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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
Recommended