shear strength as high as 13.8 MPa at 38°C and
0.68 MPa at 149°C.
Anaerobic adhesives: Polyester-acrylic resins which cured with absence of
air. Suitable for metal to metal joints. Shear strength in excess of 13.8 MPa
can be obtained on metal bond strength test.
Cyanoacrylates: Suitable for metal bonding process which cured by
moisture absorption from adherends. Shear strength can be developed as high
as 20.6 MPa.
39
2.4.2 Adhesive Mechanical Properties
In structural bonding applications, there are important mechanical properties
that must be given full attention and understood in the design process, and they are as
follows;
i. shear modulus
ii. shear strength
iii. maximum shear strain
iv. tensile modulus
v. tensile (peel) strength
All the important related properties should be obtained from the manufacturer
or by established testing methods. This is important due to the effects from durability
factors such as moisture ingression, temperature fluctuation etc. Referring at creep
property, adhesives will creep under constant load even at the room temperature
especially at elevated temperature. Usually, thermoset based adhesives have better
creep resistance than thermoplastic adhesives. Fig. 2.22 shows two different
behaviour of adhesives system that has characteristics of ductile and brittle
respectively. Brittle type adhesive normally failed at high stress level with low strain
value compared to ductile adhesive system which shows high strain to failure.
Fig. 2.22: Typical brittle and ductile adhesive behaviour [31]
40
2.4.3 Effects of Loading Configuration on Adhesive Joint
The joint structure typically loaded by several of loading systems as shown in
Fig. 2.23. The tensile, cleavage and peel loads for example should be avoided
because it will weaken the joint strength. In principal, the adhesive layers of the joint
should primarily be stressed in shear or compression, the excessive strains (due to
deformation) should also be considered at the area where non-linear behaviour of
adherends or adhesive is expected.
In bonded joint, there is four main loading modes may be subjected to most
bonded structures;
i. Out-plane loads acting on a thick adherends produce peel stresses.
ii. Tensile, torsion or pure shear loads imposed on adherends produce shear
stresses.
iii. Out-of-plane tensile loads produce tensile and bending stresses.
iv. Out-of-plane tensile loads acting on stiff and thick adherends at the end of
the joint produce cleavage.
Fig. 2.23: Loading modes or type of stresses [31]
41
2.4.4 Advantages and Limitations of Adhesive Bonding
Adhesive may be the logical choice as a fastening method for bonding any
structural materials for a variety of reasons [41]. Each type of joint has it own
advantages and disadvantages that make differences between them which are listed
as follows;
Advantages:
i. The ability to joint similar and dissimilar materials.
ii. The ability to minimize stress concentration usually associated with
mechanical joints such as bolts, rivets and spot welds.
iii. Adhesive is not a electrical conductor, therefore no formation of
electrolytic corrosion in joining dissimilar materials.
iv. Ductile adhesive system able to absorb shock and vibration which
could increase fatigue life. Normally adhesive-bonded metal have
ten times more fatigue life than mechanical joints.
v. Dissimilar materials thickness can be joined; for example, concrete
beam can be joined to very thin FRP plate in strengthening
application.
vi. Adhesives acting as a sealant in addition to bonding.
vii. The elimination of fastener holes allows lighter materials to be
used and able to maintain equal or better mechanical properties.
Limitations
i. Adhesives are more subject to deterioration due to environmental
influences especially in adhesive-metal joints.
ii. Difficult to inspect the bond quality once assembled.
iii. Poor resistance to peeling type loading and may require additional
fastener to support extra stresses (bonded-bolted joints).
iv. Polymeric based adhesives properties tend to degrade over time
especially that expose to aggressive environment conditions.
v. Proper jigs and fixtures is needed for bonding process in order to
apply heat and pressure which depend on bonding cycle.
42
vi. Most adhesive have limited shelf life.
vii. Less reliable when expose to extreme temperature above 300 °C.
2.5 The Principles of Adhesive Bonding Technology for Structural
Applications
The basic principles of adhesive bonded joints shall be follows for the
production of strong and durable adhesive bonds as well to minimize the bond
defects. There are types of adhesive joint configurations and each type offer different
criteria to be considered while applying the connection. Davis and Bond [42] have
listed few important joint principles that related to the application of adhesive
bonding in practices. Among the important preferred principles are listed as follows;
i. The basic principle for design of adhesive bonds is to design the joint
such that the adhesive is always stronger than the unnotched strength of
the adherends.
ii. The basic principle for adhesive fatigue design is therefore to ensure
that the overlap length is sufficient to enable the adhesive shear stress to
decay to near zero to make the joint resistant to creep and load effects.
iii. The basic principles of surface preparation are that the surface must be
free of contamination, sufficiently chemically active to enable
formation of chemical bonds between the adhesive and the adherends,
and resistant to environmental deterioration in service, especially by
hydration.
43
iv. The basic principle for integrity of an adhesive bond is that the
inspection will not assure quality, it must be obtained by management
of all aspects of the bonding process during production.
2.5.1 Factors Considered in Adhesive Joint Design
It is really need to give an attention to a few factors to make an appropriate
and effective adhesive bond joint. Among the important factors are need to be
seriously considered are as follows;
i. Adherend mechanical and physical characteristics to be joined.
ii. Adherend surface hardness conditions.
iii. Adherend thickness.
iv. The temperature of environment for most of service life and period
time.
v. Contamination in contact to the bond (solvents, oil and other fluids).
vi. Required joint strength.
vii. Stresses due to type of loading configurations (tensile, shear, peel,
compression, impact, vibration and etc.).
2.5.2 Bond Mechanism
The theory considers adhesion to be the result of the mechanical interlocking
of polymer adhesive into the pores and other superficial asperities of adherend. The
roughness and porosity of adherend are generally the factors as wet ability by the
adhesive is sufficient as shown in Fig. 2.24. Otherwise, the non-wetted parts
44
originate failures. However, mechanical interlocking is not a mechanism at the
molecular level. It is merely a technical means to increase the adsorption of the
adhesive to the adherends at macro level [43].
Fig. 2.24: Good wetting (A) Poor wetting (B) [43]
2.5.3 Joining Technique
Referring to EUROCOMP Design Code and Handbook [31], the joint design
process should start with recognizing the joint requirements such as for supporting
and distributing the internal forces and moments. The following stage is selecting the
joint category normally determined by loading configuration or by the required joint
efficiency as a fraction of the strength. The geometry of the adherends, suitability of
the fabrication, component dimensions, manufacturing environment and number of
components to be produced must also be considered. Another factors are includes
service environment and the lifetime of the structure, requirements set for the
reliability of the joint, disassembly or not, need or fluid and weather tightness,
aesthetics and cost.
The adhesive joint must be carefully designed and prepared. The aim of the
joint is to obtain maximum strength for a given bond area. In designing adhesive
45
joint the basic characteristics of adhesives must dictate the design. The type of joints
used in adhesive-bonding flat adherends is shown in the Fig. 2.25.
Fig. 2.25: Type of adhesive joints techniques for flat adherends [43]
2.5.4 Joint Geometry Effect on Joint Strength
The joint strength also affected by the joint geometry with certain
configuration. The most basic problems of bonded joint are the unavoidable shear
stress concentrations and inherent eccentricity of the forces. The two problems
causing peel stresses in both, adhesive and adherends. From the Fig. 2.26 it can be
seen that the shear stresses are at the maximum at the end of the overlap.
The effects of the eccentricity are the greatest in lap and strap joints. It should
be known that the static load-bearing capacity of a bonded lap or strap joint cannot
be increased significantly by increasing the lap length beyond the minimum needs.
But, the bond length must long enough to provide a moderate loaded adhesive area in
the middle to resist creep deformations of the adhesive.
46
The peel stresses can be reduced by increasing the adherend stiffness without
increasing its thickness, increasing the lap length, tapering the ends of the adherend
and using adhesive fillets. Adhesive fillets used and adherend ends tapered will
reducing stress concentrations at the end of the overlap.
Fig. 2.26 shows the typical locations of possible failure initiation and critical
strength. It can be seen that when the joint (i.e. single lap) loaded with in-plane loads,
the concentration of stress failure exist at the ends of the over lap. Fig. 2.27 shows
the shear stress distribution along the bonded length and the location where higher
shear stresses occurred. The higher shear stresses location can be said as the region
of failure initiation.
Fig. 2.26: Areas of failure initiation and critical strength [31]
Fig. 2.27: A typical adhesive shear stress distribution in a lap joint according to
elastic-plastic model [31]
47
2.5.5 Elastic Properties and Deformation
Fig. 2.28 shows the schematic diagram of a single-lap joint with uniform lap
thickness loaded in tension. By assuming the deformation of double-lap joint follows
the deformation shown in Fig. 2.28. Theoretically the deformation and initiation of
bond failure occurred at the loaded end (i.e. the most stressed region). The upper and
lower part represent as an adherends while adhesive in the middle. The members
deform concentrically and the adhesive in shear when load applied. There are two
types that the specimen can be categorized; as a rigid members and as an elastic
members. If the members were rigid, equal amount of load would transfer along the
adhesive, and the shear deformation would be equal in all part of adhesive. In reality,
the members are always have elasticity and will deform continuously through their
lengths. The greater amount of load were transferred at the center of overlap mean by
the higher displacement between the members occurs there.
Fig. 2.28: (a) Deformation of rigid members (b) Deformation of elastic members
[31]
(a) (b)
48
2.6 Double Lap Joint
The double lap joint is a balanced joint construction configuration because it
consists of two outer substrates that are bonded on both sides of centre (inner)
adherend. The joint configuration that shows in Fig. 2.29 will experience internal
bending if the outer adherends are thick. In a well symmetrical double lap joint, the
centre of the adherend experiences no net bending moment, but the outer adherend
will (if it is thick), which could increased tensile and compressive stresses at loaded
ends.
Fig. 2.29: Double lap joint configuration specimen under pull-push loads
The joint is designed based on standard bond area, maximum proportion of
bond area that contribute to strength, the direction of maximum stress applied to high
strength area and the minimum stress in direction of the weakest joint. When the
adherends are subjected to the tension load, the loading effect can divided to normal
force, shear force and internal bending moment. It is reasonable to ignore axial stress
in the bond layer as it regarded to thin layer and the adhesive is assumed more
flexible than the adherends. Another assumption consequence to the strain in vertical
direction in the adhesive is zero, makes the shear stress and shear strain were
assumed to be constant over the adhesive layers.
From the bond stress distribution shows in Fig. 2.29, it is clear that a uniform
shear stress was distributed symmetrically along the bond length. Shear stress is
directly proportional to the width of the joint, but increasing the bonded area beyond
49
certain limits is not significantly affected. The strength of the joint is depending on
the yield strength (or ultimate strength for brittle materials) of the adherend, its
modulus and thickness. The thickness of the adhesive bond is important and must be
as thin as possible to avoid joint starvation. The analysis of the bond strength and
durability are related to the following parameters;
Type of adhesive: Different adhesive provides different bond strength and
characteristic. The selection of the adhesive should be done carefully based
on the type of joint, strength needed, materials to be connected and working
environments.
Adherend materials: The adherends be used should be suitable to the
adhesive. Each adherend has it own mechanical and physical properties that
will provide different strength and durability.
Adherend preparations: Adherend should be prepared follows the correct
procedure to provide a good adhesion and absorption by the contact between
adherend and the adhesive.
Curing process; temperature and pressure: The adhesive only provide
high bond strength if it is completely cured. To reach this level, the bonding
needs enough time, dry and clean environment and standard curing
temperature. Incomplete curing process can cause bond slippage.
Adhesive thickness: The thickness of the adhesive should be controlled; not
to thick or less. Thick bond layer will create an unexpected force and
moment, finally will produce peel failure and less bond thickness could cause
lower bond strength.
50
2.7 Surface Treatments
Adherend surface treatment is really an important parameter that will affect
an adequate joint strength if not properly prepared. Therefore, all the bond surfaces
shall be properly treated prior to bonding. In order to produce a good bonding
performance, the entire adherends bond surface shall be treated by the following
procedure:
i. Solvent degreasing using a clean absorbent material which does not
itself contaminate the surface.
ii. Abraded using medium grit abrasive paper (i.e. for FRP composite),
sandblasting (i.e. for metal or concrete), etc.
iii. Degreasing.
During the surface roughening process, the pressure applied (i.e. by any type
of tool) shall be adjusted to suit with the condition as not to damage the adherend
material structure (i.e. not to produce permanent stresses within material structure).
Commonly, the prepared surface must be pretreated immediately after surface
treatment to avoid contamination or voids that can cause poor bonding.
2.8 Adhesive Joint Design Principles
In general, the loads imposed on the bonded joint structure must be obtained
from the whole structure analysis. Besides, the bond line must ensure capable to
transfer the applied loads between the joints members. While the adherends are
capable of with-standing, the joint induced internal loadings. The evaluation of the
components basic strength which to be joined under the applied external loads is a
part of the component design process.
51
The experimental specimen that to be tested is designed based on analytical
models for plate-to-plate connection and supplemented by testing. The assumption
made that the joint is a perfect bonding between the adhesive and the adherends. This
means, there are no slip occurred along the bond area and the force applied were
transferred uniformly to each part of the adherends. It shown from the failure of
cohesive in the adhesive or adherend always occur before the adhesive failure at the
interface. If the matter as follows occurred, the assumption may become invalid; so
must be considered properly:
i. Non-suitable chemical of the adhesive and adherends. The adhesive
cannot provide a good bonding and high strength needed. Besides, the
adhesive will give a chemical reaction between the adhesive matrix and
the adherends matrix.
ii. In adequate surface treatment. For examples, the surface is not roughen
perfectly, the surface of bonding area is contaminated and not fully
degrease by the solvent, the pressure applied while bonding is also not
enough.
iii. Environment factors such as temperature and pressure during bonding.
The bonding process should not been done during high humidity where
the water will dissolved between the adhesive pore and will effect the
bond strength. There must be enough time for the adhesive to cure and
should be applied on suitable dry environment.
iv. Other bonding defects.
Referring from most material testing, it is a perfect bonding if the failure
mode is not an adhesive failure. If the slip occurred, the surface treatment should be
improved or the adhesive or a joint configuration shall be changed. The design of
bonded joints shall be based on practically and tolerances of the manufacturer.
52
Referring to the Fig. 2.30, it can be seen that the different type of joint has it
own mode of failure. For double lap joint (i.e. same characteristic as double strap
joint), the major problem occurs is peel failure if compared to the others joint
technique likely to have shear failure.
Fig. 2.30: Relative joint strength of various joint configurations [31]
2.9 Failure Modes
Sheppard [43] in their study on developing damage zone model for adhesive
bonded joint were listed four types of failure modes by which an adhesive bonded
joint can fail. The four primary failure modes are summarised as follows;
i. Adhesive failure that means a rupture of an adhesive bond, such that the
separation is at the adhesive - adherend interface. This failure is mainly
due to a material mismatch or in adequate surface treatment.
ii. Cohesive failure of adhesive means that when the adhesive fails due to
loads exceeding the adhesive strength.
53
iii. Cohesive failure of adherend means that when the adherend fails due to
loads in excess of the adherend strength, for example due to bending,
tension or compression.
iv. Out-of plane adherend failure (this failure mode only occurs for
composite adherends and is in form of intra-laminar and/or inter-
laminar failure in adherends.
They also proposed three damage zone models that could be developed at
three important load levels; low load, medium load and ultimate load. The following
are the description for those three models.
i. Low load level: localised damage will occur at the end of the joint
(loaded end). This damage occurs due to the adherend is locally
subjected to excessive strain which is greater than ultimate material
strain. If the joint consist of concrete and FRP, a damage will develop
on both adherend either by fibre/matrix interface failure (inter-laminar)
or concrete shearing for FRP and concrete respectively.
ii. Medium load level: the damage zones will grow in size and the
concentration of points of specific damage will increase.
iii. Failure load level: the damage zone will grow to a critical size when
the individual components of damage will coalesce and form a crack.
54
Fig. 2.31 (a) and (b) shows the development of the damage process for out of plane
and cohesive failure modes [43]
2.10 Mathematical Model for Predicting Bond Stress Behaviour
The mathematical model of FRP Plate-concrete bonded system under pull-
push loads can be referred to elementary force diagram in Figure 2.32 (a) and (b).
The figure shows a double-lap joint under pull- push loads of a FRP plate bonded to
concrete by adhesive joint. FRP plate, adhesive layer and concrete prism are assumed
constant along the bond length. In such a joint, the adhesive layer is mainly subjected
to shear deformations. A simple mechanical model for this joint can be thus
established by treating the plate and the concrete prism as being subject to axial
deformations while the adhesive layer was assumed to be subjected to shear
deformations only. That is, both adherends are assumed to be subject to uniformly
distributed axial stresses, with any bending effect was neglected, while the adhesive
layer is assumed to be subject to shear stresses which are also constant across the
(b) (a)
(b)
55
thickness of the adhesive layer. It should be noted that in such a model, the adhesive
layer represents not only the deformation of the actual adhesive layer but also that of
materials adjacent to the adhesive layer and is thus also referred to in the paper as the
joint interfaces.
Fig. 2.32(a): Specimen geometry and material parameters of double-lap joint under
pull-push loads
Fig. 2.32 (b): Force analysis on elementary bar model
A series of pull-push shear tests on single-lap bonded joints were carried out
by Yao [44] to determine the effect of various parameters on the bond behaviour of
To To + dTo
dxc
dx
Ti Ti + dTi dxc
dxc
dxc To + dTo To
56
FRP plate-to-concrete joints. The thin FRP plates were instrumented with strain
gauges at 10 mm intervals along the bond length, L to monitor the variation of plate
strains with load. The results showed that the plate strains in the debonded zone were
substantially affected by plate bending due to the thinness of the plate and the
roughness of the cracked interface. Their mathematical model was developed
through the following assumptions for simplicity of the problems [45];
i. Adherents are homogeneous and linear elastic
ii. Adhesive is exposed only to shear forces
iii. Bending effects are neglected
iv. Normal stresses are uniformly distributed over the cross section
v. Thickness and width of the adherents are constant throughout the bond
line.
The two models of stress-slip relationship shown in Fig. 2.33 are
considered to be possible in representing the nonlinear interfacial behaviour are
introduced here. It is noted that the area below the curve represents the
interfacial fracture energy of mode II, fG , which is defined as the energy required to
bring a local bond element to shear fracture (debonding). f is the local bond
strength, and f maximum slip.
57
Fig. 2.33: Two models of stress relationship [44]
For model I, the stress-slip relation is linearly ascending before the
occurrence of interfacial fracture and the value of shear stress suddenly drops to zero
when the value of slip exceeds f without consideration of the softening behavior.
While for model II the stress-slip relation is linearly ascending when the value of the
slip is smaller than 1 . After the occurrence of an interfacial microcrack the stress
slip relation is linearly descending with a range of f 1 . The value of shear stress
is reduced to zero and an interfacial macrocrack (debonding) occurs when the value
of slip exceeds f .
For the case of the pull-push joint, the theoretical solutions can be obtained as
follows:
Model I: Linear Shear Stress-Slip Relationship with a Sudden Stress Drop
The shear stress along the FRP-concrete interface can be written in the form
L
x
b
P
sinh
cosh.
1
58
Model II: t-d Relationship with Linearly Ascending and Descending Branches
The shear stress along the FRP-concrete interface can be written in the form
aL
xf
1
1
cosh
cosh
if 0 1
and
aLxaLxaLf 2211
2 cossintanh
if f 1
where:
P=
aaaLbf
2211
2
2
1 sincostanh
222
1
11
22 1
2 tEb
b
tEG f
f
f
fG
1
221
2
ff
fG
1
222
2
21
1
2
97.0arcsin1
f
fa
Analytical solutions for adhesively bonded balanced composite and metallic
joints are conducted to reveal the adhesive peel and shear stresses [46].The coupling
between the adherents is established through the constitutive relations for the
59
interface ��resin rich�� layer, which is assumed homogeneous, isotropic and linear
elastic. The constitutive equations are suggested as follows:
dx
dwhu
dx
dwhu
h
Gaa
1101
2202
0 22
where aG is the shear modulus, aE is the elastic modulus of the interface ��resin
rich�� layer, and ra, sa are the interface ��resin rich�� layer transverse normal and
shear stress components.
Cho [37] assumed a bond-slip model type for a coarse sand coated interface
in the form of their suggested model types in order to use Yuan�s analytic solutions,
and finds appropriate model parameters for an assumed bond-slip model type
applicable to the coarse sand coated interface.
In Figure 2.34, the bond-slip model is expressed by the bond stress function,
where xuxu 21 represents the slip between adherent 1 and 2. f and f
are the bond strength and maximum slip, respectively. And, fG expresses the fracture
energy, which corresponds to the area under the curve. P is the axial force, E, t
and b are the axial stiffness, thickness and width of adherent, respectively. Subscripts
1 and 2 indicate adherent 1 and 2.
Different stress distributions are considered for the ascending and descending
parts of the bond-slip curve. When the stress in the whole bonding area occurs in the
ascending part of the curve in the bond-slip model, the solution is as follows:
xG
xf
f
2
2
60
On the other hand, when the stress in the adhesion area develops also in the
descending part of the bond-slip curve, the solution should be subdivided and
expressed separately for the ascending part aLx 0 and descending part
LxaL of the bond-slip curve, as follows:
xx ff
f
1
Fig. 2.34 : Bond slip model for pull � push joint [37]
A formularization method to obtain the bond-slip model and optimized bond-
slip model have been presented based on experiments and analyses of the bond
behavior between FRP plate and concrete. A multi-objective optimization problem
has been formulated by means of physical programming technique, which minimizes
the difference between shear bond test results and analytic solutions of the bond-slip
model derived from fracture mechanics. The optimization has been performed
through a genetic algorithm. .
Cruz and Barros [38] assumed that CFRP has a linear-elastic behavior and
neglecting the thickness of this composite material, the equilibrium of a CFRP of
length xd bonded to concrete can be given by the following expression (see Figure
2.35 and Figure 2.36)
61
dx
dtEx fff
2
where x is the bond stress acting on the contact surface between CFRP and epoxy
adhesive, and fE , ft and f are the Young�s modulus, the thickness and the strain
of the CFRP, respectively.
Fig. 2.35: Equilibrium of the CFRP [38]
Fig.2.36: Strain of the intervening materials of the bond region [38]
62
The quality of the local bond stress�slip relationship, s , has decisive
importance on the accuracy of this simulation. In the present work the local bond
stress�slip relationship is composed by the following two equations:
mm s
ss if mss
and
,
mm s
ss if mss
where m and ms are the bond strength and its corresponding slip, and and , are
parameters defining the shape of the curves.
To assure that peak pullout force and its corresponding slip obtained
numerically are similar (less than a tolerance of 1%) to the values registered
experimentally, the following method was used:
Step 1: fixing the parameters a and a0, the values of sm and sm of the best
fitting
and , , the values of ms and m of the best fitting were found
Step 2: using the values of ms and m obtained in the previous step, the values
of and , giving the best fitting were determined.
Figure 2.37 shows that the loaded end slip vs. pullout force
relationship obtained analytically (thick line) fits quite well the corresponding
experimental envelop (hatch).
63
Fig. 2.37: Loaded end slip versus pullout force relationship [38]
The error is the difference, in absolute value, between the areas
corresponding to the experimental and analytical curves. From these study, the
following observations can be pointed out:
The error of each series is quite acceptable.
A reasonable coefficient of variation was obtained in the bond strength.
Large scatter in the values of ms , and , was obtained.
Her [39] make the basic assumptions when she study about adhesively-
bonded lap joints as follows:
The shear stress in the adhesive layer do not vary through the thickness.
The longitudinal stresses in the adherends do not vary through the thickness.
The adherends and adhesive layer are linear elastic, and joint edge moment is
neglected.
64
Fig. 2.38: The free-body diagram of a single-lap joint [39]
Fig. 2.39: The free-body diagram of a double-lap joint [39]
For single-lap joint, the shear deformation in the adhesive layer as follows:
l
l
tEtE
tEtE
l
xP
ooii
ooii
cosh
sinh
sinh
cosh
2
While for double-lap joint :
2cosh
sinh
2
2
2sinh
cosh
4 l
l
tEtE
tEtE
l
xP
ooii
ooii
65
Where:
ooii
a
tEtE
G 12
oi TTP 2
and the constants iE and oE are the equivalent longitudinal moduli in upper and
lower adherends, respectively. oE and ot are the longitudinal displacement, strain,
Young's modulus, and thickness of the outer adherend, iE respectively and it are the
respective components relative to the inner adherend, aG is the shear modulus of
adhesive, and are the shear strain and thickness of the adhesive layer. l is the
length of the bonded region.
Fig. 2.40: The shear stress obtained by Eqs. (11) and FEM along the adhesive region
for a single-lap joint [39]
From these results one can observe:
The stress obtained by finite element method is higher than the analytical
solution. It may be due to the bending effect caused by the eccentric load
which has been ignored in the analytical solution.
66
The result of maximum shear stress in the analytical solution is occurred on
both the ends of overlap region. However, the maximum shear stress occurs
at a short distance away from the ends in the finite element result.
A simplified one-dimensional approach has been developed to model the
adhesive bonding for single-lap joint and double-lap joint. A simply analytical
solution is obtained, and compared with the two-dimensional finite element results.
Good agreement between these two results demonstrates that present approach can
provide a simple but accurate solution which is very useful in joint design.
The effects of varying parameters such as thickness of adhesive and
adherend, modulus of adhesive and adherend can be concluded as follows:
High stress concentration occurs on the free ends of adhesively bonding
region. The shear stress and transverse normal stress in the adhesive layer are
responsible for the initiation of the failure of the adhesively bonding joints.
Increase of the thickness of the adhesive layer, leads to the lower shear stress
in the adhesively bonding region. Thus, thicker adhesive layer is able to
improve
the strength of the adhesively bonding joint.
In the case of two different adherends connected by the adhesive joint, the
maximum shear stress occurs at the free end of adhesive region near to the
adherend with higher stiffness.
As the thickness of adherents is di�erent, the maximum shear stress occurs at
the free end of adhesive region near to the thinner adherend.
CHAPTER 3
RESEARCH METHODOLOGY
3.0 Introduction
In order to answer the research questions an equation is derived basic from
classical theories of Volkersen/ de Bruyne�s solution for double-lap. Then, from the
theory, the parameters will be varied to find out its influence to local bond stress.
The results of experimental works by Shukur [30] were compared to the theoretical
result in order to prove the validity of the equation.
3.1 The Parameters Effect
From the equation that will be derived, each parameter that is suspected effects
the local bond stress of the joint, will be verified to three different values at Other
parameters will be fixed to a constant value as shown in to make sure the effect to the
joint were caused by that parameter. Effect means the changes in maximum value of
the local bond stress and the effective bond length.
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68
3.2 Bond Test for CFRP Plate-Epoxy-Concrete Specimen
Data and results studied by Shukur [30] will be compared to the theoretical
results in order to validate the equation.
The test was conducted onto three specimens of CFRP plate-epoxy-concrete
under pull-push loading configuration and all of the specimens were loaded starts
from 0 kN till it failed and the strain readings were taken each 5 kN of incremental.
but only the bond stress at load 40 kN will be compared with the theory at that
loading the load transfer from the CFRP plate to the concrete are most fairly linear
and occurs at almost uniform rate [30].
3.2.1 Experimental Details
The experimental set-up for the test referred to Swamy [15,22] as a standard
guidelines. These include the geometry of the specimen as shown in (Fig. 3.1) and
the test rig shown in (Fig. 3.2)
69
Fig 3.1: Instrumentation set-up onto CFRP Plate-epoxy-concrete prism specimen for
this study
Fig. 3.2: Standard test rig used by Swamy [15,22] for GFRP Plate-epoxy-concrete
pull-out test
70
3.2.2 Details of Test Materials
The Selfix Carbofibre Pultruded CFRP Plate type S, 50 mm wide, 1.4 mm
thick and 555 mm in length was bonded onto concrete prism surface using Selfix
Carbofibe two parts epoxy adhesive system with 2 GPa shear stress. The epoxy
thickness was 1mm for each part. The concrete prism was ad to have design
compressive strength of 40 MPa with 100 mm thickness. The surface of concrete
prisms was roughened using air tool hammer.
71
Fig. 3.3: Arrangement of pull-out test rig onto CFRP Plate-epoxy-concrete prism specimen
3.2.3 Determination of Bond Stress Characteristics
The local longitudinal CFRP Plate force that acted along the bond length was
made from the assumption that the bonding between CFRP Plate-adhesive-concrete
was perfect, therefore the following local force, Fi and local bond stress, ô equations
were developed through local strain, åi testing data [15,22,27]. Based on statics
72
equilibrium force analysis on specimen joint element, dx shows in Fig. 3.4, the
analysis was done as follows;
Ó Fx = 0
[(ó + dó) (A) � (ó) (A)] � ô (dA) = 0
dó (w x t) = ô (dx x w)
where,
A = (t x w) is CFRP Plate cross sectional area (mm2)
ó is normal stress onto CFRP Plate cross sectional area (MPa)
therefore,
CFRP Plate local force at i location, Fcfrp,i = dó (w x t)
= Ecfrp.åi (w x t) [3.7]
and, finally the local bond stress at location i - j,
ôi-j = (Fcfrp,i � Fcfrp,j)/(dx x w) [3.8]
where,
w = CFRP Plate width (mm)
t = CFRP Plate thickness (mm)
ÄLi-j = dx = the distance between two consecutive strain gauges
(Fcfrp,i � Fcfrp,j) = ÄF i-j = the variation of the local longitudinal force
dx
Fcfrp
Fcon
dx
(ó + dó)A óA
ô (dA) adhesive
CFRP Plate
Fig. 3.4: Elementary force analysis
73
Ecfrp = CFRP Plate Young�s Modulus (GPa)
åi/cfrp = CFRP Plate local strain at location i (µå)
i. Local Force Transfer, Fi
Local CFRP Plate force at any location along the bond length can be
determined by an equation (3.7).
ii. Local Bond Stress, ôL
The local bond stress distributions along the bonded length can be
determined by assuming a linear variation of the longitudinal force along the
CFRP Plate between two consecutive strain gauge locations. By referring to two
strain readings åi/cfrp and åj/cfrp at position i and j, the plate thickness tp, its elastic
Young modulus Ecfrp, and the distance ÄLi-j between two consecutive strain
gauges positions, the local average bond stress between two consecutive gauges
position can be determined by an equation (3.8).
iii. Average Bond Stress, ôavg
An average bond stress for double lap joint system can be established and
determined by the following equation;
Average bond stress, av = 2
P
A
= 2( )B
P
b L [3.9]
where,
Average bond strength, av ,s = max
2
P
A
= max
2( )B
P
b L [3.10]
where,
P = nominal load (N)
Pmax = Ultimate load (N)
74
A = Bond area (b x LB) (mm²)
b = Width of CFRP plate (mm)
LB = Bond length (mm)
3.3 Conclusion of Research Methodology
For the comparison between theoretical and experimental, the joint will be
assumed to experience perfect bonding which the bond stress at the CFRP is equals
to adhesive shear stress. The derived equation wills valid if the result shows a good
agreement with experimental results. If validated, the parameters effect on local bond
stress distribution can be determined from the equation.
CHAPTER 4
DEVELOPMENT OF BOND GOVERNING EQUATION FOR
FRP-CONCRETE BONDED SYSTEM
4.0 Introduction
This mathematical governing equation is derived from the classical theories of
Volkersen/ de Bruyne�s solution for double-lap joint system [41]. The assumptions
made for the equation are stated as follows:
i. adherend shear deformations are neglected
ii. linear shear stress distributions through the thickness of the adherends
iii. thickness of adherend and adhesive were assumed constant along the bond
length
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76
4.1 Theoretical Analysis on Tension-Compression CFRP Plate-Concrete
Prism Bonded System
The geometry of the CFRP plate-epoxy- concrete under pull push loading
configuration is shown in Fig 4.1. The length of the overlap is L. The thicknesses of
the outer and inner adherends are ot and it respectively while at is the thickness of
adhesive. The elementary force diagram is shown in Fig 2.32 (b).
Fig. 4.1: Geometry and material parameters of the CFRP plate-epoxy-concrete prism
ti
dx
ot
0
ta
2
T
2
T
T
L
x
77
The assumption of linear shear and strain distribution through out the
thickness of the adherends is shown in Fig 4.2.
From the elementary force diagram in Fig 2.32 (b), the average adhesive shear stress
over the bond line is:
L
Tdx
L
L
aave 2
10
[1]
where a is adhesive shear stress. Following the notation in Fig.4.2, the equilibrium
equations for the basic elements of the outer and inner adherends can be written as
follows:
ve F = 0
0 oaoo TdxdTT
00 adx
dT [2]
02 dxTdTT aiii dxc
02 ai
dx
dT [3]
dxa
To +dTo To 0o
ao
to U Uo
aoU y�
Ti +dTi
Ti
dxa
2
t i
0i
ai aiU
iaU
y��
Fig. 4.2: Linear shear stress, and strain distribution through the thickness of adherends
78
Therefore, the adherend shear o for the outer adherend and i for the inner adherend
can be expressed as:
'yto
ao
[4a]
and
iai t
y ''21 [4b]
where y� and y�� are the local coordinates system with the origin at the top surface of
the outer and inner adherend. Eqns. [4a] and [4b] are based on zero shear stresses at
the top surface of the outer adherend (i.e. at y� = 0) and at the centre of the inner
adherend (i.e. at y�� = ti/2), and o = a at y�= to and ai at y��= 0. Then with a
linear material constitutive relationship the adherend shear strain o for the outer
adherend and i for the inner adherend are written as:
'ytG oo
aO
[5a]
and
ii
ai t
y
G
''21
[5b]
The longitudinal displacement functions uo for the outer adherend and ui for the inner
adherend are given by:
2'
0'
2'�'�' y
tGuydyuyu
o
aos
y
ooso
[6a]
and
i
y
i
aaiiaii t
yy
Guydyuyu
2
0
''''''�''�''
'' [6b]
79
where osu represents the displacement at the top surface of the outer adherend and
aiu is the adhesive displacements at the interface between the adhesive and inner
adherend. Note that, due to the perfect bonding of the joints, the displacements are
continuous at the interfaces between the adhesive and adherends. As a result, the aiu
should be equivalent to the inner adherend displacement at the interface and aou (the
adhesive displacement at the interface between the adhesive and outer adherend)
should be the same as the outer adherend displacement at the interface. Based on eqs.
[6a], the aou can be expressed as:
o
oaosooao G
tutyuu
2'
[7]
Using eqs. [7] eqs. [6a] can be rewritten as:
o
oa
oo
aaoo G
ty
tGuyu
2'
2' 2
[6c]
The longitudinal resultant forces To and Ti for the outer and inner adherend,
respectively, are:
ot
oo dyyT0
'' [8a]
and
2
0''''2
t
ii dyyT [8b]
where o and i are longitudinal normal stress for the outer and inner adherends,
respectively. By transforming these stresses into functions of displacement and
substituting eqs. [6b] and eqs. [6c] into the displacements, eqs. [8a] and eqs. [8b] can
be rewritten as:
80
dxG
dt
dx
dutEdy
dx
duET
o
aoaooo
to
oo
o
3'
0
[9a]
and
dxG
dt
dx
dutEdy
dx
duET
i
aiaiii
ti
ii
i
6''2
2/
0
[9b]
The adhesive shear strain a is simply defined as:
aoaia
a uut
1 [10]
The adhesive shear stress can be written as:
aoaia
aa uu
t
G [11]
By differentiating eqs. [11] with respect to x, the equation becomes:
dx
du
dx
du
t
G
dx
d aoai
a
aa [12]
Substituting eqs. [9a] and [9b] into eqs. [12] leads to:
dx
d
G
t
G
t
tE
T
tE
T
t
G
dx
d a
o
o
i
i
oo
o
ii
i
a
aa 36
[13]
By differentiating eqn. [13] with respect to x and substituting eqn. [2] and [3] into the
differential equation, the equation becomes:
2
2
2
2
36
2
dx
d
G
t
G
t
tEtEt
G
dx
d a
o
o
i
i
oo
a
ii
a
a
aa [14]
81
By rearranging eqn. [14], one obtains:
aooiia
aa
o
o
i
i
a
a
tEtEt
G
dx
d
G
t
G
t
t
G
12
361
2
2
[15]
which governs the adhesive shear stress. It can be rewritten as:
022
2
aa
dx
d
or 0'' 2 aa [16]
with
o
o
i
i
a
a
ooiia
a
G
t
G
t
t
G
tEtEt
G
361
12
2 [17]
The parameter of is redefined by and and is given as follows;
222 [18]
where
ooiia
a
tEtEt
G 122 [19]
1
2
361
o
o
i
i
a
a
G
t
G
t
t
G [20]
82
Assume the exact solution is y = emx
Therefore y� = memx
y�� = m2emx
so, m2- 02 [21]
m = [22]
The general solution for the governing eqn. [16] is:
xxa BeAe [23]
From Fig. 2.32 (b), CFRP plate-concrete prism will experience 2 times of a value
for each layer for bond length of L, the eqn. [23] becomes:
22
xx
a BeAe
[24]
The appropriate boundary conditions are stated as follows;
avgiavgo LTTLT
T 2,2
at x= 0 [25a]
and
LxatTTT io 0,0 [25b]
Based on eqn. [24] and eqn. [25a],
BAavg [26]
83
Based on eqn. [24] and eqn. [25b],
220LL
BeAe
LBeA [27]
From eqn. [26] and [27] BBe Lavg
1 L
avg
eB
[28]
From eqn. [27] and [28] 1
L
Lavg
e
eA
[29]
Therefore, the final mathematical governing equation�s:
22
21
1 xL
x
La eeeL
T
e
[30]
with condition Lx 0
This equation is not limited to any value of local bond stress. But, the fact is
if the local bond stress exceed the bond strength (shear, compressive and tensile
strength of those bonded materials), the bonding will experience micro cracking and
finally fail when the direct tensile strength exceeding the value of pull-off strength.
The bond failure is normally occurs at adhesive-concrete interface as concrete
tensile shear strength is very low compared to tensile strength of CFRP and shear
strength of epoxy [23, 30]. Then, a limitation can be estimated for the a as follows:
a Concrete tensile shear strength
84
The equation that relates the concrete Young�s modulus and concrete�s
compressive strength as follows [47]:
cE = 5.061073.4 cf
CHAPTER 5
ANALYSIS AND DISCUSSION
5.0 Introduction
In order to validate the equation, the theoretical local bond stress value was
compared to the experimental value. Then, the parametric study was done to study
the effects of material properties to local bond stress distribution.
5.1 Equation validation
For the validation of the equation, local bond stress of three specimens
(BOSTUS 1, BOSTUS 2, BOSTUS 3) at load 10 kN, 40 kN and 60 kN which
studied by Shukur [30] were compared to the results from theoretical value. The
material and physical properties of the specimens is shown in Table 5.1
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86
Table 5.1: Material and physical properties of testing specimens
Parameter Value
Epoxy shear modulus, aG (GPa) 2.7
CFRP Young�s modulus, CFRPE (GPa) 135
Concrete Young�s modulus, concreteE
(GPa)
30
Thickness of epoxy, at (mm) 1.5
Thickness of CFRP CFRPt (mm) 1.4
Thickness of concrete, concretet (mm) 100
Bond length, L (mm) 200
Local Bond Stress vs Bond Length (Theoretical and experimental value)
-1
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
Theory
BOSTUS 1
BOSTUS 2
BOSTUS 3
Load = 10 kN
Fig. 5.1: Theoretical and experimental local bond stress for BOSTUS specimens at
load 10 kN
Fig 5.1 shows the comparison between theoretical and experimental values
for BOSTUS specimens. From the graph, it can be observed that the maximum
theoretical local bond stress at loaded end for theoretical is 5.1 MPa, which is 21%
higher than BOSTUS 1, 27% higher than BOSTUS 2 and 31% higher than BOSTUS
87
3. At 15 mm bond length, the theoretical local bond stress shows the value of 1.6
MPa, while the local bond stress of BOSTUS 1 is 1.99 MPa. The difference is about
20%.The value of local bond stress for BOSTUS 2 and BOSTUS 3 at 15 mm bond
length are 18% and 16% higher respectively than the theoretical value.
For 35 mm bond length, the theoretical value is 0.2 MPa, while BOSTUS 1 is
33% higher; 0.3 MPa, and BOSTUS 3 is 20% higher; 0.25 MPa. The value for
BOSTUS 2 is the same with the theoretical value; 0.2 MPa. Both of theoretical and
experimental effective bond length is about 105 mm from the loaded end, which
means that the tensile force from CFRP plate was transferred to the concrete.
Local Bond Stress vs Bond Length (Theoretical and experimental value)
-5
0
5
10
15
20
25
30
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
Theory
BOSTUS 1
BOSTUS 2
BOSTUS 3
Load = 40 kN
Fig. 5.2: Theoretical and experimental local bond stress for BOSTUS specimens at
load 40 kN
From Fig. 5.2, it can be observed that in the experiment, debonding has
occurred at the loaded end and the maximum local bond stress has shifted to 15 mm
bond length at 40 kN load level.
At 15 mm bond length, the theoretical local bond stress shows the value of
10.71 MPa, while the local bond stress of BOSTUS 1 is 12.4 MPa. The difference is
88
about 16%.The value of local bond stress for BOSTUS 2 and BOSTUS 3 at 15 mm
bond length are 10% and 12% higher respectively than the theoretical value.
For 35 mm bond length, the theoretical value is 3.97 MPa, while BOSTUS 1
is 17% lower; 3.31 MPa, and BOSTUS 2 is 18% lower; 3.27 MPa. The value for
BOSTUS 3 is 4.01 MPa, 1% higher than theoretical value. Both of theoretical and
experimental effective bond length is about 105 mm from the loaded end.
Local Bond Stress vs. Bond Length(Theoretical and experimental)
-5
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100 120 140 160 180
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
Theory
BOSTUS 1
BOSTUS 2
BOSTUS 3
Load = 60 kN
Fig. 5.3: Theoretical and experimental local bond stress for BOSTUS specimens at
load 60 kN
Due to the growth of the crack, the maximum local bond stress has shifted to
35 mm bond length for 60 kN load level in the experiment. From Fig. 5.3, it can be
observed that experimental local bond stress values show very big differences with
the theoretical.
89
5.2 Discussion of Equation Validation
From Figs. 5.1 to 5.3, it can be observed that the equation only valid for low
and medium load level. The acceptable range of error between the theory and
experiment actually happened due to assumption that were made when the derivation
of the equation. The assumption of the thickness of adherends and adhesive were
assumed constant along the bond length which practically impossible in specimen�s
preparation also caused the error in determined the local bond stress. The error also
exists due to the assumption that all of the materials are fully linear elastic even the
concrete has a plastic region.
The higher value of maximum local bond stress for theory at loaded end
possibly because the adherends shear deformation and peeling effect was neglected
in the calculation. As we can observe from the graph, the load was transferred further
in experiment than in theoretical, which caused the experimental local bond stress at
point 15 mm and 35 mm higher than the theoretical. This happened due to a little
bond slip that happened between the concrete and CFRP plate.
The strains behaviour for BOSTUS specimens may also be affected by
roughness and irregularities of concrete surface profiles as shown in Fig. 5.4 that
reflects the strains distribution characteristics along the bond length. The mechanical
inter-locking between adhesive and adherends contributed a big effect in strain
distribution [30].
90
Fig. 5.4: Roughness and irregularities of concrete bond surface
5.3 Parametric study
From the equation that has been developed from previous chapter, the
parameters that influence the stress distributions in the adhesively bonding region
(interface) can be classified into two categories.
One is called mechanical properties which include the Modulus Young of
adherends and the shear modulus of the adhesive. The other is called physical
properties which include the thickness of the adhesive layer, the thickness of the
adherends and the bond length.
To find out the effect of those parameters, the local bond stress at load 20 kN
was calculated using the equation. Those parameters were varied with three different
values as shown in Table 5.2 while other parameters were fixed to be constant .Table
5.3 shows the parameters matrix.
91
Table 5.2: Three different parameter�s value
Parameter Value 1 Value 2 Value 3
adhesiveG (GPa) 1.5 2.0 2.5
outerE (GPa) 100 150 200
innerE (GPa) 20 30 40
adhersivet (mm) 0.5 1 1.5
outert (mm) 1 1.5 2
Bond length, L
(mm)
100 200 250
Table 5.3: Influential parameters matrix
Parameter adhesiveG
(GPa)
outerE
(GPa)
innerE
(GPa)
adhersivet
(mm)
outert
(mm)
innert
(mm)
Bond
length
(mm)
adhesiveG (GPa) varies 150 30 1 1.5 100 200
outerE (GPa) 2.0 varies 30 1 1.5 100 200
innerE (GPa) 2.0 150 varies 1 1.5 100 200
adhersivet (mm) 2.0 150 30 varies 1.5 100 200
outert (mm) 2.0 150 30 1 varies 100 200
Bond length,
L (mm)
2.0 150 30 1 1.5 100 varies
92
5.3.1 The Effect of CFRP Plate Young�s Modulus
From the graph shows in Fig. 5.5, it can be seen that local bond stress at 20
kN load level increased when the CFRP Young�s modulus increased. The maximum
local bond stress for 140 GPa CFRP Young�s modulus is 7.07 MPa, 19.8% higher
than local bond stress for 100 GPa CFRP Young�s modulus, 5.9 MPa. While for 180
GPa CFRP Young�s modulus, the local bond stress is 7.88 MPa, 11.5% higher than
140 GPa CFRP Young�s modulus.
At 20 mm bond length, local bond stress for 140 GPa and 180 GPa CFRP
Young�s modulus are 2.5 MPa and 3.11 MPa, 43.7% and 78.7% higher, respectively
to the 100 GPa CFRP Young�s modulus
For 40 mm bond length, local bond stress for 140 GPa CFRP Young�s
modulus is 0.88 MPa, 72.5% higher than local bond stress for 100 GPa CFRP
Young�s modulus, 0.51 MPa while for 180 GPa CFRP Young�s modulus, the local
bond stress was 1.22 MPa, 38.6% higher than 140 GPa CFRP Young�s modulus.
The effective bond length of local bond stress for 100 GPa CFRP Young�s
modulus was only about 80 mm, while 100 mm and 120 mm for 150 GPa and 200
GPa CFRP Young�s modulus. It can be seen that the higher CFRP Young�s modulus,
the longer bond length required to transfer the force from concrete to CFRP.
93
Local Bond Stress vs Bond Length(Effect of CFRP Young's modulus )
0
1
2
3
4
5
6
7
8
9
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
E=100GPa
E=150GPa
E=200GPa
Ga =2.0GPaEc =30GPata =1mmta =1.5mmtconcrete =100mmLoad =20kN
Fig 5.5: Local bond stress with different CFRP Young�s modulus
5.3.2 The Effect of CFRP Plate Thickness
Fig. 5.6 shows that the local bond stress at 20 kN load level is higher for the
thicker CFRP plate thickness. At loaded end, the maximum local bond stress for 1.5
mm CFRP plate thickness was 7.07 MPa, 19.8% higher than local bond stress for 1
mm thickness, 5.9 MPa. For 2 mm thickness, the local bond stress was 7.85 MPa,
11% higher than 1.5 mm thickness.
The local bond stress for 1.5 mm and 2 mm thickness were 2.5 MPa and 3.08
MPa for 20 mm bond length, 43.7% and 77% higher, respectively to the 1 mm
thickness. For 40 mm bond length, local bond stress for 1.5 mm thickness was 0.88
MPa, 72.5% higher than 1 mm thickness, 0.51 MPa while for 2 mm thickness; the
local bond stress was 1.21 MPa, 37.5% higher than 1.5 mm thickness.
94
The effective bond length for was about 80 mm for 1 mm CFRP plate
thickness and it increased to 100 mm and 120 mm for 1.5 mm and 2.0 mm CFRP
plate thickness.
Local Bond Stress vs Bond Length(Effect of CFRP thickness )
0
1
2
3
4
5
6
7
8
9
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
t=1mm
t=1.5mm
t=2mm
Ga =2.0GPaEc =30GPaEcFRP =150GPata =1mmtconcrete =100mmLoad =20kN
Fig. 5.6: Local bond stress with different CFRP thickness
5.3.3 The Effect of Concrete Young�s Modulus
Fig. 5.7 shows the variation of concrete Young�s modulus on local bond
stress at 20 kN load level. The graph indicates that the concrete Young�s modulus
does not significantly affect the interface shear stress values. However, it can be seen
that there is a marginal tendency of developing a higher interface shear stress value
when the concrete Young�s modulus is increased.
95
At loaded end, maximum local bond stress for 20 GPa concrete Young�s
modulus was 6.86 MPa, and it increased 3% to 7.07 MPa, 4% to 7.14% when the
concrete Young modulus increased to 30 GPa and 40 GPa.
At bond length 20 mm, local bond stress for 40 GPa concrete Young�s
modulus was 2.55 MPa, 8.5% higher than 20 GPa concrete Young�s modulus and
2% higher than 30 GPa concrete Young�s modulus.
For 40 mm bond length, local bond stress for 30 GPa concrete Young�s
modulus was 0.88 MPa, 8.6% higher than the local bond stress for 20 GPa concrete
Young�s modulus, 0.81 MPa while for 40 GPa concrete Young�s modulus, the local
bond stress was 0.91 MPa, 3.4% higher than 30 GPa concrete Young�s modulus.
It also can be observed from the graph that concrete Young�s modulus does
not significantly affect the effective bond length.
Fig. 5.7: Local bond stress with different concrete Young�s modulus
Local Bond Stress vs Bond Length(Effect of Concrete Young's Modulus)
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
E=20GPa(fc=18MPa)
E=30GPa(fc=40MPa)
E=40GPa(fc=70MPa)
Ga =2.0GPaECFRP =150GPata =1mmtCFRP =1.5mmtconcrete =100mmLoad =20kN
96
5.3.4 The Effect of Adhesive Shear Modulus
As can be seen from Fig. 5.8, the local bond stress at 20 kN load level
increased when the adhesive shear modulus increased. The maximum local bond
stress for 1.5 GPa adhesive shear modulus was 6.08 MPa. When the adhesive shear
modulus increased to 2.0 GPa, the maximum local bond stress increased 16.2 % to
7.07 GPa. For 2.5 GPa adhesive shear modulus, the maximum local bond stress was
8.36 MPa, 18.2 % higher than 2.0 GPa adhesive shear modulus.
Local bond stress at 20 mm bond length for 2.0 Pa and 2.5 GPa adhesive
shear modulus were 2.5 MPa and 3.50 MPa, 35.1% and 89.2% higher; respectively
to the 1.5 GPa adhesive shear modulus.
For 40 mm bond length, local bond stress for 2.0 GPa adhesive shear
modulus was 0.88 MPa, 57.1% higher than 1.5 GPa adhesive shear modulus, 0.56
MPa while for 2.5 GPa adhesive shear modulus; the local bond stress was 1.46 MPa,
65.9% higher than 2.0 GPa shear modulus. The effective bond length increased about
25% from 80 mm to 100 mm when the adhesive shear modulus increased from 1.5
GPa to 2.0 GPa and 20 % to 120 mm when the adhesive shear modulus increased to
2.5 GPa from 2.0 GPa.
97
Fig. 5.8: Local bond stress with different adhesive shear modulus
5.3.5 The Effect of Adhesive Thickness
Fig. 5.9 shows that the local bond stress at 20 kN load level is lower for the
thicker adhesive thickness. Maximum local bond stress for 1 mm adhesive thickness
was 7.07 MPa, 11.8% lower than local bond stress for 0.5 mm thickness, 8.02 MPa.
For 1.5 mm adhesive thickness, the local bond stress was 5.76 MPa, 18.5% lower
than 1 mm thickness. At 20 mm bond length, local bond stress for 1 mm and 1.5 mm
adhesive thickness were 2.5 MPa and 1.6 MPa, 22.4% and 48.4% lower, respectively
to the 0.5 mm thickness.
For 40 mm bond length, local bond stress for 1 mm thickness was 0.88 MPa,
31.8% lower than 0.5 mm thickness, 1.29 MPa while for 1.5 mm thickness, the local
Local Bond Stress vs Bond Length(Effect of Adhesive Shear Modulus )
0
1
2
3
4
5
6
7
8
9
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
G=1.5GPa
G= 2.0GPa
G= 2.5GPa
EC = 30GPaECFRP =150GPata =1mmtCFRP =1.5mmtconcrete =100mmLoad =20kN
98
bond stress was 0.48 MPa, and 45.5 % lower than 1 mm thickness. The curves show
that the effective bond length increased when the thickness of adhesive is increased.
Fig. 5.9: Local bond stress with different adhesive thickness
5.3.6 The Effect of Bond Length
Fig. 5.10 shows that the bond length has no effect to the local bond stress as
long as it is exceeding the effective bond length that is required. When the bond
length is 100 mm, the maximum local bond stress is about 8.01 MPa, 13% higher
than local bond stress with 200 mm and 250 mm bond length. It occurs due to the
effective bond length required at 20 kN load level is about 105 mm to transfer the
force from concrete to CFRP.
Local Bond Stress vs Bond Length(Effect of Adhesive Thickness )
0
1
2
3
4
5
6
7
8
9
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
t=0.5mm
t= 1mm
t= 1.5mm
Ga =2.0GPaEC = 30GPaECFRP =150GPatCFRP =1.5mmtconcrete =100mmLoad =20kN
99
Local Bond Stress vs Bond Length(Effect of Bond Length )
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
L=100 mm
L=200 mm
L=250 mm
Ga =2.0GPaECFRP =150GPata =1mmta =1.5mmtconcrete =100mmLoad =20kN
Fig. 5.10: Local bond stress with different bond length
5.4 Conclusion of Parametric Study
The local bond stress increased when the thickness of CFRP increased. This
is due to the assumption made that the linear shear stress distribution through the
thickness of adherend. The shear stress was assumed as zero at the top surface and
linearly increased with the increment of thickness untill it is equals to adhesive shear
stress at the adherend-adhesive interface.
However, the local bond stress decreased when the thickness of adhesive
increased. It is because, the adhesive shear strain, is a function of adhesive
displacement, u and thickness, at .
100
When the thickness of adhesive increased while the adhesive displacement
valu is constant, the adhesive shear strain will decreased and cause the reduction of
local bond stress.
The less-stiffness of adhesive and adherends will reduce the local bond stress
along the bond length compared to stiffer one. Assumes a point at the loaded end
(named as point i) and another point with certain distance from the loaded end
(named as point j ).
For the less stiff of materials, the jiF value is smaller than the stiffer one
for the constant of jiA because the force at point j almost equal with the force at
point i.
The concrete Young�s modulus does not significantly effect the local bond
stress due to small value compared to CFRP plate Young�s modulus.
CHAPTER 6
CONCLUSION AND SUGGESTION
6.1 Conclusion
The local bond stress calculated from the equation has show good agreement
with the experiment�s for low and medium load level and the error still in acceptable
range. Fig 6.1 shows the exponential line between theoretical and experimental
values at 10 kN load level.
The value of maximum local bond stress from the theory can be used as a
guideline for a safe design of the joint. It�s because, the displacement experienced
were not same from one joint with another joint. So, the safest way is to assume that
no bond slip occur which will produce the joint experienced the highest possible
bond stress.
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102
Local Bond Stress vs Bond Length (Theoretical and experimental value)
y = 4.7242e-0.0707x
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160 180 200
Bond length, x (mm)
Bo
nd
str
ess,
Tau
(M
Pa)
Theory
BOSTUS 1
BOSTUS 2
BOSTUS 3
Expon.(BOSTUS 3)Expon.(BOSTUS 2)Expon.(Theory)Expon.(BOSTUS 1)
Load = 10 kN
Fig. 6.1: Exponential line of theoretical and experimental local bond stress at 10 kN
load level
From the parametric study, we can conclude that:
Maximum local bond stress and effective bond length increase when
the CFRP Young modulus and thickness increase.
Maximum local bond stress and effective bond length increase when
the adhesive shear modulus increases.
Maximum local bond stress and effective bond length decrease when
the adhesive thickness increases.
Concrete Young�s modulus and compressive strength doesn�t
significantly effect the local bond stress distribution.
The bond length must exceed the required effective bond length to
transfer the load from concrete to CFRP.
For the safety of joint design, a few things must be considered:
Less-stiffness of adherends and adhesive
Low adherends thickness
High adhesive thickness
103
6.2 Suggestion For Future Study
The equation that has been derived should have a boundary condition based
on all materials strength. The CFRP plate-epoxy-concrete bonded system usually
experienced failure at concrete interface due to its lowest shear strength compared to
CFRP plate and epoxy. The boundary condition should able to predict the limitation
of maximum local bond stress for the joint before it failed. The equation also must be
developed to meet the need for cyclic loading
The effects of long term environmental exposure to the joint also can be
determined by this equation as long as all of the material properties of the joint are
known.
104
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Structural Joints and Repairs. International Journal of Adhesion & Adhesives.
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Failure Analysis of Adhesively Bonded Joints. International Journal of
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110
APPENDIX A
( Data of theoretical and experimental local bond stress )
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111
Data for Fig.5.1
Bond length,
x (mm)
BOSTUS 1
Local Bond
Stress, a (MPa)
BOSTUS 2
Local Bond
Stress, a (MPa)
BOSTUS 3
Local Bond
Stress, a (MPa)
Theoritical
Local Bond
Stress,
a (MPa)
0-15 4 3.7 3.6 5.1
15-35 1.99 1.97 1.9 1.6
35-65 0.3 0.2 0.25 0.2
65-105 0.1 0.1 0.2 0.1
105-155 0.001 0.001 0.001 0.001
155-200 0.0001 0.0001 0.0001 0.0001
Data for Fig.5.2
Bond length,
x (mm)
BOSTUS 1
Local Bond
Stress, a (MPa)
BOSTUS 2
Local Bond
Stress, a (MPa)
BOSTUS 3
Local Bond
Stress, a (MPa)
Theoritical
Local Bond
Stress,
a (MPa)
0-15 27
15-35 12.4 11.8 12 10.7
35-65 3.31 3.27 4.01 3.97
65-105 0.1 0.1 0.2 0.1
105-155 0.001 0.001 0.001 0.001
155-200 0.0001 0.0001 0.0001 0.0001
Data for Fig.5.3
Bond length,
x (mm)
BOSTUS 1
Local Bond
Stress, a (MPa)
BOSTUS 2
Local Bond
Stress, a (MPa)
BOSTUS 3
Local Bond
Stress, a (MPa)
Theoritical
Local Bond
Stress,
a (MPa)
0-15 36
15-35 9.8
35-65 7.05 7.01 5.01 2.1
65-105 6.99 6.98 4.98 0.1
105-155 2.01 2.0 2.01 0.001
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112
155-200 0.7 0.7 0.71 0.0001
113
APPENDIX B
( Data of parametric study)
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114
Data for Fig.5.5 Bond length,
x(mm)
Local bond stress
(MPa)
[ CFRPE =100 GPa]
Local bond stress
(MPa)
[ CFRPE =150 GPa]
Local bond stress
(MPa)
[ CFRPE =200 GPa]
0-20 5.90 7.07 7.88
20-40 1.74 2.50 3.11
40-60 0.51 0.88 1.22
60-80 0.15 0.31 0.48
80-100 0.04 0.11 0.19
Data for Fig.5.6
Bond length,
x(mm)
Local bond stress
(MPa)
[ CFRPt =1mm]
Local bond stress
(MPa)
[ CFRPt =1.5mm]
Local bond stress
(MPa)
[ CFRPt =2.0mm]
0-20 5.90 7.07 7.85
20-40 1.74 2.50 3.08
40-60 0.51 0.88 1.21
60-80 0.15 0.31 0.48
80-100 0.04 0.11 0.19
Data for Fig.5.7
Bond length,
x(mm)
Local bond stress
(MPa)
[ concreteE =20 GPa]
Local bond stress
(MPa)
[ concreteE =30 GPa]
Local bond stress
(MPa)
[ concreteE =40 GPa]
0-20 6.86 7.07 7.14
20-40 2.35 2.50 2.55
40-60 0.81 0.88 0. 91
60-80 0.28 0.31 0.32
80-100 0.09 0.11 0.12
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115
Data for Fig.5.8
Bond length,
x(mm)
Local bond stress
(MPa)
[ adhesiveG =1.5GPa]
Local bond stress
(MPa)
[ adhesiveG =2.0GPa]
Local bond stress
(MPa)
[ adhesiveG =2.5 GPa]
0-20 6.08 7.07 8.36
20-40 1.85 2.50 3.50
40-60 0.56 0.88 1.46
60-80 0.17 0.31 0.61
80-100 0.05 0.11 0.26
Data for Fig.5.9
Bond length,
x(mm)
Local bond stress
(MPa)
[ adhersivet =0.5mm]
Local bond stress
(MPa)
[ adhersivet =1mm]
Local bond stress
(MPa)
[ adhersivet =1.5mm]
0-20 8.02 7.07 5.76
20-40 3.22 2.50 1.66
40-60 1.29 0.88 0.48
60-80 0.52 0.31 0.14
80-100 0.21 0.11 0.04
Data for Fig.5.10
Bond length,
x(mm)
Local bond stress
(MPa)
[L=100mm]
Local bond stress
(MPa)
[L=200mm]
Local bond stress
(MPa)
[L=250mm]
0-20 8.01 7.07 7.07
20-40 3.01 2.50 2.50
40-60 1.29 0.88 0.88
60-80 0.52 0.31 0.31
80-100 0.21 0.11 0.11
116
APPENDIX C
( Determine local bond stress from governing equation )
117
Material properties:
t,inner 0.1 t,outer 0.0014
t,adhesive 0.0015 E,inner 3.00E+10 E,outer 1.35E+11
G,adhesive 2.70E+09
Determine value from material properties:
m n l
Eo*to 1/(Eo*to) Ei*ti 2/(Ei*ti) m+n Ga/ta l(m-n)
1.89E+08 5.29E-09 3.00E+09 6.67E-
10 5.96E-
09 3.86E+12 2.30E+04 151.5902
Determine the local bond stress for 20 kN load level:
x L' T/2L' exp- L x/2 Exp (- x/2) exp( x/2) m a
0 0.02 20000000 6.13252E-13 0 1 1 1 20000000
0.02 0.02 20000000 6.13252E-13 1.52 0.218712 4.572225 0.218712 4374238
0.04 0.02 20000000 6.13252E-13 3.04 0.047835 20.90524 0.047835 956697.8
0.06 0.02 20000000 6.13252E-13 4.56 0.010462 95.58348 0.010462 209241.2
0.08 0.02 20000000 6.13252E-13 6.08 0.002288 437.0292 0.002288 45763.53
0.1 0.02 20000000 6.13252E-13 7.6 0.0005 1998.196 0.0005 10009
0.14 0.02 20000000 6.13252E-13 10.64 2.39E-05 41772.77 2.39E-05 478.2684
0.16 0.02 20000000 6.13252E-13 12.16 5.24E-06 190994.5 5.12E-06 102.3725
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