THE DETERMINATION OF SHEAR PROPERTIES OF BRITTLE MATERIALS USING ARCAN TEST METHOD

FAHIS BIN TUMIN

UNIVERSITI TEKNOLOGI MALAYSIA

PSZ 19:16 (Pind. 1/97) UNIVERSITI TEKNOLOGI MALAYSIA

BORANG PENGESAHAN STATUS TESIS♦

JUDUL: THE DETERMINATION OF SHEAR PROPERTIES OF

BRITTLE MATERIALS USING ARCAN TEST METHOD

SESI PENGAJIAN : 2005/2006 Saya FAHIS BIN TUMIN

(HURUF BESAR)

mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut: 1. Tesis adalah hakmilik Universiti Teknologi Malaysia. 2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan

pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara

institusi pengajian tinggi. 4. **Sila tandakan (√) (Mengandungi maklumat yang berdarjah keselamatan atau SULIT kepentingan Malaysia sepertimana yang termaktub di dalam AKTA RAHSIA RASMI 1972)

(Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/badan di mana penyelidikan dijalankan)

√

_________(TANDATA Alamat Tet No 18, Jln K86000, KluJohor. Tarikh: 16

TERHAD

CATATAN:

TIDAK TERHAD

Disahkan oleh

________________ __________________________ NGAN PENULIS) (TANDATANGAN PENYELIA)

ap:

inabalu 2, Taman Koperasi, Dr. Yob Saed Ismailang,

Disember 2005 Tarikh: 16 Disember 2005

* Potong yang tidak berkenaan. ** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD. ♦ Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan penyelidikan, atau Laporan Projek Sarjana Muda (PSM).

Fakulti Kejuruteraan Mekanikal

Universiti Teknologi Malaysia

PENGESAHAN PENYEDIAAN SALINAN E-THESIS

Judul tesis : THE DETERMINATION OF SHEAR PROPERTIES OF BRITTLE

MATERIALS USING ARCAN TEST METHOD Ijazah : Sarjana Muda Kejuruteraan Mekanikal Fakulti : Fakulti Kejuruteraan Mekanikal Sesi Pengajian : 2005/2006 Saya FAHIS BIN TUMIN (HURUF BESAR)

No Kad Pengenalan 810113-01-6549 mengaku telah menyediakan salinan e-thesis sama seperti tesis

asal yang telah diluluskan oleh panel pemeriksa dan mengikut panduan penyediaan Tesis dan

Disertasi Elektronik (TDE), Sekolah Pengajian Siswazah; Universiti Teknologi Malaysia, November 2002. (Tandatangan pelajar) (Tandatangan penyelia sebagai saksi)

Alamat tetap :

18, JLN KINABALU 2, Nama penyelia : Dr. YOB SAED BIN ISMAIL

TAMAN KOPERASI, 86000 KLUANG, Fakulti : Fakulti Kejuruteraan

JOHOR DARUL TA’ZIM. Mekanikal

Tarikh : 16/12/2005 Tarikh : 16/12/2005

“I/We* hereby declare that I have read through this thesis and in my/our* opinion

this thesis has fulfilled the requirements in term of the scope and the quality of the

purpose of awarding the Bachelor of Mechanical Engineering Degree”

Signature : _____________________ Supervisor I : Dr. Yob Saed Ismail Date : 16 December 2005 Signature : _____________________ Supervisor II : Mr. Shukur Abu Hassan Date : 16 December 2005

*Potong yang tidak berkenaan

THE DETERMINATION OF SHEAR PROPERTIES OF BRITTLE MATERIALS USING ARCAN TEST METHOD

FAHIS BIN TUMIN

This thesis is submitted in partial fulfillment of the requirement for the Degree of

Bachelor in Mechanical Engineering

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

DECEMBER 2005

ii

“I declared that this thesis is my own work except the ideas and summaries which I have clarified their sources”.

Signature : _________________

Author’s Name : FAHIS BIN TUMIN

Date : 16 DECEMBER 2005

iii

Dedicated to…

My ever loving parents, Tumin B. Hussein and Peredah Bt. Haris, my sisters

and brother, Azlina, Hasnida, Anuar Zamani, Faezah, Fazilah, Noraini, family

members and lastly for my sweetheart Amilia Abd. Rahim, I love you so much.

iv

ACKNOWLEDGEMENT

I would like to express my gratitude and appreciation to my respectful

supervisors, Mr. Shukur Abu Hasan and Dr. Yob Saed Ismail for their guidance, advice,

support, and patience throughout the completion of this project. I also wish to thank the

staffs of Strength Lab, Mr. Rizal and Mr. Fadli, staffs of Material Lab, Mr. Ayub and

Mr. Jefri for their advice and help. A special gratitude to my friends, Mr. Shamsul Izwari,

Mr. Syed Muammar, Mr. Tahrail, Mr. Haidir, Mr. Kesavan and Mr. Munisvaran for their

support and help. Last but not least, I am very grateful to my parents and family for their

love, support and encouragement.

v

ABSTRACT

This thesis presented the test results of brittle epoxy material by using the Arcan

test method. This method was used to determine the shear strength, τ , and shear

modulus, G , of the test specimens by the relation of stress and strain. The butterfly

shape specimen was prepared and tested with the Arcan rig, in order to produce pure

shear by tensile load conditions. The Resifix-31 is one of the epoxy adhesives widely

used in civil engineering for bonding CFRP plate onto concrete surface. Thus, it is

important to test and determine the shear behaviour of the adhesive due to tropical

exposure condition. There are four types of exposure conditions that represent tropical

environment selected in this project ; namely laboratory (LB), outdoor (OD), plain water

(PW) and salt water (SW). The data obtained from the test results had showed that the

controlled specimen shear strength, τ , and shear modulus, G are 21.84% higher and 33.05% lower from the manufacturers quoted data. Apart from that, the Resifix-31 had

showed the value of shear strength decrease when exposed to selected exposure

conditions, which are about 25.4% in (LB), 18.43% in (OD), 32.01% in (PW), and

finally 26.6% in (SW), as compared to the controlled specimen. The shear modulus

value had also decreased when exposed to selected exposure conditions, which is about

12.8% in (LB), 9% in (OD), 11.1% in (PW) and 14.5% in (SW). On the other hand, the

Arcan test method has verified that a state of pure shear was present during the testing as

the stress strain curves linearly propagated on each ± 45 degree direction from the

loading axis although the different recorded strain value between strains gauges +45°

and -45º is about 7%, which may be caused by the effect of porosity (i.e. air bubbles) in

the specimens.

vi

ABSTRAK

Tesis ini membentangkan hasil kajian terhadap kekuatan tegasan ricih, τ , dan

modulus ketegaran, G, bahan perekat epoksi Resifix-31 dengan menggunakan kaedah

pengujian Arcan. Pengujian kekuatan tegasan ricih ini dibuat memandangkan perekat

epoksi ini digunakan secara meluas dalam bidang kejuruteraan awam. Kaedah pengujian

Arcan ini dibina dengan menggunakan perkaitan di antara tegasan ricih dan terikan ricih.

Spesimen berbentuk kupu-kupu telah disediakan dan diuji dengan menggunakan rig

Arcan yang akan menyebabkan spesimen gagal secara ricihan terhadap kesan bebanan

secara tegangan. Terdapat empat keadaan persekitaran yang diuji iaitu sampel makmal

(LB), jemuran pada keadaan sekeliling (OD), rendaman di dalam air paip (PW) dan juga

rendaman di dalam air masin (SW). Daripada ujian ricih yang telah dijalankan, didapati

bahawa nilai kekuatan tegasan ricih dan modulus ketegaran sampel kawalan telah

meningkat sebanyak 21.84% dan berkurang 33.05% daripada nilai yang disertakan oleh

pengeluar. Selain daripada itu, bagi keempat-empat sampel ujian didapati bahawa nilai

tegasan ricihnya telah berkurang sebanyak 25.4% bagi sampel (LB), 18.43% bagi (OD),

32.01% bagi (PW) dan 26.6% bagi (SW) berbanding spesimen kawalan (CO). Di

samping itu juga, nilai modulus ketegaran bagi sampel yang dikaji juga menurun

sebanyak 12.8% dalam (LB), 9% (OD), 11.1% (PW) dan 14.5% (SW). Berpandukan

kepada graf tegasan ricih melawan terikan ricih yang diplot bagi arah bebanan ± 45

darjah, terbukti bahawa hubungan linear di antara nilai tegasan ricih dan terikan ricih

dapat dicapai walaupun terdapat ketidakselanjaran sebanyak 7% pada nilai terikan bagi

kedua-dua arah. Secara kesimpulannya, kaedah pengujian Arcan ini terbukti dapat

digunakan untuk mencari nilai tegasan ricih tulen dan modulus ketegaran bagi bahan

komposit.

vii

TABLE OF CONTENTS

CHAPTER SUBJECTS PAGE

THESIS TITLE i

THESIS DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENT vii

LIST OF TABLE xi

LIST OF FIGURE xiii

LIST OF SYMBOL xviii

LIST OF APPENDIX xix

1 INTRODUCTION 1

1.1 Background of the Study 1

1.2 Objective 4

1.3 Scope of Study 4

1.4 Methodology 5

1.5 Planning and Scheduling 8

viii

2 BRITTLE MATERIAL 9

2.1 Introduction to Brittle Materials 9

2.2 Brittle Fracture 10

2.3 The Definition of Stress and Strain of a Solid Material 11

2.3.1 Stress 12

2.3.1.1 Analysis of Plane Stresses 15

2.3.2 Strain 18

2.3.2.1 Principal Strains and Planes 20

2.3.3 Stress-Strain Curve 21

2.3.4 Hooke’s Law for Shearing Stress and Strain 22

2.3.5 Relationship Between Young’s Modulus and 25

Shear Modulus of Inorganic Material

2.4 Adhesives 28

2.4.1 Epoxy Adhesive 29

2.4.2 Adhesive Compositions 31

2.5 Conclusion 32

3 THE ANALYSIS STUDY ON ARCAN TEST METHOD 33

3.1 Introduction 33

3.2 The Evolution of the Arcan Test Fixture and Specimen 34

3.3 Theoretical Analysis Background 38

3.4 Shear Analysis On Specimen 44

3.5 Recent Research and Development Using Arcan 48

Test Method

3.6 Conclusion 55

ix

4 SPECIMEN PREPARATION, EXPERIMENTATION AND 56

TESTING

4.1 Introduction 56

4.2 Material Details 57

4.3 Specimen Preparation 59

4.4 Experimentation 66

4.4.1 Environmental Exposures 66

4.4.2 Strain Gauge Installation 70

4.5 Arcan Fixture Setup 73

4.5.1 Arcan Fixture Installation 75

4.6 Instrumentation and Measurement 76

4.6.1 Testing Procedure 76

4.7 Microstructure Analysis 79

4.8 Conclusion 81

5 RESULTS AND DISCUSSION 82

5.1 Introduction 82

5.2 Results 82

5.2.1 Result Discussion 83

5.2.2 Test Data Sample Calculation 84

5.2.3 Experimental Results of Control Specimen 87

5.2.4 Experimental Results of Laboratory Exposure 90

5.2.5 Experimental Results of Outdoor Exposure 93

5.2.6 Experimental Results of Plain Water Wet-Dry 97

Exposure Sample

5.2.7 Experimental Results Salt Water Wet-Dry 99

Exposure Sample

5.3 Result Analysis 102

5.4 Microstructure Analysis 108

x

5.5 Chemical Elements in Resifix-31 Epoxy Adhesive 110

Determined by FESEM

5.6 Conclusion 111

6 CONCLUSION AND RECOMMENDATION 112

6.1 Conclusion 112

6.2 Recommendation 113

LIST OF REFERENCES 114

APPENDICES 117

APPENDIX A1-D1

xi

LIST OF TABLE

TABLE TITLE PAGE

1.1 Gantt chart for first semester 8

1.2 Gantt chart for second semester 8

3.1 Average shear modulus and shear strength test results of 49

various materials

4.1 Chemical formulation of Resifix-31 structural adhesives 56

4.2 Product data for Resifix-31 epoxy adhesive 58

4.3 Specimen average width, thickness and significant area 66

4.4 Exposure conditions for resifix-31 epoxy specimens 67

4.5 Water quality measurement tested in environmental 68

laboratory, Faculty of Civil Engineering, UTM

4.6 Plain water and Salt water experimentation data conditions 68

4.7 Rossete type strain gauge specifications 71

5.1 Raw experimental data for Resifix-31 ESST-C01 87

5.2 Testing results for ESST-CO sample 88

5.3 Raw experimental data for Resifix-31 ESLT-LB01 91

5.4 Testing results for ESLT-LB sample 91

5.5 Raw experimental data for Resifix-31 ESLT-OD01 94

5.6 Testing results for ESLT-OD sample 94

5.7 Raw experimental data for Resifix-31 ESLT-PW01 97

5.8 Testing results for ESLT-PW sample 97

xii

5.9 Raw experimental data for Resifix-31 ESLT-SW01 100

5.10 Testing results for ESLT-SW sample 100

5.11 Comparison of average shear strength,τ , and average shear modulus, G of Resifix-31 exposure samples 105

5.12 Chemical element in Resifix-31 epoxy for experimentation 110

purposes

xiii

LIST OF FIGURE

FIGURE TITLE PAGE

1.0 Cylinder torsion test method [9] 2

1.1 Arcan test method [12] 3

1.2 Flow chart of the thesis methodology 7

2.1 Sectioning of a body [5] 12

2.2 The normal and shearing component of stress [5] 13

2.3 The most general state of stress acting on an element [5] 14

2.4 Successive steps in the analysis of a body for stress [5] 15

2.5 Stress element showing two-dimensional state of stress [5] 16

2.6 Mohr’s circle illustrating equation 2.3 and 2.5 [19] 17

2.7 Mohr’s circle illustrating equation 2.6 and 2.7 [19] 18

2.8 Strain of cubical element subjected to uniaxial tension [5] 19

2.9 Cubical element subjected to plane shear strain [5] 19

2.10 Mohr’s circle representation of state of strain [5] 21

2.11 Normal stress-strain curve for a ductile materials [5] 22

2.12 Normal stress-strain curve for a brittle type materials [5] 22

2.13 An element of a body in pure shear [5] 23

2.14 Three representations of a state of pure plane shear stress [5] 26

2.15 Three representations of a state of pure plane shear strain [5] 26

2.16 Classifications of an adhesive [3] 28

2.17 Epoxy chemical structure [6] 30

xiv

FIGURE TITLE PAGE

3.1 The early concept of Arcan test method [2] 34

3.2 Significant section of the Arcan’s butterfly specimen [1] 35

3.3 Butterfly specimen bonded to aluminum circular plane [1] 35

3.4 Test fixture set-up and butterfly specimen modified by 36

Yen et al. [14]

3.5 Arcan fixture and butterfly specimen modified by Yen et al. [14] 37

3.6 Butterfly specimen used by Yen et al. [14] 38

3.7 Arcan fixture for shear testing with different loading 39

configurations [20]

3.8 Internal mean shear and normal stresses acting along the 39

‘significant section’ [20]

3.9 Prismatic element in state of equilibrium [19] 41

3.10 Mohr’s circle due to stress analysis [19] 43

3.11 Element deformation due to shear [19] 45

3.12 The strain results of a Graphite/PEEK specimen in shear [14] 48

3.13 Shear failure of an aluminum specimen [14] 50

3.14 Shear failure of a Graphite/PEEK specimen [14] 50

3.15 Failure mode of a Plexiglas specimen [14] 51

3.16 Effect of notch radius on shear stress profile along gage 52

section [14]

3.17 Effect of sharp notch on shear stress along the gage section [14] 53

3.18 Shear stress strain response from Arcan shear test [14] 54

3.19 Measured strain profiles at center of transverse butterfly 54

specimen during ‘pure shear’ tests [14]

4.1 Two parts structural adhesives of Resifix-31 58

xv

4.2 The butterfly specimen geometry 59

4.3 Adhesive system Part A/epoxy and Part B/hardener 60

4.4 A mixing process using slow speed electric mixer 60

4.5 Male and female parts of the butterfly mould 61

4.6 A complete assembly of mould parts 61

4.7 Surface cleaning process using soft cloth with Carnauba wax 62

4.8 Flat plate attached to male part by screws 62

4.9 Casting process of epoxy mixture 63

4.10 Male part attached to the female part 63

4.11 A 10 kg mass used to press the female part from top side 64

4.12 De-moulding process of specimen from mould 64

4.13 Surface grinding and polishing process of the specimen 65

4.14 Specimens ready to be exposed 65

4.15 Adding salt in plain water 69

4.16 Mixing ocean tropical salt and plain (tap) water 69

4.17 Specimens in plain water condition 69

4.18 Specimens in salt water condition 69

4.19 Specimens in control room condition 69

4.20 Specimens exposed to outdoor condition 69

4.21 Rosette type strain gauge installation axis at ± 450 and at 70

centre of AB line

4.22 Complete gauge installation onto the butterfly specimen 70

4.23 The adhesive film bonded onto specimen area 71

4.24 Butterfly specimen mounted to grip 71

4.25 Arcan male grip attached onto female grip 72

4.26 Complete assembly of butterfly specimen 72

4.27 Screws tightening process 72

4.28 Soldering lead wire to terminals 73

xvi

4.29 Arcan fixture set-up 74

4.30 Assembly of Arcan fixture 74

4.31 Attachment grip to holder by pin 75

4.32 Complete Arcan fixture attachment 75

4.33 Instrumentation set-up 76

4.34 Arcan test rig ready to be test 77

4.35 Strain reading initialization 77

4.36 Test data collection during testing 77

4.37 Relationship between shear stress, shear strain and shear modulus 79

4.38 Field-emission Scanning Electron Microscope (FESEM) 80

5.1 Specimen geometry for sample calculation 84

5.2 Mohr’s circle constructed based on principal strains of Resifix-31 86

ESLT-LB01 at 1000N loading condition

5.3 Shear stress-strain curve for Resifix-31 ESST-C01 89

5.4 Specimen ESST-C01 after failed 89

5.5 Brittle failure of ESST-C01 90

5.6 Shear stress-strain curve for Resifix-31 ESLT-LB01 92

5.7 Specimen ESLT-LB01 after failed 93

5.8 Brittle failure of ESLT-LB01 specimen 93

5.9 Shear stress-strain curve for Resifix-31 ESLT-OD01 95

5.10 Specimen ESLT-OD01 after failed 96

5.11 Brittle failure of ESLT-OD01 specimen 96

5.12 Shear stress-strain curve for Resifix-31 ESLT-PW01 98

5.13 Specimen ESLT-PW01 after failed 99

5.14 Brittle failure of ESLT-PW01 99

5.15 Shear stress-strain curve for Resifix-31 ESLT-SW01 101

5.16 Specimen ESLT-SW01 after failed 102

5.17 Brittle failure of ESLT-SW01 102

xvii

5.18 Shear strain versus shear stress for ESST-CO01 103

5.19 Shear strain versus shear stress for ESLT-LB01 103

5.20 Shear strain versus shear stress for ESLT-OD01 104

5.21 Shear strain versus shear stress for ESLT-PW01 104

5.22 Shear strain versus shear stress for ESLT-SW01 105

5.23 Shear strength versus exposure condition for all test samples 106

5.24 Shear modulus, G, versus sample exposure conditions for all 107

test samples

5.25 Fracture surface of Resifix-31 epoxy for ESST-CO sample 108

5.26 Porosities in ESLT-LB sample 109

5.27 Porosities in ESLT-OD sample 109

5.28 Porosities in ESLT-PW sample 109

5.29 Porosities in ESLT-SW sample 109

5.30 Porosities size in Resifix-31 epoxy ESST-CO sample 110

xviii

LIST OF SYMBOL

SYMBOLS SUBJECT

P,F - Force

τ - Shear stress

σ - Normal stress

A - Cross sectional

t - Thickness of specimen

ε - Normal strain

γ - Shear strain

α, ø, θ - Radius

G - Shear modulus

E - Elastic Modulus

l - Length

r - Notch radius

h - Gauge length

w - Width

v - Poisson’s ratio

xix

LIST OF APPENDIX

APPENDIX NO. TITLE PAGE

A1 Adhesive compositions

A2 Arcan shear test result for Resifix-31

B1 Shear stress-strain curve for Resifix-31

C1 Microstructure of fracture surface of Resifix-31

C2 Elements spectrum of Resifix-31

D1 Arcan fixture mould and rig drawing

1

CHAPTER 1

INTRODUCTION

1.1 Background of The Study

A brittle material is one which exhibits relatively small extensions to fracture so

that the partially plastic region of the tensile test graph is much reduced. In the overview

of brittle materials, mechanical behavior is determined by stress and strain associated

with material points throughout the material. Mechanical properties are measured in test

of samples in which loads or boundary displacements are applied in such way that the

relation between stress and strain at a typical point can be inferred. In brittle materials,

the situation is further complicated by the occurrence of fracture. During deformation,

the material structure is changed due to the initiation and propagation of cracks at

different locations throughout the material [8].

Among the problem in conducting the test for brittle materials is to devise

specimen and loading configuration in order to produce a state of uniform plane stress.

The problem has assumed increased significance with the application of brittle

composite materials and brittle adhesives system nowadays in mechanical and civil

engineering structures applications. For example by referring to fibre reinforced

2

polymer composites (FRP) that form of laminates in which the laminae are stacked

by the principal of bonding using resin-matrix system. In most engineering

applications, the laminae are in states of plane stress. It is therefore necessary to test

single laminae in plane stress in order to obtain mechanical properties such as shear

and stress properties and also to determine the failure criteria.

The shear properties of epoxy adhesive is one aspect that user tends to

neglect as it is only a small part but crucially important in designing the externally

bonded FRP-concrete. Selection of the adhesive must provide material integrity of

the bonded systems in order to produce uniform stress throughout the bond area.

This is important to avoid the premature failure of the systems such as adherends,

cleavage and interfacial failure of adhesive. For the same reason, this project aim to

determine the shear properties of two parts epoxy adhesives system, namely

Resifix-31 under lab controlled and tropical exposure conditions.

In general, the typical shear test method used to determine the shear

properties of most materials is the cylinder-torsion test, as shown in Fig. 1.0.

Unfortunately, this method has an advantage which is unable to produced significant

section on the sample, the grips strongly influence the state of stress.

Fig. 1.0 : Cylinder torsion test method [9]

3

In 1978, Arcan et al. [1] introduced a new method of testing material shear

properties under uniform plane–stress conditions by means of specially designed

plane specimen, as shown in Fig. 1.1.

Fig. 1.1 : Arcan test method [12]

The fixture was used to determine shear properties for various materials such

as polymer composite, sandwich materials system, human bones and solid polymers.

Photoelastic analysis [1] had show that in the significant section of the specimen it is

possible to produced uniform plane stress with high degree of accuracy. The

compact nature of the Arcan fixture offers an advantage to obtain the shear

properties in all in-plane directions in a relative simple manner [10]. The Arcan

fixture can be used to apply both shear and axial forces to the test specimen and this

special case of loading produces pure shear on the significant section and the

experimental results are encouraging and acceptable with high degree of confident

[1].

4

In this project the studies concentrated on the Arcan fixtures in order to

obtain the shear properties of the brittle structural epoxy adhesive material, namely ;

Resifix-31. The apparatus consist of specimen with butterfly shape and Arcan test

fixture. The shear properties obtained due to various types of exposure conditions

will be used for analyzing the bond stress characteristic of CFRP-epoxy-concrete

under final load test (i.e. which also exposed to various tropical conditions).

1.2 Objective

The main objective of this project is to study the in-plane shear properties of

brittle structural epoxy material using Arcan Test Method. The study focus on the

following properties ;

i) An average shear stress and shear modulus properties, τ and G of

structural epoxy adhesive Resifix-31 due to tropical exposure

conditions.

ii) Microstructure analysis due to exposure conditions.

iii) The reliability of test data.

1.3 Scope of study

The scope of this study covers the following topics ;

i. Literature study on the epoxy adhesive material (i.e. Resifix-31, which is

two parts epoxy system) supplied by Exchem, United Kingdom

ii. Literature study on the Arcan test method fixture

iii. Specimen preparation

5

iv. Specimen experimentation and final shear load test

v. Results and discussion

vi. Report writing

1.4 Methodology

The detailed project methodology are describes as follows ;

i. Literature Study

The literature studies were carried out by sourcing the related information

from journals, handbooks, books, previous thesis, and websites. Firstly,

literature review was carried out to understand the mechanical characteristic

of the adhesive system used in this study. Then, the studies were focused on

the Arcan test method in order to investigate the theoretical background of

Arcan test method which related to shear properties and to determine suitable

butterfly specimen geometry for the study. Apart from that, a study on Arcan

test rig development also been conducted in order to identify problems faced

by previous researchers.

ii. Problems identification and solving

The problems encountered during the literature studies and experiment set-up

was then discussed with project supervisor.

iii. Specimen testing

The two parts epoxy adhesive was cast in a closed mould to produce

butterfly shape specimens. The specimens were exposed to four (4) tropical

6

conditions, namely ; Control Specimens (ESST), Laboratory Exposure (LB),

Outdoor (OD), Plain Water (PW-wet/dry) and Salt Water (SW-wet/dry).

These specimens were exposed to their respective conditions for duration of

six months before prior final shear load test.

iv. Data collection and analysis

Data were gathered from the instrumented measurement that been

established during testing. The specimens failure mechanism was observed

during testing and microstructure analysis has been done in order to

investigate in depth the source of failure mechanism.

v. Report writing

All the findings and results from the experiment will be discussed and make

a comparison with previous research if necessary.

The project methodology flow chart is shown in Fig. 1.2.

7

Literature Study

Problems Identification

Problem Solving

Arcan Test Rig Study

Test Samples Experimentation

Testing

Data Analysis

Comparison

Satisfy?

Discussion

Conclusion & Suggestion

End

Fig. 1.2 : Flow chart of the project methodology

8

1.5 Planning and Scheduling

In order to make sure this thesis is on schedule, a Gantt chart was produced

from the second week after the discussion with the supervisor, as shown in Table 1.1

and Table 1.2.

Table 1.1 : Gantt chart for first semester

Week

Activities 1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16

Project Briefing *

Planning and Scheduling * *

Literature Study * * * * * * * * * * * * * *

Testing Set-up * * * * * * * * *

Problems Identification and Solving

* * * * * * *

Final Draft and Presentation I

* * * *

Table 1.2 : Gantt chart for second semester

Week

Activities 1 2 3 4 5 6 7 8 9

1

0

1

1

1

2

1

3

1

4

1

5

1

6

Project Briefing * *

Planning and Scheduling for Sample Preparation

* *

Testing Set-up * * * * * *

Result Analysis * * * * *

Final Draft and Presentation II

* * * *

9

CHAPTER 2

THE MECHANICAL PROPERTIES OF BRITTLE MATERIALS

2.1 Introduction to Brittle Materials

Brittle material behaved elastically to fracture and shows low-fracture toughness

characteristic. Brittle polymers exhibit some yielding, but it is negligible compared to

ductile polymers such as thermoplastic and metals. Brittle materials, which have

complicated crystal structures usually consist of two or three kinds of atoms, produced

high resistance slip to system among them. Even if there is limited plasticity, electrical

neutrality has also to be satisfied in covalent and ionic-bonded materials. For all these

reason, we usually do not observe any macroscopic plasticity in these materials.

By definition, the material those failure is control primarily by the presence of

flaws or cracks, are termed brittle materials. In ductile materials, cracks may be present,

but the resulting stress concentration is relieved by plastic deformation, which produced

brittle fracture. Typical examples of brittle materials are cast iron, glass, and polymer

concrete. Some strength characteristic of brittle materials are briefly described as

follows ;

10

1. Scatter of Strength Properties

Brittle materials exhibit a scatter of failure strength, unlike ductile materials, in

which plastic deformations takes place. In ductile material, the variability of

strengths is nominally identical specimen is generally not more than 4% to 8% of

its mean strength. Hence, the mean strength of a ductile material can be used in

designing, as a measure of strength. In a brittle material, the variation of strength

in nominally identical specimens can be as high as 100% of the mean strength.

Therefore, the mean strength is not an adequate measure of the strength of a

brittle material.

2. Effect of Volume Fraction

Experimental observations have revealed that the mean strength of a brittle

material depends on the volume of the material, especially when subjected to

tensile stresses. The result show that when volume is increased, mean strength

decrease (under tension).

3. Effect of Loading Systems / Conditions

The mean strength depends on the type of loading system. This can be

interpreted as when the brittle material is subjected to different types of loading,

they will behave differently.

2.2 Brittle Fracture

When a solid material is subjected to high (near to failure load) increasing load,

the solid may fracture. If such breakage comes about before the piece has thinned down

to zero thickness, it is called fracture; and if the amount of permanent deformation

preceding fracture is negligible, it is called brittle fracture. On the other hand, in a

ductile fracture, plastic deformation occurs in the final fracture such as necking [4].

According to Griffith [4], brittle fracture is due to minute crack like defects. In many

11

cases, brittle fracture gives rise to fast growth of a crack in the body [4]. Although the

ideal strength is very high for a glassy solid whose atoms are held together with primary

bonds, the severe stress concentration at sharp cracks can reduce this strength to

ordinarily observes low values.

Brittle fracture results from submicroscopic cracks with atomically sharp roots,

where the stress can become concentrated beyond the capacity of the body to resist it.

Brittle fracture is the expected mode of failure of materials like cast iron, glass, concrete,

porcelain, ceramic, are expected to show considerable distortion (and to absorb

substantial energy) before fracture can occur. This fracture often occurs suddenly and

without warning. They are associated with a release of a substantial amount of elastic

energy which may cause a loud noise. The primary factors influencing the material

brittle fracture are as follows ;

1. Low temperature

Reduced temperatures increase the resistance of the material to slip but not to

cleavage due to tensile loading.

2. Rapid loading

Rapid rates of shear deformation require greater shear stresses, and this may be

accompanied by normal stresses which exceed the cleavage strength of the

material.

2.3 The Definition of Stress and Strain of a Solid Material

In all engineering construction and application the elements of a structure must

be assigned definite physical size. Such elements must be properly proportioned to resist

the actual or probable forces that may be imposed among them. Thus, it is important to

12

understand the concepts of stress and strain, and their relation in order to summarize the

properties of the brittle materials used in this project.

2.3.1 Stress

In general, the internal force acting on infinitesimal areas of a cut may be of

varying magnitude and directions, as shown diagrammatically in Fig. 2.1. These internal

forces are vectorial in nature and maintain in equilibrium the externally applied forces in

the section. In mechanic of materials it is partially significant to determine the intensity

of these forces on the various portions of the cut, as resistance to deformation and the

capacity of materials to resist forces depend on these intensities. These intensities of

forces acting on infinitesimal areas of the cut vary from point to point, and they are

inclined with respect to the plane of the cut.

Fig. 2.1 : Sectioning of a body [5]

In engineering practice it is customary to resolve this intensity of force

perpendicular and parallel to the section investigated. Such resolution of the intensity of

the force on an infinitesimal area is shown Fig. 2.2.

13

Fig. 2.2 : The normal and shearing component of stress [5]

The intensity of the force perpendicular or normal to the section is called the

normal stress at a point. In this thesis it will be designated by the Greek letter σ (sigma).

As a particular stress generally holds true only at a point, it is defined mathematically as ;

σ = {0

lim→∆A A

P∆∆ [2.1]

where P is a force acting normal to the cut, while A is the corresponding area. It is

customary to refer to the normal stresses that cause traction or tension on the surface of

a cut as tensile stresses. On the other hand, those that are pushing against the cut are

compressive stresses.

An infinitesimal cube, as shown in Fig. 2.3, could be used as the basis for an

exact formulation of the problem in mechanics of materials. However, the methods for

the behavior of such a cube (which involve the writing of an equation for its equilibrium

and making certain that such a cube, after deformations caused in it by the action of

forces) are beyond the scope of this thesis. They are in the realm of the mathematical

theory of elasticity.

14

Fig. 2.3 : The most general state of stress acting on an element [5]

In many practical situations, if the direction of the imaginary plane cutting a

member is judiciously selected, the stresses that act on the cut will be found both

particularly significant and simple to determine. One such important case occurs in a

straight axially loaded rod in tension, provided a plane is passed perpendicular to the

axis of the rod. The tensile stress acting on such a cut is the maximum stress, as any

other cut not perpendicular to the axis provides a larger surface for resisting the applied

force. The maximum stress is the most significant one, as it tends to cause the failure of

the material.

To obtain an algebraic expression for this maximum stress, consider the case

illustrated in Fig. 2.4 (a). If the rod is assumed weightless, two equal and opposites

forces P are necessary, one at each end to maintain equilibrium. The whole body is in

equilibrium, so any part of it is also in equilibrium. A part of the rod to either side of the

cut x-x is in equilibrium. At the cut, where the cross sectional area of the rod is A, a

force of equivalent to P as shown in Fig. 2.4 (b) and (c) must be developed. Where upon,

from the definition of stress, the normal stress which acts perpendicular to the

cut is ;

15

σ = AP or

areationalcrosforce

−sec ⎥⎦

⎤⎢⎣⎡

2mN [2.2]

Fig. 2.4 : Successive steps in the analysis of a body for stress [5]

2.3.1.1 Analysis of Plane Stresses

Most stress analysis problems of engineering involve one surface which is free

of stress. In this case, all stresses on a stress element act on only two pairs of faces, as

shown in Fig. 2.5. The stress surfaces of the element is by the definition on the principal

planes (since they are subjected to zero shear stress), and the normal of these surfaces is

the principal axis. According to the shear-stress convention in previous section, both xyτ

and would be positive, and the element as a whole would be regarded as being

subject to positive shear. As the elements are viewed, positive shear stress tends to

deform the element to the right and negative shear stress to the left.

yzτ

16

Fig. 2.5 : Stress element showing two-dimensional state of stress [5]

The derivation of the analytical expressions relating the normal and shear stress

to the angle of cutting plane φ is given in elementary texts book on strength of materials

and will not be repeated here. If the stresses shown in Fig. 2.5 are known, the principal

stress with the principal directions, and the maximum shear stress may be found from

the following equations ;

1σ , 2σ = 2yx σσ + ±

22

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+ yxxy

σστ [2.3]

The principal shear stresses act on planes whose normal make angles of 45 to 0 1σ and

2σ . Principal shear stresses occur when the normal stresses are equal. The maximum

principal shear stress, maxτ , (for the case of a two-dimensional stress systems) is ;

maxτ = ± 2

2

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+ yxxy

σστ [2.4]

2φ = tan-1yx

xy

σστ−

2 [2.5]

where φ is the angle between the principal planes and the x-y planes. When φ is

positive, the principal planes are clockwise of the x and y planes. Where the principal

17

stresses are known and it is desired to find the stresses acting on a plane oriented at

angle φ from the principal plane number 1, the equations are ;

φσ = 221 σσ + +

221 σσ − cos 2φ [2.6]

φτ = 221 σσ − sin 2φ [2.7]

In Equation [2.7], φτ represents a shear stress acting on the φ plane and directed

90 from the 0 φ plane. When plotted on σ -τ coordinates, equation [2.6] and [2.7]

produce a circle which is symmetric about the σ axis. Because of the 2φ in the

equations, angle measured on the circle are twice those measured at the stress element. It

is the basis for Mohr’s circle, an extremely useful graphic technique for stress analysis.

Fig. 2.6 and 2.7 shows how Mohr’s circle illustrates equation [2.3] to [2.7].

Fig. 2.6 : Mohr’s circle illustrating equation 2.3 to 2.5 [19]

18

Fig. 2.7 : Mohr’s circle illustrating equation 2.6 and 2.7 [19]

2.3.2 Strain

Any physical bodies subjected to forces such as stresses, deforms under the

action of these forces. Strain is the elongation per unit of length [4]. The term strain can

also be describe as the direction and intensity of the deformation at any given point with

respect to a specific plane passing through that point. Thus, state of strain is a tensor and

is analogous to state of stress. Strains are always resolved into normal component ε

(epsilon) and shear component,γ (gamma). With reference to Fig. 2.8 and Fig. 2.9,

normal strain may be defined as ;

xε = {0

lim→x x

dx yε = {0

lim→y y

dy zε = {0

lim→z z

dz [2.8]

With reference to Fig. 2.9, shear strain may be defined as ;

yxγ = {0

lim→y y

dx = tan θ ≈ 0 radian [2.9]

where angleθ represent the deviation from an initial right angle. If the total elongation

19

is in a given original length, ∆ L , thus elongation per unit length,ε (epsilon) is ;

ε = LL∆ [2.10]

It is a dimensionless quantity. The quantity ε is very small, except for a few

materials such as rubber. If the strain is known, the total deformation of an axially

loaded bar is ε L. The subscript notations for strains correspond to that used with

stresses and also the sign conventions for strains follows directly from those stress.

Fig. 2.8 : Strain of cubical element subjected to uniaxial tension

(a) Three dimensional view (b) Plane view [5]

Fig. 2.9 : Cubical element subjected to plane shear strain

(a) Three dimensional view (b) Plane view [5]

20

2.3.2.1 Principal Strains and Planes

Principal strains in the x-y plane, the maximum shear strain in the xy plane, and

the orientation of the principal axes relative to the x-y axes are given by equation [2.11]

to [2.14].

1ε , 2ε = 2yx εε + ±

22

221

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟

⎠⎞

⎜⎝⎛ yx

xy

εεγ [2.11]

maxγ = ± 222

221

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟

⎠⎞

⎜⎝⎛ yx

xy

εεγ [2.12]

2φ = tan-1yx

xy

εεγ− [2.13]

Where φ is the angle between the principal planes and the x and y planes. Similarly, the

strain counterparts of stress are ;

φε = 221 εε + +

221 εε − cos 2φ [2.14]

From knowledge of the three principle strains, a Mohr’s circle representation of

the state of strain can be made, as shown in Fig. 2.10. Note that the coordinates of the

Mohr plot are normal strain and half of shear strain. The circle between points 1 and 2

represent the strain component on all planes containing the 3 axis ; the circle between 1

and 3 represents strains on all planes containing the 2 axis ; the circle between 2 and 3

represents strains on all planes containing the 1 axis. Strain components for all planes

containing none of the axes are represented by the shaded area between circles. As when

representing stresses, the largest of the three circles is referred to as the principle circle.

21

Fig. 2.10 : Mohr’s circle representation of state of strain [5]

2.3.3 Stress-Strain Curve

In the study of the properties of materials, it is customary to plot diagrams on

which a relationship between stress and strain is reported. Experimentally determined

stress-strain diagram differ considerably for different materials. One type is shown in

Fig. 2.11, which is for mild steel, a ductile material widely used in construction. The

brittle type is shown in Fig. 2.12.

22

Fig. 2.11 : Normal stress-strain curve for a ductile materials (i.e. mild steel) [5]

Fig. 2.12 : Normal stress-strain curve for a brittle type materials (i.e. concrete) [5]

2.3.4 Hooke’s Law for Shearing Stress and Strain

In the previous sections it was shown that in an element of a body the shearing

stress must occur in parallel plane acting on mutually perpendicular planes. When only

these stresses occur, the element is said to be in pure shear. Such a system of stresses

distorts an element of an elastic type shown in Fig. 2.13 (a). The diagonals OA and BC

are axes of symmetry for a distorted element.

23

Fig. 2.13 : An element of a body in pure shear [5]

If attention is confined to the study of small deformations, and further, if

behavior of an element is considered only in its elastic range, it is again found

experimentally that there is a linear relationship between the shearing stress and the

angle γ (gamma) shown in Fig. 2.13 (c). It must be noted that an extension in any one

direction will result in producing lateral contractions in the other two directions. This

effect is called Poisson’s effect and v is the parameter termed Poisson’s ratio which

takes this effect into account. Therefore, the strain in the x, y, z directions can be related

to the stresses by the following equations ;

xε = E1 ( )[ ]zyx σσνσ +−

yε = E1 ( )[ ]xzy σσνσ +−

zε = E1 ( )[ ]yxz σσνσ +− [2.15]

These equations may be solved to obtain stress components as functions of

strains, and for plane stress conditions, we have ;

24

xσ = )21)(1( νν −+E [ ])()1( zyx εενεν ++−

yσ = )21)(1( νν −+E [ ])()1( xzy εενεν ++−

zσ = )21)(1( νν −+E [ ])()1( yxz εενεν ++− [2.16]

For the special case in which the x, y, and z, axes are coincident with principal

axes 1, 2, and 3, equations [2.16] are simplified by virtue of all shear stresses and shear

strains being equal to zero ;

1ε = E1 ( )[ ]321 σσνσ +−

2ε = E1 ( )[ ]132 σσνσ +−

3ε = E1 ( )[ ]213 σσνσ +− [2.17]

1σ = )21)(1( νν −+E [ ])()1( 321 εενεν ++−

2σ = )21)(1( νν −+E [ ])()1( 132 εενεν ++−

3σ = )21)(1( νν −+E [ ])()1( 213 εενεν ++− [2.18]

25

For the commonly encountered biaxial-stress state, one of the principal stresses

is zero (e.g. 3σ = 0), the equations become ;

1ε = E1 ( 1σ - ν 2σ )

2ε = E1 ( 2σ - ν 1σ )

3ε = - Eν ( 1σ + ν 2σ ) [2.19]

Substitution of this expression in equation [2.18] gives

1σ = 21 ν−E ( 1ε + 2νε )

2σ = 21 ν−E ( 2ε + 1νε )

3σ = 0 [2.20]

2.3.5 Relationship Between Young’s Modulus and Shear Modulus

Figure 2.14 illustrates an element subjected to pure plane shear stress. The four

intercepts on the Mohr circle represent stress coordinates on x, y , 1, and 2 planes, which

are planes perpendicular to these respective axes. The Fig. 2.15 represents the resultant

strain present in the same element.

26

Fig. 2.14 : Three representations of a state of pure plane shear stress [5]

Fig. 2.15 : Three representations of a state of pure plane shear strain [5]

From equations [2.19], we can obtain the Shear Modulus in terms of the Young’s

modulus ;

1ε = E1 ( 1σ - ν 2σ )

2ε = E1 ( 2σ - ν 1σ )

and, because the xyτ in the same direction to the principal stress, thus ;

1ε = E1 ( )xyxy νττ + = E

xyτ (1+ν )

also ;

2ε = E1 (- )xyxy νττ − = - E

xyτ (1+ν ) [2.21]

27

From the Mohr strain circle in Fig.2.15 ;

2xyγ = 1ε = E

xyτ (1+ν )

and from the relationship between G, E, and ν ;

G = )1(2 ν+

E [2.22]

Rearrange equations 2.16, finally,

G = xy

xy

γτ

= )1(2 ν+

E [2.23]

where G is a constant of proportionality called the shearing modulus of elasticity or the

modulus of rigidity. The G value is a constant for a given material and measured in the

same unit as E, while γ is measured in radian. The expression for the three different sets

of shearing strains can be stated as follows ;

xyτ = G xyγ

yzτ = G yzγ

zxτ = G zxγ [2.24]

The shear stress in equation [2.24] can be determined from a thin tube subjected

to a torsion or torque. From previous experiments it is known that the appearance of

τ -γ curve is similar to that of the σ -ε diagrams of a tension test for the same material.

In this project, the Arcan test method is used in order to obtain similar properties of

shear stress when the material is subjected to pure shear.

28

2.4 Adhesives

Adhesives were first used many thousands of years ago, and most were derived

from naturally occurring vegetable, animal, or mineral substance. Synthetic polymeric

adhesives displaced many of these early products due to stronger adhesion and greater

resistance to operating environments. The classification of adhesives is shown in

Fig. 2.16.

Fig. 2.16 : Classifications of an adhesive [3]

29

An adhesive is a substance capable of holding substrates (adherends) together by

surface attachment. A material merely conforming to this definition does not necessarily

ensure success in an assembly process. For adhesives to be useful it must not only hold

materials together but also withstand operating loads and able to transfer stresses

uniformly. The successful application of adhesives depends on many factors. Adhesives

face a complex task of selecting the proper and correct processing conditions that allow

the bond to form. One must also determine the substrate-surface treatment which will

permit an acceptable degree of permanence and bond strength. The adhesive joint must

be correctly design and applied in order to avoid stresses within the joint that could

cause premature failure [2].

2.4.1 Epoxy Adhesive

The term epoxy has come to mean ‘superglue’, which bonds almost anything to

anything. Although this is certainly an exaggeration, epoxy adhesive will bond to a wide

variety of materials without requiring heat or pressure in most cases. Epoxies are

available in a great variety of forms ; some will cure at room temperature and some

require heat curing; most are two-component liquid or paste systems that require no

mixing; some are available in supported or unsupported films, and others are available

in pre-impregnated tapes or granules and powders.

Epoxy resins are generally used in adhesive applications in a two part system in

which a hardener must be added to the resin just before application. The hardener,

(usually an amine or anhydride) forms crosslink between the epoxy resin molecules,

thus converting the liquid resin into a hard matrix. This curing is achieved through an

epoxy ring opening reaction with primary or secondary amines or acid anhydrides as

hardeners.

30

Epoxies, because of their polar groups, display very high adhesives strength to

metals, ceramics, glass, and other polymers. Epoxies are famous for their versatility.

They can be used to bond most any two surfaces no matter how different. Also epoxies,

after reacting with a hardener, give very high cohesive strength as well. Other

advantages of epoxies are that they are highly reactive and do not give off high levels of

volatile reaction by-products (some amine hardeners are volatile, however, and do flash

evaporate during curing).

Epoxies shrinkage is much less than other reactive polymers such as polyester,

for example. The additions of fillers to the adhesive also reduce shrinkage even further.

Because of the toxic vapors which may be given off when working with epoxies, all

work with these resins should be done in areas having adequate ventilation.

When epoxy adhesives set, they form a very hard, strong and tough glue line. In

fact, for some applications, epoxies may be too hard. Unmodified epoxies lack

flexibility and have poor strength through wide temperature variations, special epoxy

“alloys” are formulated with NBR, urethane, acrylics, and nylon. The special “alloy”

formulations are now used extensively in aircraft construction adhesives. Fig. 2.17

shows the idealized chemical structure of a typical epoxy.

Fig. 2.17 : Epoxy chemical structure [6]

31

2.4.2 Adhesive Compositions

Modern day adhesives are often fairly complex formulations of components that

perform specialty functions. The adhesive base or binder is the primary component of an

adhesive. The binder is generally the resinous component from which the name of the

adhesive is derived. For example, an epoxy adhesive may have many components, but

the primary material is epoxy resin.

A hardener is a substance added to an adhesive formulation to initiate the curing

reaction and take part in it. Two-component adhesive systems have one component,

which is the base, and a second component, which is the hardener. Upon mixing, a

chemical reaction ensues that causes the adhesive to solidify. A catalyst is sometimes

incorporated into an adhesive formulation to speed the reaction between base and

hardener. A catalyst is a substance which markedly speeds up the cure of an adhesive

when added in a minor quantity as compared with the amounts of primary reactants [3].

Solvents are sometimes needed to lower viscosity or to disperse the adhesive to a

spread able consistency. Often, a mixture of solvents is required to achieve the desired

properties. A reactive ingredient added to a adhesive to reduce the concentration of

binder is called a diluent. Diluents are principally used to lower viscosity and modify

processing conditions of some adhesives. Diluents react with the binder during cure,

become part of the product, and do not evaporate as does as solvent.

Fillers such as calcium carbonate and catalyst are generally inorganic

particulates added to the adhesive to improve working properties, strength, permanence,

or other qualities. Fillers are also used to reduce material cost. By selective use of fillers,

the properties of an adhesive can be changed tremendously. Thermal expansion,

electrical and thermal conduction, shrinkage, viscosity, and thermal resistance are only a

few properties that can be modified by use of selective fillers.

32

2.5 Conclusion

The basic definition of brittle material was presented in this chapter to define

their characteristic such as their mode of failure and fracture surface. Apart from that,

the stress, strain, and shear stress relation briefly stated in order to relate and explain

how the basic theory of engineering was used to produce the Arcan fixture and Arcan

test method.

33

CHAPTER 3

ARCAN TEST METHOD EVOLUTION

3.1 Introduction

Over the years, there has been considerable interest in the development of a

suitable specimen and loading configuration for determining the shear deformation and

failure of composite materials with an accurate result to fit with real application.

Although torsional testing of thin-walled tubes is generally regarded as providing a

uniform and pure state of shear, grip-related failure can arise, and specimen fabrication

is more tedious than other alternative method.

The Arcan test method was first introduced and developed in 1978 [1]. The

method was tried to overcome problem such as existence of other stress component (i.e.

tensile stress) besides the shear stress on final measurement. To produce a uniform state

of plane-stress for the solid specimen, Arcan et al. (1978) developed this method to

determine mechanical properties of isotropic as well as orthotropic composite materials

under uniform plane stress conditions by means of a specially designed butterfly-shaped

specimen. Advantage of Arcan test method compared to cylinder-torsion test method

was their fixture can provide a state of uniform pure shear stress in an area known as a

34

significant section using a plane stress loading. Apart from that, this test method also

gives advantages that small specimen or anisotropic specimen can be tested with high

degree of accuracy and reliability.

3.2 The Evolution of the Arcan Test Fixture and Specimen

Arcan et al. proposed a biaxial fixture, commonly known as the Arcan fixture, to

produce biaxial states of stress. The compact nature of the Arcan fixture enables

obtaining the shear properties in any in-plane directions in a relatively manner. The

Arcan fixture can be used to apply shear force to the test specimen. Arcan and

Voloshin [1] used this method to determine the longitudinal and through-thickness shear

modulus of a unidirectional laminated CFRP composite. Their results compared

favorably to those obtained from cylinder-torsion tests. The early design concept of the

Arcan fixture is shown in Fig. 3.1.

Fig. 3.1 : The early concept of Arcan test method [2]

35

The test fixture specimen is manufactured from the material to be tested. In the

configuration, the testing is performed in shear mode. The hatched area denotes the

deformation zone. By applying the force, F, in different directions, combinations of

tension and shear loading are possible to produce. This method includes pure shear as a

special case, when the angle α = 900. The principle behind the geometry of the

specimen is that in the pure shear zone, the isostatics will intersect the sheared

cross-section (AB in Fig. 3.2) at an angle of α = ± 45 degree.

Fig. 3.2 : Significant section of the Arcan’s butterfly specimen [1]

In 1980, Arcan and Voloshin have modified the test method by bonded the test

specimen on the aluminum circular plane with the anti symmetric cut-outs, as shown in

Fig. 3.3.

Fig. 3.3 : Butterfly specimen bonded to aluminum circular plane [1]

36

The test fixture development continuously made by Yen et al. [14] in order to

eliminate the use of adhesive. The modified Arcan fixture was made of two pairs of

stainless steel parts, each pair equivalent to one half of the original Arcan fixture. A

butterfly shape cutout was machined to half the thickness in each part to house the

specimen. Three holes were drilled at each part to allow tightening the two parts

together with screws. The butterfly specimen which is joined on either side of two half

circular grips as in Fig. 3.4 are connected to a universal testing machine at the top and

bottom, respectively. The grips together with the butterfly specimen formed a circular

disk with two anti-symmetric cut-outs.

Fig. 3.4 : Test fixture set-up and butterfly specimen modified by Yen et al. [14]

The modified-Arcan fixture and its butterfly specimen are designed to determine

the shear moduli, non linear-stress strain response, and strength of thick section

pultruded composites under shear combined with different biaxial stress conditions. The

modification proposed by Yen et al. includes bolting a butterfly shaped specimen

between two identical halves of the Arcan fixture.

37

By using mechanical fastening and trapezoid cut-outs, specimens with different

thicknesses can be accommodated without the use of adhesives. The fixture used in this

study does not include a trapezoidal cut-out. Instead, a large number of bolts are used to

connect the butterfly specimen to the steel fixture. The load is applied to the fixture

using clevis pins to minimize out-of-plane forces and moments. Fig. 3.5 shows a

schematic of the modified Arcan fixture with the butterfly specimen.

Fig. 3.5 : Arcan fixture and butterfly specimen modified by Yen et al. [14]

The fixture is flexible to accommodate the pultruded specimens with various

thicknesses. The butterfly specimen design is shown in Fig 3.6. Six units of 6.4 mm

(0.25in) diameter sleeve bolts are used to transfer the load from the steel fixture to each

side of the specimen and the bolts are hand-tightened. The holes used in Arcan fixture

modified by Yen et al. to grip the butterfly specimen then eliminated by using the

clamped aluminium circular plane. The specimen is plane circular with anti symmetric

cutouts. The significant section of the specimen AB must be designed in such way that

the state of stress on AB shall be uniform as possible.

38

Fig. 3.6 : Butterfly specimen used by Yen et al. [14]

3.3 Theoretical Analysis Background

The modified Arcan fixture and its butterfly specimen can be used for pure shear

and biaxial stress conditions testing, as illustrated in Fig. 3.7. The shear response, in the

presence of various biaxial stress states, can be obtained in a relatively simple manner

by varying the angle (α ) at which the load is applied. A case of ‘pure shear’ is produced

in section AB when α = 90 degree. The basic concept behind both configurations is that

the Arcan test set-up has a well-defined section, usually referred as significant section,

where the stresses are assumed to be uniform. Fig. 3.8 shows the significant section as a

bold line at the center of the butterfly specimen. This uniformity is a result of an

appropriate choice of the geometrical parameters of the butterfly specimen in

accordance with the tested material and the biaxial loading angle. Another outcome of

the butterfly type geometry is the stresses at the significant section are the highest and

thus, failure or initial yield is more likely to occur within the section.

39

Fig. 3.7 : Arcan fixture for shear testing with different loading configurations [20]

Fig. 3.8 : Internal mean shear and normal stresses along the ‘significant section’ [20]

40

Assuming a uniform stress distribution, both shear and axial forces are applied to

the tested specimen by loading the sample as previously shown in Fig. 3.8. The mean

shear stress, τ xy , and the mean normal stress, σ y, at the significant section are defined

in a local coordinate system, where the x-axis is parallel and the y-axis is perpendicular

to the significant section. Both components can be directly determined from the forces

that are transmitted by the joints between the Arcan grips and the testing machine, as

previously shown in Fig.3.7.

The forces that act along in the positive axis of the universal testing machine

referred as the vertical applied force, Py. The force perpendicular to the vertical one is

referred to as the horizontal force, Px . The angle between the fixed axis of the testing

machined (vertical axis) and the direction of the significant section (local x-axis) is

referred as loading angle, α . Finally, A denotes the cross-sectional area of the specimen

significant section, (i.e. thickness x width).

From Fig. 3.8, the known force applied to the rig will produced shear and normal

stress at section AB. In order to determine the normal stress σ x and the shearing stress

τ xy exerted on the face perpendicular to the x-axis, a prismatic element with faces

respectively perpendicular to the x and y axes shall be considered. It can be observed, if

the area of the oblique face is denoted by ∆ A, the areas of the vertical and horizontal

faces are respectively equal to ∆ A cosθ and ∆ A sinθ . It follows that the forces exerted

on the three faces are as shown in Fig. 3.9 (No forces are exerted on the triangular faces

of the element, since the corresponding normal and shearing stresses have been assumed

equal to zero in z-direction).

41

(a) (b)

Fig. 3.9 : Prismatic element in state of equilibrium [19]

By using components along the x’ and y’ axes from Fig. 2.26 (b), the following

equilibrium equations were obtained ;

→ ∑ Fx = 0 : σ x’ ∆ A - σ x( ∆ A cosθ )cosθ - τ xy ( ∆ A cosθ )sinθ

- σ y ( ∆ A sinθ )sinθ - τ xy( ∆ A sinθ )cosθ = 0 [3.1]

↑ ∑ Fy = 0 τ x’y’ ∆ A + σ x ( ∆ A cosθ )sinθ - τ xy( ∆ A cosθ ) cosθ

- σ y ( ∆ A sinθ )cosθ + τ xy ( ∆ A sinθ )sinθ = 0 [3.2]

By solving the first and second equation for σ x’ and τ x’y’,

σ x’ = σ xcos2θ + σ ysin2θ + 2τ xy sinθ cosθ [3.3]

τ x’y’ = -(σ x - σ y) sinθ cosθ + τ xy(cos2θ - sin2θ ) [3.4]

Recalling the trigonometric relations ;

sin 2θ = 2sinθ cosθ cos 2θ = cos2θ - sin2θ [3.5]

And ;

42

cos2θ = 2

2cos1 θ+ sin2θ = 2

2cos1 θ− [3.6]

By substituting these trigonometric relations, we can write Eqn. [3.3] as follows ;

σ x’ = 2yx σσ + +

2yx σσ − cos 2θ + τ xy sin 2θ [3.7]

Using the relations Eqn. [5], we write Eqn. [4.8] as ;

τ x’y’ = - 2yx σσ − sin2θ + τ xy cos 2θ [3.8]

The expression for the normal stress, σ y’ is obtained by replacing θ in

Eqn. [5.2] by the angle (θ +90 ) that the y ’ axis forms with the x axis. Since cos (2θ +

180 ) = -cos 20 θ and sin (2θ + 180 0 ) = -sin2θ , we have ;

σ y’ = 2yx σσ + -

2yx σσ − cos 2θ - τ xy sin2θ [3.9]

Adding Eqn. [3.7] and [3.8], the below equation is obtained ;

σ x’ + σ y’ = σ x + σ y [3.10]

The equations [3.9] and [3.10] obtain previously are the parametric equations of

a circle. This mean that a set of rectangular axes and plot a point M of abscissa σ x’ and

ordinate τ x’y’ was choose for any given value of the parameter θ , all the points obtained

will lie on a circle, as illustrated in Fig.3.10.

43

Fig. 3.10 : Mohr’s circle due to stress analysis [19]

To establish this property, the θ is eliminate from Equations [3.9] and [3.10] ;

this is done by first transposing (σ x + σ y ) / 2 in Eqn. [5.1] and squaring both members

of the equation, then squaring both members of Eqn. [5.2], and finally adding both

equation. Therefore,

⎜⎜

⎝

⎛⎟⎟⎠

⎞−−

2

2yx

x

σσσ + = ''2 yxτ

2

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛ − yx σσ + [3.11] xy2τ

and, σ ave = 2yx σσ + and R = xyyx 2

2

2τ

σσ+⎟⎟

⎠

⎞⎜⎜⎝

⎛ − [3.12]

Then, Eqn. [3.11] and Eqn. [3.12] can be written in the form of equation of a circle.

(σ x’ - σ ave)2 + = R''2 yxτ 2 [3.13]

44

From Fig. 3.9, if the stresses on the significant section AB are uniform, it

follows from the previous equilibrium analysis that on significant section AB as shown

in Fig. 3.8 ;

σ xx = oA

P sinα and τ xy = oA

P cosα [3.14]

Where Ao = the area of the significant section AB

The rectilinear portions of the cut-outs are oriented at and, therefore, the

principal stresses in the vicinity are also in these directions. It follows that

045±

xyτ on AB as

given by Eqn. [3.14] is a principal shear stress. Therefore on AB,

σ xx = σ yy = oA

P sinα [3.15]

and the principal stresses are ;

σ 1 = σ xx + τ xy = oA

P (sinα + cosα )

σ 2 = σ xx - τ xy = oA

P (sinα - cosα ) [3.16]

3.4 Shear Analysis on Specimen

From the previous analysis, the maximum normal stress acted at from the

horizontal axis. Therefore, strains can be measured by applying a rosette type strain

gauge at at the center of section AB measured from horizontal axis. An analysis

045±

045±

45

has been done to find the relationship between normal strain and shear strain. For an

elastic material, when the element is subjected to shear and normal stresses, it will

deform to a new shape as show in Fig. 3.11.

Fig. 3.11 : Element deformation due to shear [19]

Firstly, the expression is derived for the normal strain ε(θ ) along a line AB forming an arbitrary angle θ with the x axis. To do so, the right triangle ABC is

considered, which has hypotenuse (Fig. 3.11(a)) and the oblique triangle A’B’C’ into

which triangle ABC is deformed (Fig. 3.11(b)). Denoting by ∆ s the length of AB, we

express the A’B’ length as s [1 + ∆ ε(θ )]. Similarly, denoting by x and y the length of sides AC and CB, we express the length of A’C and C’B’ as

∆ ∆

∆ x(1 + xε ) and ∆ y(1 +

yε ), respectively. The right angle at C in Fig. 3.11 deforms into an angle equal to

2π + γ xy in Fig. 3.11(b), and applying the law of cosines to triangle A’B’C’ ; thus

46

(A’B’)2 = (A’C’)2 + (C’B’) - 2 (A’C)(C’B’) cos ⎟⎠⎞

⎜⎝⎛ + xyγ

π2

( s)∆ 2[1 + ε (θ )]2 = ( ∆ x)2(1 + xε )2 + ( ∆ y)2(1 + yε )2

-2( ∆ x)(1 + xε )( ∆ y)(1 + yε )cos ⎟⎠⎞

⎜⎝⎛ + xyγ

π2

[3.17]

From Fig. 3.11(a), the relation between ∆ x and ∆ y is known, thus ;

x = ( s)cos∆ ∆ θ ∆ y = ( ∆ s)sinθ [3.18]

And since γ xy is very small and can be neglected, therefore ;

cos ⎟⎠⎞

⎜⎝⎛ + xyγ

π2

= - sin γ xy ≈ γ xy [3.19]

Substitute from Eqn. [3.18] and [3.19] into Eqn. [3.17], and recalling that

cos2 θ + sin2θ = 1, also neglecting second-order terms in ε(θ ),ε x,ε y, and γ xy ;

ε (θ ) = ε x cos2 θ + ε y sin2θ + γ xy sinθ cos θ [3.20]

Equation [3.20] is enable to determine the normal strain ε (θ ) in any direction AB in terms of the strain components ε x, ε y, γ xy and the angle θ that AB forms with the x axis. As an example, for the theta values, θ = 0, Eqn. [3.20] yields ε (0) = ε x and that, for θ = 90 , it yields 0 ε (90 ) = 0 ε y .

By using the trigonometric relations from Eqn. [3.5] and [3.6], we can write

Eqn. [3.20] in the alternative form of ;

ε x = 2yx εε + +

2yx εε − cos 2θ +

2xyγ sin 2θ [3.21]

47

Replacing the (θ ) value with (θ +90 ), the normal strain along the y’ axis can

be obtained. Since cos (2

0

θ + 180 ) = -cos 20 θ and sin (2θ + 180 ) = - sin 20 θ ;

ε y’ = 2yx εε + -

2yx εε − cos 2θ -

2xyγ sin 2θ [3.22]

By adding Eqn. [3.21] and Eqn. [3.22],

ε x’ + ε y’ = ε x + ε y [3.23]

From the stress and strain relation, the shear stress strain relation can be obtained,

where the shear strain in the ± 450 is ;

γ xy = ε 45o - ε -45o [3.24]

Which can be written as ;

γ xy = 2 045ε [3.25]

Therefore, the in-plane Shear modulus, G, is ;

Gxy = 00 4545 −

− εετ xy [3.26]

Gxy = 045

2ετ xy [3.27]

And finally,

Gxy = xy

xy

γτ

[3.28]

48

3.5 Recent Research and Development Using Arcan Test Method

a) S. –C. Yen, J.N. Craddock and K.T. Teh

S. –C. Yen et al. had used a modified Arcan fixture for the in-plane shear test of

materials such as aluminum, Plexiglas and composite material (i.e. Graphite/PEEK) [14].

In general, they had modified the Arcan fixture used by M. Arcan et al. [1], as

previously stated in subtitle 3.2. The objective of their study was to modify and improve

the Arcan fixture for better control shear test data.

i. Stress-Strain Relationship

From the strain and loading data from the test, the relationship between the

applied shear stress and the strain in ± 450 direction was established. The stress-strain

data for the Graphite/PEEK composite specimen is shown in Fig. 3.12.

a. based on the Von-Mises criterion b. based on the Tresca criterion c. from the [90]16 specimen

Fig. 3.12 : The strain results of a Graphite/PEEK specimen in shear [14]

49

The strain results of a Graphite/PEEK specimen in shear had verify that a state of

pure shear was present during the experiment. This is deduced from the fact that the

straining transverse to the applied load was practically zero, thus indicating no normal

stress in that direction. The principal strains in the -45-deg and +45-deg directions were

then used to calculate the shear strain. This was done by subtracting the strain in the -45

degree direction from that +45 degree direction. As a result, a shear –strain relation for

each gauge specimen were obtained. The calculated shear moduli of aluminum,

Plexiglas and Graphite/PEEK are given in Table 3.1.

Table 3.1 : Average shear modulus and shear strength test results of various

materials [14]

Average Shear Modulus,

G (GPa)

Average Shear Strength,

τ (MPa) Material

Theory Experiment Theory Experiment

Aluminum

26

28

207

220

Plexiglas

42a

36

Composite

(Graphite/PEEK)

6.0

83

The standard shear modulus and shear strength data of aluminum (6061-T6)

were obtained from a mechanics of material textbook [18] and were used to compare the

test results obtained from their research. For Plexiglas, only the tensile strength was

found from the literature published by their vendors. The data in Table 3.1 were then

used to calculate the shear strength of Plexiglas based on the Von-Mises and Tresca

criteria. For the thermoplastic composite material, the elastic shear modulus and strength

obtained from the tensile test of the [45]2s laminate was used for comparison. It was

found that the shear properties obtained from the Arcan shear test method was agreed

with reference data provided by M. Arcan [1].

50

ii. Fracture Surface

The fracture surface for the aluminum and thermoplastic composite were found

parallel to the direction of the applied load, as shown in Fig. 3.13 and Fig. 3.14. This

appearance indicates failure mechanism due to a state of shear stress. It should be

pointed out that the fracture of graphite/PEEK specimen occurred at a location slightly

away from the gauge section. This may be due to misalignment between the loading axis

and the gauge section or suspected due to initiation of sharp edges or formation of crack

within the region.

Fig. 3.13 : Shear failure of an aluminum specimen [14]

Fig. 3.14 : Shear failure of a Graphite/PEEK specimen [14]

51

The fracture mechanism of the Plexiglas initiate from the notch roots of the

specimen. As a result, the fracture surface was generated and found 450 from the loading

axis, which is the direction of the tensile principal stress corresponding to the state of

pure shear, as shown in Fig. 3.15. This fracture mechanism supports the fact that brittle

materials generally fail in a tensile mode, which was also found in the Iosipescu shear

test of vinyl-ester conducted by Sullivan et al.

Fig. 3.15 : Failure mode of a Plexiglas specimen [14]

b) Rani El-Hajjar and Rami Haj-Ali

From the experiment conducted by Rani El-Hajjar and Rami Haj-Ali [20], the

Arcan fixture with butterfly specimen are used to measure the in-plane shear properties

of thick-section pultruded FRP composites. The main objectives of their experiment are

to analyze the effect of notch radius on the shear properties study, the strains profiles

along the AB section, and to determine the materials shear modulus, G.

i. Effect of Notch Radius

There were three notch radii selected to determine the most appropriate radius

1.27 mm, 2.54 mm and 5.05 mm. Fig. 3.16 shows the effect of the notch radius on the

52

shear stress profile along the gauge section for axial roving orientation tested by them. A

normalized stress profile near to 1.0 was found near the center for the specimen with a

notch radius of 2.54 mm.

Fig. 3.16 : Effect of notch radius on shear stress profile along gage section [20]

On the other hand the simulation by isotropic assumption and orthotropic value

shows that the blunted notch results in a lower stress concentration near the notch tip,

with a more gradual stress build up compared to the sharp notch as shown in Fig. 3.17.

The stress profile is uniform near the blunted notch tip and resulting in a normalized

shear stress closer to 1.0.

53

Fig. 3.17 : Effect of sharp notch on shear stress along the gage section [20]

ii. Stress-Stain Relation of Arcan Test Method

From their test data, a stress-strain curve was plotted and it can be noted that all

specimens was perfectly failed in brittle manner. The shear stress versus shear strain

curves shown in Fig. 3.18 has verified that a state of pure shear was present during the

testing because the curve is linearly propagated. This is also deduced from the fact that

the straining transverse to the applied load was practically zero, thus indicating no

normal stress in that direction [14].

54

Fig. 3.18 : Shear stress strain response from Arcan shear test [20]

Both strains, and 45−ε 45ε linearly propagated and almost symmetry along x-axis

as shown in Fig. 3.19. This indicates that this testing method is reliable as the strain data

obtained is balance in each direction, and can be used to determine the shear properties,

shear modulus, and shear strain of brittle materials, especially for composites.

Fig. 3.19 : Measured strain profiles at center of transverse butterfly specimen during

‘pure shear’ test [20]

55

3.6 Conclusion

In this chapter the Arcan fixture development process was shown, which is

including the time-line of Arcan fixture, how the rig works, advantages of significant

section on butterfly specimen and the reliability of the Arcan test result. As a conclusion,

the Arcan test method can be used to determine the mechanical properties of composite

material such as shear strength and shear modulus.

56

CHAPTER 4

SPECIMEN PREPARATION, EXPERIMENTATION AND TESTING

4.1 Introduction

The main topics that will be discussed in this chapter are the test specimen

preparation and the testing procedure using the Arcan test method. The closed mould

method was used to produce the butterfly specimens. The specimens were exposed to

their designated conditions, namely ; Lab Control (LB-control), Plain Water (PW-

wet/dry), Salt Water (SW-wet/dry), and Outdoor (OD). The salt water, plain water and

outdoor specimens are exposed to their respective conditions for 7 days wet and 7 days

dry (i.e. alternate cycle) for duration of 6 months. After that, the specimens were tested

in order to investigate any sign of exposure conditions effects. The shear test was carried

by using the Instron Universal Testing Machine Series IX Model 4206 with Arcan test

rig (fixtures). The fracture surface of the test samples of each exposure condition was

then undergone microstructure analysis in order to investigate factors or elements that

contribute to the failure. The Arcan test fixture used in this project was almost similar to

the fixture used by Rani El. Hajjar and Rami Haj-Ali [9]. The applied load to the rig was

in tensile but the loading mode was transferred or imposed onto the specimen in the

form of pure shear.

57

4.2 Material Details

In this study, the epoxy adhesive namely Resifix-31, supplied by Exchem,

United Kingdom was used. The properties of Resifix-31 are achieved by

blending/mixing a modified epoxy resin and inorganic fillers to form a base component,

which is activated by a thixotropic formulated amine hardener. Resifix-31 epoxy is

‘smooth’, very viscous and light grey (almost white) in colour paste. Resifix-31 is

harder to mould due to its high viscosity but fast cured. It took only 24 hours for

Resifix-31 epoxy to cure, which depends on the ambient laboratory condition. These

structural epoxy adhesives consist of part A and B and their chemical formulation are

listed in Table 4.1. The adhesive materials, part A and B must be mixed by a mixture

ratio of 3:1, by following the supplier specification. The parts A and B of structural

adhesives Resifix-31 are shown in Fig. 4.1 and the properties of Resifix-31 are shown in

Table 4.2.

Table 4.1 : Chemical formulation of Resifix-31 structural adhesives

Material Chemical Formulation Colour

Resifix-31

Part A (Epoxy) : pentaethylenehexamine, m-

phenylenobis (methylamine),4,4- isopropylidene

diphenol and poly(oxy(methyl-1,2-ethandyl)),alpa-

(2-aminemethylethyl) omega-(2-amine)

Part B (Hardener) : Epoxy Constituent

White

Dark Grey

58

Table 4.2 : Product data of Resifix-31 epoxy adhesive*

Product Data

Value Shear strength (MPa) 22

Tensile strength (MPa) 28

Shear modulus (GPa) 3.8

Compressive strength (MPa) 75

Poisson’s ratio 0.28

Thermal expansion 33 x 10-6/ °C

Pot life (minutes) 45 (slow grade)

Service time (hours) 24

*As supplied by Exchem EPC Group, United Kingdom

(a) (b)

Fig. 4.1 : Two parts structural adhesives of Resifix-31

(a) Part A (b) Part B

59

4.3 Specimen Preparation

The specimen size of 60 m