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IMPACT BEHAVIOUR OF HYBRID GFRP-CONCRETE BEAM

UNDER LOW-VELOCITY IMPACT LOADING

By

Zongjun Li

A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy

School of Engineering and Information Technology

The University of New South Wales, Canberra

September 2017

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Thesis/Dissertation Sheet Surname or Family name: Li

First name: Zongjun

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Abbreviation for degree as given in the University calendar: PhD

School: SEIT

Faculty: UNSW Canberra

Title: Impact behaviour of hybrid GFRP-concrete beam under low-velocity impact loading

Abstract 350 words maximum: (PLEASE TYPE)

The combination of two or more materials into a hybrid structural system is becoming increasingly important in the construction industry. The present study focusses on the design of a hybrid beam consisting of a rectangular hollow pultruded glass fiber reinforced polymer (GFRP) composite filled with concrete. The static flexural performance of the hybrid beam showed it has potential to be used as a structural element. However, the dynamic performance of the hybrid beam has yet to be assessed. If it is to be used as a railway sleeper or bridge girder, it could be subjected to low-velocity impact loading. The aim of this study therefore is to investigate the impact behaviour of the hybrid GFRP-concrete beam under low-velocity impact.

This research comprised multiple experimental and numerical studies on the impact response of the hybrid GFRP-concrete beam subjected to low-velocity impact loading. The impact behaviour study of pultruded GFRP composites indicated that the impact energy level was the main factors that affected the response of the composite. The energy was absorbed mainly through the elastic-plastic deformation and failure mechanisms, such as matrix cracking and delamination. A numerical model was developed to analyse the development and propagation of the stress. The numerical investigation of the hybrid beam to static loading was conducted to validate the material models of the structural elements. The numerical results were highly consistent with the experimental data. Finally, the impact behaviour of the hybrid GFRP-concrete beam to the low-velocity impacts was analysed using experimentation and numerical simulations. The results indicated that the impact response could be divided into two stages, inertial resistance stage and dynamic bending resistance stage. In the former stage, the impact load was resisted completely by the inertial force. The majority of the impact energy was absorbed in the second stage. Multiple failure modes were presented in this stage, such as the punching failure and the global flexural cracks of the concrete, and the shear cracking on the pultruded composites. Declaration relating to disposition of project thesis/dissertation I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstracts International (this is applicable to doctoral theses only). ……………………………………………………… Signature

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Abstract

iv

Abstract

The combination of two or more materials into a hybrid structural system is

becoming increasingly important in the construction industry. The optimal combination

of the individual materials can result in a system that offers exceptional mechanical and

structural performance. The present study focusses on the design of hybrid beam

consisting of a rectangular hollow pultruded glass fiber reinforced polymer (GFRP)

composites filled with concrete. The hollow pultruded GFRP composites box can protect

the concrete block inside from suffering chemical attacks, while the concrete can provide

the system with bulk size, strength and structural stability.

The results of static bending tests revealed that this hybrid beam has the potential

to be used as structural element. However, the dynamic performance of the hybrid beam

has yet to be assessed. If it is to be used as railway sleeper or bridge girder, it could be

subjected to low-velocity impact or cyclic low-velocity impact loading. The aim of this

study therefore is to investigate the impact behaviour of the hybrid GFRP-concrete beam

under low-velocity impact loading.

In this thesis, an investigation on the impact behaviour of pultruded composites

samples subjected to low-velocity impacts with energies ranging from 17 to 67 J was

conducted. The results showed that the impactor mass had very little effect on the impact

response and the impact energy levels were the main factors that affected the impact

behaviour of the pultruded GFRP composites. The impact response exhibited similar

trends for different impact energy levels and the energy was absorbed mainly through the

elastic-plastic deformation and failure mechanisms, such as matrix cracking and

delamination. The extent of damage increased monotonically with respect to the impact

Abstract

v

energy levels. A non-linear finite element model was developed to analyse the

development and propagation of stress through the effective layers of the composites. The

numerical predictions were found to corroborate the experimental results in terms of load-

time and central deflection-time curves. The numerical results revealed the damage

sequences of the composites under low-velocity impacts and, the stress wave propagated

from an oblong shape into a peanut shape through the top to the bottom surface.

A finite element methodology was developed using the validated composite model

and a concrete model to simulate the static flexural behaviour of the hybrid GFRP-

concrete beam. The numerical predictions were highly consistent with the experimental

results in terms of static performance and load-displacement curve. Multiple failure

mechanisms, such as the fiber tensile failure of the composites, shear cracking of the

concrete and the debonding failure between these materials, were revealed in the

numerical simulation.

The main contribution of this research is the investigation of hybrid GFRP-concrete

beam subjected to low-velocity impact loadings. A series of drop weight tests were

performed to analyse the impact behaviour on both strong and weak axes of the hybrid

GFRP-concrete beams for different impact energy levels. The experimental results

showed that the impact response of the hybrid beam to the low-velocity impacts can be

divided into two stages: namely, inertial resistance and dynamic bending resistance. The

impact characteristics in both stages exhibited similar variation tendencies for the

penetration events. The majority of the energy was absorbed through elastic-plastic

deformation and the failure mechanisms of the hybrid beam in the second stage. A finite

element analysis was performed aiming at validating the numerical results and providing

the details of the failure mechanisms, such as the cracking pattern of the concrete. The

Abstract

vi

numerical results were found to offer high consistency with the experimental data in terms

of load-time and displacement-time curves. Multiple failure mechanisms were revealed

in the numerical simulations: in the inertial stage, the impact load was resisted completely

by the inertial force and no damage was detected during this stage. In the dynamic

bending resistance stage, minor cracks were formed on the bottom side at the first place,

followed by the shear plug in the local impact zone. As the loading process continued,

the impact energies were absorbed through the presence of the global flexural cracks.

Finally, the hybrid beam failed with the presence of the shear cracks (splitting) on the

corners of the pultruded composites. The predicted failure modes showed a good

agreement with the experimental results.

vii

Acknowledgements

First and foremost, I would like to express my very great appreciation to my

supervisors Dr Amar Khennane and Prof Paul Jonathan Hazell, for giving me the

opportunity to work on this project and their continuous support and encouragement

throughout my candidature. Their immense knowledge and insightful guidance helped

me throughout the periods of research and writing this dissertation. They trained me to be

an independent researcher and taught me the very important traits a researcher should

possess. Their valuable and constructive suggestions, untiring supports, precious

discussions and constant encouragements at the various stages throughout the research

work are highly appreciated. Without their support and guidance, this work would not

have been possible.

I am very grateful to A/Prof Alex Remennikov for his guidance on conducting the

dynamic tests in the Laboratory of University of Wollongong. Without his kind supports

and insightful suggestions, this thesis would not be accomplished smoothly.

Sincere gratitude also goes to Dr Juan Pablo Escobedo-Diaz, Dr Andrew David

Brown and Dr Hongxu Wang for helping me in conducting the drop tower tests and their

constructive suggestions.

I grateful acknowledge all the laboratory and workshop staffs from the School of

Engineering and Information Technology at UNSW Canberra and the staffs from the

School of Civil, Mining and Environmental Engineering at UOW for the help in my

experimental programs.

viii

My very special thanks are extended to Mr Jim Baxter and Mr David Sharp from

UNSW Canberra and Mr Alan Grant and Mr Cameron Neilson from UOW for their help

in tackling the experimental challenges.

I would like to thank my colleagues and officemates Biruk Hailu Tekle, Shameem

Ahmed, Yifei Cui, Vishal Naidu, Zhengliang Liu, Rakib Imtiaz Zaman, Ashraful Ismal,

Abdul Kader, Shayani Mendis and Mohammad Anwar-Us-Saadat for their support,

encouragement and friendship.

I am indebted to all my friends in Australia and China for their continuous supports

and friendship throughout my research.

I would like to take this opportunity to express my gratitude to the University of

New South Wales for the emotional and financial support.

Finally, special thanks are due to my parents and all my families for their endless

patience and love, encouragement and untiring support.

ix

Publications related to this thesis

Journal articles

1. LI, Z., KHENNANE, A. & HAZELL, P. J. 2016. Numerical investigation of a

hybrid FRP-geopolymer concrete beam. Applied Mechanics and Materials, 846,

452-457.

2. LI, Z., KHENNANE, A., HAZELL, P. J. & BROWN, A. D. 2017. Impact

behaviour of pultruded GFRP composites under low-velocity impact loading.

Composite Structures, 168, 360-371.

3. LI, Z., KHENNANE, A., HAZELL, P. J. & REMENNIKOV, A. M. 2018.

Performance of a hybrid GFRP-concrete beam subject to low-velocity impacts.

(submitted to Composite Structures).

Conference papers

1. LI, Z., KHENNANE, A., HAZELL, P. J. & REMENNIKOV, A. M. 2017.

Numerical modeling of a hybrid GFRP-concrete beam subjected to low-velocity

impact loading. The 8th International Conference on Computational Methods.

Guilin, Guangxi, China: July 25-29th.

Table of Contents

x

Table of Contents

Abstract ............................................................................................................................ iv

Acknowledgements ......................................................................................................... vii

Publications related to this thesis ..................................................................................... ix

Table of Contents .............................................................................................................. x

List of Figures ................................................................................................................. xv

List of Tables.................................................................................................................. xxi

Abbreviation .................................................................................................................. xxii

List of Symbols ............................................................................................................ xxiii

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

1.1 Background ............................................................................................................. 1

1.2 Objective of research............................................................................................... 5

1.3 Organisation of thesis .............................................................................................. 6

Chapter 2 Review of Types of Railway Sleepers and Bridge Girders .............................. 6

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

2.2 Types of railway sleepers ........................................................................................ 6

2.2.1 Timber sleepers ................................................................................................ 7

2.2.2 Concrete sleepers ............................................................................................. 8

2.2.3 Steel sleepers .................................................................................................... 9

2.3 Types of bridge girders ......................................................................................... 10

2.3.1 Plate girders .................................................................................................... 10

2.3.2 Box girders ..................................................................................................... 10

2.4 Issues of the materials used in railway sleepers and bridge girders ...................... 11

Table of Contents

xi

2.4.1 Timber ............................................................................................................ 11

2.4.2 Concrete ......................................................................................................... 13

2.4.3 Steel ................................................................................................................ 16

2.5 Review of pultruded GFRP composite materials .................................................. 17

2.5.1 Constituents of pultruded GFRP composites ................................................. 17

2.5.2 Fabrication of pultruded GFRP composites ................................................... 18

2.5.3 Characteristics of pultruded GFRP composites ............................................. 19

2.6 The combination of pultruded GFRP composites and concrete............................ 20

2.7 Summary ............................................................................................................... 21

Chapter 3 Review of Impact Behaviour of Concrete and FRP Composites ................... 23

3.1 Introduction ........................................................................................................... 23

3.2 Review of concrete structures subjected to low-velocity impacts ........................ 24

3.2.1 Testing methods ............................................................................................. 24

3.2.2 Failure mechanisms of concrete structures subject to impact loading ........... 28

3.2.3 Strain rate effects of concrete ......................................................................... 34

3.3 Review of FRP composites subjected to low-velocity impacts ............................ 36

3.3.1 Testing methods ............................................................................................. 36

3.3.2 Review of impact behaviour of different types of FRP composites .............. 37

3.3.3 Failure modes of FRP composites to low-velocity impacts ........................... 42

3.3.4 Strain rate effects of FRP composites to low-velocity impacts ..................... 48

3.4 Summary ............................................................................................................... 50

Chapter 4 Experimental Study of Pultruded GFRP Composites to Low-Velocity Impacts

......................................................................................................................................... 51

4.1 Introduction ........................................................................................................... 51

4.2 Material description .............................................................................................. 52

4.3 Test setup and procedures ..................................................................................... 55

4.4 Experimental results and discussion ..................................................................... 58

Table of Contents

xii

4.4.1 Load-time response ........................................................................................ 58

4.4.2 Central deflection-time response.................................................................... 60

4.4.3 Load-displacement response .......................................................................... 62

4.4.4 Impact performance ....................................................................................... 64

4.4.5 Damage evaluation ......................................................................................... 66

4.5 Impactor mass effect ............................................................................................. 68

4.5.1 Load-time response ........................................................................................ 69

4.5.2 Central deflection-time response.................................................................... 70

4.5.3 Load-displacement response .......................................................................... 70

4.5.4 Impact performance ....................................................................................... 71

4.6 Summary ............................................................................................................... 72

Chapter 5 Numerical Study of Pultruded GFRP Composites to Low-Velocity Impacts 74

5.1 Introduction ........................................................................................................... 74

5.2 Finite element model ............................................................................................. 75

5.3 Progressive damage model .................................................................................... 76

5.4 Numerical results .................................................................................................. 86

5.5 Summary ............................................................................................................... 94

Chapter 6 Numerical Study of the Hybrid GFRP-Concrete Beam to Static Loading ..... 96

6.1 Introduction ........................................................................................................... 96

6.2 Description of the experimental program ............................................................. 97

6.3 Finite element model ............................................................................................. 97

6.4 Material models ..................................................................................................... 98

6.4.1 Progressive damage model ............................................................................. 99

6.4.2 Concrete damaged plasticity model ............................................................... 99

6.5 Mesh sensitivity .................................................................................................. 114

6.6 Numerical results ................................................................................................ 116

6.6.1 Fully bonded model ..................................................................................... 116

Table of Contents

xiii

6.6.2 Debonding model ......................................................................................... 117

6.7 Summary ............................................................................................................. 122

Chapter 7 Hybrid GFRP-Concrete Beam Subject to Low-Velocity Impacts:

Experimental Study ....................................................................................................... 124

7.1 Introduction ......................................................................................................... 124

7.2 Specimen preparation .......................................................................................... 125

7.2.1 Description of the hybrid beam .................................................................... 125

7.2.2 Concrete mix composition ........................................................................... 126

7.2.3 Slump test ..................................................................................................... 126

7.2.4 Casting of the hybrid beams ......................................................................... 127

7.2.5 Curing of the hybrid beams .......................................................................... 128

7.2.6 Cylinder tests ................................................................................................ 128

7.3 Test procedures and setup ................................................................................... 131

7.3.1 Test procedures ............................................................................................ 131

7.3.2 Test instrumentation ..................................................................................... 133

7.3.3 Test setup ..................................................................................................... 134

7.4 Experimental results and discussion of the weak axis tests ................................ 136

7.4.1 Failure modes ............................................................................................... 136

7.4.2 Load-time response ...................................................................................... 138

7.4.3 Midspan displacement-time response .......................................................... 140

7.4.4 Impact performance ..................................................................................... 141

7.5 Strong axis tests .................................................................................................. 142

7.5.1 Failure modes ............................................................................................... 142



7.5.4 Impact performance ..................................................................................... 146

7.6 Summary ............................................................................................................. 147

Table of Contents

xiv

Chapter 8 Hybrid GFRP-Concrete Beam Subject to Low-Velocity Impacts: Numerical

Study ............................................................................................................................. 149

8.1 Introduction ......................................................................................................... 149

8.2 Finite element model ........................................................................................... 150

8.2.1 Description of the numerical models ........................................................... 150

8.2.2 Material models ............................................................................................ 151

8.3 Numerical results for the strong axis tests .......................................................... 153



8.3.3 Failure modes ............................................................................................... 156

8.4 Numerical results for the weak axis tests ............................................................ 161



8.4.3 Failure modes ............................................................................................... 163

8.5 Damage sequence analysis .................................................................................. 167

8.6 Comparison studies ............................................................................................. 170

8.6.1 Numerical results of original size beam ....................................................... 171

8.6.2 Numerical results of life-size rail sleepers ................................................... 175

8.7 Summary ............................................................................................................. 178

Chapter 9 Conclusion and Recommendations for Future Work ................................... 180

9.1 Concluding remarks ............................................................................................ 180

9.2 Recommendations for future work ..................................................................... 183

References ..................................................................................................................... 186

List of Figures

xv

List of Figures

Figure 1.1 Different types of hybrid beams (a:

http://www.archiproducts.com/en/products/manni-sipre/mixed-steel-concrete-beam-

and-column-composite-beams_90969; b: Winter et al. (2012); c:Correia et al. (2009)) .. 2

Figure 2.1 Timber sleepers (http://www.railroad-fasteners.com/railway-sleepers.html) . 7

Figure 2.2 Concrete sleepers (http://www.dayaengineering.com/concrete-sleepers-

mono-blocks-2838238.html) ............................................................................................. 8

Figure 2.3 Steel sleepers (a: https://www.coldforge.com.au; b: http://www.peiner-

traeger.de/en/products/product-range.html) ...................................................................... 9

Figure 2.4 Biological failure of timber (By Lamiot - Own work, CC BY-SA 3.0,

https://commons.wikimedia.org/w/index.php?curid=22029957) ................................... 12

Figure 2.5 End splitting of timber sleeper (Ferdous and Manalo, 2014) ........................ 12

Figure 2.6 Effect of sulfate attack (Béton, 1992) ............................................................ 13

Figure 2.7 Effect of alkali silica reactions (Béton, 1992) ............................................... 15

Figure 2.8 Pultrusion process (http://fibrolux.com/main/knowledge/pultrusion/) .......... 19

Figure 3.1 Impact test setup of Wang et al. (1996) ......................................................... 25

Figure 3.2 Impact test setup by Kishi et al. (2002) ......................................................... 26

Figure 3.3 Impact test setup by Fujikake et al. (2009) .................................................... 26

Figure 3.4 Experimental setup by Tachibana et al. (2010) ............................................. 27

Figure 3.5 Experimental setup of Bhatti and Kishi (2010) ............................................. 27

Figure 3.6 Failure modes of Kishi et al. (2002) .............................................................. 29

Figure 3.7 Failure modes of Fujikake et al. (2009) ......................................................... 30

Figure 3.8 Failure modes of Bhatti et al. (2009) ............................................................. 31

List of Figures

xvi

Figure 3.9 Failure modes of Kishi and Bhatti (2010) ..................................................... 32

Figure 3.10 Contact-impact problem of a concrete beam ............................................... 34

Figure 3.11 Impact device (ASTM-D7136, 2012) .......................................................... 37

Figure 3.12 Transverse view of a damage induced 0/90/0 composite plate (Richardson

and Wisheart, 1996) ........................................................................................................ 44

Figure 3.13 Schematic diagram of a matrix crack due to the stress distribution

(Richardson and Wisheart, 1996) .................................................................................... 44

Figure 3.14 Delamination area of a [0/90]s composite plate ........................................... 46

Figure 4.1 Specimen preparation for microscopic examination (a: cylindrical moulds; b:

Struers Tegramin-25 grinding and polishing machine) .................................................. 52

Figure 4.2 ZEISS Axio Imager M2m optical microscope .............................................. 53

Figure 4.3 Microscopic views of pultruded GFRP composites ...................................... 54

Figure 4.4 Test setup ....................................................................................................... 57

Figure 4.5 Impact support fixture.................................................................................... 58

Figure 4.6 Impact force-time curves of four impact energy levels ................................. 60

Figure 4.7 Central deflection-time of four impact energy levels .................................... 61

Figure 4.8 Snapshots of specimen LD3 during the impact test....................................... 62

Figure 4.9 Force-displacement curves of four energy levels .......................................... 64

Figure 4.10 Relationship of maximum load/impact energy and maximum

deflection/impact energy ................................................................................................. 65

Figure 4.11 Comparison of top surfaces for four energy levels ...................................... 67

Figure 4.12 Comparison of bottom surfaces for four energy levels ............................... 67

Figure 4.13 Relationship of damage area in back surface/impact energy....................... 68

Figure 4.14 Load-time curves of three ascending impactor mass ................................... 69

Figure 4.15 Central deflection-time curves of three ascending impactor mass .............. 70

List of Figures

xvii

Figure 4.16 Load-displacement curves of three ascending impactor mass ..................... 71

Figure 5.1 Assembled FEM with boundary conditions .................................................. 76

Figure 5.2 Typical relationship between equivalent stress and displacement ................ 81

Figure 5.3 Schematic diagram of experimental test and numerical simulation in progress

......................................................................................................................................... 86

Figure 5.4 Comparison between numerical and experimental results for force-time at all

impact energies................................................................................................................ 87

Figure 5.5 Comparison of numerical and experimental results for central deflection

versus time curves at all impact energies ........................................................................ 89

Figure 5.6 Comparison of maximum load and central deflection between numerical and

experiment results ........................................................................................................... 89

Figure 5.7 Schematic diagrams of von Mises stress propagation in top layer ................ 91

Figure 5.8 Schematic diagrams of von Mises stress propagation in bottom layer .......... 91

Figure 5.9 Schematic diagrams of Minimum in-plane principal stress propagation in top

layer ................................................................................................................................. 92

Figure 5.10 Schematic diagrams of Maximum in-plane principal stress propagation in

bottom layer .................................................................................................................... 92

Figure 5.11 Schematic diagrams of Tresca stress propagation in top layer .................... 93

Figure 5.12 Schematic diagrams of Tresca stress propagation in bottom layer.............. 93

Figure 5.13 The comparison of experimental and numerical results .............................. 94

Figure 6.1 Schematic diagram of the experimental setup (Ferdous et al., 2013) ............ 97

Figure 6.2 Assembled FEM for the hybrid GFRP-concrete beams ................................ 98

Figure 6.3 Yield surface in plane stress (ABAQUS, 2014) .......................................... 102

Figure 6.4 A typical stress-strain relationship for compressive and tensile behaviour in

CDPM (ABAQUS, 2014) ............................................................................................. 107

List of Figures

xviii

Figure 6.5 Compressive stress-strain curve .................................................................. 111

Figure 6.6 Tensile stress-displacement curve ............................................................... 113

Figure 6.7 Numerical models with different mesh sizes ............................................... 114

Figure 6.8 Computational time (Intel Core i7-3770 @ 3.40GHz) ................................ 115

Figure 6.9 Mesh sensitivity – Failure load .................................................................... 115

Figure 6.10 Comparison between numerical and experimental results for load-

displacement curves (Fully bonded model) .................................................................. 116

Figure 6.11 Typical relationship between traction and separation (ABAQUS, 2014) . 117


displacement curves (Debonding model) ...................................................................... 120

Figure 6.13 Hashin’s fiber tensile damage view on the bottom side ............................ 121

Figure 6.14 Debonding failure occurring at the bottom side of the interface ............... 121

Figure 6.15 Concrete cracks development .................................................................... 122

Figure 7.1 The cross-sectional dimension of hybrid beam and the microscope view of

the composites ............................................................................................................... 125

Figure 7.2 Concrete slump test ..................................................................................... 127

Figure 7.3 Casting of the hybrid beams ........................................................................ 127

Figure 7.4 Curing of the hybrid beams ......................................................................... 128

Figure 7.5 Cylinders in grinding machine .................................................................... 129

Figure 7.6 Cylinder tests (a: compressive test; b: elastic modulus test; c: indirect tensile

test) ................................................................................................................................ 130

Figure 7.7 High capacity drop-weight impact machine in University of Wollongong . 132

Figure 7.8 High-speed camera ...................................................................................... 133

Figure 7.9 Dynamic loading cell (http://www.interfaceforce.com) .............................. 134

Figure 7.10 Schematic diagram of the experimental setup ........................................... 135

List of Figures

xix

Figure 7.11 Support conditions of the impact tests ....................................................... 135

Figure 7.12 Failure modes at the time of ultimate failure ............................................. 136

Figure 7.13 End slipping of the concrete ...................................................................... 137

Figure 7.14 Shear cracks formed on the contacting surfaces of the profiles ................ 137

Figure 7.15 Loading history for 300 mm dropping height ........................................... 139



Figure 7.18 Midspan displacement curves of three ascending impact energy levels ... 141

Figure 7.19 Failure modes at the time of ultimate failure ............................................. 143

Figure 7.20 Loading histories for the strong axis tests ................................................. 145

Figure 7.21 Midspan displacement curves for strong axis ............................................ 146

Figure 8.1 Assembled FEM with boundary conditions for strong axis tests ................ 151

Figure 8.2 Assembled FEM with boundary conditions for weak axis tests .................. 151

Figure 8.3 Compressive stress-strain relationship curve............................................... 152

Figure 8.4 Tensile stress-strain relationship curve ........................................................ 152

Figure 8.5 Comparison of loading histories for strong axis testing groups .................. 154

Figure 8.6 Comparison of midspan displacement-time curves for strong axis ............. 155

Figure 8.7 Minor flexural cracks formed in the concrete at 1 ms ................................. 156

Figure 8.8 Flexural cracks formed in the concrete at 2 ms ........................................... 157

Figure 8.9 Global flexural cracks formed across the beam ........................................... 157

Figure 8.10 Initial flexural cracks of the concrete at the bottom of the beam .............. 158

Figure 8.11 Local shear plug formed downwards to the bottom surface ...................... 158

Figure 8.12 Global flexural response of the hybrid beam ............................................. 159

Figure 8.13 Vertical flexural cracks formed at supports ............................................... 159

Figure 8.14 Shear cracks formed at the ultimate failure ............................................... 160

List of Figures

xx

Figure 8.15 Schematic diagram of experimental and numerical observations after test

....................................................................................................................................... 160

Figure 8.16 Comparison of loading histories for weak axis tests ................................. 162

Figure 8.17 Comparison of experimental and numerical results for displacement-time

curves ............................................................................................................................ 163

Figure 8.18 Minor cracks formed in the concrete at the centre of the beam................. 164

Figure 8.19 Local shear plug formed in the early dynamic resistance stage ................ 164

Figure 8.20 Global flexural cracks for the weak axis tests ........................................... 165

Figure 8.21 Vertical flexural cracks formed at supports ............................................... 165

Figure 8.22 Shear cracks formed at the ultimate failure for weak axis tests ................ 166

Figure 8.23 A representation of numerical model after the impact loading ................. 166

Figure 8.24 Damage sequence analysis ........................................................................ 169

Figure 8.25 Test setup of Kaewunruen and Remennikov (2009b) ............................... 170

Figure 8.26 Numerical setup of the impact events ........................................................ 171

Figure 8.27 load-time response due to 100 mm drop height......................................... 172

Figure 8.28 Load-time response due to 500 mm drop height ....................................... 172

Figure 8.29 Failure modes due to 100 mm drop height ................................................ 173

Figure 8.30 Failure modes due to 500 mm drop height ................................................ 174

Figure 8.31 Numerical setup of the parametric study ................................................... 175

Figure 8.32 Load-time response of 100 mm drop height for the life-size beam ........... 176

Figure 8.33 Load-time response of 500 mm drop height for the life-size beam ........... 176

Figure 8.34 Failure modes of large size beam due to 100 mm drop height .................. 177

Figure 8.35 Failure modes of large size beam due to 500 mm drop height .................. 178

List of Tables

xxi

List of Tables

Table 4.1 Mechanical properties of the pultruded GFRP composites (Li et al., 2017a) . 54

Table 4.2 Details of test specimens ................................................................................. 55

Table 4.3 Testing results summary ................................................................................. 65

Table 4.4 Testing results summary ................................................................................. 72

Table 5.1 Damage stabilization parameters for pultruded GFRP composites ................ 85

Table 5.2 Material properties of pultruded GFRP composites ....................................... 85

Table 5.3 Damage initiation parameters of pultruded GFRP composites ....................... 85

Table 5.4 Damage evolution parameters for pultruded GFRP composites ..................... 86

Table 6.1 Properties of high performance concrete (Ferdous, 2012) ............................ 108

Table 6.2 Comparison results for different meshes ...................................................... 114

Table 7.1 Mix ingredients for concrete ......................................................................... 126

Table 7.2 Measurement of cylinders after grinding: ..................................................... 129

Table 7.3 Testing results of cylinders: .......................................................................... 131

Table 7.4 Testing results summary ............................................................................... 142

Table 7.5 Testing results summary ............................................................................... 147

Table 8.1 Impact performance of the hybrid beam and prestressed concrete sleepers

(Kaewunruen and Remennikov, 2009b) ....................................................................... 174

Table 8.2 Impact performance of the large size hybrid beam and prestressed concrete

sleepers (Kaewunruen and Remennikov, 2009b).......................................................... 178

Abbreviation

xxii

Abbreviation

AFRP Aramid Fibers Reinforced Polymers

ASTM American Society for Testing and Materials

C3D8R Linear eight-node three-dimensional solid elements with reduced

integration

CDPM Concrete Damaged Plasticity Model

CFRP Carbon Fibers Reinforced Polymers

FEA Finite Element Analysis

FEM Finite Element Model

FRP Fiber Reinforced Polymers

GFRP Glass Fibers Reinforced Polymers

GP General Purpose

OPC Ordinary Portland cement Concrete

R3D4 Four-node three-dimensional discrete rigid elements

RC Reinforced Concrete

SC8R Eight-node quadrilateral in-plane general-purpose continuum shell

elements

List of Symbols

xxiii

List of Symbols

| | absolute value

⟨ ⟩ Macaulay bracket operator

𝑏𝑏 width of concrete

𝑏𝑏𝑓𝑓 width of GFRP composites

𝐶𝐶𝑑𝑑 damaged elasticity matrix

𝐶𝐶𝐸𝐸 specified ratio of impact energy to specimen thickness

C1 a constant value of 3

C2 a constant value of 6.93

𝑑𝑑 calculated damage variable

𝑑𝑑𝑐𝑐 scalar damage variable in compression

𝑑𝑑𝑓𝑓 internal fiber damage variable

𝑑𝑑𝑓𝑓𝑐𝑐 damage variable in fiber compression failure

𝑑𝑑𝑓𝑓𝑡𝑡 damage variable in fiber tension failure

𝑑𝑑𝑖𝑖 diameter of impactor

𝑑𝑑𝑚𝑚 internal matrix damage variable

dmax maximum aggregate size in mm

𝑑𝑑𝑚𝑚𝑐𝑐 damage variable in matrix compression failure

𝑑𝑑𝑚𝑚𝑡𝑡 damage variable in matrix tension failure

𝑑𝑑𝑠𝑠 internal shear damage variable

𝑑𝑑𝑡𝑡 scalar damage variable in tension

𝑑𝑑𝑣𝑣 regularised damage variable

List of Symbols

xxiv

𝑑𝑑�̇�𝑣 true value of the damage variable in the viscous system

𝑑𝑑′ degradation variables

dγvp volumetric shear strain rate

dεvp volumetric strain rate

𝐷𝐷 central deflection

𝐷𝐷𝑒𝑒 damaged elastic stiffness

𝐷𝐷𝑜𝑜𝑒𝑒 undamaged elastic stiffness

𝐸𝐸 potential energy of impactor prior to drop

𝐸𝐸𝑎𝑎𝑎𝑎𝑠𝑠𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒𝑑𝑑 absorbed energy

𝐸𝐸𝑐𝑐 Young’s modulus

𝐸𝐸𝐷𝐷 absorbed energy at the point of delamination failure

𝐸𝐸𝑓𝑓 flexural modulus

𝐸𝐸𝑓𝑓′ absorbed energy at the point of fiber failure

𝐸𝐸𝑖𝑖 initial modulus of elasticity

𝐸𝐸𝑖𝑖𝑡𝑡 initial tangent modulus

𝐸𝐸𝑘𝑘𝑖𝑖𝑘𝑘𝑒𝑒𝑡𝑡𝑖𝑖𝑐𝑐 kinetic energy

𝐸𝐸𝑝𝑝 absorbed energy at the point of penetration failure

𝐸𝐸𝑡𝑡𝑜𝑜𝑡𝑡𝑎𝑎𝑡𝑡 initial energy

𝐸𝐸1 Young’s modulus in longitudinal direction

𝐸𝐸2 Young’s modulus in transverse direction

𝑓𝑓𝑐𝑐 compressive stress

𝑓𝑓𝑐𝑐𝑡𝑡𝑚𝑚 the average concrete tensile strength

𝑓𝑓𝑐𝑐′ maximum compressive strength

ft tensile stress

List of Symbols

xxv

𝑓𝑓𝑡𝑡′ maximum tensile strength

𝐹𝐹 damage initiation factor

𝐹𝐹′ yield surface

𝐹𝐹(𝐷𝐷) the force curve (function of deformation)

𝐹𝐹(𝑡𝑡) force acquired by the data acquisition system

𝑔𝑔 gravitational acceleration constant

𝐺𝐺 shear modulus

𝐺𝐺′ plastic potential flow

𝐺𝐺𝐶𝐶 fracture energy

Gf tensile fracture energy

ℎ nominal thickness of the specimen

𝐼𝐼 identity matrix

𝑘𝑘 fitting constant

𝑘𝑘𝑘𝑘𝑘𝑘 stiffness in normal direction

𝑘𝑘𝑠𝑠𝑠𝑠 stiffness in shear direction

𝑘𝑘𝑡𝑡𝑡𝑡 stiffness in through-thickness direction

𝑘𝑘1′ material factor for high strength concrete

𝑘𝑘2′ fitting factor for high strength concrete

𝐾𝐾 bond stiffness matrix

𝐾𝐾𝑐𝑐 the ratio of tensile to compressive meridian stress

𝐿𝐿 unsupported length

𝐿𝐿𝐶𝐶 characteristic length

𝑀𝑀 damage operator

𝑀𝑀𝑎𝑎 maximum value between 0.33 and the ratio of bf/b

List of Symbols

xxvi

𝑀𝑀′ total weight

𝑛𝑛 curve fitting factor

�̅�𝑝 effective hydrostatic pressure

𝑞𝑞𝐶𝐶𝐶𝐶 second stress invariant on the compressive meridian

𝑞𝑞𝑇𝑇𝐶𝐶 second stress invariant on the tensile meridian

𝑞𝑞� effective Mises equivalent stress

𝑟𝑟 weight factor

𝑠𝑠𝑚𝑚 slip under the maximum shear stress

𝑆𝑆𝐿𝐿 shear strength in longitudinal direction

𝑆𝑆𝑇𝑇 shear strength in transverse direction

𝑆𝑆̅ effective stress deviator

𝑡𝑡 time

𝑡𝑡′ specimen thickness

𝑡𝑡𝑘𝑘 nominal traction in the normal direction

𝑡𝑡𝑠𝑠 nominal in-plane shear stress

𝑡𝑡𝑡𝑡 nominal out-plane shear stress

𝑇𝑇 traction stress

𝑤𝑤 width

𝑋𝑋𝐶𝐶 compressive strength in longitudinal direction

𝑋𝑋𝑇𝑇 tensile strength in longitudinal direction

𝑌𝑌𝐶𝐶 compressive strength in transverse direction

𝑌𝑌𝑇𝑇 tensile strength in transverse direction

𝛼𝛼 coefficient that presents the ratio of the shear stress to tension

𝛼𝛼′ dimensionless constant

List of Symbols

xxvii

𝛽𝛽 material parameter that depends on the shape of the stress-strain

diagram

𝛽𝛽′ dimension coefficient

𝛾𝛾 dimensionless material constant

𝛾𝛾𝑓𝑓 fracture energy

𝛿𝛿 displacement of the contacting surfaces

𝛿𝛿𝑒𝑒𝑒𝑒 current state equivalent displacement

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓 equivalent displacement at which the composite material is fully

damaged

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑐𝑐 current equivalent displacement in the post fiber compression

failure

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑡𝑡 current equivalent displacement in the post fiber tension failure

𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑐𝑐 current equivalent displacement in the post matrix compression

failure

𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑡𝑡 current equivalent displacement in the post matrix tension failure

𝛿𝛿𝑒𝑒𝑒𝑒0 initial equivalent displacement at the point of damage initiated

𝛿𝛿𝑘𝑘 displacement in normal direction

𝛿𝛿𝑠𝑠 displacement in shear direction

𝛿𝛿𝑡𝑡 displacement in through-thickness direction

𝜀𝜀 current strain

𝜀𝜀𝑐𝑐 strain in compression

𝜀𝜀𝑐𝑐′ strain when the compressive strength reaches the maximum value

𝜀𝜀�̃�𝑐𝑝𝑝 equivalent plastic strain in compression

𝜀𝜀�̃�𝑚𝑎𝑎𝑚𝑚𝑝𝑝 maximum eigenvalue of the plastic strain

List of Symbols

xxviii

𝜀𝜀�̃�𝑚𝑖𝑖𝑘𝑘𝑝𝑝 minimum eigenvalue of the plastic strain

𝜀𝜀�̃�𝑡𝑝𝑝 equivalent plastic strain in tension

𝜀𝜀11 principal strain in longitudinal direction

𝜀𝜀12 principal shear strain

𝜀𝜀22 principal strain in transverse direction

𝜀𝜀𝑒𝑒 elastic strain

𝜀𝜀𝑖𝑖𝑘𝑘 inelastic strain

𝜀𝜀𝑝𝑝 plastic strain

𝜀𝜀̇𝑝𝑝 plastic strain increment

𝜀𝜀𝑡𝑡 total strain

𝜂𝜂 viscosity coefficient controlling the rate of relaxation time

�̇�𝜆 proportionality coefficient

𝑣𝑣12 Poisson’s ratio in longitudinal direction

𝑣𝑣21 Poisson’s ratio in transverse direction

𝜋𝜋 mathematical constant

𝜎𝜎 true normal or shear stress

𝜎𝜎� effective stress in the damaged material model

𝜎𝜎�� effective stress tensor

𝜎𝜎′ stress in the concrete elements

𝜎𝜎𝑎𝑎0 initial equibiaxial compressive yield stress

𝜎𝜎𝑐𝑐 current compressive stress

𝜎𝜎𝑐𝑐0 initial uniaxial compressive yield stress

𝜎𝜎�𝑐𝑐 effective uniaxial stress in compression

𝜎𝜎�𝑐𝑐(𝜀𝜀�̃�𝑐𝑝𝑝) effective compressive cohesion

List of Symbols

xxix

𝜎𝜎𝑒𝑒𝑒𝑒𝑓𝑓𝑐𝑐 current equivalent stress in the post fiber compression failure

𝜎𝜎𝑒𝑒𝑒𝑒𝑓𝑓𝑡𝑡 current equivalent stress in the post fiber tension failure

𝜎𝜎𝑒𝑒𝑒𝑒𝑚𝑚𝑐𝑐 current equivalent stress in the post matrix compression failure

𝜎𝜎𝑒𝑒𝑒𝑒𝑚𝑚𝑡𝑡 current equivalent stress in the post matrix tension failure

𝜎𝜎𝑓𝑓 flexural strength

𝜎𝜎��𝑖𝑖 principal stress

𝜎𝜎��𝑚𝑚𝑎𝑎𝑚𝑚 maximum effective principal stress

𝜎𝜎𝑡𝑡 current tensile stress

𝜎𝜎�𝑡𝑡 effective uniaxial stress in tension

σt0 uniaxial tensile stress at failure

𝜎𝜎�𝑡𝑡(𝜀𝜀�̃�𝑡𝑝𝑝) effective tensile cohesion

𝜎𝜎11� effective normal stress in longitudinal direction

𝜎𝜎22� effective normal stress in transverse direction

𝜏𝜏 interlaminar shear strength (ILSS)

𝜏𝜏′ shear stress

𝜏𝜏𝑚𝑚 maximum shear stress

𝜏𝜏12 tangential strain

𝜏𝜏12� effective shear stress

Ψ dilation angle

ω crack opening displacement

ωc crack opening displacement at the complete release of stress

ϵ eccentricity parameter

Chapter 1

Introduction

1.1 Background

The combination of two or more materials into a hybrid structural system is

becoming increasingly important in the construction industry. The optimal combination

of these materials can utilise the demand characteristics of each one of them in the place

where they perform best. This results in an optimised structural system that performs to

the best of its abilities and achieves the criteria it was designed for.

The most commonly used materials are timber, steel, fiber reinforced polymers

(FRP), and concrete. Figure 1.1 shows some examples of hybrid structures. These hybrid

structures typically consist of a combination of the mentioned common materials chosen

for their inherent qualities such as strength, durability, cost, aesthetic, and so on. They are

chosen to provide simple, buildable and competitive high-quality structures that offer

consistent performance. It is not surprising, therefore, that hybrid structures constitute the

current trend in construction. Indeed, combining materials is essential to achieve

performance targets such as durability, sustainability, a lower carbon footprint, seismic

resistance, and architectural appeal, just to cite a few; in other words, to achieve a

performance based design, which is the current approach in modern design and

construction.

Chapter 1 - Introduction

2

Figure 1.1 Different types of hybrid beams (a:

http://www.archiproducts.com/en/products/manni-sipre/mixed-steel-concrete-beam-

and-column-composite-beams_90969; b: Winter et al. (2012); c:Correia et al. (2009))

Depending on the prescribed performance targets, different hybrid structural

systems have been proposed in the literature. Seismic resistance, sustainability, rapid

construction, and a low carbon footprint can be achieved by combining timber with other

materials. It is the approach favoured in Japan and New Zealand (Sakamoto et al., 2001,

Buchanan et al., 2008). Timber is not only very light but also serves as a carbon sink,

while steel, for example, ensures dissipation of energy through ductility, which can be

found commonly in hybrid steel-concrete structures or hybrid steel-FRP composite

structures (Tavakkolizadeh and Saadatmanesh, 2003, Nie et al., 2004, Teng et al., 2007,

Zhao and Zhang, 2007, Teng et al., 2012, Feng et al., 2015, Satasivam and Bai, 2016).

However, the real drives behind the development of hybrid structures are by far the

technical progress achieved in composites materials and the deteriorating world

infrastructure. Composites materials offer many advantages such as low weight, excellent

durability, impact resistance, high strength to weight ratio, and design flexibility. The

latter makes them particularly suitable to be combined with each other (Harris et al., 1998,


3

Hejll et al., 2005, Hai et al., 2010) or with other materials when designing hybrid

structures for durability (Van Erp et al., 2002, Keller et al., 2007, Correia et al., 2007b,

Sá et al., 2016).

The present study focusses on the design of hybrid beam consisting of a rectangular

hollow pultruded glass fiber reinforced polymer (GFRP) composites filled with concrete.

The aim is to study its suitability as a railway sleeper or as bridge girder by studying its

dynamic behaviour under low-velocity impact. The combination of concrete and

pultruded GFRP composites in a hybrid beam can utilise the desired properties of each

material in a more efficient way. The pultruded GFRP composites with larger strength

(tensile in particular) are placed further to the neutral axis and the GFRP composites in

compression is restrained by the concrete core (therefore preventing lateral buckling).

Moreover, the hollow pultruded GFRP composites box protects the concrete block inside

from suffering chemical attacks, while the concrete provides the system with bulk size,

strength and structural stability. Concrete has been shown to offer excellent mechanical

performance when combined with FRP in a hybrid beam (Deskovic et al., 1995, Canning

et al., 1999, Hulatt et al., 2003, Khennane, 2009, Chakrabortty et al., 2011, Ferdous et al.,

2015). In addition, pultruded GFRP profiles offer a distinct advantage in that they are

economically affordable for construction applications (Zureick and Scott, 1997, Li et al.,

2017a). As a result, they are being used in many infrastructure applications (Bank and

Gentry, 2001, Williams et al., 2003, Neely et al., 2004, Lee et al., 2007, Liu et al., 2008,

Chakrabortty et al., 2011, Ferdous et al., 2015).

Ferdous (2012) performed a series of four-point bending static tests to investigate

the static flexural behaviour of the hybrid pultruded GFRP composites-concrete beam.

The results revealed that this hybrid beam has the potential to be used as railway sleeper


4

(Ferdous et al., 2015) or girder in short span bridges. However, the dynamic performance

of the hybrid beam has yet to be assessed. The current standard of design of railway

sleepers only focus on the results from the static and quasi-static tests, no design codes

based on the impact scenarios were specified (Standards, 2003a). As summarized by

Murray and Cai (1998), the major cause of the damage to the railway sleepers is the

infrequent but high magnitude impact loads. When the proposed hybrid beam is used as

railway sleeper, it could be subjected to low-velocity impact or cyclic low-velocity impact

loading caused by the imperfections of wheel and rail or the wheel-track interactions

(Kumaran et al., 2003, Kaewunruen and Remennikov, 2009a). The magnitude of these

impact loads could be over 400 kN per railseat with the duration last from 1 to 10 ms

(Kaewunruen and Remennikov, 2009b). On the other hand, if this hybrid beam is to be

used as bridge girder, it could be subjected to accidental low-velocity impact loads caused

by traffic accidents or flood-induced impacts (Kim et al., 2008, Prasad and Banerjee,

2013). Most design codes and standards for the bridge girder use different values (impact

factor) to transfer the impact loads as additional static loads. For example, AASHTO (the

American Association of State Highway and Transportation Officials) specify the value

of impact factor as a function of the span length (Aashto, 1998), in NAASRA (National

Association of Australian State Road Authorities) and Canadian Highway bridge design

codes (Specification.NAASRA, 1976, Canadian.Standards.Association, 2006), the

impact factor values are expressed as the function of the flexural frequency of the bridge.

The design codes with considering the accidental impact loads have not been established

yet in any of above standards. So far, very limited research has been done to investigate

the impact response of the hybrid GFRP-concrete beam as a railway sleeper or bridge

girder. The knowledge of the failure mechanisms and failure modes of the hybrid GFRP-

concrete beam and the interaction between the pultruded GFRP composites and the


5

concrete under impact loading is limited. Hence, the aim of this research is to investigate

the impact performance of the hybrid GFRP-concrete beam, to detect the failure modes

and understand the failure mechanisms of the hybrid beam subjected to low-velocity

impacts.

1.2 Objective of research

The aim of this research is to investigate the impact behaviour of a hybrid pultruded

GFRP composites-concrete beam subjected to low-velocity impact loading. To achieve

this research goal, multiple experimental and numerical investigations were conducted.

The scope of this research is listed as follows:

• To investigate the impact behaviour of pultruded GFRP composites subjected to

low-velocity impact loading by using the drop tower testing machine;

• To investigate the effects of impact energy levels and impactor weights to the

dynamic performance of pultruded GFRP composites;

• To develop a numerical model using finite element to analyse the propagation of

a stress wave;

• Conduct experimental investigations to study the impact behaviour of hybrid

GFRP-concrete beam subjected to low-velocity impacts by using the high

capacity drop weight machine; and

• To simulate the behaviour of the hybrid beam during impact and understand the

details of the recorded failure mechanisms.


6

1.3 Organisation of thesis

The content of this thesis is presented in nine chapters. The present chapter provides

an introduction stating the significance and layout of this research.

Chapter 2 reviews the existing materials used for railway sleepers and bridge

girders and their specific shortcomings. The mechanical properties of the pultruded GFRP

composites are also discussed.

Chapter 3 is devoted to the review of the failure mechanisms of concrete and FRP

composites subjected to low-velocity impacts. A critical review of the literature is

presented in order to identify the gaps in knowledge.

In Chapter 4, an experimental investigation into the impact behaviour of pultruded

GFRP composites subjected to low-velocity impact loading is presented. The effects of

impact energy levels and impactor weights are investigated. The results of impact

characteristics, impact performance and damage evaluation are discussed in detail.

Chapter 5 presents a numerical simulation of the behaviour of pultruded GFRP

composites subjected to low-velocity impacts. The obtained results are compared with

the experimental ones reported in Chapter 4. The mechanisms of the progressive damage

model are described in detail.

In Chapter 6, the validated FRP model from Chapter 5 is used with a suitable

concrete model to conduct a numerical investigation of the static behaviour of a hybrid

GFRP-concrete beam. The input parameters of the FRP model, such as damage initiation,

evolution parameters, and the fracture properties of the GFRP composites, obtained from

the preceding chapter are used to describe the pultruded composites. The mechanisms and

input parameters of the concrete model are described in detail. The numerical results are


7

compared with experimental data, and the verified model is used to present a reference

setup parameters for the experimental program of impact tests on hybrid beams.

Chapter 7 is devoted to the experimental investigation of the impact behaviour of

hybrid GFRP-concrete beam subjected to low-velocity impact loading. The impact

characteristics and performance are compared for different impact energy levels, and the

Experimentation alone does not reveal the failure modes of the concrete hidden

inside the pultruded profile. Details such as the cracking pattern of the concrete and the

damage sequences of the hybrid beam can only be understood through numerical analysis.

For this purpose, numerical models of hybrid GFRP-concrete beams subjected to low-

velocity impact loading are developed in Chapter 8. The numerical results are compared

with the experimental ones. The verified model is used to understand the details of the

failure mechanisms during the impact events.

Finally, Chapter 9 presents the concluding remarks of this research together with

some recommendations for future work.

Chapter 2

Review of Types of Railway Sleepers and

Bridge Girders

2.1 Introduction

In this chapter, different types of materials used in the manufacture of railway

sleepers and bridge girders and their respective shortcomings are discussed. Also included

is the review of pultruded GFRP composite materials and the advantages of the proposed

hybrid GFRP-concrete beam. This review will help in identifying the issues with the

existing materials and expanding on the advantages of the combination of pultruded

GFRP composites and concrete.

2.2 Types of railway sleepers

Railway sleepers are one major component amongst a railway track system. They

are transverse beams laid in ballast to provide supports for the rails. The key functions of

sleepers are to uniformly transfer loads to the ballast bed, to keep the rails in position and

hold the rails at the correct gauge (Kaewunruen and Remennikov, 2008).

So far, more than 2.5 billion railway sleepers have been installed in the world

(Manalo et al., 2010). Among the large number of railway sleepers, the majority are made

from timber, followed by concrete and steel. The specific characteristics of each type of

railway sleepers are discussed in the following sections.

Chapter 2 - Review of Types of Railway Sleepers and Bridge Girders

7

2.2.1 Timber sleepers

Timber sleepers have been used for centuries in the railway industry. Even today,

the majority of railway sleepers are made from timber. Timber sleepers are normally

made from hardwood, such as oak wood and jarrah wood. For some less heavy traffic

routes, treated softwood, like pinewood and Douglas fir wood, have been applied for

sleepers (Hay, 1982). The main advantages of timber sleepers are their affordability,

workability and adaptability. Timber sleepers are relatively cheaper to produce than other

types of sleepers (Mitchell et al., 1987). Timber is available in most parts of the world

and the manufacture technology and labour costs are comparatively low. Moreover,

timber is lighter than other types of materials used for sleepers. It is easy to handle and

install in the railway system. In addition, timber sleepers can be applied in most of railway

environments (Manalo et al., 2010).

Figure 2.1 Timber sleepers (http://www.railroad-fasteners.com/railway-sleepers.html)

http://www.railroad-fasteners.com/railway-sleepers.html


8

2.2.2 Concrete sleepers

Currently, concrete sleepers are commonly used in modern high-speed railway

track lines. In general, the production process of concrete sleepers is similar to that of

reinforced concrete beams. The sleepers are composed of concrete blocks with steel

reinforcements installed internally (Kaewunruen, 2007). Compared to timber sleepers,

concrete sleepers are more durable and stable, and require less maintenance (Manalo et

al., 2010). Unlike timber, concrete is not sensitive to the change of environment. Concrete

sleepers are immune to insect infestation and have a much better fire resistance to keep

themselves withstand fire hazards than timber sleepers. Furthermore, concrete sleepers

are much heavier than timber sleepers; their great weight can maintain themselves in the

correct position and improve the stability of the track system during the service (Manalo

et al., 2010).

Figure 2.2 Concrete sleepers (http://www.dayaengineering.com/concrete-sleepers-

mono-blocks-2838238.html)

http://www.dayaengineering.com/concrete-sleepers-mono-blocks-2838238.html

http://www.dayaengineering.com/concrete-sleepers-mono-blocks-2838238.html


9

2.2.3 Steel sleepers

Steel sleepers have been applied increasingly in low-speed railway lines. Currently,

over 13% of railway sleepers are made from steel in Australia (Manalo et al., 2010). There

are two types of steel sleepers in railway systems, as shown in Figure 2.3. Traditional

steel sleepers are trough-shaped pressed steel plates with spade-shaped ends on both

sides. Y shape steel sleepers include two adjacent steel sleepers, with I-shaped beam in

section, form into “Y” shape arrangement instead of parallel arrangement. The major

advantage of steel sleepers is their adaptability. Compared to other types of sleepers like

concrete sleepers, steel sleepers are lighter and easier to handle and install. In addition,

steel sleepers require much less ballast to support than concrete and timber sleepers do.

Figure 2.3 Steel sleepers (a: https://www.coldforge.com.au; b: http://www.peiner-

traeger.de/en/products/product-range.html)

https://www.coldforge.com.au/

http://www.peiner-traeger.de/en/products/product-range.html

http://www.peiner-traeger.de/en/products/product-range.html


10

2.3 Types of bridge girders

Girders are the main supports for the deck in a bridge. Generally, they are parallel-

aligned beams laid under the bridge deck. The major function of bridge girders is to

transfer the load from the deck to the bridge foundation. There are two common types of

girders used in bridge design, plate girders and box girders. The specific characteristics

of each type are discussed in the following sections.

2.3.1 Plate girders

In general, plate girders are I-shaped beams in cross-section. Two common types

of plate girders can be found in modern bridge design, concrete plate girders and steel

plate girders. Concrete plate girders are made of high strength concrete with steel or other

reinforcements, while for the steel plate girders, they are fabricated from structural steel

and welded together to form into the required shape (Hirol, 2008). The sections of plate

girders are not limited to a standard stipulation. The depth and dimensions of the sectional

design can be changed in respect to the changes of the applications. As a result, the plate

girders can be applied for both short and long spans. However, the I-shaped steel beams

are not able to provide sufficient torsion stiffness for some particular cases. To the address

of limited torsional stiffness, two common design preferences are used in modern bridge

design. One is the use of bracing systems and/or stringer beams, and the other is using

box girders structures.

2.3.2 Box girders

Box girders are rectangular (or trapezoidal) hollow box beams. They are normally

constructed of prestressed concrete, structural steel or the combination of reinforced

concrete and structural steel (Sennah and Kennedy, 2002). For concrete box girders, the

girders are normally cast in situ or precast in segments and are emplaced into a complete


11

set of structure. For steel box girders, the girders are usually fabricated off-site and are

assembled during the construction of the bridge. Compared to plate girders, box girders

can provide an excellent torsion performance. However, they are more difficult to

transport and erect due to their large dimensions.

2.4 Issues of the materials used in railway sleepers and

bridge girders

Despite the advantages mentioned in previous sections, some issues associated with

the materials could have detrimental effects on the performance and durability of the

structures.

2.4.1 Timber

The major problem in using timber for structural elements is that they are

susceptible to creep, biological and mechanical degradation, which can eventually lead to

the failure of the structure (Qiao et al., 1998).

Fungal decay and insect infestation are the two most common manifestations of

biological degradation in timber, as shown in Figure 2.4. To prevent biological attacks,

the majority of timber sleepers are soaked in chemical preservatives such as creosote

(Pruszinski, 1999). However, there is a growing concern about the use of chemical

preservatives in timber. As timber sleepers are gradually replaced, the discarded sleepers

constitute a threat to the environment and health, which should be treated as hazardous

waste (Thierfelder and Sandstrom, 2008).


12

Figure 2.4 Biological failure of timber (By Lamiot - Own work, CC BY-SA 3.0,

https://commons.wikimedia.org/w/index.php?curid=22029957)

End splitting is a major failure mode of mechanical degradation in timber, as shown

in Figure 2.5. The majority of end splitting failure of timber sleepers are caused by the

transverse shear loadings on the timber beams (Hibbeler, 2004).

Figure 2.5 End splitting of timber sleeper (Ferdous and Manalo, 2014)

https://commons.wikimedia.org/w/index.php?curid=22029957


13

2.4.2 Concrete

The durability of concrete, when exposed directly to the environment, is a major

concern in civil engineering applications. The deterioration of concrete, such as potholes,

cracking and spalling, may occur within 10 years or sooner if the concrete structures were

not properly designed and/or constructed (Foster et al., 2000). The two major causes of

deterioration of concrete are sulfate attack and alkali silica reactions (Fenwick and

Rotolone, 2003).

2.4.2.1 Sulfate attack

Concrete can deteriorate as the result of sulfate attack when it is exposed to the

sulfate sources from the environment. Sulfate attack is a destructive process in which the

expansive reaction products are formed inside the concrete. The expansive reaction

products can lead to cracks in the concrete, as shown in Figure 2.6 (Béton, 1992).

Figure 2.6 Effect of sulfate attack (Béton, 1992)


14

In general, sulfate attack can be categorised into two major sulfate reactions. The

first reaction is that the external sulfate ions (SH) penetrate the concrete and react with

the tricalcium aluminate (C3A) and its hydration products to form ettringite (C6AS3H32)

(Tian and Cohen, 2000). The sum of this reaction can be represented by:

𝑆𝑆𝑆𝑆 + 𝐶𝐶3𝐴𝐴 + 𝐶𝐶𝐶𝐶𝑆𝑆𝑂𝑂4 ∙ 2𝑆𝑆2𝑂𝑂 → 𝐶𝐶6𝐴𝐴𝑆𝑆3𝑆𝑆32

The second reaction is that the external sulfate ions penetrate the concrete and react

with the calcium hydroxide (CH) to form gypsum (CSH2). The formed gypsum reacts

with the tricalcium aluminate to form ettringite (Tian and Cohen, 2000). The mechanism

of the second reaction can be represented by:

𝑆𝑆𝑆𝑆 + 𝐶𝐶𝑆𝑆 → 𝐶𝐶𝑆𝑆𝑆𝑆2

𝐶𝐶3𝐴𝐴 + 3𝐶𝐶𝑆𝑆𝑆𝑆2 + 26𝑆𝑆 → 𝐶𝐶6𝐴𝐴𝑆𝑆3𝑆𝑆32

2.4.2.2 Alkali silica reactions

In contrast to sulfate attack, where the chemical reactions are acting on the

substance in the cement, alkali silica reactions occur only in the aggregates (Béton, 1992).

Alkali silica reactions are the swelling reactions occurring between the alkali solution or

paste and the reactive silica components in aggregates (Ichikawa and Miura, 2007). Alkali

silica reactions can cause spalling, and eventually lead to the failure of the concrete

structures. Figure 2.7 shows the effect of alkali silica reactions in concrete.


15

Figure 2.7 Effect of alkali silica reactions (Béton, 1992)

The mechanism of alkali silica reactions can be explained as follows: the alkalis

(NaOH or KOH) from the environment or within the pore system diffuse into the concrete

and react with the silica acid (H4SiO4) from the aggregates to form disodium dihydrogen

silicate hydrates (Na2H2SiO4) or dipotassium dihydrogen silicate hydrates (K2H2SiO4).

The formed products then react with calcium hydroxide (Ca(OH)2) to form the hydrated

calcium silicates (CaH2SiO4.2H2O) (Béton, 1992). During the reactions, the colloidal

sodium silicate can get swelling when absorbing the water from the environment, which

results in the cracking in the concrete. The sum of alkali silica reactions can be expressed

in the following chemical equations:

2𝑁𝑁𝐶𝐶(𝑂𝑂𝑆𝑆) + 𝑆𝑆4𝑆𝑆𝑆𝑆𝑂𝑂4 → 𝑁𝑁𝐶𝐶2𝑆𝑆2𝑆𝑆𝑆𝑆𝑂𝑂4 ∙ 2𝑆𝑆2𝑂𝑂

𝑁𝑁𝐶𝐶2𝑆𝑆2𝑆𝑆𝑆𝑆𝑂𝑂4 ∙ 2𝑆𝑆2𝑂𝑂 + 𝐶𝐶𝐶𝐶(𝑂𝑂𝑆𝑆)2 → 𝐶𝐶𝐶𝐶𝑆𝑆2𝑆𝑆𝑆𝑆𝑂𝑂4 ∙ 2𝑆𝑆2𝑂𝑂 + 2𝑁𝑁𝐶𝐶𝑂𝑂𝑆𝑆


16

Based on the results of the reactions, the presence of alkali hydroxides can be

considered as the catalyst. Thus, the mechanism of this reaction can be simplified as

follows:

𝐶𝐶𝐶𝐶(𝑂𝑂𝑆𝑆)2 + 𝑆𝑆4𝑆𝑆𝑆𝑆𝑂𝑂4 → 𝐶𝐶𝐶𝐶𝑆𝑆2𝑆𝑆𝑆𝑆𝑂𝑂4 ∙ 2𝑆𝑆2𝑂𝑂

2.4.3 Steel

The major concern in using steel for railway sleepers or bridge girders is that they

are susceptible to corrosion. The corrosion of steel is a destructive process in which the

expansive products are formed in the steel structures (Schweitzer, 2009). The corrosion

of steel cannot only lead to the financial cost of repairment or replacement, but also pose

a threat to the safety of the structure.

The mechanism of the corrosion of steel can be explained as follows: when the steel

is in contact with the moisture and oxygen from the environment, the iron (Fe) from the

steel decomposes into ferrous ions (Fe++) and electrons (e-). Simultaneously, the released

electrons react with water (H2O) and oxygen (O2) to form hydroxyl ions (OH-). The

produced ferrous ions further react with the hydroxyl ions to form ferrous hydroxide

(Fe(OH)2). Parts of the produced ferrous hydroxide react with water and oxygen to form

hydrated ferric oxide (Fe2O3.nH2O). The sum of these reactions can be simplified as:

𝐹𝐹𝐹𝐹 + 𝑂𝑂2 + 𝑆𝑆2𝑂𝑂 → 𝐹𝐹𝐹𝐹2𝑂𝑂3 ∙ 𝑛𝑛𝑆𝑆2𝑂𝑂

Besides the fear of corrosion, another limitation of steel being used as sleeper

material is the electric insulation problem, which may pose a potential safety issue during

the service or maintenance.


17

2.5 Review of pultruded GFRP composite materials

Over the past decades, fiber reinforced polymer (FRP) composite materials have

been developed and proposed as railway sleepers (Qiao et al., 1998, Miura et al., 1998,

Ferdous et al., 2015) and bridge girders (Stallings et al., 2000, Aidoo et al., 2004, Wang

et al., 2007, Ahmed et al., 2009). Compared to traditional materials like steel and

reinforced concrete, FRP materials are not only immune to corrosion, but they also offer

a low weight-to-strength ratio (Li et al., 2017a). The high initial costs however limits the

use of FRP materials in the construction industry. To address this issue, large volume

automated processes such as pultrusion and filament winding have been developed.

Besides the mentioned advantages of FRP materials, pultruded glass fiber reinforced

polymer (GFRP) composites manufactured through the pultrusion process offer another

advantage in that they are economically affordable for construction applications (Li et al.,

2017a). As a result, the pultruded GFRP composites are considered as an ideal material

to be used in infrastructure. The constituents, fabrication process and the material

characteristics of pultruded GFRP composites are discussed in the following sections.

2.5.1 Constituents of pultruded GFRP composites

The major constituents of pultruded GFRP composites are glass fibers and matrix.

Glass fibers are small diameter fibers made by the extrusion of silica-based glass. The

most common types of glass fibers are E-glass and S-glass. These fibers typically offer

high strength and modulus in terms of mechanical properties. However, when used on

their own, they are unable to provide effective compressive or shear capacities (Hollaway,

1980). The most commonly used resins are thermosetting and thermoplastic resins. The

resin systems can provide excellent thermoresistance and chemical resistance but have a

low strength and modulus in terms of mechanical properties. However, when reinforced


18

by fibers in a hybrid composite system, they have shown to offer exceptional performance

as a combination (Holmes and Just, 1983).

In a FRP composite structure, fibers are the main load-carrying constituent, which

provide the majority of the strength and stiffness for the composites (Richardson and

Wisheart, 1996). The matrix, on the other hand, provides the protection for the fibers from

damaging themselves and environmental attacks, and aligns the fibers in the desired

direction. It also plays the role of a transmitting vector by transferring the load to the

fibers (Hollaway, 2001).

2.5.2 Fabrication of pultruded GFRP composites

The manufacture of pultruded GFRP composites can be divided into multiple

stages. First, glass fibers and a continuous filament mat are pulled from separate racks

and sent into the resin bath. Second, the combination of glass fibers, mat and resin is

pulled into a preforming system to form the combination into the desired shape. Third, a

surface veil is added to provide a smooth surface and erosion resistance. Then, the

combination is pulled through a heated curing die (which process is also called

polymerization). Next, an extrusion-forming machine (also called pulling system) is

employed to form the products into a permanent shape. Lastly, a cut-off saw is used to

cut the products into the desired length at the end of the pultrusion process (Meyer, 1985,

Campbell, 2003). Figure 2.8 shows the schematic diagram of a typical pultrusion process.


19

Figure 2.8 Pultrusion process (http://fibrolux.com/main/knowledge/pultrusion/)

2.5.3 Characteristics of pultruded GFRP composites

A complete pultruded GFRP composites product (also called pultruded GFRP

profile) contains two types of effective layers, roving and mat layer. The majority of glass

fibers are laid in the longitudinal direction in the roving layers, which results in a high

tensile strength and stiffness in the longitudinal direction. On the other hand, the

continuous filament mat is applied in the mat layers, which improves the transverse

properties of the pultruded GFRP composite. The detailed advantages and disadvantages

http://fibrolux.com/main/knowledge/pultrusion/


20

of pultruded GFRP composites are listed as follows (Meyer, 1985, Campbell, 2003,

Correia et al., 2007a, Witcher, 2009, Gonilha et al., 2013, Li et al., 2017a):

Advantages:

a. High strength-to-weight ratio;

b. Economically affordable for construction applications;

c. Excellent erosion resistance;

d. Excellent corrosion resistance;

e. Stable electric insulation;

f. High impact resistance;

g. Spark-free material; and

h. Ease of installation.

Disadvantages:

a. Constant cross-section shape;

b. High initial cost;

c. High deformability;

d. Brittle failure; and

e. Combustibility and poor fire resistance.

2.6 The combination of pultruded GFRP composites

and concrete

When used as structural elements on their own, pultruded GFRP composites suffer

from the high deformability, the brittle failure and the susceptibility to instability (Correia

et al., 2007a, Gonilha et al., 2013, Li et al., 2017b). The limitations of the single material

have inspired researchers to look for a more efficient system, such as the combination of


21

two or more materials into a hybrid system. The combination of pultruded GFRP

composites and concrete seems to be an ideal combination particularly for applications

as railway sleepers and/or bridge girders. Concrete is considered as the most successful

material due to its affordability and excellent compressive performance. Secondly,

pultruded GFRP composites are immune to corrosion and chemical attacks, and they are

capable of providing satisfactory tensile strength for the hybrid system. Moreover, closed

pultruded profiles can protect the concrete from the erosion by the water and sulfate

solutions from the environment, which are the necessary components for the sulfate attack

and alkali silica reactions of the concrete. Lastly, concrete is a high stiffness, ductile and

heavy material, the concrete block cast inside the pultruded profile can overcome its high

deformability, brittle failure and instability problems. As a result, the combination of

pultruded profiles and concrete in a hybrid system can utilise the desired physical and

mechanical properties of each material in a more efficient way.

2.7 Summary

In this chapter, the descriptions of different types of materials used for railway

sleepers and bridge girders have been reviewed. It was found that when the traditional

materials (timber, concrete and steel) are used as structural elements, the durability and

performance of the structure could be affected by the weaknesses of these materials, such

as biological degradation, chemical attacks and corrosion. Alternative materials, such as

pultruded GFRP composites, could be an option to overcome the limitations of these

traditional materials. However, the use of pultruded composite materials brings new

issues, such as the high deformability, brittle failure, and instability. The alternative is to


22

combine these materials in a hybrid system as to overcome the deficiencies of each one

of them.

In this research, a hybrid beam made of a rectangular hollow pultruded GFRP

composites filled with concrete was chosen. The presence of the pultruded profile can

protect the concrete from chemical attacks and improve the tensile performance of the

structure. On the other hand, the concrete block can overcome the issue of instability and

high deformability and improve the compressive performance of the structure. The

combination of these two materials utilises the desired properties of each material in the

place where they perform the best.

Chapter 3

Review of Impact Behaviour of Concrete

and FRP Composites

3.1 Introduction

Ferdous et al. (2015) developed a hybrid system for use as a railway sleeper. The

results from the static flexural behaviour tests revealed that the hybrid sleeper possesses

all the necessary attributes of strength and stiffness. However, the dynamic behaviour was

not studied. Indeed, when used as a railway sleeper or bridge girder, the hybrid beam can

be subjected to low-velocity impacts during its service life. Therefore, it is of vital

importance to investigate the impact behaviour of the hybrid GFRP-concrete structure.

So far, to the author’s knowledge there has never been a study on the impact

behaviour of hybrid pultruded GFRP composites-concrete beams. The failure modes of

the hybrid structure and/or the interaction between the two materials during impact events

are yet to be studied. However, that being said, there are many studies on the impact

behaviours of concrete and FRP composites carried out separately. In this chapter, the

impact behaviour of concrete and FRP composites are reviewed. Details such as failure

mechanisms (failure modes), testing methods and strain rate effects are discussed in the

following sections. This review will help in understanding the failure modes and damage

sequences of hybrid GFRP-concrete beam subjected to impacts.

Chapter 3 – Review of Impact Behaviour of Concrete and FRP Composites

24

3.2 Review of concrete structures subjected to low-

velocity impacts

When subjected to impact loadings, concrete structures may respond in different

ways depending on the impact loading conditions, such as loading rates, the effects of

geometry and weight of the impactor. To understand the behaviour of concrete structures

subjected to low-velocity impacts, the testing methods, failure mechanisms and strain rate

effects are reviewed in the following sections.

3.2.1 Testing methods

The testing method should correspond to the potential loading scenario that may

occur during service. The two common testing methods for concrete structures subjected

to impact loadings are the Charpy pendulum test and the drop weight test. The former one

is less likely to be chosen for testing concrete structures. Due to the specific requirements

of the Charpy pendulum test setup, the dimensions of the tested specimens are normally

limited to the short-span beams, which is unable to meet the loading conditions of beam

structures in service (Pham and Hao, 2016b). In addition, the testing results from the

Charpy pendulum tests normally contain high frequency oscillations caused by the natural

vibration frequencies of the impactors (Cantwell and Morton, 1991). Thus, drop weight

testing is more commonly used in the testing of concrete structures.

Wang et al. (1996) performed impact tests on nine short concrete beams reinforced

with different fiber composition. As shown in Figure 3.1, the tests were conducted on an

instrumented drop weight machine with a fixed dropping weight (60.3 kg) and dropping

height (150 mm) to determine the energy absorption capacities of the beams.


25

Figure 3.1 Impact test setup of Wang et al. (1996)

Kishi et al. (2002) conducted a study to investigate the impact performance of shear-

failure-type reinforced concrete (RC) beams. A total number of 27 simply supported

beams was tested by using a 300 kg impactor for different impact energy levels, as shown

in Figure 3.2.


26

Figure 3.2 Impact test setup by Kishi et al. (2002)

Fujikake et al. (2009) performed a series of concrete beam tests to investigate the

effect of the amount and arrangement of reinforcement. Three different types of beams

were tested using a 400 kg drop hammer striking in the mid-span of the beams. Figure

3.3 shows the details of the testing setup.

Figure 3.3 Impact test setup by Fujikake et al. (2009)


27

Tachibana et al. (2010) conducted a study of the impact performance of RC beams

subjected to low-velocity impacts. Twenty-one simply supported concrete beams were

tested by the use of a curved contacting surface impactor for different dropping weights

and energy levels, as shown in Figure 3.4.

Figure 3.4 Experimental setup by Tachibana et al. (2010)

Bhatti and Kishi (2010) performed both experimental and numerical studies to

investigate a RC girder subjected to impacts. Four concrete girders were tested by using

a 5000 kg impactor for different dropping heights. Figure 3.5 shows the details of the

experimental setup.

Figure 3.5 Experimental setup of Bhatti and Kishi (2010)


28

The above researches recommend that the impact behaviour study of a concrete

structure should be conducted by dropping a large mass weight onto the mid-span of

specimens (the most critical situation).

3.2.2 Failure mechanisms of concrete structures subject to

impact loading

The failure mechanisms of concrete structures may be presented diversely due to

the different loading scenarios. The dynamic loading factors, such as dropping weight,

dropping height, geometry of the impactor and supporting conditions, could lead to

multifarious failure modes. By identifying the different types of failure modes, the cause

of the failure and the damage criteria of the concrete structures could be understood and

established. Therefore, it is essential to identify the failure mechanisms of the structure.

Mindess and Bentur (1985) reported experimental tests of three types of concrete

structures including plain concrete, fiber reinforced concrete and plain concrete with

conventional reinforcement. All the beams were tested by the use of 345 kg hammer with

the impact velocity of 3 m/s. The entire loading process of each test was recorded by a

500 frames per second high speed camera. During the observations of the experiments, it

was found that the plain concrete beam failed with a vertical flexural crack propagated

from the bottom to the top surface at the mid span. Similar observations were achieved

for fiber reinforced concrete but with diagonal cracks presenting on the bottom side of

the beam. While for conventional reinforced concrete, besides the flexural cracks

occurred in the mid span, another two failure modes were detected. The first one was the

surface crushing occurred on the contact zone of the beam. The second one was the local

punching shear failure with the presence of multiple shear cracks.


29

Kishi et al. (2002) tested twenty-seven RC beams, which had a cross section of 250

× 150 mm, with different initial impact velocities. From the observations, with the

increase of impact velocity, the dominant failure mode of the concrete beam changed

from the flexural-failure to the shear-failure. As the stress wave was transferred away

from the impact area towards the ends (support locations), the entire beam started to

respond to the impact in flexure. The ductile flexural response was first observed with the

initiation of vertical flexural cracks at the mid span. As the beam continued to deform,

diagonal cracks developed and propagated at an angle of approximately 45 degrees

upward.

Figure 3.6 Failure modes of Kishi et al. (2002)

Tang and Saadatmanesh (2005) performed a series of tests on the investigation of

impact behaviour of FRP strengthened concrete beams. A total number of 27 beams with

the cross section of 203 × 95 mm was tested. The test results showed the flexural cracks

initiated on the bottom side of the beams and propagated towards the top surface. With

the increase of impact duration, diagonal shear cracks occurred and propagated upward

to the top surface, which is the main failure mode causing the ultimate failure of the

beams.


30

Fujikake et al. (2006) conducted experimental tests on the impact response of

reactive powder concrete beams subjected to different impact energy levels. The

observations showed that the tested beams failed with the presences of multiple flexural

cracks initiated at the mid span of the beams. Similar to the failure modes of Mindess and

Bentur (1985), vertical flexural cracks were obtained at the centre of the beams, followed

by the diagonal cracks in the impact area which formed into a local shear plug failure.

Fujikake et al. (2009) performed a series of tests to investigate the impact

performance of RC beams subjected to low-velocity impact loadings. The effect of

dropping height and reinforcement arrangement was evaluated in this study. Three types

of RC beams with different amount of reinforcement were tested for various dropping

heights. The failure modes obtained from the tests showed the vertical flexural cracks

along with multiple diagonal shear cracks were observed across all the impact events. The

local surface crushing and shear plug developed progressively with respect to the

ascending impact energy levels.

Figure 3.7 Failure modes of Fujikake et al. (2009)


31

Bhatti et al. (2009) conducted both experimental and numerical investigations on

the impact response study of RC beams subjected to free falling loads. All the beams (400

× 200 mm in cross section) were tested by using a 400 kg cylindrical impactor. The results

showed the shear cracks were the main failure modes for this beam. Two types of shear

cracks, local shear plug and global diagonal shear cracks, were detected during the

experimental observations. The failure modes were governed mainly by shear cracks due

to the short-span length of the tested beams.

Figure 3.8 Failure modes of Bhatti et al. (2009)

The shear dominance failure modes were also confirmed by Saatci and Vecchio

(2009). Besides the occurrence of the shear cracks, they reported that in the early stage of

loading, no reaction force from the supports was obtained when the impact load reached

the maximum values, a phenomenon that was also reported by other researchers

(Cotsovos et al., 2008, Cotsovos, 2010, Pham and Hao, 2016a). This phenomenon could

be explained in that: in the early stage of impact events, the stress wave did not propagate


32

through the beam, the impact load was completely resisted by the inertial forces (Pham

and Hao, 2016b), which stage can also be called inertial resistance stage.

Kishi and Bhatti (2010) performed a study on the behaviour of RC girder subjected

to low-velocity impact loadings. The beam was tested by the use of a 2000 kg spherical

impactor at the mid span of the girder. Multiple failure modes were observed in the impact

event: local surface crushing occurred at the contact zone, followed by the local shear

plug as well as the flexural shear cracks initiated between the mid span and the supports.

Another interesting failure mode is that the flexural cracks were formed vertically when

they were near the supports. This failure mode was also observed by Saatci and Vecchio

(2009) for the impact performance analysis of RC beams subjected to impact loadings.

Figure 3.9 Failure modes of Kishi and Bhatti (2010)

Adhikary et al. (2013) tested twenty-four RC beams on short span supports. Three

types of RC beams were evaluated for different loading rates. The results indicated that

the shear cracks were the main failure mode for this beam. The local surface crushing of

the concrete was shown only in dynamic loading events and, the local shear plug

propagated from the supports to the impact location due to the short span of the beams.

The described failure modes of concrete structures subjected to low-velocity impact

loadings from the above studies can be summarised as follows (Figure 3.10):


33

a. Shear dominance failure is the most common failure mode in concrete

structures, which includes two major forms of crack patterns, local shear

plug and diagonal shear cracks;

b. Vertical flexural cracks at the centre of the concrete beams are normally

considered as the first failure mode when subjected to impacts, followed by

the diagonal shear cracks;

c. The local surface crushing of concrete is caused by the local shear loading

due to the high shear-stress rate in the impact area;

d. Local shear plug is normally formed in a relatively higher speed impact

event, where the punching failure occurred before the entire beam has time

to respond in bending;

e. The global flexural response occurs in three areas of the concrete beam, mid

span area, support area and the area between the centre and support location.

The flexural cracks at the mid span and near the support locations are

normally vertical, and the flexural cracks between these two areas are

typically formed with an angle of approximately 45 degrees upwards to the

top surface; and

f. In some particular cases, the maximum impact load occurred in the very

early stage of the impact events. The stress wave did not propagate through

the entire beam and, the impact load during this stage was completely

resisted by the inertial forces, which stage is also called inertial resistance

stage.


34

Figure 3.10 Contact-impact problem of a concrete beam

3.2.3 Strain rate effects of concrete

The effect of strain rate on the impact behaviour of concrete is questionable. On

one hand, it was claimed the strain rate effect of concrete has a significant influence on

its behaviour, and the constitutive model of concrete is a rate dependent model in which

the strain rate effect should be considered in the model (Cusatis, 2011, Ozbolt and

Sharma, 2011, Adhikary et al., 2012, Adhikary et al., 2013). On the other hand, it was

also found that the strain rate effect of concrete was not considered for analysing the

impact behaviour of concrete subjected to lower loading rates (Mindess and Bentur, 1985,

Mindess et al., 1986, Kishi et al., 2002, Fujikake et al., 2006, Bhatti et al., 2009, Jiang et

al., 2012). Similar to these findings, Bhatti et al. (2011) reported that the effects of strain

rate of concrete and rebar should not be considered for analysing the impact response of

concrete structures subjected to the low-velocity impacts. Unfortunately, this study did

not reveal the reason for this.

Besides the above opinions, many other different opinions on the strain rate effect

of concrete can be found as well. Suaris and Shah (1982) conducted a series of dynamic

tests to investigate the strain rate effects on fibre reinforced concrete. It was found that


35

the energy absorption capacity increases with respect to the increase in strain rate.

However, the bond properties between the FRP reinforcements and the concrete section

were not affected by the strain rate.

Naaman and Gopalaratnam (1983) performed experimental studies on the impact

behaviour of steel fiber reinforced concrete. The results showed that the strain rate could

have a significant influence on the impact properties only when it reaches a certain value.

This phenomenon was also confirmed by other researchers (Ross et al., 1995, Malvar and

Ross, 1998).

Fu et al. (1991) proposed a review on the effects of loading rate on RC. In this

review, they stated that the impact performance of concrete could be affected with respect

to the differences in strain rate. However, they also claimed that the high strength concrete

is less likely to be affected by strain rate.

In addition, Fujikake et al. (2009) stated that the strain rate effects on concrete

structures should be considered based on the support conditions as well. This theory was

also confirmed by Kishi and Bhatti (2010).

Even though the strain rate effects on concrete structures are questionable,

researchers should consider the influence of strain rate based on the loading and

supporting conditions. If the strain data is difficult or impossible to be collected during

the impact events, the simply supported conditions with horizontal sliding allowed as well

as the relatively lower loading rates are recommended to minimise the strain rate effect

of the concrete structures.


36

3.3 Review of FRP composites subjected to low-

velocity impacts

Damage resistance properties of FRP composite materials is a key criterion for

engineers to evaluate the structure and select suitable FRP products for the targeted

applications. Different impact factors, such as testing methods, failure mechanisms to the

damage and failure criterion are required to assess the damage resistance properties. To

develop an understanding of impact behaviour of FRP composites subjected to impact

loadings, the testing method, failure modes, strain rate effects and the review of different

types of FRP composites subjected to impacts are discussed in the following sections.

3.3.1 Testing methods

There are two common testing methods for assessing FRP composites subjected to

low-velocity impacts, Charpy impact testing and drop weight impact testing. The former

one is aimed at evaluating the energy absorption capacity of FRP composites during

fracture. However, the results usually contain a number of high frequency oscillations

caused by the natural vibration frequencies of the impactor (Cantwell and Morton, 1991).

Drop weight impact tests are set to test the impact performance on FRP composite plates,

which is more closely to the potential events in the field. Thus, drop weight impact tests

are more commonly used to assess the impact behaviour of FRP composites.

In a typical drop weight test, an impactor is raised to a certain dropping height, and

then released to strike the targeted specimen. A standard test method (ASTM-D7136,

2012) of a drop weight impact test for composite materials is recommended in many

researches (Ardakani et al., 2008, Perez et al., 2011, Sebaey et al., 2013, Saharudin et al.,


37

2013, Alomari et al., 2013, Koricho et al., 2015, Li et al., 2017a). Figure 3.11 shows an

example of impact device with double column impactor guide mechanism.

Figure 3.11 Impact device (ASTM-D7136, 2012)

3.3.2 Review of impact behaviour of different types of FRP

composites

3.3.2.1 Carbon fiber reinforced polymer (CFRP)

The impact response of CFRP subjected to low-velocity impacts was first

investigated by Cantwell and Morton (1989a). A series of low and high velocity impact

tests were performed on CFRP laminated plates to identify the differences of damage

development and damage initiation under differing loading conditions. The results

showed the impact response and energy absorbing capacity were mainly governed by the


38

geometry of the structure when subjected to low velocity impacts. On the other hand, the

geometrical parameters such as width and length had very little effect on the impact

response under high-velocity impacts.

Robinson and Davies (1992) performed a small number of tests to evaluate the

effects of impactor mass and specimen diameter on two types of laminated composites.

Both of the tests’ results showed that the impact response of laminated composites was

independently governed by the impact energy level. The impactor mass and geometry had

very little effect on the impact response. They also concluded that the low-velocity impact

of the tested specimens is a quasi-static process.

Davies and Zhang (1995) developed a simple linear FEM to predict the coupon test

results on the CFRP laminated composite plates. The numerical results were found to

corroborate the experimental ones in terms of force-time and displacement-time histories.

However, a non-linear behaviour was required to be implemented into the FEM due to

the gross deformations and in-plane material degradation.

The impact response of CFRP composites with pre-load subjected to low-velocity

impacts were investigated by Whittingham et al. (2004) and Heimbs et al. (2009). The

results showed the tensile preload had not affected the impact response of the CFRP

composites, whilst the compressive preload had affected the impact behaviour mainly in

terms of deflection response.

Ghelli and Minak (2011) performed a series low velocity impact tests on thin CFRP

laminates. The results showed the impact response from the coupons tests were governed

mainly by the geometry and thickness of the specimens, whilst the stacking sequences

had no effects on either the impact response nor the residual strength of CFRP laminates.


39

3.3.2.2 Complex structures of FRP composites

Gustin et al. (2005) conducted a series of low velocity tests on carbon fiber and

Kevlar combination sandwich composites. By replacing the impact-side face sheet of

carbon fiber with Kevlar or hybrid combination, the impact properties such as energy

absorbed capacity and maximum impact force were improved. Whilst, the reduction of

the compressive strength and stiffness of the hybrid combination was also found.

An experimental study of aluminium/nomex honeycomb sandwich panels with 8

ply CFRP skins subjected to low velocity impacts was performed by Zhou and Hill

(2009). This investigation revealed that the majority of the impact energies was absorbed

through core crushing and skin delamination. The damage mechanisms and the energy

absorption capacity did not variate distinctly with the difference of core materials.

Petrone et al. (2013b) presented a dynamic behaviour investigation on the sandwich

panels made from eco-friendly honeycomb cores. The results showed that the presence

of fiber-reinforced cores lead to a great improvement on the mechanical properties. Later,

Petrone et al. (2013a) conducted a comparison study between continuous fibers reinforced

PE honeycombs and short-random fibers reinforced PE honeycombs subjected to low

velocity impacts. The structure with continuous fibers reinforced composites presented a

better impact response in terms of energy absorption capacity and maximum impact

loads.

3.3.2.3 Pultruded GFRP composites

Most of above studies have presented the understanding of natural fiber or carbon

fiber reinforced structures subjected to low-velocity impacts. There are few studies on the

dynamic behaviour of pultruded GFRP composites currently available in the literature.


40

Tabiei et al. (1996) performed a series of impact velocity effect tests on the mid-

span of pultruded composite box-beams. The impact characteristics in terms of load-

displacement curves of two matrix material systems, polyester and vinylester, were

determined for the different impact velocities ranging from 2.2 to 7.7 m/s. This study

investigated the failure performance of the pultruded box-beams but the investigation of

damage sequence and failure modes were not studied.

Having recognised the lack of understanding of damage in pultruded composites,

Chotard and Benzeggagh (1998) performed a dynamic behaviour study of pultruded

GFRP beams in “U” shapes with the impact velocities ranging from 1.8 to 6.0 m/s. The

impact characteristics in terms of micro strain-time and load-time curves were obtained

for a series of impact energies. Damage identification was also conducted to analyse the

sequence of damage mechanisms and development. However, a loss of contact between

projectile and target occurred during the impact events due to the “U” shape geometry of

the pultruded beams, the primary results of the impact performance were actually from

the second strike by the impactor.

Later, Chotard et al. (2000) conducted a comparison study between box beams and

“U” sections. In this study, the flexural rigidity of pultruded box beams was found to be

nearly three times higher than the “U” sections due to the confinement effect of structural

geometry. Moreover, the first contact force was not shown in the pultruded box beams in

terms of load-time curves. The results obtained from the box beam tests were presented

differently from which in “U” sections for the impact characteristics due to the influence

of different structural geometry.

Bank and Gentry (2001) performed both experimental and numerical investigations

on the impact behaviour of guardrail prototypes made by multiple rectangular cells of


41

pultruded composites with the impact velocities ranging from 2.8 to 9.7 m/s. The impact

characteristics in terms of acceleration-time, velocity-time and displacement-time curves

were compared between experimental and numerical results. Unlike the previous studies,

in which the failure initiated at the corners of the beams, in this investigation the pultruded

beam failed from the tearing and splitting of the pultruded composites because of the

combination of multiple rectangular cells geometry.

Sutherland et al. (2017) performed an experimental investigation on the impact

response of bridge deck panels made of multicellular pultruded GFRP composites with

different impact energies. The test results were compared to those obtained with quasi-

static tests in terms of maximum force, displacement and absorbed energy. They found

that the “base line 3C” geometry is able to present the most complete and accurate

response when compared to the other two geometries mentioned in the paper. The failure

modes including local cruciform cracks, longitudinal split and transverse cracks were

captured from the tests. Different failure modes were shown in the tests due to the effect

of structural geometry.

Because of structural geometry, all the described pultruded composites structures

subjected to low-velocity impacts followed different failure patterns and locations, such

as shear cracks forming on the corners, buckling on the sides, tearing and splitting of the

material. None of the above studies investigated the impact energy absorbed completely

from the elastic-plastic behaviour of the material. When the pultruded composites are to

be used in hybrid systems, with concrete, the impact energy will most likely be absorbed

from the elastic-plastic behaviour of the material rather than the failure of the structure.

To reduce the influence of structural geometry and evaluate the impact behaviour of


42

pultruded composites, a shape of rectangular panel is recommended by the standard

ASTM-D7136 (2012).

Zhang and Richardson (2007) conducted a non-destructive impact study of

pultruded GRP composites in slim rectangular shapes. A series of tests conducted at very

low impact energies ranging from 6 to 19 J resulted in minimal visible damage. The

impact characteristics in terms of force-time and force-displacement curves were obtained

and compared. In this study, there was no indication of damage on the top surface and

barely visible cracks were presented on the bottom surface. Damage identification was

evaluated through the deformation mechanisms of the materials, which could be caused

by fiber pull-out, fiber breakage, and delamination or debonding between fiber and

matrix. The failure mechanisms and damage sequence of pultruded composites cannot be

fully understood with inconspicuous indication of damage in such low energy tests.

Different failure modes of composite materials would appear in low-velocity

impact induced non-penetration cases, including matrix cracking, delamination and fiber

failure. Each mode of failure requires some certain amount of impact energy. To analyse

the impact behaviour and failure modes of pultruded composites, higher impact energies

are required to be introduced. In next section, the major failure modes of FRP composites

to low-velocity impacts are introduced in detail to explain the causes of the failure modes.

3.3.3 Failure modes of FRP composites to low-velocity

impacts

By identifying the mode of failure from the impact events, the true cause and the

required energy levels to the failure can be identified, which would help in understanding


43

the failure initiation and damage propagation of FRP composites when subjected to

impact loading and, consequently, the assessment of damaged FRP composites.

Richardson and Wisheart (1996) summarized four major failure modes of

composite materials that would appear in low-velocity impact cases, including matrix

cracking, delamination, fiber breakage and penetration.

3.3.3.1 Matrix cracking

Matrix cracking is considered as the first type of the failure mode in low-velocity

impacts. This failure mode usually occurs when FRP composites are subjected to impact

energies ranging from 1 to 5 J depending on the thickness of the FRP plates (Richardson

and Wisheart, 1996). Joshi and Sun (1985) presented a typical failure pattern for a 0/90/0

composite shown in Figure 3.12. The matrix cracks in the top layer initiated along the

edges of the impactor. The matrix cracking direction are longitudinal, following the fiber

direction in the top layer (Li et al., 2017a). From the transverse view, we can see that

these cracks are inclined at approximately 45 degrees to the layer stacking direction.

These cracks occur due to the property mismatching between the fibers and matrix. The

transverse shear stress caused by the impact propagates through the material, and the low

stiffness matrix is not able to carry the high shear stress, which results in the matrix

cracking initiated (Richardson and Wisheart, 1996).


44

Figure 3.12 Transverse view of a damage induced 0/90/0 composite plate (Richardson

and Wisheart, 1996)

Choi et al. (1991) performed an investigation to analyse the failure mechanisms of

the matrix cracking in detail, which concluded that the matrix cracking in the top layer is

a result of interaction of stress distribution in different directions, as shown in Figure 3.13.

They also stated that the initiation of matrix cracking requires certain amount of energy

and the through-thickness stress (𝜎𝜎33) was very small compared to other stresses (𝜎𝜎22 and

𝜎𝜎23).

Figure 3.13 Schematic diagram of a matrix crack due to the stress distribution

(Richardson and Wisheart, 1996)


45

3.3.3.2 Delamination

As shown in Figure 3.9, delamination failure is referred to as the crack between

layers of different fibers orientation, which is similar to that of debonding failure in

concrete strengthened structures. Delamination only occurs when the absorbed energy

reaches a threshold point (Richardson and Wisheart, 1996). Dorey (1988) proposed a

simplified equation for estimating the required energy for delamination failure:

𝐸𝐸𝐷𝐷 = 2𝜏𝜏2𝑤𝑤𝐿𝐿3

9𝐸𝐸𝑓𝑓𝑡𝑡′ (3.1)

where

𝐸𝐸𝐷𝐷 = absorbed energy at the point of delamination failure;

𝜏𝜏 = interlaminar shear strength (ILSS);

𝑤𝑤 = width;

𝐿𝐿 = unsupported length;

𝐸𝐸𝑓𝑓 = flexural modulus; and

𝑡𝑡′ = specimen thickness.

Liu (1988) claimed that the delamination failure was a result of the stiffness

mismatching between two adjacent layers. Once the impact load is initiated, the FRP

composite plate starts to respond to the load in bending. The FRP plate/coupon tends

to bend concave along the major fiber direction (longitudinal direction), whilst the bend

is convex in the transverse direction. The difference of the bending directions results

in the occurrence of the delamination failure.


46

Liu (1988) also reported that the delamination areas were usually formed into an

oblong shape along the major fibers direction for unidirectional layer, and for 0/90

laminates, the shape of delamination became that of a peanut shape. These observations

have been reported widely by many other researchers as well (Chang et al., 1990, Guild

et al., 1993, Wu and Shyu, 1993, Li et al., 2017a). Figure 3.14 shows a typical example

of peanut shaped delamination area of a [0/90]s composite plate.

Figure 3.14 Delamination area of a [0/90]s composite plate

3.3.3.3 Fiber breakage

The failure of fibers in FRP composites usually occurs much later than matrix

cracking and delamination failure. It is also referred as a precursor to the penetration

failure mode (Richardson and Wisheart, 1996). Similar to the previous mentioned failure

modes, fiber breakage also requires certain amount of energy to be absorbed. Dorey

(1988) provided a simple expression for estimating the required energy for fiber failure:


47

𝐸𝐸𝑓𝑓′ = 𝜎𝜎2𝑤𝑤𝑡𝑡′𝐿𝐿18𝐸𝐸𝑓𝑓

(3.2)

where

𝐸𝐸𝑓𝑓′ = absorbed energy at the point of fiber failure;

𝜎𝜎 = flexural strength;

w = width;

𝑡𝑡′ = specimen thickness;

L = unsupported length; and

𝐸𝐸𝑓𝑓 = flexural modulus.

Fiber breakage can be found in both top (contacting) and bottom layers. The failure

of fibers on the top layer is mainly caused by the local high shear stresses, which is a

result of impactor indentation effect (Richardson and Wisheart, 1996, Li et al., 2017a).

The failure of fibers on the bottom layer usually occurs at the back surface of impact area.

This type of failure is a result of high tensile stress due to the specimen bending during

the impact event (Li et al., 2017a).

3.3.3.4 Penetration

There are two types of penetration failure for FRP composites subjected to impact

loading. The first type is normally referred to as perforation, which occurs when the

impactor completely passes through the specimen. This type of failure mainly occurs in

the ballistic or high-speed impact tests. In low-velocity impact tests, penetration occurs

when the fibers failure reaches a critical extent, the specimen is unable to carry any impact


48

load and break into pieces before the impactor passing through it. A simplified equation

was given by Dorey (1988) for calculating the required energy for the penetration failure:

𝐸𝐸𝑝𝑝 = 𝜋𝜋𝛾𝛾𝑑𝑑𝑡𝑡′ (3.3)

where

𝐸𝐸𝑝𝑝 = absorbed energy at the point of penetration failure;

𝜋𝜋 = mathematical constant;

𝛾𝛾 = fracture energy;

𝑑𝑑 = diameter of impactor; and

𝑡𝑡′ = specimen thickness.

However, Cantwell and Morton (1989b) stated that the energy required for the

penetration failure mostly depends on the geometry and thickness of the specimen rather

than the fracture energy. In their work, the majority of the energy was absorbed through

the shear-out form of the material response. The penetration failure is an extension of the

fiber failure, which is unlikely to occur in the low-energy modes.

3.3.4 Strain rate effects of FRP composites to low-velocity

impacts

Typically, strain rate effects on carbon fibers reinforced polymers (CFRP) are not

considered in engineering design because the strength and modulus of CFRP are not

affected by the change in loading rates (Daniel et al., 1981, Caprino, 1984, Sjoblom et al.,

1988, Richardson and Wisheart, 1996, Gilat et al., 2002). On the other hand, aramid fibers

reinforced polymers (AFRP) are usually considered as a strain rate dependent material.


49

The modulus and stiffness of AFRP increases with respect to the increase of strain rates

(Rodriguez et al., 1996, Benloulo et al., 1997).

However, the strain rate effects of glass fibers reinforced polymers (GFRP) to low-

velocity impacts are questionable. On one hand, it was reported that the strength and

stiffness of GFRP composites increase with the increasing strain rate in the tensile split

Hopkinson bar tests (Caprino, 1984, Barre et al., 1996, Shokrieh and Omidi, 2009, Naik

et al., 2010). On the other hand, Caprino et al. (1984) claimed that the strain rate effects

do not affect the material properties of GFRP when subjected to low-velocity impacts in

the drop weight tests. Interestingly, Hayes and Adams (1982) performed pendulum

apparatus tests on an unidirectional composite material. They reported that the modulus

of GFRP increases with respect to the increase of strain rate, but the strength of the

specimens decreases with the increased strain rate.

Robinson and Davies (1992) stated that the impact properties of GFRP materials,

especially the through-thickness properties, were not affected by the change in strain rate

when subjected to low-velocity impacts. This opinion was also supported by the findings

of Richardson and Wisheart (1996) and Li et al. (2017a).

To conclude, in low-velocity impact cases, the impact loads are mainly resisted

based on the material stiffness and strength in longitudinal and transverse directions. The

through-thickness properties can be ignored for laminated GFRP composites. However,

in a dynamic loading scenario, the in-plane (both longitudinal and transverse direction)

material strength and stiffness increase with respect to the loading rate. Hence, the in-

plane properties of GFRP laminates should be considered as rate dependent.


50

3.4 Summary

In this chapter, a review of the impact behaviour of concrete structures and FRP

composite subjected to low-velocity impacts is presented. The review of the testing

methods and strain rate effects on concrete structures provides a recommendation for the

experimental setup of the hybrid beam proposed in this thesis. The failure mechanisms of

concrete/reinforced concrete structures are also summarised as is the impact behaviour of

FRP composites subjected to low-velocity impacts. For FRP composites, four types of

failure modes, including matrix cracking, delamination, fiber breakage and penetration,

and their failure mechanisms were identified.

A critical review of pultruded GFRP composites subjected to low-velocity impacts

is also presented in this chapter. Very limited studies were focussed on the impact

response of pultruded composites. To fully identify and understand the failure modes and

their corresponding mechanisms, higher impact energies need to be introduced. The

review of the impact response of FRP composites and concrete provides a reference base

and scope for the study of pultruded GFRP composites and hybrid beam.

Chapter 4

Experimental Study of Pultruded GFRP

Composites to Low-Velocity Impacts1

4.1 Introduction

As mentioned in Chapter 3, very limited studies focus on tests involving the higher

range of impact energy on pultruded composites. Therefore, the aim of this chapter is to

develop an understanding of the impact response of pultruded GFRP composites

subjected to low-velocity impacts with higher impact energies ranging from 17 to 67 J.

In this investigation, an instrumented drop tower impact test machine (INSTRON

CEAST 9350) is used to introduce the impact tests on the pultruded composites. All the

specimens are placed and supported based on the requirement of the standard ASTM-

D7136 (2012). The results of impact characteristics and performance are compared for

different impact energy levels. The damage evaluation is also introduced to compare the

failure modes of pultruded composites subjected to different energy levels. Moreover, the

impactor mass effects are evaluated with using three ascending weights of impactor.

Finally, the chapter provides a summary of the main findings from the drop tower tests.

1 Results discussed in this chapter form part of the following publication:

LI, Z., KHENNANE, A., HAZELL, P. J. & BROWN, A. D. 2017. Impact behaviour of pultruded GFRP composites under low-velocity impact loading. Composite Structures, 168, 360-371.

Chapter 4 - Experimental Study of Pultruded GFRP Composites to Low-Velocity Impacts

52

4.2 Material description

The pultruded GFRP composites used in this study were manufactured through the

pultrusion process and are composed of isophthalic resin and glass fibers with a fiber

volume fraction of 60 %. A microscopic examination of the cross-sections of pultruded

GFRP composites was performed. The composites were cut into small pieces

(approximately 10 × 10 mm in cross section) to acquire the complete view in both

longitudinal and transverse directions of the layers. The cut pieces were placed into

cylindrical moulds (with a diameter of 25 mm), and then mounted with specific resins

(EpoFix) to form a matrix, as shown in Figure 4.1 (a). After curing, the matrix were

ground by the use of Struers Tegramin-25 grinding and polishing machine (Figure 4.1 b).

The observation surfaces of the matrix were ground by 500, 800, 2000, and 4000 grit SiC

foils under wet grinding conditions. The ground matrices were then polished by the use

of a finely napped cloth.

Figure 4.1 Specimen preparation for microscopic examination (a: cylindrical moulds; b:

Struers Tegramin-25 grinding and polishing machine)


53

Figure 4.2 ZEISS Axio Imager M2m optical microscope

The microstructures of the pultruded GFRP composites were examined using a

ZEISS Axio Imager M2m optical microscopic system (Figure 4.2). From the

examinations, the pultruded GFRP composites consisted of three layers of roving, each

layer approximately 3 mm thick, and separated by two layers of glass fiber mat, each

approximately 0.5 mm thick. In addition, there was a very thin surface veil

(approximately between 0.1 mm and 0.2 mm thick) placed on both the top and bottom

roving surfaces to provide a smooth surface. The majority of glass fibers were laid along

the longitudinal direction in the roving layers. The distribution of layers is shown in

Figure 4.3.


54

Figure 4.3 Microscopic views of pultruded GFRP composites

The mechanical properties and physical properties are achieved from manufacturer

and coupons tests investigated by Chakrabortty et al. (2011) as shown in Table 4.1. All

of the specimens were cut into a rectangular shape with dimensions of 150 × 100 × 10

mm based on the requirement of test standard ASTM-D7136 (2012). Details of test

specimens are listed in Table 4.2.

Table 4.1 Mechanical properties of the pultruded GFRP composites (Li et al., 2017a)

Mechanical and physical properties Magnitudes Density (g/cm3) 1.790 Fiber volume fraction* 60% Major Poisson’s ratio* 0.21 Longitudinal modulus (GPa) 28.87 Transverse modulus (GPa) 3.510 Shear modulus (GPa) 2.980 Longitudinal tensile strength (MPa) 301.198 Transverse tensile strength (MPa) 29.78 Longitudinal compressive strength (MPa) 310.785 Transverse compressive strength (MPa) 31.97

*Obtained from the manufacturer’s sheet


55

Table 4.2 Details of test specimens

Energy (J) Impactor mass (kg) Test sample Thickness (mm) Mean

(mm)

16.75 5.48 test_1 SR2 9.34 9.35 9.42 9.37

test_2 SL2 9.46 9.7 9.66 9.61

test_3 LD6 9.04 8.9 9.15 9.03

33.5 5.48 test_4 LU1 9.81 9.72 9.75 9.76

test_5 SR3 9.11 9.33 9.35 9.26

test_6 LU6 9.83 9.67 9.74 9.75

50.25 5.48 test_7 SL3 9.43 9.69 9.55 9.56

test_8 LD2 9.04 8.86 9.03 8.98

test_9 LU5 9.64 9.81 9.72 9.72

67 5.48 test_10 LD3 9.07 8.94 9.05 9.02

test_11 LD1 8.86 9.09 9.01 8.99

test_12 SR1 9.17 9.33 9.37 9.29

67 10.48 test_13 LU3 9.83 9.67 9.8 9.77

test_14 LU2 9.77 9.66 9.78 9.74

test_15 SL5 9.45 9.66 9.59 9.57

67 15.48 test_16 LD5 9.07 8.89 9.08 9.01

test_17 LD4 9.07 8.88 9.06 9.00

test_18 SR5 9.35 9.13 9.31 9.26

4.3 Test setup and procedures

An INSTRON CEAST 9350 drop weight tower was used to conduct the impact

tests presented in this study, which meet the requirements of ASTM-D7136 (2012). The

general features of the machine and data acquisition system are shown in Figure 4.4. The

drop tower is equipped with a free-falling carriage system that includes an impactor and

a load cell. The system operates on the principle of energy conservation, balancing

potential and kinetic energy by varying the drop height of the carriage and the option of


56

adding additional mass to the system. The system can simulate drop heights upwards of

30 m by accelerating the carriage via springs at the top of the system. The rectangular test

specimens were subjected to a concentrated impact by using a 20 mm diameter

hemispherical striker with 5.5 kg of total weight from various heights. The striker weight

alone is 1.2 kg, while the rest of the carriage system weighs an additional 4.3 kg.

According to the recommendation of ASTM-D7136 (2012), the impact energy required

for evaluating the damage resistance of composite materials is governed by the following

equation:

𝐸𝐸 = 𝐶𝐶𝐸𝐸ℎ (4.1)

where

𝐸𝐸 = the potential energy of impactor prior to drop;

𝐶𝐶𝐸𝐸 = the specified ratio of impact energy to specimen thickness, 6.7 J/mm; and

ℎ = the nominal thickness of the specimen.

Utilizing Eq. 4.1, the impact energy of 67.00 J was calculated for the pultruded

GFRP composite testing. Three additional levels of energy (16.75, 33.50 and 50.25 J)

were also applied in this study to provide additional insight into the mechanical response

of the pultruded GFRP composites. The impact velocities and drop heights of the four

chosen energy levels were 2.47, 3.49, 4.27 and 4.94 m/s, and 311, 621, 932 and 1242 mm,

respectively. The minimum drop height requirement of 300 mm is satisfied for all testing

conditions, as per ASTM-D7136 (2012). Three specimens were tested for each energy

level to determine repeatability. During the test, the specimen was placed centred relative

to the cut-out (125 × 75 mm) on the impact support fixture. To prevent the rebounding of

the specimen during the impact event, four clamps with rubber tips in the end were used


57

to secure the specimen in place. An anti-rebound system that catches the impactor was

also implemented to prevent the striker from reloading the specimen. A high speed

camera (Phantom v12) with the sample rate of 11000 frames per second was used for

recording the impact events. To increase the light intensity, a HIVE plasma lamp was

used as a low temperature lighting source. The support conditions are shown in Figure

4.5.

Figure 4.4 Test setup


58

Figure 4.5 Impact support fixture

4.4 Experimental results and discussion

A total number of 12 specimens (test 1 to test 12) were tested at four different

energy levels for investigating the impact behaviour of pultruded GFRP composites. The

impact performance and characteristics are reported in terms of load-time, central

deflection-time and load-displacement. These material response histories are presented in

sections 4.4.1, 4.4.2, and 4.4.3, respectively, and are discussed in detail in section 4.4.4

and 4.4.5.

4.4.1 Load-time response

The loading histories for all impact energy levels recorded in-situ by the load cell

are presented in Figure 4.6. As shown, the impact force-time curves of four impact energy

levels exhibit similar trends, which can be divided into four stages. Just after contact is

initiated between the impactor and the top surface of specimen, the first stage is

represented by a linear increase in load. No damage occurs in the first stage and the

dynamic response of the specimens is purely elastic. The average values of load at the


59

end of this stage for four ascending energy levels are 1.95, 2.47, 2.76 and 3.20 kN

respectively. The magnitude of the load at the end of the first stage is up to approximately

20% of the maximum load for the entire event. The second stage begins with the onset of

inelastic behaviour at approximately 0.2 ms. There are another two linear increases in

load at this stage, indicating that the stress propagates to the second and third roving layers

showing a response to the impact load in sequence. The total number of linear increases

in the first two stages matches the number of roving layers, where the majority of fibers

are laid. The third stage lasts from the end of second stage to the maximum load of impact

(approximately 2 ms). The through-thickness stress waves do not play a significant role

in the stress distribution in these low-velocity impact events (ranging from 2.5 to 5.0 m/s).

The majority of impact loads are resisted through the bending of the pultruded GFRP

composites. Since all the custom-made specimens have the same bending stiffness, and

hence the same natural frequency, the maximum impact force of different impact energy

levels events occurs at nearly the same time. The average values of maximum load for

four ascending energy levels are 9.52, 11.74, 13.48 and 15.15 kN respectively. During

the third stage, the impact force remains increasing with the presence of significant

oscillations in the data from the activation of two different damage mechanisms: shear

damage occurring at the onset of inelastic deformation followed by the delamination

between the mat and roving layers with increasing load. In the fourth, and final, stage the

loading curves decrease down to zero at varying slopes with respect to impact energy.

During this period, the impactor starts to rebound and leave the target, however, the

specimens are still ringing, which is confirmed by the video recorded from the Phantom

high-speed camera.


60

Figure 4.6 Impact force-time curves of four impact energy levels

4.4.2 Central deflection-time response

The central deflection of the specimen can be calculated from a double integration

of force-time curve:

𝐷𝐷 = ∬𝐹𝐹(𝑡𝑡)−𝐶𝐶𝑀𝑀𝐶𝐶

𝑑𝑑2𝑡𝑡 (4.2)

where

𝐷𝐷 = the central deflection;

𝐹𝐹(𝑡𝑡) = the force acquired by the data acquisition system;

𝑀𝑀 = the total weight (5.5 kg);

𝑔𝑔 = the gravitational acceleration constant (9.81 m/s2); and

𝑡𝑡 = time.


61

The central deflection-time curves of four impact energy levels are shown in Figure

4.7, which are verified by the video recorded from the Phantom high-speed camera with

an average difference of 3.5 % at the maximum calculated deflection. The snapshots from

the video at t = 0 and t = maximum deflection time for specimen LD3 are shown in Figure

4.8. Similar trends are observed for the deflection-time plots across all impact energies

tested; the maximum deflection increases with increasing energy and the time at which

the maximum deflection occurs also increases with increasing energy.

Figure 4.7 Central deflection-time of four impact energy levels


62

Figure 4.8 Snapshots of specimen LD3 during the impact test

4.4.3 Load-displacement response

The absorbed energy during the impact loading is another primary parameter for

analysing the dynamic response of pultruded GFRP composites. The value of absorbed

energy for each specimen can be calculated through an integration of the force-

displacement curve:

𝐸𝐸𝑎𝑎𝑎𝑎𝑠𝑠𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒𝑑𝑑 = ∫𝐹𝐹(𝐷𝐷)𝑑𝑑𝐷𝐷 (4.3)

where

𝐸𝐸𝑎𝑎𝑎𝑎𝑠𝑠𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒𝑑𝑑 = the absorbed energy;

𝐹𝐹(𝐷𝐷) = the force curve (function of deformation); and

𝐷𝐷 = the central deflection.

The force-displacement curves of the four ascending energy levels tested are

illustrated in Figure 4.9. Similar to the force-time curves, the force-displacement curves

can be divided into four stages. The first stage is identical to what is shown in force-time

curves, exhibiting a linear increase of force up to approximately 20% of maximum load


63

that is indicative of recoverable elastic deformation. The second stage begins with the

onset of inelastic deformation to the first large extent drop. Matrix cracks begin to occur

through the top roving layer to the bottom one in sequence. No fiber damage is expected

in this stage and the majority of impact energies are absorbed through the elastic

behaviour of pultruded composites. The third stage starts from the onset of plastic

deformation. Matrix cracks and delamination begin to grow distinctly as the curve starts

to grow with a series of fluctuations up to the maximum value of displacement. In this

stage, the deformation is plastic, or permanent, and will not be recovered upon unloading.

Finally, the last stage sees the impactor leaving the target and the load decreases to a

measurable degree of unrecoverable deformation. During the higher energy impacts, the

stress starts to grow and satisfy multiple damage criterions, such as matrix cracking,

delamination and fiber breakage. The pultruded composites experience multiple modes

of failure and absorb more energy with increasing energy. The post-failure stiffness of

the pultruded composite decreases with the increased impact energy and hence damage.

As a result, the unloading slope varies with respect to impact energy. The area described

under the force-displacement curve provides the energy absorbed by the pultruded GFRP

composites, which can be verified through the following equation:

𝐸𝐸𝑡𝑡𝑜𝑜𝑡𝑡𝑎𝑎𝑡𝑡 = 𝐸𝐸𝑎𝑎𝑎𝑎𝑠𝑠𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒𝑑𝑑 + 𝐸𝐸𝑘𝑘𝑖𝑖𝑘𝑘𝑒𝑒𝑡𝑡𝑖𝑖𝑐𝑐 (4.4)

where

𝐸𝐸𝑡𝑡𝑜𝑜𝑡𝑡𝑎𝑎𝑡𝑡 = the initial energy;

𝐸𝐸𝑎𝑎𝑎𝑎𝑠𝑠𝑜𝑜𝑎𝑎𝑎𝑎𝑒𝑒𝑑𝑑 = the absorbed energy; and

𝐸𝐸𝑘𝑘𝑖𝑖𝑘𝑘𝑒𝑒𝑡𝑡𝑖𝑖𝑐𝑐 = the kinetic energy when the impactor starts to rebound.


64

Figure 4.9 Force-displacement curves of four energy levels

4.4.4 Impact performance

Test results including initial energy, dropping height, maximum load, impact

velocity and absorbed energy are summarised in Table 4.3. The results indicate that

similar percentage (approximately 67%) of the energy is absorbed through all impact

events, with a slight increase of percent energy absorption with increasing impact energy.

The relationships between the average maximum load (Fmax) and impact energy, average

maximum deflection (Dmax) and impact energy are shown in Figure 4.10. The average

value of the maximum load increases at a near-linear (R2=0.993) trend with the increasing

impact energy. Similar to the maximum load, the maximum deflection increases at a near-

linear (R2=0.997) trend with the increasing impact energy.


65

Figure 4.10 Relationship of maximum load/impact energy and maximum

deflection/impact energy

Table 4.3 Testing results summary

Specimen ID

Test No. Initial Energy measured (J)

Dropping Height (mm)

Maximum Load (kN)

Maximum Deflection

(mm)

Impact Velocity

(m/s)

Absorbed Energy

(J)

SR2 16.75J #1 17.269 311 8.86 3.326 2.51 11.116 SL2 16.75J #2 17.269 311 10.35 3.187 2.51 10.854 LD6 16.75J #3 17.406 311 9.36 3.347 2.52 11.336 LU1 33.50J #1 33.769 621 12.27 4.890 3.51 23.187 SR3 33.50J #2 33.962 621 11.25 5.191 3.52 22.821 LU6 33.50J #3 33.962 621 11.70 4.851 3.52 23.352 SL3 50.25J #1 50.446 932 13.61 6.406 4.29 34.206 LD2 50.25J #2 50.446 932 13.39 6.475 4.29 34.133 LU5 50.25J #3 50.446 932 13.45 6.276 4.29 35.679 LD3 67.00J #1 70.179 1242 15.77 8.033 5.06 48.923 LD1 67.00J #2 70.179 1242 15.49 8.073 5.06 47.843 SR1 67.00J #3 70.179 1242 14.20 8.337 5.06 50.788


66

4.4.5 Damage evaluation

The front and back surfaces of pultruded GFRP composites for all impact energy

levels are shown in Figure 4.11 and Figure 4.12 respectively. The results are obtained

from the observation and ultrasonic measurement detections, and the magnitude of the

damage are produced from the Image J measurement analysis. On the front surfaces,

besides the indentation caused by the impactor, all the failure modes are presented with a

similar cracking pattern. The matrix cracking directions for all the different impact energy

events are longitudinal, following the fiber direction in the top layer (roving layer). The

growth and the magnitude of damage are increasing significantly with the increased

impact energy: only one crack of length 40 mm is observed in a typical 16.75 J impact

energy test. In Figure 4.11, it is observed that two cracks of length 30 and 44 mm, and 78

and 81mm are shown for 33.50 J and 50.25 J test respectively. Lastly, three longitudinal

cracks of length 99, 84 and 96 mm are shown in 67.00 J test shown in Figure 4.11. As the

impact energy increases, another cracking pattern (from 30o to 45o) is shown close to the

indentation, which is caused by the shear loading due to the high shear-stress rate in this

area. This shear cracking is highly visible in the 67.00 J specimen shown in Figure 4.11.

On the back surfaces, there is a monotonic increase of damage area with increasing impact

energy and the propagation of damage follows along the longitudinal direction on the

bottom (roving) layer. The total damage areas for each energy level are 1104, 1908, 2911

and 3819 mm2 respectively, which value increases at a near-linear (R2=0.998) trend with

the increasing impact energy, shown in Figure 4.13. One crack was discovered on the

centre of back surface for higher impact energy events, which is a result of the high tensile

stress due to the specimen bending during the impact. For both front and back surfaces

damage evaluation, the damage areas are increasing monotonically with the increased


67

impact energy, indicating a similar pattern of energy absorption formed, which is

confirmed by the force-displacement curves and energy absorption results.

Figure 4.11 Comparison of top surfaces for four energy levels

Figure 4.12 Comparison of bottom surfaces for four energy levels


68

Figure 4.13 Relationship of damage area in back surface/impact energy

4.5 Impactor mass effect

The effect of the impactor mass upon the damage initiation and development of

pultruded GFRP composites to low-velocity impacts has not been revealed yet. For this

purpose, this section examines the effect of varying the mass of the impactor with a fixed

radius on the impact response of pultruded GFRP composites.

A total number of nine specimens (test 10 to test 18) were tested for three ascending

weights of impactor mass and a fixed impact energy. Three specimens were tested for

each impactor mass to determine the repeatability. The impact velocities for the

corresponding impactor mass were 5.06, 3.59 and 2.97 m/s respectively. The impact

characteristics results in terms of load-time, central deflection-time and load-


69

displacement curves are illustrated in sections 4.5.1, 4.5.2 and 4.5.3, respectively, and are

discussed in detail in section 4.5.4.


The loading histories for three ascending impactor mass are presented in Figure

4.14. As shown, the loading curves exhibit similar trends. However, the contact duration

increases with respect to the increase of impactor mass. This is the result of reduction for

the initial impact velocity. The maximum impact load decreases slightly with respect to

the increase of impactor mass. As mentioned in section 3.3.3, the in-plane properties of

the pultruded GFRP composites can be considered as rate dependent. Therefore, the

decrease of the maximum impact load might be caused by the decrease of the impact

velocity rather than the mass effect of the impactor.

Figure 4.14 Load-time curves of three ascending impactor mass


70

4.5.2 Central deflection-time response

The central deflection-time curves of three different impactor mass are shown

inconsistently in Figure 4.15. The duration of deflection curves increases with respect to

the reduction of impact velocities. The pattern of variation tendency for three ascending

impactor mass is not clear. The maximum deflections for the highest impact velocity are

larger than the other two groups, however, the value of maximum deflections of 15.5 kg

group is greater than that of 10.5 kg group but smaller than 5.5 kg group.

Figure 4.15 Central deflection-time curves of three ascending impactor mass

4.5.3 Load-displacement response

The absorbed energy for the impact event can be evaluated through the load-

displacement curve. The load-displacement curves of three different impactor mass are

shown in Figure 4.16. As shown, the absorbed energy for every test remains the same

regardless of the difference of the impactor mass. Similar percentage of energy

(approximately 70%) is absorbed across all the impact events.


71

Figure 4.16 Load-displacement curves of three ascending impactor mass


Testing results including initial energy, percentage of energy absorption, maximum

load, maximum deflection, impact velocity and absorbed energy are summarized in Table

4.4. As shown, the average maximum load decreases with respect to the reduction of

impact velocity. However, the variation of maximum deflection is not clear, and the

energy absorption capacity does not vary with the increase of impactor mass. Therefore,

the impactor mass has very little effect on the impact response for the pultruded GFRP

composites subjected to low-velocity impacts.


72


Specimen ID

Test No.

Initial Energy

measured (J)

Percentage of Energy absorption

(%)

Maximum Load (kN)

Maximum Deflection

(mm)

Impact Velocity

(m/s)

Absorbed Energy (J)

LD3 5.5 kg #1 70.179 69.71 15.77 8.033 5.06 48.923 LD1 5.5 kg #2 70.179 68.82 15.49 8.073 5.06 47.843 SR1 5.5 kg #3 70.179 72.37 14.20 8.317 5.06 50.788 LU3 10.5 kg #1 67.171 69.30 13.69 7.546 3.58 46.550 LU2 10.5 kg #2 67.547 72.34 14.15 7.565 3.59 48.863 SL5 10.5 kg #3 67.547 67.61 14.31 7.627 3.59 45.669 LD5 15.5 kg #1 68.283 69.74 13.48 8.051 2.97 47.621 LD4 15.5 kg #2 68.283 68.29 13.91 7.942 2.97 46.630 SR5 15.5 kg #3 68.283 71.82 12.96 8.037 2.97 49.041

4.6 Summary

In this chapter, 18 specimens were tested using an instrumented drop tower testing

machine for different impact energy levels and impactor mass. The impact characteristics

in terms of load-time curves, central deflection-time curves and load-displacement curves

were presented to demonstrate the damage initiation and propagation of pultruded GFRP

composites subjected to low-velocity impacts. The impact performance in terms of

maximum load and deflection were compared for different impact factor studies. The

findings of this chapter can be summarised as follows:

1. The impact characteristics (load-time, displacement-time and load-displacement

curves) of pultruded GFRP composites subjected to different impact energies

exhibit similar variation tendencies;

2. The pultruded GFRP composites behave in a purely elastic fashion until

approximately 20% of the maximum impact load for all impact events, and the


73

number of linear increases of load in elastic regime matches the number of

roving layers;

3. The maximum impact force and central deflection increases at a near-linear trend

with respect to the impact energy. Similar percentage of energy is absorbed for

different loading cases. There is a slight increase of percentage of energy

absorption with the increase of impact energy, whilst such percentage remains

the same for different impactor mass;

4. The extent of damage on both front and back surfaces is monotonically increasing

with the increased impact energy. Multiple failure modes including matrix

cracking and delamination occur when pultruded GFRP composites are

subjected to higher level of impact energy; and

5. The impactor mass has very little effect on the impact response for the pultruded

GFRP composites subjected to low-velocity impacts. Impact energy is the main

factor that have a significant effect to the pultruded GFRP composites.

Chapter 5

Numerical Study of Pultruded GFRP

Composites to Low-Velocity Impacts2

5.1 Introduction

The experimental investigations of the impact behaviour of pultruded GFRP

coupons subjected to low-velocity impacts were conducted in Chapter 4. Results, such as

the impact characteristics (load-time curves, displacement-time curves) and impact

performance (maximum impact load, energy absorption capacity) were obtained from the

experimental study. However, experimentation alone does not reveal the development

and propagation of the stress, which can be better understood through numerical

simulation. For this purpose, a non-linear finite element model (FEM) is developed using

a progressive damage model to simulate the impact behaviour of pultruded composites.

The numerical results will be compared with the experimental data for verification, and

the validated numerical model will be employed in the numerical investigations of hybrid

GFRP-concrete beams subjected to impact loadings.


LI, Z., KHENNANE, A., HAZELL, P. J. & BROWN, A. D. 2017. Impact behaviour of pultruded GFRP composites under low-velocity impact loading. Composite Structures, 168, 360-371.

Chapter 5 - Numerical Study of Pultruded GFRP Composites to Low-Velocity Impacts

75

5.2 Finite element model

A non-linear FEM was developed using a progressive damage model to simulate

the impact behaviour of pultruded GFRP coupons in the commercial software

ABAQUS/Explicit. As mentioned in section 3.3.3, the through-thickness stress wave

plays no significant part in the stress distribution in a low-velocity impact event; hence,

the pultruded GFRP composites were modelled without considering the through-

thickness properties (Robinson and Davies, 1992, Richardson and Wisheart, 1996, Li et

al., 2017a). Therefore, a continuum shell element is chosen for the pultruded GFRP

composites instead of a three dimensional continuum solid element.

The impactor was modelled with discrete rigid elements (R3D4) and all the

effective layers of the pultruded GFRP composites were modelled using eight-node

quadrilateral in-plane general-purpose continuum shell elements (SC8R). The mesh

density was chosen as 2 × 2 mm on the basis of mesh sensitivity analysis in terms of

computational time and convergence. To reduce the computational time, the dimensions

corresponding to the size of the unsupported region of the specimens in the experimental

set-up were modelled (125 × 75 mm). The computational time of a single simulation for

the reduced model was approximately 1.5 hours (Intel Core i7-3770 CPU @ 3.4 GHz). A

mass of 5.5 kg was assigned to the impactor, matching the experimental test conditions.

Different initial impact velocities were imposed to the impactor to simulate different

impact energy levels events. Boundary conditions were accordingly assigned with the

reduced size of specimen, which are reported in Figure 5.1. The interaction between the

specimen and impactor was simulated by surface to surface contact pairs and the

mechanical constraint formulation was enforced using the kinematic contact algorithm.


76

Figure 5.1 Assembled FEM with boundary conditions

5.3 Progressive damage model

The damage model for fiber-reinforced composites, which is associated with plane

stress formulation, has been used to predict the onset of failure and post-failure

development of pultruded GFRP composites in ABAQUS/Explicit. This progressive

damage model is based on the work of Camanho and Davila (2002), which is aimed to

describe the linear elastic behaviour of the undamaged composite materials using the

combination of damage initiation criteria. The damage initiation criteria of the composite

material are evaluated by using Hashin’s criteria (Hashin and Rotem, 1973, Hashin,

1980), which is used to predict the onset of degradation of pultruded GFRP composites

in this study. Once the damage initiation criteria are satisfied, the degradation of the

material stiffness coefficients would be presented. This behaviour can be modelled by


77

damage evolution and the corresponding variables based on a damage evolution law

(Matzenmiller et al., 1995, Camanho and Davila, 2002, Lapczyk and Hurtado, 2007).

Details of the mechanisms of this progressive damage model and its implementation can

be found in ABAQUS documentation (ABAQUS, 2014). In order to explain the input

parameters implemented in this study, a brief description of the mechanisms of this model

is presented as follows (ABAQUS, 2014):

The damage initiation criteria of fiber and matrix failure are given in the following

equations:

Fiber tension failure (𝜎𝜎11� ≥ 0):

𝐹𝐹𝑓𝑓𝑡𝑡 = �𝜎𝜎11�𝑋𝑋𝑇𝑇�2

+ 𝛼𝛼 �𝜏𝜏12�𝑆𝑆𝐿𝐿�2 (5.1)

Fiber compression failure (𝜎𝜎11� < 0):

𝐹𝐹𝑓𝑓𝑐𝑐 = �𝜎𝜎11�𝑋𝑋𝐶𝐶�2 (5.2)

Matrix tension failure (𝜎𝜎22� ≥ 0):

𝐹𝐹𝑚𝑚𝑡𝑡 = �𝜎𝜎22�𝑌𝑌𝑇𝑇�2

+ 𝛼𝛼 �𝜏𝜏12�𝑆𝑆𝐿𝐿�2 (5.3)

Matrix compression failure (𝜎𝜎22� < 0):

𝐹𝐹𝑚𝑚𝑐𝑐 = �𝜎𝜎22�2𝑆𝑆𝑇𝑇

�2

+ �� 𝑌𝑌𝐶𝐶

2𝑆𝑆𝑇𝑇�2− 1� 𝜎𝜎22�

𝑌𝑌𝐶𝐶+ �𝜏𝜏12�

𝑆𝑆𝐿𝐿�2 (5.4)

where

𝐹𝐹 = the damage initiation factor (when the respective value of 𝐹𝐹 equals one, the

representative tensile/compressive damage in fiber or matrix begins to be

initiated);


78

𝜎𝜎11� = the effective normal stress in longitudinal direction;

𝜎𝜎22� = the effective normal stress in transverse direction;

𝜏𝜏12� = the effective shear stress;

𝛼𝛼 = the coefficient that presents the ratio of the shear stress to tension;

𝑋𝑋𝑇𝑇 = the tensile strength in longitudinal direction;

𝑆𝑆𝐿𝐿 = the shear strength in longitudinal direction;

𝑋𝑋𝐶𝐶 = the compressive strength in longitudinal direction;

𝑌𝑌𝑇𝑇 = the tensile strength in transverse direction;

𝑆𝑆𝑇𝑇 = the shear strength in transverse direction; and

𝑌𝑌𝐶𝐶 = the compressive strength in transverse direction.

The effective stress 𝜎𝜎� (𝜎𝜎11� , 𝜎𝜎22� and 𝜏𝜏12� ) can be calculated from the following

equation:

𝜎𝜎� = 𝑀𝑀𝜎𝜎 (5.5)

where

𝑀𝑀 = the damage operator; and

𝜎𝜎 = the true normal or shear stress.

From Eq. 5.5, the effective stress 𝜎𝜎� in the damage criterion (Eq. 5.1 – 5.4) is

converted from the true stress by using the damage operator 𝑀𝑀. The operator 𝑀𝑀 is a tensor

that is modified with the changes of damage variables. The relationship between the

damage variables and the damage operator is formulised in Eq. 5.6.


79

𝑀𝑀 =

⎣⎢⎢⎢⎡

1�1−𝑑𝑑𝑓𝑓�

0 0

0 1(1−𝑑𝑑𝑚𝑚) 0

0 0 1(1−𝑑𝑑𝑠𝑠)⎦

⎥⎥⎥⎤

(5.6)

where

𝑑𝑑𝑓𝑓 = the internal fiber damage variable;

𝑑𝑑𝑚𝑚 = the internal matrix damage variable; and

𝑑𝑑𝑠𝑠 = the internal shear damage variable.

The damage variables 𝑑𝑑 present the current state of the damage, when 𝑑𝑑 is equal to

zero, no damage has been initiated. Conversely, when 𝑑𝑑 reaches one, the fiber or matrix

is fully damaged and no further load can be carried. The current state of fiber or matrix

damage variables corresponds to the respective effective values, and the shear damage

variable is the result of a complex combination of the fiber and matrix damage variables,

as shown in the following equations:

𝑑𝑑𝑓𝑓 = �𝑑𝑑𝑓𝑓𝑡𝑡 𝑆𝑆𝑓𝑓 𝜎𝜎11� ≥ 0𝑑𝑑𝑓𝑓𝑐𝑐 𝑆𝑆𝑓𝑓 𝜎𝜎11� < 0

(5.7)

𝑑𝑑𝑚𝑚 = �𝑑𝑑𝑚𝑚𝑡𝑡 𝑆𝑆𝑓𝑓 𝜎𝜎22� ≥ 0𝑑𝑑𝑚𝑚𝑐𝑐 𝑆𝑆𝑓𝑓 𝜎𝜎22� < 0 (5.8)

𝑑𝑑𝑠𝑠 = 1 − �1 − 𝑑𝑑𝑓𝑓𝑡𝑡��1 − 𝑑𝑑𝑓𝑓𝑐𝑐�(1 − 𝑑𝑑𝑚𝑚𝑡𝑡 )(1− 𝑑𝑑𝑚𝑚𝑐𝑐 ) (5.9)

where

𝑑𝑑𝑓𝑓𝑡𝑡 = the damage variable in fiber tension failure;

𝑑𝑑𝑓𝑓𝑐𝑐 = the damage variable in fiber compression failure;

𝑑𝑑𝑚𝑚𝑡𝑡 = the damage variable in matrix tension failure; and


80

𝑑𝑑𝑚𝑚𝑐𝑐 = the damage variable in matrix compression failure.

After the initiation of the damage, the material response is calculated through the

use of a modified stiffness matrix tensor 𝐶𝐶𝑑𝑑 in ABAQUS/Explicit, expressed by Eq. 5.10.

𝜎𝜎 = 𝐶𝐶𝑑𝑑𝜀𝜀 (5.10)

where

𝐶𝐶𝑑𝑑 = the damaged elasticity matrix; and

𝜀𝜀 = the current strain.

In ABAQUS, the damaged elasticity matrix can be expressed by:

𝐶𝐶𝑑𝑑 = 1𝐷𝐷�

�1 − 𝑑𝑑𝑓𝑓�𝐸𝐸1 �1 − 𝑑𝑑𝑓𝑓�(1− 𝑑𝑑𝑚𝑚)𝑣𝑣21𝐸𝐸1 0�1 − 𝑑𝑑𝑓𝑓�(1 − 𝑑𝑑𝑚𝑚)𝑣𝑣12𝐸𝐸2 (1 − 𝑑𝑑𝑚𝑚)𝐸𝐸2 0

0 0 (1 − 𝑑𝑑𝑠𝑠)𝐺𝐺𝐷𝐷� (5.11)

𝐷𝐷 = 1 − �1 − 𝑑𝑑𝑓𝑓�(1 − 𝑑𝑑𝑚𝑚)𝑣𝑣12𝑣𝑣21 (5.12)

where

𝐸𝐸1 = the Young’s modulus in longitudinal direction;

𝐸𝐸2 = the Young’s modulus in transverse direction;

𝑣𝑣12 = the Poisson’s ratio in longitudinal direction;

𝑣𝑣21 = the Poisson’s ratio in transverse direction; and

𝐺𝐺 = the shear modulus.

From the above equations, the damaged stiffness matrix depends on the modified

values of the damage variables. The stiffness decreases as the damage variables increase.


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Therefore, the calculation of the damage variables is essential to analyse the residual

stiffness of the composite material.

The post-failure damage variables for different failure modes can be expressed as a

function of the corresponding equivalent displacement, as shown in Eq. 5.13:

𝑑𝑑 =𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓 �𝛿𝛿𝑒𝑒𝑒𝑒−𝛿𝛿𝑒𝑒𝑒𝑒0 �

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓 �𝛿𝛿𝑒𝑒𝑒𝑒

𝑓𝑓 −𝛿𝛿𝑒𝑒𝑒𝑒0 � (5.13)

where

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓 = the equivalent displacement at which the composite material is fully

damaged;

𝛿𝛿𝑒𝑒𝑒𝑒 = the current state equivalent displacement; and

𝛿𝛿𝑒𝑒𝑒𝑒0 = the initial equivalent displacement at the point of damage initiated.

The equivalent displacement for each mode can be presented as a function of the

equivalent stress in a damage evolution law. The relationship between the equivalent

stress and displacement is shown in Figure 5.2.

Figure 5.2 Typical relationship between equivalent stress and displacement


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As shown in Figure 5.2, the area of the triangle OAC stands for the energy

dissipated due to the failure in each mode. Point A represents the point at which the

damage initiated and point C represents the point at which the composite material

completely failed. Before reaching point A, no damage is expected for the material.

Beyond point A, the evolution law will calculate the drop in the equivalent stress as the

equivalent displacement increases. The calculations of equivalent displacement 𝛿𝛿𝑒𝑒𝑒𝑒 and

equivalent stress 𝜎𝜎𝑒𝑒𝑒𝑒 are shown in the following equations:

Fiber Tension (𝜎𝜎11� ≥ 0):

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑡𝑡 = 𝐿𝐿𝐶𝐶�⟨𝜀𝜀11⟩2 + 𝛼𝛼𝜀𝜀122 (5.14)

𝜎𝜎𝑒𝑒𝑒𝑒𝑓𝑓𝑡𝑡 = ⟨𝜎𝜎11⟩⟨𝜀𝜀11⟩+𝛼𝛼𝜏𝜏12𝜀𝜀12

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑓𝑓 𝐿𝐿𝐶𝐶�

(5.15)

Fiber Compression (𝜎𝜎11� < 0):

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑐𝑐 = 𝐿𝐿𝐶𝐶⟨−𝜀𝜀11⟩ (5.16)

𝜎𝜎𝑒𝑒𝑒𝑒𝑓𝑓𝑐𝑐 = ⟨−𝜎𝜎11⟩⟨−𝜀𝜀11⟩

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑓𝑓 𝐿𝐿𝐶𝐶�

(5.17)

Matrix Tension (𝜎𝜎22� ≥ 0):

𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑡𝑡 = 𝐿𝐿𝐶𝐶�⟨𝜀𝜀22⟩2 + 𝜀𝜀122 (5.18)

𝜎𝜎𝑒𝑒𝑒𝑒𝑚𝑚𝑡𝑡 = ⟨𝜎𝜎22⟩⟨𝜀𝜀22⟩+𝜏𝜏12𝜀𝜀12𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑓𝑓 𝐿𝐿𝐶𝐶⁄ (5.19)

Matrix Compression (𝜎𝜎22� < 0):

𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑐𝑐 = 𝐿𝐿𝐶𝐶�⟨−𝜀𝜀22⟩2 + 𝜀𝜀122 (5.20)

𝜎𝜎𝑒𝑒𝑒𝑒𝑚𝑚𝑐𝑐 = ⟨−𝜎𝜎11⟩⟨−𝜀𝜀11⟩+𝜏𝜏12𝜀𝜀12𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑓𝑓 𝐿𝐿𝐶𝐶⁄ (5.21)


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where

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑡𝑡 = the current equivalent displacement in the post fiber tension failure;

𝛿𝛿𝑒𝑒𝑒𝑒𝑓𝑓𝑐𝑐 = the current equivalent displacement in the post fiber compression failure;

𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑡𝑡 = the current equivalent displacement in the post matrix tension failure;

𝛿𝛿𝑒𝑒𝑒𝑒𝑚𝑚𝑐𝑐 = the current equivalent displacement in the post matrix compression failure;

𝜎𝜎𝑒𝑒𝑒𝑒𝑓𝑓𝑡𝑡 = the current equivalent stress in the post fiber tension failure;

𝜎𝜎𝑒𝑒𝑒𝑒𝑓𝑓𝑐𝑐 = the current equivalent stress in the post fiber compression failure;

𝜎𝜎𝑒𝑒𝑒𝑒𝑚𝑚𝑡𝑡 = the current equivalent stress in the post matrix tension failure;

𝜎𝜎𝑒𝑒𝑒𝑒𝑚𝑚𝑐𝑐 = the current equivalent stress in the post matrix compression failure;

𝜀𝜀11 = the principal strain in longitudinal direction;

𝜀𝜀22 = the principal strain in transverse direction;

𝜀𝜀12 = the principal shear strain;

𝜏𝜏12 = the tangential strain;

𝐿𝐿𝐶𝐶 = the characteristic length; and

⟨ ⟩ = the Macaulay bracket operator (when 𝑥𝑥 ∈ 𝑅𝑅 as ⟨𝑥𝑥⟩ = (𝑥𝑥 + |𝑥𝑥|) 2⁄ ).

In either way, loading or unloading, the equivalent stress will drop down to zero.

The values of the equivalent displacement at this point are controlled by the fracture

energy 𝐺𝐺𝐶𝐶 (the input parameters 𝐺𝐺𝑓𝑓𝑡𝑡𝐶𝐶 , 𝐺𝐺𝑓𝑓𝑐𝑐𝐶𝐶 , 𝐺𝐺𝑚𝑚𝑡𝑡𝐶𝐶 , 𝐺𝐺𝑚𝑚𝑐𝑐𝐶𝐶 represent the energies dissipated

during the damage in the failure of fiber tension, fiber compression, matrix tension and


84

matrix compression respectively). Beyond point A in Figure 5.2, when the model is

unloaded before the occurrence of complete failure, the equivalent stress will drop back

linearly from point B. The modified fracture energy is then presented by the area of the

triangle OBC. When the damage variables continuously develops to the value of one

(point C), the composite material is completely damaged and no more load can be carried.

In ABAQUS/Explicit, the behaviour of rate-dependent material can be modelled by

introducing the viscous regularisation coefficients. The viscous regularisation of a

composite material can be defined as follows:

𝑑𝑑�̇�𝑣 = 1𝜂𝜂

(𝑑𝑑 − 𝑑𝑑𝑣𝑣) (5.22)

where

𝑑𝑑�̇�𝑣 = the true value of the damage variable in the viscous system;

𝜂𝜂 = the viscosity coefficient controlling the rate of relaxation time;

𝑑𝑑 = the calculated damage variable; and

𝑑𝑑𝑣𝑣 = the regularised damage variable used in the damaged stiffness matrix 𝐶𝐶𝑑𝑑.

Four input parameters (𝜂𝜂𝑓𝑓𝑡𝑡, 𝜂𝜂𝑓𝑓𝑐𝑐, 𝜂𝜂𝑚𝑚𝑡𝑡, 𝜂𝜂𝑚𝑚𝑐𝑐) represent the viscosity coefficients used

for fiber failure in tension, compression, and matrix in tension and compression

respectively. The rate of increase of damage can be decelerated by introducing the

viscosity coefficients, which will result in an increase of the dissipated energy as well as

the rates of deformation. This behaviour can be treated as the method of modelling rate-

dependent materials. In ABAQUS/Explicit, a small value of the viscosity input parameter

is recommended. Since the method for calculating the viscosity coefficients has not been

established, extensive trials have been done to determine the reliable input for the

viscosity regularisation model, as shown in Table 5.1.


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Table 5.1 Damage stabilization parameters for pultruded GFRP composites

ƞft ƞfc ƞmt ƞmc 0.0001 0.0001 0.00015 0.00015

Moreover, there is no established method for calculating the fracture energy of

pultruded GFRP composites in the literature as well; however, there are some reference

data and studies available in the literature for glass fiber-reinforced laminates (Pinho et

al., 2006, Lapczyk and Hurtado, 2007, Canal et al., 2012, Barbero et al., 2013, Philippidis

and Antoniou, 2013). Therefore, extensive numerical trials with different parameters have

been developed to determine the reliable input parameters for this model. The ratio

between the input parameters of the fracture energy and the material mechanical

properties used in this simulation match with what is reported in the literature. From the

numerical results of different input values for the fracture energy, the value of matrix

tensile fracture energy played a significant role, which indicates matrix cracking is a

primary failure mode in this numerical investigation. This corroborates the experimental

results reported in the preceding chapter, in which the major failure mode is matrix

cracking. The material properties (obtained from coupon tests) and input parameters are

shown in Table 5.2 – 5.4.

Table 5.2 Material properties of pultruded GFRP composites

E1[MPa] E2[MPa] G12[MPa] Nu12 εft = εfc εtt = εtc = εs 28870 3505 2980 0.21 0.011 0.013

Table 5.3 Damage initiation parameters of pultruded GFRP composites

XT[MPa] XC[MPa] YT[MPa] YC[MPa] SL[MPa] 301.198 310.785 29.78 31.97 33.0


86

Table 5.4 Damage evolution parameters for pultruded GFRP composites

Gft,c [N/mm] Gfc,c [N/mm] Gmt,c [N/mm] Gmc,c [N/mm] 55.0 95.0 11.5 11.5

5.4 Numerical results

A representation of the FEM is shown in Figure 5.3. The predicted results were

compared with the experimental ones. A comparison of load histories for all the impact

energy levels is shown in Fig. 5.4. A reasonably good agreement is achieved between the

experimental results and the numerical ones.

Figure 5.3 Schematic diagram of experimental test and numerical simulation in progress


87

Figure 5.4 Comparison between numerical and experimental results for force-time at all

impact energies

In the early loading stage, three linear increases of load in the elastic regime were

well simulated in all the numerical models. After that, an inelastic behaviour was shown

till up to the maximum load. The peak force predicted by the FEMs were 8.25, 11.54,

13.74 and 15.69 kN, respectively for four energy levels, which was slightly

underestimated for lower impact energy events, as shown in Figure 5.6. In the unloading

stage, the tendency of impact force was slightly overestimated for lower energy levels

when compared to the experimental results. It was assumed that some internal damage,

such as delamination between mat and roving layers, reduced the bending stiffness of the

pultruded GFRP composites during the higher energy impact tests. The comparison of


88

central deflection histories for all the impact energy levels are shown in Figure 5.5. A

reasonable agreement is achieved compared with the experimental data. In the loading

stage, the slope of the curve presented a good match with the experimental results. As

shown in Figure 5.6, the maximum central deflections predicted by FEMs were 3.391,

4.945, 5.996 and 7.037 mm respectively for four energy levels. The deflection was

slightly overestimated for lower impact energy event. However, the central deflection

were underestimated for higher energy tests. The composite material was simulated stiffer

during higher impact energy events when compared to the experimental tests. In the

unloading stage, the predicted rebound behaviour was faster than that in the experimental

tests, and the unrecoverable deformation (end of deflection-time curves) were predicted

smaller than the experimental results. This indicated that the post-failure strength of

pultruded GFRP composites were modelled stiffer after the impact events, and more

impact energies were absorbed in the experiments. This matches the impact behaviour

shown in the force-time curves; the internal damage during the experimental tests reduced

the stiffness of the material. The comparison of impact performance in terms of maximum

load and central deflection between numerical and experimental results is shown in Figure

5.6. Similar to the findings in the experimental results, the maximum impact load and the

maximum central deflection increase near linearly with respect to the impact energy. The

impact performance presents a fairly good agreement between the experimental results

and the numerical ones in terms of maximum impact load and deflection.


89

Figure 5.5 Comparison of numerical and experimental results for central deflection

versus time curves at all impact energies

Figure 5.6 Comparison of maximum load and central deflection between numerical and

experiment results


90

The development and propagation of stress was evaluated through the visualization

of the numerical results. During the numerical analysis, the transverse stress in the top

layer increased quickly and matched the initiation criteria of the progressive damage

model, which indicated the matrix cracking first occurred during the simulation. With the

increase in contact duration, the stress propagated from oblong shape into peanut shape

through the top layer to the bottom layer, which matched the damage area shape shown

on the back surface from the experiment. The schematic diagrams of the von Mises stress,

the minimum in-plane principal stress, and the Tresca stress propagations are shown in

Figure 5.7 – Figure 5.12 respectively. The four subfigures in each figure correspond to

the numerical results for the four different impact energy levels. Since the vertical

displacement in the top layer of the experimental results were not available, these figures

are introduced only to present how the stress were developed and propagated, no colour

scales were required. A representation of the comparison between the experimental

results and numerical ones is shown in Figure 5.13. The numerical results were found to

corroborate the experimental ones in terms of cracking patterns and damage areas with

respect to the impact energy levels.


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Figure 5.7 Schematic diagrams of von Mises stress propagation in top layer

Figure 5.8 Schematic diagrams of von Mises stress propagation in bottom layer


92

Figure 5.9 Schematic diagrams of Minimum in-plane principal stress propagation in top

layer

Figure 5.10 Schematic diagrams of Maximum in-plane principal stress propagation in

bottom layer


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Figure 5.11 Schematic diagrams of Tresca stress propagation in top layer

Figure 5.12 Schematic diagrams of Tresca stress propagation in bottom layer


94

Figure 5.13 The comparison of experimental and numerical results

5.5 Summary

In this chapter, a numerical study of impact response of pultruded GFRP composites

subjected to low-velocity impact loadings was conducted. A non-linear FEM was

developed using the progressive damage model to simulate such behaviour. The

numerical predictions were found to corroborate the experimental results in terms of load-

time and central deflection-time curves. The numerical simulation indicates that the


95

tensile stress in the transverse direction of the top layer exceeds the limitation after the

elastic stage and satisfies the damage initiation criteria of the progressive damage model.

In the unloading stage, the miss-match of the load-time and displacement-time curves

between the experimental and the numerical results show the internal damage in the

experimental tests reduced the bending stiffness of the pultruded GFRP composites. The

validated numerical model from this chapter will be employed in the numerical

investigations of hybrid GFRP-concrete beams.

Chapter 6

Numerical Study of the Hybrid GFRP-

Concrete Beam to Static Loading3

6.1 Introduction

In Chapter 5, numerical investigations of pultruded GFRP coupons subjected to

low-velocity impacts were performed. A good agreement was achieved between the

numerical results and the experimental ones. The progressive damage model proved to be

reliable for simulating the behaviour of pultruded GFRP composites. In this chapter, the

validated GFRP material model and the concrete damaged plasticity model (CDPM) are

employed for the different materials used in the hybrid members. The hybrid GFRP-

concrete beam, which consists of high strength ordinary Portland cement concrete (OPC)

filled into the rectangular hollow pultruded profiles, is investigated numerically using the

commercial software ABAQUS/Standard. A non-linear numerical model is developed to

predict the flexural behaviour of the hybrid structure under four-point static loadings. The

effect of mesh dimensions and the use of a debonding model are also reported in this

chapter. The numerical results are compared with the published experimental data from

the literature. The main purpose of this numerical investigation is to validate the

numerical model of hybrid GFRP-concrete system with experimental results and to


LI, Z., KHENNANE, A. & HAZELL, P. J. 2016. Numerical investigation of a hybrid FRP-geopolymer concrete beam. Applied Mechanics and Materials, 846, 452-457.

Chapter 6 - Numerical Study of the Hybrid GFRP-Concrete Beam to Static Loading

97

present the reference setup parameters for the experimental program of the hybrid beams

subjected to impact loadings.

6.2 Description of the experimental program

To validate the numerical model of the hybrid GFRP-concrete beam, an

experimental test case of this hybrid system has been reported here (Ferdous et al., 2013).

Three hybrid beams were cast with base-plates on both ends. The hybrid beams were

tested along the weak axis under a four-point bending test to evaluate its flexural

behaviour. The total length of each beam was 2000 mm and the span length was 1440mm.

The schematic diagram of the experimental setup is shown in Figure 6.1.

Figure 6.1 Schematic diagram of the experimental setup (Ferdous et al., 2013)


A non-linear FEM was developed using the commercial software

ABAQUS/Standard to simulate the flexural behaviour of the hybrid GFRP-concrete

beam. Linear eight-node three-dimensional solid elements with reduced integration


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(C3D8R) were used to model the concrete volume, while the pultruded GFRP profiles

were modelled by using eight-node quadrilateral in-plane general-purpose continuum

shell elements (SC8R). The pultruded GFRP composites and the concrete inside were

fully bonded through all the contact surfaces to ensure the kinetic continuity during the

loading period. Due to the symmetry of loading and geometry, only half of the beam was

modelled. Displacement control was used for the arrangements of the test, as per the

experimental setup. The assembled FEM boundary conditions is shown in Figure 6.2.

Figure 6.2 Assembled FEM for the hybrid GFRP-concrete beams

6.4 Material models

Two material models of concrete and FRP composites were used in this analysis.

The concrete section of the hybrid beam was modelled using the CDPM and, the

pultruded GFRP composites were modelled using the progressive damage model (Hashin

damage model).


99

6.4.1 Progressive damage model

The progressive damage model used for the pultruded GFRP composites in Chapter

5 was employed in this analysis. Details of the failure mechanisms and the input

parameters can be found in the preceding chapter.

6.4.2 Concrete damaged plasticity model

There are three different material models integrated in ABAQUS for modelling the

non-linear behaviour of concrete, smeared crack concrete model, brittle crack concrete

model and CDPM. The latter approach was chosen, which is aimed at providing a general

capability for modelling concrete by using the concepts of isotropic damaged elasticity in

combination with isotropic tensile and compressive plasticity to represent the inelastic

behaviour of concrete.

6.4.2.1 Mechanisms of CDPM

The detailed description of the CDPM and its implementation are available in the

ABAQUS Documentation (ABAQUS, 2014). To explain the input parameters used in

this model, a brief description of the CDPM is presented (ABAQUS, 2014) next.

The total strain at a Gauss point within an element can be either elastic or elasto-

plastic. Hence, the differential of the deformations consists of two parts, elastic and plastic

strain, which can be expressed as:

𝜀𝜀 = 𝜀𝜀𝑒𝑒 + 𝜀𝜀𝑝𝑝 (6.1)

where

𝜀𝜀 = the total strain;

𝜀𝜀𝑒𝑒 = the elastic strain; and


100

𝜀𝜀𝑝𝑝 = the plastic strain.

The stress in each element of the concrete block is governed by a function of the

variables of strain:

𝜎𝜎′ = (1 − 𝑑𝑑)𝐷𝐷𝑜𝑜𝑒𝑒 ∶ (𝜀𝜀 − 𝜀𝜀𝑝𝑝) = 𝐷𝐷𝑒𝑒 ∶ (𝜀𝜀 − 𝜀𝜀𝑝𝑝) (6.2)

where

𝜎𝜎′ = the stress in the concrete elements;

𝑑𝑑 = the degradation variables;

𝐷𝐷𝑜𝑜𝑒𝑒 = the undamaged elastic stiffness; and

𝐷𝐷𝑒𝑒 = the damaged elastic stiffness.

From the Eq. 6.2, the stiffness of the element decreases with the increase of the

damage variable. When the value of the damage variable raises up to one, the stiffness of

the element decreases down to zero and no further load can be carried by the Gauss point.

The effective stress in a damaged model can be expressed as:

𝜎𝜎� = 𝐷𝐷𝑒𝑒 ∶ (𝜀𝜀 − 𝜀𝜀𝑝𝑝) (6.3)

𝜎𝜎′ = (1 − 𝑑𝑑)𝜎𝜎� (6.4)

where

𝜎𝜎� = the effective stress in the damaged material model.

From the Eq. 6.3 and 6.4, the effective stress is governed by the strain and the

damaged variable. When the damage begins to be initiated (1 > 𝑑𝑑 > 0), the material

response is presented in a plastic behaviour. During this period, the damage states under


101

compression and tension are represented by the hardening variables, 𝜀𝜀�̃�𝑐𝑝𝑝 and 𝜀𝜀�̃�𝑡

𝑝𝑝

respectively, which can be determined by:

𝜀𝜀�̃�𝑐𝑝𝑝 = −𝜀𝜀�̃�𝑚𝑖𝑖𝑘𝑘

𝑝𝑝 ∙ �1 − 𝑟𝑟(𝜎𝜎��)� (6.5)

𝜀𝜀�̃�𝑡𝑝𝑝 = −𝜀𝜀�̃�𝑚𝑎𝑎𝑚𝑚

𝑝𝑝 ∙ 𝑟𝑟(𝜎𝜎��) (6.6)

where

𝜀𝜀�̃�𝑐𝑝𝑝 = the equivalent plastic strain in compression;

𝜀𝜀�̃�𝑡𝑝𝑝 = the equivalent plastic strain in tension;

𝜀𝜀�̃�𝑚𝑖𝑖𝑘𝑘𝑝𝑝 = the minimum eigenvalue of the plastic strain;

𝜀𝜀�̃�𝑚𝑎𝑎𝑚𝑚𝑝𝑝 = the maximum eigenvalue of the plastic strain;

𝜎𝜎�� = the effective stress tensor; and

𝑟𝑟 = the weight factor.

The effects of the weight factor into stress can be calculated from:

𝑟𝑟(𝜎𝜎��) = ∑ ⟨𝜎𝜎��𝑖𝑖⟩3𝑖𝑖=1 ∑ |𝜎𝜎��𝑖𝑖|3

𝑖𝑖=1⁄ (6.7)

where

𝜎𝜎��𝑖𝑖 = the principal stress;

⟨ ⟩ = the Macaulay bracket operator (when 𝑥𝑥 ∈ 𝑅𝑅 as ⟨𝑥𝑥⟩ = (𝑥𝑥 + |𝑥𝑥|) 2⁄ ); and

| | = the absolute value.

The hardening variables, 𝜀𝜀�̃�𝑐𝑝𝑝 and 𝜀𝜀�̃�𝑡

𝑝𝑝, from Eq. 6.5 and 6.6 can be determined as a

tabular function of the equivalent stress in the specified compression hardening and


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tension softening behaviour of concrete in CDPM. The weight factor 𝑟𝑟, ranging from 0

to 1, is incorporated with the effective stress tensor to represent the ratio of the principal

stress.

In ABAQUS, the yield function (Lubliner et al., 1989, Lee and Fenves, 1998) is

employed to introduce the damage evolution of strength in the compressive and/or tensile

failure of the concrete. The yield function is defined as an effective surface which

represents the states of the damaged model in terms of the effective stress, as shown in

Figure 6.3.

Figure 6.3 Yield surface in plane stress (ABAQUS, 2014)

To determine the evolution of the yield surface by the use of the effective stresses

and hardening variables, the yield function can be formulated as:


103

𝐹𝐹(𝜎𝜎�, 𝜀𝜀̃𝑝𝑝) = 11−𝛼𝛼

(𝑞𝑞� − 3𝛼𝛼�̅�𝑝 + 𝛽𝛽(𝜀𝜀̃𝑝𝑝)⟨𝜎𝜎��𝑚𝑚𝑎𝑎𝑚𝑚⟩ − 𝛾𝛾⟨𝜎𝜎��𝑚𝑚𝑎𝑎𝑚𝑚⟩) − 𝜎𝜎�(𝜀𝜀̃𝑝𝑝) ≤ 0 (6.8)

where

𝐹𝐹 = the yield surface;

𝛼𝛼 = the dimensionless constant;

𝛽𝛽 = the dimension coefficient;

𝛾𝛾 = the dimensionless material constant;

�̅�𝑝 = the effective hydrostatic pressure;

𝑞𝑞� = the effective Mises equivalent stress; and

𝜎𝜎��𝑚𝑚𝑎𝑎𝑚𝑚 = the maximum effective principal stress.

The values of 𝛼𝛼, 𝛽𝛽, 𝛾𝛾, �̅�𝑝, 𝑞𝑞� can be obtained from:

𝛼𝛼 =�𝜎𝜎𝑏𝑏0 𝜎𝜎𝑓𝑓0� �−1

2�𝜎𝜎𝑏𝑏0 𝜎𝜎𝑓𝑓0� �−1, 0 ≤ 𝛼𝛼 ≤ 0.5 (6.9)

where

𝜎𝜎𝑎𝑎0 = the initial equibiaxial compressive yield stress; and

𝜎𝜎𝑐𝑐0 = the initial uniaxial compressive yield stress.

The ratio of the initial equibiaixal compressive yield stress to the initial uniaxial

compressive yield stress can be implemented as a constant value in the CDPM.

𝛽𝛽 = (1 − 𝛼𝛼) 𝜎𝜎�𝑓𝑓(𝜀𝜀�𝑓𝑓𝑝𝑝)

𝜎𝜎�𝑓𝑓(𝜀𝜀�𝑓𝑓𝑝𝑝)− (1 + 𝛼𝛼) (6.10)

where


104

𝜎𝜎�𝑐𝑐(𝜀𝜀�̃�𝑐𝑝𝑝) = the effective compressive cohesion; and

𝜎𝜎�𝑡𝑡(𝜀𝜀�̃�𝑡𝑝𝑝) = the effective tensile cohesion.

𝛾𝛾 = 3(1−𝐾𝐾𝑓𝑓)2𝐾𝐾𝑓𝑓−1

(6.11)

𝐾𝐾𝑐𝑐 = 𝑞𝑞𝑇𝑇𝐶𝐶/𝑞𝑞𝐶𝐶𝐶𝐶 (6.12)

where

𝑞𝑞𝑇𝑇𝐶𝐶 = the second stress invariant on the tensile meridian;

𝑞𝑞𝐶𝐶𝐶𝐶 = the second stress invariant on the compressive meridian; and

𝐾𝐾𝑐𝑐 = the ratio of 𝑞𝑞𝑇𝑇𝐶𝐶 to 𝑞𝑞𝐶𝐶𝐶𝐶 at initial yield for any given value of the pressure

invariant 𝑝𝑝 when 𝜎𝜎�𝑚𝑚𝑎𝑎𝑚𝑚 < 0; 0.5 < 𝐾𝐾𝑐𝑐 ≤ 1.0.

The 𝐾𝐾𝑐𝑐 can be determined as a constant value in CDPM, which is recommended to

be 2/3.

�̅�𝑝 = −13∙ 𝑡𝑡𝑟𝑟𝐶𝐶𝑡𝑡𝐹𝐹(𝜎𝜎�) (6.13)

𝑞𝑞� = �32𝑆𝑆̅ ∶ 𝑆𝑆̅ (6.14)

𝑆𝑆̅ = 𝜎𝜎� + �̅�𝑝𝐼𝐼 (6.15)

where

𝑆𝑆̅ = the effective stress deviator; and

𝐼𝐼 = the identity matrix.

In the CDPM, the growth of the cracks and the concrete crushing are governed by

the variation of the plastic strain. When it is transformed into the corresponding


105

equivalent strain, the evolution of the yield surface would be controlled by the generated

equivalent strain. Hence, the failure of the concrete elements relies on the transforming

rate of the plastic strain. The amount of the plastic strain during this stage can be

determined by the non-associated plastic flow rule, which is expressed as:

𝜀𝜀̇𝑝𝑝 = �̇�𝜆 𝜕𝜕𝐺𝐺′

𝜕𝜕𝜎𝜎� (6.16)

where

𝜀𝜀̇𝑝𝑝 = the plastic strain increment;

�̇�𝜆 = the proportionality coefficient; and

𝐺𝐺′ = the plastic potential flow.

The potential flow can be defined by the Drucker-Prager hyperbolic plastic

potential function:

G′ = �(ϵσt0 tanψ)2 + 𝑞𝑞�2 − p� tanψ (6.17)

where

ϵ = the eccentricity parameter;

σt0 = the uniaxial tensile stress at failure; and

Ψ = the dilation angle.

The eccentricity ϵ can be implemented as a constant parameter in CDPM, which is

recommend to equal to 0.1. The dilation angle Ψ is defined in the p-q plane, which can

be expressed as:

ψ = dεvp

dγvp (6.18)


106

where

dεvp = the volumetric strain rate; and

dγvp = the volumetric shear strain rate.

The typical uniaxial compressive and tensile behaviour (stress-strain relationship)

of the concrete defined in the CDPM is shown in Figure 6.4. When the response of

concrete element behaves in the strain-softening zone due to compression and/or tension,

the internal damage has been initiated. The stiffness of the concrete decreases non-linearly

in the plastic zone. The degraded material response of concrete element is then expressed

as function of damage variables. The stress-strain relationships in this stage can be

formulised as:

For compression:

𝜎𝜎𝑐𝑐 = (1 − 𝑑𝑑𝑐𝑐)𝐸𝐸𝑖𝑖�𝜀𝜀 − 𝜀𝜀�̃�𝑐𝑝𝑝� (6.19)

For tension:

𝜎𝜎𝑡𝑡 = (1 − 𝑑𝑑𝑡𝑡)𝐸𝐸𝑖𝑖�𝜀𝜀 − 𝜀𝜀�̃�𝑡𝑝𝑝� (6.20)

where

𝜎𝜎𝑐𝑐 = the current compressive stress;

𝜎𝜎𝑡𝑡 = the current tensile stress;

𝑑𝑑𝑐𝑐 = the scalar damage variable in compression;

𝑑𝑑𝑡𝑡 = the scalar damage variable in tension;

𝐸𝐸𝑖𝑖 = the initial modulus of elasticity;


107

𝜀𝜀�̃�𝑐𝑝𝑝 = the plastic strain in compression; and

𝜀𝜀�̃�𝑡𝑝𝑝 = the plastic strain in tension.

Figure 6.4 A typical stress-strain relationship for compressive and tensile behaviour in

CDPM (ABAQUS, 2014)

After the plastic behaviour is presented, the cracks are initiated and propagate

through the elements. As a result, the effective load-carrying area is reduced, which

thereby leads to an increase of the corresponding effective stress. The effective stress in

compression 𝜎𝜎�𝑐𝑐 and tension is presented in Eq. 6.21 and 6.22 respectively.

𝜎𝜎�𝑐𝑐 = 𝜎𝜎𝑓𝑓1−𝑑𝑑𝑓𝑓

= 𝐸𝐸𝑖𝑖(𝜀𝜀 − 𝜀𝜀�̃�𝑐𝑝𝑝) (6.21)

𝜎𝜎�𝑡𝑡 = 𝜎𝜎𝑓𝑓1−𝑑𝑑𝑓𝑓

= 𝐸𝐸𝑖𝑖(𝜀𝜀 − 𝜀𝜀�̃�𝑡𝑝𝑝) (6.22)

where


108

𝜎𝜎�𝑐𝑐 = the effective uniaxial stress in compression; and

𝜎𝜎�𝑡𝑡 = the effective uniaxial stress in tension.

6.4.2.2 Input parameters study of CDPM

The material properties for the concrete (OPC) used in this study are shown in Table

6.1.

Table 6.1 Properties of high performance concrete (Ferdous, 2012)

Type of concrete

Modulus of elasticity,

[MPa]

Poisson’s ratio

Maximum compressive

strength, [MPa]

Maximum tensile

strength, [MPa]

OPC 30000 0.18* 57 3.4 *Assumed

Compression:

In the CDPM, the compressive behaviour of concrete is simulated by the use of an

elastic-plastic hardening model. In a typical uniaxial compressive loading case, the

concrete behaves elastically up to 30 – 50 % of its maximum compressive strength

(Beletich and Uno, 2003). In this study, the linear elastic behaviour is taken up to 45 %,

which is equivalent to 25.65 MPa. Beyond this, the material response is presented by the

use of the inputted tabular functions of stress and inelastic strain.

To describe the compressive behaviour of concrete, two different stress-strain

relationship models have been used to represent the stress-strain relationship of the

compression-hardening and strain-softening zone respectively. The expression for stress-

strain relationship of Popovics (1973), modified by Thorenfeldt et al. (1987) is chosen to

describe the compressive hardening behaviour, which is given by the following equation:


109

𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓′

= 𝜀𝜀𝑓𝑓𝜀𝜀𝑓𝑓′∙ 𝑘𝑘

𝑘𝑘−1+�𝜀𝜀𝑓𝑓𝜀𝜀𝑓𝑓′ �

𝑛𝑛𝑛𝑛 (6.23)

where

𝑓𝑓𝑐𝑐 = the compressive stress;

𝑓𝑓𝑐𝑐′ = the maximum compressive strength;

𝜀𝜀𝑐𝑐 = the strain in compression;

𝜀𝜀𝑐𝑐′ = the strain when the compressive strength reaches the maximum value;

𝑛𝑛 = the curve fitting factor; and

𝑘𝑘 = the fitting constant (𝑘𝑘 = 1, when 𝜀𝜀𝑐𝑐 𝜀𝜀𝑐𝑐′⁄ ≤ 1).

Collins and Mitchell (1991) recommended, for OPC, the factor n to be estimated

as:

𝑛𝑛 = 0.8 + 𝑓𝑓𝑓𝑓′

17 𝑆𝑆𝑛𝑛 𝑀𝑀𝑃𝑃𝐶𝐶 𝑢𝑢𝑛𝑛𝑆𝑆𝑡𝑡 (6.24)

Collins et al. (1993) also suggested the value of 𝜀𝜀𝑐𝑐′ to be calculated through the

following expression:

𝜀𝜀𝑐𝑐′ = 𝑓𝑓𝑓𝑓′

𝐸𝐸𝑓𝑓∙ 𝑘𝑘𝑘𝑘−1

(6.25)

where

𝐸𝐸𝑐𝑐 = the Young’s modulus.

The expression for the stress-strain relationship from Carreira and Chu (1985),

modified by Wee et al. (1996) is chosen to describe the behaviour in strain softening zone

of concrete, which is given by the following equation:


110

𝑓𝑓𝑐𝑐 = 𝑓𝑓𝑐𝑐′

⎩⎨

⎧ 𝑘𝑘1′ 𝛽𝛽�𝜀𝜀𝑓𝑓𝜀𝜀𝑓𝑓′�

𝑘𝑘1′ 𝛽𝛽−1+�𝜀𝜀𝑓𝑓𝜀𝜀𝑓𝑓′ �

𝑛𝑛2′ 𝛽𝛽

⎭⎬

⎫ (6.26)

where

𝑘𝑘1′ = the material factor for high strength concrete;

𝑘𝑘2′ = the fitting factor for high strength concrete; and

𝛽𝛽 = the material parameter that depends on the shape of the stress-strain diagram.

When the maximum compressive strength of the concrete is less than 50 MPa, the

factors 𝑘𝑘1′ and 𝑘𝑘2′ are taken as unity (𝑘𝑘1′ = 𝑘𝑘2′ = 1). If the maximum compressive strength

is larger than 50 MPa, the factors 𝑘𝑘1′ and 𝑘𝑘2′ can be calculated by:

𝑘𝑘1′ = �50𝑓𝑓𝑓𝑓′�3 (6.27)

𝑘𝑘2′ = �50𝑓𝑓𝑓𝑓′�1.3

(6.28)

For the material parameter 𝛽𝛽, it is recommended to be calculated as:

𝛽𝛽 = 1

1−� 𝑓𝑓𝑓𝑓′

𝜀𝜀𝑓𝑓′ 𝐸𝐸𝑖𝑖𝑓𝑓� (6.29)

where

𝐸𝐸𝑖𝑖𝑡𝑡 = the initial tangent modulus.

The initial tangent modulus can be estimated by:

𝐸𝐸𝑖𝑖𝑡𝑡 = 10200(𝑓𝑓𝑐𝑐′)1 3⁄ (6.30)

The compressive stress-strain curve of the OPC is presented in Figure 6.5.


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Figure 6.5 Compressive stress-strain curve

It is worth noting that the input compressive hardening data are presented in terms

of inelastic strain values instead of the plastic strain values for the implementation of the

compressive behaviour of concrete. The inelastic strain values can be calculated from:

𝜀𝜀𝑖𝑖𝑘𝑘 = 𝜀𝜀 − 𝜎𝜎𝑓𝑓𝐸𝐸𝑖𝑖

(6.31)

where

𝜀𝜀𝑖𝑖𝑘𝑘 = the inelastic strain.

The corresponding implemented compression damage variables can be obtained by:

𝜎𝜎𝑐𝑐 = (1 − 𝑑𝑑𝑐𝑐)𝐸𝐸𝑖𝑖(𝜀𝜀 − 𝜀𝜀𝑝𝑝) (6.32)

Tension:

Since no reinforcement is embedded inside of the concrete block, the tensile-

softening behaviour is recommended to be defined on the crack-opening law and fracture


112

energy cracking criterion in ABAQUS (ABAQUS, 2014). The mechanisms of this

method are briefly described as follows: once the tensile stress exceeds the damage

criterion, cracks are assumed to be formed perpendicular to the stress direction. After the

formation of the cracks, the effective area of the elements decreases, which results in an

increase of the tensile stress. With further loading, the damaged elements will be removed

and the cracking length will increase accordingly, which behaviour can be determined by

the opening at the cracks.

To simulate this tensile behaviour, the Hordijk (1991) tensile model is chosen, in

which the tensile behaviour of concrete is characterised by a stress-displacement

response. In this model, the concrete response is assumed to be linearly elastic before the

damage is introduced and a fracture energy value is employed to control the area in the

tension softening zone. The post-cracking behaviour is expressed by:

ft = 𝑓𝑓𝑡𝑡′ ��1 + (C1ωωc

)3� exp �−C2ωωc� − ω

ωc(1 + C13)exp (−C2)� (6.33)

where

ft = the tensile stress;

𝑓𝑓𝑡𝑡′ = the maximum tensile strength;

ω = the crack opening displacement;

ωc = the crack opening displacement at the complete release of stress;

C1 = a constant value of 3; and

C2 = a constant value of 6.93.

The value of ωc can be expressed as a function of the tensile fracture energy:


113

ωc = 5.14 Gf𝑓𝑓𝑓𝑓′

(6.34)

where

Gf = the tensile fracture energy.

According to Ueda (2004), the maximum tensile strength for OPC and the tensile

fracture energy can be calculated from:

𝑓𝑓𝑡𝑡′ = 0.23(𝑓𝑓𝑐𝑐′)2 3⁄ (6.35)

Gf = 10(dmax)1/3(𝑓𝑓𝑐𝑐′)1/3 (6.36)

where

dmax = the maximum aggregate size in mm (14 mm in this study).

The tensile stress-crack opening displacement curve of the OPC is shown in Figure

6.6.

Figure 6.6 Tensile stress-displacement curve


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6.5 Mesh sensitivity

Mesh sensitivity is an important factor in finite element analysis. A proper FE mesh

will provide an accurate result with minimum computational time. To determine the

optimum mesh, three models with different mesh sizes were investigated, as shown in

Figure 6.7. The comparative results are summarised in Table 6.2.

Figure 6.7 Numerical models with different mesh sizes

Table 6.2 Comparison results for different meshes

Total elements Mesh size [mm] Failure load [kN] Diff [%] Mesh 1 159400 5 × 5 124.56 7.41 Mesh 2 20900 10 × 10 124.97 7.71 Mesh 3 4500 20 × 20 128.62 10.33

Considering the computational time (Figure 6.8) and the results for the failure load

(Figure 6.9), Mesh 2 produced a better compromise than Meshes 1 and 3, therefore Mesh

2 was selected for this analysis.


115

Figure 6.8 Computational time (Intel Core i7-3770 @ 3.40GHz)

Figure 6.9 Mesh sensitivity – Failure load


116

6.6 Numerical results

6.6.1 Fully bonded model

In the fully bonded model, kinematic continuity is assumed between the concrete

and the GFRP composites. As a result, the two different materials experience the same

deformation and no debonding failure is allowed. A comparison of the load-displacement

curves between the numerical and the experimental results is shown in Figure 6.10. The

slope of the curve from the numerical analysis matched with experimental data. The

ultimate failure load from the numerical analysis is 140 kN, while the ultimate failures

from the experimental tests take place at 120, 111 and 115 kN. The relative difference is

more than 20 % for this model.


displacement curves (Fully bonded model)


117

6.6.2 Debonding model

The bond behaviour between the concrete and the pultruded profile is modelled by

using the surface-based cohesive behaviour because the interface thickness is negligibly

small. This model assumes the bonding behave as a linear elastic traction-separation law

before damage and, the failure of the cohesive bond is characterized by the progressive

degradation of the cohesive stiffness, which is driven by damage progress. A typical

relationship between traction and separation is shown in Figure 6.11.

Figure 6.11 Typical relationship between traction and separation (ABAQUS, 2014)

The elastic behaviour is formulated in terms of an elastic constitutive model, which

presents the relations of the normal and shear separations across the interface. The

traction-separation model is expressed based on an uncoupled stiffness matrix:

𝑇𝑇 = �𝑡𝑡𝑘𝑘𝑡𝑡𝑠𝑠𝑡𝑡𝑡𝑡� = �

𝑘𝑘𝑘𝑘𝑘𝑘 0 00 𝑘𝑘𝑠𝑠𝑠𝑠 00 0 𝑘𝑘𝑡𝑡𝑡𝑡

� �𝛿𝛿𝑘𝑘𝛿𝛿𝑠𝑠𝛿𝛿𝑡𝑡� = 𝐾𝐾𝛿𝛿 (6.37)

where

𝑇𝑇 = the traction stress;


118

𝐾𝐾 = the bond stiffness matrix;

𝛿𝛿 = the displacement of the contacting surfaces;

𝑡𝑡𝑘𝑘 = the nominal traction in the normal direction;

𝑡𝑡𝑠𝑠 = the nominal in-plane shear stress;

𝑡𝑡𝑡𝑡 = the nominal out-plane shear stress;

𝛿𝛿𝑘𝑘 = the displacement in normal direction;

𝛿𝛿𝑠𝑠 = the displacement in shear direction;

𝛿𝛿𝑡𝑡 = the displacement in through-thickness direction;

𝑘𝑘𝑘𝑘𝑘𝑘 = the stiffness in normal direction;

𝑘𝑘𝑠𝑠𝑠𝑠 = the stiffness in shear direction; and

𝑘𝑘𝑡𝑡𝑡𝑡 = the stiffness in through-thickness direction.

According to Henriques et al. (2013), 𝑘𝑘𝑘𝑘𝑘𝑘, 𝑘𝑘𝑠𝑠𝑠𝑠 and 𝑘𝑘𝑡𝑡𝑡𝑡 can be calculated as follows:

𝑘𝑘𝑠𝑠𝑠𝑠 = 𝑘𝑘𝑡𝑡𝑡𝑡 = 𝜏𝜏𝑚𝑚 𝑠𝑠𝑚𝑚⁄ (6.38)

𝑘𝑘𝑘𝑘𝑘𝑘 = 100𝑘𝑘𝑠𝑠𝑠𝑠 = 100𝑘𝑘𝑡𝑡𝑡𝑡 (6.39)

where

𝜏𝜏𝑚𝑚 = the maximum shear stress; and

𝑠𝑠𝑚𝑚 = the slip under the maximum shear stress.

The quadratic traction model is chosen for modelling the traction-separation

behaviour. The maximum stress required for the damage initiation can be calculated

through the equation developed by the National-Research-Council (2004):


119

𝜏𝜏′ = 0.64�2−𝐶𝐶

1+𝑏𝑏𝑓𝑓400

�𝑓𝑓𝑐𝑐′𝑓𝑓𝑐𝑐𝑡𝑡𝑚𝑚 (6.40)

where

𝜏𝜏′ = the shear stress;

𝑀𝑀 = the maximum value between 0.33 and the ratio of 𝑏𝑏𝑓𝑓 𝑏𝑏⁄ ;

𝑏𝑏 = the width of concrete;

𝑏𝑏𝑓𝑓 = the width of GFRP composites; and

𝑓𝑓𝑐𝑐𝑡𝑡𝑚𝑚 = the average concrete tensile strength.

The power law based on the fracture energy is chosen for the damage evolution,

which values can be referenced from the literature (Wong et al., 2012).

In the debonding FEM, the bonding properties based on the surface-based cohesive

behaviour were implemented. A comparison of load-displacement curves between

numerical and experimental results is illustrated in Figure 6.12.


120


displacement curves (Debonding model)

As shown in Figure 6.12, the ultimate failure load from the debonding model is

125kN, and the ultimate failures from the experimental tests are 120, 111, 115 kN. The

relative difference is 8 % between the numerical and experimental results. The failure of

the beam was initiated in the pultruded profile in the early loading stage, which is shown

in Figure 6.13. When the load increased to a certain level (approximately 40 kN), the

damage in the pultruded profile initiated in the bottom side according to Hashin’s fiber

tensile damage initiation criterion (red colour). The flexural behaviour predicted by the

debonding model is similar to the experimental one. The hybrid beam behaved in a purely

elastic fashion until approximately 10 % of the total load, and then the response became

non-linear until failure.


121

Figure 6.13 Hashin’s fiber tensile damage view on the bottom side

The result of the bonding model is shown in Figure 6.14, the ultimate failure of the

beam occurred because of debonding at the interface between the concrete and the

pultruded profile on the bottom side. This behaviour is reasonably simulated, and is in

accordance with the experimental observations. The equivalent plastic strain is shown in

Figure 6.15, the cracking patterns in the concrete were governed by the shear failure, the

cracks were following a diagonal direction from the bottom to the top surface, which

indicate that the concrete inside suffered a significant amount of shear stresses.

Figure 6.14 Debonding failure occurring at the bottom side of the interface


122

Figure 6.15 Concrete cracks development

6.7 Summary

In this chapter, the static flexural behaviour of the hybrid GFRP-concrete beam was

investigated numerically in the commercial software ABAQUS. A non-linear FEM was

developed using the progressive damage model and CDPM to simulate the static

performance of the hybrid beam. Mesh sensitivity analysis was performed to provide a

suitable mesh density for subsequent analysis. The numerical results of the fully bonded

method and the debonding model were compared with the experimental results. It was

found that the debonding model is more accurate, and debonding failure at the interface

between the concrete and the pultruded profile is the main reason for failure in the static

analysis, which is consistent with the experimental results. The bond properties between

the concrete and the pultruded GFRP composites should be considered and assigned in

the numerical analysis. The validated material models, progressive damage model and


123

the CDPM will be employed in the analysis of the hybrid system subjected to impact

loadings.

Chapter 7

Hybrid GFRP-Concrete Beam Subject to

Low-Velocity Impacts: Experimental

Study4

7.1 Introduction

The static flexural performance of the hybrid GFRP-concrete beam has shown that

it has potential to be used as a structural element. However, its dynamic performance

under low-velocity impacts has yet to be assessed. If the hybrid beam is to be used as a

bridge girder or a railway sleeper, it can be subjected to low-velocity impacts during its

service life. Therefore, the aim of this chapter is to investigate the dynamic performance

of the hybrid GFRP-concrete beam subjected to low-velocity impacts.

To achieve this, a high capacity drop-weight machine is used to introduce the

impact loading on two axes of the hybrid beam. The specimens are placed on the rollers

supports, and then subjected to a concentrated impact. The results of the impact

characteristics and performance are compared for different impact energy levels. The

failure modes of the hybrid beam subjected to impacts are identified from the


LI, Z., KHENNANE, A., HAZELL, P. J. & REMENNIKOV, A. M. 2017. Numerical modeling of a hybrid GFRP-concrete beam subjected to low-velocity impact loading. The 8th International Conference on Computational Methods. Guilin, Guangxi, China: July 25-29th.

Chapter 7 - Hybrid GFRP-Concrete Beam Subject to Low-Velocity Impacts:Experimental Study

125

experimental observations. The main findings from the drop weight tests are summarised

in the last section.

7.2 Specimen preparation

Nine hybrid GFRP-concrete beams were prepared. Each beam consisted of 2 m

long hollow rectangular section pultruded GFRP profile and high performance concrete.

A total number of 18 cylinders from the same mix were cast at the same time to capture

the values of the compressive strength, elastic modulus and indirect tensile strength of the

concrete on the testing date.

7.2.1 Description of the hybrid beam

Figure 7.1 shows a picture of the cross section of the beam and a microscope view

of the pultruded profile. As detailed in Chapter 4, the pultruded GFRP composites were

fabricated through the pultrusion process. The profile is composed of an isophthalic resin

and glass fibers with a fiber volume fraction of 60 %.

Figure 7.1 The cross-sectional dimension of hybrid beam and the microscope view of

the composites


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7.2.2 Concrete mix composition

The cement used in this mix was a type GP Portland cement. The coarse aggregates

were categorised by the sizes of the crushed stone, and the fine aggregates were river

sand. All the aggregates, including the coarse and the fine aggregates, were in saturated

surface dry condition. The design method of the mix can be found in Ferdous (2012) and

the ingredients of the concrete mix are shown in Table 7.1.

Table 7.1 Mix ingredients for concrete

Material Mass per m3

(kg/m3) Mass per Mix (kg)

Coarse aggregate,

(SSD)

14 mm 262 26.232

10 mm 524 52.464

7 mm 352 35.243

Fine aggregate, (SSD) 614 61.475

Cement 399 39.949

Super-plasticiser (OPC) 3 0.300366

Water 187 18.723

Total 2341 234.386

7.2.3 Slump test

The conventional slump test was used to assess the workability of the high strength

concrete used. A slump value of 50 mm (with an error of 5 mm) was recorded for all the

concrete batches (Figure 7.2).


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Figure 7.2 Concrete slump test

7.2.4 Casting of the hybrid beams

To facilitate the pouring of the concrete, all the pultruded hollow profiles were

placed with an angle of approximately 45 degrees to the ground floor, as shown in Figure

7.3. Steel base-plates were bonded to both ends of the beams to provide a support at the

bottom during the casting.

Figure 7.3 Casting of the hybrid beams


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7.2.5 Curing of the hybrid beams

Since the moisture of in-filled concrete can be encapsulated within the pultruded

profiles, all the beams were placed under room temperature condition with steel plates

and plastic bags sealed on both ends of the beams (Figure 7.4). The corresponding

cylinders were also stored under sealed conditions in the same room.

Figure 7.4 Curing of the hybrid beams

7.2.6 Cylinder tests

The cylinders were tested on the same day as the beam tests. Before testing, both

sides of the cylinders were ground by a grinding machine to provide smooth surfaces to

avoid the stress concentrations during loading (Figure 7.5).


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Figure 7.5 Cylinders in grinding machine

The summary of measurement after the grinding of the cylinders is presented in

Table 7.2.

Table 7.2 Measurement of cylinders after grinding:

Sample ID

Diameter (mm) Height (mm) Section (mm2)

Weight (g)

Density (g/cm3) 1 2 3 Average 1 2 3 Average

M1S1 100.6 100.5 100.5 100.5 194.6 194.7 194.7 194.7 7932.7 3593.8 2.33

M1S2 100.1 100.1 99.8 100.0 195.2 195.0 194.9 195.0 7854.0 3514.0 2.29

M1S3 100.1 100.0 100.0 100.0 194.7 194.9 194.7 194.8 7854.0 3569.7 2.33

M1S4 99.7 99.7 100.1 99.8 194.4 194.1 194.2 194.3 7822.6 3547.4 2.33

M2S1 100.5 100.0 100.2 100.2 197.1 197.1 197.6 197.2 7885.4 3610.6 2.32

M2S2 100.6 100.3 100.6 100.5 194.7 195.2 195.3 195.0 7932.7 3560.5 2.30

M2S3 100.4 100.4 100.6 100.5 195.0 194.8 195.2 195.0 7932.7 3561.0 2.30

M2S4 100.5 100.5 99.7 100.3 196.0 195.9 195.7 195.9 7901.2 3629.9 2.35

M3S1 99.9 99.9 99.8 99.9 194.4 194.3 194.3 194.3 7838.3 3490.2 2.29

M3S2 99.9 99.9 100.0 99.9 194.8 194.9 195.0 194.9 7838.3 3563.3 2.33

M3S3 100.0 99.9 100.0 100.0 195.4 195.4 195.5 195.4 7854.0 3592.8 2.34

M3S4 99.8 99.7 99.6 99.7 195.1 194.9 194.9 194.9 7806.9 3589.9 2.34


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Figure 7.6 shows the equipment used for the compressive strength, elastic modulus

and indirect tensile tests. The compressive strength tests were conducted in accordance

with the standard ASTM-C39 (2012). In the elastic modulus tests, the cylinders were

compressed with cyclic loadings (up to 40 % of ultimate compressive strength) for four

times. The values of the elastic modulus were averaged over the last three loading and

unloading cycles for each cylinder (ASTM-C469, 2014). The indirect tensile tests were

conducted based on the requirements of the standard ASTM-C496 (2011). The testing

results are listed in Table 7.3.

Figure 7.6 Cylinder tests (a: compressive test; b: elastic modulus test; c: indirect tensile

test)


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Table 7.3 Testing results of cylinders:

Sample ID

Compression test Elastic modulus test (N/mm2) Indirect tensile test

Maximum load (kN)

Compressive strength (MPa)

1 2 3 Average Resistance

section (mm2)

Maximum load (kN)

Indirect tensile

strength (MPa)

M1S1 554.3 69.88

M1S2 519.4 66.13

M2S1 535.6 67.92

M2S2 540.5 68.14

M3S1 552.0 70.42

M3S2 600.1 76.56

M1S3 33769.7 33357.2 33206.7 33444.5 30599.1 129.72 4.24

M1S4 33708.7 33151.7 33010.6 33290.3 30459.5 135.55 4.45

M2S3 33786.6 33340.4 33104.2 33410.4 30783.7 153.05 4.97

M2S4 34710.5 34671.9 34002.6 34461.7 30848.5 146.90 4.76

M3S3 34292.6 34234.5 34211.8 34246.3 30693.4 171.88 5.60

M3S4 34931.7 34783.7 34534.3 34749.9 30523.0 153.56 5.03

Average 550.3 69.84 33933.9 148.44 4.84

7.3 Test procedures and setup

7.3.1 Test procedures

The impact tests were conducted on a high capacity drop weight impact testing

machine at the University of Wollongong, Australia. The general features of the drop

weight machine and data acquisition system are shown in Figure 7.7. This machine is

equipped with a free-fall carriage system that includes an impactor, weight and a loading

cell. The total weight of the impactor, weight and loading cell is fixed and equal to 592

kg. The carriage system can be dropped from a maximum height of 6 m, or equivalent to

a maximum impact velocity of 10 m/s. This machine operates on the principle of energy

conservation, balancing potential and kinetic energy by varying the drop height of the


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carriage system. For each test, the impactor was hoisted to the required drop height by

using the control system, and then released by the electronic quick release system. The

initiation of the impact load recording was triggered by using a laser sensor, and the

impact loading was recorded by a 50 kHz frequency dynamic loading cell connected to

the data acquisition system.

Figure 7.7 High capacity drop-weight impact machine in University of Wollongong


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7.3.2 Test instrumentation

7.3.2.1 High-speed camera

A high-speed camera with the sample rate of 250 frames per second was employed

to record the impact events and to capture the failure modes as shown in Figure 7.8. In

addition, the impact velocity and the displacement can be verified with video recording.

A reference point was marked to verify the displacement recorded from the movement of

the hybrid beam, and the impact velocity was calculated from the moving frames of the

video.

Figure 7.8 High-speed camera

7.3.2.2 Dynamic loading cell

The impact loading history was measured by a dynamic loading cell, as shown in

Figure 7.9. The captured loading points are shown as much as 50000 points per second.


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Figure 7.9 Dynamic loading cell (http://www.interfaceforce.com)

7.3.3 Test setup

In total nine hybrid GFRP-concrete beams were tested. Six tests were conducted on

the weak axis of the hybrid GFRP-concrete beams for three ascending energy levels. Two

specimens were tested for each energy level to determine repeatability. The impact

velocities and drop heights of the three chosen energy levels were 2.43, 2.97 and 3.43

m/s, and 300, 450 and 600 mm, respectively. The remaining three hybrid GFRP-concrete

beams were tested on the strong axis for three different impact energies. The impact

velocities and dropping heights of the three chosen energy levels were 2.21, 3.13 and 3.84

m/s, and 250, 500 and 750 mm, respectively.

The schematic diagram of the experimental setup is shown in Figure 7.10. The

beams are simply supported and free to slide along the horizontal directions to minimise

the effect of strain rate for concrete. Therefore, the hybrid beams were placed on roller

support fixtures. All the hybrid beams were subjected to a concentrated impact using a

118.6 mm diameter cylindrical impactor. To prevent the rebounding of the specimen

during the impact event, two frames consisting of rubber belts were used to secure the

http://www.interfaceforce.com/


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specimen in place (Figure 7.11). Shock absorbers were also used to prevent the striker

from reloading the targets.

Figure 7.10 Schematic diagram of the experimental setup

Figure 7.11 Support conditions of the impact tests


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7.4 Experimental results and discussion of the weak

axis tests

7.4.1 Failure modes

All the tested hybrid beams had been subjected to a concentrated impact until

ultimate failure occurred for three ascending impact energy levels. From the experimental

observations recorded by the high-speed camera, the hybrid beams started to respond to

the impact loading in bending up to the occurrence of ultimate failure. All the tested

specimens failed ultimately with the presence of shear cracks (splitting of the profiles) on

the corners of the pultruded profiles. The failure modes of the tested specimens at the

time of ultimate failure for three energy levels are shown in Figure 7.12. It can be seen

that the magnitude of the shear damage and the deflection at the time of the ultimate

failure increases with respect to ascending energy levels.

Figure 7.12 Failure modes at the time of ultimate failure

The debonding failure between the pultruded GFRP composites and the concrete

was observed after the impact events. As shown in Figure 7.13, end slipping of concrete


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was found at the end of the hybrid beams. The average value of the maximum end slipping

measured for the three ascending impact energy levels was 13, 15 and 63 mm,

respectively. The length of the maximum end slip increases with the increase in the impact

energies.

Figure 7.13 End slipping of the concrete

Another failure mode was observed on the contacting surfaces of the composites as

shown in Figure 7.14. The failure modes of all the three impact energy levels were shown

with a similar cracking pattern. Multiple shear cracks were formed around the edges of

the impactor. The shear cracking directions are longitudinal, following the direction in

which the majority of fibers were laid. It can be seen that the growth and the magnitude

of damage increase with ascending energy levels.

Figure 7.14 Shear cracks formed on the contacting surfaces of the profiles


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The loading histories for the three ascending energy levels recorded in situ by the

dynamic loading cell are represented in Figure 7.15, Figure 7.16 and Figure 7.17

respectively. As shown, the impact force-time curves of the three impact energy levels

exhibit similar trends, which can be divided into two stages: inertial resistance stage and

dynamic bending resistance stage. Just after contact is initiated between the impactor and

the top surface of the hybrid beam, the first stage is represented by an enormous and rapid

increase in load to the maximum value, and a quick dropping back to a certain degree.

During this stage, the hybrid beam reduces the velocity of the impactor at first and then

the velocity of the hybrid beam increases as the impacting process continues, which

results in a rapid and short-term peak of inertial force as can be noticed in the loading

curve. The average values of the inertial force at this stage for the three ascending energy

levels are 201.0, 249.4 and 307.3 kN respectively. The true impact resistance of the hybrid

beam is represented by the dynamic bending resistance stage. The second stage lasts from

the onset of the damage to the occurrence of the ultimate failure. In this stage, the hybrid

beam starts to respond to the impact load with the presence of multiple failure

mechanisms, including debonding failure between the concrete and the profiles, shear

cracks on the corners of the profiles and the flexural cracks of the concrete. The average

maximum experimental impact loads recorded in this stage are 84.8, 100.3 and 110.2 kN,

respectively for the three ascending energy levels. The ultimate failure of the hybrid beam

is represented by the occurrence of the shear cracks on the corners of the pultruded

composites (splitting of the composites), which is confirmed by the video recorded from

the high-speed camera.


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Figure 7.15 Loading history for 300 mm dropping height



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7.4.3 Midspan displacement-time response

The midspan deflection of the hybrid beam can be calculated from a double

integration of load-time curves:

D = ∬𝐹𝐹(𝑡𝑡)−𝐶𝐶𝑀𝑀𝐶𝐶

𝑑𝑑2𝑡𝑡 (7.1)

where

D = the midspan displacement;

𝐹𝐹(𝑡𝑡) = the load acquired by the data acquisition system;

𝑀𝑀 = the total weight (592 kg);

𝑔𝑔 = the gravitational acceleration constant (9.81m/s2); and

𝑡𝑡 = time.


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The midspan displacement-time curves of the three impact energy levels are shown

in Figure 7.18, the symbol points are the displacement recorded from the high-speed

camera. An average difference of 5.3% at the time of ultimate failure are compared

between the video recorded from the high-speed camera and the calculated curves.

Similar trends are observed for the displacement-time plots across all the impact energies

tested: the midspan displacement increases non-linearly with the increase of contacting

time. The average values of displacement at the time of ultimate failure for three

ascending energy levels are 29.1, 36.2 and 39.5 mm respectively. The midspan

displacement at the time of ultimate failure increases with respect to the increased impact

energy.

Figure 7.18 Midspan displacement curves of three ascending impact energy levels


Testing results including dropping height, impact velocity, maximum load, midspan

deflection, total energy and absorbed energy are summarised in Table 7.4. The results


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indicate that the average maximum load in both stages increase with respect to the

increase of impact energy. Separately, the midspan deflection at the time of ultimate

failure increases with the corresponding absorbed energy instead of the initial impact

energy. The absorbed energy is calculated through the integration of the load-

displacement history. The average values of absorbed and total energies show that the

majority of the impact energies were absorbed through the elastic-plastic behaviour and

the damage failure mechanisms of the hybrid GFRP-concrete beams. The rest are

represented in the form of residual kinetic energies.


Specimen ID Test No.


Impact Velocity

(m/s)

Maximum Load in

stage one (kN)

Maximum Load in

stage two (kN)

Midspan deflection at time of ultimate failure (mm)

Total energy

measured (J)

Absorbed Energy at

time of ultimate

failure (J)

HBW1 300 mm #1 M1 300 2.43 204.3 79.0 28.6 1746.3 1410.3

HBW2 300 mm #2 M2 300 2.43 197.7 90.6 29.6 1713.0 1600.2

HBW3 450 mm #1 M2 450 2.97 267.3 91.7 35.2 2553.1 2126.0

HBW4 450 mm #2 M1 450 2.97 231.6 111.9 37.2 2568.2 2448.4

HBW5 600 mm #1 M3 600 3.43 316.7 126.2 44.7 3465.6 3334.3

HBW6 600 mm #2 M2 600 3.43 297.3 94.2 34.3 2860.0 2083.6

7.5 Strong axis tests

7.5.1 Failure modes

The tested hybrid beams were subjected to a concentrated impact load on the strong

axis for different impact energy levels. As can be observed on the videos recorded by the


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high-speed camera, the hybrid beams started to respond to the impacts in bending. For

the dropping height of 250 mm, the impactor stroke the hybrid beam for a certain degree

and rebounded. For 500 mm and 750 mm dropping height, the tested beams failed with

the presences of shear cracks (splitting of the profiles) on the corners of the pultruded

composites. The failure modes of the tested specimens at the time of ultimate failure

(onset of rebounding for 250 mm case) are shown in Figure 7.19.

Figure 7.19 Failure modes at the time of ultimate failure

The debonding failure between the pultruded profiles and the concrete was

evaluated after the impact events. Identical to the findings for the weak axis tests, end

slipping of the concrete was observed at the ends of the hybrid beams for all cases. Similar

to the weak axis results, the length of the end slip increases with respect to the ascending

energies. The average value of the measured end slip was 2, 10 and 65 mm, respectively

for the three ascending energy tests.

However, the shear cracks on the contacting surfaces observed for the weak axis

tests were not presented for the strong axis tests. The reason for is that the diameter of the

impactor is larger than the width of the contacting surfaces.


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The loading histories for the strong axis tests recorded in situ by the dynamic

loading cell are illustrated in Figure 7.20. As for the weak axis results, the loading

histories can be divided into two stages: inertial resistance stage and dynamic bending

resistance stage. The mechanisms of the impact behaviour in the first stage are similar to

that of the weak axis tests. The inertial resistant forces are 186.4, 310.0 and 398.6 kN

respectively for the three tests. In the second stage, the 250 mm testing results presented

a rebound behaviour in the dynamic bending resistance stage. The timing of the maximum

load in this stage occurs much later than that of the 500 and 750 mm dropping height

cases. Moreover, the first significant fluctuation took place between approximately 1 and

2 ms, and was not presented in Test 7 (250 mm dropping height). The maximum impact

loads recorded in this stage are 148.5, 120.9 and 150.7 kN respectively for the three

ascending levels. The differences of the impact performance (maximum impact load in

stage 2) may be the result of the different concrete mix: Test 7 and Test 9 were from the

same concrete mix, and the compressive strength for the concrete used in Test 8 was

slightly weaker than that of the concretes used in Test 7 and Test 9. For the 500 and 750

mm cases, the ultimate failure is similar to that observed in the weak axis tests. The

ultimate failure was represented by the shear cracks formed on the corners of the

pultruded composites.


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Figure 7.20 Loading histories for the strong axis tests


Similarly to the weak axis results, the midspan displacement of the hybrid beam

can be calculated from a double integration of the load-time curves. Figure 7.21 shows

the midspan displacement curves for the three ascending energy levels, the symbol points

are recorded from the high-speed camera. Due to the interval of the videos, limited points

can be captured for comparison. For the 250 mm dropping height, the midspan

displacement increases non-linearly to the maximum value (17.1 mm) and rebounds back

to the original level. For the 500 and 750 mm dropping heights, the midspan displacement

increases at a near-linear trend up to ultimate failure. The values of the displacement at

the time of ultimate failure for these two loading cases are 19.9 and 17.6 mm respectively.

As explained in the section 7.5.2, the difference of the maximum displacement may be a


146

result of the different concrete mixes. The stiffness of the hybrid beams in Test 7 and Test

9 are relatively higher than the one in Test 8.

Figure 7.21 Midspan displacement curves for strong axis


The results of the impact tests on the strong axis are summarised in Table 7.5.

Similar to the findings in the weak axis tests, the maximum load in the first stage (inertial

force) increases with the initial impact energy. Moreover, the midspan deflection at the

time of ultimate failure increases with the corresponding absorbed energy instead of the

initial impact energy levels. The absorbed energy is calculated through the integration of

the load-displacement curve. The values of the absorbed and total energies indicated that

for the penetration case, the majority of the impact energy was absorbed through the

elastic-plastic behaviour and the damage failure mechanisms of the hybrid beams. The


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rest are represented in the form of residual kinetic energies. For the rebounding case, only

a small percentage of the energy was absorbed by the failure mechanisms of the hybrid

beam, the majority of the energy is represented by the rebounding kinetic energy.


Specimen ID Test No.


Impact Velocity

(m/s)

Maximum Load in

stage one (kN)

Maximum Load in

stage two (kN)

Midspan deflection at time of ultimate failure (mm)

Total energy

measured (J)

Absorbed Energy at

time of ultimate

failure (J)

HBS1 250 mm #7 M3 250 2.21 186.4 148.5 - 1443.4 132.5

HBS2 500 mm #8 M1 500 3.13 310.0 120.9 19.9 2893.6 1747.1

HBS3 750 mm #9 M3 750 3.84 398.6 150.7 17.6 3942.5 1516.4

7.6 Summary

Nine hybrid beams were tested on both the strong and the weak axes to determine

the impact behaviour for different impact energies. The impact characteristics in terms of

load-time curves and midspan deflection-time curves were presented to demonstrate the

damage propagation in the hybrid beam subjected to low-velocity impact loading. The

impact performance in terms of maximum load and deflection and the absorbed energy

were discussed. The main findings of this chapter can be summarised as follows:

1. When subjected to a concentrated impact loading, the hybrid GFRP-concrete

beam suffers from debonding failure between the pultruded profile and the

concrete and the shear cracking failure on the contacting surfaces of the

composites during loading. The hybrid beams failed ultimately with through

shear cracks (splitting of the profiles) forming at the corners of the profiles;


148

2. The impact response of the hybrid beam to low-velocity impacts can be divided

into two stages, inertial resistance stage and dynamic bending stage. The former

one is represented in a rapid and short-term peak of inertial force. While the true

impact resistance is represented by the second stage, in which the majority of

the damage takes place; and

3. The maximum impact load increases with respect to the initial impact energy.

However, the midspan deflection increases with the corresponding absorbed

energy instead of the initial impact energy. The majority of the energy is

absorbed through the elastic-plastic behaviour and the failure mechanisms of

the hybrid beam.

Chapter 8

Hybrid GFRP-Concrete Beam Subject to

Low-Velocity Impacts: Numerical Study5

8.1 Introduction

The experimental study of impact behaviour of the hybrid GFRP-concrete beam

subjected to low-velocity impact loadings was presented in the preceding Chapter. The

impact characteristics, impact performance and failure modes were obtained for both the

strong and the weak axes. However, experimentation alone cannot reveal the failure

modes of the concrete hidden inside the pultruded profile. Details such as the cracking

pattern and damage sequences can only be understood through numerical analysis. For

this purpose, a numerical study is performed to analyse the development and propagation

of damage in the concrete. The validated numerical model is used for the analysis of the

cracking patterns in order to further explain the failure mechanisms of the hybrid beam

during the impact events.


LI, Z., KHENNANE, A., HAZELL, P. J. & REMENNIKOV, A. M. 2017. Numerical modeling of a hybrid GFRP-concrete beam subjected to low-velocity impact loading. The 8th International Conference on Computational Methods. Guilin, Guangxi, China: July 25-29th.

Chapter 8 - Hybrid GFRP-Concrete Beam Subject to Low-Velocity Impacts: Numerical Study

150


8.2.1 Description of the numerical models

In both the strong and weak axes models, the impactor was modelled using discrete

rigid elements (R3D4). A mass of 592 kg was assigned to the impactor as per the

experimental conditions. For the concrete and pultruded GFRP profile, the same types of

the elements as those used in Chapter 6 were used. The orientations of the fibers in each

layer were assigned according to the corresponding coordinate systems. Because of the

dynamic nature of the experiment, ABAQUS/Explicit was used instead of

ABAQUS/Standard. The mesh density was chosen to be 20 × 20 mm on the basis of the

mesh sensitivity analysis. The computational time for a single simulation was

approximately 0.2 h (Intel Core 17-3770 CPU@ 3.4 GHz). Different initial impact

velocities were imposed to the impactor to simulate the initial impact velocities as per the

experimental setup. The interaction between the impactor and the hybrid beam was

simulated though the use of surface-to-surface contact pairs. The mechanical constraint

formulation was enforced using the kinematic contact algorithm, and the friction

coefficient was set to 0.5 based on the material properties. The interaction between the

pultruded profiles and the concrete inside was also simulated through surface-to-surface

contact pairs but with 0.3 as the friction coefficient factor. The separation of the

interaction was allowed after the contact and the constraint enforcement method was

applied between the contact surfaces. Moreover, the “Hard” contact was defined for the

pressure-overclosure behaviour. The boundary conditions of the assembled FEMs for

both strong and weak axis are illustrated in Figure 8.1 and Figure 8.2 respectively.


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Figure 8.1 Assembled FEM with boundary conditions for strong axis tests

Figure 8.2 Assembled FEM with boundary conditions for weak axis tests

8.2.2 Material models

The Concrete Damage Plasticity model (CDPM) for concrete and the progressive

damage model for fiber reinforced polymers described in Chapter 6 were used for the

concrete block and the pultruded profile respectively. Different from the description given


152

in Chapter 6, the tensile stiffening behaviour of the concrete was defined with the post-

failure stress as a function of the cracking strain in this study because no convergence

issues were encountered in ABAQUS/Explicit. The compressive and tensile stress-strain

relationship curves, shown in Figure 8.3 and Figure 8.4 respectively, were implemented

in this study.

Figure 8.3 Compressive stress-strain relationship curve

Figure 8.4 Tensile stress-strain relationship curve


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8.3 Numerical results for the strong axis tests


The comparison of the numerical and experimental results for the three loading

histories are shown in Figure 8.5. A good agreement was achieved between the

experimental results and the numerical predictions. In the inertial resistance stage, the

short-term peaks of the inertial forces were simulated for all the energies. Since the

impactor was modelled as a rigid part, instead of a deformable steel one, the value of the

mechanical impedance of the rigid impactor is much higher than that of the steel impactor.

This could be the reason that the predicted values in the first stage are relatively higher

than the experimental results. The maximum load from the experimental results for the

three ascending impact energy levels are 186.4, 310.0 and 398.6 kN, respectively. The

corresponding numerical predictions are 290.8, 395.7 and 473.8 kN respectively.

In the dynamic bending resistance stage, the predicted loading histories were found

to agree with the experimental results. As mentioned in Chapter 7, the concrete mix in

Test 8 was slightly different to that of Test 7 and Test 9. This might explain why the

maximum value of Test 8 in this stage is smaller than the predicted value. For all the three

testing cases, the maximum impact loads of the experimental results recorded in this stage

are 148.5, 120.9 and 150.7 kN, respectively. The corresponding numerical ones are 148.7,

161.1 and 156.1 kN respectively. The average difference of maximum load recorded in

stage 2 between the experimental results and numerical ones for the three tests is 9.5 %.


154

Figure 8.5 Comparison of loading histories for strong axis testing groups


155


The midspan displacement-time curves are shown in Figure 8.6. Reasonable

agreements were achieved between the numerical results and the experimental ones. The

maximum midspan deflection predicted by the FEMs were 19.5, 20.7 and 18.0 mm

respectively. The corresponding experimental values were 17.1, 19.9 and 17.6 mm

respectively. The numerical predictions were slightly higher than the experimental

results. The average difference between the experimental results and the numerical

predictions is 6.1 %.

Figure 8.6 Comparison of midspan displacement-time curves for strong axis


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8.3.3 Failure modes

8.3.3.1 Non-penetration failure modes

Multiple failure modes of the concrete inside the pultruded profile were identified

in the numerical analysis of the non-penetration impact event (250 mm dropping height).

In the inertial resistance stage, just after the contact was initiated between the impactor

and the top surface, the reduction of the impact velocity of the impactor was detected.

Simultaneously, the velocity of the contacting area in the top surface of the beam

increased. However, no reaction force and damage was formed in this stage. The impact

load during this stage was completely resisted by the inertial force.

With the increase of contact duration, the stress wave propagated to the bottom of

the beam, and the beam started to respond to the impact in bending. Figure 8.7 presents

the value of plastic strain in concrete at approximately 1 ms after the initiation of the

contact between the impactor and the hybrid beam, when two minor flexural cracks

formed on the bottom of the contacting area.

Figure 8.7 Minor flexural cracks formed in the concrete at 1 ms

As the loading process continued, two vertical flexural cracks were formed due to

the local shear plug effects mentioned in Chapter 3. Figure 8.8 presents the state of plastic


157

strain (cracks development) at approximately 2 ms. Besides these two cracks, other

flexural cracks formed in the area between the centre and the support location due to the

global bending response to the impacts (Figure 8.8). Details of the mechanisms of local

shear plug and global flexural response can be found in section 3.2.2.

Figure 8.8 Flexural cracks formed in the concrete at 2 ms

Multiple flexural cracks formed upwards to the top surface in the last stage of the

loading. The hybrid beam responded to the impact with global flexural cracks, as shown

in Figure 8.9. In the non-penetration event, the majority of the energies were absorbed

through the elastic-plastic behaviour and the global flexural cracks of the hybrid beam.

Figure 8.9 Global flexural cracks formed across the beam


158

8.3.3.2 Penetration failure modes

For the dropping heights of 500 and 750 mm events, all the beams were penetrated

by the impactor. In the inertial resistance stage, the beams behaved in the same way as

the non-penetration event. No damage was predicted in this stage. Minor flexural cracks

at the centre of the beams first initiated in both impact events, Figure 8.10 presents the

state of tensile damage criterion (cracks due to tensile stress).

Figure 8.10 Initial flexural cracks of the concrete at the bottom of the beam

Before the stress wave propagated to the entire beam, the shear plug in the concrete

was formed with an angle of approximately 45 degrees. The shear plug cracks propagated

from the edges of the impactor downwards to the bottom of the beam, as shown in Figure

8.11.

Figure 8.11 Local shear plug formed downwards to the bottom surface


159

As the loading process continued, multiple global flexural cracks formed between

the impact zone and the support locations. Unlike the global response of the

concrete/reinforced concrete structures, the global flexural cracks were formed in the top

surface of the beam and they propagated downwards to the bottom surface. The flexural

cracks near the support locations are vertical, and the cracks between the loading zone

and the support locations are formed with an angle of approximately 45 degrees parallel

to the local shear plug shape (Figure 8.12).

Figure 8.12 Global flexural response of the hybrid beam

With the increase of the contact duration, the magnitude of the damage and the

length of the flexural cracks increased. Besides the flexural cracks between the impact

zone and support locations, a vertical flexural crack was formed at the support location

(Figure 8.13).

Figure 8.13 Vertical flexural cracks formed at supports


160

As the loading continued, the magnitude of the concrete damage increased slightly

up to the ultimate failure. The hybrid beam failed ultimately with the presence of the shear

cracks formed on the corners of the pultruded composites. Figure 8.14 presents the state

of shear damage criterion (Hashin damage model). The shear cracks formed on both the

top and bottom surface of the contacting zone and propagated horizontally to the end of

the beam. A representation of the experimental and numerical observations after

unloading the beams is shown in Figure 8.15.

Figure 8.14 Shear cracks formed at the ultimate failure

Figure 8.15 Schematic diagram of experimental and numerical observations after test


161

8.4 Numerical results for the weak axis tests


The comparison between the experimental and numerical results for the weak axis

tests are shown in Figure 8.16. A reasonable agreement was achieved between the

numerical predictions and the experimental data. Similar to the strong axis tests, the short-

term peak of the inertial forces was simulated higher than that of the experimental results.

The cause of this phenomenon can be found in section 8.3.1. The average maximum load

of the experimental results in this stage are 201.0, 249.4 and 307.3 kN respectively. The

corresponding results from the numerical models are 323.7, 362.4 and 441.4 kN,

respectively.

In the dynamic bending resistance stage, the predicted loading histories were found

to corroborate the experimental data. The multiple rises and drops were well simulated in

the numerical analysis. The average maximum loads recorded from the experimental

results in this stage are 84.8, 100.3 and 110.2 kN, respectively for the three ascending

energy levels. The predicted values are 96.9, 104.9 and 105.5 kN respectively. The

average difference of the maximum load recorded in stage 2 between the experimental

results and the numerical ones is 7 %.


162

Figure 8.16 Comparison of loading histories for weak axis tests


163


The comparison of midspan displacement histories for all the impact events are

shown in Figure 8.17. A reasonable agreement is obtained between the predicted results

and the experimental ones. The maximum deflections predicted by the FEMs were 37.2,

42.8 and 41.9 mm, respectively for the three ascending energy levels. The average

corresponding values from the experimental data were 33.1, 39.1 and 40.2 respectively.

The average difference of maximum deflection recorded between the experimental and

the numerical results is 7.9 %.

Figure 8.17 Comparison of experimental and numerical results for displacement-time

curves

8.4.3 Failure modes

For the weak axis tests, the impact response of the hybrid beam is similar to that of

the penetration events of the strong axis tests. In the inertial resistance stage, no damage


164

was detected in the numerical models. Figure 8.18 shows the state of tensile damage in

the concrete. In the early dynamic bending resistance stage, minor flexural cracks were

formed on the bottom side of the contacting zone.

Figure 8.18 Minor cracks formed in the concrete at the centre of the beam

As the loading continued, the minor cracks transformed into crushing due to the

local shear plug. In this stage of loading, the punching failure occurred before the entire

beam had time to respond in bending, which resulted in the occurrence of the local shear

plug (Figure 8.19).

Figure 8.19 Local shear plug formed in the early dynamic resistance stage


165

As the loading continued, the flexural cracks formed from the contacting zone to

the support locations. Unlike the response of the strong axis tests, the flexural cracks

formed vertically downwards to the bottom side of the beam as shown in Figure 8.20.

Figure 8.20 Global flexural cracks for the weak axis tests

In the late stage of the dynamic resistance stage, with the increase of loading

duration, the number of flexural cracks increased and they propagated to the bottom

surface of the beam. In addition to the flexural cracks between the impact area and the

support locations, vertical flexural cracks initiated at both the support locations as shown

in Figure 8.21.

Figure 8.21 Vertical flexural cracks formed at supports


166

The hybrid GFRP-concrete beam failed ultimately with the presence of the shear

cracks formed at the corners of the pultruded profiles. Figure 8.22 shows the shear

damage state in the pultruded profile (Hashin damage model). A representation of the

experimental and numerical observations after unloading the beam is shown in Figure

8.23.

Figure 8.22 Shear cracks formed at the ultimate failure for weak axis tests

Figure 8.23 A representation of numerical model after the impact loading


167

8.5 Damage sequence analysis

The numerical predictions of the response of the hybrid GFRP-concrete beam

subjected to low-velocity impacts were found to corroborate the experimental results in

terms of load-time and midspan deflection-time curves. The failure modes predicted by

the numerical models provided a detailed understanding of the failure mechanisms of the

hybrid beam, especially of the internal damage in the concrete block. A damage sequence

analysis of the impact resistance was investigated with a combination of experimental

observations and numerical simulation.

Taking the 450 mm dropping heights on the weak side event as an example, a

typical impact event can be divided into six stages as shown in Figure 8.24. The first

stage, inertial resistance stage, is represented as a rapid and short-term peak of inertial

force. No damage occurs in this stage. The second stage begins with the onset of inelastic

behaviour at approximately 0.5 ms. In this stage, the stress wave propagates from the

contacting surface to the bottom of the hybrid beam. Minor flexural cracks are formed at

the centre of the concrete part. The third stage lasts from the presence of reloading to the

multiple drops at approximately 1 ms. During this stage, the punching failure (local

crushing) occurs before the entire beam has time to respond in bending, which results in

the presence of the local shear plug. The fourth stage is represented in multiple significant

drops at approximately 3 ms. With the increase of the contact duration, the stress wave

propagates from the local zone to the entire beam and the hybrid beam starts to respond

to the impact in bending. The global flexural cracks are formed between the loading area

and the support locations. These cracks propagate from the top surface downwards to the

bottom of the beam. It is noted that for the strong axis tests, the flexural cracks are formed

with an angle of approximately 45 degrees parallel to the local shear plug. On the other


168

hand, the global flexural cracks are formed vertically for the weak axis tests. The fifth

stage lasts from the end of fourth stage to the maximum load of impact. In this stage, most

of the impact load is carried by the pultruded profile due to the failure of the concrete

inside. Vertical flexural cracks are formed at the support locations during this stage. In

the sixth and final stage, the loading curves decrease dramatically down to zero. During

this stage, the hybrid beam fails ultimately with the presence of the shear cracks formed

at the corners of the pultruded profile. The impactor penetrates the hybrid beam and no

more energy can be absorbed from the hybrid beam.


169

Figure 8.24 Damage sequence analysis


170

8.6 Comparison studies

As discussed in the above sections, the developed numerical model is validated

from the experimental results and is proven reliable of simulating the impact events for

targeted applications. In this section, the performance of the verified numerical model is

used to compare to the published results of railway sleepers from the literature.

Kaewunruen and Remennikov (2009b) conducted a series of experimental tests on

evaluating the impact capacity of the railway prestressed concrete sleepers. In their tests,

the specimens were impacted by a 5.81 kN projectile from the dropping height of 100 and

500 mm. The impact energy and experimental setup were set to simulate the impact events

of railway sleepers that may occur during the service. As shown in Figure 8.25, the setup

of the experimental program was arranged in accordance with the Australian standard for

static tests of railway sleeper (Standards, 2003c, Standards, 2003b).

Figure 8.25 Test setup of Kaewunruen and Remennikov (2009b)


171

In order to compare to the performance of prestressed concrete sleepers, in this

numerical analysis, the loading and supporting conditions are used as per Kaewunruen

and Remennikov (2009b). The schematic diagram of this investigation is shown in Figure

8.26. The additional loading and supporting fixture is modelled by the use of rigid

elements. The description of the numerical model can be found in section 8.2.1.

Figure 8.26 Numerical setup of the impact events

8.6.1 Numerical results of original size beam

The numerical results of the original size beam under 100 and 500 mm dropping

heights are presented in Figure 8.27 and Figure 8.28, respectively. Similarly to the

previous sections, in both cases, the beam experienced the inertial resistance stage and

the dynamic bending resistance stage. The first stage was represented as a rapid and short-

term peak of inertial force, no damage occurred during this stage. The dynamic bending

stage lasted from the onset of the second increase in load to the presence of ultimate

failure.


172

Figure 8.27 load-time response due to 100 mm drop height

Figure 8.28 Load-time response due to 500 mm drop height


173

The failure modes of the original size beam under 100 and 500 mm drop heights

are presented in Figure 8.29 and Figure 8.30, respectively. For 100 mm dropping height

event, with the increase of contact duration, the failure modes propagated from the minor

flexural cracks on the local impact area to the global flexural cracks throughout the beam.

For 500 mm dropping height event, before the stress wave propagated to the entire beam,

the shear plug was formed with an angle of approximately 45 degrees. The beam failed

ultimately with the presence of the shear cracks formed on the corners of the pultruded

profiles. Different from the results of Kaewunruen and Remennikov (2009b), the beam

failed ultimately at the dropping height of 500 mm, no further load can be carried by the

beam. The impact performance of the hybrid GFRP-concrete beams and the prestressed

concrete sleepers is presented in Table 8.1. As shown, even though the maximum impact

load of the hybrid GFRP-concrete beam is much larger than the results of the prestressed

concrete sleepers, the moment capacity is smaller than the one of the prestressed concrete

sleepers.

Figure 8.29 Failure modes due to 100 mm drop height


174

Figure 8.30 Failure modes due to 500 mm drop height

Table 8.1 Impact performance of the hybrid beam and prestressed concrete sleepers

(Kaewunruen and Remennikov, 2009b)

Types of beams

Cross-section (mm)

Target conditions

True Max Load (kN)

True moment capacity (kN m)

Energy absorbed

(J)

Residual strength

Hybrid beams

100×190

Crack (100mm)

980 - 580 Yes

Fail (500mm) 2540 78 2660 No

concrete sleepers

(204+250)

×227

Crack (100mm)

310 42 580 Yes

Fail (500mm) 550 90 2900 Yes

To conduct the parametric study and evaluate the impact capacity of the hybrid

GFRP-concrete system, additional numerical model has been developed with the use of

same cross-sectional dimensions of railway sleepers’ design from Kaewunruen and

Remennikov (2009b). To compare to the experimental results of prestressed concrete

sleepers, the loading and supporting conditions are used as per Kaewunruen and

Remennikov (2009b). The schematic diagram of the numerical model is shown in Figure

8.31.


175

Figure 8.31 Numerical setup of the parametric study

8.6.2 Numerical results of life-size rail sleepers

The numerical results of the large size beam under 100 and 500 mm dropping

heights are presented in Figure 8.32 and Figure 8.33, respectively. Similarly to the hybrid

with the original size, the beam experienced the inertial resistance stage and the dynamic

bending resistance stage. The first stage was represented by the rapid and short-term peak

of inertial force, no damage was expected during this stage. The dynamic bending stage

lasted till the presence of ultimate failure.


176

Figure 8.32 Load-time response of 100 mm drop height for the life-size beam

Figure 8.33 Load-time response of 500 mm drop height for the life-size beam


177

The failure modes of the large size beam under 100 and 500 mm drop heights are

presented in Figure 8.34 and Figure 8.35, respectively. For 100 mm dropping height,

flexural cracks were first formed on the impact area. With the increase of the contact

duration, multiple crack patterns were shown, including the flexural cracks formed on the

local impact zone and supporting area, and the shear cracks propagated from the edge of

the impactor to the supports. For 500 mm dropping height, a shear plug was formed at the

early loading stage. As the loading process continued, two significant shear cracks as well

as the global flexural cracks were formed. Different from the results of the original size

beam, no shear cracks or damage were observed on the pultruded profiles, which indicates

that the hybrid beam remain the residual strength and further load can be carried. The

impact performance of the large size hybrid GFRP-concrete beams and the prestressed

concrete sleepers is presented in Table 8.2. The maximum impact load and the moment

capacity of the same size hybrid GFRP-concrete beam is larger than the ones of the

prestressed concrete beam, which indicates that the large size hybrid beam has the

potential to observe more impact energy.

Figure 8.34 Failure modes of large size beam due to 100 mm drop height


178

Figure 8.35 Failure modes of large size beam due to 500 mm drop height

Table 8.2 Impact performance of the large size hybrid beam and prestressed concrete

sleepers (Kaewunruen and Remennikov, 2009b)

Types of beams

Cross-section (mm)

Target conditions

True Max Load (kN)

True moment capacity (kN m)

Energy absorbed

(J)

Residual strength

Hybrid beams

(204+250)

×227

Crack (100mm)

540 - 580 Yes

Fail (500mm) 3780 151 2900 Yes

concrete sleepers

(204+250)

×227

Crack (100mm)

310 42 580 Yes

Fail (500mm) 550 90 2900 Yes

8.7 Summary

In this chapter, a nonlinear finite element analysis was conducted to simulate the

impact behaviour of the hybrid beam on both its strong and weak axes. The numerical

results were found to corroborate the experimental results in terms of load-time, midspan

deflection-time and failure modes. The numerical results provided more details of the

failure mechanisms, such as the cracking pattern of the concrete and the damage

sequences. The numerical results showed that the punching failure (local crushing) due


179

to the formation of a shear plug and the global flexural cracks are the main failure modes

of the concrete part. Minor flexural cracks occur in the first place, followed by the shear

plug in the local impact zone. As the loading process continues, the impact energies are

absorbed through the presence of the global flexural cracks. The hybrid beam fails

ultimately due to the occurrence of the shear cracks on the corners of the pultruded

composites. The majority of the impact energies are absorbed through the elastic-plastic

deformation and the failure mechanisms (commonly regarded as material “pseudo”

ductility) of the hybrid beam members. The comparison between the proposed hybrid

beam and the existing sleeper data is performed. A parametric study of the life-size rail

sleeper simulation for the proposed beam is conducted and compared to the data from the

literature. The numerical results show that the impact performance of the hybrid GFRP-

concrete beam behave much better than the existing design of railway sleeper.

Chapter 9

Conclusion and Recommendations for

Future Work

9.1 Concluding remarks

This thesis reports on a study undertaken to analyse the impact behaviour and

failure mechanisms of a hybrid GFRP-concrete beam subjected to low-velocity impact

loading. It is comprised of a literature review, an experimental program and the results of

finite element simulations. The aim is to contribute to the understanding of the impact

characteristics and failure mechanisms of this innovative structural system, which could

find targeted applications in infrastructure applications such as rail sleepers and/or bridge

girders.

Different types of materials used for railway sleepers and bridge girders have been

reviewed in Chapter 2. It was found that when the traditional materials (timber, concrete

and steel) are used as structural elements, the durability and performance of the structure

could be affected by the weaknesses of these materials, such as biological degradation,

chemical attacks and corrosion. Alternative materials, such as pultruded composites,

could be an option to overcome these limitations. However, the use of pultruded

composites brings new issues, such as the high deformability, brittle failure and

instability. The alternative is to combine these materials in a hybrid GFRP-concrete

Chapter 9 - Conclusion and Recommendations for Future Work

181

system as to overcome the deficiencies of each one of them and at the same utilise the

desired properties of each material in the place where it performs the best.

The impact behaviour of concrete and FRP composites have been reviewed to

provide a reference base and scope for the study of hybrid GFRP-concrete beam. The

review of the testing methods and strain rate effects on concrete structures provides a

recommendation for the experimental setup of the hybrid beam tests. The failure

mechanisms of concrete and FRP composites are summarised to present the potential

failure modes associated with the materials used in the hybrid structure, such as the shear

dominance failure and global flexural response on concrete, matrix cracking and

delamination on composite materials.

A critical review of the impact behaviour of pultruded GFRP composites was

presented in Chapter 3. Very limited studies focus on the impact response of pultruded

composites; there was a knowledge gap of understanding of failure mechanisms and

damage sequence of pultruded composites subjected to the higher range of impact energy.

For this purpose, a series of impact tests was carried out on pultruded coupons with impact

energies ranging from 17 to 67 J. The results showed that the impactor mass had very

little effect on the impact response of pultruded composites, the effect of impact energy

levels was the main factor which had a significant influence on the composite material.

Moreover, the pultruded composites behaved in a pure elastic fashion up to approximately

20 % of the maximum impact load. In addition, the extent of damage increased

monotonically with respect to the ascending impact energy. Multiple failure modes

occurred when subjected to higher levels of impact energy. Matrix cracking was detected

as the first failure mode of pultruded GFRP composites subjected to low-velocity impacts,

followed by the delamination and fiber breakage in non-penetration cases.


182

A finite element model was developed using the progressive damage model, and

the concrete damaged plasticity model (CDPM) available in Abaqus to simulate the static

flexural behaviour of the hybrid GFRP-concrete beam. The main purpose of this

numerical investigation is to validate the numerical model with experimental results, and

to present the reference setup parameters for the experimental program of the hybrid

beams subjected to impact loadings. The numerical results were highly consistent with

the experimental results in terms of load-displacement curve and static performance.

Multiple failure modes were revealed when the hybrid GFRP-concrete beam was

subjected to static loading. Tensile failure of the pultruded composites was observed as

the first failure mode, followed by shear cracking on the concrete inside and the

debonding failure at the interface between the concrete and the pultruded composites.

Since the primary objective of this thesis was the analysis of the impact behaviour

and failure mechanisms of the hybrid GFRP-concrete beam subjected to low-velocity

impacts, a series of experimental tests was performed on both strong and weak axes of

the hybrid beam. The results showed that when subjected a concentrated impact loading,

the hybrid beam suffers from debonding failure between the pultruded profile and the

concrete and the shear cracking failure (matrix cracking) on the contacting surfaces of the

composites during loading. The hybrid beam failed ultimately with through shear cracks

(splitting of the profiles) forming at the corners of the composites. Furthermore, the

impact response of the hybrid beam can be divided into two stages: namely, inertial

resistance and dynamic bending resistance. The former one is represented in a rapid and

short-term peak of inertial force. While the true impact resistance is represented by the

second stage, in which the majority of the damage takes place.


183

The experimentation alone cannot reveal the failure modes of the concrete hidden

inside the pultruded profile. Details such as the cracking pattern and damage sequences

can only be understood through numerical analysis. For this purpose, a numerical

investigation was performed to analyse the development and propagation of damage in

the concrete. The numerical results were found to corroborate the experimental data in

terms of load-time, midspan deflection-time curves and failure modes. The numerical

analysis provided more details of the failure mechanisms, such as the shear dominance

cracks and global flexural cracks of the concrete and the damage sequences of the hybrid

beam subjected to low-velocity impacts. The validated model can be applied for further

analysis of the hybrid beam under different loading/supporting conditions in the future

study.

The results obtained from this study show that the proposed hybrid GFRP-concrete

beam has the capacity to carry the impact loading with adequate stiffness and strength,

and is suitable for use as a railway sleeper. Indeed, in a real life application, the impact

loads caused by the wheel-track interactions are transferred by the railway sleepers to the

ballast bed, and only a small portion of impact energies is absorbed through the railway

sleepers, which is equivalent to a very limited magnitude of impact loading on the

sleepers. The parametric study of life-size simulation also present that the hybrid beam

outperforms the prestressed concrete sleeper in terms of impact performance.

9.2 Recommendations for future work

As this research is one of the first studies to assess the impact performance of the

pultruded GFRP composites-concrete hybrid beam, there are many issues that can be

improved. Some potential areas related to the extension of this study are listed as follows:


184

1. The damage initiation and the post-failure behaviour of the pultruded

composites were described by the use of unidirectional damage criterion in

the progressive damage model. This damage model was not capable of

modelling accurately the stiffness reduction and describing the accurate

internal damage caused by the interactions between the roving and the mat

layers. Hence, a new damage model is warranted to be developed to provide

a more accurate description of the impact properties of the pultruded GFRP

composites;

2. This study focused on the impact behaviour of the pultruded composites and

the hybrid structures subjected to low-velocity impacts. However, the

pultruded profile or the hybrid structure could be subjected to a blast impact

if explosion occurs. Hence, research into the performance of pultruded

composites or hybrid structure subjected to high velocity impacts is warranted;

3. The impact performance of the hybrid GFRP-concrete beam was tested on a

simply supported condition. As mentioned in Chapter 2, the hybrid structure

has the potential to be used as railway sleeper. Therefore, the research of

impact performance of the hybrid beam with a ballast support condition is

warranted. Since the freedoms of the hybrid beam would be restrained in

multi-directions, the strain rate effect should be evaluated as well;

4. The failure mechanisms of the hybrid GFRP-concrete beam were assessed

under a critical loading situation. However, when used as a railway sleeper,

it can suffer from the cyclic low-velocity loading during the service.

Therefore, the dynamic fatigue behaviour of the hybrid beam is also

warranted; and


185

5. The finite element model can be also improved by considering strain rate

effects.

References

AASHTO, L. 1998. Bridge design specifications. American Association of State

Highway and Transportation Officials, Washington, DC.

ABAQUS 2014. ABAQUS Documentation, Providence, RI, USA, Dassault Systèmes.

ADHIKARY, S. D., LI, B. & FUJIKAKE, K. 2012. Dynamic behavior of reinforced

concrete beams under varying rates of concentrated loading. International

Journal of Impact Engineering, 47, 24-38.

ADHIKARY, S. D., LI, B. & FUJIKAKE, K. 2013. Strength and behavior in shear of

reinforced concrete deep beams under dynamic loading conditions. Nuclear

Engineering and Design, 259, 14-28.

AHMED, E. A., EI-SALAKAWY, E. F. & BENMOKRANE, B. 2009. Shear

performance of RC bridge girders reinforced with carbon FRP stirrups. Journal

of Bridge Engineering, 15, 44-54.

AIDOO, J., HARRIES, K. A. & PETROU, M. F. 2004. Fatigue behavior of carbon fiber

reinforced polymer-strengthened reinforced concrete bridge girders. Journal of

Composites for Construction, 8, 501-509.

ALOMARI, A., ALDAJAH, S., HAYEK, S., MOUSTAFA, K. & HAIK, Y. 2013.

Experimental investigation of the low speed impact characteristics of

nanocomposites. Materials & Design, 47, 836-841.

ARDAKANI, M. A., KHATIBI, A. A. & GHAZAVI, S. A. A study on the

manufacturing of Glass-Fiber-Reinforced Aluminum Laminates and the effect of

interfacial adhesive bonding on the impact behavior. Proceedings of the XI

International Congress and Exposition, 2008.

References

187

ASTM-C39 2012. Standard test method for compressive strength of cylindrical concrete

specimens. ASTM C39/C39M. West Conshohocken, PA: ASTM International.

ASTM-C469 2014. Standard Test Method for Static Modulus of Elasticity and

Poisson’s Ratio of Concrete in Compression. ASTM C469/469M. West

Conshohocken, PA: ASTM International.

ASTM-C496 2011. Standard Test Method for Splitting Tensile Strength of Cylindrical

Concrete Specimens. ASTM C496/C496M. West Conshohocken, PA: ASTM

International.

ASTM-D7136 2012. Standard Test Method for Measuring the Damage Resistance of a

Fiber-Reinforced Polymer Matrix Composite to a Drop-weight Impact Event.

ASTM D7136. West Conshohocken, PA: ASTM International.

BANK, L. C. & GENTRY, T. R. 2001. Development of a pultruded composite material

highway guardrail. Composites Part a-Applied Science and Manufacturing, 32,

1329-1338.

BARBERO, E. J., COSSO, F. A., ROMAN, R. & WEADON, T. L. 2013.

Determination of material parameters for Abaqus progressive damage analysis

of E-glass epoxy laminates. Composites Part B-Engineering, 46, 211-220.

BARRE, S., CHOTARD, T. & BENZEGGAGH, M. L. 1996. Comparative study of

strain rate effects on mechanical properties of glass fibre-reinforced thermoset

matrix composites. Composites Part a-Applied Science and Manufacturing, 27,

1169-1181.

BELETICH, A. S. & UNO, P. J. 2003. Design handbook for reinforced concrete

elements. UNSW press.

References

188

BENLOULO, I. S. C., RODRIGUEZ, J., MARTINEZ, M. A. & GALVEZ, V. S. 1997.

Dynamic tensile testing of aramid and polyethylene fiber composites.

International Journal of Impact Engineering, 19, 135-146.

BÉTON, C. E.-I. D. 1992. Durable Concrete Structures: Design Guide.

BHATTI, A. Q. & KISHI, N. 2010. Impact response of RC rock-shed girder with sand

cushion under falling load. Nuclear Engineering and Design, 240, 2626-2632.

BHATTI, A. Q., KISHI, N. & MIKAMI, H. 2011. An applicability of dynamic response

analysis of shear-failure type RC beams with lightweight aggregate concrete

under falling-weight impact loading. Materials and Structures, 44, 221-231.

BHATTI, A. Q., KISHI, N., MIKAMI, H. & ANDO, T. 2009. Elasto-plastic impact

response analysis of shear-failure-type RC beams with shear rebars. Materials &

Design, 30, 502-510.

BUCHANAN, A., DEAM, B., FRAGIACOMO, M., PAMPANIN, S. & PALERMO, A.

2008. Multi-storey prestressed timber buildings in New Zealand. Structural

Engineering International, 18, 166-173.

CAMANHO, P. P. & DAVILA, C. G. 2002. Mixed-mode decohesion finite elements

for the simulation of delamination in composite materials. NASA/TM-2002-

211737. NASA.

CAMPBELL, F. C. 2003. Manufacturing processes for advanced composites, Elsevier.

CANADIAN.STANDARDS.ASSOCIATION 2006. Canadian highway bridge design

code, Canadian Standards Association.

CANAL, L. P., GONZALEZ, C., SEGURADO, J. & LLORCA, J. 2012. Intraply

fracture of fiber-reinforced composites: Microscopic mechanisms and modeling.

Composites Science and Technology, 72, 1223-1232.

References

189

CANNING, L., HOLLAWAY, L. & THORNE, A. M. 1999. Manufacture, testing and

numerical analysis of an innovative polymer composite/concrete structural unit.

Proceedings of the Institution of Civil Engineers-Structures and Buildings, 134,

231-241.

CANTWELL, W. J. & MORTON, J. 1989a. Comparison of the Low and High-Velocity

Impact Response of Cfrp. Composites, 20, 545-551.

CANTWELL, W. J. & MORTON, J. 1989b. Geometrical Effects in the Low Velocity

Impact Response of Cfrp. Composite Structures, 12, 39-59.

CANTWELL, W. J. & MORTON, J. 1991. The Impact Resistance of Composite-

Materials - a Review. Composites, 22, 347-362.

CAPRINO, G. 1984. Residual Strength Prediction of Impacted Cfrp Laminates. Journal

of Composite Materials, 18, 508-518.

CAPRINO, G., VISCONTI, I. C. & DIILIO, A. 1984. Elastic Behavior of Composite

Structures under Low Velocity Impact. Composites, 15, 231-234.

CARREIRA, D. J. & CHU, K.-H. Stress-strain relationship for plain concrete in

compression. Journal Proceedings, 1985. 797-804.

CHAKRABORTTY, A., KHENNANE, A., KAYALI, O. & MOROZOV, E. 2011.

Performance of outside filament-wound hybrid FRP-concrete beams.

Composites Part B-Engineering, 42, 907-915.

CHANG, F. K., CHOI, H. Y. & JENG, S. T. 1990. Study on Impact Damage in

Laminated Composites. Mechanics of Materials, 10, 83-95.

CHOI, H. Y., WU, H. Y. T. & CHANG, F. K. 1991. A New Approach toward

Understanding Damage Mechanisms and Mechanics of Laminated Composites

Due to Low-Velocity Impact .2. Analysis. Journal of Composite Materials, 25,

1012-1038.

References

190

CHOTARD, T. J. & BENZEGGAGH, M. L. 1998. On the mechanical behaviour of

pultruded sections submitted to low-velocity impact. Composites Science and

Technology, 58, 839-854.

CHOTARD, T. J., PASQUIET, J. & BENZEGGAGH, M. L. 2000. Impact response and

residual performance of GRP pultruded shapes under static and fatigue loading.


COLLINS, M. P. & MITCHELL, D. 1991. Prestressed concrete structures, Prentice

Hall.

COLLINS, M. P., MITCHELL, D. & MACGREGOR, J. G. 1993. Structural design

considerations for high-strength concrete. Concrete international, 15, 27-34.

CORREIA, J. R., BRANCO, F. A. & FERREIRA, J. G. 2007a. Flexural behaviour of

GFRP-concrete hybrid beams with interconnection slip. Composite Structures,

77, 66-78.

CORREIA, J. R., BRANCO, F. A. & FERREIRA, J. G. 2007b. Flexural behaviour of

GFRP–concrete hybrid beams with interconnection slip. Composite Structures,

77, 66-78.

CORREIA, J. R., BRANCO, F. A. & FERREIRA, J. G. 2009. Flexural behaviour of

multi-span GFRP-concrete hybrid beams. Engineering Structures, 31, 1369-

1381.

COTSOVOS, D. M. 2010. A simplified approach for assessing the load-carrying

capacity of reinforced concrete beams under concentrated load applied at high

rates. International Journal of Impact Engineering, 37, 907-917.

COTSOVOS, D. M., STATHOPOULOS, N. D. & ZERIS, C. A. 2008. Behavior of RC

Beams Subjected to High Rates of Concentrated Loading. Journal of Structural

Engineering-Asce, 134, 1839-1851.

References

191

CUSATIS, G. 2011. Strain-rate effects on concrete behavior. International Journal of

Impact Engineering, 38, 162-170.

DANIEL, I. M., LABEDZ, R. H. & LIBER, T. 1981. New Method for Testing

Composites at Very High-Strain Rates. Experimental Mechanics, 21, 71-77.

DAVIES, G. A. O. & ZHANG, X. 1995. Impact Damage Prediction in Carbon

Composite Structures. International Journal of Impact Engineering, 16, 149-

170.

DESKOVIC, N., TRIANTAFILLOU, T. C. & MEIER, U. 1995. Innovative Design of

Frp Combined with Concrete - Short-Term Behavior. Journal of Structural

Engineering-Asce, 121, 1069-1078.

DOREY, G. 1988. Impact damage in composites – development, consequences, and

prevention. 6th International Conference on Composite Materials and 2nd

European Conference on Composite Materials. Imperial College, London.

FENG, P., CHENG, S., BAI, Y. & YE, L. P. 2015. Mechanical behavior of concrete-

filled square steel tube with FRP-confined concrete core subjected to axial

compression. Composite Structures, 123, 312-324.

FENWICK, J. M. & ROTOLONE, P. 2003. Risk management to ensure long term

performance in civil infrastructure. Australian Journal of Civil Engineering, 1,

29-34.

FERDOUS, W. 2012. Static flexural behaviour of fly ash-based geopolymer composite

beam: An alternative railway sleeper. Master of Engineering, University of New

South Wales, Canberra.

FERDOUS, W., KHENNANE, A. & KAYALI, O. 2013. Hybrid FRP-concrete railway

sleeper. 6th International Conference on Advanced Composites in Construction.

ACIC 2013, Sep 10th.

References

192

FERDOUS, W. & MANALO, A. 2014. Failures of mainline railway sleepers and

suggested remedies - Review of current practice. Engineering Failure Analysis,

44, 17-35.

FERDOUS, W., MANALO, A., KHENNANE, A. & KAYALI, O. 2015. Geopolymer

concrete-filled pultruded composite beams - Concrete mix design and

application. Cement & Concrete Composites, 58, 1-13.

FOSTER, D. C., RICHARDS, D. & BOGNER, B. R. 2000. Design and installation of

fiber-reinforced polymer composite bridge. Journal of Composites for

Construction, 4, 33-37.

FU, H. C., ERKI, M. A. & SECKIN, M. 1991. Review of Effects of Loading Rate on

Reinforced-Concrete. Journal of Structural Engineering-Asce, 117, 3660-3679.

FUJIKAKE, K., LI, B. & SOEUN, S. 2009. Impact Response of Reinforced Concrete

Beam and Its Analytical Evaluation. Journal of Structural Engineering-Asce,

135, 938-950.

FUJIKAKE, K., SENGA, T., UEDA, N., OHNO, T. & KATAGIRI, M. 2006. Study on

Impact Response of Reactive Powder Concrete Beam and Its Analytical Model.

Journal of Advanced Concrete Technology, 4, 99-108.

GHELLI, D. & MINAK, G. 2011. Low velocity impact and compression after impact

tests on thin carbon/epoxy laminates. Composites Part B-Engineering, 42, 2067-

2079.

GILAT, A., GOLDBERG, R. K. & ROBERTS, G. D. 2002. Experimental study of

strain-rate-dependent behavior of carbon/epoxy composite. Composites Science

and Technology, 62, 1469-1476.

References

193

GONILHA, J. A., CORREIA, J. R. & BRANCO, F. A. 2013. Dynamic response under

pedestrian load of a GFRP-SFRSCC hybrid footbridge prototype: Experimental

tests and numerical simulation. Composite Structures, 95, 453-463.

GUILD, F. J., HOGG, P. J. & PRICHARD, J. C. 1993. A Model for the Reduction in

Compression Strength of Continuous Fiber Composites after Impact Damage.

Composites, 24, 333-339.

GUSTIN, J., JONESON, A., MAHINFALAH, M. & STONE, J. 2005. Low velocity

impact of combination Kevlar/carbon fiber sandwich composites. Composite

Structures, 69, 396-406.

HAI, N. D., MUTSUYOSHI, H., ASAMOTO, S. & MATSUI, T. 2010. Structural

behavior of hybrid FRP composite I-beam. Construction and Building

Materials, 24, 956-969.

HARRIS, H. G., SOMBOONSONG, W. & KO, F. K. 1998. New ductile hybrid FRP

reinforcing bar for concrete structures. Journal of composites for construction, 2,

28-37.

HASHIN, Z. 1980. Failure Criteria for Unidirectional Fiber Composites. Journal of

Applied Mechanics-Transactions of the Asme, 47, 329-334.

HASHIN, Z. & ROTEM, A. 1973. Fatigue Failure Criterion for Fiber Reinforced

Materials. Journal of Composite Materials, 7, 448-464.

HAY, W. W. 1982. Railroad Engineering, John Wiley & Sons.

HAYES, S. V. & ADAMS, D. F. 1982. Rate Sensitive Tensile Impact Properties of

Fully and Partially Loaded Unidirectional Composites. Journal of Testing and

Evaluation, 10, 61-68.

References

194

HEIMBS, S., HELLER, S., MIDDENDORF, P., HAHNEL, F. & WEISSE, J. 2009.

Low velocity impact on CFRP plates with compressive preload: Test and

modelling. International Journal of Impact Engineering, 36, 1182-1193.

HEJLL, A., TÄLJSTEN, B. & MOTAVALLI, M. 2005. Large scale hybrid FRP

composite girders for use in bridge structures—theory, test and field application.

Composites Part B: Engineering, 36, 573-585.

HENRIQUES, J., DA SILVA, L. S. & VALENTE, I. B. 2013. Numerical modeling of

composite beam to reinforced concrete wall joints: Part I: Calibration of joint

components. Engineering Structures, 52, 747-761.

HIBBELER, R. C. 2004. Statics and mechanics of materials: SI edition, Singapore:

Prentice Hall.

HIROL, I. 2008. Plate-girder construction, BiblioBazaar.

HOLLAWAY, L. C. 1980. Glass fibre reinforced plastics in construction: Engineering

aspects, London, United Kindom, Taylor & Francis Ltd.

HOLLAWAY, L. C. 2001. The evolution of and the way forward for advanced polymer

composites in the civil infrastructure. Frp Composites in Civil Engineering, Vols

I and Ii, Proceedings, 27-40.

HOLMES, M. & JUST, D. J. 1983. GRP in structural engineering, Applied Science.

HORDIJK, D. A. 1991. Local approach to fatigue of concrete. PhD Thesis, Delft

University of Technology.

HULATT, J., HOLLAWAY, L. & THORNE, A. 2003. Short term testing of hybrid T

beam made of new prepreg material. Journal of Composites for Construction, 7,

135-144.

ICHIKAWA, T. & MIURA, M. 2007. Modified model of alkali-silica reaction. Cement

and Concrete Research, 37, 1291-1297.

References

195

JIANG, H., WANG, X. W. & HE, S. H. 2012. Numerical simulation of impact tests on

reinforced concrete beams. Materials & Design, 39, 111-120.

JOSHI, S. P. & SUN, C. T. 1985. Impact Induced Fracture in a Laminated Composite.

Journal of Composite Materials, 19, 51-66.

KAEWUNRUEN, S. 2007. Experimental and numerical studies for evaluating dynamic

behaviour of prestressed concrete sleepers subject to severe impact loading.

PhD thesis, University of Wollongong.

KAEWUNRUEN, S. & REMENNIKOV, A. M. 2008. Probabilistic impact fractures of

railway prestressed concrete sleepers. Structural Integrity and Failure, 41-42,

259-264.

KAEWUNRUEN, S. & REMENNIKOV, A. M. 2009a. Dynamic flexural influence on

a railway concrete sleeper in track system due to a single wheel impact.

Engineering Failure Analysis, 16, 705-712.

KAEWUNRUEN, S. & REMENNIKOV, A. M. 2009b. Impact capacity of railway

prestressed concrete sleepers. Engineering Failure Analysis, 16, 1520-1532.

KELLER, T., SCHAUMANN, E. & VALLÉE, T. 2007. Flexural behavior of a hybrid

FRP and lightweight concrete sandwich bridge deck. Composites Part A:

Applied Science and Manufacturing, 38, 879-889.

KHENNANE, A. 2009. Manufacture and testing of a hybrid beam using a pultruded

profile and high strength concrete. Australian Journal of Structural Engineering,

10, 145-155.

KIM, Y. J., GREEN, M. F. & FALLIS, G. J. 2008. Repair of bridge girder damaged by

impact loads with prestressed CFRP sheets. Journal of Bridge Engineering, 13,

15-23.

References

196

KISHI, N. & BHATTI, A. Q. 2010. An equivalent fracture energy concept for nonlinear

dynamic response analysis of prototype RC girders subjected to falling-weight

impact loading. International Journal of Impact Engineering, 37, 103-113.

KISHI, N., MIKAMI, H., MATSUOKA, K. G. & ANDO, T. 2002. Impact behavior of

shear-failure-type RC beams without shear rebar. International Journal of

Impact Engineering, 27, 955-968.

KORICHO, E. G., KHOMENKO, A., HAQ, M., DRZAL, L. T., BELINGARDI, G. &

MARTORANA, B. 2015. Effect of hybrid (micro-and nano-) fillers on impact

response of GFRP composite. Composite Structures, 134, 789-798.

KUMARAN, G., MENON, D. & NAIR, K. K. 2003. Dynamic studies of railtrack

sleepers in a track structure system. Journal of Sound and Vibration, 268, 485-

501.

LAPCZYK, I. & HURTADO, J. A. 2007. Progressive damage modeling in fiber-

reinforced materials. Composites Part A: Applied Science and Manufacturing,

38, 2333-2341.

LEE, J. H. & FENVES, G. L. 1998. Plastic-damage model for cyclic loading of

concrete structures. Journal of Engineering Mechanics-Asce, 124, 892-900.

LEE, J. H., KIM, Y. B., JUNG, J. W. & KOSMATKA, J. 2007. Experimental

characterization of a pultruded GFRP bridge deck for light-weight vehicles.

Composite Structures, 80, 141-151.

LI, Z., KHENNANE, A., HAZELL, P. J. & BROWN, A. D. 2017a. Impact behaviour of

pultruded GFRP composites under low-velocity impact loading. Composite


LI, Z., KHENNANE, A., HAZELL, P. J. & REMENNIKOV, A. M. 2017b. Numerical

modeling of a hybrid GFRP-concrete beam subjected to low-velocity impact

References

197

loading. The 8th International Conference on Computational Methods. Guilin,

Guangxi, China: July 25-29th.

LIU, D. H. 1988. Impact-Induced Delamination - a View of Bending Stiffness

Mismatching. Journal of Composite Materials, 22, 674-692.

LIU, Z. H., COUSINS, T. E., LESKO, J. J. & SOTELINO, E. D. 2008. Design

Recommendations for a FRP Bridge Deck Supported on Steel Superstructure.

Journal of Composites for Construction, 12, 660-668.

LUBLINER, J., OLIVER, J., OLLER, S. & ONATE, E. 1989. A Plastic-Damage Model

for Concrete. International Journal of Solids and Structures, 25, 299-326.

MALVAR, J. & ROSS, A. 1998. Review of Strain Rate Effects for Concrete in

Tension. Materials Journal, 95, 735-739.

MANALO, A., ARAVINTHAN, T., KARUNASENA, W. & TICOALU, A. 2010. A

review of alternative materials for replacing existing timber sleepers. Composite


MATZENMILLER, A., LUBLINER, J. & TAYLOR, R. 1995. A constitutive model for

anisotropic damage in fiber-composites. Mechanics of materials, 20, 125-152.

MEYER, R. W. 1985. Handbook of pultrusion technology, Springer US.

MINDESS, S., BANTHIA, N. & BENTUR, A. 1986. The response of reinforced

concrete beams with a fibre concrete matrix to impact loading. The International

Journal of Cement Composites and Lightweight Concrete, 8, 165-170.

MINDESS, S. & BENTUR, A. 1985. A Preliminary-Study of the Fracture of Concrete

Beams under Impact Loading, Using High-Speed Photography. Cement and

Concrete Research, 15, 474-484.

References

198

MITCHELL, R., BAGGOTT, M. G. & BIRKS, J. 1987. Steel sleepers - an engineering

approach to improve productivity. Conference on Railway Engineering. Perth,

Australia: National conference publication.

MIURA, S., TAKAI, H., UCHIDA, M. & FUKUDA, Y. 1998. The mechanism of

railway tracks. Japan Railway & Transport Review, 3, 38-45.

MURRAY, M. & CAI, Z. 1998. Literature review on the design of railway prestressed

concrete sleeper. RSTA Research Report. Australia.

NAAMAN, A. E. & GOPALARATNAM, V. S. 1983. Impact properties of steel fibre

reinforced concrete in bending. The International Journal of Cement Composites

and Lightweight Concrete, 5, 225-233.

NAIK, N. K., YERNAMMA, P., THORAM, N. M., GADIPATRI, R. & KAVALA, V.

R. 2010. High strain rate tensile behavior of woven fabric E-glass/epoxy

composite. Polymer Testing, 29, 14-22.

NATIONAL-RESEARCH-COUNCIL 2004. Guide for the design and construction of

externally bonded FRP systems for strengthening existing structures. CNR-

DT200.

NEELY, W. D., COUSINS, T. E. & LESK, J. J. 2004. Evaluation of in-service

performance of Tom's Creek Bridge fiber-reinforced polymer superstructure.

Journal of Performance of Constructed Facilities, 18, 147-158.

NIE, J. G., FAN, J. S. & CAI, C. S. 2004. Stiffness and deflection of steel-concrete

composite beams under negative bending. Journal of Structural Engineering-

Asce, 130, 1842-1851.

OZBOLT, J. & SHARMA, A. 2011. Numerical simulation of reinforced concrete

beams with different shear reinforcements under dynamic impact loads.

International Journal of Impact Engineering, 38, 940-950.

References

199

PEREZ, M. A., GIL, L. & OLLER, S. 2011. Non-destructive testing evaluation of low

velocity impact damage in carbon fiber-reinforced laminated composites.

Ultragarsas" Ultrasound", 66, 21-27.

PETRONE, G., RAO, S., DE ROSA, S., MACE, B. R., FRANCO, F. &

BHATTACHARYYA, D. 2013a. Behaviour of fibre-reinforced honeycomb core

under low velocity impact loading. Composite Structures, 100, 356-362.

PETRONE, G., RAO, S., DE ROSA, S., MACE, B. R., FRANCO, F. &

BHATTACHARYYA, D. 2013b. Initial experimental investigations on natural

fibre reinforced honeycomb core panels. Composites Part B-Engineering, 55,

400-406.

PHAM, T. M. & HAO, H. 2016a. Impact Behavior of FRP-Strengthened RC Beams

without Stirrups. Journal of Composites for Construction, 20.

PHAM, T. M. & HAO, H. 2016b. Review of Concrete Structures Strengthened with

FRP Against Impact Loading. Structures, 7, 59-70.

PHILIPPIDIS, T. P. & ANTONIOU, A. E. 2013. A progressive damage FEA model for

glass/epoxy shell structures. Journal of Composite Materials, 47, 623-637.

PINHO, S. T., ROBINSON, P. & IANNUCCI, L. 2006. Fracture toughness of the

tensile and compressive fibre failure modes in laminated composites.


POPOVICS, S. 1973. A numerical approach to the complete stress-strain curve of

concrete. Cement and concrete research, 3, 583-599.

PRASAD, G. G. & BANERJEE, S. 2013. The Impact of Flood-Induced Scour on

Seismic Fragility Characteristics of Bridges. Journal of Earthquake

Engineering, 17, 803-828.

References

200

PRUSZINSKI, A. 1999. Review of the landfill disposal risks and potential for recovery

and recycling of preservative treated timber. Environment protection agency,

South Australia.

QIAO, P. Z., DAVALOS, J. F. & ZIPFEL, M. G. 1998. Modeling and optimal design of

composite-reinforced wood railroad crosstie. Composite Structures, 41, 87-96.

RICHARDSON, M. O. W. & WISHEART, M. J. 1996. Review of low-velocity impact

properties of composite materials. Composites Part a-Applied Science and

Manufacturing, 27, 1123-1131.

ROBINSON, P. & DAVIES, G. A. O. 1992. Impactor Mass and Specimen Geometry-

Effects in Low Velocity Impact of Laminated Composites. International Journal

of Impact Engineering, 12, 189-207.

RODRIGUEZ, J., CHOCRON, I. S., MARTINEZ, M. A. & SANCHEZGALVEZ, V.

1996. High strain rate properties of aramid and polyethylene woven fabric

composites. Composites Part B-Engineering, 27, 147-154.

ROSS, A., TEDESCO, J. W. & KUENNEN, S. T. 1995. Effects of Strain Rate on

Concrete Strength. Materials Journal, 92, 37-47.

SÁ, M. F., GOMES, A. M., CORREIA, J. R. & SILVESTRE, N. 2016. Flexural creep

response of pultruded GFRP deck panels: Proposal for obtaining full-section

viscoelastic moduli and creep coefficients. Composites Part B: Engineering, 98,

213-224.

SAATCI, S. & VECCHIO, F. J. 2009. Effects of Shear Mechanisms on Impact

Behavior of Reinforced Concrete Beams. Aci Structural Journal, 106, 78-86.

SAHARUDIN, M. S., AIDAH, J., KAHAR, A. Z. & AHMAD, S. The influence of

alumina filler on impact properties of short glass fiber reinforced epoxy.

Applied Mechanics and Materials, 2013. Trans Tech Publ, 88-93.

References

201

SAKAMOTO, I., OKADA, H., KAWAI, N., YAMAGUCHI, N. & ISODA, M. 2001. A

research and development project on hybrid timber building structures.

Innovative Wooden Structures and Bridges, 283-288.

SATASIVAM, S. & BAI, Y. 2016. Mechanical performance of modular FRP-steel

composite beams for building construction. Materials and Structures, 49, 4113-

4129.

SCHWEITZER, P. A. 2009. Fundamentals of corrosion: Mechanisms, causes and

preventative methods, CRC Press.

SEBAEY, T., GONZÁLEZ, E., LOPES, C., BLANCO, N. & COSTA, J. 2013. Damage

resistance and damage tolerance of dispersed CFRP laminates: The bending

stiffness effect. Composite Structures, 106, 30-32.

SENNAH, K. M. & KENNEDY, J. B. 2002. Literature review in analysis of box-girder

bridges. Journal of Bridge Engineering, 7, 134-143.

SHOKRIEH, M. M. & OMIDI, M. J. 2009. Tension behavior of unidirectional

glass/epoxy composites under different strain rates. Composite Structures, 88,

595-601.

SJOBLOM, P. O., HARTNESS, J. T. & CORDELL, T. M. 1988. On Low-Velocity

Impact Testing of Composite-Materials. Journal of Composite Materials, 22,

30-52.

SPECIFICATION.NAASRA 1976. National Association of Australian State Road

Authorities. Sydney.

STALLINGS, J. M., TEDESCO, J. W., EI-MIHILMY, M. & MECAULEY, M. 2000.

Field performance of FRP bridge repairs. Journal of Bridge Engineering, 5, 107-

113.

STANDARDS, A. 2003a. Australian standard AS 1085.(2003). Railway track material.

References

202

STANDARDS, A. 2003b. Railway track material. Part 14: Prestressed concrete

sleepers. Australia: Australian Standard (AS1085.14).

STANDARDS, A. 2003c. Railway track material. Part 19: Resilient fastening

assemblies. Australia: Australian Standard (AS1085.19).

SUARIS, W. & SHAH, S. P. 1982. Strain-Rate Effects in Fiber-Reinforced Concrete

Subjected to Impact and Impulsive Loading. Composites, 13, 153-159.

SUTHERLAND, L. S., SA, M. F., CORREIA, J. R., SOARES, C. G., GOMES, A. &

SILVESTRE, N. 2017. Impact response of pedestrian bridge multicellular

pultruded GFRP deck panels. Composite Structures, 171, 473-485.

TABIEI, A., SVANSON, A. & HARGRAVE, M. 1996. Impact behavior of pultruded

composite box-beams. Composite Structures, 36, 155-160.

TACHIBANA, S., MASUYA, H. & NAKAMURA, S. 2010. Performance based design

of reinforced concrete beams under impact. Natural Hazards and Earth System

Sciences, 10, 1069-1078.

TANG, T. & SAADATMANESH, H. 2005. Analytical and experimental studies of

fiber-reinforced polymer-strengthened concrete beams under impact loading. Aci

Structural Journal, 102, 139-149.

TAVAKKOLIZADEH, M. & SAADATMANESH, H. 2003. Strengthening of steel-

concrete composite girders using carbon fiber reinforced polymers sheets.

Journal of Structural Engineering-Asce, 129, 30-40.

TENG, J. G., YU, T. & FERNANDO, D. 2012. Strengthening of steel structures with

fiber-reinforced polymer composites. Journal of Constructional Steel Research,

78, 131-143.

References

203

TENG, J. G., YU, T., WONG, Y. L. & DONG, S. L. 2007. Hybrid FRP-concrete-steel

tubular columns: Concept and behavior. Construction and Building Materials,

21, 846-854.

THIERFELDER, T. & SANDSTROM, E. 2008. The creosote content of used railway

crossties as compared with European stipulations for hazardous waste. Science

of the Total Environment, 402, 106-112.

THORENFELDT, E., TOMASZEWICZ, A. & JENSEN, J. Mechanical properties of

high-strength concrete and application in design. Proceedings of the symposium

utilization of high strength concrete, 1987. Tapir Trondheim Norway, 149-159.

TIAN, B. & COHEN, M. D. 2000. Does gypsum formation during sulfate attack on

concrete lead to expansion? Cement and Concrete Research, 30, 117-123.

UEDA, T. 2004. Standard Specifications for Concrete Structures-2002. JSCE, Hokosha

Co., Ltd, Japan, 24-32.

VAN ERP, G., HELDT, T., CATTELL, C. & MARSH, R. A new approach to fibre

composite bridge structures. Proceedings of the 17th Australasian conference on

the mechanics of structures and materials, ACMSM17, Australia, 2002. 37-45.

WANG, N. Z., MINDESS, S. & KO, K. 1996. Fibre reinforced concrete beams under

impact loading. Cement and Concrete Research, 26, 363-376.

WANG, Y. C., LEE, M. G. & CHEN, B. C. 2007. Experimental study of FRP-

strengthened RC bridge girders subjected to fatigue loading. Composite


WEE, T., CHIN, M. & MANSUR, M. 1996. Stress-strain relationship of high-strength

concrete in compression. Journal of Materials in Civil Engineering, 8, 70-76.

References

204

WHITTINGHAM, B., MARSHALL, I. H., MITREVSKI, T. & JONES, R. 2004. The

response of composite structures with pre-stress subject to low velocity impact

damage. Composite Structures, 66, 685-698.

WILLIAMS, B., SHEHATA, E. & RIZKALLA, S. H. 2003. Filament-wound glass

fiber reinforced polymer bridge deck modules. Journal of Composites for


WINTER, W., TAVOUSSI, K., PIXNER, T. & PARADA, F. R. 2012. Timber-steel-

hybrid beams for multi-storey buildings. World Conference on Timber

Engineering. Auckland.

WITCHER, D. A. 2009. Why fiber reinforced polymer (FRP) structural shapes have

become a material of choice. Structure magazine.

WONG, K., GONG, X., AIVAZZADEH, S. & TAMIN, M. Numerical simulation of

mode I delamination behaviour of multidirectional composite laminates with

fibre bridging effect. 15th European Conference on Composite Materials, 2012.

WU, E. B. & SHYU, K. 1993. Response of Composite Laminates to Contact Loads and

Relationship to Low-Velocity Impact. Journal of Composite Materials, 27,

1443-1464.

ZHANG, Z. Y. & RICHARDSON, M. O. W. 2007. Low velocity impact induced

damage evaluation and its effect on the residual flexural properties of pultruded

GRP composites. Composite Structures, 81, 195-201.

ZHAO, X. L. & ZHANG, L. 2007. State-of-the-art review on FRP strengthened steel

structures. Engineering Structures, 29, 1808-1823.

ZHOU, G. & HILL, M. D. 2009. Impact Damage and Energy-absorbing Characteristics

and Residual In-plane Compressive Strength of Honeycomb Sandwich Panels.

Journal of Sandwich Structures & Materials, 11, 329-356.

References

205

ZUREICK, A. & SCOTT, D. 1997. Short-term behavior and design of fiber-reinforced

polymeric slender members under axial compression. Journal of Composites for


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