PSZ 19:16 (Pind. 1/07)
DECLARATION OF THESIS / UNDERGRADUATE PROJECT PAPER AND COPYRIGHT
Author’s full name : MOHD AMIRUL AZRI BIN MAHAT
Date of birth : 4 JANUARY 1990
Title : FINITE ELEMENT MODELING OF ARCAN TESTING METHOD
SPECIMEN UNDER DIFFERENT LOADING CONFIGURATION
Academic Session: 2013/2014
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SIGNATURE SIGNATURE OF SUPERVISOR
900104-10-5899 DR. SHUKUR BIN ABU HASSAN (NEW IC NO. /PASSPORT NO.) NAME OF SUPERVISOR
Date : 24 JUNE 2014 Date : 24 JUNE 2014
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UTM(FKM)-1/02
Faculty of Mechanical Engineering
Universiti Teknologi Malaysia
VALIDATION OF E-THESIS PREPARATION
Title of the thesis : FINITE ELEMENT MODELING OF ARCAN TESTING METHOD
SPECIMEN UNDER DIFFERENT LOADING CONFIGURATION
Degree: BACHELOR OF ENGINEERING (MECHANICAL)
Faculty: FACULTY OF MECHANICAL ENGINEERING
Year: 2013/2014
I MOHD AMIRUL AZRI BIN MAHAT
(CAPITAL LETTER)
declare and verify that the copy of e-thesis submitted is in accordance to the Electronic Thesis and
Dissertation’s Manual, Faculty of Mechanical Engineering, UTM
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Name of Supervisor: DR.SHUKUR BIN ABU
HASSAN
Faculty: FACULTY OF MECHANICAL
ENGINEERING
Note: This form must be submitted to FKM, UTM together with the CD.
“I hereby declare that I have read this report and in my opinion this report is
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Engineering (Mechanical).”
Signature :…………………………………..
Name : DR. SHUKUR BIN ABU HASSAN
Date : 24 JUNE 2014
i
FINITE ELEMENT MODELING OF ARCAN TESTING METHOD SPECIMEN
UNDER DIFFERENT LOADING CONFIGURATION
MOHD AMIRUL AZRI BIN MAHAT
A report submitted in partial fulfillment of the
requirements for the award of the degree of
Bachelor of Engineering (Mechanical)
Faculty of Mechanical Engineering
Universiti Teknologi Malaysia
JUNE 2014
ii
I declare that this report entitled “Finite Element Modeling of Arcan Testing Method
Specimen under Different Loading Configuration” is the result of my own research
and experience except as cited in the references. The report has not been accepted for
any degree and is not concurrently submitted in candidature of any other degree.
Signature :…………………………………..
Name : MOHD AMIRUL AZRI BIN MAHAT
Date : 24 June 2014
iii
To my beloved family, teachers and lecturers, supportive friends and acquaintances
who have put most effort and give encouragement to me towards my study
iv
ACKNOWLEDMENT
Alhamdulillah, I would like to express my grateful to Allah SWT for all good
things during Final Year Project period. With all of endless patience and effort, I can
finish this thesis with success.
Firstly, I would like to thank to my supervisor, Dr. Shukur Abu Hasan for his
kindness and guidance during this one year of research. He committed himself with
great dedication on the supervision of my final year project. I have gained a lot of
practical knowledge and expertise through working alongside him.
I would like to thank my parents, Mr. Mahat b. Mahmood and Mrs. Rosiah bt
Sarif for believing in my dreams and supporting the best possible way they could.
I would like to express my appreciation to those who had helped me along
with this thesis, especially to course mate that never stop sharing knowledge
everywhere and every time.
Finally, I would like to thank to these people:
• All Centre for Composite Department staff for willingness to guide me
especially during specimen preparation works.
• All Metallurgy Laboratory staff for willingness to guide me especially during
polishing epoxy specimen.
• All Mechanics of Material Laboratory staff for willingness to guide me
especially during conducting load test.
• Dr Behzad Abdi for willingness to invite me joining his ANSYS Workbench
workshop for free.
v
ABSTRACT
This project is based on the application of Arcan test method introduced by Arcan et
al to determining the shear strength and shear moduls of material. In this research, the
objective has been systematically approached using ANSYS finite element analysis software.
The approach involves investigation of the problem and analysis of the butterfly specimens
subjected to a load with different loading configuration. The condition are simulated in
ANSYS which involved CAD and finite element modelling of the butterfly specimen, and
then the finite element model is validated geometrically by ANSYS element shape checking
capability. The finite element model subjected to static structural analysis confirmed the
stress concentration and crack initiation take place which indicated cause of the failure. The
performance of tensile data of Arcan test affect by notch. Finally, this research concludes
with a proposal to revised specimen model and recommendation for further analysis.
vi
ABSTRAK
Projek ini adalah berdasarkan penggunaan kaedah ujian Arcan yang diperkenalkan oleh
Arcan et al untuk menentukan kekuatan ricih dan modulss ricih bahan. Dalam kajian ini,
objektif tertumpu secara sistematik dengan menggunakan perisian analisis unsur ANSY.
Kajian ini juga bertujuan untuk membuktikan analisis kaedha unsur terhingga adalah mampu
memberikan keputusan yang hamper sama dengan ujian makmakl. Pendekatan ini
melibatkan pengenalpastian masalah dan analisis spesimen rama-rama yang bergantung
kepada konfigurasi beban yang berbeza. Keadaan ini disimulasi dalam ANSYS yang
melibatkan CAD dan pemodelan unsur terhingga spesimen rama-rama, dan kemudian
analisis model unsur terhingga dilakukan terhadap geometri specimen. Analisis model unsur
terhingga menggunakan struktur statik mengesahkan bahawa tegasan tertumpu dan
permulaan rekahan yang berlaku menunjukkan punca kegagalan terhadap specimen. Prestasi
data tegangan ujian Arcan terjejas disebabkan oleh takuk pada specimen. Akhir sekali, kajian
ini diakhiri dengan cadangan untuk pengubahsuaian model spesimen dan cadangan untuk
analisis lanjut.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGMENTS iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF FIGURE xi
LIST OF TABLE xvi
LIST OF SYMBOLS xviii
LIST OF APPENDICES xix
1 INTRODUCTION
1.0 Introduction 1
1.1 Objective 2
1.2 Scope 3
1.3 Thesis Framework 3
2 LITERATURE REVIEW
2.0 Introduction 5
2.1 Arcan Test Method 6
2.1 .1The Evolution of Arcan Fixture and Specimen 6
2.1.2 Previous Research on Arcan Test 10
viii
2.1.3 Previous Finite Element Analysis on Arcan Test 15
2.1.4 Theoretical Background of Arcan Test 19
2.1.5 Stress Analysis 20
2.2 Standard Test Method for Tensile Properties 21
2.2.1 Previous Research on Tensile Test 22
2.3 Summary 23
3 RESEARCH METHODOLOGY
3.0 Introduction 24
3.1 Specimen Preparation and Experimental Setup 25
3.1.1 Specimen Geometry 25
3.1.2 Material Details 27
3.1.3 Mixing and Casting Process for Epoxy 28
3.1.4 Specimen Preparation for Aluminium 32
3.1.4 Strain Gauge Installation 34
3.1.6 Tensile Test Set-Up and Test Procedure 35
3.1.7 Arcan Test Setup 36
3.2 Specimen Modelling and Analysis Setup 38
3.2.1 Specimen Modelling 39
3.2.2 Input Material Data 39
3.2.3 Meshing 40
3.2.4 Boundary Condition and Loading Setup 41
3.3 Summary 41
4 RESULTS AND DISCUSSION
4.0 Introduction 42
4.1 Sample Testing Evaluation 43
4.1.1 Test –Rig Specimen Evaluation of
Tensile Method for Epoxy 43
4.1.2 Test Rig-Specimen Evaluation for Arcan
Test Method 44
4.1.2.1 Shear Test for Epoxy and Aluminium
Sample 45
ix
4.1.2.2 Tensile Test for Epoxy and Aluminium
Sample 47
4.1.2.3 Tensile Shear Test for Epoxy and
Aluminium Sample 49
4.2 Experimental Result for Arcan Test Method 51
4.2.1 Experimental Results for Shear Loading
of Epoxy 51
4.2.2 Experimental Results for Shear Loading
of Aluminium 52
4.2.3 Experimental Results for Tensile Loading
of Epoxy 52
4.2.4 Experimental Results for Tensile Loading
of Aluminium 53
4.2.5 Experimental Results for Tensile Shear
Loading of Epoxy 54
4.2.6 Experimental Results for Tensile Shear
Loading of Aluminium 55
4.3 Experimental Result for Tensile Test 56
4.3.1 Experimental Data of Tensile Test Method
for Epoxy 56
4.4 Finite Element Analysis 58
4.4.1Finite Element Analysis Result for Shear
Loading of Epoxy 59
4.4.2 Finite Element Analysis Result for Shear
Loading of Aluminium 61
4.4.3 Finite Element Analysis Result for Tensile
Loading of Epoxy 64
4.4.4 Finite Element Analysis Result for Tensile
Loading of Aluminium 66
4.4.5 Finite Element Analysis Result for Tensile
Shear Loading of Epoxy 69
4.4.6 Finite Element Analysis Result for Tensile
Shear Loading of Aluminium 71
4.5 Notch Sensitivity Analysis 73
x
4.6 Tensile Test Performance Analysis 76
5 CONCLUSION AND RECOMMENDATION
5.0 Conclusion 78
5.1 Recommendation 79
REFFERENCE 80
Appendices A1-A3 82-83
xi
LIST OF FIGURE
FIGURE NO TITLE PAGE
1.1 The concept of cylinder torsion test method [4] 3
1.2 Significant section of the Arcan‟s butterfly specimen [5] 4
2.1 The early design concept of Arcan Test method [5] 8
2.2 Significant section of the Arcan‟s butterfly specimen [5] 8
2.3 Butterfly specimen bonded to aluminium circular
plate test fixture [6] 9
2.4 Modified test fixture and butterfly specimen
set-up by Yen et al. [7] 10
2.5 Arcan fixture and butterfly specimen loading
configuration [7] 10
2.6 Butterfly specimen geometry used by Yen et al. [8] 11
2.7 Mohr‟s circle constructed base principal strains of
ESLT-LB01 at 1000N case [8] 12
2.8 Brittle failure of ESLT-SW01 [8] 12
2.9 Failed axial and transverse specimen after reaching the
ultimate stress α=90° [9] 13
2.10 Shear stress-strain response from Arcan shear test [9] 13
xii
2.11 Measured axial strain profiles at centre of axial
butterfly specimen during „pure shear‟ test [9] 14
2.12 Measured axial strain profiles at centre of transverse butterfly
specimen during „pure shear‟ test [9] 14
2.13 Shear stress-strain response from Arcan biaxial
testing [9] 15
2.14 Experimental results in pure tensile of non-welded 6056T78
Aluminium specimen [10] 15
2.15 Original experimental shape and boundary condition [11] 15
2.16 Effect of notch radius on shear stress profile along gauge
section [9] 17
2.17 Effect of sharp notch on shear stress along the
gauge section [9] 17
2.18 Effect of roving orientation on the shear stress along the
gage section [9] 18
2.19 Stress field of tensile loading before rupture [12] 19
2.20 Stress field of shear loading before rupture [12] 19
2.21 Arcan fixture for shear test with different loading
configurations [9] 20
2.22 Internal mean shear and normal stress along the
‘significant section’ 20
2.23 Dumbbell-shaped specimen dimension [24] 23
2.24 Stress-strain curve of graphine reinforced epoxy [23]
3.1 Two parts of Selfix Carbofibe adhesive (a) Part A (b) Part B 27
3.2 A mixing process using low speed electric mixer 29
3.3 Flat plate attached to male part by screws
xiii
(a)Flat plate before installation
(b) Flat plate after installation 29
3.4 Casting process by pouring the mixtures into the female
mould
(a)Butterfly specimens
(b) Dumbbell-shaped specimens 30
3.5 (a) Male part attached to the female part and
(b) 10 kg mass used 30
3.6 Demoulding process 36
3.7 Surface grinding and polishing process of the specimen
(a) Mecapol P255 U polishing machine
(b) Manula polishing technique 31
3.8 Specimens ready for experiment 31
3.9 Aluminium scrap 32
3.10 (a) Milling machine (b) Specimen ready for labelling
The butterfly specimen geometry 32
3.11 Strain gauge on dumbbell specimens 33
3.12 Tensile test set-up 34
3.13 Instrumentation set-up 35
3.14 Arcan test fixture and butterfly specimen [8] 36
3.15 Attached Arcan fixture to the holder 36
3.16 Arcan fixture set-up configuration
(a)Tensile (b) Shear (c) Tensile shear 37
3.17 The butterfly specimen geometry 39
3.18 Butterfly specimen of epoxy in ANSYS 39
3.19 Properties of material in ANSYS 40
3.20 Meshed model specimen 41
3.21 Boundary condition and loading setup
(a)Shear (b) Tensile shear (c) Tensile 42
4.1 Brittle failure of T1epoxy occurred at ±0 44
xiv
4.2 Brittle failure of ES1 occurred at ±45° 46
4.3 Ductile failure of AS1specimen occurred at ±90° 47
4.4 Brittle failure of ET2 specimen occurred at ±90° 48
4.5 Ductile failure of AT occurred at ±45° 49
4.6 Brittle failure of ETS3occurred at ±30° 50
4.7 Ductile failure of ATS2Aluminium occurred at ±90° 51
4.8 Stress-strain curve for ASTM1 Specimen 59
4.9 Shear stress-strain curve of Selfix Carbofibre epoxy 61
4.10 (a) Maximum principal stress
(b) Maximum shear stress
(c) Equivalent elastic strain 62
4.11 Stress distribution along significant section
AB of Selfixe Carbofibre epoxy due to shear loading 63
4.12 Shear stress-strain curve for aluminium 64
4.13 (a) Maximum principal stress
(b) Maximum shear stress
(c) Equivalent elastic strain 65
4.14 Stress distribution along significant section AB
of aluminium due to shear loading 66
4.15 Stress-strain curve for epoxy 67
4.16 (a) Maximum principal stress
(b) Maximum normal stress
(c) Equivalent elastic strain 68
4.17 Stress distribution along significant section
AB of Selfix Carbofibre epoxy due to tensile 69
4.18 Stress-strain curve for aluminium 71
xv
4.19 (a) Maximum principal stress
(b) Maximum normal stress
(c) Equivalent elastic strain 72
4.20 Stress distribution along significant section AB
of aluminium due to tensile. 73
4.21 (a) Maximum principal stress 74
4.22 Stress distribution along significant section AB
of aluminium due to tensile shear load. 75
4.23 (a) Maximum principal stress 76
4.24 Stress distribution along significant section AB
of aluminium due to tensile shear load. 77
4.25 Effect of notch on stress distribution of Selfix Carbofibre
due to shear load. 78
4.26 Effect of notch on stress distribution of Selfix Carbofibre
due to shear tensile. 78
4.28 Effect of notch on stress distribution of aluminium due
to shear load. 79
4.29 Stress-strain curve of Selfix Carbofibre epoxy with
different notch radius. 80
4.30 Stress-strain curve of aluminium with different notch radius 81
xvi
LIST OF TABLE
TABLE NO. TITLE PAGE
2.1 Simulation results – parameter based on Arcan
tests properties [30] 19
3.1 Chemical formulation of Selfix epoxy adhesive [8] 26
3.2 Typical mechanical and physical properties of
Selfix Carbofibe epoxy adhesive [8] 27
3.3 Material properties Selfix Carbofibe epoxy
adhesive from Shukur. A. H [8] 28
3.4 Mechanical properties of 6061 alloy [22] 28
3.5 Rossete type strain gauge specifications [25] 33
4.3 Experiment data for shear loading of ES specimens 52
4.4 Experiment data for shear loading of AS specimens 53
4.5 Experiment data for shear loading of ET specimens 54
4.6 Experiment data for shear loading of AT specimens 55
4.7 Experiment data for shear loading of ETS specimens 56
4.8 Experiment data for shear loading of ATS specimens 57
4.9 Experiment data for ASTM1 specimen 58
4.10 Test results for ASTM specimens 58
4.11 Analysis result for shear loading of Selfix
Carbofibre epoxy 60
4.12 Analysis result for shear loading aluminium 64
xvii
4.13 Analysis result for tensile loading of Selfix
Carbofibre epoxy 67
4.14 Analysis result for tensile loading of Aluminium 70
4.15 Analysis result for tensile shear loading of Selfix
Carbofibre epoxy 73
4.13 Analysis result for tensile shear loading of
aluminium 75
xviii
LIST OF SYMBOLS
F - Force
P - Force
σ - Normal Stress
τ - Shear Stress
A - Cross-sectional Area
xix
LIST OF APPENDICES
APPENDIX TITLE PAGE
A1 Type and dimension of Dumbbell shape specimen 82
A2 Engineering drawing of epoxy adhesive butterfly
specimen mould 82
A3 Engineering drawing of modified Arcan shear test
fixture 83
1
CHAPTER 1
INTRODUCTION
1.0 Introduction
The finite element method is a numerical procedure that can be applied to
obtain solutions to a variety of problems in engineering. Applications range from
deformation and stress analysis of automotive, aircraft, building, and bridge structure
to field analysis of heat flux, fluid flow, magnetic flux, seepage, and flow problem
[1]. Finite element analysis also is a numerical method of deconstructing a complex
system into very small pieces called element. The software implements equations
that govern the behaviour of these elements and solves them all; creating a
comprehensive explanation of how the system acts as a whole. These results then can
be presented in tabulated or graphical forms. This type of analysis is typically used
for the design and optimization of a system far too complex or impossible to analyse
by calculation. Systems that may fit into this category are too complex due to their
geometry, scale, or governing equations.
In 1978, Arcan et al. [2] introduced a new method of testing material shear
properties under uniform plane stress conditions by means of a specially designed
plane specimen. The fixture was used to determine shear properties for various
materials such as polymer composite, isotropic, orthotropic, ductile and brittle. The
2
compact nature of the Arcan fixture offered an advantage to obtain the shear
properties in all in-plane directions in a relatively simple manner. The Arcan fixture
also capable to produce axial, shear, and combined both forces to the test specimen.
Special case of pure shear produced on the significant section when angle α=90° was
introduced.
In recent year, many scientist use finite element analysis of Arcan test method
to validate their experiment outcome. The usage of finite element modeling in Arcan
testing method provides several result which impossible to obtain by considering
basic theoretical approach. 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 uniformity of the shear stress in studied material was
investigated. The presence of the direct stresses and their relative effect on the shear
properties is also examined. FE analyses are used to investigate the effect of notch
radius and material orthotropy on the uniformity and distribution of stresses in the
significant section of the butterfly specimen
In this study, Selfix Carbofibre Epoxy and Aluminium 6061 was chosen to be
material for Arcan test method and finite element analysis. All three loading
configuration will be perform in study to investigate the characteristic of material. In
addition to that, the studies will provide data and results on the performance of
testing method which can be comparing with common test method. The finding is
vital and will be used as a reference in future studies and projects.
3
1.1 Objective
The aim of this project is to study the behaviour of brittle and ductile
materials samples under ARCAN test method using FEA. Therefore, the following
objectives are listed as follows;
i. To model and analyse Arcan specimen geometry using FEA
ii. To study characteristics of samples material along significant section
under different loading configurations using Finite Element Software
iii. To compare the FEA results with samples testing outcomes
1.2 Scope
Firstly, the scope of this project covers the study of Arcan testing method and
specimen geometry. After that, the project focuses on the specimen preparation for
Arcan test and tensile test. Tensile test for epoxy will be conduct to obtain its
mechanical properties for finite element analysis purpose and data comparison. Later
on, Arcan test method will be conduct for Aluminium 6061 and Selfix Carbofibre
epoxy in order to obtain maximum loading which to be apply in finite element
analysis. The specimen is model and analyse using ANSYS Workbench software.
Lastly, the project focuses on data collection for comparison analysis and discussion
which will be including in report writing.
1.3 Thesis Framework
The thesis is structured according to the overall programme methodology by
taking into consideration the most prioritised research works. The arrangement of the
overall thesis presentation framework is briefly described as follows;
4
i. In Chapter 2, the study focuses on reviewing the technical aspects of
Arcan test method applications and studying finite element analysis
applications from previous researchers.
ii. In Chapter 3, the study focuses on research methodology which
includes specimen preparation, testing procedure, specimen modelling
and finite element analysis.
iii. In Chapter 4, the discussion focuses on outcomes of load test on the
experimentation specimens and finite element analysis of epoxy and
aluminium. The discussion also focuses on stress distribution on
butterfly specimens, the performance of Arcan testing method for
tensile test and notch sensitivity effect on result outcome.
iv. In Chapter 5, the research programme findings conclude by focusing
on the loading configuration on the test samples. From the research
programme experience, a few suggestions have been made to conduct
and explore more studies on the testing performances.
5
CHAPTER 2
LITERATURE REVIEW
2.0 Introduction
The mechanical properties of material play important role in engineering
application. The selection of material also is important to provide sufficient material
integrity. Many test method proposed by scientist as an alternative to determine
properties of material. In general, the typical shear test method used to determine the
shear properties of most materials is the cylinder-torsion test method. The method is
able to determine the shear properties by analysing stress elements at various angles
or distances from cylindrical section centre as shown in Fig. 1. Unfortunately, this
method has a weakness that it is unable to produce a significant section on the
specimen, and the grips strongly influence the state of stress [3].
Fig. 2.1: The concept of cylinder torsion test method [3]
6
In 1978, Arcan et al. [2] introduced a new method of testing material shear
properties under uniform plane stress conditions by means of a specially designed
plane specimen, as shown in Fig 1.2. The fixture was used to determine shear
properties for various materials such as polymer composite, isotropic, orthotropic,
ductile and brittle. The compact nature of the Arcan fixture offered an advantage to
obtain the shear properties in all in-plane directions in a relatively simple manner.
The Arcan fixture also capable to produce axial, shear, and combined both forces to
the test specimen. Special case of pure shear produced on the significant section
when angle α=90° was introduced.
Fig 2.2: Significant section of the Arcan‘s butterfly specimen [2]
2.1 Arcan Test Method
2.1.1 The Evolution of Arcan Fixture and Specimen
Arcan et al. [2] introduced biaxial test fixture called Arcan fixture to produce
biaxial states of stress. The design concept of Arcan fixture enabled the obtaining in
any in-plane directions of shear properties. Fig. 2.1 show early design concept of
Arcan Fixture.
7
Fig. 2.3: The early design concept of Arcan Test method [2]
In the early design concept, the fixture was fabricated from material to be
tested. The combinations of tension and shear loading are possible to be produced
when applying different directions tensile force, F. This method provide pure shear
loading when the angle α= 90º. 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. 2.2) at an angle of α=±45º.
Fig. 2.4: Significant section of the Arcan‘s butterfly specimen [2]
In 1978, Arcan et al. [5] have modified the previous test fixture by bonding
the test specimen on the aluminium circular plane with anti-symmetric cut-outs as
shown in Fig. 2.3.
8
Fig.2.5: Butterfly specimen bonded to aluminium circular plate test fixture [5]
In 1988, Yen et al [6] continued on development of Arcan test fixture by
modified Arcan fixture into two pairs of stainless steel parts, each pair equivalent to
one half of the original Arcan fixture. A butterfly shape cut-out was fabricated to half
the thickness in each part to house the specimen. Three holes were drilled for screws
at each part to allow for the tightening of the two parts together. The butterfly
specimen which was joined on either side of two half circular grips as in Fig. 2.4
were 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. 2.6: Modified test fixture and butterfly specimen set-up by Yen et al. [6]
Voloshin and Arcan [6] used this method in determining the through
thickness and longitudinal shear modulus in unidirectional laminated FRP composite.
9
The Arcan test also used to determine the strength of thick section pultruded
composites under shear and non-linear stress-strain response, combined with
different biaxial stress conditions. The modification proposed by Yen et al. [6]
included bolting a butterfly shaped specimen between two identical halves of the
Arcan fixture. Fig. 2.5 shows a schematic of the modified Arcan fixture with the
butterfly specimen.
Fig. 2.7: Arcan fixture and butterfly specimen loading configuration [6]
The fixture was flexible to accommodate the pultruded specimens with
various thicknesses. The butterfly specimen design is shown in Fig 2.6. Six units of
6.4 mm diameter sleeve bolts were used to transfer the load from the fixture to each
side of the specimen and the bolts were hand-tightened. The significant section of the
specimen AB was designed in such way that the state of stress on AB was as uniform
as possible.
10
Fig. 2.8: Butterfly specimen geometry used by Yen et al. [6]
2.1.2 Previous research on Arcan Test
In 2007, Shukur A. H [7] conducted an experiment to determine mechanical
performance of structure epoxy adhesive exposed to tropical condition. A brittle
epoxy adhesive was tested using Arcan test method in pure shear condition to
determine shear strength and shear modulus. Based on the data from strain gage, the
pure shear state is proven reliable since the value of average strain at zero (Fig. 2.7).
The shifted of shear state location are due to experimental error that impossible to
avoid. The pure shear state also become more reliable since the fracture surface was
found in 45°as shown in Fig. 2.8, which also the direction of tensile principal stress.
11
Fig 2.9: Mohr‘s circle constructed base principal strains of ESLT-LB01 at 1000N
case [7]
Fig 2.10: Brittle failure of ESLT-SW01 [7]
A group of researcher conducted a testing method to examine a modified
Arcan fixture for measuring the non-linear stress-strain shear response in thick
section pultruded FRP composite materials [8].
The specimen were fabricated from one pultruded plate with 12.2mm
thickness and has been cut by water-jet machining system into butterfly shape with
precise tolerance of ±0.08 mm. The load was applied by using MTS 810 servo
hydraulic machine with 90° load angle to perform ―pure shear‖.
12
The results of from the experiment indicate that Arcan test fixture is capable
for the measurement of the entire response up to ultimate failure. The examination of
the α = 90° reveal that the failure initiate at the notch and propagate along section
AB as show in Fig. 2.9.
Fig. 2.11: Failed axial and transverse specimen after reaching the ultimate stress
α=90° [8].
From their stress-strain curve plotted, it can be noted that all specimens
perfectly failed in brittle behaviour. The linearly propagated shear stress- strain
curves in Fig.2.10 indicate a state of pure shear was present during the testing.
Although the present of small axial strain, it doesn‘t affect the shear response
observed throughout its non-linear response [8].
Fig.2.12: Shear stress-strain response from Arcan shear test [8]
13
Strains of ε −45 and ε+45 are linearly with shear stress and almost symmetry
along x-axis as shown in Fig. 2.11 and Fig. 2.12. This result proves that the testing
method was reliable as the strain data obtained were balanced in each direction. The
testing method also suitable in determine the shear properties, shear modulus, and
shear strain of brittle materials, especially for Fibre Reinforced Polymer composites.
The failure of Arcan test specimens also depend on the angle of biaxial load as
shown in Fig 2.13.
Fig 2.13: Measured strain profiles at centre of axial butterfly specimen during ‗pure
shear‘ test [8]
Fig 2.14: Measured strain profiles at centre of transverse butterfly specimen during
‗pure shear‘ test [8]
14
Fig 2.15: Shear stress strain response from biaxial testing [8]
In 2006, Samuel et al [9] used Arcan test method to study material behaviour
in 6056T78 Friction Stir Welding (FSW) specimens. Arcane tensile test and tensile
test of non-welded (base material) was firstly introduced in order to determine any
comparison parameter. From the result, specimen shapes are likely influence the data
especially during the necking process. The maximum strain achieve before rupture
has found differ around 9% for both test as shown in Fig. 2.14.
Fig. 2.16: Experimental results in pure tensile of non-welded 6056T78 Aluminium
specimen [9]
15
2.1.3 Previous research of Finite Element Analysis of Arcan test
Finite Element Method was applied to nonlinear problems and large
deformation in late 1960s and early 1970s [1]. Nonlinear analysis enables a design
engineer to make sound design decisions. In nonlinear stress analysis is becoming
important for designers in order to employing a wider variety of materials in a
multitude of different applications.
Finite element analysis also has been considered by most scientists in their
research and experiment. An error occur during experiment has made the finite
element analysis are more relevant to produce accurate data. In Arcan test method,
the result obtain still are not accurate even strong theoretical background. The
problem become more complicated since orthotropic type of material was
introduced.
In year 2010, R. Rinaldi et al [10] conducted a research on modelling
structure polycarbonate. A finite element method is used in order to confirm the
prediction capability of Arcan test in various loading condition. Analysis for ―pure
shear‖ loading show boundary condition proposed for the shear test was set to be
fixed at left segment of specimen with the direction of load are based on Arcan test
practice (α=90°) at right segment as shown in Fig. 2.15. Roller condition at right
segment of specimen only applied at ―pure shear‖ loading.
Fig. 2.17: Original experimental shape and boundary condition [10]
16
In year 2003, Rani El-Hajjar at el [8] used finite element analyses of to
stimulate the effect of notch radius and material orthotropic on the uniformity and
distribution of stresses in the significant section of the butterfly specimen of Arcan
test method under shear loading. There were three notch radii selected to determine
the most appropriate radius of 1.27mm, 2.54mm and 5.05mm. Fig. 2.16 shows the
shear stress profile along the gauge section for FRP axial orientation. A normalised
stress profile near to 1 was found near the centre for the specimen with a notch radius
of 2.54 mm.
Fig. 2.18: Effect of notch radius on shear stress profile along gauge section [8]
The simulation by isotropic assumption and orthotropic value showed non-
uniformity of stress profile in the significant section resulted in a lower stress
concentration near the notch tip, with a more gradual stress built up compared to the
sharp notch as shown in Fig. 2.17. The normalized shear stress closer to 1.0 was
found near the centre as it far from notch effect at the tip.
17
Fig. 2.19: Effect of sharp notch on shear stress along the gauge section [8]
By considering the effect of roving orientation on shear stress along the
significant section as shown in Fig. 2.18, the value show that axial (90°) fibre
produce more uniform stress compare to transverse (0°) fibre and isotropic material.
Transverse fibre resulted highest stress concentration at the notch tip.
Fig 2.20: Effect of roving orientation on the shear stress along the gage section [8]
In year 2008, David Delsart et al [11] used finite element method to study the
material through thickness and out- of-plane shear properties identified of Fibre
18
Reinforced Composite from Arcan test method. The stress concentration generated
at the mid-section of the specimen was observed until fracture occurs as shown in
Fig. 2.19 and Fig 2.20. From the result, max tensile and shear load of numerical was
found less than experiment with -40% and -24% respectively.
Table 2.1: Simulation results – parameter based on Arcan tests properties [11]
Load configuration Experimental Max. Force (N) Numerical Max. Force (N)
0° 1904 1146
90° 2535 1928
Fig. 2.21: Stress field of tensile loading before rupture [11]
Fig. 2.22: Stress field of shear loading before rupture [11]
19
2.1.4 Theoretical background of Arcan Test Method
The modified Arcan fixture and its butterfly shape specimen capable to
produce pure shear and biaxial stress conditions, as shown in Fig. 2.21. The shear
response from various biaxial stress states can be obtained in a relatively simple
manner by varying the angle of α at which the load is applied. A special case of ‗pure
shear‘ can be produce section AB when α = 90 degree. The basic concept of
configurations is that the Arcan test set-up has a well-defined as significant section
AB, where the stresses are assumed to be uniform. Fig. 2.22 shows the significant
section at the centre of the butterfly specimen. This uniformity of stresses is a result
of appropriate geometrical parameters of the butterfly specimen. Another outcome of
the butterfly type geometry is the stresses at the significant section are the highest
because of small cross-sectional area in segment and thus, initial yield or failure is
more likely to occur within the section.
Fig. 2.23: Arcan fixture for shear test with different loading configurations [8]
20
Fig. 2.24: Internal mean shear and normal stress along the ‘significant section’ [8]
The mean normal stress, σ y, and the mean shear stress, τ xy at the significant
section are defined in a local coordinate system, where the x-axis is perpendicular
and the y-axis is parallel to the significant section. Both components of stress can be
directly determined from the forces that are transmitted by the joints between the
testing machine and the Arcan grips, as previously shown in Fig. 2.21.
For pure shear testing, the forces that act along axis of the universal testing
machine referred as the vertical applied force, Py while perpendicular to the universal
testing machine is referred to as the horizontal force, Px. The angle, α, indicated the
angel between perpendicular axis of significant section to the load direction of
testing machine. Finally, A denotes the cross-sectional area of the specimen
significant section, (i.e. width x thickness).
2.1.5 Stress Analysis
The force applied to the rig as shown in Fig. 2.22 will produced shear and
normal stress at section AB. In order to determine the normal stress σx and the
shearing stress τxy acting on the face perpendicular to the x-axis, an element in state
21
of equilibrium to the x and y axes shall be considered. By assuming the uniform
stresses on the significant section AB, the equilibrium analysis that on significant
section AB as shown in Fig. 2.16 write as
→ Σ Fx = 0; Pcosα - σ xx A = 0
σ yy =
[2.1]
↑ Σ Fy = 0; Psinα -τ xyA = 0
τ xy =
[2.2]
The rectilinear portions of the cut-outs element are oriented at ± 45 shows the
principal stresses in the vicinity are also in these directions. It follows that τxy on AB
as given by equation [2.5] is a principal shear stress. Therefore on AB,
σ xx = σ yy =
[2.3]
and the principal stresses are
σ 1 = σ xx + σ xy =
[2.4]
σ 2 = σ xx - σ xy =
[2.5]
2.2 Standard Test Method for Tensile Properties
According to ASTM International [24], the standard method for tensile test of
plastic material is subjected under D638. This test was specified to unreinforced and
22
reinforced in the form of standard dumbbell-shaped test when tested under defined
condition of temperature, humidity, pre-treatment and testing machine speed. For the
rigid and semi-rigid plastic, the specimen should conform to the dimension as shown
in Fig. 2.23.
Fig. 2.25: Dumbbell-shaped specimen dimension [12]
2.2.1 Previous Research on Tensile Test
In year 2014, Shahin Shadlou [13] used ASTM D638 to measure the Young
Modulus of graphine reinforced epoxy under different strain rates. There were 4
strain rates selected to determine the behaviour of 0.01, 0.1, 1, 10/s under tensile
loading. Typical stress-strain curve for each strain rates under tensile loading are
illustrated in Fig. 2.24. The Young modulus of graphine reinforced increase with
strain rates.
23
Fig.2.26: Stress-strain curve of graphine reinforced epoxy [13]
2.3 Summary
The literature on the Arcan testing method was briefly discussed in this
chapter. 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 finite element analysis and the reliability of the Arcan
test result. As a conclusion, the Arcan test method can be used to determine the
mechanical properties of material such as shear strength and shear modulus.
24
CHAPTER 3
RESEARCH METHODOLOGY
3.0 Introduction
In this section, the discussion focused on the specimen preparation,
experimentation, instrument and measurement. Every topic was discussed in detail in
order to make the objective of this study can be achieved.
For this study, nine sample of butterfly specimen were produced from each
Selfix Carbofibre and Aluminium 6061. Three samples from group material were
selected for each loading configuration. Three sample of dumb-bell specimen were
produced in this study to determine the tensile modulus of Celfix Carbofibre. Instron
Universal Testing Machine Series IX Model 4206 used for the test. After tensile for
dumb-bell specimen was carried out, mechanical properties Selfix Carbofibre were
recorded for finite element analysis material requirement. The maximum strength for
each loading configuration will be record to represent the maximum load applied in
ANSYS.
25
3.1 Specimen Preparation and Experimental Setup
3.1.1 Specimen Geometry
The specimen size 60 mm long x 45 mm wide with an average thickness of 4
mm for epoxy and 2mm for aluminium as shown in Fig. 3.17. The 90º notches were
formed at the centre of 60 mm length (at the top and bottom) such that the distance
between notches was left about 10 mm at the middle to introduce stress field on the
significant section, AB. 1.5 mm of notch radius was produced to minimise stress
concentration beside to produce a uniform shear stress distribution along the
significant section [7].
*All dimension in mm
Fig 3.1: The butterfly specimen geometry [7]
R1.5
26
3.1.2 Material Details
The epoxy namely Selfix Carbofibe adhesive, supplied by Exchem, United
Kingdom was used. The properties of Selfix Carbofibe adhesive were achieved by
blending/mixing a modified epoxy resin and inorganic fillers to form a base
component, which was activated by a thixotropic formulated amine hardener. This
epoxy adhesive consisted of two parts, namely; part A and part B (Fig. 3.1). Both
parts were mixed with a ratio of 3:1 as stated in the supplier‘s specification. Their
chemical formulations and cast properties are listed as in Table 3.1 and Table 3.2.
Material properties obtained from experiment conducted by Shukur. A. H [7] is
shown in Table 3.3.
Table 3.1: Chemical formulation of Selfix epoxy adhesive [7]
Materials Chemical formulation Colour
Part A (Epoxy)
Part B
(Hardener)
Contains 35 to 45% reaction
product of Epichorohydrin
Bisphenol A epoxide resin of
average molecular weight <
700
Contains 3,6,9,12-tetra-
azatetradecamethylenediamine
(<20%) and 4,4-
isopropylidenediphenol (<
10%)
White
Dark Grey
27
Table 3.2: Typical properties of Selfix Carbofibe epoxy adhesive [7]
Property Value
Compressive strength (MPa) aged of 7 days at 20 °C 90
Tensile strength (MPa) 23
Thermal expansion /°C 33 x 10-6
Shear modulus (GPa) na
Single lap shear strength (MPa) > 18
Glass transition temperature (DMTA) °C > 65
Water absorption 0.4%
(a) (b)
Fig. 3.2: Two parts of Selfix Carbofibe adhesive (a) Part A (b) Part B
Table 3.3: Material properties Selfix Carbofibe epoxy adhesive from Shukur. A. H
[7]
Specimen Ult. Load
(kN)
Shear
Modulus,
(GPa)
Shear
Strength,
(MPa)
Shear
strain, γ
(με)
Time to
failure
(sec)
Control* 1.43 2.97 29.24 9275 66.4
*Ref. Shukur. A. H [11]
The type of aluminium used for this project was 6061 as the selection of
isotropic ductile material. Material properties obtained from ASTM which refers to
standard specification for aluminium and aluminium-alloy sheet and plate.
28
Table 3.4: Mechanical properties of 6061 alloy [14]
Alloy Tensile
Strength, Mpa
Yield Strength,
Mpa Poisson ratio, v
6061 310 276 0.33
3.1.3 Mixing and Casting Process for Epoxy
The both of dumb-bell and butterfly shaped epoxy specimen were prepared
by mixing two parts of adhesive system consist of epoxy and hardener was mixed
with ratio of 3:1 (270 gram epoxy and 70 gram hardener). Then, both shapes of
specimens were produced by casting the mixtures onto a female mould.
A low speed electric mixer was then used to mix the materials until it turns
soft grey in colour as shown in Fig. 3.2. The mixing process was done in the
laboratory control room where the temperature and relative humidity was in range of
24°C to 26°C and 40% to 55% (i.e. by depending on the ambient laboratory
condition).
Fig 3.3: A mixing process using low speed electric mixer
Both shaped specimens were cast by using mild steel moulds which consisted
of male parts (top) and female parts (base). Before the specimens were casting, the
male and female mould surface were clean by using soft cloth and Canauba wax to
29
ensure the dirt remove away. Two flat plates were attached to cover the back part of
the mould by screws as shown in Fig. 3.3 (a) and (b). Then, the mixtures poured into
the female part mould as shown in Fig. 3.4 (a) and (b). This process was done
carefully to ensure minimum air trapped in the specimen.
(a) (b)
Fig 3.4: Flat plate attached to male part by screws
(a)Flat plate before installation (b) Flat plate after installation
(a) (b)
Fig. 3.5: Casting process by pouring the mixtures into the female mould
(a) Butterfly specimens (b) Dumbbell-shaped specimens
The male mould part was then attached to the female part and a metal block
weight of about 10 kg was placed onto the top of the mould to produce an extra
uniform pressure on the mould as shown in Fig 3.4(a) and (b). Finally the specimens
30
were left to solidify in a laboratory environment with temperature ranging from 23 to
33°C before demoulding process.
(a) (b)
Fig. 3.6: (a) Male part attached to the female part and (b) 10 kg mass used
Demoulding process of the specimens was carefully done by applying a soft
knocking force onto the butterfly shaped Teflon block using a wood hammer (Fig.
3.6). The Mecapol P255 U Polish Machine was used to make the surfaces of the
specimen smoother and the sharp edges rounder. The process is shown in Fig. 3.7 (a)
and (b).
Fig. 3.7: Demoulding process
31
(a) (b)
Fig. 3.8: Surface grinding and polishing process of the specimen
(a) Mecapol P255 U polishing machine (b) Manual polishing technique
Lastly, the specimens were checked for their final quality, established
(marked) the code name as shown in Fig. 3.8. Three specimens for each group of
samples were selected for the experimentation study of Arcan test method. Five
specimens for tensile test were selected for experimentation study of tensile test.
Fig. 3.9: Specimens ready for testing
The recorded data showed that the average specimen width, thickness and
cross sectional area of Arcan test method were in the range of 10.48 to 11.18 mm,
4.35 to 4.51 mm and 48.73 to 49.44 mm2 respectively for butterfly specimen, as
shown in Table 3.5.
32
Table 3.5: Butterfly specimen‘s width, thickness and significant area average
measurement
Sample Code Thickness(mm) Width(mm) Significant area
(mm2)
ES 4.48 10.75 48.16
ET 4.59 10.53 47.17
ETS 4.38 10.79 47.62
For dumbbell specimen, the recorded data showed that the average specimen
width, thickness and cross sectional area of Arcan test method were in the range of
10.48 to 11.18 mm, 4.35 to 4.51 mm and 48.73 to 49.44 mm2 respectively, as shown
in Table 3.6.
Table 3.6: Dumbbell specimen‘s width, thickness and significant area
average measurement
Sample Code Thickness(mm) Width(mm) Significant area
(mm2)
ST 3 13.15 39.45
3.1.3 Specimen Preparation for Aluminium
There were aluminium scraps with 2mm of thickness used for aluminium
specimen as shown in Fig. 3.9. All the specimens fabricated into 9 sample of
butterfly specimen using milling machine as shown in Fig.3.10(a) and (b)
33
Fig. 3.10: Aluminium scrap
(a) (b)
Fig. 3.11: (a) Milling machine (b) Specimen ready for labelling
.
The recorded data showed that the aluminium average specimen width,
thickness and cross sectional area of Arcan test method were in the range of 10.48 to
11.18 mm, 4.35 to 4.51 mm and 48.73 to 49.44 mm2 respectively, as shown in Table
3.5.
34
Table 3.7: Butterfly specimen‘s width, thickness and significant area average
measurement
Sample Code Thickness(mm) Width(mm) Significant area
(mm2)
AS 2.05 10.06 48.16
AT 2.05 10.33 47.17
ATS 2.04 10.04 47.62
3.1.5 Strain Gauge Installation
A rosette type strain gauge, TML FCA-1-11 with 1 mm gauge length was
installed onto the dumbbell specimen at the gauge section (Fig. 3.11). The gauge
bond surface in the significant area was prepared (roughened) with 1000 grade grain
size sand paper prior to cleaning by using liquid acetone to remove grease, dust or
dirt. Then, the strain gauge was attached onto the specimen in the direction of 0°
measured from the specimen‘s horizontal axis by referring to standard installation
procedure. The important parameters of the gauge specification are shown in Table
3.5.
Fig. 3.12: Strain gauge on dumbbell specimens
35
Table 3.8: Rossete type strain gauge specifications [15]
Manufacturer Tokyo Sokki Kenkyujo Co. Ltd. Japan
Gauge type TML FLA-1-17
Gauge factor 1 = 2.08, 2 = 2.08 1%
Coefficient of thermal expansion 11.8 x 10-6/°C
Tolerance ± 0.85 (μm/m)/°C
Temperature coefficient of gauge factor + 0.1 ± 0.05%/10°C
3.1.6 Tensile Test Set-Up and Test Procedure
Fig.3.12 showed the set-up of tensile test using dumbbell specimen. Both end
of specimen were attached to the loading machine. The tensile loads were applied
onto the specimen to produce tensile stress onto the specimen. The complete
measurement and instrumentation system is shown in Fig.3.13. It was equipped with
the following important features;
i. A load frame the dumbbell specimen was installed and loaded in tensile.
ii. A control panel that controlled the loading rate
iii. A computer for the user to key-in the properties and the information of the
specimen and set the format for the plotting of grapph and results.
iv. A data logger to record and print out the strain readings.
36
Fig. 3.13: Tensile test set-up
Fig. 3.14: Instrumentation set-up
3.7 Arcan Test Setup
The modified Arcan test fixture used in this study programme consisted of a
pair of male and female parts, as shown in Fig. 3.14. The butterfly specimen was
mounted into the female part followed by the male part. Both parts were tightened by
screws to ensure that the specimen was tightly gripped between the fixtures to
prevent from slippage and misalignment during loading. The complete assembly of
the fixtures was attached to the holder at the lower and upper parts accordingly prior
Cross Head
Load Cell
Instron Machine
Load Frame
Fixture Data Logger
37
to attachment to the Instron Universal Testing Machine, as shown in Fig. 3.15. The
Arcan fixture set-up at 0, 45, and 90 for tensile, tensile shear and shear loading
configuration respectively, as shown in Fig. 3.16 (a), (b), and (c)
Fig. 3.15: Arcan test fixture and butterfly specimen [7]
Fig. 3.16: Attached Arcan fixture to the holder
38
(a) (b) (c)
Fig. 3.17: Arcan fixture set-up configuration
(a)Tensile (b) Shear (c) Tensile shear
3.2 Specimen Modeling and Analysis Setup
The literature studies were carried out by sourcing the related information
from journals, handbooks, books, previous theses, and websites. Firstly, literature
review was carried out to understand the mechanical characteristic of the adhesive
system used in this study. Then, the studies focused on the Arcan test method in
order to investigate the theoretical background related to properties and to determine
related information on finite element analysis.
All the information and data about the material was obtained from ASTM and
experiment conducted by Shukur. A. H [7]. The modelling was divided into three
type of material which is epoxy and aluminium. Epoxy and aluminium was chosen to
investigate the characteristic of brittle and ductile isotropic material while carbon
fibre was chosen for brittle orthotropic material. The modelling and analysis was
carried out by using ANSYS in order to investigate the stress characteristic and
response of the butterfly specimen. The load and boundary condition were applied to
the specimen modelling to perform exact condition of Arcan test method experiment.
Data were gathered from the result that was established during analysis finite
element analysis. The contour of critical area was observed in order to investigate the
factor and location that influent the data.
39
3.2.1 Specimen Modeling
The specimen was model using ANSYS WORKBENCH as shown in
Fig.3.18. The thickness of modeled specimen was referred to the type of material as
discussed before.
Fig.3.18: Butterfly specimen of epoxy in ANSYS
3.2.2 Input Material Data
All the gathered data was enter to the ANSYS table for finite element
analysis as shown in Fig. 3.19.
40
Fig. 3.19: Material properties table in ANSYS
3.2.3 Meshing
A simple mesh was used to represent the element of adhesive material in the
test section. Fig. 3.20 shows the mesh used for all specimens modelling. Multiple
elements were used to model the test section even though a single element would
have been sufficient to approximate the nature of the Arcan test. Fine element with
size of 1mm was used to provide accurate analysis in the significant section.
Fig. 3.20: Meshed model specimen
41
3.2.4 Boundary Condition and Loading Setup
Based on literature study, the boundary condition and load direction proposed
by R. Rinaldi [10] was used to for finite element analysis. The load applied to the
specimen in which direction of loading configuration discussed before. The boundary
condition and loading setup for shear, tensile shear and tensile of butterfly model in
ANSYS is shown in Fig. 3.21 (a), (b), and (c).
Fig 3.21: Boundary condition and loading setup
(a) Shear (b) Tensile shear (c) Tensile
3.3 Summary
In this chapter, the explanations from specimen preparations until the
experimentation and test set up were briefly discussed. For the specimen
preparations, discussions focused on the materials, specimen geometry, process to
produce specimens and finite element analysis. Then for the experimentation and test
set-up, the discussion based on the Arcan rig installation, specimen testing
procedure, and data analysis from the tested experimentation. The testing procedure
must be followed strictly in order to obtain reliable data.
42
CHAPTER 4
RESULTS AND DISCUSSION
4.0 Introduction
In this chapter, the discussion was focused onto the characteristic of different
loading configuration onto the aluminium and epoxy system by discussing the result
of the Arcan test method and finite element analysis. The result were analysed and
presented in term of graphs and table established a comprehensive technical
discussion. The result discussion was based one specimen of each loading
configuration of test sample with final conclusion will be focused on the average
performance result between experimental and finite element analysis. Then, the
performance of tensile test result from Arcan test method will be evaluate by
comparing the data with the common tensile test method using dog bone specimen.
43
4.1 Sample Testing Evaluation
The result and discussion were focus on the experiment data analysis and
finite element analysis of butterfly specimen. The determination of characteristic of
Selfix Carbofibe adhesive and aluminium specimens due to different loading
configuration through Arcan test method was the main parameter discussed. The
result were analysed and presented in term of graphs, tables, and figures in order to
provide a more comprehensive technical discussion. Overall, the discussion was
referred to a selected significant specimen from each group of test sample. The
overall discussion also covered the uniformity of stress based on notch radius and the
performance of tensile result from Arcan test method compare to common tensile test
using dumbbell specimen through finite element analysis.
4.1.1 Test Rig-Specimen Evaluation of Tensile Method for Epoxy
From load test, it could be observed that all epoxy specimens fail in the brittle
form. The fracture line occurs at 90° angle measured from the direction of load as
shown in Fig. 4.7. This situation confirmed that the specimen failed in the direction
of principal stresses which was the direction of the tensile principle stress
corresponding to the state of pure tensile.
Fig. 4.1: Brittle failure of ST1 epoxy
44
Therefore, the maximum load applied to all specimens before fracture are
recorded for finite element analysis. Finally, by assuming the stress distribution
along significant section AB was uniform, the following calculation was done in
order to evaluate the alignment of specimen stress element. A sample calculation was
done for specimen ST1 as follow;
Specimen thickness, t = 2.73mm,
Specimen significant section, AB = 13mm
Load carried by specimen at load, F= 100N
Specimen cross section area, A = t x h mm2
The average tensile stress can determine as follow;
From equation, the average shear stress is:
4.1.2 Test Rig-Specimen Evaluation for Arcan Test Method
From load test, it could be observed that different type of fracture occur are
based on direction of loading configuration. All epoxy and aluminium specimens fail
in the form of brittle and ductile behaviour respectively. Therefore, the maximum
load applied to all specimens before fracture are recorded for finite element analysis.
45
4.1.2.1 Shear Test for Epoxy and Aluminium Sample
From load test, it could observe that the fracture line of epoxy specimen
occurred at about 45° angle measured from the specimen principal axis to the line of
significant section AB as shown in Fig. 4.2. This situation confirmed that the
specimen failed in the direction of principal stresses which was the direction of the
tensile principle stress corresponding to the state of pure shear.
Fig. 4.2 Brittle failure of ES1 occurred at 45°
Finally, by assuming the stress distribution along significant section AB was
uniform, the following calculation was done in order to evaluate the alignment of
specimen stress element. A sample calculation was done for specimen ES1 as follow;
Specimen thickness, t = 4.57mm,
Specimen significant section, AB = 10.6mm
Load carried by specimen at load, F= 100N
Specimen cross section area, A = t x h mm2
The average shear stress can determine as follow;
From equation, the average shear stress is:
46
From load test, it could observe that the fracture line of AS2 specimen
occurred at about 90° angle measured from the specimen principal axis to the line of
significant section AB as shown in Fig 4.3. This situation confirmed that the
specimen failed in the direction of shear stress which was the direction of stress
corresponding to the state of pure shear. It also can be confirmed that shear strength
of aluminium are low compare to tensile strength.
Fig. 4.3: Ductile failure of AS1specimen occurred at 90°
Finally, by assuming the stress distribution along significant section AB was
uniform, the following calculation was done in order to evaluate the alignment of
specimen stress element. A sample calculation was done for specimen AS1 as
follow;
Specimen thickness, t = 2.06mm,
Specimen significant section, AB = 10.05mm
Load carried by specimen at load, F= 100N
Specimen cross section area, A = t x h mm2
The average shear stress and shear strain can determine as follow;
From equation, the average shear stress is:
47
4.1.2.2 Tensile Test for Epoxy and Aluminium Sample
From load test, it could observe that the fracture line of ET2 specimen
occurred at about 90° angle measured from the specimen principal axis to the line of
significant section AB as shown in Fig. 4.4. This situation confirmed that the
specimen failed in the direction of principal stresses which was the direction of the
tensile principle stress corresponding to the state of pure tensile.
Fig. 4.4: Brittle failure of ET2 specimen occurred at ±90°
Finally, by assuming the stress distribution along significant section AB was
uniform, the following calculation was done in order to evaluate the alignment of
specimen stress element. A sample calculation was done for specimen ET1 as follow;
Specimen thickness, t = 4.62mm,
Specimen significant section, AB = 10.5mm
Load carried by specimen at load, F= 100N
Specimen cross section area, A = t x h mm2
The average shear stress and shear strain can determine as follow;
From equation, the average normal stress is:
48
From load test, it could observe that the fracture line of AT1 specimen
occurred at about 45° angle measured from the specimen principal axis to the line of
significant section AB as shown in Fig. 4.5. This situation confirmed that the
specimen failed in the direction of principle stress which was the direction of shear
principle stress corresponding to the state of pure shear. It also can be confirmed that
shear strength of aluminium are low compare to tensile strength.
Fig. 4.5: Ductile failure of AT occurred at ±45°
Finally, by assuming the stress distribution along significant section AB was
uniform, the following calculation was done in order to evaluate the alignment of
specimen stress element. A sample calculation was done for specimen S1 as follow;
Specimen thickness, t = 1.99mm,
Specimen significant section, AB = 10.03mm
Load carried by specimen at load, F= 100N
Specimen cross section area, A = t x h mm2
The average shear stress and shear strain can determine as follow;
From equation, the average normal stress is:
49
4.2.2.3 Tensile Shear Test for Epoxy and Aluminium Sample
From load test, it could observe that the fracture line of ETS3 specimen
occurred at about 30° angle measured from the specimen principal axis to the line of
significant section AB as shown in Fig. 4.6. This situation confirmed that the
specimen failed in the direction of principal stresses which was the direction of the
tensile principle stress corresponding to combination tensile and shear loading.
Fig. 4.6: Brittle failure of ETS3occurred at ±30°
Finally, by assuming the stress distribution along significant section AB was
uniform, the following calculation was done in order to evaluate the alignment of
specimen stress element. A sample calculation was done for specimen ETS1 as
follow;
Specimen thickness, t = 4.62mm,
Specimen significant section, AB = 10.5mm
Load carried by specimen at load, F= 100N
Specimen cross section area, A = t x h mm2
The average shear stress and shear strain can determine as follow;
From equation, the average shear stress is:
50
From load test, it could observe that the fracture line of ATS2 specimen
occurred at about 90° angle measured from the specimen principal axis to the line of
significant section AB as shown in Fig. 4.7. This situation confirmed that the
specimen failed in the direction of shear stress although the direction of tensile
principle stress is about 30° from principle axis. It also can be confirmed that shear
strength of aluminium are low compare to tensile strength.
Fig. 4.7: Ductile failure of ATS2Aluminium occurred at ±90°
Finally, by assuming the stress distribution along significant section AB was
uniform, the following calculation was done in order to evaluate the alignment of
specimen stress element. A sample calculation was done for specimen ATS1 as
follow;
Specimen thickness, t = 2.03mm,
Specimen significant section, AB = 10.01mm
Load carried by specimen at load, F= 100N
Specimen cross section area, A = t x h mm2
The average shear stress and shear strain can determine as follow;
From equation, the average shear stress is:
51
4.2 Experimental Result for Arcan Test Method
4.2.1 Experimental Results for Shear Loading of Epoxy
There were three (3) specimens for the epoxy sample. All specimens, ES1 to
ES3 have shown brittle characteristics of failure, which occurred at 45° from the
specimen‘s principal axis, and the complete test data for the epoxy sample, which
was calculated from previously stated equations, are shown in Table 4.3.
Table 4.1: Shear test data for ES samples
Sample Ultimate Load
(kN)
Cross Sectional Area
(m2)
Shear Strength
(MPa)
ES1 1.037 4.84x10-5
21.43
ES2 1.006 4.76x10-5
21.13
ES3 1.109 4.85x10-5
22.87
Average 1.051 4.82x10-5
21.81
(0.93)
Note: The value listed in bracket represent the standard deviation
From Table 4.3, it can be seen that the highest of ultimate failure load was 1.1
kN and the lowest ultimate load was 1.006 kN. The average ultimate failure loading
for this sample was 1.051kN. The value of average shear stress obtain from
experiment was 21.81 MPa (i.e. about 4.3% of specimens data value deviated from
their average value). From manufacturer specification, the shear strength for Selfix
Carbofibre adhesive was higher than 18 MPa (i.e under shear lap shear test method).
By comparing shear strength with experiment conducted by Shukur A. H [8], the
value obtained was 17.43% higher.
52
4.3.2 Experimental Results for Shear loading of Aluminium
There were three (3) specimens for the aluminium sample. All specimens,
AS1 to AS3 have shown ductility characteristics of failure, which occurred at 90°
from the specimen‘s principal axis due to low shear strength. The complete test data
for the aluminium sample, which was calculated from previously stated equations,
are shown in Table 4.2.
Table 4.2: Shear test data for ES samples
Sample Ultimate Load
(kN)
Cross Sectional Area
(m2)
Shear Strength
(MPa)
AS1 4.45 2.07x10-5
215.12
AS2 4.47 2.05x10-5
218.1
AS3 4.54 2.07x10-5
219.37
Average 4.49 2.06x10-5
217.53
(2.18)
Note: The value listed in bracket represent the standard deviation
From Table 4.4, it can be seen that the highest of ultimate failure load was
4.54 kN and the lowest ultimate load was 4.45 kN. The average ultimate failure
loading for this sample was 4.488 kN. The value of average normal stress obtain
from experiment was 217.53 MPa (i.e. about 1% of specimens data value deviated
from their average value).
.
4.3.3 Experimental Results for Tensile Loading of Epoxy
There were three (3) specimens for the epoxy sample. All specimens, ET1 to
ET3 have shown brittle characteristics of failure, which occurred at 90° from the
specimen‘s principal axis, and the complete test data for the epoxy sample, which
was calculated from previously stated equations, are shown in Table 4.5.
53
Table 4.3: Tensile test data for TS samples
Sample Ult. Load (kN) Cross Sectional Area(m2) Tensile Strength (MPa)
ET1 0.827 4.85x10-5
17.05
ET2 0.913 4.89x10-5
18.67
ET3 0.918 4.79x10-5
19.16
Average 0.886 4.82x10-5
18.29
(1.1)
Note: The value listed in bracket represent the standard deviation
From Table 4.5, it can be seen that the highest of ultimate failure load was
0.918kN and the lowest ultimate load was 0.827 kN. The average ultimate failure
loading for this sample was 0.886kN. The value of average normal stress obtain from
experiment was 18.29 MPa (i.e. about 6% of specimens data value deviated from
their average value).
4.3.4 Experimental Results for Tensile Loading of Aluminium
There were three (3) specimens for the aluminium sample. All specimens,
AT1 to AT3 have shown ductile characteristics of failure, which occurred at 45°
from the specimen‘s principal axis, and the complete test data for the aluminium
sample, which was calculated from previously stated equations, are shown in Table
54
Table 4.4: Tensile test data for AT samples
Sample Ult. Load (kN) Cross Sectional Area(m2) Tensile Strength (MPa)
AT1 6.6 2.03x10-5
325.07
AT2 6.52 2.27x10-5
287.31
AT3 6.71 2.26x10-5
296.77
Average 6.61 2.19x10-5
303.05
(19.65)
Note: The value listed in bracket represent the standard deviation
From Table 4.6, it can be seen that the highest of ultimate failure load was
6.71N and the lowest ultimate load was 6.52kN. The average ultimate failure loading
for this sample was 6.61kN. The value of average normal stress obtain from
experiment was 303.05 MPa (i.e. about 6.5% of specimens data value deviated from
their average value).
4.3.5 Experimental Results for Tensile Shear Loading of Epoxy
There were three (3) specimens for the epoxy sample. All specimens, ETS1
to ETS3 have shown brittle characteristics of failure, which occurred at 30° from the
specimen‘s principal axis, and the complete test data for the epoxy sample, which
was calculated from previously stated equations, are shown in Table
4.7.
55
Table 4.5: Tensile Shear test data for ETS samples
Sample Ult. Load (kN) Cross Sectional Area(m2) Shear Strenght (MPa)
ETS1 0.74 4.77x10-5
15.43
ETS2 0.81 4.61x10-5
17.53
ETS3 0.81 4.77x10-5
16.87
Average 0.78 4.72x10-5
16.61
(1.07)
Note: The value listed in bracket represent the standard deviation
From table, it can be seen that the highest of ultimate failure load was 0.81kN
and the lowest ultimate load was 0.74kN. The average ultimate failure loading for
this sample was 0.78kN. The value of average normal stress obtain from experiment
was 16.61 MPa (i.e. about 6.4% of specimens data value deviated from their average
value).
4.3.6 Experimental Results for Tensile Shear loading of Aluminium
There were three (3) specimens for the epoxy sample. All specimens, ATS1
to ATS3 have shown brittle characteristics of failure, which occurred at 90° from the
specimen‘s principal axis, and the complete test data for the epoxy sample, which
was calculated from previously stated equations, are shown in Table 4.8.
56
Table 4.6: Tensile Shear test data for ATS samples
Sample Ult. Load (kN) Cross Sectional Area(m2) Shear Strenght (MPa)
ATS1 5.57 2x10-5
278.45
ATS2 5.63 2.07x10-5
272.03
ATS3 5.54 2.08x10-5
266.25
Average 5.58 2.05 x10-5
272.24
(6.1)
Note: The value listed in bracket represent the standard deviation
From Table 4.8, it can be seen that the highest of ultimate failure load was
5.57kN and the lowest ultimate load was 5.54kN. The average ultimate failure
loading for this sample was 5.58kN. The value of average normal stress obtain from
experiment was 272.24 MPa (i.e. about 2.2% of specimens data value deviated from
their average value).
4.3 Experimental Result for Tensile Test
4.3.1 Experimental Data of Tensile Test Method for Epoxy
There were three (5) specimens for epoxy sample. All specimens, ST1 to ST5
have shown brittle characteristics of failure, which occurred at 90° from the
specimen‘s principal axis. The raw data for ST1 specimen are shown in Table 4.9
and the complete test data sample, which was calculated from previously stated
equations, are shown in Table 4.10.
57
Table 4.7: Experiment data for ST1 sample
P(kN) σ(MPa) ey1(µmm) ey2(µmm) ey(µmm) E(GPa) ey(m)
0.1 2.87 498 486 492 5.82 0.000492
0.2 5.73 741 717 729 7.86 0.000729
0.3 8.60 1043 1010 1026.5 8.37 0.001027
0.4 11.5 1388 1349 1368.5 8.37 0.001369
0.5 14.3 1641 1598 1619.5 8.85 0.00162
0.6 17.2 2092 2036 2064 8.33 0.002064
0.7 20.1 2478 2407 2442.5 8.21 0.002443
0.8 22.9 2884 2794 2839 8.07 0.002839
0.9 25.8 3374 3253 3313.5 7.78 0.003314
1.0 28.7 3928 3781 3854.5 7.43 0.003855
Table 4.8: Test results for ST samples
Sample Ult. Loading
(kN)
Strain near
failure
Tensile
modulus (Gpa)
Tensile
strength (MPa)
ST1 0.90 0.0033915 7.43 25.4
ST2 1.10 0.003491 8.56 29.9
ST3 1.00 0.0038545 7.78 28.7
ST4 0.9 0.003757 7.68 27.7
ST5 1.1 0.003702 7.54 26.7
Average 1.00 0.003692 7.79
(0.45)
27.7
(1.74)
Note: The value listed in bracket represent the standard deviation
From table 4.10, it can be seen that the highest ultimate failure load was 1.10
kN and the lowest was 0.9 kN. The average for ultimate load was 1kN. The average
tensile modulus and tensile strength are 7. (i.e. about 6% of specimens data value
deviated from their average value) and 2.77 MPa (i.e. about 6.3% of specimens data
value deviated from their average value), respectively. By comparing to
manufacturer specification, the tensile strength for Selfix Carbofibre was 17% higher
than the minimum manufacturer quoted value.
58
The normal stress and normal strain data in Table 4.9 were used in plotting
the normal stress versus normal strain curve as shown in Figure 4.8. The stress-strain
curve shows that strain on each specimen was linearly propagated.
Fig. 4.8: Stress-strain curve for ST1 sample
4.4 Finite Element Analysis
From finite element analysis, it can be observed that different characteristic
of stress in field based on different type of loading configuration. The stress
distribution was found concentrated at the significant AB section of specimen. This
scenario satisfies with theoretical analysis which means high stress developed due to
small cross sectional area. Therefore, maximum stress and strain from finite element
analysis are obtained which refer to average maximum load from experiment.
59
4.4.1 Finite Element Analysis Result for Shear Loading of Epoxy
A load step of 100N was applied to the modelled specimen until it reach
ultimate loading. All the data gathered from the gauge section as shown in Table
4.11.
Table 4.9: Analysis result for shear loading of Selfix Carbofibre epoxy
Load (kN) Shear Stress (MPa) Shear Strain, xy Normal strain, x
0.1 2.303 7.7543e-004 -1.789e-005
0.2 4.6061 1.5509e-003 -3.578e-005
0.3 6.9091 2.3263e-003 -5.367e-005
0.4 9.2122 3.1017e-003 -7.156e-005
0.5 11.515 3.8772e-003 -8.945e-005
0.6 13.818 4.6526e-003 -1.0734e-004
0.7 16.121 5.428e-003 -1.2523e-004
0.8 18.424 6.2035e-003 -1.4312e-004
0.9 20.727 6.9789e-003 -1.6101e-004
1.0 23.03 7.7543e-003 -1.789e-004
1.051 24.205 8.1498e-003 -1.8802e-004
From Table 4.11, it can be seen that maximum stress generated at the gauge
section about 24.437 Mpa, which also indicate as shear strength. As compared to the
experimental data, the shear stress was found 10.75% higher. The maximum shear
strain is 8255µε when ultimate load were applied. The existence of normal strain
shows that Arcan test method was not perfectly producing shear stress. Meanwhile,
normal strains generated are too small and can be neglect.
The stress and strain data were used in plotting the stress versus strain curve
as shown in Fig. 4.10. The stress-strain curve show that strain was linearly
propagated. From the curve, it can shear modulus of material was found about
29.7GPa which indicate the gradient of the curve. By comparing to experiment
conducted by shukur[8], the value of shear modulus from finite element method was
60
almost similar. This means that Arcan test methods proven by finite element analysis
in order to measure shear modulus of material.
Fig 4.9: Shear stress-strain curve of Selfix Carbofibre epoxy
From experiment, the epoxy specimens failed in direction of tensile principle
stress when ultimate load about 1015N are applied to the specimen. Therefore, finite
element analysis on the maximum principle stress, maximum shear stress and
maximum shear strain regarding to the ultimate shear loading condition are shown in
Fig 4.10(a), 4.10(b) and 4.10(c) respectively
(c)
Fig. 4.10: (a) Maximum principal stress (b) Maximum shear stress (c) Equivalent
elastic strain
By observing the stress field on the modelled specimen, the maximum
principle stress about 64.97Mpa was located at the notch of the significant section
AB. The stress field also show almost similar shape of fracture line specimen that
61
can be seen during experiment. The maximum shear stress about 32.58Mpa located
at the notch. The maximum shear strain about 7776µ located at the notch of gauge
section. Both situations clearly describe that the fracture initiated at the notch of the
significant section AB.
The linearized stress data were used in plotting uniformity of stress along the
significant section AB as shown in Fig.4.11. The stress was found uniform at the
middle and high at the both end. This confirmed that the state of ―pure shear‖ stress
was form regarding to the direction of load applied. The high stress located at the
both end of significant section is due to effect of notch which generated stress
concentration.
Fig. 4.11: Stress distribution along significant section AB of Selfixe Carbofibre
epoxy due to shear loading
4.4.2 Finite Element Analysis Result for Shear Loading of Aluminium
A load step of 500N was applied to the modelled specimen until it reach
ultimate loading. All the data gathered from the gauge section as shown in Table
4.12.
62
Table 4.10: Analysis result for shear loading aluminium
Load (kN) Shear Stress (Mpa) Shear Strain, xy Normal strain, x
0.5 22.791 8.7657e-004 2.1625e-005
1.0 45.582 1.7531e-003 4.325e-005
1.5 68.372 2.6297e-003 6.4875e-005
2.0 91.163 3.5063e-003 8.6501e-005
2.5 113.95 4.3828e-003 1.0813e-004
3.0 136.74 5.2594e-003 1.2975e-004
3.5 159.54 6.136e-003 1.5138e-004
4.0 182.33 7.0125e-003 1.73e-004
4.49 204.6 7.8693e-003 1.9414e-004
From Table 4.12, it can be seen that maximum stress generated at the gauge
section about 204.6 Mpa, which also indicate as maximum shear stress. The
maximum shear strain was 7869.3µ when ultimate load applied.
The stress and strain data were used in plotting the stress versus strain curve
as shown in Fig.4.12. The stress-strain curve show that strain was linearly
propagated. From the curve, it can shear modulus of material was found about 26GPa
which indicate the gradient of the curve. By comparing to ASTM [22], the value of
shear modulus from finite element method was almost similar. This means that finite
element analysis prove that Arcan test methods are suitable to measure shear
modulus of material.
Fig. 4.12: Shear stress-strain curve for aluminium
63
From experiment, the epoxy specimens failed in direction of tensile principle
stress when ultimate load about 4488.7N are applied to the specimen. Therefore,
finite element analysis on the maximum principle stress, maximum shear stress and
maximum shear strain regarding to the ultimate shear loading condition are shown in
Fig 4.13(a), 4.13(b) and 4.13(c) respectively
(c)
Fig. 4.13: (a) Maximum principal stress (b) Maximum shear stress (c) Equivalent
elastic strain
By observing the stress field on the modeled specimen, the maximum
principle stress about 505.8Mpa was located at the notch of the significant section
AB. The stress field also show almost similar shape of fracture line specimen that
can be seen during experiment. The maximum shear stress about 253.63MPa located
at the notch. The maximum shear strain about 0.009412µ also located at the notch of
gauge section. Both situations clearly describe that the fracture initiated at the notch
of the significant section AB.
The linearized stress data were used in plotting uniformity of stress along the
significant section AB as shown in Fig. 4.14. The stress was found uniform at the
middle and high at the both end. This confirmed that the state of ―pure shear‖ stress
was form regarding to the direction of load applied. The high stress located at the
both end of significant section is due to effect of notch which generated stress
concentration.
64
Fig. 4.14: Stress distribution along significant section AB of aluminium due to shear
loading
4.4.3 Finite Element Analysis Result for Tensile Loading of Epoxy
A load step of 100N was applied to the modelled specimen until it reach
ultimate loading. All the data gathered from the gauge section as shown in Table
4.13.
Table 4.11: Analysis result for tensile loading of Selfix Carbofibre epoxy
Load (kN) Normal Stress (MPa) Normal strain, µx
0.1 1.5702 162.03
0.2 3.1404 324.06
0.3 4.7107 486.08
0.4 6.2809 648.11
0.5 7.8511 810.14
0.6 9.4213 972.17
0.7 10.992 1134.2
0.8 12.562 1296.2
0.89 13.923 1436.7
65
From table, it can be seen that maximum stress generated at the gauge section
about 24.437 Mpa, which also indicate as shear strength. The maximum shear strain
was 1436.7µε when ultimate load applied.
The stress and strain data were used in plotting the stress versus strain curve
as shown in Fig. 4.15. The stress-strain curve show that strain was linearly
propagated. From the curve, it can shear modulus of material was found about
96.97GPa which indicate the gradient of the curve.
Fig. 4.15: Stress-strain curve for epoxy
From experiment, the epoxy specimens failed in direction of tensile principle
stress when ultimate load about 886.69N are applied to the specimen. Therefore,
finite element analysis on the maximum principle stress, maximum shear stress and
maximum shear strain regarding to the ultimate shear loading condition are shown in
Fig 4.16(a), 4.16(b) and 4.16(c) respectively
Fig. 4.16: (a) Maximum principal stress (b) Maximum normal stress (c) Equivalent
elastic strain
66
By observing the stress field on the modeled specimen, the maximum
principle stress about 52.4Mpa was located at the notch of the significant section AB.
The maximum normal stress about 48.76Mpa located at the notch. The maximum
shear strain about 5850µ also located at the notch of gauge section. Both situations
clearly describe that the fracture initiated at the notch of the significant section AB.
The linearized stress data were used in plotting uniformity of stress along the
significant section AB as shown in Fig.4.17. The stress was found uniform at the
middle and high at the both end. This confirmed that the state of tensile stress was
form regarding to the direction of load applied. The high stress located at the both
end of significant section is due to effect of notch which generated stress
concentration.
Fig. 4.17: Stress distribution along significant section AB of Selfix Carbofibre epoxy
due to tensile.
4.4.4 Finite Element Analysis Result for Tensile Loading of Aluminium
A load step of 1000N was applied to the modelled specimen until it reach
ultimate loading. All the data gathered from the gauge section as shown in Table 4.1.
67
Table 4.12: Analysis result for tensile loading of Aluminium
Load (kN) Normal Stress (Mpa) Normal strain, µx
1.0 31.606 368.79
2.0 63.212 737.58
3.0 94.818 1106.4
4.0 126.42 1475.2
5.0 158.03 1844
6.0 189.64 2212.8
6.6 208.91 2437.7
From table, it can be seen that maximum normal stress generated at the gauge
section about 208.91 Mpa. The maximum shear strain is 2437µ when ultimate load
were applied.
The stress and strain data were used in plotting the stress versus strain curve
as shown in Fig. 4.18. The stress-strain curve show that strain was linearly
propagated. From the curve, it can shear modulus of material was found about
85.7GPa which indicate the gradient of the curve.
Fig. 4.18: Stress-strain curve for aluminium
From experiment, the epoxy specimens failed in direction of tensile principle
stress when ultimate load about 6609.9N are applied to the specimen. Therefore,
finite element analysis on the maximum principle stress, maximum shear stress and
68
maximum shear strain regarding to the ultimate shear loading condition are shown in
Fig 4.19(a), and 4.20(c) respectively.
Fig. 4.19: (a) Maximum principal stress (b) Maximum normal stress (c) Equivalent
elastic strain
By observing the stress field on the modelled specimen, the maximum
principle stress about 787Mpa was located at the notch of the significant section AB.
The maximum normal stress about 731Mpa located at the notch. The maximum
normal strain about 10142µ also located at the notch of gauge section. Both
situations clearly describe that the fracture initiated at the notch of the significant
section AB.
The linearized stress data were used in plotting uniformity of stress along the
significant section AB as shown in Fig. 4.20. The stress was found uniform at the
middle and high at the both end. This confirmed that the state of tensile stress was
form regarding to the direction of load applied. The high stress located at the both
end of significant section is due to effect of notch which generated stress
concentration.
69
Fig. 4.20: Stress distribution along significant section AB of aluminium due to
tensile.
4.4.5 Finite Element Analysis Result for Tensile Shear Loading of Epoxy
A load step of 100N was applied to the modelled specimen until it reach
ultimate loading. All the data gathered from the gauge section as shown in Table
4.15.
Table 4.13: Analysis result for tensile Shear Loading of Selfix Carbofibre epoxy
Load Y Direction
(kN)
Load X Direction
(kN)
Magnitude
(N)
Principle Stress
(Mpa)
0.1 0.1 0.141 3.576
0.2 0.2 0.283 7.1521
0.3 0.3 0.424 10.728
0.4 0.4 0.566 14.304
0.5 0.5 0.707 17.88
0.522 0.522 0.739 18.684
From table, it can be seen that maximum principle stress generated at the
gauge section about 18.684Mpa.
70
From experiment, the epoxy specimens failed in direction of tensile principle
stress when ultimate load about 738.9N are applied to the specimen. Therefore, finite
element analysis on the maximum principle stress is shown in Fig 4.21.
Fig. 4.21: (a) Maximum principal stress
By observing the stress field on the modelled specimen, the maximum
principle stress about 326Mpa was located at the notch of the significant section AB.
This situation clearly describe that the fracture initiated at the notch of the significant
section AB. In addition, the high stress generated due to existence of bending
moment.
The linearized stress data were used in plotting uniformity of stress along the
significant section AB as shown in Fig. 4.22. The stress was found concentrated only
at one end of significant section AB. This situation can be considered that the stress
generated due to bending. The high stress located at the both end of significant
section is due to effect of notch which generated stress concentration.
71
Fig. 4.22: Stress distribution along significant section AB of aluminium due to
tensile shear load.
4.4.6 Finite Element Analysis Result for Tensile Shear Loading of Aluminium
A load step of 500N was applied to the modelled specimen until it reach
ultimate loading. All the data gathered from the gauge section as shown in Table
4.16.
Table 4.14: Analysis result for tensile shear loading of aluminium
Load y direction
(kN)
Load x direction
(kN)
Magnitude
(kN)
Principle Stress
(Mpa)
0.5 0.5 0.707 35.508
1.0 1.0 1.414 71.016
1.5 1.5 2.121 106.52
2.0 2.0 2.828 142.03
2.5 2.5 3.535 177.54
3.0 3.0 4.141 213.05
3.5 3.5 4.949 248.56
3.85 3.85 5.579 275.72
72
From table, it can be seen that maximum stress generated at the gauge section
about 275.71Mpa, which also indicate as shear strength.
From experiment, the aluminium specimens failed in direction of tensile
principle stress when ultimate load about 5579N are applied to the specimen.
Therefore, finite element analysis on the maximum principle stress regarding to the
ultimate tensile shear loading condition are shown in Fig 4.23.
Fig. 4.23: (a) Maximum principal stress
By observing the stress field on the modelled specimen, the maximum
principle stress about 4813Mpa was located at the notch of the significant section
AB. This situation clearly describe that the fracture initiated at the notch of the
significant section AB. In addition, the high stress generated due to existence of
bending moment.
The linearized stress data were used in plotting uniformity of stress along the
significant section AB as shown in Fig. 4.24. The stress was found concentrated only
at one end of significant section AB. This situation can be considered that the stress
generated due to bending. The high stress located at the both end of significant
section is due to effect of notch which generated stress concentration.
73
Fig. 4.24: Stress distribution along significant section AB of aluminium due to
tensile shear load.
4.5 Notch Sensitivity Analysis
From finite element analysis, it can be seen that stress concentration take
place at the notch of significant section AB. There were three notch radii selected to
determine most appropriate radius of 1.5mm, 2.5mm, and 3.5mm. Both Selfix
Carbofibre and aluminium with brittle and ductile behaviour respectively, were used
in this analysis to identify the effect on notch radius. The linearized stress data were
used in plotting neutralized stress with different notch radius along the significant
section AB as shown in Fig. 4.25, Fig. 4.26, Fig. 4.27, and Fig 4.28.
74
Fig. 4.25: Effect of notch on stress distribution of Selfix Carbofibre due to shear
load.
From Fig 4.26, the effect of notch was found higher when 1.5mm radius on
Selfix Carbofibre epoxy, which resulting about 20% high of stress than average value
1. The notch effect reduced as an increase of notch radius. Therefore, the most
optimum notch was 3.5mm as it provides most uniform stress along significant
section AB.
Fig. 4.26: Effect of notch on stress distribution of Selfix Carbofibre due to tensile
load.
From Fig. 4.27, it can be seen that the effect of notch to tensile stress of
Selfix Carbofibre epoxy reduce as increase of notch radius. Therefore, the uniformity
of stress can be improved by increasing the notch radius until it reaches optimum
value.
75
Fig. 4.27: Effect of notch on stress distribution of aluminium due to shear load.
From Fig. 4.25, the effect of notch was found higher when 1.5mm radius on
Aluminium, which resulting about 5% high of stress than average value 1. Therefore,
the most optimum notch was found between 2.5mm and 3.5mm as it provides most
uniform stress along significant section AB.
Fig. 4.28: Effect of notch on stress distribution of aluminium due to tensile load.
From Fig 4.26, it can be seen that the effect of notch to tensile stress of
Aluminium reduce as increase of notch radius. Therefore, the uniformity of stress
can be improved by increasing the notch radius until it reaches optimum value.
76
4.6 Tensile Test Performance Analysis
According to Arcan et.al, tensile stress can be produce to the butterfly
specimen when applying load at α=0°. In order to measure the performance of tensile
data of both materials, ASTM data of each material was introduced in the analysis as
the reference. Two selection of notch radius of 2.5mm and 3.5mm from Arcan
method was made to identify the notch effect on tensile data. The stress versus strain
data of Selfix Carfibre epoxy and aluminium were used in plotting stress versus
strain curve as show Fig. 4.29 and Fig. 4.30 respectively.
Fig. 4.29: Stress-strain curve of Selfix Carbofibre epoxy with different notch radius.
Fig. 4.30: Stress-strain curve of aluminium with different notch radius.
77
From both Fig.4.29 and Fig. 4.30, it can be seen the gradient of each curve
indicate the tensile modulus of the material. The tensile modulus of both materials
from ASTM was found almost the same with experimental data. By comparing both
notches of Arcan test method with ASTM data, it was found that 1.5mm of notch
radius showing large percentage of difference. This means that notch effect take
place in the performance of tensile data of Arcan test method. Based on the data, the
performance of tensile data can be improved by increasing notch radius.
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CHAPTER 5
CONCLUSION AND RECOMMENDATION
5.0 Conclusion
The major conclusions that can be made from this study are summarised as
follows;
i. The study objective to finite element modelling of the butterfly
specimen was achieved. The significant section of butterfly specimen
has proven that Arcan test was reliable, as the shear stress and strain
relationship was linearly propagated. The existences of normal strain
indicate that pure shear loading are not perfectly produce by Arcan
test. But the result can be accepted since the value was too small.
ii. The stress distribution through specimen body can be observed. The
location of maximum stress and maximum strain can be determined
where the failure and fracture initiate.
iii. The uniformity of stress along significant section AB affected by
notch. A notch with 1.5mm radius still not sufficient to overcome
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stress concentration especially for brittle and ductile material. For
shear test epoxy, the optimum radius was 3.5mm. For shear test of
aluminium, the optimum radius was between 2.5mm and 3.5mm.
iv. The tensile test from Arcan test method capable to perform reliable
tensile data. The present of notch affected the performance of tensile
test.
v. The performance of improve as increasing the notch radius in order to
reduce stress concentration.
5.1 Recommendation
Some of the recommendation will be suggested here in order to obtain a
better test result in the future;
i. The designs of the butterfly mould need to be modified to reduce
stress concentration effect especially at the notch area of butterfly
specimen.
ii. A number of specimens have to be increased in order to obtain
consistent data for accurate result.
iii. Modification on butterfly specimen design for tensile test by
introducing gauge location.
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82
APPENDIX
Fig. A1 Type and dimension of Dumbbell shape specimen
Fig. A2 Engineering drawing of epoxy adhesive butterfly specimen mould
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Fig. A3 Engineering drawing of modified Arcan shear test fixture