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Test Method for Tensile Strength of FRP like Brittle Materials
Test Method for Tensile Strength of FRP like Brittle Materials Page 2 of 94
EXECUTIVE SUMMARY Understanding Fibre Reinforced Polymer behaviour is still a huge area of investigation because of the
complexity and difficulties in analysis of this material. Available tensile test standards methodology
does not accurately account for FRP’s nature as current test results, presented in many research papers,
show a large scatter and give lower tensile parameters than expected or specified by the manufacturers.
Therefore, the aim of this research was to improve the existing and most common industry standard of
tensile testing ASTMD3039/D3039M-08 of FRP by developing a reliable test method that captures more
accurately FRP’s tensile parameters: the ultimate strain, the ultimate stress and the Young’s modulus.
This research is a thorough study of tensile testing of FRP like brittle materials and is based on a
population of 44 specimens that were tested in tension until failure according to the specification
contained within the ASTM D3039. The research provided improvements to both experimentation
procedures in order to increase the quality control of the CFRP coupons as well as to the analysis by
accounting for the bending effects induced in the specimens during testing. Five analysis methods are
introduced, which consist of both existing (ASTM D3039, the Rule of Mixtures) and proposed
(Method ‘1’ – Jakubowski and Rycerz 2012 as well as Method B&B and Axial Method – both being
proposals of the Author) methods. Lastly, the validity of the results is checked by the statistical analysis
and how closely they represent the predictions produced by the Rule of Mixtures.
Overall, the analysis described by the Method B&B is recommended to replace the existing standard
method ASTM D3039 by giving higher values for ultimate strain and stress by 8.22 % and 8.31 %
accordingly, whereas it adopted the approach for Young’s modulus determination with 7.51 %
dispersion.
It can be concluded that the aim of the project, to introduce improvements to the existing industry
standard of tensile testing ASTM D3039, was successfully achieved by meeting all defined objectives.
Therefore, this research is believed to have far reaching implications and the beneficiaries will include
FRP design specialists and FRP manufacturers as the tensile parameters are fundamental for
underpinning any structural design and analysis work.
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Table of Contents Executive Summary............................................................................................................................................................... 2
Table of Contents .................................................................................................................................................................. 3
Notation ................................................................................................................................................................................ 7
Tensile Parameters ........................................................................................................................................................... 7
Rule of Mixtures ................................................................................................................................................................ 7
ASTM D3039 Method........................................................................................................................................................ 7
Method ‘1’ ........................................................................................................................................................................ 8
Method B&B ..................................................................................................................................................................... 8
Chapter 1 - Introduction ....................................................................................................................................................... 9
1.1. Problem Statement ............................................................................................................................................... 9
1.2. Aims and Objectives ............................................................................................................................................ 10
Chapter 2 - Literature Review ............................................................................................................................................. 12
2.1. What is Fibre Reinforced Polymer Composite? .................................................................................................. 12
2.1.1. Fibres ............................................................................................................................................................. 12
2.1.2. Polymer Matrix ............................................................................................................................................. 13
2.1.3. Interface ........................................................................................................................................................ 14
2.1.4. Curing Procedures ......................................................................................................................................... 14
2.2. Mechanical Properties of FRP Composite ........................................................................................................... 14
2.2.1. Ways of Analysing Mechanical Properties of FRP Composite ....................................................................... 16
2.2.1.1. Macromechanics of a Lamina ............................................................................................................... 16
2.2.1.2. Micromechanics of a Lamina................................................................................................................ 16
2.2.2. Rule of Mixtures ............................................................................................................................................ 17
2.3. Methods of Forming FRP Composites ................................................................................................................. 17
2.3.1. Wet Lay-up Method ...................................................................................................................................... 17
2.3.2. Prefabrication of FRP Composites................................................................................................................. 18
2.4. FRP Application ................................................................................................................................................... 18
2.4.1. Strengthening and Retrofitting of Structures ............................................................................................... 18
2.4.2. Flexural Strengthening of Beams .................................................................................................................. 18
2.4.3. Shear Strengthening of Beams ...................................................................................................................... 19
2.4.4. Seismic Retrofitting of Walls and Columns ................................................................................................... 19
2.4.5. Flexural Strengthening of Slabs..................................................................................................................... 19
2.5. FRP Test Methods ............................................................................................................................................... 20
2.5.1. Flat Coupon Test - ASTM D3039/D3039M .................................................................................................... 20
2.5.2. Failure Criteria............................................................................................................................................... 21
2.5.2.1. Intralaminar Failure .............................................................................................................................. 21
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2.5.2.2. Interlaminar Failure .............................................................................................................................. 22
2.5.3. Failure Modes according to ASTM D3039 ..................................................................................................... 22
2.5.4. Split Ring Test ................................................................................................................................................ 23
2.5.5. Novel Methods of FRP Testing ...................................................................................................................... 23
2.5.6. Findings ......................................................................................................................................................... 24
2.6. Tensile Testing of FRP-like Brittle Materials ....................................................................................................... 25
2.6.1. Tensile Testing Proposed Methods ............................................................................................................... 25
2.6.2. Improved Analysis Methods ......................................................................................................................... 26
2.6.2.1. Method ‘1’ ............................................................................................................................................ 26
2.6.2.2. Method ‘2’ ............................................................................................................................................ 27
2.6.2.3. Method ‘3’ ............................................................................................................................................ 27
2.6.3. Results Comparison ...................................................................................................................................... 27
2.6.4. Report’s Conclusions ..................................................................................................................................... 28
2.7. Relevant Researches ........................................................................................................................................... 29
2.7.1. Possible Enhancements to Tensile Testing of FRP ........................................................................................ 29
2.7.1.1. Geometrical Improvements ................................................................................................................. 29
2.7.2. Standard ASTM D3039 Testing ..................................................................................................................... 30
2.8. Chapter Conclusions ........................................................................................................................................... 30
Chapter 3 – Experimental Procedure .................................................................................................................................. 31
3.1. Specimen Preparation and Experimental Set-up ................................................................................................ 31
3.1.1. Safety Precautions & Requirements ............................................................................................................. 31
3.1.1.1. Key Watch Points ................................................................................................................................. 31
3.1.1.2. Required PPE ........................................................................................................................................ 31
3.1.2. Resources ...................................................................................................................................................... 31
3.1.3. Preparation of CFRP Specimens .................................................................................................................... 31
3.1.3.1. Materials .............................................................................................................................................. 32
3.1.3.1.1. Fibres ............................................................................................................................................... 32
3.1.3.1.2. Epoxy Resin ..................................................................................................................................... 33
3.1.3.1.3. Mould .............................................................................................................................................. 33
3.1.3.1.4. Tabs ................................................................................................................................................. 33
3.1.3.2. Preparation Procedure ......................................................................................................................... 34
3.1.3.2.1. Filling the Moulds ............................................................................................................................ 34
3.1.3.2.2. Curing, Inspection & Bonding of Aluminium Tabs ........................................................................... 36
3.1.4. Strain Gauge Application .............................................................................................................................. 37
3.1.5. Testing of CFRP Coupons .............................................................................................................................. 38
3.1.5.1. Improvements to Testing ..................................................................................................................... 38
3.1.5.2. Experimental Set-up and Test Procedure............................................................................................. 38
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3.2. Chapter Conclusions ........................................................................................................................................... 39
Chapter 4 – Data Analysis ................................................................................................................................................... 41
4.1. Control Tests ....................................................................................................................................................... 41
4.2. Failure Modes ..................................................................................................................................................... 42
4.3. Environmental Adjustment of the Raw Data ...................................................................................................... 44
4.4. Rule of Mixtures .................................................................................................................................................. 44
4.4.1. Analysis Approach ......................................................................................................................................... 44
4.4.2. Data Analysis ................................................................................................................................................. 45
4.4.3. Results ........................................................................................................................................................... 45
4.5. ASTM D3039 ....................................................................................................................................................... 46
4.5.1. Analysis Approach ......................................................................................................................................... 46
4.5.2. Data Analysis ................................................................................................................................................. 47
4.5.3. Results ........................................................................................................................................................... 48
4.6. Method ‘1’ .......................................................................................................................................................... 49
4.6.1. Analysis Approach ......................................................................................................................................... 49
4.6.2. Data Analysis ................................................................................................................................................. 50
4.6.3. Results ........................................................................................................................................................... 52
4.7. Proposed Improvements .................................................................................................................................... 53
4.7.1. Method B&B ................................................................................................................................................. 53
4.7.1.1. Analysis Approach ................................................................................................................................ 53
4.7.1.2. Data Analysis ........................................................................................................................................ 55
4.7.1.3. Results .................................................................................................................................................. 55
4.7.2. Axial Method for Ultimate Strain’s Calculation............................................................................................. 56
4.7.2.1. Analysis Approach ................................................................................................................................ 56
4.7.2.2. Data Analysis ........................................................................................................................................ 57
4.7.2.3. Results .................................................................................................................................................. 58
4.8. Chapter Conclusions ........................................................................................................................................... 59
Chapter 5 - Reanalysed Data from Jakubowski & Rycerz 2012 Research ........................................................................... 60
5.1. Coupons with 3 Strain Gauges ............................................................................................................................ 60
5.2. Coupons with 4 Strain Gauges ............................................................................................................................ 61
5.3. Chapter Conclusions ........................................................................................................................................... 63
Chapter 6 – Statistical Summary ......................................................................................................................................... 64
6.1. Statistical Comparisons ....................................................................................................................................... 64
6.2. Chapter Conclusions ........................................................................................................................................... 71
Chapter 7 – Discussion ........................................................................................................................................................ 72
7.1. Overall ................................................................................................................................................................. 72
7.2. Project Planning Review ..................................................................................................................................... 73
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7.3. Future Work ........................................................................................................................................................ 74
Chapter 8 – Conclusions ..................................................................................................................................................... 75
References .......................................................................................................................................................................... 77
Appendix A - Risk Assessment ............................................................................................................................................ 80
Appendix B - Required Resources ....................................................................................................................................... 81
Appendix C - SikaWrap Hex 230C Properties ...................................................................................................................... 82
Appendix D - Sikadur 330 Properties .................................................................................................................................. 82
Appendix E - Failure Modes for CFRP Coupons .................................................................................................................. 83
Appendix F - Author Research Results ................................................................................................................................ 84
F1. Rule of Mixtures ........................................................................................................................................................ 84
F2. ASTM D3039 .............................................................................................................................................................. 85
F3. Method ‘1’ ................................................................................................................................................................. 86
F4. Method ‘B&B’ ............................................................................................................................................................ 87
Appendix G - Jakubowski & Rycerz 2012 Reanalysed Data Results .................................................................................... 87
G1. Coupons with 3 Strain Gauges .................................................................................................................................. 87
G1.1. Rule of Mixture .................................................................................................................................................. 87
G1.2. ASTM D3039 + Axial Method ............................................................................................................................. 88
G1.3. Method ‘1’ ......................................................................................................................................................... 88
G2. Coupons with 4 Strain Gauges .................................................................................................................................. 89
G2.1. Rule of Mixture .................................................................................................................................................. 89
G2.2. ASTM D3039 + Axial Method ............................................................................................................................. 89
G2.3. Method ‘2’ ......................................................................................................................................................... 90
G2.4. Method ‘3’ ......................................................................................................................................................... 90
Appendix H - Test Data vs. Predictions for Dataset of 29 Coupons .................................................................................... 91
Appendix I - Project Planning .............................................................................................................................................. 92
I1. Critical Activities ......................................................................................................................................................... 92
I2. Milestones.................................................................................................................................................................. 92
I3. Gantt Charts ............................................................................................................................................................... 93
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NOTATION
TENSILE PARAMETERS
RULE OF MIXTURES
[
⁄ ]
ASTM D3039 METHOD
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METHOD ‘1’
METHOD B&B
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1. CHAPTER 1 - INTRODUCTION
In recent years, there has been an ever-growing interest in the use of innovative methods in structural
and civil engineering industries. One particular group of materials dominates in these fields. These are
composite materials, which have been around for a long time and solved many technological problems.
They captured the attention of the construction industry in the year 1960 with the introduction of
polymeric-based composites. They have a great potential to replace widely used materials in
engineering, such as steel or aluminium. For example by replacing steel with composite elements, 60 to
80% of component weight can be saved (Mazumdar, 2002). This introduces huge advantages, such as
lower application costs, smaller additional permanent loading when strengthening, or shifted design
boundaries, which are usually limited by weight of the structure.
Among all, there is one particular composite material prevailing in our modern society – Fibre
Reinforced Polymer (FRP). It was developed in the 1990s (Teng et al., 2002) and is widely used in
automotive, aerospace, recreational and marine industries (Jain et al., 2012). The main reasons for
moving away from the universally known materials like steel are demand for increase in profits,
improvement in productivity and decrease in failings as well as accidents. Other factors that drive
construction industry towards fibre-reinforced polymers are improved durability and safety along with
reductions in labour costs and construction time (Hollaway, 2009a). Therefore, FRP brings a lot of
advantages over commonly used construction materials. There is a growing need for composite
materials and production expected to reach ten million tonnes at the end of 2025 (Bunsell, 2005). Thus,
FRP has already been very well received by the market. The UK Department of Trade and Industry
stated that “the UK fibre-reinforced polymer (FRP) composite industry produces 240 000 t of FRP
products a year, with 11% of this being used in the construction industry” (Conroy et al., 2005).
1.1. PROBLEM STATEMENT
There are several Fibre Reinforced Polymers (FRP) applications in civil engineering industry. FRP is
used in the new construction as reinforcement in bridge decks and concrete, or as a formwork for
manufacturing entire elements (Jain et al., 2012). The alternative methods such as FRP strengthening
show their merits in the large number of ageing structures that require increased maintenance. Cost is
the main influencing factor whilst deciding on strengthening structural components with FRP because a
complete replacement of the structure often leads to a large financial burden. The most common way of
strengthening existing structures to increase their load carrying capacity is an external bonding of FRP
to structural members i.e. bonding FRP plates to beams or wrapping the columns (Darby, 1999).
A high demand and new manufacturing techniques have steadily decreased the initially very high costs
of FRP material (Teng et. al., 2002). This became possible thanks to great amount of research work
happening over recent decades, which produced a constantly growing number of research papers
(Rycerz, 2012). However, understanding FRP behaviour is still a huge area of investigation because of
the complexity and difficulties in analysis of FRP (Yu et al., 2009). The majority of research concentrates
mainly on material behaviour under loading, internal interaction between FRP’s constituents (fibres vs.
matrix) as well as FRP behaviour with other materials like concrete i.e external FRP plating of RC
members (Hollaway and Leeming, 1999).
The presented research looks into behaviour of FRP under tensile loading and will investigate the
current state of tensile testing of FRP as this property underpins all of its applications in the industry.
Available tensile test standards are based on the knowledge of a common construction material - steel.
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Therefore, the methodology does not accurately account for FRP’s nature as current test results,
presented in many research papers, show a large scatter and give lower tensile parameters than
expected or specified by the manufacturers (Rycerz, 2012). Therefore, the development of a reliable
test method that captures FRP’s tensile parameters is required and will be identified in this research. It
is going to be accomplished by providing more accurate measurement data through improvements
made to both specimens’ preparation and analysis in order to validate an improved method of tensile
testing previously proposed by Jakubowski and Rycerz in their BEng report 2012. This method will be
compared to the current standard – ASTM ASTMD3039/D3039M-08 and cross checked with theoretical
values obtained using the Rule of Mixtures. The outcome of this research is believed to have far
reaching implications and the beneficiaries will include FRP design specialists and FRP manufacturers
as the tensile strength is a fundamental property underpinning any design work.
1.2. AIMS AND OBJECTIVES
The aim of this research is to improve the existing and most common industry standard of tensile
testing ASTMD3039/D3039M-08 of FRP by developing a reliable test method that captures more
accurately FRP’s tensile parameters. FRP’s properties are very sensitive to fabrication because of
material complexity; therefore a lot of care needs to be taken in sample preparation and testing
(Jakubowski, 2012). Hence, it has been identified that the improvements can be made to both the test
method and data analysis in order to increase the accuracy, repeatability, and reliability of derived
tensile parameters i.e. tensile strength, ultimate strain and chord modulus, which ultimately leads to
improved and more accurate structural design and analysis.
To achieve the aim of the project, a number of objectives need to be satisfied. They were identified
based on those proposed by Jakubowski and Rycerz in their report 2012 and updated to meet the
improvements proposed by the Author:
Undertake a comprehensive literature review in order to gather broad knowledge on the
investigated subject;
Obtain raw data from the tests carried out by Jakubowski and Rycerz 2012;
Prepare a series of CFRP rectangular test specimens according to the guidelines given in
ASTMD3039/D3039M-08 with slightly altered preparation techniques to identify any
improvements or recommendations to the standard technique (Section 3.1.);
Test the specimens according to the ASTMD3039/D3039M-08 standard for Flat Coupon Tests
using Instron 4505 Universal Testing Machine with introduced improvement to account for
laboratory varying conditions or heating from the current supplying power to the data logger
(Section 3.1.5.) and record the stress-strain response for each coupon using strain gauges and
data logger;
Analyse the tension test data obtained from a number of tensile tests according to:
o The Rule of Mixtures (Section 4.4.)
o The ASTM D3039 standard (Section 4.5.)
o The Method ‘1’ proposed by Jakubowski and Rycerz 2012 (Section 4.6.)
o Proposed any further improvements to the analysis methods (Section 4.7.)
Review, reanalyse, compare and critically evaluate the previous work completed by Jakubowski
2012 and Rycerz 2012 in the light of this research (Chapter 5);
Provide a comparison of the results obtained from the proposed methods by performing
statistical analysis to validate any differences in the analyses (Chapter 6);
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Provide overall discussion and draw conclusions with recommendations to the choice of the
method that provides the most reliable test results and tensile parameters, in a format that will
be used for publication purposes (Chapter 7);
Identify and propose any improvements or requirements for future analysis.
The above objectives are presented in the chronological order. The key objectives to satisfy the aim of
the project are testing a wide range of CFRP specimens and obtaining the raw test results from
Jakubowski and Rycerz 2012 in order to have a statistically significant database from which conclusions
and proposed changes to the ASTMD3039/D3039M-08 standard can be drawn.
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2. CHAPTER 2 - LITERATURE REVIEW
This chapter provides a comprehensive literature overview in order to provide broad knowledge on
Fibre Reinforced Polymers as a composite material with the aim to identify possible improvements to
the preparation as well as analysis procedures. The composite components’ properties as well as
structural composition at micro level determine the mechanical and physical properties of the FRP that
this research looks into. Therefore, the chapter will look into different levels of FRP formation and
properties as well as its applications in the industry. For this purpose various test methods are
introduced and discussed that will aid better understanding of the aim of the research and provide a
base for comparison.
2.1. WHAT IS FIBRE REINFORCED POLYMER COMPOSITE?
Fibre reinforced polymer or fibre-reinforced plastics (abbreviated as FRP) is a composite material,
which consists of two or more substances in order to create a new matter exhibiting a combination of
properties that are far more efficient than functions of a single substance. The properties as well as a
microscopic structural composition of those components determine the mechanical and physical
properties of FRP. Therefore, a good knowledge of the material properties is required to perform the
design and analysis of FRP structural section (Hollaway, 2009a).
FRP is composed of fibres and a matrix, hence it exhibits anisotropic properties. The function of the
fibre is to produce stiffness and strength of the material, while the matrix provides a bonding medium
and shield against environmental impact (Tuakta, 2005).
FRP is more preferable than other materials because, in comparison to steel, it is lighter and stronger,
which is why it became a huge success in the construction industry for reinforcing or retrofitting
structures by replacing standard methods like steel plates. Table 1 looks into the main properties of
FRP and compares them with common civil engineering materials such as steel and concrete. It can be
concluded that FRP is most favourable in terms of tensile strength, weight and corrosion. Its drawbacks
lie in compressive strength and ductility.
Table 1 - FRP vs. Common Civil Engineering Materials
2.1.1. FIBRES
Conventional types of fibres that make up the vast majority of the market and research are Carbon
(CFRP), Glass (GFRP) and Aramid (AFRP) fibres (Ku H. et al., 2011). Fibres are the main load carrying
component of the composite (70 to 90% load carried by fibres), which is due to high modulus of
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elasticity (Table 2 for reference). Their main functions are providing strength of the order of 3000 MPa,
stiffness equivalent to aluminium or even steel and thermal stability. Moreover, they are durable by
being non-corrosive and resistant to chloride attack. Fibres’ light weight can significantly decrease
labour cost and by being non-magnetic and non-toxic at the same time, makes them beneficial in niche
applications. Fibres can also provide electrical conduction or insulation, which purely depends on the
type of fibre used (Mazumdar, 2002 and Burgoyne, 2009). A comparison of the properties of different
fibres vs. bulk materials is shown in Table 2.
Table 2 - Properties of Fibres vs. Conventional Bulk Materials (Mazumdar, 2002)
It is worth pointing out that all types of fibres presented in Table 2 have higher tensile strength, specific
modulus and strength, as well as relative cost when compared to steel or aluminium alloys. Despite
many advantages, fibres also have their weaknesses shown in Table 3 below. The main is brittleness
due to small per cent of elongation at break when compared to bulk materials.
Weaknesses Reasons
“Cost
o In comparison to steel - glass FRP reinforcing bars cost 3 times more whilst aramid or carbon fibres for pre-stressing tendons cost up to 10 times more;
o The FRP manufacturing industry decided to target low-volume hi-cost aerospace industry, rather than low-cost high-volume construction industry.
Brittleness
o Need for application of high safety factors as consequences of failure are severe. This largely increases the costs;
o Inapplicability of plasticity theory that is virtually used in all current codes with the assumption that all materials can deform plastically.
Anchorage o Very difficult to grip fibres, which introduces very high costs.
Durability
o Glass and aramid fibres can hydrolyse in the presence of high alkalinity, which is present in concrete;
o The epoxy resin is prone to various mechanisms of degradation.
Creep & Stress Rupture
o Fibres do not behave in a constant manner. They are prone to stress rupture in which fibres can creep to failure”
Table 3 - Fibre Weaknesses (Burgoyne, 2009)
2.1.2. POLYMER MATRIX
A matrix (polymer) is composed of molecules formed by a chemical combination of identical and much
smaller units of large molecular mass called monomers. The process of polymer formation is called
polymerisation. There are many polymer materials on the market, but they all consist of two main
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components: the resin and the curing agent (hardener) (Hollaway, 2009b). In comparison to fibres, a
matrix has low-modulus and low-strength. In the same respect as fibres, polymer has also crucial
functions to fulfil as part of the composite material, presented in Table 4.
Matrix’s Functions
“to bind together the fibres and protect their surface from abrasion and environmental corrosion; to wet out the fibre and to cure satisfactorily in the manufacturing process; to disperse the fibres and separate them in order to avoid any catastrophic propagation of crack; to transfer stresses to the fibres efficiently by adhesion and/or friction, and in addition, to reduce the
chance of failure in the matrix (..); to be thermally compatible with fibres; to be chemically compatible with the fibres over long periods of time; to have appropriate fire resistance and limit smoke propagation; to provide finish colour and surface finish for connections.”
Table 4 - Matrix's Functions (Hollaway, 2009b)
The two types of polymers that can be distinguished are thermoplastic and thermoset polymers.
Preferred type of matrix in structural applications is thermoset resins. This category encloses epoxies,
unsaturated polyesters, vinylesters, aminos, phenolics, and urethane resins (Mosallam, 2002).
Thermoplastic matrices, however, consist of polypropylene (PP), polyethylene and poly vinyl chloride
(PVC) (Ku et al., 2011).
2.1.3. INTERFACE
It is a surface interaction (physical and chemical bond) between fibres and a polymer. This is the region
where the anisotropic properties of the material are exhibited. Therefore, the quality of the fibre–matrix
interface constitutes the final mechanical and physical properties as well as performance of a composite
(Hollaway, 2009c & Tuakta, 2005). Two assumptions are made when it comes to the analytical and
experimental analysis of a composite material. The first one assumes a perfect bond between fibre and
matrix, hence no strain discontinuity occurs at the interface, which is used in the Rule of Mixtures
approach (Section 4.4). The second assumption says, however, that fibres are arranged in a regular and
repeatable array (Gdoutos et al., 2003).
2.1.4. CURING PROCEDURES
There are two types of curing procedures for fibre-polymer composites. The cold cure method is
undertaken in situ and uses cold cure resin that has two main functions: “to impregnate dry fibres to
form the FRP composite, or to produce an adhesive” (Hollaway, 2009b). This method provides great
flexibility in the application process. The second curing methodology is for automated manufacturing
purposes of structural members with a use of hot cure resin, either for pultrusion, or for the fibre pre-
impregnation, which allows better quality control (Hollaway, 2009b & Teng et al., 2002).
2.2. MECHANICAL PROPERTIES OF FRP COMPOSITE
Fibre-reinforced composites possess high specific strength and moduli through taking an advantage of
low-density continuous fibre embedded in the matrix (Callister, 2007). These desirable mechanical
properties of an FRP composite depend for instance, on the properties of the two component materials
(i.e. the fibre and the polymer) (Yu et al., 2009). Therefore, it is important to understand the behaviour
of a composite in relation to each component that is presented in Fig. 1. Initially both a fibre and a
matrix deform elastically under applied load as seen on Graph (a). When overlapping this behaviour
with the composite stress-strain relationship, it can be noticed that composite roughly yields with the
Test Method for Tensile Strength of FRP like Brittle Materials Page 15 of 94
matrix, which begins to deform plastically, whereas fibre still stretches elastically - Stage II, Graph (b).
Thus, the yield strength of a matrix is significantly lower than tensile strength of a fibre. Therefore, it
can be concluded that the fibre strain dominates the failure and composites strain-stress relationship is
somewhere in between both FRP constituents (Callister, 2007).
Figure 1 - Stress-strain curves for brittle fibre, ductile matrix material and aligned fibre-reinforced composite
(Callister, 2007)
In general all FRP composites exhibit the same stress-strain behaviour under tension, linear elastic until
brittle rupture. Stress-strain curves for GFRP and CFRP are illustrated on Fig. 2 and are contrasted with
ductile nature of mild steel. The main drawback of strengthening with FRP is its brittle nature, which
limits ductile behaviour of RC members. Secondly, brittleness puts restrictions on the redistribution of
stresses within a member or a structure (Teng et al., 2002).
Figure 2 - Typical stress-stain curves showing CFRP, GFRP & mild steel (Teng et al., 2002)
Test Method for Tensile Strength of FRP like Brittle Materials Page 16 of 94
For typical values of FRP composite’s properties refer to Table 5, however it is important to bear in
mind that presented values are only valid for a specific fibre content considered (Teng et al., 2002). It is
also worth mentioning that in obtaining those tensile values, either the fibre sheet thickness (Ahmed,
1999) or a nominal thickness provided by the manufacturer is commonly used. (Teng et al., 2000).
Table 5 - Typical mechanical properties of most common FRP composites (Teng et al., 2002)
2.2.1. WAYS OF ANALYSING MECHANICAL PROPERTIES OF FRP COMPOSITE
Fibre-reinforced polymer composite is created by embedding the continuous fibres in the matrix, which
forms laminae. Then FRP laminate is formed by applying two or more unidirectional laminae on top of
each other. These laminates make the majority of FRP products used in the construction industry. There
are two ways of analysing a unidirectional FRP lamina’s mechanical properties. Macroscopically lamina
is quasi-homogeneous meaning that it has uniform mechanical properties everywhere. On the other
hand, lamina is a combination of two constituents; hence at a microscopic level it is heterogeneous (Yu
et al., 2009). FRP composites are widely used for structural applications; therefore civil engineering is
mainly concerned with mechanical properties at macroscopic level. In order to determine those
properties a two-step analysis is commonly undertaken. The first step looks into mechanical properties
of two constituent materials and their volume fraction by performing micromechanical analysis.
Secondly, by using classic lamination theory the mechanical properties of the laminate are established
by undertaking macromechanical analysis (Yu et al., 2009).
2.2.1.1. MACROMECHANICS OF A LAMINA
FRP lamina at this level has different elastic modulus, shear modulus and Poisson’s ratios which vary
with direction. It is because of different mechanical properties of the fibres in a longitudinal direction in
comparison to other two orthogonal directions. Therefore, unidirectional FRP lamina is taken to be
treated as an orthotropic material (Yu et al., 2009).
2.2.1.2. MICROMECHANICS OF A LAMINA
It has been said that FRP lamina is heterogeneous, which means that it is formed from two constituents:
a fibre and a polymer. Hence, the mechanical properties are obtained from those two materials and
their volume fraction. Considering the local stresses, deformations and interactions of fibres and a
matrix, the micromechanics approach is undertaken in mechanical properties determination (Jones,
1999; Daniel and Ishai, 2006). There are many of them available, but only two are regarded as simple
and hence are used widely (Yu et al., 2009):
1. Mechanics of materials approach
2. Semi-empirical approach
However, detailed overviews of these two methods are outside the scope of this research. Only a basic
method of mechanics of materials approach is presented below, which will be used as one of the
Test Method for Tensile Strength of FRP like Brittle Materials Page 17 of 94
theoretical methods of analysis to produce predictions of results, which will be compared to ASTM
D3039 standard.
2.2.2. RULE OF MIXTURES
The fibres and the matrix have the same strain in a particular direction under the assumption that two
constituents of the FRP lamina with uniaxial loading applied deform compatibly in the longitudinal
direction (fibre direction). This means that Bernoulli’s assumption of ‘plane sections remain plane’
stays valid. Hence, based on the above assumptions, the rule of mixtures allows estimating the
longitudinal modulus of laminae E1 – an upper limit of the elastic modulus of the composite. The
fundamental Rule of Mixture’s equation is:
(2.1)
The above relationship shows a linear relation between the longitudinal modules of lamina (Ef & Em)
and the volume fractions of fibres, Ef, and matrix, Em. Knowing that fibres are much stiffer than the
matrix, the E1 value is dominated by fibre property. The research results confirmed that Eq. 2.1
produces good estimations (Yu et al., 2009). It is important to keep in mind that the above Eq. 2.1 is
based on the assumption of uniform distribution of fibres within the matrix. However, in reality, under
laboratory conditions the fibres come into contact with each other as well as are randomly scattered in
the matrix (Jones, 1999). To account for these effects, other approaches are taken into consideration
such as the Halpin-Tsai equation; however they introduce complexity and are not a part of this paper’s
investigation.
2.3. METHODS OF FORMING FRP COMPOSITES
There are two methods of application that are most commonly used in civil engineering for
strengthening structures with FRP composite: the wet lay-up method and the prefabrication process.
They differ in terms of place of fabrication, cost of application/production and quality of the final
product (Teng et al., 2002).
2.3.1. WET LAY-UP METHOD
It is an in-situ method pictured in Fig. 3, which requires skilled labour and involves direct application of
a resin to a unidirectional carbon tow sheet or a woven glass fabric. This method is versatile as it allows
wrapping different shapes like corners and curved surfaces etc. (Teng et al., 2002). It is also the
cheapest alternative to all other bonding methods. However, it is difficult to control the quality of FRP
composite application (Pham et al., 2005).
Figure 3 - Beam FRP wet lay up (CPS Construction Group, 2012)
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2.3.2. PREFABRICATION OF FRP COMPOSITES
Prefabrication results in a very good quality control as it is done in a controlled, factory environment. It
is thanks to computer-controlled machinery that also allows for a high productiveness (Ye et al., 2010).
However, the use of technology leads to increase in the cost of the material. This method is used for
example for flexural strengthening by pultrusion for plates as well as for column strengthening by
filament winding for FRP shells for confining the columns (Teng et al., 2002). Some common shapes of
FRP Products are shown on Fig. 4 below.
Figure 4 - Different shapes of FRP products (T&D Publications, 2013)
2.4. FRP APPLICATION
Advanced polymer composites are used widely in the construction industry for rehabilitation and
retrofitting of metallic, masonry, and timber structural members as well as prestressed and reinforced
concrete (abbreviated as PC and RC respectively). Apart from restoration possibilities in construction,
FRP is also used in prestressed and post-tensioned tendons or as FRP rebar reinforcement for RC
(Hollaway, 2009a).
2.4.1. STRENGTHENING AND RETROFITTING OF STRUCTURES
Every structure reaches the end of its design life or becomes deficient for various reasons. These can
happen in a result of an environmental attack (corrosion, cracking), change of design codes and loads,
or alteration of the structure by changing its function, removing columns etc. Therefore, there is always
a question whether the place should be demolished or strengthened. The latter seems often more
attractive. For this purpose FRP becomes very effective and advantageous as it has high strength, low
weight, very good corrosion resistance and it is easy to apply. There are number of ways and purposes
of strengthening deficient structural members which are presented below (Hollaway, 2009d).
2.4.2. FLEXURAL STRENGTHENING OF BEAMS
Traditionally, there are two methods for this type of strengthening: external post-tensioning or bonding
of steel plates. The main shortcomings of these methods are difficult application and low durability. In
recent years, flexural strengthening with FRP plates became more popular, resulting in replacement of
steel plates. The replacing material offers higher strength and lightness, which led to a substantial
research in this field. As mentioned previously, the FRP plate may be prefabricated or applied in a wet
lay-up process to the tensile face of an RC beam. However, before any application takes place, the
surface needs to be adequately prepared in order to remove weak surfaces, expose aggregate for better
bonding and even-up the surface.
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The soffit plates might be either unstressed or prestressed, however in each scenario the type of
anchorage system plays very important role, so U strips at the plate ends or steel bolts are in interest of
reducing the risk of debonding (Teng et al., 2002). However, there are number of failure modes
associated with this type of strengthening technique such as:
Flexural failure that involves FRP rupture or concrete compression failure;
Beam shear failure;
Debonding failure occurring through concrete cover separation or plate end interfacial
debonding;
Intermediate crack induced interfacial debonding (Teng et al., 2002).
Out of all, flexure failure is the best scenario because of its ductile behaviour, which means that the
stress redistribution is possible and a warning is given before catastrophic failure happens, which may
be a threat to occupants’ life (Teng et al., 2002).
2.4.3. SHEAR STRENGTHENING OF BEAMS
Along with flexural failures discussed above, shear failures are the second most common types of
failures of unstrengthened RC beams. They are greatly undesirable as they lead to brittle failure that is
sudden and catastrophic to both the structure, and its residents. Knowing that flexural failure is
preferred over shear failure implies that the beam must have shear capacity exceeding flexural capacity.
The proposed methods to accomplish that include side bonding, U jacketing, or wrapping. Use of FRP
strips or sheets along with different orientation or distribution of fibres can lead to many different
strengthening schemes. All of the above should be carefully considered to produce the best possible
strengthening solution. The typical failure modes associated with shear strengthening technique are
shear failure with or without FRP rupture and shear failure due to FRP debonding (Teng et al., 2002).
2.4.4. SEISMIC RETROFITTING OF WALLS AND COLUMNS
Vertical elements of the building such as walls or columns are very susceptible to cyclic lateral motion
of the ground. This type of loading is experienced by the structural element during an earthquake event.
Hence, the structural members or a whole structure have to behave in ductile manner in order to
diminish the possibility of collapse. For this reason retrofitting is used, which is divided into retrofitting
for strength and retrofitting for ductility. The former is achieved by bonding FRP sheets, so that the
fibres are aligned in the longitudinal direction. The latter is achieved by external FRP jackets, which can
be formed in a wet lay-up process through wrapping, filament winding or application of prefabricated
shell jackets. The purpose of these strengthening techniques is to mitigate the following failure modes:
shear failure, flexural plastic hinge failure, or lap splice failure (Teng et al., 2002).
2.4.5. FLEXURAL STRENGTHENING OF SLABS
There is much less research done in the field of flexural strengthening of slabs. The reasons for that are
complexity and cost involved in a laboratory slab preparation and testing. Moreover, the failure
mechanism is much more complex than in the RC beam testing. The strengthening scheme of slabs
involves either FRP strips, or FRP sheets, which are bonded to the tensile face of the slab. Use of wider
strips is preferred over narrow strips because of the larger contact area (Teng et al., 2002).
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2.5. FRP TEST METHODS
There are many test methods available to determine the properties of composite materials. However
they are not fully exploited and standardised yet as it is with metals. The differences in the properties of
two testing media are presented in the Table 6 below. Other reasons for variations in the test data are:
the chosen test method, the specimen’s design, the composite fabrication method and the void content
(Munjal, 1989).
Table 6 - Metals vs. Composite Testing (Munjal, 1989)
A comprehensive overview of existing methods for determination of tensile properties of FRP materials
was compiled by Ashok K. Munjal and is presented in Table 7 below.
Test Method Overview
ASTM D638
o Dog-bone shape specimens with dimensions of 165.1 mm x 19.05 mm and thickness of 3.2 mm;
o Problems arise with the testing machine and load transfer due to the unique shape (Hylton, 2004).
ASTM D2290 o Split disk test method for apparent tensile strength; o Recommended quality control – initial fibre/resin screening (Davé et al., 2000).
ASTM D2585 o Method of preparation and tension testing of filament-wound pressure vessels; o Relatively expensive (Davé et al., 2000).
ASTM D3039
o Rectangular flat coupons test; o Standardised method for testing composites in industry; o Recommended for designs (ASTM D3039, 2008).
Table 7 – Different Methods Overview
2.5.1. Flat Coupon Test - ASTM D3039/D3039M
Standard test method for testing polymer matrix composites that allows in-plane tensile properties to
be determined. Rectangular coupons are placed in the grips of the mechanical testing machine (for
example Instron 4505) and monotonically loaded. The maximum force before specimen’s failure allows
for an ultimate strength calculation. When using strain gauges, the stress-strain response can be
recorded and this allows deriving the ultimate tensile strain, the tensile modulus of elasticity, Poisson’s
ratio, and transition strain for specimens that show a bilinear response. Tensile unidirectional specimen
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geometry recommendations are 25 mm in length, 15 mm in width and 1.5 mm in thickness. The
standard method also emphasises the use of tabs when testing unidirectional specimens to prevent
gripping damage and premature failure (ASTM D3039, 2008). However, for detailed guidelines refer to
the complete ASTM D3039 standard which goes step by step through sample preparation and testing.
Standard method described by ASTM D3039 gives also guidance for analysing tensile data for three
strain gauges set up that is summarised in Section 4.5. It is important to mention that close attention
has to be paid to factors affecting the tensile response and any deviations needed to be reported as they
can have a significant impact on the final results. These include, but are not limited to:
the material itself;
the material’s preparation and lay-up;
the specimens curing;
the environment of preparation of specimens and testing;
the specimens alignment and gripping;
the rate of testing;
the void content (ASTM D3039, 2008).
It is important to recognise that one of the crucial factors in determining FRP parameters is its failure.
Therefore, general overview of the FRP failure in terms of its structure is described below at different
levels, with a discussion leading to failure modes issues associated with the Tensile Testing of FRP
Composites according to ASTM D3039 standard.
2.5.2. FAILURE CRITERIA
When describing FRP composite, it is necessary to know its failure modes, and why particular
phenomenon occurs and its implications. In general, as for any composite material, the FRP has a
complex failure mechanism that depends on factors such as a stress state, the properties of the fibres
and the matrix, and a direction as well as layered arrangement of fibres (Jones, 1999 & Daniel and Ishai,
2006). At the microscopic level the FRP failure can be associated with three elements or their various
combinations. These are fibre failures like rupture, buckling or splitting, matrix failure (transverse
tension, transverse compression, shear) (Soden et al., 1998) and fibre-matrix failure. The prediction of
the strength and the failure of an FRP composite is therefore very difficult despite numerous
microscopic approaches, which have their attributes in predicting mechanical properties of the FRP
composite (Daniel and Ishai, 2006). From macroscopic point of view, there are two common failure
modes: the intralaminar and the interlaminar failure.
2.5.2.1. INTRALAMINAR FAILURE
This type of failure is associated with the failure inside individual laminae that is caused by stresses and
strains in each layer. There are four most popular failure criteria for that: the maximum stress criterion,
the maximum strain criterion, the Tsai-Hill criterion, and the Tsai-Wu criterion. They are based on the
strength parameters of lamina subjected to in-plane loading. These parameters are the longitudinal
tensile or compressive strength, transverse tensile or compressive strength, and in-plane shear strength
(Yu et al., 2009).
According to experimental studies, the best effectiveness in predicting the strength parameters has the
Tsai-Wu criterion. However, the maximum stress and strain criterion creates significant errors (Soden
et al., 1998). The interaction between four different criterions is illustrated on Fig. 5 underneath.
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Figure 5 - Comparison of four different failure criteria (Yu at al., 2009)
2.5.2.2. INTERLAMINAR FAILURE
It is associated with the failure between adjacent laminae that can occur through either a separation of
the bonded laminae, or sliding of adjacent laminae. They are caused respectively by interlaminar
normal and interlaminar shear stresses (Yu et al., 2009). These stresses occur near free edges and
hence are called ‘free-edge stresses’. Common places of occurrence may be bolt holes or various
geometrical breaches. Free-edge stresses depend on material properties and moulding sequence,
occurring because of a mismatch in the effective properties of neighbouring laminae (Tuttle, 2004).
2.5.3. FAILURE MODES ACCORDING TO ASTM D3039
Having a detailed, background knowledge on failure modes at the microscopic and macroscopic levels
with associated factors, it is necessary to introduce typical failure modes associated with tensile testing
of FRP Coupons. ASTM distinguishes nine typical failure modes presented in Fig. 6 below.
Figure 6 - Tensile Test’s Typical Failure Modes (ASTM D3039, 2008)
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These modes are classified according to the failure type, the failure area and the failure location. When
these three characteristics are determined, the sample is assigned a three letter code, where each letter
corresponds to specific failure character (Table 8).
First Character Second Character Third Character
Type Code Area Code Location Code
Angled A Inside grip/tab I Bottom B Edge Delamination D At grip/tab A Top T Grip/tab G <1 W from grip/tab W Left L Lateral L Gage G Right R Multi-mode M Multiple areas M Middle M Long. Splitting S Various V Various V eXplosive X Unknown U Unknown U
other O
Table 8 - Tensile Test’s Failure Codes (ASTM D3039, 2008)
2.5.4. SPLIT RING TEST
Typically tensile properties of Fibre Reinforced Polymers are determined with a use of flat coupon test
method described in depth above. However, for prefabricated FRP tubes, split ring test is more
commonly used, which is believed to give better estimates of tensile strength (Teng et al., 2002). It is
most commonly used to obtain the hoop strength and the rupture’s strain (Chen, 2011). This standard
test method uses the tubular ring–shaped specimens, which are placed in the recommended test
fixtures (Fig. 7). When fixtures are loaded (pulled apart), they apply tensile stress to the test ring, and
consequently to the specimen. This testing allows determination of the comparative apparent tensile
strength (ASTM D2290, 1987).
Figure 7 - Schematic split ring test device (left) & fixtures
(right) (Henninger et al., 2002)
Figure 8 - Definitions of AE event (Huang et al., 1998)
2.5.5. NOVEL METHODS OF FRP TESTING
Acoustic Emission (AE) is a non-destructive testing method that can be defined as “the class of
phenomena where transient elastic waves are generated by the rapid release of energy from localised
sources within a material, or the transient waves so generated” (Miller, 1987). AE technique examines
the internal structure of the material with the use of resonance transducer through monitoring the
signal waves travelling away from the geometrical discontinuity (Fig. 9 below) (Huang et al., 1998). The
typical frequency sensitivity of such device is between 150 to 500 kHz. The transducer measures
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parameters such as the amplitudes, the total emission counts, the duration time, the energy etc. These
parameters are then used in the analysis to classify the failure modes of the specimens (Johnson, 2000).
The peak of the signal is said to be the amplitude, and the area below the acoustic emission event is the
energy. The duration time is calculated between the rising edge of the first count and the falling edge of
the last count (Huang et al., 1998). The commonly used parameters of AE technique are presented in
Fig. 8 above.
Figure 9 - Specimen for AE testing (Rajendraboopathy, 2008)
In Rajendraboopathy, Sasikumar, Usha & Vasudev experiment, an acoustic emission technique was used
to predict failure strength of composite tensile coupons. They tested a total of 18 coupons loaded to
failure with arrangement presented in Fig. 9. The test was divided into three batches with different
loading levels of 30%, 40% and 50% of theoretical collapse load. The results were plotted and
compared to the actual failure load, which can be seen in Fig. 10. It can be concluded that 50 % loading
level was found to be close enough to actual failure load with 1.22 % error of tolerance
(Rajendraboopathy, 2008).
Figure 10 - Results Plot (Rajendraboopathy, 2008)
2.5.6. FINDINGS
Presented Section 2.5 on FRP Test Methods, focused on the Flat Coupon Method, the Split Ring Method
and the Novel Method (use of Acoustic Emission) for FRP Testing. It has been identified that tensile
testing is important and the accurate estimates of tensile parameters are crucial because they are not
only used for research or development, but also in engineering designs, quality control, as well as for
acceptance or rejection under specifications (ASTM D2290, 1987).
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2.6. TENSILE TESTING OF FRP-LIKE BRITTLE MATERIALS
Tensile Testing of FRP coupons was undertaken by Jakub Rycerz and Jakub Jakubowski in their
Bachelor’s research in 2012. Their aim was to develop alternative method of analysis of carbon epoxy
coupons from one proposed in ASTM D3039, which determines material’s ultimate strength, ultimate
strain and elastic modulus. As a result, their developed alternative method that gave a smaller scatter,
hence better tensile parameters’ estimates. Therefore, the intention of this research is to build upon
Jakubowski and Rycerz findings by reanalysing their data and combining it with the new set of
experimental results, which will allow further validation of methods proposed and provide valid
recommendations (Jakubowski & Rycerz, 2012).
2.6.1. TENSILE TESTING PROPOSED METHODS
Jakubowski and Rycerz began work with preparation of ten control specimens. They were tested in
Instron 4505 machine to determine the typical failure mode (Fig. 6) and typical ultimate tensile
strength (Table 9). This resulted in an average ultimate strength of 850 MPa with 10% coefficient of
variation. The failure area was around tabs, so the tab thickness was increased from 1.5 mm to 3 mm to
limit premature failure due to gripping pressure (Jakubowski & Rycerz, 2012).
Table 9 - Control Tests (Jakubowski, 2012)
After control tests, a number of specimens were prepared according to specifications and only twenty
two of them passed a quality control check. Eleven specimens were fitted with three strain gauges
according to ASTM D3039 and another eleven with proposed alignment of four strain gauges
(Jakubowski & Rycerz, 2012). The comparison of the set-up of the strain gauges to the surface of CFRP
coupon is presented in Figs. 11 & 12.
Figure 11 – Cross section with 3 strain gauge set-up (Rycerz, 2012)
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Figure 12 – Cross section with 4 strain gauge set-up (Rycerz, 2012)
2.6.2. IMPROVED ANALYSIS METHODS
ASTM D3039 analysis calculates the average strain from all three strain gauges on both faces of CFRP
specimen (look up Chapter 2.5.1 for reference). However, this approach does not take into account
stresses and strains that are being non-uniformly distributed. This is due to composites being
orthotropic in nature, having imperfections created during a preparation phase, and possible bending
effects due to eccentricity when samples in the testing machine are wrongly aligned. Therefore, the
alternative method to ASTM standard is based on the assumption that the actual strain can be resolved
into three independent components (Eq. 2.2), which aims to increase the reliability of the tensile
parameters of Fibre Reinforced Polymer composites (Jakubowski & Rycerz, 2012). It is important to
note that the principle axis for the analysis below is set at the coupon’s centre point, C (Figs. 11 & 12).
| | | | | | (2.2)
2.6.2.1. METHOD ‘1’
This method proposes that for the specimens with three strain gauges the strain is resolved according
to the Eq. 2.3:
(…)
(2.3)
(...)
Figure 13 - Set of Equations for three strain gauges (Rycerz, 2012)
The above set of Equations (Fig. 13) can be represented in the matrix form (Fig. 14) with
,
which will allow solving for three unknowns
{
} [
] {
} (2.4)
Figure 14 - Matrix form for 3 strain gauges system (Rycerz, 2012)
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2.6.2.2. METHOD ‘2’
The proposed Method ‘2’ deals with four strain gauge set up and uses the same set of equations as for
three strain gauge approach (Method ‘1’), but there is a fourth redundant equation introduced to the
matrix (Fig. 13). In order to solve such a system a least square method is used that deals with over-
determined systems and improves the accuracy of the results (Jakubowski & Rycerz, 2012).
{
} [
] {
} (2.5)
Figure 15 - Matrix form for 4 strain gauges system (Rycerz, 2012)
The above matrix gives four equations with only three unknowns, which entails an overdetermined
system. The way to solve such system is using a least square rule method, which gives an approximate
solution. The general form of the above matrix can be expressed as: { } { }.
In order to calculate 3x1 matrix - ɛab, the steps underneath are followed:
{ } { } (2.6)
{ } { } (2.7)
{ } { } (2.8)
Using Eq. 2.8 allows solving for
2.6.2.3. METHOD ‘3’
Last approach proposed by Jakubowski and Rycerz is to take the specimen with four strain readings
and to analyse it with the Method ‘1’ by excluding the strain readings one at a time. The set of results
will be produced and the ultimate strain will be taken as the average of these four results of
(Jakubowski & Rycerz, 2012).
2.6.3. RESULTS COMPARISON
Method ‘1’ which analyses specimens with three strain gauges gives the results that in comparison to
ASTM values exhibit 20 % higher ultimate strength and 18 % larger strain values, but only 1 % increase
in elastic modulus. The method decreased the scatter of the results by improving the coefficient of
variation by 2.86 %, 2.66 % and 0.64 % for ultimate strength, the ultimate strain and the elastic
modulus correspondingly.
For Methods ‘2’ and ‘3’, a significant increase in tensile parameters was also noticed. When compared to
ASTM values, the average ultimate tensile strength, the ultimate strain and the elastic modulus
increased respectively for:
Method ‘2’ by 11%, 16% and 13%
Method ‘3’ by 14%, 20% and 11%
However, these eleven samples with four strain gauges, analysed according to Methods ‘2’ and ‘3’ did
not show a reduction in coefficient of variance meaning there was no reduction in an average scatter
(Jakubowski & Rycerz, 2012).
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Table 10 - Statistical analysis (Rycerz, 2012)
The Table 10 above summarises the results for various methods with different parameters. The scatter
of all results combined into three different categories is also presented in the Fig. 16 below:
Figure 16 - Comparison of all results analysed according to different methods (Rycerz 2012)
2.6.4. REPORT’S CONCLUSIONS
The presented research work aimed to develop a method that can produce more reliable and repeatable
results of tensile parameters for CFRP composites. Jakubowski and Rycerz proposed three methods for
determining the ultimate tensile strength, the ultimate strain and the elastic modulus parameters. They
were based on the assumption that the maximum strain due to bending occurs at the corners of the
specimen with the Bernoulli’s assumption of ‘plane sections remain plane’ still valid.
The obtained parameters were all compared against the ASTM D3039 standard. In overall, the methods
produced an average increase in the tensile properties, however the additional use of strain gauge did
not decrease the scatter of the results for Methods ‘2’ and ‘3’, and hence there is no significant benefit
from using this set-up for tensile testing of FRP materials. Researchers identified premature failure of
the strain gauges as a significant problem associated with their experiments. Therefore, they adopted
the solution of extrapolation beyond the point of failure based on the linear best fit. Moreover, the
researchers identified that the accuracy of their strain gauge readings, hence its sensitivity using
different methods, was the main limitation of the proposed methods (Jakubowski & Rycerz, 2012).
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2.7. RELEVANT RESEARCHES
In general the past investigations conducted on the FRP properties, nature, and the standard test
methods led to improved methods for the tensile testing of fibre reinforced composites. Three areas can
be identified:
the set-up of the experiment: limiting any imperfections, which are a prime reason for
premature failures;
the specimen's geometry: to be again in a control of failure modes;
the analysis method of the results (Maheri, 1995).
The following two research papers are introduced with the aim of providing the data and statistical measurements, which our test results will be compared to. The author also gives recommendations on improvements that will inform the approach.
2.7.1. POSSIBLE ENHANCEMENTS TO TENSILE TESTING OF FRP
2.7.1.1. GEOMETRICAL IMPROVEMENTS
A study carried out by M. R. Maheri in 1995 looked at two ways of improving the tensile test method for
unidirectional FRP composites. The changes were implemented to the specimen preparation and its
physical shape in order to improve the repeatability, reliability and efficiency of the tensile testing of
composite materials. The investigation consisted of three different tensile specimens (Fig. 17). Each of
them was moulded using 8 layers of carbon woven fabric
Figure 17 - Geometrical Overview of Specimens (Maheri, 1995)
Table 11 - The comparison between three types of specimens and their test results (Maheri, 1995)
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It is clear that uniform thickness tabs exhibit the lowest strength (Table 11). These types of coupons are
prone to fracture near the ends, where the compressive gripping pressure is applied. Therefore, the
tensile properties of unidirectional FRPs are in general underestimated. On the other hand, the tapered
specimens show up to 14 % increase in measured strength with much less data scatter. This increase in
the load carrying capacity is believed to be due to the failure mechanism. In case of exposed-taper
specimens, this failure was shifted to the middle because of splitting of the taper interface.
Furthermore, the covered-taper coupons failed at the outer layer due to stress concentration, which
caused a strength reduction by 4 % in comparison to exposed-taper specimens (Maheri, 1995).
2.7.2. STANDARD ASTM D3039 TESTING
A paper written by L. Lam and J. G. Teng also provides results from the flat coupon tests which have
been carried out according to the ASTM D3039 standard. The dimensions of the samples are provided
below and they were tested in a screw-driven material testing machine under 2 mm/min cross-head
movement. The stresses and elastic moduli were calculated by using a nominal thickness and the actual
widths as well as stress-strain curves respectively.
Figure 18 - Flat Coupon Arrangement & Test Results (Lam et al., 2004)
All 36 CFRP coupon tests (presented in Fig. 18) display a lower scatter with the average ultimate strain
of 1.515 % with a standard deviation of 0.063 %. It has been found that the lower strains were
attributed to misalignment of the fibres implying that a very precise guidance and execution of the
specimen preparation is essential (Lam et al., 2004).
2.8. CHAPTER CONCLUSIONS
It has been identified that tensile testing and accurate estimation of tensile parameters are crucial for
obtaining data used not only for research or development, but also for engineering designs, quality
control, and acceptance or rejection under specifications (ASTM D2290, 1987). Presented broad
literature overview along various studies provided deep understanding of the subject and reference
data to which the results of this project analysis are aimed to be compared. It was found that the
improvements can be made to both the test method and the data analysis in order to increase the
accuracy and the reliability of derived tensile parameters i.e. tensile strength, ultimate strain and chord
modulus.
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3. CHAPTER 3 – EXPERIMENTAL PROCEDURE
The aim of the tests is to determine the stress-strain response of FRP specimens subjected to a tensile
force. These experimental data will then allow calculation of the tensile parameters of the FRP like
brittle materials such as the ultimate strength, the ultimate strain and the elastic modulus. The
following research follows the ASTM D3039/D3039M-08 guidance of coupons preparation; however,
the following improvements were investigated to obtain better quality of samples and, subsequently
test data:
Three different types of tapes were considered when covering the mould in order to minimise
sticking of the FRP coupons and producing even, clean edges and uniform surface areas for
strain gauges tapping.
15 mm wide brush was used for aligning fibres in the longitudinal direction when placing each
layer of carbon fibre sheets in a slit.
Stainless steel spatula together with the pressure of a finger was adopted to remove the air
bubbles and excess of the epoxy resin.
This chapter looks clearly and deeply into every stage of laboratory preparation and subsequent testing
of CFRP coupons. The aim of the following discussion is to allow anyone to reproduce the samples and
testing procedures with all health and safety precautions in mind.
3.1. SPECIMEN PREPARATION AND EXPERIMENTAL SET-UP
3.1.1. SAFETY PRECAUTIONS & REQUIREMENTS
All experimental work requires careful consideration of the risks (Appendix A) and the ways to
overcome them. Therefore, two following elements should be kept in mind and used at all times during
the laboratory work:
3.1.1.1. KEY WATCH POINTS
Good ventilation is required at all times, especially when mixing and using the adhesive, and any skin
contact must be avoided (use PPE for instance gloves). Secondly, safe and clean working area is needed
during mixing, bonding with adhesives and beyond.
3.1.1.2. REQUIRED PPE
The main PPE required are glasses, gloves, mask, safety boots and lab coat. It must be worn at all times.
In order to perform the experiment safely and accurately the training by experienced staff is needed on
the use of Instron Testing Machine, the Data Logger and application of the Strain Gauges.
3.1.2. RESOURCES
Every experiment requires a good set-up before any work can commence. The inconsistency in
specimen preparation in Jakubowski and Rycerz 2012 work serves as an example of a bad set-up and its
consequences. Hence, the full list of necessary resources is presented in Appendix B. The specimens’
preparation procedure is explained below, in order to successfully, reliably and repeatedly prepare
specimens in the future.
3.1.3. PREPARATION OF CFRP SPECIMENS
The procedure for CFRP preparation follows closely the ASTM D3039/D3039M-08. The Tables 12 & 13
outline the adopted values for coupon as well as tab requirements.
Test Method for Tensile Strength of FRP like Brittle Materials Page 32 of 94
Parameters’ signage was marked on the cross-sectional drawings of a coupon as shown in Fig. 19 & 29.
Parameter ASTM Recommendation Adopted
Shape Constant Rectangular Cross-section Constant Rectangular Cross-section
Minimum Length, l [mm] 250 250
Specimen Width, w [mm] 15 15
Specimen Thickness, t [mm] 1.0 2.0
Specimen Thickness Tolerance 1% of thickness 1% of thickness
Specimen Flatness Flat with light finger pressure Flat with light finger pressure
Table 12 - CFRP Coupon Requirements (ASTM D3039, 2008)
Parameter ASTM Recommendation Adopted
Tab Material Continuous E-glass fibre-reinforced polymer matrix or steel tabs Aluminium
Fibre Orientation 0ᵒ unidirectional 0ᵒ unidirectional
Tab Length, a (mm) 56 56
Tab Width, c (mm) Not specified 20
Tab Thickness, b (mm) 1.5 3
Tab Bevel Angle (ᵒ) 90 90
Table 13 - Tab Requirements (ASTM D3039, 2008)
It can be concluded that in terms of the dimensions of the coupons the ASTM standard has been
followed closely with only one diversion - slightly higher specimen’s thickness of 2 mm due to moulds
dimensions. Secondly, the tab’s material is unique with exactly specified width and two times higher
thickness than ASTM specifications. These tab arrangements were found to prevent as much as possible
the premature failure due to gripping pressure, which was confirmed through control testing
(Chapter 4.1.).
Figure 19 - Coupon's cross section in x-direction
3.1.3.1. MATERIALS
3.1.3.1.1. FIBRES
Roll of unidirectional carbon fibre sheet called SikaWrap Hex 230C was used from which 250 FRP strips
of the dimensions of 250 x 15 x 1.5 mm were cut out. The material properties adopted in the rule of
mixtures method (Section 4.4) are provided by the manufacturer in Appendix C .
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3.1.3.1.2. EPOXY RESIN
Fibre sheets were saturated in Sikadur330 and layer by layer fitted into the mould (Fig. 20). Before
mixing of the adhesive, the MSDS and instructions were closely studied. Manufacturer specifies mixing
ratio 4:1 of components A to B. It was found out that 150 grams of mixture is sufficient for a batch of ten
coupons with 5 layers. The manufacturer’s data is presented in Appendix D that should be referred to
when using the Rule of Mixtures (Section 4.4).
3.1.3.1.3. MOULD
Stainless mould (Fig. 20) was used with perfectly laser cut slits matching adopted dimensions of the
CFRP coupons. This technique allowed better quality control, like homogeneity and increased the
repeatability of the specimens’ preparation. It can also be noticed in Fig. 20 that each slit in the mould is
open at one end for any excess of the resin and the air to be removed during pressure application.
Figure 20 - Stainless Steel Mould
3.1.3.1.4. TABS
Aluminium tabs of dimensions 56 x 20 x 3 mm (length, width & thickness respectively) were cut from
long aluminium rods. They were then sand graved and cleaned with propyl alcohol (Fig. 21) for better
bonding between the CFRP coupon and the aluminium surface (Jakubowski, 2012).
Figure 21 - Sand graved Aluminium Tabs
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3.1.3.2. PREPARATION PROCEDURE
3.1.3.2.1. FILLING THE MOULDS
The mould was carefully cleaned with propyl alcohol, placed on a piece of glass for smooth bottom
surface and covered in electrical tape (PVC Insulation Tape), which was found to be the most effective
in giving smooth surfaces and edges, illustrated on Fig. 22. No gaps should be left behind as epoxy sticks
to the steel mould and the extraction of the specimens becomes then a major difficulty, which can cause
disturbance or even damage to the coupons. Bond between the epoxy resin and the steel is very strong
as was stated in “FRP Strengthened RC Structures” book by Teng et al., 2002. Ones the two moulds were
masked with the tape; everything should be sprayed with Palm Oil to prevent any further sticking. For a
good implementation, the mould should be firmly attached to the surface of the glass to have stable, safe
working environment (Jakubowski, 2012).
Figure 22 - Preparation of the mould
In the meantime, precise strips of carbon fibre sheets of 250 mm in length and 15 mm in width were cut
from SikaWrap Hex 230C unidirectional carbon fibre fabric with Kevlar Scissors, which is illustrated in
Fig. 23 below. Firstly, carbon mat was closely inspected for any defects or permanent bends as this
could affect the tensile parameters calculation or premature failure of the coupons. Secondly, each strip
was very precisely cut out to make sure that fibres are not mechanically damaged or separated. As can
be seen in Fig. 23, each strip consisted of 4 bundles of fibres allowing quantity of carbon fibres in each
strip to be precisely controlled.
Once the mould and CFRP strips were ready, an amount of 150 grams of epoxy was mixed in a plastic
cup according to manufacturer’s specifications and stirred for at least 3 minutes until a uniform colour
was achieved. The stated weight of epoxy resin was sufficient for one batch of 10 FRP coupons each
Test Method for Tensile Strength of FRP like Brittle Materials Page 35 of 94
consisting of 5 layers. This was due to the fact that after a while the epoxy became more firm and tough
in application due to its ongoing curing process, hence each batch of 10 specimens was done separetely.
Figure 23 - Cutting out procedure for carbon fibre strips
Each carbon strip was closely inspected again for any fibres cuts or pull outs and then soaked in the
epoxy resin. Subsequently, each strip was carefully placed in one of the mould’s slits with special care
taken to align fibres in the longitudinal direction with the aid of a paint brush and then any air voids
were squezeed out by means of a spatuala and finger pressure. This procedure was repeated for each
layer until CFRP specimens of 5 layers were formed.
Figure 24 - CFRP specimens covered with strips of electric tape for even surface
Once all 20 specimens were completed, the top surface of each sample was covered with a strip of
electrical tape to obtain an even surface once the sample cured (Fig. 24). Then, the mould with
Test Method for Tensile Strength of FRP like Brittle Materials Page 36 of 94
specimens was sprayed with Palm oil, covered in thick foil and glass sheet and loaded with a stack of
books with single cubical weights on top as seen in Fig. 25 . This further loading aimed to remove any
air in the coupons through an open end in every slit of the mould and also create uniformly bonded
CFRP coupons. All the tools were also immediately cleaned by solvent wipe and adhesive was disposed
via the normal waste route.
Figure 25 - Two batches of CFRP coupons pressured during curing
3.1.3.2.2. CURING, INSPECTION & BONDING OF ALUMINIUM TABS
After at least 24 hours, samples were removed from the moulds and cured in a room temperature and
relative humidity for at least seven days to develop full strength. Each sample was also labelled with the
sample batch number Fig. 27. Before application of the aluminium tabs, each sample went through a
very carefull quality check to reject any samples with uneven surface area, disturbed fibre orientation in
the matrix, or peeled fibres (Fig. 26).
Figure 26 - Fatigued CFRP coupons
Having the right samples, sand graved aluminium tabs with dimensions of 56 x 20 x 3 mm (length x
width x thickness) were bonded with the Sikadur 330 adhesive to the ends of CFRP samples in order to
prevent gripping pressure during testing. The tabs once attached to the coupon were taped around to
prevent them from sliding away as shown in Fig. 28. The samples with bonded aluminium tabs were left
for curing under loading for at least seven days.
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Figure 27 - Numbered, Fully Cured Samples
Figure 28 - Samples with Tapped Aluminium Tabs
3.1.4. STRAIN GAUGE APPLICATION
In order to obtain the stress-strain diagrams for each of the FRP coupons, specimens were assembled
with three TML, FLA-5-11 strain gauges with gauge factor of 2.11 ± 1 %, gauge length of 5 mm, and
gauge resistivity of 120 ± 0.3 Ω. They were placed in the middle of the coupon,
, with two
strain gauges on one face placed a distance of m = 2 mm from the edges and one gauge on opposite side
in the middle,
, as seen in Fig. 29.
Figure 29 - Coupon's Cross Section in y-direction
Gauge application required graving surface of tapping with sand paper to obtain an even surface
(remove oil & impurities) without damaging the fibres underneath epoxy, which could cause premature
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failures or defects to the coupons. Then surfaces were cleaned with an alcoholic liquid (propyl alcohol).
Furthermore, exact locations of strain gauges were carefully marked with a black, thin marker by
determining the middle of each coupon in longitudinal direction and 2 mm positions from the edges.
The strain gauges were carefully soaked in adhesive and placed at marked locations. Same was done to
the terminals that needed to be placed as closely as possible to strain gauges as the connecting wires
are very brittle (Jakubowski, 2012). The final result of strains gauges and terminals placed on coupons
can be seen in Fig. 30.
Figure 30 - Tapped Strain Gauges
Figure 31 – Connecting Cables
3.1.5. TESTING OF CFRP COUPONS
3.1.5.1. IMPROVEMENTS TO TESTING
In order to obtain more accurate strain measurements from the tested coupons with strain gauges
1, 2 & 3, an additional strain gauge was attached to one of the controlled samples with the aim to
measure the strain at all times to account for any laboratory varying conditions or heating from the
current, which supplies power to the data logger. These readings were then subtracted away from the
strain gauges readings for each time increment (Section 4.3).
3.1.5.2. EXPERIMENTAL SET-UP AND TEST PROCEDURE
Fully assembled FRP coupons with aluminium tabs at each end and strain gauges with terminals tapped
in the middle of the samples to measure strains across middle cross-section were equipped with the
cables one at a time. This was accomplished by soldering strain gauge’s brittle wires to one end of the
terminal and cables from the memory card, which forms part of a data logger, to the other end (Fig. 31
above).
CFRP coupon was then carefully placed in the grips of the Instron 4505 machine and aligned with the
long axis of testing by means of a spirit level. The aligning procedure is a crucial moment, so any
bending effects due to misalignment can be minimised. The grips were then lightly tightened on the
aluminium tabs and all cables were connected to the memory card of the data logger. It is important to
note that the cables were connected for each sample in the same order, so strain gauges’ names directly
transferred to the naming created in the data logger spreadsheet, which is important for consistency in
results. Plastic shield was placed around the FRP coupon to contain explosive failures and allow for
reassembling of the sample and identifying failure modes (Section 4.2).
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The test was carried out under room temperature with head displacement rate of 0.5 mm/min. The
required input data to the Instron software consists of the specimen’s dimensions (Table 12, Section
3.1.3), sample information, cross head speed and load threshold. Later, the Instron 4505 was
synchronised with external data logger with 10 V corresponding to both 40 kN applied force limit and
10 mm head extension. Moreover, the initial force and displacement were zeroed. The power supplied
to the strain gauges was 5 V as any higher voltage caused overheating of the strain gauges and its
damage. Furthermore, the test was running until brittle failure of each coupon with strains,
displacements and forces being measured every second by a data logger, which later on was used to
perform different types of analysis presented in Chapter 4. The whole set up is shown in Fig. 32.
Figure 32 - Experimental Set-up
3.2. CHAPTER CONCLUSIONS
Overall, 50 specimens were prepared according to the guidelines given in ASTMD3039 for obtaining the
test data in order to perform the statistical verification of the proposed methods of analysis, but only 44
of those were deemed to be suitable for testing after a quality check. It was found that 150 grams of
mixture is required for a batch of ten coupons with 5 layers. The preparation techniques were slightly
altered, which were found to provide improvements to the standard technique.
It is recommended that Powerlink Plus PVC Insulation Tape 19 mm x 33 m is used to provide an even
surface of epoxy on either surfaces of the FRP sample in order to minimise the sticking effect, thus
making the procedure more reliable and repeatable.
Another recommendation is to use 15 mm paint brush to spread the fibres in longitudinal direction and
stainless steel spatula together with the pressure of a finger to remove air voids and produce uniform
samples.
Furthermore, the flat coupon test was performed with the use of Instron 4505 Universal Testing
Machine at room temperature with head displacement rate of 0.5 mm/min. Moreover, the stress-strain
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response was obtained for each coupon with the strain gauges and the data logger synchronised with
the machine (10 V corresponding to both 40 kN applied force limit and 10 mm head extension). The
power supplied to the strain gauges was 5 V as any higher voltage caused overheating of the strain
gauges and its damage. An improvement to the accuracy of strain measurements was also introduced
during testing stage and it consisted of an additional strain gauge attached to the data logger, which
constantly produced strain readings due to laboratory varying conditions or heating from the current,
which supplies power to the data logger.
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4. CHAPTER 4 – DATA ANALYSIS
After careful preparation of CFRP coupons discussed above, the tensile testing was conducted on 44
samples that comprised of 10 control tests and 34 tests with 3 strain gauges according to ASTMD3039
for flat coupon testing.
Initially, control tests were undertaken to obtain an approximate idea of the ultimate strengths of the
samples and examine their failure modes. Finally, remaining coupons were tested, their failure modes
examined and different types of analysis methods (Rule of Mixtures – 4.4, ASTM D3039 – 4.5,
Method ‘1’ – 4.6, Method B&B – 4.7.1 and Axial Method – 4.7.2) implemented to obtain the material
properties for CFRP coupons. The procedure of derivation of these tensile parameters is shown step by
step for CFRP coupon 4-2 regarded as ‘perfect’ – no strain gauges failure and 3-1 specimen that had one
strain gauge failing before ultimate coupon’s failure.
4.1. CONTROL TESTS The initial step in CFRP coupons testing was simple tensile control tests. Control tests aimed to check
the adequacy of each batch of samples prepared, derive ultimate strengths of samples, examine their
failure modes as well as familiarize with the use of equipment. The results are presented in Table 14
below.
Sample Average
Thickness [mm]
No. of CFRP
Layers
Extension [mm]
Max. Load [kN]
Ultimate Tensile Strength [MPa]
Failure Type
Failure Area
Failure Location
1 2.37 5 4.99 28.81 809.27 L G M
2 2.65 5 6.22 24.31 611.57 S G M
3 2.58 5 8.49 29.45 760.49 S G M
4 2.81 5 5.88 33.39 792.17 L G M
5 2.60 5 6.00 33.14 848.66 S A T
6 2.68 5 6.04 33.23 825.59 S G M
7 2.62 5 5.71 27.87 710.06 L G M
8 2.65 5 4.80 27.43 690.06 S G M
9 2.67 5 5.29 31.39 783.77 S G M
10 2.71 5 5.17 28.01 689.90 S A T
Table 14 - Control Tests Results
The tested samples comprised of 5 layers of FRP sheets giving an average coupons’ thickness of
2.63 mm. This resulted in achieving average ultimate tensile strengths of 752.15 MPa with 9.90 %
coefficient of variance. The maximum loads that the CFRP coupons resisted were on average around
29.70 kN at the extension around 5.86 mm. It is important to note that the extensions are for the whole
system rather than only elongation of the sample, because the results accord to the Instron readings,
which take into account slippage of the aluminium tabs, grip deflection and time for grips to become
effective. This means that the machine’s arm extends more than the actual sample’s elongation.
It can be concluded that the failure occurred in 80 % of samples in the middle around the gauges with
either lateral or longitudinal splitting failure type, Table 14. Only two samples had failure at the grip or
the tab. Therefore, the dimensions of aluminium tabs can be confirmed to be sufficient in resisting
and/or uniformly distributing the gripping pressure and/or local bending near the grips which could be
a cause of premature failure.
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4.2. FAILURE MODES
Every tested sample was photographed and its failure was carefully examined by determining the mode
and location of failure. Three-part failure mode code (Table 15) was adopted from the ASTM D3039
specifications. The results for each of the specimen are presented in Appendix E, which was based also
on tensile test typical modes presented in Fig. 6 in Section 2.5.3. Failure depictions were chosen for each
coding type and are presented in Fig. 34 to 41 below.
First Character Second Character Third Character
Type Code Area Code Location Code
Angled A Inside grip/tab I Bottom B Edge Delamination D At grip/tab A Top T Grip/tab G <1 W from grip/tab W Left L Lateral L Gage G Right R Multi-mode M Multiple areas M Middle M long. Splitting S Various V Various V eXplosive X Unknown U Unknown U
Other O
Table 15 - Tensile Test Failure Codes (ASTM D3039, 2008)
Figure 33 - LGM failure mode (Ideal Gauge Failure)
Figure 34 - SGM failure mode (Long splitting failure started in the middle)
Figure 35 – SAT failure mode (Longitudinal failure likely started at the tab at the top)
Figure 36 – SIT failure mode (Longitudinal splitting started inside the tab at the top)
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Figure 37 – SAV failure mode (Longitudinal splitting started inside the tab in various locations)
Figure 38 – MWT failure mode (Multi-mode failure from the tab at the top)
Figure 39 – XIT failure mode (Explosive failure likely initiated in the grip at the top)
Figure 40 – XWT failure mode (Explosive failure likely initiated from the tab at the top)
Figure 41 - XGM failure mode (Explosive failure likely initiated at the gage in the middle)
It can be concluded that 39 out of 44 samples failed either laterally or by longitudinal splitting with
failure mostly at the gauge with a couple of samples failing inside or at the grip/tab. Subsequently the
failure location was determined to be the middle or the top of the CFRP coupon. Only three samples
were identified to fail in an explosive manner.
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4.3. ENVIRONMENTAL ADJUSTMENT OF THE RAW DATA
The first stage of each sample analysis required strains adjustment for any environmental variations at
each time increment, and conversion of extension and force into SI units. In order to obtain more
accurate strain measurements, control strain readings were subtracted at each time step from each of
the coupon’s gauge readings to account for any laboratory varying conditions or heating from the
current, which supplies power to the data logger. Secondly, knowing that 10 V corresponds both to
40 kN force and 10 mm extension, the extensions and forces were converted. Initial five seconds for
CFRP coupon 4-2 is given in Tables 16 and 17 to show the procedure’s results.
Time [Secs] Gauge 1 [μɛ] Gauge 2 [μɛ] Gauge 3 [μɛ] Control Strain [μɛ] Extension [V] Force [V]
14:57:40 0.0419 -9.0769 9.0518 -0.0188 0.0063 0.0025
14:57:41 0.0419 -9.0769 18.0849 -0.0188 0.0088 0.0050
14:57:42 9.0771 -0.0419 36.1517 -0.0188 0.0113 0.0152
14:57:43 45.2193 36.0996 72.2873 -0.0210 0.0175 0.0325
14:57:44 81.3644 54.1715 99.3909 -0.0210 0.0263 0.0450
Table 16 - Raw Data from Data Logger (4-2 Coupon)
Time [Secs] Gauge 1 [%] Gauge 2 [%] Gauge 3 [%] Extension [mm] Force [N]
14:57:40 6.07E-06 -0.00091 0.00091 0.00000 0
14:57:41 6.07E-06 -0.00091 0.00181 0.00250 10
14:57:42 0.00091 -2.3E-06 0.00362 0.00500 50
14:57:43 0.00452 0.00361 0.00723 0.01125 120
14:57:44 0.00814 0.00542 0.00994 0.02000 170
Table 17 - Adjusted/Converted Readings (4-2 Coupon)
4.4. RULE OF MIXTURES
4.4.1. ANALYSIS APPROACH
The rule of mixtures allows estimating the longitudinal modulus of a laminae E1 – an upper limit of the
elastic modulus of the composite under the Bernoulli’s assumption of ‘plane sections remain plane’ and
compatible deformation in longitudinal direction (fibre direction) of two constituents of the FRP lamina
with uniaxial loading applied. Hence, based on the above assumptions, the rule of mixtures is derived by
following steps (for variables descriptions refer to Notation’s section):
Assuming that total strain in the composite is equal to:
(4.1)
.: the stress in fibres, , and matrix, , is described respectively as:
(4.2)
The total area of the composite is defined as: (4.3)
Remembering that where
and knowing that , we can show
that equals to (University of Cambridge, 2012):
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(4.4)
.: where
which leads to the fundamental Rule of Mixtures equation1:
(4.5)
4.4.2. DATA ANALYSIS
Based on the close inspection of failed CFRP coupons and knowing that the yield strength of a matrix is
significantly lower than tensile strength of a fibre, it was assumed that the failure was controlled by
brittle failure of fibres; hence the ultimate coupon’s strain was assumed to be the one of manufacturer’s
fibre strain of the order of ɛult. = 1.5% (Appendix C).
Each specimen was prepared from 5 layers of CFRP, where each FRP strip weighed 0.82 grams. The
dimensions of all coupons were carefully measured with micrometre and the only variations were in
thickness with Average = 2.62 mm and CoV = 6% (Appendix F1).
The Young’s modulus, Eult., was calculated using Eq. (4.5), with the manufacturer’s data
(Appendix C & D) of: Ef = 230000 MPa, Em = 4500 MPa, ρf =0.0018 g/mm3, wstrip = 0.82 g and sample’s
4-2 data of Vcoupon=250*15*2.52 = 9450 mm3:
( )
(4.6)
Therefore, for specimen 4-2: Vf = 0.24 and Vm = 0.76 that gives ultimate Young’s modulus of 58.85 GPa.
Finally, the stress for each coupon is:
(4.7)
.: hence for 4-2 CFRP coupon, σult. = (1.5/100) * (58.85*1000) = 882.80 MPa.
4.4.3. RESULTS
The results for the rule of mixtures analysis according to procedure in section (4.4.2) are presented in
the in Appendix F1. These are the values that predict the ultimate strain, stress and Young’s modulus for
each individual tested CFRP coupon. It is important to note that the specimens marked in purple had at
least one of the strain gauges failing before brittle failure of CFRP coupon. The remaining samples can
be regarded as ‘perfect’ and are suitable for ASTM D3039 analysis. This is a set of 17 samples which is
summed up by a simple statistical analysis presented in Table 18 below that gives average value,
coefficient of variance and standard deviation. Subsequently, the whole range of 29 samples is also
statistically summarised in Table 19.
It can be noted that for more samples the ultimate stress and Young’s modulus increase with
coefficients of variance for both variables also increasing. The strain remains constant because of the
assumption of brittle fibres failure. The volume fractions stay constant for both batches with average
value of 0.77 and 0.23 for matrix and fibres respectively. However, a detailed results discussion and
comparison with other methods will be presented in Chapter 6.
1 Yu et al., 2009
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Variables
17 Specimens
Average SD CoV [%]
Vm 0.77 0.01 1.71
Vf 0.23 0.01 5.73
ɛult. [%] 1.50 0.00 0.00
Eult. [GPa] 56.34 2.97 5.27
σult. [MPa] 845.16 44.50 5.27
Table 18 - Statistical Result’s Summary (Rule of Mixtures)
Variables
29 Specimens
Average SD CoV [%]
Vm 0.77 0.02 1.89
Vf 0.23 0.02 6.28
ɛult. [%] 1.50 0.00 0.00
Eult. [GPa] 56.74 3.28 5.78
σult. [MPa] 851.08 49.19 5.78
Table 19 - Statistical Result’s Summary (Rule of Mixtures)
4.5. ASTM D3039
4.5.1. ANALYSIS APPROACH
Standard method described by ASTM D3039 gives guidance on how to analyse tensile data for three
strain gauges set up. In order to analyse any sample with ASTM method, one primary assumption needs
to be valid: all strain gauges must fail at the moment of ultimate, brittle sample failure.
Figure 42 - Typical stress vs. strain CFRP coupon response (ASTM D3039)
Firstly, in order to determine the ultimate strain of the sample, the three strain gauge readings need to
be graphed and readings closely inspected, so that they are increasing until maximum failure stress
(Fig. 42). Firstly, the ultimate strain, , is the average value of the three maximum strain gauge
readings at the failure load (for variables descriptions refer to Notation’s section):
(4.8)
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Secondly, ultimate tensile elastic modulus, , is the ratio of sums of differences in tensile stresses to
the differences in strains for the lower portion of σ-ɛ response (Fig. 42).. The strains are for 3000μɛ and
1000μɛ points for each gauge (ASTM D3039, 2008) and stresses are the corresponding values at these
strain points. can be calculated accordingly:
∑
∑
∑
∑
(4.9)
Finally, the ultimate stress, , is the maximum/failure load divided by the cross-sectional failure
area:
(4.10)
4.5.2. DATA ANALYSIS
The adjusted raw data for the environmental strain as shown in Section 4.3 is plotted in Fig. 43. The
strain gauges 1, 2 & 3 readings are respectively represented by blue, red and green lines. The point of
failure of the coupon is determined from the graph as well as from the data as coloured in Table 20. The
average value of all three strains at failure Eq. (4.8) is the ultimate strain of the sample according to
ASTM D3039 and for sample 4-2 this value is 1.32%.
Figure 43 – Stress vs. Strain Response for Specimen 4-2
Furthermore, the ultimate tensile Young’s modulus Eq. (4.9) is calculated using a lower part of the
curves, hence there are no significant changes in the slopes of the stress-strain curves. The values
required for this calculation are marked by vertical and horizontal dash lines in the Fig. 43. For
sample 4-2 ultimate Young’s modulus for range of strains of 0.2 % and their corresponding stresses is
57.35 GPa.
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Lastly, the ultimate tensile strength Eq. (4.10) is found by determining the failure load, 29740 N
(Table 20) and subsequently the ultimate stress is 786.77 MPa for 4-2 specimen, which agrees with the
curves’ ends seen in Fig. 43.
Load [N] Stress [MPa] ɛ1 [%] ɛ2 [%] ɛ3 [%]
29700 785.7143 1.3389 1.1932 1.4235
29740 786.7725 1.3398 1.1950 1.4245
29710 785.9788 1.3389 1.1969 1.4180
-240 -6.3492 1.2974 3.8074 -3.8039
Table 20 - Data at Failure Point for 4-2 Coupon
4.5.3. RESULTS
The results according to ASTM D3039 analysis are shown in Fig. 44. Each point corresponds to the
result of each coupon’s ultimate strain and stress. This set of 17 samples is summed up by a simple
statistical analysis presented in Table 21 that gives average value, coefficient of variance and standard
deviation. All the results for ASTM D3039 analysis are presented (along with Axial Method results
marked in purple that are discussed in Section 4.7.2) in tabular form in Appendix F2.
Figure 44 - ASTM D3039 Analysis's Results
It can be noted that ASTM D3039 analysis gives an average ultimate stress of 770.42 MPa with an
average 1.28 % ultimate strain. The Young’s modulus has been found out to be approx. 58.48 GPa. All
three tensile parameters have a coefficient of variance lying between 7.5 % and 8.7 %. However, a
detailed results discussion and comparison with other methods is presented in Chapter 6.
Test Method for Tensile Strength of FRP like Brittle Materials Page 49 of 94
Variables
17 Specimens
Average SD CoV [%]
ɛult. [%] 1.28 0.10 7.97
Eult. [GPa] 58.48 4.39 7.51
σult. [MPa] 770.42 66.10 8.58
Table 21 - Statistical Result’s Summary (ASTM D3039)
4.6. METHOD ‘1’
4.6.1. ANALYSIS APPROACH
The alternative method to ASTM standard proposed by Jakubowski & Rycerz 2012 is based on the
assumption that the actual strain can be resolved into three independent components Eq. (4.11), which
aims to increase the reliability of the tensile parameters of Fibre Reinforced Polymer composites. First
component is axial strain, , caused by the applied stress and assumed to be uniform across the
coupon’s cross-section. Two remaining components, , are caused by the induced bending about
major and minor axis, here y & z-axis respectively (Rycerz & Jakubowski, 2012). The following
approach is specifically adjusted to the sign and numbering convention used (Figure 45), therefore it
differs from that summarised in Section 2.6.1.
Figure 45 - Cross-section of CFRP coupon
The maximum strain2, , is found at one of the four cross-section’s corners according to (for
variables descriptions refer to Notation’s section):
| | | | | | (4.11)
Method ‘1’ proposes that for the specimens with three strain gauges the strain is resolved according to
the following set of equations3:
(...)
(4.12)
(…)
2 Rycerz, 2012 3 Rycerz, 2012
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The above set of Eq. (4.12) can be represented in the matrix form (4.13) with
. Subsequently, the
matrix properties (4.14) will allow solving for three unknowns
(
) (
)(
) (4.13)
.:
(
) (
)
(
) (4.14)
Once we know can be determined by using Eq. (4.11). Having all variables,
graphs of and lines of best fit are fitted to the linear part of each
curve. It is crucial to remember that for those samples that any of the strain gauges failed before the
final failure of the whole sample, all the curves are plotted up to the point of the first strain gauge
failure. By rearranging the equations of lines of best fit, strains for each strain gauge can be found for
failure strains, . Then the ultimate strain, , of the sample is averaged between those
n – numbers of failure strains.
Secondly, the ultimate Young’s modulus, , is proposed to be the gradient of the line of best fit of a
curve of .
Finally, the ultimate tensile strength, , is calculated accordingly:
(4.15)
4.6.2. DATA ANALYSIS
Adjusted data logger’s strain readings are resolved at each time increment into
according to Eq. (4.14) using Excel spreadsheet. This allows calculating the maximum strain, ,
using Eq. (4.11) at each time step. Since all the variables are calculated, graphs of can
be plotted (Fig. 46). Finally, lines of best fit are fitted to linear part of each of the curves. The derived
relationships shown next to the curves (Fig. 46) allow prediction of the ultimate strain of the CFRP
sample.
Test Method for Tensile Strength of FRP like Brittle Materials Page 51 of 94
Figure 46 - Relationship of Gauge Strain Readings vs. Max. Strain for 4-2 CFRP Coupon
In case of specimen 4-2, all three strain gauges took measurements up to failure point; hence the
ultimate strain will be the average of the three maximum strain values. From the Table 20, the failure
strains are 1.34, 1.20 & 1.42 respectively.
(4.16)
(4.17)
(4.18)
Equations 4.16, 4.14 & 4.18 give maximum strains of 1.51%, 1.52% & 1.50% respectively that allow
determining the ultimate tensile strain of 1.51% for specimen 4-2.
In order to find out the ultimate Young’s modulus, , a graph of tensile stress vs. axial strain is plotted
(Fig. 47) and linear relationship found for the linear part of the curve. The slope of the line
y = 614.06x - 25 is said to be the ultimate Young’s modulus of the sample, here equal to 61.41 GPa for
4-2 specimen.
Finally, the ultimate tensile strength, , can be determined assuming the linear relationships between
. Hence, for coupon 4-2, it is 925.18 MPa, which is established according to Eq. (4.15).
Test Method for Tensile Strength of FRP like Brittle Materials Page 52 of 94
Figure 47 - Tensile Stress vs. Axial Strain for 4-2 CFRP Coupon
4.6.3. RESULTS
The above analysis procedure was applied to every sample and its summary is shown in Figure 48
below. Each point corresponds to the result of coupon’s ultimate strain and stress. Samples marked in
purple represent 12 samples that had any of the strain gauge failing before ultimate failure of the CFRP
coupon. The remaining 17 samples in marine colour represent samples that are suitable for ASTM
D3039 analysis and those will be accordingly compared. All the results for Method ‘1’ analysis with
12 samples marked in purple are presented in tabular form in Appendix F3. Two sets of results,
17 samples & 29 samples, are summed up by a simple statistical analysis and presented in Tables
22 and 23. It can be noted that for more samples the ultimate strain, Young’s modulus and stress are
increasing. The coefficient of variance for strain is dropping, whereas CoV for the Young’s modulus and
stress slightly increases. However, a detailed results discussion and comparison with other methods
will be presented in Chapter 6.
Variables
17 Samples
Average SD CoV [%]
ɛult. [%] 1.39 0.11 7.87
Eult. [GPa] 61.21 4.31 7.05
σult. [MPa] 847.67 83.71 9.88
Table 22 - Statistical Result’s Summary (Method ‘1’)
Variables
29 Samples
Average SD CoV [%]
ɛult. [%] 1.43 0.11 7.65
Eult. [GPa] 61.33 4.38 7.14
σult. [MPa] 880.01 92.99 10.57
Table 23 - Statistical Result’s Summary (Method ‘1’)
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Figure 48 - Method '1' Analysis Results
4.7. PROPOSED IMPROVEMENTS
4.7.1. METHOD B&B
4.7.1.1. ANALYSIS APPROACH
Looking closer through the analysis proposed by Jakubowski and Rycerz 2012 (Method’1’ – Section
4.6), new changes have been proposed to optimise the results for determination of tensile properties of
FRP like brittle material and match them as closely as possible to the results given by the Rule of
Mixture (Section 4.4).
The ultimate strain analysis is adopted from Method ‘1’ proposed by Jakubowski and Rycerz 2012 and
is based on the assumption that the actual strain can be resolved into three independent components
Eq. (4.11). This seems to give best results for ultimate strain estimation by giving significantly close
values to those predicted by the Rule of Mixture.
The ultimate tensile Young’s modulus is advised to be predicted with the use of ASTM D3039 method
through Eq. (4.9) as those values match the closest the Rule of Mixture.
The proposed change concerns determination of the ultimate tensile stress. It is known that the stresses
and strains are not uniform through the coupon’s cross-section, which is due to material’s orthotropic
nature (Yu et al., 2009), sensitivity to any imperfections (Maheri, 1995) and bending effects due to
eccentricity caused by inappropriate alignment of the specimen in the grips (Jakubowski, 2012).
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Therefore, the following is recommended that accounts for bending strains and is also based on the
pure failure load:
Figure 49 - Cross-section of CFRP coupon
The standard equation for determination of stress, is (for variables descriptions refer to Notation’s
section):
(4.19)
Knowing that the samples are subjected to bending effects that are caused by the eccentricity (Fig. 49)
of the applied load, the moment can be expressed as:
(4.20)
.:
(4.21)
or
(4.22)
Eq. (4.22) can be represented as (4.23), therefore ignoring at a time either y or z
component, the following ratio can be determined:
(4.24)
.: correspondingly,
(4.25)
Substituting Eq. (4.24) & Eq. (4.25) into Eq. (4.22), the following relationship is derived:
(4.26)
Finally, the ultimate stress, , can be expressed in terms of failure force, cross-sectional area and
bending strains at failure that are taken as absolute values as their signage is difficult to determine:
( |
| |
|) (4.27)
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The bending strains about z and y axis are calculated according to the ASTM D3039 (Eq. 4.28 & Eq. 4.29
respectively) and the magnitude of bending is obtained from the samples results for each time
increment:
(4.28)
(4.29)
.: where
(4.30)
4.7.1.2. DATA ANALYSIS
Initially the axial strain Eq. (4.30) is found for each time step and then the bending strains about z
(Eq. (4.28)) and y (Eq. (4.29)) axis are determined accordingly. Knowing the bending strains along with
the load at the failure point (Table 24) allows calculating the ultimate stress of the sample Eq. (4.27).
Load [N] ɛa [%] By [%] Bz [%]
29700 1.320 -1.136 11.843
29700 1.320 -1.153 11.603
29740 1.320 -1.135 11.546
29710 1.320 -1.189 11.139
-240 0.650 -99.730 -781.174
Table 24 - Improved Ultimate Stress Determination Process
For sample 4-2, it is as follows:
( |
| |
|)
As stated in Section 4.7.1.1, the ultimate strain is calculated according to Method ‘1’ (Section 4.6.1) and
for sample 4-2 is . Subsequently, the ultimate Young’s modulus is recommended to be
determined according to ASTM D3039 method (Eq. (4.9)). For sample 4-2 ultimate Young’s modulus is
57.35 GPa for a range of strains of 0.2 % and their corresponding stresses
4.7.1.3. RESULTS
The summary of results according to Method B&B is shown in Fig. 50 below. It is important to note that
determination of stress according to Eq. (2.27) can be only done for those samples where strain gauges
give reliable readings until brittle failure of the CFRP coupon, hence method’s limitation. Therefore,
Method B&B worked only on 17 samples as shown in Fig. 50, which are summed up by a simple
statistical analysis presented in Table 20. The Appendix F3 presents all results according to
specifications of Method B&B along with the failure bending strains about z & y-axis for each specimen.
Detailed results discussion and comparison with other methods is presented in Chapter 6.
Test Method for Tensile Strength of FRP like Brittle Materials Page 56 of 94
Variables
17 Samples
Average SD CoV [%]
ɛult. [%] 1.39 0.11 7.87
Eult. [GPa] 58.48 4.39 7.51
By [%] 1.21 4.05 335.18
Bz [%] 0.36 6.36 1790.29
σult. [MPa] 834.42 74.48 8.93
Table 25 – Statistical Results Summary (Method ‘B&B’)
Figure 50 - Method B&B Analysis Results
4.7.2. AXIAL METHOD FOR ULTIMATE STRAIN’S CALCULATION
4.7.2.1. ANALYSIS APPROACH
Axial Method for strain calculation is introduced to supplement the ASTM D3039 analysis for those
specimens where any gauge fails before failure of the whole coupon. As it was stated in Section 4.5,
ASTM D3039 allows only estimation of ultimate strains for those coupons, which have reliable strain
readings up to the point of brittle failure of the specimen. In order to improve this method, a prediction
of the ultimate strain at failure stress after any of the strain gauges breaks can be done according to
axial strain equation4:
(4.31)
4 ASTM D3039, 2008
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The remaining tensile parameters, the Young’s modulus and the ultimate stress, are predicted with the
use of ASTM D3039 method through using the Eq. 4.9 and 4.10 respectively as described in
Section 4.5.1.
4.7.2.2. DATA ANALYSIS
Figure 51 below shows a stress vs. strain relationship for 3-1 specimen. It is clear that the strain gauge
one failed just before brittle failure of the coupon; hence prediction of ultimate strain Eq. (4.8) using
ASTM D3039 method is impossible. The purple line represents the axial strain according to Eq. (4.31)
that is plotted for each time increment until failure of gauge one. By fitting line of best fit into the linear
part of the axial strain curve a linear relationship is determined that can be projected to the failure load
and used to estimate the ultimate strain as presented below:
Figure 51 – Stress vs. Strain Response for Specimen 3-1
For 3-1 CFRP coupon, by rearranging the equation of line of best fit (Fig. 51), the ultimate strain is:
Furthermore, the ultimate tensile Young’s modulus (4.9) is calculated using a lower part of the curves,
hence there are no significant changes in the slopes of the stress-strain curves. For sample 3-1 ultimate
Young’s modulus is 51.71 GPa.
Lastly, the ultimate tensile strength Eq. (4.10) is found by determining the failure load, 31130 N and
subsequently the ultimate stress is 738.55 MPa for 3-1 specimen, which agrees with the Fig. 51.
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4.7.2.3. RESULTS
The results of supplemented ASTM D3039 method (Section 4.5) are shown in Fig. 52 below. Purple
triangles represent specimens analysed with axial method and the remaining 17 orange samples show
ASTM results. Set of 29 results is presented in tabular form in Appendix F2 with samples analysed with
axial method (marked in purple) along with ASTM D3039 results. Both sets are summed up by a simple
statistical analysis presented in Tables 26 and 27. It can be noted that the Axial Method drops down the
coefficients of variance for ultimate strain, ultimate stress and Young’s modulus. However, the detailed
results comparison is presented in Chapter 6.
Figure 52 – ASTM (orange) + Axial Method (purple) Analysis Results
Variables
17 Samples
Average SD CoV [%]
ɛult. [%] 1.28 0.10 7.97
Eult. [GPa] 58.48 4.39 7.51
σult. [MPa] 770.42 66.10 8.58
Table 26 - Statistical Summary (ASTM D3039)
Variables
29 Samples
Average SD CoV [%]
ɛult. [%] 1.29 0.09 6.92
Eult. [GPa] 58.28 4.31 7.39
σult. [MPa] 772.16 61.88 8.01
Table 27 - Statistical Summary
(ASTM + Axial Method)
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4.8. CHAPTER CONCLUSIONS
Out of 34 tests, four samples reached a premature failure of one or multiple gauges, whereas one
sample had slippage at the tabs. Controlled tests confirmed that the dimensions of aluminium tabs are
sufficient in uniformly distributing the gripping pressure eliminating in most cases premature failure.
CFRP coupons failed mostly laterally or through longitudinal splitting with failure mostly occurring at
the gage with couple samples failing inside or at the grip/tab.
Only 17 results produced reliable strain readings up to coupon’s failure and hence were deemed to be
analysed according to ASTM D3039 and proposed Method B&B. The remaining 12 coupons, with one
strain gauge failing before ultimate condition, were analysed with proposed Axial Method, which is
regarded as a supplementary method for ASTM D3039. It was found that it slightly drops the coefficient
of variance for tensile parameters therefore it fits well within the ASTM’s results’ range. The dataset of
29 samples was also analysed according to the Rule of Mixtures and Method ‘1’. The procedures, results
and statistical analysis were presented along each method and the comparison with thorough
discussion is followed in the Chapter 6.
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5. CHAPTER 5 - REANALYSED DATA FROM JAKUBOWSKI & RYCERZ 2012 RESEARCH
One of the objectives of this research paper is to review, reanalyse, compare and critically evaluate the
previous work completed by Jakubowski and Rycerz 2012. Both researches presented a set of 11
samples with three strain gauges and 11 specimens with four strain gauges (all 22 samples had 6 layers
of FRP sheets, which make them unfeasible to be combined with this research that is based on CFRP
coupons with 5 layers). This chapter is divided into two sections: first one focuses on analysis of
coupons with 3 strain gauges and the second - with 4 strain gauges. On top of what Jakubowski and
Rycerz presented in their work, additional comparison has been introduced to the results given by the
Rule of Mixtures.
5.1. COUPONS WITH 3 STRAIN GAUGES
Researchers could not analyse their samples according to ASTM D3039 standard (Section 4.5) as they
identified premature failure of the strain gauges as a significant problem associated with their
experiments. Therefore, they adopted the solution of extrapolation beyond the point of failure based on
the linear best fit (Rycerz & Jakubowski, 2012). Therefore, the CFRP coupons with 3 strain gauges were
analysed by Jakubowski and Rycerz using ASTM D3039 combined with Axial Method (in this research
proposed supplementary method to ASTM, Section 4.7.2) and compared to their proposed, improved
Method ‘1’ (Section 4.6).
Figure 53 presents the plot of reanalysed results for ultimate stress vs. ultimate strain for coupons that
were analysed with ASTM D3039 (blue diamonds), Axial Method (green triangle) & Method ‘1’ (orange
squares). The dashed, blue lines give mean values for samples under investigation for ultimate strain
and stress predicted using the Rule of Mixtures (Section 4.4). These are the theoretical tensile
properties that the analysis methods aim for. It can be concluded by looking at the plot that Method ‘1’
gives clearly closer values to Rule of Mixture’s mean.
The 11 specimens with 3 strain gauges (Table 28) analysed with ASTM and Axial Method compared
against Method ‘1’ yielded higher values for mean ultimate strain, stress and Young’s modulus by
12.43 %, 18.51 % and 10.49 % respectively. Secondly, the Rule of Mixtures is compared against mix of
ASTM D3039 with Axial Methods and Method ‘1’. The ASTM D3039 plus Axial Method analysis gave on
average by 27.10 %, 34.74 % and 10.87 % lower results for ultimate strain, stress and Young’s modulus
respectively, whereas for Method ‘1’ had mean ultimate strain, stress and Young’s modulus by 13.05 %,
13.70 % and 0.34 % lower than results provided by the Rule of Mixtures.
All the results for coupons with 3 strain gauges that were analysed with Rule of Mixtures, ASTM D3039,
Axial Method and Method ‘1’ are presented respectively in a tabular form in Appendix G1 .
Variables ASTM + Axial Method Method ‘1’ Rule of Mixtures
Average SD CoV [%] Average SD CoV [%] Average SD CoV [%]
ɛult. [%] 1.18 0.11 9.58 1.33 0.09 6.44 1.50 0.00 0.00
Eult. [GPa] 70.79 5.17 7.31 78.21 6.30 8.05 78.48 6.50 8.29
σult. [MPa] 873.68 95.10 10.89 1035.39 77.85 7.52 1177.20 97.55 8.29
Table 28 - Statistical Analysis of Results for Coupons with 3 Strain Gauges for 11 coupons
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Figure 53 - Comparison of ASTM with Axial Method to Method '1'
5.2. COUPONS WITH 4 STRAIN GAUGES
Subsequently, Jakubowski and Rycerz proposed two more methods (Sections 2.6.2.2 & 2.6.2.3) used to
analyse coupons with four strain gauges. Two comparisons are shown in this section.
The first plot (Fig. 54) gives ultimate stress vs. ultimate strain for coupons analysed with ASTM + Axial
Method (red diamonds) & Method ‘2’ (blue triangles). Secondly, the Fig. 55 shows the same type of plot,
but this time for coupons that were analysed with ASTM + Axial Method (red diamonds) & Method ‘3’
(blue squares). In both cases the dashed, orange lines present mean values for coupons under
investigation for ultimate strain and stress predicted with the use of Rule of Mixtures (Section 4.4).
These are the theoretical tensile properties that the analysis Methods ‘2’ & ‘3’ aim for. It can be
concluded from the plots that Method ‘2’ as well as Method ‘3’ give clearly closer values to the Rule of
Mixture’s mean, hence all the results shifted closer to the dashed lines predicting the tensile parameters
more accurately than ASTM + Axial Method.
When 11 specimens with 4 strain gauges (Table 29) are compared to the mix of ASTM and Axial Method
than Method ‘2’ yielded higher values for mean ultimate strain, stress and Young’s modulus by 9.64 %,
14.70 % and 11.36 % respectively, whereas for Method ‘3’ they were also higher by 12.67 %, 17.81%
and 10.88% accordingly. Secondly, those three methods are compared in respect to the Rule of
Mixtures. The ASTM + Axial Method analysis gave on average 24.25 %, 40.36 % and 19.80 % lower
results for ultimate strain, stress and Young’s modulus respectively. For Method ‘2’, mean ultimate
strain, stress and Young’s modulus were lower by 13.32 %, 22.38 % and 7.57 % as well as for
Method ‘3’ the results are lower by 10.27 %, 19.14 % and 8.04 % accordingly.
All the results for coupons with 4 strain gauges that were analysed with the Rule of Mixtures, ASTM
D3039, Axial Method, Method ‘2’ and ‘3’ are presented respectively in a tabular form in Appendix G2.
Test Method for Tensile Strength of FRP like Brittle Materials Page 62 of 94
Figure 54 - Comparison of ASTM with Axial Method to Method '2'
Figure 55 - Comparison of ASTM with Axial Method to Method '3'
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Variables ASTM D3039 + Axial Method Method ‘2’ Method ‘3’
Average SD CoV [%] Average SD CoV [%] Average SD CoV [%]
ɛult. [%] 1.21 0.11 8.77 1.32 0.14 10.59 1.36 0.11 8.37
Eult. [GPa] 68.10 4.95 7.27 75.84 5.63 7.42 75.51 5.25 6.96
σult. [MPa] 872.00 62.50 7.17 1000.00 89.13 8.91 1027.00 110.98 10.81
Variables
Rule of Mixtures
Average SD CoV [%]
Vm 0.67 0.03 4.29
Vf 0.33 0.03 8.67
ɛult. [%] 1.50 0.00 0.00
Eult. [GPa] 81.58 3.65 4.47
σult. [MPa] 1224.00 54.73 4.47
Table 29 - Statistical Analysis of Results for Coupons with 4 Strain Gauges
5.3. CHAPTER CONCLUSIONS
After careful study of Jakubowski and Rycerz 2012 raw data and its repeated analysis, it was found from
a set of specimens with three strain gauges that only two samples (3-3 & 3-7) were suitable for ASTM
D3039 standard analysis and the remaining coupons had at least one of the strain gauges failing before
ultimate condition, hence the specimens where analysed according to the Axial Method presented in
this research paper as an improvement and supplementary method to the ASTM D3039.
The 11 specimens with 3 strain gauges were analysed with ASTM + Axial Method and compared against
Method ‘1’ and the Rule of Mixtures. Subsequently, the remaining 11 specimens with 4 strain gauges
were also analysed with ASTM + Axial Method, Method ‘2’, and Method ‘3’ as well as the Rule of
Mixtures.
In the light of above findings, it was found that the results agree with those discussed in the literature
review chapter, Section 2.6. Jakubowski and Rycerz identified that their premature failure of the strain
gauges was a significant problem associated with their experiments. Therefore, they adopted the
solution of extrapolation to supplement the only two possible ASTM results. Hence, it can be concluded
that Jakubowski and Rycerz 2012 did not meet their objective of truly comparing ASTM D3039
standard with their proposed Methods for determining the tensile properties of CFRP coupons.
However, they developed methods that can produce more reliable and repeatable results of tensile
parameters for CFRP composites and give closer results to the prediction given by the Rule of Mixtures.
However, for Methods ‘2’ and ‘3’ the coefficients of variance significantly increased and only Method ‘1’
gave much more reliable data by also decreasing the CoV. Hence, this is why this research concentrated
on further investigating the reliability, repeatability of Method ‘1’ as well as had a strong focus on
development of improvements to the preparation as well as testing stage in order to overcome
limitations identified by Jakubowski and Rycerz.
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6. CHAPTER 6 – STATISTICAL SUMMARY
Conducted research is based on a population of 44 specimens which were tested in tension until failure
according to the specification contained within ASTM D3039. Group of 10 coupons was chosen as
control tests; hence, a total of 34 specimens provided raw data for further analysis according to the set
aim. However, only 29 of them gave a representative set of data for analysis because 4 specimens had
one of the strain gauges flawed and 1 sample had clear tab slippage. This dataset was narrowed further
to 17 coupons, which were identified to provide full range of strain readings up to failure point, hence
satisfying the ASTM D3039 analysis requirements.
The results for subsequent methods were shown in the Results sections in Chapter 4. Therefore, the
intention of this chapter is to sum up all the experimental results and give comparisons between
existing and proposed methods through normal distribution, scatter plots and results vs. predictions
plots as well as statistical analysis.
6.1. STATISTICAL COMPARISONS Two types of comparisons were provided to prove different types of improvements to the proposed
methods. The first comparison is based on the dataset of 17 coupons, whereas the second, on all 29
specimens. The below comparisons can be identified on the normal distribution plots as shown in Fig.
56, 57 and 58 as well as through Table 30.
For 17 CFRP coupons, firstly ASTM D3039 is compared against Method ‘1’ and Method B&B. Therefore,
when compared to ASTM D3039 (blue curve on normal plots), Method ‘1’ (black curve on normal plots)
yielded higher values for mean ultimate strain, stress and Young’s modulus by 8.22 %, 10.03 % and
4.66 % respectively, whereas Method B&B gave mean ultimate strain higher by 8.22 %, the same
Young’s modulus and by 8.31 % higher mean ultimate stress.
Secondly, the Rule of Mixtures (purple curve on normal plots) is compared against ASTM D3039,
Method ‘1’ and Method B&B. The ASTM D3039 analysis gave approximately 14.62 %, 8.84 % lower
results for ultimate strain and stress respectively, and 3.79 % higher values when it comes to Young’s
modulus. For Method ‘1’, mean ultimate strain was 7.61 % lower, whereas ultimate stress and Young’s
modulus were 0.30 % and 8.63 % higher than results provided by the Rule of Mixtures.
Lastly, proposed Method B&B provided mean ultimate strain and stress values to be 7.61 % and 1.27 %
lower, and 3.79 % higher for Young’s modulus than those given by the Rule of Mixtures.
Therefore, Method B&B provides the best estimates of the tensile properties of FRP as well as gives the
greatest improvements in comparison to the ASTM D3039.
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Figure 56 - Normal Plot for Strain (based on μ & SD for 17 coupons - Table 30)
Figure 57 - Normal Plot for Young's Modulus (based on μ & SD for 17 coupons - Table 30)
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Figure 58 - Normal Plot for Stress (based on μ & SD for 17 coupons – Table 30)
For 29 CFRP coupons, combination of ASTM and Axial Method results is compared against Method ‘1’
results that yielded higher values for mean ultimate strain, stress and Young’s modulus by 11.58 %,
13.97 % and 5.24 % respectively.
Secondly, the Rule of Mixtures is compared against mix of ASTM and Axial Methods as well as
Method ‘1’. The ASTM D3039 plus Axial Method analysis gave about 16.66 % and 10.22 % lower results
for ultimate strain and stress respectively and by 2.64 % higher value for Young’s modulus. For Method
‘1’, mean ultimate strain was by 4.54 % lower, whereas ultimate stress and Young’s modulus were
higher by 3.29 % and 7.49 % accordingly than the results provided by the Rule of Mixtures.
Data Series
Ultimate Strain, ɛult. Ultimate Young’s
modulus, Eult. Ultimate Stress, σult.
Mean
[%] SD [%]
CoV [%]
Mean [GPa]
SD [GPa]
CoV [%]
Mean [MPa]
SD [MPa]
CoV [%]
17
Co
up
on
s
Rule of Mixtures 1.50 0.00 0.00 56.34 2.97 5.27 845.16 44.50 5.27
ASTM D3039 1.28 0.10 7.97 58.48 4.39 7.51 770.42 66.10 8.58
Method ‘1’ 1.39 0.11 7.87 61.21 4.31 7.05 847.67 83.71 9.88
Method B&B 1.39 0.11 7.87 58.48 4.39 7.51 834.42 74.48 8.93
29
Co
up
on
s Rule of Mixtures 1.50 0.00 0.00 56.74 3.28 5.78 851.08 49.19 5.78
ASTM + Axial Method
1.29 0.09 6.92 58.28 4.31 7.39 772.16 61.88 8.01
Method ‘1’ 1.43 0.11 7.65 61.33 4.38 7.14 880.01 92.99 10.57
Table 30 - Statistical Analysis of Obtained Results
Test Method for Tensile Strength of FRP like Brittle Materials Page 67 of 94
Therefore, for the dataset of 29 coupons Method ‘1’ is most appropriate for estimation of the tensile
properties of FRP giving greatest improvements in comparison to the ASTM D3039.
To check the validity of the results, the statistical analysis was conducted on these two sets of coupons,
summarising all methods in Tables 30 above and 31 below.
Data Series
Ultimate Strain, ɛult. Ultimate Young’s
modulus, Eult. Ultimate Stress, σult.
Min. [%]
Median [%]
Max. [%]
Min.
[GPa] Median [GPa]
Max. [GPa]
Min.
[MPa] Median [MPa]
Max. [MPa]
17
Co
up
on
s
Rule of Mixtures
1.50 1.50 1.50 51.19 57.11 61.57 767.92 856.70 923.56
ASTM D3039 1.12 1.28 1.42 52.27 57.90 66.12 654.63 765.59 886.77
Method ‘1’ 1.17 1.39 1.57 55.39 61.81 71.29 733.90 849.03 974.09
Method B&B 1.17 1.39 1.57 52.27 57.90 66.12 727.33 811.66 950.81
29
Co
up
on
s
Rule of Mixtures
1.50 1.50 1.50 51.19 57.11 62.62 767.92 856.70 939.31
ASTM + Axial Method
1.12 1.29 1.43 51.35 58.48 66.12 654.63 778.96 900.69
Method ‘1’ 1.17 1.44 1.65 52.96 61.94 71.29 733.90 903.23 1050.55
Table 31 – Minimum, Median and Maximum values for each Method
Now the two datasets of 17 and 29 CFRP coupons were represented on stress vs. strain plots to discuss
the scatter of the results given by various methods in respect to each other.
For dataset of 17 coupons (Fig. 59), it was found that Method ‘1’ gave lower dispersion for ultimate
strain by 1.34 % and for Young’s modulus by 6.10 %, and yielded higher data scatter for ultimate stress
results by 15.09 % in comparison to ASTM D3039. Therefore, Method B&B was proposed by giving
lower dispersion for ultimate strain by 1.34 %, the same scatter for Young’s modulus and only slightly
higher scatter for ultimate stress by 4.04 % when compared to ASTM D3039.
In comparison, for 29 coupons shown in Fig. 60, Method ‘1’ provided higher dispersion for ultimate
strain by 10.45 % and stress by 31.87 % and slightly lower for Young’s modulus by 3.29 % when
compared to the combination of ASTM with Axial Method.
Ultimately, the Rule of Mixture is more closely matched through Method B&B for a dataset of 17
specimens and through Method ‘1’ for dataset of 29 coupons.
Test Method for Tensile Strength of FRP like Brittle Materials Page 68 of 94
Figure 59 – Ult. Stress vs. Ult. Strain Scatter Plot for 17 CFRP Coupons
Figure 60 – Ult. Stress vs. Ult. Strain Scatter Plot for 29 CFRP coupons
Test Method for Tensile Strength of FRP like Brittle Materials Page 69 of 94
Closeness of the results to their predictions is shown through plotting test data against predictions. The
perfect match would result in a straight line through the origin and this line is shown in the Fig. 61, 62
and 63 for the Rule of Mixtures predictions. Additional conclusions that can be drawn are whether or
not the methods indicate a tendency to over- or under- estimate.
The ultimate Young’s modulus plot (Fig. 61) indicates how the data scatters around the Rule of
Mixtures’ predictions showing that ASTM D3039 matches the predictions closer (scattered on both
sides of perfect match line) than Method ‘1’, which provides overestimated results. Therefore, ASTM
D3039 procedure for ultimate Young’s modulus estimation was adopted in Method B&B. The same
conclusions were made for a dataset of 29 specimens, which is shown in Appendix H on Graph 2.
Figure 61 - Young's modulus Plot (ASTM vs. Method '1')
Furthermore, two plots showing ultimate stress are provided showing comparisons of ASTM D3039
against Method ‘1’ (Fig. 62) and Method B&B (Fig. 63). It is clear that the scatter of the test data for
Method B&B is smaller with minimum and maximum values being 727.33 MPa and 950.81 MPa
respectively, which is directly cross-checked for Method ‘1’ with values of 733.90 MPa and 974.09 MPa
accordingly (Table 31). However, both Methods ‘1’ and B&B give better predictions to the Rule of
Mixtures by being equally scattered on both sides of the black line with ASTM D3039 giving
underestimation of the results. Similar conclusions were drawn for a dataset of 29 specimens, where
ASTM + Axial Method and Method ‘1’ are checked for their match with the Rule of Mixtures that is
presented on the Graph 1 in Appendix H.
Test Method for Tensile Strength of FRP like Brittle Materials Page 70 of 94
Figure 62 - Stress Plot (ASTM vs. Method '1')
Figure 63 - Stress Plot (ASTM vs. Method B&B)
Test Method for Tensile Strength of FRP like Brittle Materials Page 71 of 94
6.2. CHAPTER CONCLUSIONS It was validated that the best results for Young’s modulus are produced by ASTM D3039 method with
the use of chord modulus that takes into account lower parts of the σ-ɛ curve. Subsequently,
the Method ‘1’ for predicting strains was validated to give the best results for ultimate strain by
resolving the strain components in the principal directions. Finally, the proposed approach for
calculation of stresses by accounting for bending strains is deemed to give the best predictions of
tensile strength.
Therefore, the proposed Method B&B is the combination of the above three analysis for the specimens
providing full range of strain readings up to the failure point. This method gave much closer estimates
to the predictions obtained by the Rule of Mixtures with increase in mean ultimate strain by 8.22 % and
mean ultimate stress by 8.31 % compared to ASTM D3039 and the same mean result for Young’s
modulus. In contrast to ASTM D3039, Method B&B also yielded lower dispersion for ultimate strain by
1.34 %, the same scatter for Young’s modulus and only slightly higher scatter by 4.04 % for ultimate
stress, which is 11.05 % smaller than the dispersion obtained by Method ‘1’ .
Finally, an Axial Method, for those specimens whose gauges flawed before ultimate failure, gave almost
identical results to the ASTM D3039 method, which suggests valid supplementary method for ASTM
standard and increases the dataset of reliable results.
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7. CHAPTER 7 – DISCUSSION
7.1. OVERALL
All analysis methods described in this research rely on the accuracy of the strain readings. It was also
stated by Jakubowski and Rycerz 2012, who identified premature failure of the strain gauges as a
significant problem associated with their experiments. Therefore, a careful preparation of coupons,
providing even and uniform specimens, was identified to be essential for gauges to record reliable
readings. Hence, special attention was given into experimental stage of the project by introducing
improvements to minimise imperfections, air entrainment and strain gauge’s sensitivity to varying
laboratory conditions, which was successfully achieved through the use of recommended type of tape,
15 mm brush, stainless steel spatula and a finger pressure as well as additional environmental strain
gauge. The result is that 59 % (17 out of 29 coupons with 3 strain gauges) of specimens had reliable
strain readings until the ultimate failure of the CFRP coupons with further 41 % suitable for proposed
method’s analysis, whereas Jakubowski and Rycerz obtained 18 % (2 out of 11 coupons with 3 strain
gauges) of coupons having up-to-failure strain readings.
Overall, the proposed Methods ‘1’ and B&B reflect better behaviour of CFRP coupons than ASTM
analysis, which underestimates their properties. They both yield higher values for tensile properties of
FRP with only slight variations in the dispersion of data that matches closer the predictions given by the
Rule of Mixtures. One of the reasons for that is the fibre alignment in the coupon and its inconsistency;
therefore its quality control is critical (ASTM D3039). The results for strains (Method ‘1’) as well as for
stresses (Method B&B) by providing better results validate the strain distribution assumption within
the sample, which is likely to be due to bending, orthotropic nature or imperfections of the material.
It is important to note that release of strain energy when the FRP fibres break is very violent, which can
potentially damage any of the strain gauges on the CFRP coupon’s surface before ultimate condition is
reached. This can be the case when the specimen is subject to large bending or the fibres’ distribution is
non-uniform. It has been observed that couple of samples had stress values dropping, when hearing the
‘cracking sound’ of fibres in the specimens. This phenomenon was observed as a “kink” in the stress-
strain plot due to sudden load drop. Secondly, large bending induced in the coupon due to poor
alignment in the grips or poor sample preparation can lead to premature failure as well as highly
inaccurate determination of the Young’s modulus (ASTM D3039, 2008)
FRP composites exhibit linear elastic stress-strain curve until brittle failure, however non-linearity of
couple strains was noticed in the upper strain regions, which could be due to the behaviour of two
constituent at the interface caused by the matrix reaching its strength and affecting the linear
stress-strain relationship of CFRP composite (Jakubowski, 2012).
The proposed Method ‘1’ by Jakubowski and Rycerz assumes that the maximum strain occurs at one of
the corners. Therefore, any cross-section’s imperfections, like rounded corners or non-rectangular
coupon’s shape could potentially influence (most likely underestimate) the ultimate strain and stress,
affecting the scatter of the data. This was minimised as much as possible through the use of laser cut
slits in the mould that match adopted dimensions of the CFRP coupons and through uniformly
spreading fibres with the use of brush or a spatula.
Moreover, many tested specimens had identified longitudinal splitting failure, which implies that main
assumption of plane section remain plane was not fully satisfied. It was identified that clusters of fibres
slipped past each other in the longitudinal direction, which led to discontinuities because of potentially
Test Method for Tensile Strength of FRP like Brittle Materials Page 73 of 94
weak interface. This could be due to poor saturation of FRP strips, gaps or air entrainment at the
interface leading to non-linear re-distribution of stresses.
FRP is highly complex in analysis as opposed to other structural materials like steel. Results scatter can
be due to lack of control over fibres alignment or inappropriate specimen machining (ASTM D3039,
2008). These are only a few out of many factors affecting the test data, which were identified in
Table 32. Therefore, its behaviour is varied and affected by many factors, hence close attention needs to
be paid during the whole tensile experimentation and any deviations need to be reported as they can
have a significant impact on the final results.
Preparation Stage Experimental Stage
Deformation of the FRP mat;
Misalignment of fibres in the coupon, causing distorted array;
Strain discontinuity at the interface due to poor bond between fibre and matrix;
Fibres in contact with each other;
Air entrainment in the specimen;
Discontinuity of fibres due to mechanical damage;
Poor saturation of FRP strips leading to inadequate bonding;
Localised fibres damage during surface preparation for strain gauges application;
Uneven coupons geometry in either direction;
Curing conditions;
Contamination by foreign matter;
o Poor surface preparation under strain gauges; o Single fibre breaking under strain gauge during
testing leading to its damage; o Coupon’s misalignment in the grips leading to
bending; o Gripping pressure causing possible premature
failures; o Tabs slippage; o The rate of testing; o Environment of testing;
Table 32 - Factors potentially affecting the Tensile Response
Each method introduced in this research has its own limitations, which are described in the following
Table 33:
Rule of Mixtures Method ‘1’ Method B&B
Decision on whether the failure is controlled by brittle failure of fibres or failure of matrix is based on the close inspection of failed CFRP coupons, but this decision determines the value of the ultimate strain used for the method.
Prone to strain readings accuracy because any of the strain readings being non-linear affect the strain components - axial strain and bending strains, showing also non-linear tendency.
It adopts analysis methods, hence limitations, for strain from Method ‘1’ and for Young’s modulus from ASTM D3039.
Linear best fit used to arrive at the ultimate strain and Young’s modulus results is purely based on the researcher’s own judgment, which is non-repetitive and prone to error.
Stress calculation uses bending strains, which can be only suitable for those specimens with full range of strain readings.
Table 33 - Limitations of Different Methods
7.2. PROJECT PLANNING REVIEW
In order to succeed with any project, it is necessary to identify the activities needed to be completed
and their logical sequence. This was accomplished through the help of MS Project software and the
outcomes are presented on the Gantt Charts in Fig. 1 & 2 in Appendix I3 for the interim report and the
final report respectively.
Test Method for Tensile Strength of FRP like Brittle Materials Page 74 of 94
The overall duration of the whole project is estimated to be 188 days. The biggest difference between
two planning sheets is the finalisation of the write-up, as well as changed order of the final activates.
Having deep understanding towards the end of the project and an accurate knowledge of the sequence
of the activities, critical activities (Appendix I1) and milestones (Appendix I2) confirmed to be valid and
will be met on time.
Overall, the project is a success according to the schedule with no major problems identified on the way.
7.3. FUTURE WORK
The coefficient of variance of FRP’s tensile properties through Method B&B did not significantly
decrease, even though the analysis was taking into account the bending effects. Therefore, the
dispersion could be also largely affected by the geometry, experimental preparation, testing etc. Hence,
the discussion of the results brought new light into the research and stated unanswered questions,
which could be tackled in the future study. The following list provides investigation ideas:
It is recommended to have a closer look into geometry improvements to enhance the
repeatability, the reliability and the efficiency of the tensile testing of composite materials as it
was discussed in Section 2.7.1. To begin with the recommended type of geometry would be
exposed-taper, as it has been identified to give the highest strength with low data scatter.
However, there should be identified way of obtaining such shape without cutting the fibres.
Further tensile tests could be carried out with coupons having rotationally self-aligning grips
rather than aluminium tabs, which would possibly highly minimise bending stresses in the
specimens, hence improve the scatter of the test data.
Further investigation into stress calculation improvements could be introduced for Method ‘1’
to account for bending within the samples that had any of the strain gauges failing before
ultimate condition.
Higher order analysis could be undertaken to validate the Bernoulli’s assumption of plane
sections remain plane for the proposed improved methods.
Different types of fibres or polymers could be investigated as well as experimentations could
look into fibre to matrix ratio to identify any correlations and their possible effects on the
methods.
The Rule of Mixtures is based on the assumption of uniform distribution of fibres within the
matrix. However, in the reality, under laboratory conditions the fibres become in contact with
each other as well as they can be randomly scattered in the matrix (Jones, 1999). To account for
these effects, the Halpin-Tsai equation could be taken into consideration rather than the Rule of
Mixtures.
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8. CHAPTER 8 – CONCLUSIONS This research was a thorough study of tensile testing of FRP like brittle materials that was concerned
with the analysis technique of three key parameters: the ultimate strain, the ultimate stress and Young’s
modulus. The report focused on providing deep understanding of the subject through a comprehensive
literature review, problem statement, clear aims and objectives that further led to experimentation and
full analysis with both existing (ASTM D3039, the Rule of Mixtures) and proposed (Method ‘1’, Method
B&B and Axial Method) methods, which was finalised by a statistical validation and comparison.
In respect to the experimental procedure, it is recommended that Powerlink Plus PVC Insulation Tape
19 mm x 33 m is used, while providing an even surface of epoxy on either surface of the FRP sample
after curing, in order to minimise the sticking effect to facilitate procedure of extraction from the mould
and making coupon’s preparation more reliable as well as repeatable. Secondly, application of each
layer of FRP strips should be completed with the help of 15 mm paint brush to spread the fibres in
longitudinal direction and a use of spatula together with the pressure of a finger to effectively remove
the air bubbles and excess of epoxy resin, ultimately producing uniform samples. Lastly, an introduction
of an additional strain gauge, attached to the data logger during testing is advised to improve the
accuracy of the strain readings and to account for laboratory varying conditions or heating from the
current, which supplies power to the data logger.
In relation to the analysis procedures, it is recommended that the proposed Method B&B is used for the
analysis of tensile parameters of FRP for those specimens providing full range of strain readings up to
the failure point. This method gave much closer estimates to the predictions obtained by the Rule of
Mixtures with increase in mean ultimate strain by 8.22 % and mean ultimate stress by 8.31 %
compared to ASTM D3039 and the same mean result for Young’s modulus. In contrast to the ASTM
D3039, Method B&B also yielded lower dispersion for the ultimate strain by 1.34 %, the same scatter
for the Young’s modulus and only slightly higher scatter by 4.04 % for the ultimate stress, which is
11.05 % smaller than dispersion obtained by Method ‘1’ .
Secondly, it is advised to use an Axial Method, for those specimens whose gauges flawed before ultimate
failure, because it gave almost identical results to the ASTM D3039 strain analysis, which suggests valid
supplementary method for ASTM standard. Moreover, the method increases the dataset of reliable
results, which in case of presented 29 coupons reduced the scatter by 1.05 % for the ultimate strain,
0.12 % for the Young’s modulus and 0.57 % for the ultimate stress.
Furthermore, careful reanalysis of Jakubowski and Rycerz 2012 BEng data concluded that the main
objective of truly comparing ASTM D3039 standard with proposed Methods for determining the tensile
properties of CFRP coupons was not achieved. However, they developed methods that can produce
more reliable and repeatable results of tensile parameters for CFRP composites and give closer results
to the predictions given by the Rule of Mixtures.
Overall, the experimental results revealed that the scatter of the tensile properties is still quite
significant by being subjected to both samples preparation and various analyses assumptions. It was
confirmed that the tensile parameters are not only affected by bending that Method B&B accounted for,
but also its orthotropic nature, imperfections and geometry sensitivity as well as non-uniform stress
distribution.
To conclude, the aim of the project, to improve the existing and most common industry standard of
tensile testing ASTMD3039/D3039M-08 of Fibre Reinforced Polymer by developing a reliable test
Test Method for Tensile Strength of FRP like Brittle Materials Page 76 of 94
method that captures more accurately FRP’s tensile parameters, was successfully achieved through
meeting all the objectives within the time constraints and producing much better estimates for FRP’s
ultimate strain, ultimate stress and Young’s modulus.
Test Method for Tensile Strength of FRP like Brittle Materials Page 77 of 94
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APPENDIX A - RISK ASSESSMENT
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APPENDIX B - REQUIRED RESOURCES
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APPENDIX C - SIKAWRAP HEX 230C PROPERTIES
Fibres’ Properties (Sika, 2013a)
APPENDIX D - SIKADUR 330 PROPERTIES
Matrix’s Properties (Sika, 2013b)
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APPENDIX E - FAILURE MODES FOR CFRP COUPONS
No. Sample Name
Average Thickness
[mm] CFRP Layers
Extension [mm]
Max. Load [kN]
Failure Type
Failure Area
Failure Location
1 1-5 2.45 5 8.30 27.04 S G M
2 1-8 2.40 5 6.42 30.71 L G M
3 1-9 2.59 5 5.27 30.57 S A T
4 2-2 2.88 5 4.34 28.28 S A T
5 2-3 2.67 5 6.15 33.03 S G M
6 2-4 2.86 5 4.82 28.21 L A T
7 2-5 2.85 5 5.20 31.68 L M V
8 2-7 2.93 5 5.59 30.40 L G M
9 2-8 2.88 5 5.63 31.50 S G M
10 2-9 2.79 5 5.80 32.04 L G M
11 2-10 2.93 5 5.41 31.29 M W T
12 3-1 2.81 5 6.43 31.13 S I T
13 3-2 2.41 5 5.16 29.53 S A V
14 3-3 2.36 5 6.02 32.44 L G M
15 3-4 2.50 5 7.11 30.34 S G M
16 3-5 2.58 5 7.47 31.01 S G M
17 3-8 2.51 5 7.38 30.11 S A T
18 3-10 2.64 5 5.93 33.72 X I T
19 4-2 2.52 5 5.97 29.74 L G M
20 4-4 2.55 5 6.27 29.06 L G M
21 4-5 2.63 5 6.13 27.40 L A T
22 4-6 2.42 5 5.94 28.92 L G M
23 4-7 2.43 5 7.29 32.83 X W T
24 4-8 2.60 5 5.93 28.38 S A T
25 4-9 2.52 5 6.85 33.54 S A T
26 4-10 2.36 5 5.90 28.60 S G M
27 5-2 2.62 5 6.26 33.33 S A T
28 5-3 2.68 5 5.84 31.41 S G M
29 5-4 2.60 5 6.85 31.07 S G M
30 5-5 2.63 5 5.79 30.73 S I T
31 5-6 2.56 5 6.13 28.51 S G M
32 5-7 2.63 5 5.60 28.95 L I T
33 5-8 2.48 5 5.17 27.95 L G M
34 5-10 2.48 5 5.63 29.25 X G M
Test Method for Tensile Strength of FRP like Brittle Materials Page 84 of 94
APPENDIX F - AUTHOR RESEARCH RESULTS
F1. RULE OF MIXTURES
Specimens in purple had one of the gauges failing before brittle failure of the CFRP coupon.
No. Specimen Avg. Thickness [mm] Vm Vf ɛult. [%] E [GPa] σult. [MPa]
1 1-8 2.40 0.75 0.25 1.50 61.57 923.56
2 1-9 2.59 0.77 0.23 1.50 57.32 859.75
3 2-2 2.88 0.79 0.21 1.50 52.11 781.71
4 2-4 2.86 0.79 0.21 1.50 52.39 785.88
5 2-5 2.85 0.79 0.21 1.50 52.56 788.40
6 2-7 2.93 0.79 0.21 1.50 51.19 767.92
7 2-8 2.88 0.79 0.21 1.50 52.11 781.71
8 2-9 2.79 0.78 0.22 1.50 53.53 803.02
9 2-10 2.93 0.79 0.21 1.50 51.19 767.92
10 3-1 2.81 0.78 0.22 1.50 53.19 797.79
11 3-2 2.41 0.75 0.25 1.50 61.41 921.19
12 3-4 2.50 0.76 0.24 1.50 59.29 889.32
13 3-5 2.58 0.76 0.24 1.50 57.52 862.81
14 3-10 2.64 0.77 0.23 1.50 56.32 844.76
15 4-2 2.52 0.76 0.24 1.50 58.85 882.80
16 4-4 2.55 0.76 0.24 1.50 58.21 873.21
17 4-5 2.63 0.77 0.23 1.50 56.65 849.69
18 4-7 2.43 0.75 0.25 1.50 60.87 913.00
19 4-8 2.60 0.77 0.23 1.50 57.25 858.73
20 4-9 2.52 0.76 0.24 1.50 58.93 883.88
21 4-10 2.36 0.74 0.26 1.50 62.62 939.31
22 5-2 2.62 0.77 0.23 1.50 56.78 851.68
23 5-3 2.68 0.77 0.23 1.50 55.67 835.08
24 5-4 2.60 0.77 0.23 1.50 57.11 856.70
25 5-5 2.63 0.77 0.23 1.50 56.58 848.70
26 5-6 2.56 0.76 0.24 1.50 58.07 871.11
27 5-7 2.63 0.77 0.23 1.50 56.58 848.70
28 5-8 2.48 0.76 0.24 1.50 59.73 895.95
29 5-10 2.48 0.75 0.25 1.50 59.80 897.06
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F2. ASTM D3039
Specimens in purple had one of the gauges failing before brittle failure of the CFRP coupon.
No. Specimen Avg. Thickness [mm] FMax [N] ɛult. [%] E [GPa] σult. [MPa]
1 1-8 2.40 30710 1.24 66.12 853.06
2 1-9 2.59 30570 1.25 59.73 786.87
3 2-2 2.88 28280 1.16 54.92 654.63
4 2-4 2.86 28210 1.22 52.27 657.58
5 2-5 2.85 31680 1.31 65.41 741.05
6 2-7 2.93 30400 1.31 52.43 691.70
7 2-8 2.88 31500 1.17 60.96 729.17
8 2-9 2.79 32040 1.39 53.25 765.59
9 2-10 2.93 31290 1.28 53.56 711.95
10 3-1 2.81 31130 1.37 51.71 738.55
11 3-2 2.41 29530 1.29 61.27 816.87
12 3-4 2.50 30340 1.28 61.77 809.07
13 3-5 2.58 31010 1.35 56.09 801.29
14 3-10 2.64 33720 1.40 57.90 851.52
15 4-2 2.52 29740 1.32 57.35 786.77
16 4-4 2.55 29060 1.24 59.93 759.74
17 4-5 2.63 27400 1.29 51.35 694.55
18 4-7 2.43 32830 1.43 62.30 900.69
19 4-8 2.60 28380 1.14 62.75 727.69
20 4-9 2.52 33540 1.42 58.48 887.30
21 4-10 2.36 28600 1.22 63.52 807.91
22 5-2 2.62 33330 1.39 58.98 848.09
23 5-3 2.68 31410 1.36 55.90 781.34
24 5-4 2.60 31070 1.40 54.95 796.67
25 5-5 2.63 30730 1.29 58.50 778.96
26 5-6 2.56 28510 1.14 61.56 742.45
27 5-7 2.63 28950 1.25 55.86 733.84
28 5-8 2.48 27950 1.12 65.03 751.34
29 5-10 2.48 29250 1.28 56.22 786.29
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F3. METHOD ‘1’
Specimens in purple had one of the gauges failing before brittle failure of the CFRP coupon.
No. Specimen Avg. Thickness [mm] ɛult. [%] E [GPa] σult. [MPa]
1 1-8 2.40 1.31 71.29 933.52
2 1-9 2.59 1.31 64.64 849.03
3 2-2 2.88 1.31 57.72 754.25
4 2-4 2.86 1.31 56.78 745.37
5 2-5 2.85 1.39 55.39 767.59
6 2-7 2.93 1.53 52.96 809.89
7 2-8 2.88 1.50 64.07 963.48
8 2-9 2.79 1.41 55.60 784.77
9 2-10 2.93 1.40 56.01 785.16
10 3-1 2.81 1.44 55.45 796.11
11 3-2 2.41 1.44 64.73 930.14
12 3-4 2.50 1.65 63.24 1041.13
13 3-5 2.58 1.48 61.81 912.99
14 3-10 2.64 1.42 61.94 881.92
15 4-2 2.52 1.51 61.41 925.18
16 4-4 2.55 1.60 62.92 1006.98
17 4-5 2.63 1.44 56.13 810.38
18 4-7 2.43 1.47 64.61 950.35
19 4-8 2.60 1.17 62.49 733.90
20 4-9 2.52 1.50 65.04 974.09
21 4-10 2.36 1.54 68.11 1050.55
22 5-2 2.62 1.54 63.21 972.99
23 5-3 2.68 1.46 59.16 863.00
24 5-4 2.60 1.57 58.33 913.32
25 5-5 2.63 1.51 60.82 917.53
26 5-6 2.56 1.22 63.35 773.86
27 5-7 2.63 1.34 59.49 799.20
28 5-8 2.48 1.37 66.01 903.23
29 5-10 2.48 1.47 65.92 970.31
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F4. METHOD ‘B&B’
No. Specimen ɛult. [%] E [GPa] By (%) Bz (%) σult. [MPa]
1 1-8 1.31 66.12 4.43 -5.20 935.17
2 1-9 1.31 59.73 4.58 -2.66 843.87
3 2-2 1.31 54.92 1.72 -11.21 739.27
4 2-4 1.31 52.27 7.54 3.07 727.33
5 2-5 1.39 65.41 -1.78 -4.81 789.88
6 2-9 1.41 53.25 -0.13 -0.53 770.65
7 2-10 1.40 53.56 3.50 -6.37 782.18
8 3-5 1.48 56.09 8.71 4.48 906.98
9 3-10 1.42 57.90 0.37 0.59 859.70
10 4-2 1.51 57.35 -1.13 11.55 886.54
11 4-8 1.17 62.75 -0.53 2.21 747.69
12 4-9 1.50 58.48 2.91 4.31 950.81
13 5-2 1.54 58.98 2.37 -9.01 944.61
14 5-4 1.57 54.95 1.83 10.55 895.30
15 5-6 1.22 61.56 -4.34 4.98 811.66
16 5-7 1.34 55.86 -2.23 4.59 783.90
17 5-8 1.37 65.03 -7.26 -0.50 809.63
APPENDIX G - JAKUBOWSKI & RYCERZ 2012 REANALYSED DATA RESULTS
G1. COUPONS WITH 3 STRAIN GAUGES
G1.1. RULE OF MIXTURE
No. Specimen Avg. Thickness [mm] ɛult. [%] E [GPa] σult. [MPa]
1 3-3 1.99 1.50 84.5 1267
2 3-4 2.05 1.50 83.8 1257
3 3-6 1.99 1.50 83.2 1248
4 3-7 2.07 1.50 84.4 1265
5 4-4 2.04 1.50 84.0 1260
6 4-7 2.22 1.50 79.2 1188
7 4-8 2.26 1.50 77.2 1158
8 5-2 2.59 1.50 68.3 1025
9 11 2.34 1.50 74.1 1112
10 14 2.21 1.50 78.3 1175
11 17 2.63 1.50 66.3 995
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G1.2. ASTM D3039 + AXIAL METHOD
ASTM D3039 ASTM D3039 + Axial
Method
No. Specimen Avg. Thickness
[mm]
FMax
[N]
ɛult.
[%]
E
[GPa]
σult.
[MPa]
ɛult.
[%]
E
[GPa]
σult.
[MPa]
1 3-3 1.99 27400 1.17 73.64 919.46 1.17 73.64 919.46
2 3-4 2.05 29625
1.19 79.61 964.98
3 3-6 1.99 27638
1.20 63.94 927.43
4 3-7 2.07 27275 1.10 74.26 881.26 1.10 74.26 881.26
5 4-4 2.04 30875
1.35 72.52 1010.64
6 4-7 2.22 30763
1.20 73.00 923.80
7 4-8 2.26 27463
1.12 67.27 808.91
8 5-2 2.59 29913
1.22 61.32 770.94
9 11 2.34 28713
1.24 71.06 819.19
10 14 2.21 29913
1.28 68.53 903.70
11 17 2.63 26825
0.91 73.51 680.84
G1.3. METHOD ‘1’
No. Specimen Avg. thickness [mm] ɛult. [%] E [GPa] σult. [MPa]
1 3-3 1.99 1.27 80.61 1023.54
2 3-4 2.05 1.36 83.46 1132.50
3 3-6 1.99 1.25 82.10 1028.56
4 3-7 2.07 1.24 83.19 1033.10
5 4-4 2.04 1.38 80.23 1109.74
6 4-7 2.22 1.33 76.93 1022.64
7 4-8 2.26 1.28 76.23 973.23
8 5-2 2.59 1.34 73.12 982.76
9 11 2.34 1.54 65.47 1007.26
10 14 2.21 1.35 87.31 1175.58
11 17 2.63 1.26 71.70 900.41
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G2. COUPONS WITH 4 STRAIN GAUGES
G2.1. RULE OF MIXTURE
No. Specimen Avg. thickness [mm] FMax [N] ɛult. [%] E [GPa] σult. [MPa]
1 3-1 2.30 26188 1.50 75.9 1138
2 3-2 2.00 29075 1.50 86.5 1298
3 3-5 2.00 28363 1.50 86.0 1290
4 4-1 2.22 26375 1.50 78.6 1180
5 4-2 2.12 27088 1.50 82.0 1230
6 4-3 2.06 28575 1.50 84.2 1262
7 4-5 2.16 29213 1.50 80.7 1211
8 4-6 2.18 26800 1.50 79.8 1197
9 4-9 2.22 29650 1.50 78.5 1178
10 4-10 2.01 26150 1.50 86.1 1292
11 20 2.21 30225 1.50 79.0 1185
G2.2. ASTM D3039 + AXIAL METHOD
No. Specimen Avg. thickness [mm] ɛult. [%] E [GPa] σult. [MPa]
1 3-1 2.30 1.11 64.5 758
2 3-2 2.00 1.20 73.0 967
3 3-5 2.00 1.18 73.0 937
4 4-1 2.22 1.16 63.3 793
5 4-2 2.12 1.17 67.9 851
6 4-3 2.06 1.37 63.0 905
7 4-5 2.16 1.24 68.5 903
8 4-6 2.18 1.13 68.3 819
9 4-9 2.22 1.23 69.0 890
10 4-10 2.01 1.07 77.4 865
11 20 2.21 1.42 61.2 902
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G2.3. METHOD ‘2’
No. Specimen Avg. thickness [mm] ɛult. [%] E [GPa] σult. [MPa]
1 3-1 2.30 1.12 73.0 815
2 3-2 2.00 1.33 81.2 1078
3 3-5 2.00 1.15 85.0 978
4 4-1 2.22 1.24 71.5 884
5 4-2 2.12 1.41 77.8 1095
6 4-3 2.06 1.48 73.1 1079
7 4-5 2.16 1.42 75.6 1072
8 4-6 2.18 1.28 76.1 978
9 4-9 2.22 1.43 74.2 1059
10 4-10 2.01 1.18 82.0 970
11 20 2.21 1.54 64.7 994
G2.4. METHOD ‘3’
No. Specimen Avg. thickness [mm] ɛult. [%] E [GPa] σult. [MPa]
1 3-1 2.30 1.19 72.0 857
2 3-2 2.00 1.37 81.0 1106
3 3-5 2.00 1.41 83.4 1173
4 4-1 2.22 1.22 71.8 877
5 4-2 2.12 1.49 75.3 1124
6 4-3 2.06 1.48 74.3 1102
7 4-5 2.16 1.48 76.2 1124
8 4-6 2.18 1.31 76.5 1002
9 4-9 2.22 1.43 73.9 1056
10 4-10 2.01 1.20 81.5 978
11 20 2.21 1.39 64.8 900
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APPENDIX H - TEST DATA VS. PREDICTIONS FOR DATASET OF 29 COUPONS
Graph 1 - Ultimate Stress
Graph 2 – Young’s Modulus
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APPENDIX I - PROJECT PLANNING
I1. CRITICAL ACTIVITIES
Table 1 – Critical Activities
I2. MILESTONES
Table 2 - Milestones
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I3. GANTT CHARTS
Figure 1 – Interim Report
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Figure 2 – Final Report