i

Finite Element Analysis of Bond Characteristics at the FRP-Concrete

Interface

By

Mani Balazadeh Minouei

Department of Civil Engineering and Applied Mechanics

McGill University, Montreal

Quebec, Canada

December, 2013

A thesis submitted to McGill University in partial fulfillment of the requirements of the degree

of Master of Engineering

© Mani Balazadeh Minouei, 2013

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Dedicated

To my hero, my father, Alireza Balazadeh Minouei

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Abstract

Reinforced concrete structures are prone to corrosion in harsh environments. Fibre-Reinforced

Polymer (FRP) laminates are more resistant than steel elements, such as bars and plate in

aggressive environments; they can be used as a barrier to protect concrete structures; however,

poor bond between FRP composite laminates and structural concrete can prevent utilizing the

full structural and protective capacity of FRP-concrete composite system, therefore, it is

important to develop good bond between concrete and the FRP to ensure the integrity and

durability of the FRP-concrete system.

There is a need to understand the bond characteristics at the FRP laminates-concrete interface,

and the various parameters influencing the bond performance of the composite system. This

research program consists of numerical modeling of the double lap pull-off tests conducted by

Ali et.al (2012) and comparing the computed values with the experimental results for two

different batches, along with an evaluation of the various parameters influencing bond between

FRP laminates and concrete.

The ABAQUS 6.10.1 program was used to model the double lap pull-off test. Shell elements

were used to model FRP laminates, solid elements for concrete and steel and cohesive elements

for modeling the epoxy joint. The constitutive models for the materials were selected based on

their experimental behavior. A linear elastic model was used for modeling FRP laminates and

steel, elastoplastic behavior was used for modeling epoxy and damaged plasticity model was

used for modeling concrete.

Numerical and experimental curves reflected similar responses. In the first batch the average

ultimate load in the tests was 70.7 kN , while the ultimate load for the numerical analysis was

73.8 kN, showing a difference of 4.6% . Also, the average experimental value of strain at the

center of the FRP laminate was 2657×10 , while the ultimate strain in numerical simulation

was 3023×10 , showing an acceptable difference of 12.1 %. In the second batch, the average of

experimental ultimate load was 54.5kN, while the ultimate load in numerical analysis was

58.6kN, with a difference of only 5.4%. The computed ultimate strain is 2320 ×10 , while the

average of ultimate strain in experimental study was 2173×10 , showing a discrepancy of 6.3%.

Also, the effect of different geometrical factors on the bond behavior of FRP and concrete was

iv

studied; it was concluded that, the most effective geometrical parameter influencing bond

between FRP and concrete was the bonded width of the FRP laminate.

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Sommaire

Les structures en béton armé sont sujettes à la corrosion dans des environnements difficiles.

Dans ces conditions, les couches de polymère renforcé de fibres (PRF) sont plus résistants que

les plaques d'acier, ils peuvent ainsi être utilisés comme une barrière pour protéger les structures

en béton armé; Cependant, un faible (mauvais) collage entre les couches composites de PRF et le

béton peut empêcher l'utilisation de la pleine capacité de ce composite. Par conséquent, il est

important de développer une adhérence complète entre le béton et le PRF pour assurer l'intégrité

et la durabilité de ce système.

Il est nécessaire de comprendre les caractéristiques des liaisons à l'interface des couches de

polymère renforcé de fibres - béton, et les différents paramètres influençant les performances de

ces liaisons. Cet recherche comprend la modélisation numérique des essais de traction à

recouvrement double effectués par Ali et.al (2012) et la comparaison des valeurs calculées avec

les résultats expérimentaux pour deux groupes différents, avec une évaluation des paramètres

influençant les liaisons entre les couches de polymère renforcé de fibres et le béton.

Le programme d’éléments finis ABAQUS 6.10.1 a été utilisé pour l’analyse numérique d’essai

en traction à recouvrement double. Des éléments coques ont été utilisés pour modéliser les

couches de polymère renforcé de fibres, des éléments solides pour modéliser le béton et l'acier et

des éléments de cohésion pour modéliser le joint en résine époxyde. Les modèles pour les

matériaux ont été choisis en fonction de leur comportement expérimental. Un modèle élastique

linéaire a été utilisé pour les couches de polymère renforcé de fibres et de l'acier, un modèle

élasto-plastique a été utilisé pour la résine époxyde et le modèle de plasticité endommagée a été

utilisé pour le béton.

Les résultats entre les tests numériques et expérimentaux montrent une réponse similaire. Dans le

premier groupe, la moyenne de la charge ultime des essais expérimentaux était égale à 70.7 kN

tandis que celle de l’analyse numérique était égal à 73.8, ce qui montre une différence de 4.6%.

De plus, la valeur moyenne expérimentale de la contrainte au centre des couches de PRF était

égale à 2657×10 , tandis que celle de la souche ultime dans la simulation numérique était de

3023×10 , montrant une différence de 12.1%. Dans le deuxième groupe, la moyenne de la

charge ultime expérimentale était égal à 54.5kN, alors que celle de l’analyse numérique était

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égale à 58.6kN, il y a donc une différence de seulement 5.4%. La contrainte ultime calculée était

égale à 2320 ×10 , alors que la moyenne de celle de l'étude expérimentale était égale à

2173×10 , montrant une différence de 6.3%. Les effets de plusieurs facteurs géométriques sur

les liaisons entre les couches de polymère renforcé de fibres et le béton ont été étudiés. Les

résultats de cette enquête ont montré que le paramètre géométrique ayant le plus d’influence sur

la liaison entre les couches de PRF et le béton était la largeur de ces liaisons.

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Acknowledgements

The author would like to thank Professor Saeed Mirza for his encouragement, guidance, caring,

patience, great support and untiring help during the research project. His in-depth knowledge on

a broad spectrum of different structural topics has been extremely beneficial for me. Professor

Saeed Mirza is a great teacher and a great human being who taught me lessons for life.

I particularly wish to thank Muhammad Shafqat Ali. Throughout this thesis, he broadened my

knowledge on the concept of composite materials. I would like to thank him for always being

accessible and willing to help, despite his busy schedule.

I would like to acknowledge the involvement of Professor Dimitrios Lignos for his guidance in

this research project and his invaluable advice.

My deepest gratitude goes for my family for their unconditional love and support, especially

Yasaman, my sister and Ali, my brother-in-law for encouraging me throughout these years. I am

glad to have the opportunity to express my gratitude to my grandmother, Louba Milani whose

her smile meant a world to me.

I wish to express my appreciation to my great friends, Mahmoud Motahari and Jamshid Sourati.

They have been my brothers and beyond.

Lastly, and most importantly, I wish to thank my mother, Maryam Milani who bore me, raised

me and loved me. She is in my heart and will always remain.

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Table of Contents

ABSTRACT……………………………………………………………………………...………………..iii

SOMMAIRE....................................................................................................................................... ….....v

ACKNOWLEDGEMENTS…………………………………………………………………...………...vii

TABLE OF CONTENTS…………………………………………………………………...…………..viii

LIST OF SYMBOLS………………………………………………………………………………...…...xi

LIST OF FIGURES……………………………………………………………………………………..ixv

LIST OF TABLES………………………………………………………………………………...……xvii

1.INTRODUCTION……………………………………...………………………………………………..1

1.1 Thesis overview………………………………………………………........………………………2

1.2 Problem statement ………………………………………..………………………………………3

1.3 Research objectives…………….…………………………………………………………………3

2. LITERATURE REVIEW………………………………………..…………………………………….4

2.1 Introduction of FRP……………………………………………………………………..………4

2.2 History of FRP application………………………………………...……………………………7

2.3 FRP application in civil engineering………………………………………..……………..……8

2.4 Bond behavior……………………………………………..……………………………………10

2.4.1 Bond mechanism……………………….…………………… ……….……….……..……10

2.4.2 Bond behavior of FRP…………………………………….… ……………………………12

2.4.3 Recent experimental works on bond behavior of FRP and concrete…………..……….…12

2.4.4 Recent numerical modeling on bond behavior of FRP and concrete interface…...….……14

2.5 Summary and recommendations ………………………………...……………...……………..17

3. EXPERIMENTAL WORK……………………………………………………………….…………..19

3.1 Concrete tests………………………………………………………………....………………….19

3.1.1 Compressive strength of concrete…………………………………………………………19

3.1.2 Tensile strength of concrete……………………………………………………..…...…….21

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3.1.3 Interfacial fracture energy…………………………………………………..……………… 23

3.2 Mechanical properties of epoxy……………………………………………………………….....24

3.2.1 Tensile strength of epoxy……………………………………………………………………24

3.2.2 Shear strength of epoxy…………………………………………………………….………..26

3.3 Mechanical properties of FRP………………………………………………………………..….27

3.4 Experimental tests on bond behavior of FRP-concrete interface………………..………….…28

3.5 Instrumentation and testing…………………………………...…………………….………...…30

4. FINITE ELEMENT MODELING……………………………………………………….…………..32

4.1 Technique used in this study………………………………………………...………..………..32

4.2 ABAQUS……………………………………...…………..…………………………….....…….33

4.3 Elements used in numerical modeling……………………………………………..…..….…...34

4.3.1 Solid elements………………………………………………..……………………………36

4.3.2 Shell elements………………………………………………..……………………………38

4.3.3 Cohesive elements…………………………………………..……………………………..38

4.4 Model assembly………………………………….......................................…………………....39

4.5 Meshing……………………………………………………….…………………...……………40

4.6 Material properties…………………………………………….…..…………………………..41

4.6.1 Elastic Properties………………………….………………………………………………42

4.6.2 Elastoplastic behavior………………………………………………...………………….43

4.6.3 Constitutive models for concrete……………………………………………...…………43

5.RESULTS AND DISCUSSIONS…………………………………………..…..….………………....45

5.1 Experimental results………………………………………………….…..….………………..45

5.2 Numerical modeling……………………………………………………..….…………………51

5.2.1 Data analysis……………………….…………………………………………………….52

5.3 Parametric study………………………………………………....….…………………………67

5.3.1 Mesh sensitivity analysis……………………….………………………….…..……..…..68

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5.3.2 Effect of epoxy thickness……………………….…………..…………………………….70

5.3.3 The effect of FRP geometry……………………….…………………………...…………72

5.3.3.1 The effect of bonded length……………………….……………………………….72

5.3.3.2 The effect of bonded width……………………….………………………………..73

5.3.3.3 The effect of FRP thickness……………………….…………..……………...……74

6. CONCLUSIONS AND FUTURE RESEARCH……………………………………………………..77

6.1 General…………………………………………………..……………………………………..77

6.2 Limitations of the study………………………………………………………………………78

6.3 Recommendation for future research work………………...……………………………....79

REFRENCES…………………………………………………………………………………………….80

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List of Symbols

a Distance from the rupture point

A Cross section area

fA Cross section area of FRP laminate

b Width of the beam

cb Width of concrete block

fb Width of FRP laminate

COV Coefficient of variation

CTE Coefficient of thermal expansion

d Depth of the beam

ad Maximum aggregate diameter

meanD Average of cylindrical specimen diameters

elD Elasticity tensor

fE Tensile modulus of FRP

blf Tensile strength of concrete from bending test

cf Compressive strength of concrete

'cf Compressive strength of concrete

stf Tensile strength of concrete from splitting test

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G Shear modulus

fG Fracture energy

GPa Giga Pascal

ch Cohesive zone height

in Inch

kg Kilograms

kN Kilo Newton

L Span length

LVDT Linear variable differential transformers

m Metre

3m Cubic metre

mm Millimetre

2mm Square millimetre

MPa Mega Pascal

N Newton

P Axial load

P Splitting load

psi Pound-force/square inch

s Second

2s Square second

SG Strain gauge

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ft Thickness of FRP

gt Thickness of glue

gT Glass transition temperature

V Voltage℉ Degree Fahrenheit℃ Degree Celcius

w Load capacity

Stress

Ω Ohm

ε Strain∞ Infinity

Poisson’s ratio

µ Micro

Deformation

Stress

11 Tensile strain

12 Shear strain

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List of Figures

Figure 2.1 AFRP, CFRP and GFRP…………………………………………………………....4

Figure 2.2 Stress-strain diagram of FRP and steel……………………………………………..6

Figure 2.3 Failure modes of FRP strengthened concrete……………………………………..11

Figure 3.1 Tensile coupon detail……………………………………………………………...25

Figure 3.2 Tensile stress-strain curve for epoxy……………………………………………...25

Figure 3.3 Shear stress-strain curve for epoxy………………………………………………..26

Figure 3.4 Double lap pull-off test specimen………………………………………………....29

Figure 3.5 Double lap pull-off test……………………………………………………………30

Figure 4.1 Linear element and quadratic element…………………………………………….35

Figure 4.2 First order element under pure bending…………………………………………...37

Figure 4.3 Cohesive elements constrained with tie contacts…………………………………39

Figure 5.1 Load-displacements relationships for Group 1 specimens……………………….46

Figure 5.2 Strain variation in FRP laminates in specimen G1S1 at different load levels……47

Figure 5.3 Strain distribution along the FRP laminate……………………………………….48

Figure 5.4 Load-displacement diagram for Group 2 specimens…………..…………………49

Figure 5.5 Load-displacement diagram for G2S4 …………………………………………...49

Figure 5.6 Load-strain diagrams for Group 2 specimens………………………..…………...50

Figure 5.7 Load distribution in in concrete block for 30×10 mesh for Group 1…………......51

Figure 5.8 Load transition through the concrete block for different mesh sizes for Group 1……….52

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Figure 5.9 Specimen configuration…………………………………………………………..52

Figure 5.10 Load-displacement diagram for numerical modeling of Group 1 specimens...…53

Figure 5.11 Load-strain diagram for finite element model of Group 1 specimens…………..54

Figure 5.12 Load-displacement diagram for Group 2 specimens…………………………….55

Figure 5.13 Load-strain diagram for Group 2 specimens ……………………………………55

Figure 5.14 Stress distribution in FRP laminates up to the middle of laminate for Group 1

specimens ………………………………………………………………..……………………...56

Figure 5.15 Stress distribution in epoxy layer in Group 1 specimens………………...……...57

Figure 5.16 Stress distribution in concrete in Group 1 specimens……………………………57

Figure 5.17 Stress distribution in FRP laminates in Group 2 specimens……………………..58

Figure 5.18 Stress distribution in concrete in Group 2 specimens.…………………………...58

Figure 5.19 Stress distribution in concrete in the epoxy layer for Group 2 specimens………59

Figure 5.20 Strain distribution along FRP laminate…………….……………………………59

Figure 5.21 Strain distribution along FRP laminate at different load levels………….……...60

Figure 5.22 Load transition through FRP laminate………………………………….….…….60

Figure 5.23 Load distribution along the concrete block at ultimate load…………….………61

Figure 5.24 Concrete block scheme…………………...……………………………………...61

Figure 5.25 Load distribution along the steel bar at ultimate load…………………………...62

Figure 5.26 Load distribution along the specimen in different elements at ultimate load…...63

Figure 5.27 Load-displacement diagram………………………………………………....…..63

Figure 5.28 Load-strain variation along the FRP laminate…………………………………...65

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Figure 5.29 Specimen configuration…………………………………………………..……...65

Figure 5.30 Load distribution along the FRP laminate in experimental tests and numerical

simulation……………………………………………………………………………...…….…...66

Figure 5.31 Load-strain variation in steel rod………………………………………….……..66

Figure 5.32 Load vs. strain in concrete………………………...……………………………..67

Figure 5.33 Load-displacement diagram for different mesh sizes……………………………68

Figure 5.34 Load transfer for the primary mesh……………………………………………...69

Figure 5.35 Load transition procedure for the finest mesh…………………………………...69

Figure 5.36 Strain distribution for different mesh sizes………………………………………70

Figure 5.37 Load-slip characteristics for different epoxy thicknesses…………….………….71

Figure 5.38 Specimen configuration………………………………………………………….71

Figure 5.39 Load-displacement diagram for different bond lengths…………………………73

Figure 5.40 Load-displacement diagram for different bond widths………………………….74

Figure 5.41 Load-displacement diagram for different FRP thicknesses……………………...75

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List of Tables

Table 2.1 Properties of typical commercially produced FRP strengthening strips…………….5

Table 2.2 General material properties of concrete, steel and epoxy…………………………...6

Table 3.1 Compressive strength results……………………………………………………….21

Table 3.2 Tensile strength of concrete………………………………………………………..23

Table 3.3 Interfacial fracture energy of specimens…………………………………………...24

Table 3.4 Mechanical properties of FRP……………………………………………………...28

Table 5.1 Experimental results………………………………………………………………..45

Table 5.2 Elements’ contribution in load transfer…………………………………………….64

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Chapter 1: Introduction

The economy of a country depends mainly on the condition of its infrastructure; industrialized

countries have invested significantly in their infrastructures, for development and rehabilitation.

For example, Canada as a developed country needs to spend 123 billion dollars on its

infrastructures to retain their quality and performance at an acceptable level (Mirza 2007).

Bridges are among the most important elements of transportation infrastructure and are exposed

to aggressive environments; consequently they deteriorate more rapidly, requiring millions of

dollars for their rehabilitation and renovation. Millions of dollars have been invested in

rehabilitation of Champlain, Jacques Cartier and Mercier Bridges in Montreal. A detailed

examination of the Champlain Bridge revealed that many elements of the bridge were in

extremely poor and deficient condition, especially the underwater portions of the piers.

Consequently, a rehabilitation program was initiated in the 1980’s which consisted of replacing

expansion joints and repairing prestressed concrete girders. These damages appeared after only

28 years of operation, mainly due to the corrosion of embedded reinforcing and prestressing steel

caused by de-icing salts, used to facilitate bridge operations during the harsh winter months.

Applying a barrier on the concrete surface could be a good solution to prevent the penetration of

chloride ions from de-icing salts. Fibre-Reinforced Polymer (FRP) laminates are resistant in

aggressive environments; therefore, they can be a good choice for use as a barrier for bridge

construction.

In the past, steel plates were used to repair concrete bridges. This method was applied for repairing Port

Wakefield Bridge in South Australia, and Pit River Bridge in California, but the major problem remained

unsolved because steel plates deteriorate in corrosive and harsh environments, therefore FRP sheets

which are resistant to ingress of salts in aggressive environments can be useful.

The prevalent method for the rehabilitation of these infrastructure assets is repairing and

re-repairing; however, there are alternative methods to increase the effective life of bridge

structures. Use of Fibre Reinforced Polymer (FRP) sheets as a barrier can be helpful for

increasing their service life. FRP composite materials can be used for both existing structures

and new construction. In existing structures, application of FRP composites is mostly for repair,

strengthening and rehabilitation, aimed at increasing the shear and flexural capacity of beams,

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columns, slabs and other components. Besides increasing the life span of new structures, FRP

elements are comparatively lightweight and possess higher thermal insulation. A detailed state-

of-the art review of application of FRP is presented in Chapter 2.

Despite many advantages of FRP composites over other construction materials, there are several

concerns about some of their properties and unknown aspects such as:

Unknown behavior of FRP elements under cyclic loading.

Brittle behavior under tensile load. FRP sheets show a linear elastic behavior without any

significant plastic deformation up to failure.

Economic concerns: FRP sheets are normally more expensive than steel elements.

Health issues: There are serious concerns about respiratory problems caused by Glass

Fibre Reinforced Polymers.

Some types of FRPs like AFRP and GFRP have low moduli of elasticity. If these sheets

are applied to concrete, this property will lead to design of the structure based on the

serviceability limit states, such as crack width and deflection.

Bond behavior of FRP sheets and concrete surface is not adequately understood yet. This

thesis will examine this issue.

1.1. Problem statement

The behavior of a reinforced concrete member depends on the transfer of load at the concrete-

reinforcement interface, for example; in design and analysis of concrete section with reinforcing

steel bars, strain compatibility is assumed, which means that there is no slip between concrete

and the reinforcing steel, and the load is transferred from the concrete to the reinforcing bar

through interfacial bond. The composite behavior depends on the interfacial bond quality at the

steel reinforcement and concrete, but practically, full composite action cannot be achieved due to

slip between the steel reinforcement and the concrete. Any slip at the interface will lead to less

than perfect force transfer at the interface.

To understand bond behavior between concrete and FRP plate components, an experimental

study was conducted at McGill University (Ali, 2012). The experiments were performed on

several specimens to examine the bond behavior at the concrete-FRP interface in detail. It can be

quite time consuming and expensive to conduct experiment to determine the effective geometric

and other parameters; therefore an alternative method- numerical modeling is used for

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investigating the bond behavior at the concrete-FRP interface. Numerical modeling is much less

time consuming and more economical than experimental work and can be useful in

understanding the effects of different influencing parameters.

1.2. Research objectives:

This research program is aimed at examining bond behavior at the concrete- FRP interface to

develop design recommendations to ensure the composite action at the interface. The objectives

of this study are summarized below:

Developing a numerical model for the bond at the concrete-FRP interface

Comparing numerical results with the experimental data to verify the accuracy of

numerical simulation

Evaluating the effect of different parameters on bond behavior including strength and

stiffness of the specimens tested

1.3. Thesis overview

This thesis consists of six chapters. The first chapter provides a general introduction, followed by

a brief introduction to FRP, and the history of FRP applications in different industries and

technologies in Chapter 2. This chapter also reviews the concept of bond between FRP and

concrete, and reviews the literature on bond behavior, along with the existing guidelines for

providing bond resistance. It also reviews the effective parameters for bond quality.

Chapter 3 summarizes experimental data from tests conducted on different components along

with tests to study bond between FRP and concrete.

The methodology used for finite element modeling of bond behavior at the concrete – FRP

interface is presented in Chapter 4, along with a summary of the various parameters studied in

the modeling process. The types of elements used in the analysis and the method of their

assemblage is also presented.

The results of numerical modeling are presented and compared with the experimental data in

Chapter 5 along with a parametric study of some significant parameters involved.

In Chapter 6, a summary of the study and some suggestions for future research work are

outlined.

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Chapter2: Literature Review

2.1. Introduction of FRP

Fiber-reinforced polymers (FRP) are made of resin matrix reinforced with fibres. Load is carried

mostly by the fibres and the matrix works as a protector of fibres and the load transfer from fibre

to fibre, therefore the matrix must have good bond with fibres to transfer the load effectively to

them.

The nature of the matrix can be materials such as polyester or vinyl ester. The fibres can be made

of glass, carbon, or aramid. The combination of these fibres and matrices will result in different

kinds of FRPs, such as GFRP and CFRP and AFRP, which are the most used types of FRPs.

GFRP or Glass Fibre Reinforced Polymer is durable in harsh environments and also light in

weight. It has a high tensile strength but -it is weak in shear. It can have problems in alkaline

environments, such as concrete.

CFRP or Carbon Fibre Reinforced Polymer is more ductile than GFRP but its resistance of

CFRP under cyclic loading is seriously doubtful.

AFRP or Aramid Fibre Reinforced Polymer is less used than the other two types. It has high

resistance against heat, but it is usually weak against moisture and ultraviolet radiation.

Therefore, painting and coating is needed to protect AFRP against ultraviolet radiation,

Figure 2.1 show the surfaces of CFRP, GFRP and AFRP.

Figure 2.1 from left right AFRP, CFRP and GFRP (Täljsten, 1994)

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Depending on the type of the fibre used in FRP, the properties can vary significantly. Even for a

specific type of FRP, such as a CFRP, depending on the type and quantity of the carbon fibre,

different stiffnesses and strengths can be achieved. To provide a perfectly composite material

with appropriate properties, the type fibres and resin must also be compatible with each other.

The properties reported by most fabricators are normally in the longitudinal direction (the basic

direction of the fibres). Consequently, the stiffness and strength are considerably higher in the

longitudinal direction than in the transverse direction. Therefore, the properties of FRP are

direction dependent. Typical properties of commercial FRP strengthening strips are shown in

Table 2.1.

TABLE 2.1. Properties of Typical Commercially Produced FRP Strengthening Strips (Bank,2006)

StandardModulusCarbon-

ReinforcedEpoxy Strips

High ModulusCarbon-

ReinforcedEpoxy Strips

Glass-Reinforced

Epoxy Strips

Carbon-ReinforcedVinylester

Strip

Fiber volume (estimated)(%) 65-70 65-70 65-70 60Fiber Architecture Unidirectional Unidirectional Unidirectional UnidirectionalNominal thickness(in.) 0.047-0.075 0.047 0.055-0.075 0.079Width(in.) 2-4 2-4 2-4 0.63Strength 3( 10 )psiTensile, Longitudinal

390-406 188 130 300

Rupture Strain (%)Tensile Longitudinal 1.8 NR 2.2 1.7

Stiffness 6( 10 )psiTensile, Longitudinal

22.5-23.9 43.5 6.0 19

CTE, Longitudinal 6(10 )F NR NR NR -4.0-0.0

CTE, Transverse 6(10 )F NR NR NR 41-58

Source: Data from CarboDur®, Tyfo ®, MBrace®, Aslan ®Note: CTE, is coefficient of Thermal Expansion, and NR means not reported.

The designer should be aware of the glass transition temperature or of an FRP; at this

temperature, the material transforms from a hard state to a molten or rubbery state, therefore the

stiffness and strength of an FRP system decreases considerably when the temperature exceeds

6

the glass transition temperature. In case of fire, this phenomenon will lead to the breakdown of

FRP, with release of fibres which can cause health problems.

Because of a wide variety of FRP products, it is difficult to compare their properties directly;

however, some codes like ACI 440R, CSA S806, ASTM D3039, and other guides recommend

different tests to determine the properties of FRPs. Figure 2.2 and Table 2.2 present typical

properties of different kinds of FRPs, steel, and structural concrete.

Property (at 20℃) Cold-curedEpoxy-adhesive

Concrete Mild Steel

Density3[ ]Kg

m1100 - 1700 2400 7800

Modulus of Elasticity[GPa] 0.5-20 20-50 205Shear Modulus[GPa] 0.2-8.0 8-21 80Poisson’s Ratio 0.3 – 0.4 0.2 0.3Tensile Strength [MPa] 9-30 1-4 200 - 600

Shear Strength[MPa] 10 - 30 2 - 5 200 - 600Compressive Strength[MPa] 55 – 110 25 – 150 200 - 600Ultimate Tensile Strain[%] 0.5 - 5 0.015 25Approximate Fracture Energy[ ] 200 - 1000 100 10 − 10Coefficient of Thermal Expansion[10 /℃]Water Absorption: 7 days 25℃[%w/w]Glass Transition Temperature[℃] 25 – 35

0.1 - 345-80

11 – 135

NA

10 – 150NA

Table 2.2 General material properties of concrete, steel and epoxy (Täljsten, 1994)

Figure 2.2 Stress –Strain Diagram of FRP and Steel (ACI 440R-96)

7

2.2. History of FRP application:

The history of incorporating reinforcing material dates back to 800 B.C. when straw was used as

reinforcement for bricks. Use of glass fibres in cement concrete dates back to the 1930s and is an

example of using fibres as reinforcement; however, the Fibre Reinforced Polymers was first

produced in early 1940s.

Due to its resistance against corrosion and high strength and low weight, it was first used in the

automotive industry in the 1950s.These characteristics of FRPs led to many different application

of FRPs, and considerable investments to develop the desired properties of FRP which led to

new manufacturing procedures, such as pultrusion.

These characteristics also attracted recreation industries to use FRP in producing tennis rackets,

golf equipment, etc. Also in the aerospace industry composite materials were applied for

pressure vessels and in some non-structural airplane parts due to their light weight. FRP were

also used in military applications such as mine sweeping, and in manufacturing submarine

products.

Using FRP for architectural aesthetics is another application of FRP in buildings. FRP is used for

developing architectural features. For example, an FRP cladding was used for Mondial House on

the bank of Thames River in London in 1984.

Generally, the applications of FRPs are broad and attract different industries. For example,

because of its high stiffness, CFRP is used for loudspeaker construction, or in radio controlled

vehicles, such as helicopters because of its lightweight, for example, the rudder of Airbus A310

is made of CFRP. Other examples are laptops and other electronic devices; for example,

Lenovo/IBM and SONY laptops utilize CFRP. CFRP is also used in manufacture of professional

sports equipment, such as racing bikes, racing canoes, hockey sticks, and even in the

construction of artificial legs for amputee athletes. Applying CFRP in automobile industry due to

its light weight has led to the production of lighter frame and therefore faster vehicles, using the

same power. BMW i3 is an example of using carbon fibres in automobile industries. Generally,

CFRP can be a good choice where the high strength to weight ratio is required.

8

GFRPs are deployed in the production of tanks and vessels, MRI scanners, wind turbines, piping

systems and in the telecommunication industry. AFRPs are used in the aerospace industry, or in

military applications and also in heat protective clothing due to its low flammability.

The principal applications of FRPs are for diverse purposes in civil engineering. Different

applications of FRP in civil engineering are summarized in the following section.

2.3. FRP applications in civil engineering

In the past, steel plates were applied to the surface of concrete for strengthening (around the mid-

1960s). However, due to its vulnerability to aggressive environment and weight, this method was

abandoned in favour of composite materials for rehabilitation. Most of the FRP application in

structural engineering are mainly for rehabilitation and repair of old deteriorated structures.

Application of FRP to old structures can be due to the lack of strength, stiffness or durability.

Occasionally an old structure, designed and constructed based on older codes might need a

seismic retrofit based on new codes, or the functionality of structure may change over time and

based on new functionality, it may need rehabilitation.

Although FRP sheets are much more expensive than steel plates but they are much lighter, which

makes the installation much easier and less labour intensive. FRP sheets are also considerably

more resistant to any aggressive environments. These advantages make FRP, a promising

material for retrofitting existing structures, and in some cases FRP is the only appropriate

material for rehabilitation

One of the first applications of FRP sheets in retrofitting existing bridges was in Lucerne,

Switzerland, where they used FRP tendons to repair a damaged bridge.

Application of FRP in older deteriorated structures can be for different purposes including:

1. Flexural strengthening of reinforced concrete structures: FRP sheets are pasted to the

tensile zone of the structure with epoxy to increase the flexural capacity of the structural

elements, which can be a column, a beam, or a plate.

9

Shear strengthening of reinforced concrete elements: FRP sheets are attached to the web

of the member to increase its shear capacity.

2. Near Surface Mounting Reinforcement (NSMR): FRP sheets are vulnerable to ultraviolet

light and fire. The NSMR method is proposed to solve these shortcomings. In this

method, FRP sheets are placed in a gap in the near surface of the concrete.

3. Column confinement is performed in both seismic and non-seismic regions. In seismic

regions, to increase the ductility by column concrete confinement is performed by FRP

wrapping, while in non-seismic regions this method is useful when the axial load has

increased for any reasons. For example, in some structures extra floors were added to the

building, which led to extra axial load in the columns. Reggio Emilia Soccer Stadium in

Italy and Aigaleo Soccer Stadium in Greece are well known examples of retrofitting of

columns using FRP.

4. Retrofitting of masonry structures: FRP sheets and rods are used in masonry structures

for various reasons. One of the major applications of FRP in masonry structures is

rehabilitation of masonry shear walls, to improve their seismic resistance. Also, FRP is

widely used to strengthen historical masonry structures. The Basilica of St. Francis of

Assisi and Vercelli Castle in Italy are some of the outstanding examples of retrofitting of

historical masonry structures with FRP.

5. Prestressed Systems: This application of FRP is not as widespread, because there is not

enough analytical and practical experimental data in this area, but application of FRP in

prestressed system can have several advantages such as increasing the total stiffness of

the system and postponing the crack initiation.

There are several codes for design, analysis, and construction of concrete structures strengthened

with FRP, including JSCE (Japan Society of Civil Engineers), 2001; Concrete Society, 2002;

FIB(Federation Internationale du Beton), 2001; ICC-ES (International Code Council-Evaluation

Service), 1997, ACI (American Concrete Institute), 2008; CNR(Consiglio Nazionale delle

Ricerche), 2004. In addition, there are other design and analysis guides proposed by the

fabricators of FRP strengthening systems.

10

2.4 Bond behavior

2.4.1 Bond mechanism

The load is transferred through the interface of the FRP sheet and the concrete. The strength and

stiffness of interface substrate is critical here. When the FRP strengthening system is used for

compressive strengthening, for example wrapping a concrete column, FRP would provide a

confining pressure. For this purpose FRP should be in close contact with the concrete.

The mechanism of load transfer is similar to the one between concrete and steel plate, and

consists of three components;

1) Epoxy applied at the interface of concrete and FRP

2) Friction between FRP and concrete which depends on the roughness of surfaces

3) Mechanical interlocking, can be in different forms, such as gluing aggregates on the surface of

FRP or by applying mechanical anchors. In mechanically-fastened FRP, the laminates are

fastened to FRP with steel fasteners and bolts to increase the bond strength.

The concrete beams, strengthened with FRP sheets, when loaded, fail in different modes.

Although the desirable mode of failure is FRP rupture (meaning when the maximum capacity of

the system is attained), the most common mode of failure is debonding. The debonding mode of

failure is brittle and takes place before crushing in the concrete or rupture in the FRP sheets.

Nevertheless, it is important to understand all modes of failures, because these modes lead to

different ultimate loads at failure.

There have been many experimental and analytical studies to determine the different modes of

failure. Smith and Teng (2001) indicated six modes of failures including; crushing of concrete,

11

concrete cover separation, FRP rupture, plate end interfacial debonding, the interfacial crack

induced interfacial debonding, and shear failure. These modes are shown in Figure 2.3. Concrete

cover separation, plate end interfacial debonding and intermediate crack induced are debonding

modes of failures. In intermediate crack induced debonding, debonding takes place at the crack

near mid-span and then spreads towards the end of the beam. In plate end debonding, the failure

occurs at the end of the beam and then spreads to its middle. This type of failure can pervade to

the longitudinal reinforcement and then propagates along the reinforcing bars (rebars) and causes

concrete cover debonding. This phenomenon is also called concrete cover separation, as

mentioned earlier. The common feature among the different debonding modes of failure is the

stress concentration at the location of failure initiation and its rapid propagation (Smith et al.,

2001)

The modes of failure are almost the same for shear failure, and consist of FRP rupture and

interfacial debonding.

Figure 2.3 Failure modes of FRP strengthened concrete (Smith and Teng, 2001)

12

There are different methods to postpone debonding mode of failure, including using mechanical

anchors, applying U-wraps or transverse FRP sheets.

2.4.2 Bond behavior of FRP

Bond behavior at the FRP-concrete interface is different from the bond behavior at the steel-

concrete interface in structural concrete. The basic difference is the anisotropic behavior of FRP

as opposed with the isotropic behavior of the steel reinforcement. This behavior is affected by

the type and orientation of fibres and resins. (Cosenza et al., 1997) This property will control the

failure mechanism, and therefore, it should be considered in design equations. (JSCE 11997, ACI

2002)

Depending on the method of processing FRP sheets, there are different characteristics in the

surface texture of FRP, in addition to the different properties in both longitudinal and transverse

directions.

Generally, the bond mechanism depends on the friction between the surfaces and the adhesive

layer characteristics at the interface (Ehsani et al., 1999). A more detailed review of the various

factors affecting the bond behavior at the FRP-concrete interface are presented in the following

section.

2.4.3. Recent experimental work on bond behavior of FRP and concrete

There have been several experimental studies of bond behavior at the FRP-concrete interface, to

study the mechanism of load transfer and examine the various parameters which influence the

bond quality. Some selected examples are presented in the following:

Triantafillou et al. (1992) investigated the debonding failure at the interface of FRP and

concrete, and concluded that failure takes place due to the crack propagation at the FRP-

concrete interface. It was recommended that the bonding concrete should not have any

loose particles to prevent any fracture. They proposed empirical expressions to predict

the bond strength between FRP laminates and concrete.

Mullins et al (1998) added a steel disk to the surface of FRP to apply the load through the

disk,. It was concluded that the tensile capacity of concrete is less than the tensile

13

capacity of the adhesive, therefore failure occurred inside the concrete, near the contact

surface of FRP and concrete

Bizindavyi and Neale (1999) conducted several experimental and analytical studies to

understand the load transition mechanism of FRP laminates attached to concrete. Pull-out

tests were conducted for different types of FRP laminates with different thicknesses and

geometrical properties and also different types of concrete. Based on the experimental

results, empirical expressions were proposed for ultimate load. It was concluded that the

most important factor affecting the bond quality is the surface preparation. The empirical

expressions had some restrictions and significant errors were found for stiff composite

laminates.( Ueda et.al 2005)

Nakaba et al. (2001) conducted double lap shear tests to investigate the bond behavior

between FRP and concrete; different types of fibres and concrete mixtures were studied

to determine the influence of the strength of concrete and FRP. It was concluded that the

local bond stress-slip is affected by concrete properties, but the FRP properties were not

as effective as concrete in local bond stress-slip.

Lorenzis et al. (2001) performed flexural tests to determine the effectiveness of concrete

strength, FRP stiffness, bonded length and surface preparation. It was concluded that, the

bonded length does not have a significant effect on the ultimate load but the stiffness of

FRP sheets influenced the ultimate load. Also, it was concluded that a roughened surface

performs much better than a sand blasted surface.

Chen et.al (2001) conducted five different types of tests to examine the bond behavior of

FRP and concrete. It was concluded that the type of test affects the bond strength and also

a slight change in the geometry of elements can influence the final results.

Ueda et.al (2003) tested several single lap pull-out specimens with different types of FRP

and adhesive, to understand the interfacial behavior of FRP and concrete. Applying high

strength FRP laminates and low shear stiffness epoxy was recommended to improve the

bond behavior of FRP and concrete, but other parameters influencing the bond behavior

such as the surface condition and concrete properties were neglected.

Yao et al. (2004) investigated the bond shear strength of FRP and concrete interface and

the results were compared with the existing analytical models. It was concluded that, the

method of specimen preparation can strongly affect the results and they recommended

14

that the analytical model of Cheng and Teng is the most accurate model among the

analytical models.

Lopez et.al (2006) conducted several single lap pull-out tests and evaluated the strain

distribution and load at failure of specimens with different FRP sheets with varying

geometry. It was concluded that the most important factor for improving the capacity of

specimen is the bonded width. Also, it was also concluded that the edge effect could

influence the behavior of a specimen if the bonded width decreases significantly. Also,

the experimental results were compared with the existing empirical expressions and it

was concluded that the most accurate model is that of Miller and Nanni (2001).

Ouyang(2007) investigated the effect of moisture on bond between FRP and concrete and

developed a new concept, named RTC (Residual Thickness of Concrete). The residual

thickness of concrete which was still attached to the plate was measured. It was

concluded that RTC and the relative humidity of the interface region are inversely

proportional, or in other words, in dry condition, a thicker portion of the concrete will

remain attached to the plate.

2.4.4 Recent numerical modeling of bond behavior of FRP and concrete interface

As discussed earlier, the complete behavior of a system and the associated load transfer

mechanism is complex; and comprehensive experimental research is required to distinguish all

relevant parameters, which can be quite expensive and time-consuming. Using numerical

methods for predicting the failure of concrete members strengthened with FRP sheets is more

useful to save money and time. As a result finite element analysis can be very useful to evaluate

the nonlinear behavior of the FRP-concrete interface and the associated slip phenomenon.

However, the focus on numerical methods has been rather scant, particularly when compared

with the volume of experimental research in this area.

Simulating cracks in numerical analysis is critical. Lopez et al. (2010) and Holmer et al. (2009)

applied cohesive elements at a close distance from the interface of FRP and concrete. In this

case, numerical results show a good agreement with experimental results, and the debonding

mode of failure occurred within the concrete but close to the interface. It is critical to determine

15

the cohesive zone, Bazant and Planas (1998) proposed cohesive zone width 3c ah d where

is the maximum aggregate size.

As discussed earlier, one of the governing mechanisms of failure takes place within a thin layer

of concrete below the interface of concrete and FRP. It should be noted that concrete

demonstrates brittle behavior, therefore the method of modeling concrete is critical.

There are three models applied for modeling concrete

Discrete crack model

Smeared crack model

Damaged plasticity model

The studies of Hearing et al. (2000) showed that the smeared cracking model is unable to

evaluate the stress intensity at the interface of concrete and FRP. Also, the agreement between

the bond stresses from the pullout test and the values computed using the smeared cracking

model was not good. This shortcoming motivates using a fracture energy-based model which is

basically a damaged plasticity-based model.

Summary of some previous numerical studies follow:

Kotynia et al (2008) conducted several numerical simulations and bending tests on

reinforced concrete beams strengthened with CFRP laminates and proposed equations for

the fracture energy and load capacity of reinforced beams. A nonlinear finite element

analysis was conducted, using 8-node brick elements, 4-node orthotropic membrane

elements and 2-node truss elements. To verify the numerical model and discover the

effective parameters in debonding phenomenon, several bending tests were conducted.

The equation proposed for load capacity and fracture energy are as follows:

2.25

1.25

f

cw

f

c

bbbb

(2.1)

16

where w is the load capacity, fb is the width of the FRP and cb is the width of the

c concrete. Based on this equation a new equation for fracture energy was proposed:

20.308f w cG f (2.2)

where fG is the fracture energy and cf is the compressive strength of concrete.

Ueda et.al (2001) used a fracture based energy model for concrete simulation. The

ADINA program was utilized to model the bond behavior at the FRP-concrete interface,

which FRP was modeled by considering friction coefficient. The numerical results

showed good agreement with the experimental results. Also, it was concluded that the

premature cracks which form at the interface of concrete and FRP are localized

phenomena and depend on the concrete properties; this cannot be controlled by numerical

modeling

- Coronado and Lopez (2005) studied the behavior of CFRP- concrete interface bond and

estimated the failure load, and the failure mechanism. The results were compared with the

results of single lap pull-off tests. ABAQUS was used to model the test. The sequence of

formation of macrocracks leading to debonding was described in detail. The damaged

plasticity model and tensile strain softening curve were used to simulate the interface

behavior

- Obaidats et al. (2009) studied the benefits of a cohesive model zone for modeling the

interface of concrete and FRP. ABAQUS was used for numerical modeling; along with a

four point bending test to verify the numerical results. To display proper function of the

cohesive zone, two separate models were studied. In the first model, the interface was

modeled using perfect bond; in the second model, the interface was modeled using the

cohesive zone model. The results were compared with the experimental results, showing

that the cohesive zone model can predict failure mechanism and fracture with a higher

level of accuracy; however the level of accuracy was not mentioned. They also

investigated the relationship between the length of CFRP and the ultimate load and found

that there is an optimum length, and increasing beyond the optimum level does not affect

the ultimate load.

17

- Coronado and Lopez (2010) improved the previous model by considering a damage band

inside the concrete. To prove the accuracy of the model, another model was formed

without considering the damaged band. The computed results were compared with the

experimental results from tests on 14 specimens to verify the method of modeling the

damage band. In this study, the method proposed by Elices et al. (2002) was applied to

determine the fracture energy. Three point bending test were performed to reinforced

concrete beams strengthened with FRP laminates. Plain strain elements with reduced

integration method were used to model the FRP and concrete. It was also concluded that

the numerical results are independent of mesh size or element size.

Mohammadi et al. (2011) also studied the debonding mode of failure of FRP-concrete

interface using cohesive elements to model the interface. Damaged plasticity model was

also used to simulate the behavior of concrete. For this purpose, the equation by Bazant et

al.(2002) for fracture energy was used. It was noted that fracture energy depended on the

concrete compressive strength, water/cement ratio and the aggregate size. Plain strain

elements were used to model the FRP and concrete and 2-noded truss elements were used

for steel bars. The sensitivity of the damaged band width was studied and it was

concluded that, it is not a key parameter and increasing the width of damage band does

not affect the ultimate load. It was also concluded that penetration of the adhesive resin

used for bonding FRP laminates into the concrete can affect the concrete properties and

as a result can affect the failure mechanism.

2.5 Summary and recommendations

Applying FRP laminates to concrete elements in old and new construction has become very

popular recently. The weakest link in the load transfer in a concrete element strengthened with

FRP laminates is the bond between the FRP and the concrete; therefore it is important to

understand the bond behavior between FRP and concrete. There has been considerable

experimental research, including single lap double lap pull-off tests to explain the bond behavior

and estimate the ultimate load and other effective parameters on bond quality, such as material

properties but there are shortcomings in applying steel reinforcement. Double lap pull-off tests

are conducted on two types of specimens in this research program. The first type of specimens

18

are reinforced with longitudinal and transverse reinforcement, while the second batch specimens

involve only plain concrete.

Also, there have been some numerical modeling procedures to examine the bond behavior at the

interface of concrete and FRP. Available literature in numerical modeling of the bond between

FRP and concrete is limited. These procedures were based on two methods. In the first method

which is more popular the interface interaction between FRP and concrete were modeled by

defining a friction coefficient, and in the second method, the interaction was defined by

considering a layer of adhesive resin between FRP and concrete. The second method is a very

recent method, and not much information is available in the literature. This method is capable of

accurately modeling the interaction properties. In this thesis the interaction between FRP and

concrete is modeled using the second method. The effect of geometrical properties is the other

shortcoming in the available literature; therefore a detailed analysis is conducted on the effect of

different geometrical properties on the strength of bond between FRP and concrete.

19

Chapter 3: Experimental Work

The most appropriate method to investigate the bond characteristics at the FRP-concrete

interface is through experimental research; therefore a double lap pull-off test was designed and

several specimens were tested. However, conducting a large number of experimental tests to

understand the effective parameters which influence bond behavior at the FRP concrete interface

is time consuming and expensive, therefore numerical modeling coupled with adequate

experimental work was undertaken as an alternative. Comparing numerical results with the

experimental outcomes requires reasonably accurate modeling. Importing “accurate” material

properties is necessary in the numerical modeling procedure. Therefore different tests were

conducted on the component materials– concrete, epoxy and FRP; these are briefly described in

the following along with the double lap pull off test.

3.1. Concrete tests

Due to practical problems, concrete strength tests are conducted on small samples. The strength

of the concrete depends on various factors, such as the test type, the sample size, loading

procedure, the rate of loading, and the environmental conditions, such as moisture, temperature,

etc. Also, the type of machine (its stiffness) and the test set-up influence the results; therefore it

is crucial to standardize the tests on concrete samples.

Tensile and compressive strengths of concrete are needed in any numerical analysis of a

structural concrete system; therefore these two tests were conducted on cylindrical concrete

samples with a 100 mm diameter and 200 mm height.

3.1.1 Compressive strength of concrete

The ASTMC470-81 method requires compressive strength test to be performed on 150×300 mm

(6×12 inches) cylindrical samples. In the BS method, this test is conducted on cube samples

(6×6×6 inches) or (150×150×150 mm). Nevertheless, depending on the aggregate size, test can

be conducted on smaller samples. Determining the compressive strength of concrete using cube

specimens involves some inaccuracies. For example, because of the Poisson effect in the cubic

specimen, the stress is not truly uniaxial and there are lateral shearing stresses. The concrete

specimen tends to expand laterally but it is constrained by steel plates, this phenomenon will lead

20

to lateral shearing stresses which results in a higher compressive strength. Based on the ASTM

C470-81, cylindrical samples with a height/diameter ratio of 2 can be made in reusable or

disposable molds. Molds could be made of steel, cast iron, plastic, etc., however, presently the

use of plastic and reusable molds is more prevalent. Using a standard mold is critical because the

dimensions of the sample can significantly influence the strength of the concrete obtained from a

destructive test on the sample.

The ASTM C 42-84a recommends correction coefficients for the samples with different

dimensions, and therefore different height/diameter ratios (other than 2) to correct the concrete

strength.

Normally, concrete sticks to the wall of the mold; therefore a thin layer of oil is applied to the

wall and bottom of mold to facilitate removal of the cylindrical concrete specimen from the

mold. During concreting, concrete is poured in cylindrical molds in three layers and each layer is

tamped 25 times using a standard bullet-pointed to compact the concrete. This can also be

implemented by using a shake table. The cylindrical concrete sample was from the same batch

which was used for making the double lap pull-off test specimen. After pouring concrete in the

cylindrical mold, the upper surface of sample was levelled and smoothened by a trowel but a

deviation of 0.05 mm is permissible. Despite these efforts, the cylinder top might not be

completely smooth; therefore some abrasion methods, such as diamond grinder are applied to

make the surface smooth and level. After finishing these processes, the cylindrical samples are

kept in controlled moisture and temperature conditions (ASTM C192-81).The compressive

strength of concrete is evaluated based on ASTM Standard C92-83b. The loading procedure is

important, because it is difficult to provide a pure compression condition. Due to the contact of

concrete surface with the steel plates, some lateral forces will occur due to lateral constraint from

the supports on the sample. This phenomenon will lead to an increase in the apparent

compression strength of the concrete, along with a different mode of failure.

The test was conducted using an MTS machine. The concrete compressive strength is obtained

as the ratio of, the maximum recorded load divided by the area of the sample. (Equation 3.1)

PA

(3.1)

21

The compressive strength of the concrete was obtained as an average strength value from tests on

seven samples from each batch and their other geometrical properties are summarized in

Table 3.1

Table 3.1 Compressive strength results

1( )D mm 2 ( )D mm ( )meanD mmArea

(mm2)Peak

load(kN)

'cf

(MPa)1 100.69 100.55 100.62 7952.70 501.7 63.092 100.6 100.52 100.56 7943.22 491.9 61.933 100.9 100.6 100.75 7973.27 503.7 63.174 100.5 100.6 100.55 7941.64 507.3 63.885 100.5 100.6 100.55 7941.64 502.2 63.246 100.5 100.6 100.55 7941.64 500 62.967 100.5 100.6 100.55 7941.64 487.3 61.36

Standard deviation of the compressive strength of samples is 0.86 MPa and the coefficient of

variation is 1.37% which shows the compressive strength of the samples were very close to each

other.

3.1.2 Tensile strength of concrete:

There are two methods for determining the tensile strength of concrete: the direct tensile test and

the indirect tensile test.

The tensile strength of concrete can be determined by applying tension directly to a prismatic

concrete specimen; however, the direct tension test is quite complex, and difficult and costly to

perform. Methods to determine the indirect tensile strength are usually easier to implement and

relatively inexpensive. Splitting test and bending test are two instances of indirect tension tests.

Indirect tension tests usually result in a value of the tensile strength which is greater than the

direct tensile strength. In fact, the tensile strength of concrete is a function of the strain field at

the point.

In a bending test, the direct strain varies linearly across the specimen depth and the maximum

tensile stress occurs in the bottom fibres of the beam. It is called termed the modulus of rupture,

which is used in designing highway pavements. The BS 5328: 1981recommends methodology

for the bending test. The modulus of rupture depends on the shape and dimensions of the beam

22

and the loading pattern on the beam specimen. The current method of loading is applying two

equally spaced concentrated loads at 13 of the span from each beam end.

The beam cross-sectional dimensions are recommended to be 150×150×750 mm, while the

maximum aggregate size is less than 25 mm. (BS 1881: Part 118: 1983)

The ASTM Standard C 78-84 recommends a similar bending test with the beam cross-section

measuring 152×152×508 mm or (6×6×20 inches).

In the BS method (BS 1881: Part 118: 1983), the tensile strength is calculated based on Equation

(3.2) as:

3blP lf

b d

(3.2)

where P is the maximum load, l is the span length, d is the depth and b is the width of the beam.

This formula is valid until the rupture takes place in the mid 13 of the beam, otherwise the test

result is ignored.

The ASTM allows rupture to take place out of the mid 13 , but recommends a new expression:

3

3bl

Pafb d

(3.3)

where a is the distance from the rupture point to the closest support, but rupture must take place

such that ( ) 0.053l a l

The bending test is usually conducted on prismatic samples with a square section. The splitting

test can be conducted on prisms with square or circular sections. It is considerably simpler to

conduct the splitting test on a cylindrical specimen, while conducting a bending test is

comparatively more difficult. The concrete tensile strength was determined using the splitting

test on cylindrical specimen in this research program.

23

ASTM C496/ C496 M-11 provides details of the splitting test. In this method, a diametrical

compression load is applied along the length of concrete sample. It is crucial to specify the exact

value of diameter and the length of the concrete sample. The diameter is determined by

averaging three diameters with an accuracy of 0.01 inch (0.25mm). For determining the length of

the cylindrical sample, two lengths are measured with an accuracy of 0.1 inch (0.25 mm). The

average values of the diameter and length of cylindrical sample are used in the Equation (3.4) to

determine the tensile strength as:

2st

PfLD

(3.4)where P is the splitting load, L is the length and D is the diameter of the sample.

There are usually high local stresses along the loading lines, and normally plywood strips are

used to apply the load at the bottom and top surfaces of the cylindrical concrete specimen. The

maximum applied load, length, diameter and the concrete tensile strength are summarized in

Table 3.2:

Table 3.2 Tensile Strength of Concrete

1D

(mm)

2D

(mm)

3D

(mm)

meanD

(mm)

1L

(mm)

2L

(mm)

meanL

(mm)

P

(N)

TENSILE

STRENGTH

(MPa)

100.5 100.7 100.5 100.6 199 199.1 199 136776 4.35

100.7 100.7 100.6 100.6 198.8 199 198.9 144672 4.6

100.5 100.6 100.6 100.6 198.9 199.1 199 143029 4.55

Standard deviation of the tensile strength was 0.13 MPa, and the coefficient of variation of the

tensile strengths was 3%

3.1.3 Interfacial fracture energy:

Another property which was used in numerical modeling was the interfacial fracture energy in

cases where the governing model of concrete is damage plasticity model.

24

The required energy to create and develop a crack of unit length is known as interfacial fracture

energy. There are a couple of recommendations for modifying the fracture energy. One of the

most well-known methods is recommended by Wu et al.(2001). In this method, the fracture

energy is calculated using Equation (3.5), therefore the interfacial fracture energy of each

specimen is calculated and the average value is assigned for numerical simulation for each batch

are summarized in Table 3.3.

2max

22ff f f

PGb E t

(3.5)

where: maxP is the ultimate load

fb is the FRP laminate width

fE is the tensile modulus of FRP laminate

ft is the thickness of FRP laminate

Table 3.3 Interfacial Fracture energy of Specimens

Batch 1 ( )fNG mm

Batch 2 ( )fNG mm

Specimen 1 2.56 Specimen 1 1.72Specimen 2 2.78 Specimen 2 1.46Specimen 3 2.77 Specimen 3 1.50Specimen 4 2.43 Specimen 4 1.67

Average 2.635 Average 1.5875

3.2.Mechanical properties of epoxy

In double lap pull-off test, tensile and shear strengths of epoxy are crucial for the double lap pull-

off test. Tensile and shear strength tests were conducted on epoxy specimens to determine the

mechanical properties of epoxy:

3.2.1.Tensile strength of epoxy:

Epoxy glue was mixed in a 1:2 ratio by weight to form a homogeneous mixture, and poured into

a mold. It is important to mix well and pour epoxy slowly into the mold to prevent small bubbles

25

0

10

20

30

40

50

0 5000 10000 15000 20000 25000 30000

Stress(MPa)

Strain

and voids in the mixture, which could damage the integrity of the epoxy specimen, and as a

result decrease its tensile strength. The specimen was cured in a controlled temperature and

humidity condition for one week, and removed from the mold; rectangular specimens were cut to

the desired coupon dimension (Fig 4.1).

The coupons were then loaded in tension. As the behavior of epoxy is sensitive to temperature,

the tests were conducted at a controlled room temperature of around 22℃.

The displacement rate of the testing machine was maintained constant at about 5 ( ).

The applied load was measured and the displacement was recorded for the entire length of the

specimen.

Thestress-strain curve for the epoxy sample is presented in Figure 4.2. It must be noted that these stress and strain

values are nominal, based on theinitial undeformed dimensions and it was computed based on 57 mm gauge length.

Fig 3.2. Tensile stress-strain curve for epoxy

Fig.3.1. Tensile coupon detail (ASTM D638) (Values are in mm)

26

05

1015202530354045

0 10000 20000 30000 40000 50000

Stress(MPa)

Strain

3.2.2. Shear strength of epoxy:

The procedure of preparing epoxy is the same as for the tension test, but specimen preparation is

different.

There are different methods to examine the shear strength of epoxy. One of the methods is

the napkin-ring test. In this method the specimen forms in two thin-walled cylinders. This

method secures a condition of pure shear. This method is quite difficult, labour-intensive, and

expensive. Also, the required equipment for this test is very complicated, therefore this method is

not normally used. Instead, the ASTM D1002 (standard test method for shear strength of single

lap adhesively bonded specimens) , a simple single-lap joint test can be used. This method is

very simple and inexpensive, but can be affected easily by some parameters.

Based on the ASTM D1002 (standard test method for shear strength of single lap adhesively

bonded specimens), two clean metal plates, free of grease and organic matter (removed by sand

blasting) were attached to each other with the specific epoxy. The dimensions of lap shear

specimen are 25.4mm (1") wide and 12.7mm (0.5") overlap and the overall length of specimen

was 177.8 mm (7").

After installing the specimen in the grips, the specimen was pulled at a constant displacement

rate of 0.05 ( )inmm until it failed. The grips must be adjusted to keep the specimen aligned

during the test. Figure 4.3 represents the shear stress-strain curve for the epoxy.

Figure 3.3 Shear stress-strain curve for epoxy

27

3.3 Mechanical properties of FRP:

The FRP sheets can act as barrier against the penetration of aggressive agents such as chlorides,

and thus enhance the durability of the system in aggressive environments. As mentioned earlier,

FRP laminates are formed of fibres and matrix. The fibres are considered non-absorbent and the

matrix can absorb moisture up to about 3.5% by mass. Also, the diffusion coefficient is assumed

to remain constant at 1423 10 ( )m

s It is also assumed that the FRP is dry and there is no

moisture after 365 days of exposure. These assumptions led to a total thickness of FRP is 3.7 mm

to prevent the moisture from reaching the concrete substrate after 100 years of exposure.

Hybrid FRP laminates were formed from glass and carbon fibres saturated with epoxy. As

mentioned earlier, hand lay-up method with vacuum bagging was applied to form the FRP

laminates. Two plies of glass and 2 plies of carbon fibres were used to benefit from the different

characteristics of the carbon and glass fibres. FRP plates were demolded after 24 hours and then

were cut in to 100×400 mm plates. After checking the quality of FRP plates, epoxy was applied

to the surface of plates with roller. The roller was used to secure a constant thickness of FRP and

preventing any deficiencies, and then coarse aggregates were added to the surface of FRP plates

evenly.

The values obtained in Table 3.4 are obtained from MLAM software and also experimental

tensile tests on FRP coupons by Ali et al. (2012)

The ASTM D-3039 ( standard test method for tensile properties of polymer matrix composite

materials) was used for tests on FRP coupons to determine the mechanical properties. The FRP

properties are summarized in Table 4.3; these mechanical properties of FRP are used for the

numerical modeling of double lap pull-off test.

28

Table 3.4.Mechanical properties of FRP

Properties GFRPLaminates

CFRPLaminates

Hybrid FRP Laminate

Estimated usingMLAM

Experimentalresults

Tensile strength (MPa) 374 750 390 376

Tensile modulus (GPa) 22 44.4 34.5 24.4

Ultimate elongation (%) 2.1 1.0 --- 3.5

Poisson’s ratio 0.25 0.28 0.27 0.17

Thickness (mm) 1.02 1.27 3.6 3.56

*CFRP and GFRP properties are provided by the manufacturer.

3.4. Experimental tests on bond behavior of FRP-concrete interface

This test is designed to study the bond behavior at the FRP-concrete interface. The ACI do not

have any guidelines for such a test. Different factors can influence the bond behavior which can

accelerate the debonding at the interface. For example, a coarse grained surface of concrete may

lead to an inappropriate load distribution along the bonded area, or inadequate epoxy thickness

or voids may be unable to secure composite action. These phenomena can be more widespread in

existing structures. Any existing flexural or shear crack can lead to a premature failure. The

material properties of concrete, FRP sheets and epoxy glue, can influence the bond behavior at

the interface. For example, the epoxy must be compatible with the concrete and the FRP,

otherwise a slippery surface may form, causing problems at the interface. Other environmental

conditions are also important such as the relative humidity of bonding surface. Bond behavior at

the interface can be improved by applying mechanical interlocking to the contact surface.

Generally, any method that leads to the increase of the roughness of contact surface will improve

the bond behavior. In this study, a layer of coarse aggregates was installed on the surface of the

FRP laminates.

In this study, wet lay-up method with vacuum molding was used to fabricate the FRP laminates.

After gluing coarse aggregates to the surface of FRP laminates, they were placed in the bond

29

specimen mold. Concrete was then poured in the mold to produce a double lap pullout specimen

with the FRP sheets bonded to the cast-in-place concrete. Eight specimens were constructed and

double lap pull-out test were conducted on these specimens to evaluate the bond behavior at the

FRP-concrete interface.

First of all, different elements, such as the steel rod and FRP sheets were prepared along with

molds with the specified geometry. The JSCE C1.101 guidelines (recommendation for design

and construction of concrete structures using continuous fibre reinforcing materials) were used to

prepare the specimens for the double lap pull-out test. The dimensions of the mold was 150×150

mm in cross section and the width of FRP sheet was 100 mm, therefore there was a 25 mm

clearance on each side. The length of the mold was 502 mm; a 2 mm thick wooden plate was

installed at the center of the mold to separate two 250 mm lengths of concrete blocks. The length

of the FRP sheet was 400 mm, therefore a 50 mm clearance existed at each side along the

specimen. Two FRP sheets were placed symmetrically on the sides of the concrete blocks before

the concreting operation. Figure 3.4.shows the geometric configuration of the specimen.

Dimensions are in mm.

Here, SG-1, SG-2, SG-3, SG-4, SG-5 are the locations of strain gauges.

Two types of specimens were constructed for the double lap pull-out test. Each type included

four samples. In the first type, the specimens were reinforced longitudinally and transversely. For

this purpose, 6 mm diameter steel bars were used for longitudinal reinforcement and 6 mm

diameter ties were used for transverse reinforcement. These ties were placed at 55 mm spacing.

The second batch was plain concrete reinforced with only the FRP sheets and with no

longitudinal or transverse reinforcement.

Fig 3.4. Double lap pull-off test specimen(Ali et al., 2012)

30

(d)(a) (b) (c)

After casting the concrete and curing for two weeks, the double lap pull-off test was performed

on the specimens to determine the bond behavior at the FRP-concrete interface. The tensile load

was applied to the steel rod, and then the load was transferred to the concrete through the bond

between the steel bar and the concrete; the load was then transferred to the FRP sheets through

the bond between FRP laminates and the concrete.

3.5. Instrumentation and testing:

The strain values were measured along the centerline of the FRP sheet. Strain gauges with a

resistance of (120±0.3)Ω were installed at 50,125,200,275,300 mm spacing from the edge of the

Figure 3.5. Double lap pull-off test: (a) the specimen is prepared and painted. The strain gaugesand LVDT’s are installed and connected to laptop computer; (b) the specimen during the pull-off test; (c) and (d) the specimen failure; the concrete is spalled from the specimen and FRPlaminates have popped out from the specimen (Ali et al., 2012)

31

FRP sheets. Figure 3.4 presents the location of strain gauges on the FRP sheets. The first and the

last strain gauges are located at spacing 50 mm from the edge of the FRP sheet, and the middle

one is located exactly in the middle of FRP laminate where the whole load is transferring.

Also, two 10V LVDTs were installed to record the displacement between concrete blocks.

Data were collected and monitored using the computer which was connected to the LVDT’s and

the strain gauges. The test data are presented and discussed in Chapter 5, and compared with the

computed results.

.

32

Chapter4: Finite Element Modeling

4.1 Technique used in this Study:

Different methods are available to analyse the behavior of a concrete structural element and

investigate the internal forces and displacements in the member. These methods are experimental

tests, analytical methods, including numerical modeling.

Experimental tests are normally the most reliable, but they also have shortcomings. For example,

it can be difficult, or in some cases impossible to test a prototype specimen for various reasons,

besides being very expensive and time-consuming.

Analytical methods are normally limited to simple elements, due to the difficulty of reproducing

the boundary conditions and any geometry limitations. Also most of the analytical methods used

for modeling bond at FRP-concrete interface are limited to the linear range and they are unable

to explain the nonlinear behavior. (Li et.al, 2009)

The above imitations lead to the preference to use analytical or numerical methods. There are

three primary analytical methods:

Boundary Element Method (BEM)

Finite Element Method (FEM)

Finite Difference Method(FDM)

These methods are reviewed briefly to show why FEM is the best method for numerical

simulation.

BEM method applies Green’s Function as the response of differential equation to specify the

variables like displacement and stress within a closed boundary. This method is only valid in

linear and homogenous media, therefore it cannot be used to investigate the bond characteristics

at the FRP-concrete interface.

FDM method applies finite difference equations to analyze internal forces and displacement in a

structure. To solve these equations, the structure is broken into small components in to nodal

33

regions. This method is not suitable for systems with complicated geometry, or where the

variables change fast.( Monteleone et al., 2008)

Analysis by the finite element method (FEM) is based on the laws of mechanics, and considering

the nature of the problem, it can be solid or structural mechanics, fluid mechanics, or thermo-

mechanics. The process of modeling for analysis normally forms a loop. First, the physical

problem is idealized by a numerical model governed by differential equations, to develop the

finite element model- a close representation of the structure. This model is then subjected to

applied load to determine the various displacements at the nodes, and followed by analysis of

strains and stress in the system. These results are interpreted for the structure. Based on a review

of the analysis results, the numerical model is occasionally refined and improved, and the system

is reanalysed for the same applied loads. Again, based on the results and their interpretation, the

mathematical model can be improved further until the results closely resemble the “known”

(normally experimental) response of the system to the same set of loads. The finite element

method involves choice of elements, mesh, and boundary conditions. After solving the problem

numerically, the accuracy of the solution obtained is assessed. The type of elements must be

reliable for geometry, boundary conditions and the mesh used for the numerical model.

The bond behavior of FRP sheets bonded to concrete, involves different modes of failure,

extensive cracking, etc. Many of these phenomena are inherently complex and nonlinear;

therefore a proper nonlinear finite element analysis program is necessary. For this purpose, the

ABAQUS 6.10.1 program is used for analysis of the double lap pullout specimens. A brief

review of ABAQUS 6.10.1 and its suitability to model and analyse the problem follows.

4.2. ABAQUS

There are different finite element analysis tools which can be used for numerical simulation and

analysis, including ABAQUS, ANSYS, ADINA, DIANA, OPENSEES, ZEUS-NL, NASTRAN,

and others.

Each of these programs has specific characteristics. In the following a summary of the

characteristics of these programs are presented and compared with ABAQUS to show why

ABAQUS is selected as the best choice for modeling the bond behavior at the FRP-concrete

interface.

34

ADINA is an abbreviation for Automatic Dynamic Incremental Nonlinear Analysis. This

software is mainly used for modeling fluid-structure interactions, heat transfer and also linear

and nonlinear analysis of structures.

DIANA utilizes the displacement method mainly used for analysis of structures and modeling

soil-structures interaction. This program is capable of linear and nonlinear static and linear and

nonlinear dynamic analyses.

OPENSEES is an open source program used for assessing the behavior of structures subjected to

earthquakes.

ZEUS-NL is often used for dynamic analysis of structures and solving eigenvalue problems.

NASTRAN is a FORTRAN based program. This program is developed by NASA and has been

mainly used for nonlinear static and dynamic analyses, buckling analysis and static and dynamic

aero elastic analyses.

ANSYS is another nonlinear analysis program used for simulation in different technologies

including structural mechanics, fluid dynamics and even electromagnetics.

ABAQUS is a finite element analysis program which is similar to ANSYS. They are both used to

simulate structural elements, and are also capable of assembling different simple parts to form a

more complicated structural element. The ability of ABAQUS to model cohesive elements more

accurately makes it the preferred choice for numerical modeling and nonlinear analysis of bond

characteristics at the FRP-concrete interface. A review of the capabilities of the various finite

element analysis programs makes ABAQUS a perfect choice for simulating the bond

characteristics at the FRP-concrete interface.

4.3. Elements used in numerical modeling

Selecting proper elements for modeling the bond behavior of FRP-concrete interface is important

for accurately modeling the phenomenon and for accuracy of the results. The elements were

selected based on their characteristics; these elements had the closest similarity with the

experimental behavior of concrete, FRP, steel and epoxy in the physical prototype.

35

Three types of element were used in numerical modeling of bond behavior at the FRP- concrete

interface: solid elements, shell elements and cohesive elements. Each of these elements has

characteristics which distinguish them from the other types of elements.

For each element, the family type, number of nodes and the order of interpolation, type of

formulation and integration method are normally different from other types of elements, which

leads to different properties or characteristics for each element.

The geometry of an element and the related restrictions are determined by the family type of an

element. For example, shell elements are appropriate for geometries with negligible thicknesses.

This property of shell elements makes them a good choice for modeling FRP laminates.

The accuracy of the element is determined by the number of nodes in an element, or the order of

interpolation. In linear interpolation functions, the nodes are at the corner of the elements, but in

higher order elements with quadratic or cubic interpolation functions, there are intermediate

nodes between corner nodes. For example in an 8 node cubic concrete element, the nodes are

only assigned at the corners and the shape function is linear, but adding extra nodes can simulate

the concrete behavior more precisely; however, this can be quite time-consuming. Figure 4.1

shows a linear cubic element and a quadratic cubic element.

The mathematical theory used to define the behavior of an element is known as formulation, and

the numerical method used to integrate quantities over the volume of the element which is

termed the integration method can influence the type of the element.

As mentioned earlier, solid, shell and cohesive elements were selected in numerical modeling,

but in modeling each of the element, there were several considerations which are explained in the

following section.

Figure 4.4 Linear element and quadratic element

36

4.3.1 Solid elements

Generally, solid elements can consist of a homogeneous or a composite material. They are used

in different patterns for linear or nonlinear analysis, one, two or three dimensional, and first or

higher order analysis, reduced or full integrations. In two dimensional analysis, the elements are

provided in triangle or quadrilateral form, and in 3-D elements are provided in bricks or

triangular prisms shape. There are wide choices for choosing an element, and choosing a proper

element is crucial.

There are several considerations in choosing solid elements for modeling concrete and steel.

These considerations are reviewed in the following

First or higher order elements: Choosing a first- order element could prevent mesh

locking but typically the accuracy of the first order elements is not adequate, therefore

higher order elements are selected instead. In stress analysis problems, first order

elements are significantly stiff and mesh refinement is essential to the convergence of the

solution; therefore first order elements are not useful and almost ineffective. They are

also inadequate for simulation of elements with a complex geometry.

Full or reduced integration: Applying reduced integration results in considerable time

savings, because in this method, a significantly lower number of integration points are

used to formulate the stiffness matrix, which results in time savings. For example, for an

element, such as C3D20, more than three times more is consumed than for the element

C3D20R; however there are some restrictions in using reduced integration which are

explained in the following.

Hourglassing problem: The most common consequence of applying reduced integration

method was hourglassing mode. If there is only one integration point in an element, the

strains might be zero at the Gauss points and the finite element model offers no resistance

to the load that activates this mode, therefore the stiffness matrix will be zero. This

problem usually takes place with the first order elements with the reduced integration

method, but it might also occur with other elements such as C3D27R with 27 nodes. It

takes place when all 27 nodes are used. This is a nonphysical mode of response which

should be controlled. The hourglassing mode is controlled when the reduced integration

method is applied.

37

The type of applied load on the structure can also control the hourglass mode. For

example there is lower probability for a distributed load to cause hourglassing.

Shear Locking: Applying reduced integration method is useful to prevent the shear

locking mode. Based on classical beam theory, a block material under pure bending

experiences a curved shape change and 90 ° angles must continue to remain right angles,

but the edges of the fully integrated first order element are not able to bend to the curves

and 90° angles will not remain 90°, therefore an artificial shear stress will develop

there(Figure 4.2). According to the beam theory, when a beam aspect ratio approaches

zero meaning when the ratio of the height of the beam to the width of the beam reaches to

zero ( → 0), the shear strain must approach zero value and therefore all the load must be

carried by tensile strain . Equation 4.1 shows the relation between the shear and

tensile strain with the beam’s dimensions:

12

11

( )bh

(4.1)

where is the shear strain and is the tensile strain

Note that when hb

→ 0, 12

11

→ ∞This means that the entire load is carried by shear strain and not by tensile strain.

Shear locking usually takes place in the full integrated method.

Volumetric Locking: Applying reduced integration method is useful to prevent

volumetric locking. This problem occurs in fully integrated elements in incompressible

elements. In volumetric locking, when elements are subjected to a deformation with no

Figure 4.2 First order element under pure bending (Lignos, 2012)

38

volume change, some “counterfeit” pressure forms at the integration point, due to the

incompressible property of the material. This problem does not exist in modeling the

bond behavior at FRP-concrete interface.

Solid elements (C3D8R) were employed for modeling concrete and steel.

4.3.2. Shell elements

Shell elements (S4R) are employed for modeling FRP sheet.

In shell elements, thickness is relatively small compared with the other dimensions of the

element; therefore they have different behavior characteristics in the thickness direction

compared with that in the in-plane direction.

The positive surface of shell elements is the top surface and is represented by SPOS and the

negative surface is the bottom surface of the shell element and is abbreviated SNEG. The

positive and negative surface of membrane elements is determined to be the same.

4.3.3 Cohesive elements:

A cohesive element (COH3D8) with traction-separation modeling procedure is employed for

modeling the epoxy.

One of the applications of cohesive elements is modeling adhesive materials and bond interface

which is a key characteristic. The behavior of cohesive elements depends on several factors, such

as their physical properties, their application, and the type of the responses simulated. There are

three types of possible responses: traction-separation based modeling, modeling of gaskets, and

continuum -based modeling. A brief description of each response is reviewed and the reason for

suitability of the traction separation model as the best model for simulating epoxy is explained:

Traction-separation based modeling: This model is perfect when the thickness of glue is

negligible and near zero. This constitutive model assumes the behavior of bonding to be

linear before crack initiation. This model can predict debonding initiation, damage

propagation, etc. The material properties play a major role in this model. All of these

characteristics of traction separation model make it a perfect choice for modeling

cohesive zone.

39

Continuum -based modeling: Unlike traction- separation based modeling, this model is

perfect when the thickness of the glue is considerable and finite. This response can

anticipate crack initiation and propagation.

Modeling of gaskets: As the name of this response suggests, some additional abilities are

incorporated to model the gaskets. Some of these properties are as follows: they are fully

nonlinear, they can be used in dynamic analyses, and that this model can be defined by

material properties of glue.

In these cohesive elements, with traction-separation modeling

procedure was used for modeling the interaction between the FRP

laminates and the concrete.

Connecting cohesive elements to adjacent elements was crucial,

because the mesh density in epoxy layers is much finer than the

adjacent elements, therefore, lack of convergence can be a common

error during analysis. Tied contacts are applied to connect epoxy

layers with the FRP laminates and concrete to prevent convergence

problem (Figure 4.3)

There are also many other types of elements available in ABAQUS 6.10.1, such as membrane

elements, beam elements, surface elements, pipe soil elements, user defined elements, etc. but as

they are not employed in numerical modeling of bond behavior of FRP and concrete, no further

explanation is provided here.

4.4. Model assembly

Models usually consist of components which are assembled together to form the final shape.

These components are known as part instances. For example the model in this study consisted of

FRP laminates, concrete blocks, steel rods and epoxy layer. It is more convenient to model each

of these elements separately and then assemble them. This method is considerably helpful for

forming complex configurations.

Concrete blocks, FRP sheets, steel rods and epoxy layers are parts of the numerical model and

are used repeatedly in the model and assembled. Each of these (part instances) components has

the same mechanical properties within themselves and are modeled separately. These parts are

Figure 4.3 cohesiveelements constrainedwith tie contacts

40

not analysed individually, but analysed within a complete model. Mesh can be applied to either

individual parts or the whole model; however, it is more convenient to apply the mesh to each

part separately due to the complex configuration of the concrete block which has a hole in it, and

also mesh is more refined in some parts, such as the epoxy layers. Other properties of the model,

depending on the type of the property, can be defined either at the model level, or at the part

level. For example, interaction properties, or the type of relationship between the surfaces must

be defined at the model level, while constraints can be used either within a part or at the

assembly level.

4.5. Mesh:

The first step in any finite element analysis is the discretization of the domain into smaller

subdomains.

There are different methods available to generate the mesh in the modeling procedure, such as:

Manual discretization

Automatic mesh generation

Automatic mesh generation includes methods such as Octree method, Tesselation method and

Bottom-up approach. These methods are not applicable for meshing of different elements of

the specimen; therefore a manual discretization method was used to mesh the elements.

Meshing process depends on different factors, such as the geometric specifications. For example,

meshing a complex part such as concrete block with a hole in it is more difficult than meshing a

FRP laminate.

Generally, meshing process is straightforward. The process consisted of two stages. In the first

stage, seeds are assigned to the edge of the components and in the second stage, meshes are

assigned to the each part. Based on the desired level of accuracy, the mesh size is determined.

For example, in some areas such as epoxy layers with a high failure risk, more accuracy is

needed and therefore, a more refined mesh is required.

After determining the mesh size, the number of elements on the edge of element is determined;

therefore numbers of seeds at the edge of the parts are recognized.

41

Due to the effect of the mesh size and quality on the final results, several factors are considered

in devising a better mesh aimed at achieving more reliable results. The size of the elements,

location of the nodes, and the number of elements are some of the more important factors which

affect the mesh quality.

The aspect ratio is important in determining the size of the elements, because it determines the

shape of the element. The aspect ratio is the ratio of the largest dimension of element to the

smallest dimension. The best aspect ratio in modeling procedure is normally one.

Putting nodes depends on the existence of any disruption in the material property, geometry, or

load. In modeling the concrete block, more nodes are necessary to model the hole; however,

there is no discontinuity, like the FRP laminates, it can be divided in equal partitions without any

extra nodes.

As mentioned earlier, the number of elements depends on the desired level of accuracy. In the

modeling procedure, the first selected mesh may not provide accurate results; therefore, a more

refined mesh is used at the second stage. Note that increasing the number of elements does not

necessarily improve the accuracy of the solution indefinitely, because after a certain point, it

merely adds to the time complexity and may result in an increasing number of computational

errors.

4.6. Material properties:

In the numerical analysis of the debonding behavior of FPR sheets bonded to concrete prisms, it

is imperative to import the “accurate” properties of materials determined in the experimental

program into the properties module of ABAQUS.

ABAQUS offers a wide range of material characteristics, such as elastic mechanical properties,

inelastic mechanical properties, mass diffusion properties, electrical properties, thermal

properties, etc. Depending on the type of the material used in numerical modeling, the desired

material behavior can be incorporated.

The type of element used in numerical modeling, does not include the type of material behavior

needed for the component. For example, a solid element or a shell element could reflect either

42

elastic or inelastic behavior. In this modeling, elastic behavior was the dominant characteristic

for FRP and steel, therefore a brief discussion of the elastic properties is included here:

4.6.1 Elastic properties:

This type of mechanical properties includes a wide range of elastic behaviors such as linear

elasticity, hyperelasticity, foam hyperelasticity, plane stress orthotropic elasticity, porous

elasticity, anisotropic elasticity, viscoelasticity, etc. In this study, linear elastic properties are

chosen for modeling the FRP laminates and steel rods. This type of elastic behavior is briefly

reviewed here:

Linear elasticity: This type of elasticity is valid for small elastic strains, and is the

simplest type of elastic behavior. In linear elasticity stress and strain are related with the

following equation:el elD (4.2)

where D is the elasticity tensor. The matrix form of this equation in the simplest form is

as follows:

11 11

22 22

33 33

12 12

13 13

23 23

1

1 0

1

1 0 0

10 0 0

10 0

E E E

E E E

E E E

G

G

G

(4.3)

where E is Young’s modulus, is the Poisson’s ratio, and G is shear modulus defined

by E and with the following equation:

2(1 )EG

(4.4)

43

In these equations elD must be positive definite. This is one of terms of Drucker

stability. The Drucker stability requirements should be satisfied for linear and other

types of elasticity.

4.6.2. Elastoplastic behavior:

Adhesive materials suffer large deformations before failure, which means large strains before

final failure; therefore the behavior of epoxy is highly nonlinear. This type of behavior requires

an elastoplastic model, to simulate its behavior as accurately as possible. Among the existing

elastoplastic models for the epoxy modeling, the Von Mises model represents a perfect choice,

because it was the closest existing model to the real behavior of epoxy, while the other existing

models such as the linear Drucker-Prager and the exponent Drucker-Prager do not reflect the

“actual” behavior of the adhesive (Dean and Crocker, 2004). The Von Mises model is discussed

briefly to show why this model is suitable for modeling the epoxy behavior:

Von Mises material model: In this model, yield criteria are defined based on pure shear

deformations, i.e., when the effective shear stress reaches the critical value, failure occurs. The

effective shear stress is defined as:

12 2 2 21 2 2 3 3 1

1[ [( ) ( ) ( ) ]]2e (4.5)

where 1 2 3, , are the principal stress components.

4.6.3.Constitutive models for concrete in ABAQUS

There are three types of constitutive models for concrete available in ABAQUS 6.10.1; smeared crack

concrete model, brittle crack concrete model, and concrete damage plasticity model.

Each of these constitutive models has its own distinct characteristics. The material properties of concrete can

be provided by the user in any of these constitutive models. In the following, a summary of these constitutive

models are discussed briefly to show why the damage plasticity model is the best choice for modeling

concrete:

1) Smeared cracking model: This model is capable of discerning discontinuous macrocracks

in concrete. These cracks are taken into account by considering their influence on material

44

stiffness. Smeared cracking model used to be very popular for modeling concrete behavior among

researchers; however, there were serious concerns about its efficiency. The experimental results for

bond stresses at the FRP-concrete interface had significant differences with the numerical models,

modeled with smeared cracking model. For this reason, a more fracture energy based constitutive

model for concrete is recommended. In general applications, there was a problem with mesh

sensitivity, namely mesh refinement which led to completely different results compared with the

primary model.

A more thorough discussion of the shortcomings of the smeared cracking model can be

found in Hillerborg, 1976

2) Damaged plasticity model for concrete: This model was first proposed by Lubinier et al.

(1989) and then extended by Lee et al. (1998). In addition to concrete, damaged plasticity

model is valid for quasi-brittle materials such as rock or mortar. Damaged plasticity

model is a more energy based model and this property makes it a perfect choice for

modeling the concrete in the double-lap pull-off test.

There are different parameters required to define the damaged plasticity model. The most

important factor is the fracture energy, fG . As mentioned earlier, fracture energy is the

energy required to propagate a unit-length crack. This value was estimated based on the

work by Wu et.al 2001. Also, tensile strength of concrete is important in the damaged

plasticity model, because it can control the initiation of crack and damage in concrete.

3) Brittle cracking model: This model only considers linear compressive behavior and there

is no plastic straining in this model. Generally, the behavior of concrete in this approach

is determined by the concrete tensile strength, therefore, in this model, when the tensile

stress exceeds the tensile strength, damage initiates and the direction of principal stress

determines the direction of crack.

In this approach, there are two types of post-cracking behavior. In the first mode, the

tensile mode, behavior is determined by the maximum tensile strain and in the second

mode which is the shear mode, the behavior is determined by the shear stiffness.

This model is similar to the damaged plasticity model, and is valid for quasi-brittle

materials as well.

This model is not usually recommended for numerical modeling, especially for fracture

energy based applications.

45

Chapter 5: Experimental and Analysis Results and Discussion

The results from the analytical models are compared with Ali’s experimental results (Ali et al.

2012) in this Chapter. The effects of different parameters on bond behavior of FRP-concrete

interface are reviewed.

5.1. Experimental results:

As mentioned earlier, two types of specimens were tested in this experimental work. In the first

set, the concrete blocks were reinforced by longitudinal and transverse reinforcement and in the

second batch, they were unreinforced; each set consisted of four specimens.

As mentioned earlier, the strain values were recorded by the strain gauges at five locations on the

FRP laminates. In addition, the displacements at the gap between the two concrete blocks were

recorded by an LVDT. The maximum strain value, which was recorded at the center of FRP

laminates, the recorded displacement at the ultimate load and the ultimate load for each specimen

are summarized in Table 5.1.

Specimen Ultimate Load(kN) Maximum Strain(× 610 )

Ultimate

Displacement(mm)

G1S1 70.66 2504 1.09

G1S2 73.67 2713 0.586

G1S3 73.59 2657 1.159

G1S4 68.9 2396 0.677

G2S1 57.91 2261 0.478

G2S2 53.37 2063 0.463

G2S3 54.16 2113 0.472

G2S4 57.1 2210 0.519

Table 5.1. Experimental result

46

The average ultimate load of the specimen in Group 1 (70.7 kN) is larger than that for

Group 2 specimens (54.5kN), basically due to the provision of tensile and transverse

reinforcement in the first batch.

Comparison of the ultimate displacements in Table 5.1 shows that the specimens in the Group 1

behaved in less brittle manner than the specimens in Group 2, which failed in a very brittle

manner accompanied by a large release of energy. Also, the measured strains in Group 1

specimens were larger than those in Group 2 specimens because of the higher load and

displacement levels recorded in Group 1 specimens. Also, a higher load was transferred through

the FRP laminates, resulting in a higher stress and strain in the FRP laminates. The average

ultimate strain in Group 1(2567 (× 610 )) is larger than that for Group 2 (2173 (× 610 )).

The load applied to the specimen by SINTECH 30/G Universal Testing Machine was recorded

using the computer, therefore the load-displacement diagrams for the various specimens were

plotted directly by the computer. Figure 5.1 presents the load-displacement relationships for the

double lap pull-off tests for Group 1 specimens.

Two distinct stages can be discerned in the load-displacement diagrams for the Group 1

specimens. In the first stage, which is about 55% of ultimate load, the behavior is basically linear

Figure 5.1. Load-displacements relationships forGroup 1specimens

47

elastic; this is followed by a decrease in the slope of load-displacement diagram, showing a

decrease in the stiffness of specimens. There is some scatter in the displacements of Group 1

specimens at the ultimate load. For example, the specimens G1S1 and G1S3 had nearly the same

ultimate displacement, while the displacements in specimens G1S2 and G1S4 displacement were

close. However, in design, the service load displacements are the controlling factor, which is

approximately the end of the linear part of the load –displacement curve.

Figure 5.1 shows that the displacements for all specimens at the end of the linear part of the

diagram (about 55% of ultimate load) are almost the same and around 0.21mm.

The average of ultimate load for Group 1 specimens was 70.7 (kN) with a coefficient of variation

(COV) of 3.25 %.

The load-strain distribution diagram for one of the specimens of Group1 (G1S1) is plotted in

Figure 5.2.

It can be observed that, as expected, the strains in the FRP laminate increase towards the center

of the FRP. The trend of load-strain relationship resembles the trend in the load-displacement

diagram. Thus, there are two parts in the load-strain diagram, with the slope of the diagram in the

Figure5.2. Strain variation in FRP laminates in Specimen G1S1at different load levels

48

second part decreasing. The average value of strain at ultimate load for Group 1 specimens is

2567(× 610 ) with a COV of 5.6%.

Figure 5.3 represents the strain distribution along the FRP laminates at different load stages for

the Specimen G1S1.

It can be observed from Figure 5.3 that the slope of strain diagram from SG 2 to SG 3 and from

SG3 to SG4 is significant, because more load is developing through this length and strain gauges

show higher strain values at these points at every load stage.

In the second batch the load-deflection behavior of the first three specimens was very similar to

each other but the fourth specimen behaved differently. A separate load-displacement diagram is

shown for Specimen G2S4 in Figure 5.5.

Figure 5.3. Strain distribution along the FRP laminate

49

0

10

20

30

40

50

60

0 0.1 0.2 0.3 0.4 0.5 0.6

Load

(kN)

Pull off Displacement(mm)

The load-displacement diagrams for Group 2 specimens consist of two parts like those of

Group 1. Up to almost 55%, they behaved linearly and then the stiffness decreased. Unlike

Group 1 specimens, all of the specimens in Group 2 have almost the same ultimate

displacements; also the displacement in the first linear part is almost the same. The average of

ultimate load for Group2 specimens was 54.5 (kN) with a COV of 4.0%.

Figure 5.4 Load-displacements relationships for Group 2specimens

Figure 5.5 Load -displacement diagram for G2S4

50

The behavior and the mode of failure of specimen G2S4 was different from the other specimens

in Group 2, and occurred at the interface of concrete and FRP, through the aggregates. The

ultimate load for this specimen was 57.1kN which was close to that for the other specimens, but

the final displacement of this specimen was slightly more than that of the other specimens. Also,

unlike the other specimens, G2S4 behaved linearly up to a load of 40kN which is almost 70% of

its ultimate load and the stiffness of this specimen was slightly higher than that for the other

specimens.

The load-displacement diagrams for Group 2 specimens are shown in Figure 5.6.

The value of strain around the first 50 mm length of the FRP laminate does not change

significantly; however, as the load increases the strain at the center of FRP laminate increases

significantly, reaching a value of 2261(× 610 ) at the ultimate load. The average of ultimate strain

for Group 2 specimens is 2173× ( 610 ) with a COV of 4.2%. These values show that the data are

close to each other.

Figure 5.6 Load-strain diagrams for the Group 2specimens

51

5.2. Numerical modeling

The experimental double-lap pull-off tests which were conducted on two groups of specimens

were modeled using the ABAQUS 6.10.1, and the experimental and analytical results were

compared.

In the first finite element analysis, a 30×10 mesh was used for concrete; however, after analyzing

the results, the load transfer discrepancies were noted in the concrete block. This was different

from the experimental behavior for load transfer in the concrete block, which is always smooth

with no sudden changes. Figure 5.7 presents the load transition through concrete for the 30×10

mesh.

In the test specimens, the load transferred gradually from one component to the other, and

normally these transitions are gradual; however, the numerical results in Figure 5.7 showed a

sharp change in the load transfer in the concrete. Therefore, to obtain accurate results from

modeling, a finer mesh a 60×20 mesh was used for concrete and “more realistic” behavior was

observed. For all other parametric studies, the same mesh size (60×20 mesh) was used for

analysis. The effect of mesh size on modeling is discussed separately in Section 5.3.1

Figure 5.7. Load distribution in concrete block for 30×10 mesh for Group 1

52

Figure 5.8 presents the effect of using a finer mesh and compares this effect with the primary

model with a mesh of 30×10.

.

It can be observed from Figure 5.8 that using a finer mesh, the load transfer through the concrete

block is smoother. A slight increase can be observed in the maximum load transferred through

the concrete.

5.2.1. Data analysis

Figure 5.9 shows the configuration of the specimen; the locations of the strain gauges used in

physical model and for the finite element model are shown.

Figure 5.8. Load transfer through the concrete block for different mesh sizes for Group 1

Figure 5.9 Specimen configuration (Ali et al.,2012)

53

The total length of FRP laminate is 400mm and the length of each concrete block is 250 mm

which are separated by a 2mm gap. The FRP laminate ends commence at a distance of 50mm

from the outside edge of the concrete block. The strain gauges are located distances of 50, 125,

200, 275 and 350 mm from the edge of the FRP laminate along its center line. The FRP

laminates are 100mm wide. The concrete blocks are 150×150 mm in cross section. Therefore,

the edges of the FRP laminates are located at a distance of 25mm from the edge of concrete in

the section width.

As the first step, load-displacement diagram was plotted for Group 1 specimens to compare the

load capacity, deformation and stiffness of experimental specimens with the numerical model.

Figure 5.10 shows the load-displacement relationships for both the physical and finite element

models.

The ultimate load for the finite element model for Group 1specimens is 73.8(kN) and the final

displacement is 0.78mm, while the displacement in linear part is 0.21 mm, showing a difference

of 4.6% in the ultimate load evaluated from the numerical analysis and the experimental results.

The average displacement in the linear part of the load-displacement curve for the experimental

results is 1.9 mm, demonstrating a difference of 5.2%. A comparison of finite element and the

Figure 5.10 Load - displacement diagram from numerical modeling of Group 1 specimens

54

experimental results for the load-displacement relationships is shown in Figure 5.10. The first

part of the load-displacement curve is linear until a load of 40kN, followed by a decrease in the

stiffness and a higher displacement in the second part.

The experimental and the finite element results for identical locations on the specimens are

compared in Figure 5.11.

The average experimental value of strain at the center of the FRP laminate was 2657× 610 , while

the ultimate strain in numerical simulation was 3023× 610 showing a difference of 12.1 %.

The shape of the computed load-strain curve resembles the experimental

load-displacement diagram. It comprises two parts, the initial linear part and the second part with

a lower stiffness. The load-displacement curves for Group 2 are shown in Figure 5.12.

Figure 5.11 Load-strain diagram for the finite element model of Group 1 specimens

55

The average ultimate load for Group 2 specimens was 56.8kN with an average displacement of

0.53mm at the ultimate load; the average displacement at the end of the linear part of the load

displacement curve was 0.11 mm. The average value of experimental ultimate load was 54.5kN,

with a difference of only 4.6%. The average displacement in the linear part was 0.1mm, with a

difference of 8.7%. The average experimental displacement at ultimate load was 0.48 mm, with a

difference of 9.7%.

The ultimate load and the computed displacement at the ultimate load for the specimens from the

two groups shows that the Group 1 specimens have higher strength due to the reinforcement along

with a higher deformability, demonstrating lower brittleness.

Figure 5.12 Load -displacement diagram for Group 2 specimens

Figure 5.13 Load-strain diagram for Group 2 specimens

56

Figure 5.13 shows the computed load-strain diagram for Group 2 specimens. The strain is

compared with the experimental results at the center of specimen. The computed ultimate strain

was 2320 × 610 ,with the average ultimate strain in experimental study being 2173× 610 ,

showing a discrepancy of 6.3%, which is quite small.

The normal stress distributions in different elements are shown in the following figures (Figure

5.14, Figure 5.15, Figure 5.16, Figure 5.17, Figure 5.18 and Figure 5.19), which represent left

half of the specimen, with the right side representing the plane of specimen symmetry B.

The colour spectrum shows the stress variation in the half specimen. The blue color means the

lowest stress values, and the red color implies highest stress values.

Figure 5.14 shows normal stress distribution along the FRP laminate for Group 1 specimens.

Point A is located at the edge of the FRP, point B is located at the center of the laminate and

point C is in the middle of points A and B. Around the edge of the FRP laminate (point A) the

stress in the FRP laminate is low (coloured blue), according to the legend, this shows that the

amount of stress is small (around 7.5 MPa). Around the middle of laminate (point C) the amount

of stress in FRP laminate is intermediate (around 65 MPa) represented by the green colour,

which shows a higher stress level than at point A and finally at the point B, the stress in the FRP

laminate is around 100 MPa, which is higher than that at points A and C, because at this point

the entire load is transferring through the FRP laminate. It can be concluded that the load is

developing gradually along the FRP laminate. This observation is verified in Figure 5.22 where

the load distribution along the FRP laminate is discussed.

Figure 5.14 Stress distribution in FRP laminates up to themiddle of laminate for the Group 1 specimens

57

Figure 5.15 shows normal stress distribution in the epoxy layer for Group1 specimens. Finer

mesh is used to analyze the epoxy layer for more accurate modeling. The epoxy layer works as a

bonding medium between the FRP laminate and the concrete blocks. Points A and B are located

at the edge of the epoxy layer. According to the legend, the stress levels at points A and B are

around 40 MPa, respectively; the stresses at C and D are lower than that at A and B .

Figure 5.16 shows normal stress distribution in concrete block for Group 1 specimens. The steel rod is

attached to concrete block at point A and point B is located at the middle of the concrete block. According

to the legend the stress is almost zero at point A, but the load transfers gradually to the concrete

between steel rod and concrete, and stress reaches its maximum at point B. This observation is

verified in Figure 5.24 where the load distribution in concrete block is discussed.

The mechanism of stress distribution in Group 2 specimens is almost the same as that for Group

1 specimens. Figure 5.17 shows the normal stress distribution in FRP laminates for Group 2

Figure 5.15 Stress distribution in the epoxy layer in Group 1specimens

Figure5.16 Stress distribution in the concrete in Group 1 specimens

58

specimens. The point A is located at the edge of the FRP laminate and point B is on the center

line of the laminate at the end of the concrete block. The stress distribution is similar to that for

the specimens in Group 1 (Figure 5.14), with colour variation form being blue around point A

across the width of the specimen (the lowest stress level). The stress distribution for Group 1

specimens around Point B is similar to that in Group 2 specimens, with a higher value around

100MPa. In general, stresses in the FRP laminate for Group 2 specimens is lower than those for

Group 1 specimens and more areas display the blue or green colour. This is due to the lower

level of ultimate load for Group 2 specimens.

Figure 5.18 shows normal stress distribution in concrete block for Group 2 specimens. The point

A is located where the steel rod is attached to concrete block, and point B is at the middle of the

concrete block. Again, the stresses around point A are small and negligible; the load is developed

in the concrete block gradually and attains its maximum at point B (orange colour); however,

most of the concrete block has stresses in safe range.

Figure5.17 Stress distribution in FRP laminate for Group 2 specimens

Figure5.18 Stress distribution in concrete in Group 2 specimens

59

Figure 5.19 shows normal stress distribution in epoxy layer for Group 2 specimens. Most of the

epoxy layer shows red colour (around 45 MPa) which shows that it is a high stress region. The

amount of stress is maximum around the edge of the epoxy layer (regions A and B) but then

stress decreases slightly towards the middle of the glued joint, region C.

Figure 5.20 presents the strain distribution along the center-line of the FRP laminate at ultimate

load.

Figure 5.20 Strain distribution along the FRP laminate

Figure 5.19 Stress distribution in the epoxy layer for Group2 specimens

60

It is noted again that the numerical strain increases gradually from 178(× 610 ) at the tip of the

laminate and reaches its maximum value (2759 (× 610 )) at the center, and then it decreases. The

average experimental strain increases gradually from 200(× 610 ) and reaches its maximum value

2657( × 610 ) near the middle of the FRP laminate. This diagram presents only the strain

distribution at the ultimate load and compares the experimental results with the computed values.

Figure 5.21 shows strain values at different load levels.

Figure 5.21 illustrates only the computed results of strain values at strain gauges locations at

different load levels. As expected, the maximum strain occurs at the center of the FRP laminate.

Also, it can be observed that as the load increases, the strain also increases linearly.

The load development along the length of the FRP laminate is shown in Figure 5.22 .

Figure 5.21 Strain distribution along the FRP laminate at different load levels

Figure 5.22 Load transfer between FRP laminate and concrete

61

It can be observed from Figure 5.22 that the load is transferred gradually along the length of the

laminates. The development rate is slow for the first 50 mm, and then increases and finally

reaches its maximum value at 200 mm which is the center of FRP laminate.

Figure 5.23 presents the load distribution in half of the length of the concrete block.

The loads at the beginning of concrete block (point A) and the end of concrete block (point B)

are both zero. The load increases gradually and reaches a maximum value near the middle of the

Figure 5.23 Load distribution along the concrete block at ultimate load

Figure 5.24 Concrete block scheme(Ali et al.,2012)

62

concrete block. This point is close to the position of a steel plate attached to the end of the steel

rod. Figure 5.25 presents the load distribution along the steel bar

Total length of the steel bar is 250 mm of which 140 mm extends out of the concrete block.

Therefore, the force is constant in the first 140mm length, and the load is transferred to the

concrete from the rod along the remainder of the bar. The load in the steel bar decreases, but it

does not reduce to zero because of the plate at the end of the bar.

Figure 5.26 presents the load variation in the steel bar, concrete and the FRP laminate along the

length of the specimen at ultimate load.

Figure 5.25 Load distribution along the steel bar at ultimate load

63

Figure 5.26 shows how the load is transferred through the different elements at ultimate load. For

the first 140 mm, where the rod is extending out of the specimen, the load is constant at 73.2kN,

then the load is transferred to the concrete through the steel-concrete interface. The FRP laminate

is located at 50mm from the edge of the concrete block. As the load in steel decreases, the load

in the FRP laminate increases slowly and the load in concrete reaches its maximum around the

middle of the concrete block. Closer to the middle of the specimen, the entire load is transferred

through the FRP laminates.

The contribution of each element at four points of the load-displacement diagram is summarized in

Table5.2 to show partial details of the load transfer. These points (A, B, C, D) are defined on Figure 5.27

Figure 5.26 Load distribution along the specimen in different elements at ultimate load

Figure 5.27 Load -displacement diagram

64

At point A the load is 23.1(kN), while at points B,C and D the load values are 35.9kN, 53.6kN

and 73.2kN respectively.

The contribution of the various elements is evaluated at four points. Two points are defined

within the linear part (points A and B) and two points are defined in inelastic behavior range

(points C and D).

In addition to evaluating the load distribution among the different elements; the load

development in each element is discussed separately. Several points are picked in each element

to examine the load development.

Figure 5.28 presents the load-strain variation in the FRP laminate.

Locationfrom theend of

concreteblock(mm)

Load=23.1 kN Load=35.9 kN Load=53.6 kN Load=73.2 kN

50 5.45 17.63 0 9.17 29.65 0 12.64 40.88 0 17.47 55.73 0

100 14.63 6.93 0.7 24.64 11.67 1.16 33.93 16.09 1.6 46.39 21.67 2.13

150 8.18 0 7.35 13.8 0 12.45 19.03 0 17.15 25.74 0 23.35

200 3.45 0 9.65 5.86 0 16.28 8.11 0 22.51 11.11 0 30.59

250 0 0 11.55 0 0 19.42 0 0 26.77 0 0 36.6

Table5.2 Contribution of the various elements in load transfer

65

Here X1, X2, X3 and X4 are the distances from the edge of the FRP laminate.

The strain values were measured at four points from the edge of the FRP laminates (X1=50 mm,

X2=100 mm, X3=150 mm, X4=200 mm) as the applied load was increased. It can be observed

that as the applied load increases, the strain increases at each of the four points; however, the

increment at X=50 mm is negligible. For example, the amount of strain at point A

(Load=23.1kN) is 58× 610 , while at point D (Load=73.2kN) the strain reaches a value of 184

×10 .

At A (X2=100 mm), (Load=23.1kN), the strain is 600 × 610 i.e., the strain increases by a factor

of more than 10 times from the first point (X1=50 mm) to the second point (X2=100mm). At the

ultimate load, the strain reaches a value of 1878 × 610 , which is more than 10 times the ultimate

strain at point(X1=50mm). Also as the load increases at point (X2=100mm) from zero to

ultimate load, as expected, the variation in strain values increase. The strain at point D

Figure 5.28 Load-strain variation along the FRP laminate

Figure 5.29 Specimen configuration(Ali et al., 2012)

66

(X2=100 mm) at ultimate load is 2.9 times the strain at point A (Load=23.1 kN). The same trend

is also observed at points (X2=150 mm) and (X3=200 mm).

Figure 5.30 shows the load distribution along the FRP laminate and demonstrates that, at the first

50 mm (point X1) the rate of load development in FRP laminate is not significant but after that,

the slope of the diagram increases, which means load is developing in FRP laminate.

Figure 5.31 presents the load-strain values for the steel bar at two specific points.

Figure 5.30 Load distribution along the FRP laminate inexperimental tests and numerical simulation

Figure 5.31 Load-strain variation in the steel rod

67

In the steel bar, the situation is different; the strain value decreases along the rod as it can be seen

in Figure 5.31. The strain at X1=50 mm is greater than X2=100 mm at every load level, along

the steel bar in the specimen, because of the transfer of load from the steel bar to the concrete.

Figure 5.32 presents the load-strain diagram for concrete at specific points; the strain increases at

first (from X1=50 to X2=100mm) then it starts to decrease.

A comparison between strains at point A (Load=23.1kN) and point D (Load=67.5kN) at all

points ( X1, X2 ,X3,X4) along the concrete block demonstrate that the strain at ultimate load is

almost 3 times more than that at point A. Also, the relationship between load and strain in

concrete is almost linear at each section.

5.3. Parametric study

Examining the effect of different factors on bond behavior at the FRP-concrete interface is

important. However, it can be time consuming and expensive to examine this behavior by

conducting detailed tests, therefore finite element analysis is used to examine the effect of

different parameters on the overall behavior of the double lap pull-off test specimens.

Figure 5.32 Load –strain diagram for concrete

68

5.3.1 Mesh sensitivity analysis

In examining the effect of mesh size, three different mesh sizes were considered. As mentioned

earlier, initially a 30×10 finite element mesh was used for modeling concrete, but then the model

was changed to a 60×20 mesh, with each element being one-quarter of the original element size.

Subsequently, a 90×30 finite element mesh size was used for the model; each element was 1 9of the original element used in the 30 by 10 model.

Figure 5.33 compares the effect of using the different mesh sizes on the load-displacement

diagram. Using a finer mesh led to a slightly increased load capacity and specimen deformation.

Figure 5.33 shows that using a quarter size mesh (60 by 20) resulted in an 8.2% increase in load

capacity of model, and the final displacement of model at the ultimate load increased by 4.8%.

Using 19 size mesh (90 by 30) sizes, the load capacity increased by 7.5% compared with the

primary model and the ultimate load displacement increased by only 2.1% which is negligible.

It can be concluded that the optimum mesh size (60×20 mesh) can give reasonably accurate

results, and also save computational time.

Figure 5.33 Load -displacement diagram for different mesh sizes

69

The effect of using three different mesh sizes is considered in the load transfer among the three

materials comprising the composite specimen. Figure 5.34 outlines the load transfer between

steel and concrete and between concrete and the FRP laminate for the primary finite element

mesh (30 by10).

Figure 5.35 summarizes the load transfer between the three components for the finest mesh (90

by 30).

Figure 5.34 Load transfer for the primary mesh (30 by 10)

Figure5.35 Load transfer procedure for the finest mesh

70

It can be observed the basic load transfer characteristics are similar in all three meshes, with the

load level increasing with the fineness of the mesh, and the transfer becoming more gradual with

the finer meshes.

The strain distribution for the different mesh sizes was also studied. Figure 5.36 compares the

strain distributions for different mesh sizes. It can be observed that using the finer mesh resulted

in slightly higher strain values; however, the difference of the results with the two finer meshes

is negligible, and the curves nearly coincide with each other.

5.3.2 Effect of epoxy thickness

The effect of epoxy thickness is studied in this section to determine how the thickness of the

epoxy joint would influence the load-slip behavior of the specimen. Figure 5.37 compares the

load-slip response for the primary model with an epoxy joint thickness of 0.1 mm, and the

second model with an epoxy joint thickness of 0.3 mm.

Figure 5.36 Strain distributions for different mesh sizes

71

Increasing the thickness of epoxy joint led to an increased slip between the FRP and the

concrete.

Figure 5.38 shows the equilibrium of forces acting on the composite double specimen

1 2 3P P P F (5.1)

Figure 5.37 Load-slip characteristics for different epoxy thicknesses

Figure 5.38 Specimen configuration

72

where 1P = the force in the first FRP laminate,

2P = the force in the concrete block and,

3P = the force in the second FRP laminate

In the FRP laminate 3 23 FP A (5.2)

where F FA b L (5.3)

323

F

Pb L

(5.4)

In the epoxy joint 2323 G → (5.5)= 3

F

Pb L G

(5.6)

where 23Gt

(5.7)

and 3F

G

G b LPt

(5.8)

It can be noted from Equation (5.8) that a relationship exists between the epoxy joint thickness

( )and the deformation ( ); any increase in the epoxy joint thickness increases the deformation.

This expression confirms the result of the earlier numerical analysis, which showed similar

results.

5.3.3 The effect of FRP geometry

Examining the effect of applying FRP laminates with varying bonded length or varying bonded

width are discussed in this section and the variation in stiffness and load capacity of specimen is

studied. Only one parameter is varied at a time; the remaining parameters are maintained

constant. The effect of the width, length and thickness of the FRP laminates are evaluated to

determine the most effective parameter to improve the bond behavior between FRP and concrete.

73

5.3.3.1 The effect of bonded length:

The length of the FRP laminate in the experimental program was 200 mm. To evaluate the effect

of the epoxy-bonded length, this length was reduced to 150 mm and then increased to 250mm.

(The bonded width maintained at 100 mm, while the FRP laminate thickness was held constant

at 3.56 mm).

Figure 5.39 presents the effect of the bonded length on load-displacement diagram.

Decreasing the bonded length by 50 mm led to a decrease of 12% in the ultimate load. Also the

slope of load-displacement diagram, which represents the stiffness of the specimen, decreased

slightly.

Increasing the bonded length to the whole length of concrete led to a slight increment in the

ultimate load (only 1.5 %) and also the slope of the load-displacement diagram, which represents

the stiffness of the specimen increased slightly. This observation is related to the effective

bonded length. These observations show the concept of effective bond length, which means that

Figure 5.39 Load -displacement diagram for different bonded lengths

74

there is an optimum length for the bonded length for a given laminate width, and increasing it

beyond that will not affect the behavior of specimen significantly. (Täljsten et al.1998)

5.3.3.2 The effect of bonded width:

The bond width reduced from 100 mm to 50mm and then increased to the whole width of

concrete block width which is150 mm. The bonded length was maintained constant at 200 mm,

along with a constant FRP laminate thickness of 3.56mm. Figure 5.40 presents the load-

displacement diagram for different bonded widths.

Therefore, decreasing the bonded width, for a given bonded length, has a significant effect on the

ultimate load and stiffness of the specimen. As the width of the bonded width is decreased, the

stiffness decreases, which means that for a specific load there is a larger deformation.

By decreasing the bonded width from 100 mm to 50mm, the ultimate load decreased by 39%,

while increasing the bonded width by 50 mm which covers the whole width of concrete led to an

increment of 13% in ultimate load. This shows that increasing the width significantly affects the

ultimate load but a nonlinear manner. This shows that increasing the bonded width from 50 mm

to 100 mm led to an increment of 39% in load capacity but increasing from 100mm to 150 mm

led to an increment of only 13% in the ultimate load.

Figure 5.40 Load - displacement for different bond widths

75

The significant effect of the bonded width on the capacity of specimen led to the conclusion that

the best approach to increase the capacity and stiffness of the FRP-concrete system is increasing

the bonded width but this is limited to the width of concrete specimen and the bonded length

must be maintained at an optimal level.

5.3.3.3 The effect of FRP thickness:

To study the effect of FRP laminate thickness on numerical results, the FRP thickness was

assumed to be halved (one ply of each CFRP and GFRP). The primary thickness was 3.56 mm.

Decreasing the thickness of FRP had a considerable effect on the ultimate load and stiffness of

the specimen. This effect was not as significant as the bonded width but it caused a decrease of

19% in the ultimate load and the slope of load-displacement diagram, which represents the

stiffness of the specimen, decreased slightly)

In conclusion, the most effective geometrical factor influencing bond between FRP and concrete

is the bonded width (with other parameters being held constant), followed by the thickness of the

FRP laminate, with the remaining parameters being held constant. The bonded length has the

least influence on bond between FRP and concrete (with the other parameters being constant),

Figure 5.41 Load - displacement diagram for different FRP thicknesses

76

therefore the most effective way to increase the strength of bond between FRP and concrete is to

increase the bonded width, for an optimum bonded length.

77

Chapter 6: Conclusions and Future Research Work

6.1. General:

The principal objective of this study was to investigate the bond behavior of FRP-concrete

composite system and evaluate the different parameters influencing this Phenomenon.

A literature review of the characteristics of FRP laminates, historical structural and non-

structural applications of FRP, and the mechanism of bond between FRP and concrete is

presented, along with a review of the previous experimental and analytical work. The procedure

for determining the different material properties, and the test set-up for the double lap pull-off

tests are presented, along with the details of numerical modeling. The numerical modeling

procedure, the type of elements and constitutive models used in numerical modeling are

reviewed. This is followed by a discussion of the results of the experimental work and numerical

analysis, and the influence of some parameters on FRP-concrete bond are studied. The results of

experimental work and numerical analysis led to the following conclusions:

Applying FRP laminate reinforcement to specimens leads to a less brittle behavior, an

increased load capacity and a higher deformation in the double lap pull-off tests.

The complete behavior of specimens in double lap pull-off tests is reflected in the load-

displacement characteristics. This curve consists of two segments. In the first segment,

the behavior is linear, which means that all of the bonding agents including friction,

cohesion and interlocking perform linearly; however, after their partial exhaustion, the

slope of the curve decreases.

Numerical analysis results are compared with the experimental results. Both sets of

curves reflected similar responses. The ultimate load, ultimate displacement and the

associated strain were close to each other.

Elements types are selected based on elements behavior. Cohesive elements(COH3D8)

are selected for modeling epoxy and solid elements are selected for modeling concrete

and steel, also shell elements(S4R) are selected for modeling FRP sheets.

78

Reduced integration method is used to prevent hourglassing and shear locking

phenomena.

The load transfer between the concrete and the FRP laminate is studied. The analytical

strain distributions in FRP laminates are compared with the experimental results at the

same locations.

The effect of epoxy thickness on bond behavior between FRP and concrete shows that

increasing the thickness of the epoxy joint increases the slip between the FRP laminate

and concrete.

A mesh sensitivity analysis determines that if the size of element is enlarged, the

behavior of concrete cannot be modeled well and also applying very fine elements cannot

be useful after a certain point, and it can only lead to an increased time consumption and

increasing computational errors.

The most effective parameter which influences the response of the composite is the width

of FRP, for an optimum bonded length. Decreasing the width of FRP led to a reduction in

stiffness and load capacity of the model for a constant bonded width. Decreasing the

thickness of FRP led to a decrease in the stiffness and load capacity of the composite

system. The least influencing geometric parameter was the length of the FRP laminate.

The concept of the effective bonded length which was previously observed by Lopez et

al.(2006) was noted here. Increasing the length of FRP did not have any significant effect

on load capacity and stiffness of the model, but reducing the bonded length led to a

reduction in both stiffness and load capacity of the model. It should be emphasized that

there is an optimum combination of bonded length, width and epoxy joint thickness for a

given situation.

6.2 Limitations of the study

There are some limitations in this study that must be considered and rectified in future studies.

These limitations are:

One can run more tests with varying geometric and material properties to examine their

effect on bond behavior and ensure the accuracy of the numerical results with a

parametric study.

79

In modeling bond between FRP and concrete, the effect of coarse aggregates was

neglected, while in the tests one of the effective parameters in bond behavior was the

interlocking of coarse aggregates which were connected to the FRP laminate with epoxy

glue.

6.3 Recommendations for future research work

In view of the lack of data in the literature, considerable research is required as follows:

Conducting experimental work on specimens with different types of fibres and matrices

to determine the effect of fibres and matrices on bond behavior and the overall response

of the FRP-concrete system.

Evaluating the response of the FRP-concrete system with different concrete properties,

for example, the effect of applying high strength concrete on bond behavior of the

FRP-concrete interface.

Experimental evaluation of the durability of FRP-concrete system to determinate the

effect of aggressive environments on bond between FRP and concrete.

Applying different types of epoxy resins with different properties, to determinate the best

glue to enhance bond behavior

Conducting tests on specimens with different geometric parameters.

Modeling the aggregates at the FRP face in numerical simulations.

80

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