An Experimental and Numerical Investigation of the Biaxial Tensile Behaviour of Biomedical Alloys, Nitinol and SS304

Uladzislau Ivashyn

A Thesis submitted for the Degree of Doctor of Philosophy to Department of Design and Manufacturing Technology, Faculty of Science and Engineering, University of Limerick, Ireland

Supervisor: Dr. Peter Tiernan

May 2015 Contents

LIST OF FIGURES VII

LIST OF TABLES XII

LIST OF ABBREVIATIONS XIII

DECLARATION XIV

STATEMENT XIV

DEDICATION XV

ACKNOWLEDGEMENTS XVI

ABSTRACT XVII

CHAPTER 1 1

1 INTRODUCTION 2

1.1 Research Objectives 4

1.2 Research Hypotheses 5

1.3 Methodology 5

1.4 Thesis Review 9

CHAPTER 2 10

2 LITERATURE REVIEW 11

2.1 Biomedical Materials 11 2.1.1. Introduction 11 2.1.2. Stainless Steel 304/304L. Properties 15 2.1.3. Nickel Titanium (Nitinol). 26 2.1.4 Summary 37

2.2. Sheet Metal Formability 38 2.2.1. Introduction 38 2.2.2. Uniaxial Tensile Testing 40 2.2.3. Multistage Tensile Test 43 2.2.4. Biaxial Testing 46 2.2.5 Summary 52

2.3. Biaxial Planar Testing Systems 53 2.3.1. Introduction 53 2.3.2. Link attachment mechanics for biaxial testing 55 2.3.3. Stand-alone biaxial testing machines 58 2.3.4. Commercial biaxial testing machines 67 2.3.5. Summary 71

2.4. Design of Cruciform Specimens 72 2.4.1. Introduction 72 2.4.2. Historic overview of the design of cruciform specimens 74 2.4.3 Summary 87

2.5 Literature Review Summary 88

CHAPTER 3 90

3 DESIGN AND MANUFACTURE OF BIAXIAL TENSILE SYSTEM 91

3.1. Introduction 91

3.2. Testing system design 92

3.3. Specimen design 98

3.4 System of Grips 103

3.5 Summary 105

CHAPTER 4 106

4 TESTING SYSTEM CONTROLS AND DATA ACQUISITION SYSTEM 107

4.1. Introduction 107

4.2. LabVIEW control system design 107

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4.3. Force measurement 113

4.4. Displacement measurement 120

4.5 Summary 128

CHAPTER 5 129

5 TEST SYSTEM VALIDATION 130

5.1. Introduction 130

5.2. Comparative analysis of uniaxial and biaxial testing for validation purposes 130

5.3. Comparative analysis of biaxial testing results for validation purposes 135 5.3.1 Comparison of CR4 mild steel results 136 5.3.2 Biaxial Testing of Aluminium 1050 H12 138

5.4. Validation of ABAQUS Models 139 5.4.1 Modelling Stainless Steel (SS304) 142 5.4.2 Modelling NITINOL 145

5.5 Summary 147

CHAPTER 6 148

6 RESULTS AND ANALYSIS 149

6.1. Introduction 149

6.2. Finite Element Analysis (ABAQUS) 149 6.2.1 Finite Element Analysis of Stainless Steel SS304 Cruciform Specimen 150 6.2.2 Finite Element Analysis of Nitinol Cruciform Specimen 152

6.3. Testing results and analysis of material properties 154 6.3.1 The results of testing stainless steel SS304 155 6.3.2 The results of testing Nitinol cruciform samples 157

6.4. Microscopic analysis of the specimen (SEM) 162 6.4.1 Microscopic analysis of stainless steel SS304 163 6.4.2 Microscopic analysis of Nitinol 165

6.5. Summary 167

CHAPTER 7 168

7 DISCUSSION 169

7.1. Introduction 169

7.2. Biaxial Testing System 169

7.3. Optimisation of Cruciform Specimen 170

7.4. Establishing the Biaxial Tensile Properties of Biomedical Materials 172

7.5 Summary 173

8 CONCLUSIONS AND RECOMMENDATIONS 175

8.1 Introduction 175

8.2 Conclusions 175

8.3 Recommendations 177

8.4 Summary 180

9 REFERENCES 181

APPENDICES 186

Appendix A Drawings of the Biaxial Test System 187

Appendix B Drawings of the Cruciform Specimens 201

Appendix C Tensile Test Machine Specifications (Tinius Olsen) 208

Appendix D Mechanical Properties of Tested Materials 210

Appendix E LCM 203 Series Load Cell Specifications 216

Appendix F Olympus iSpeed Camera Specifications 219

Appendix G Modelling Specimen Deformation in ABAQUS 222

Appendix H Strain Distribution in Testing Area (Various Load Ratios) 229

Appendix I Load − Strain Diagrams (Various Load Ratios) 236

Appendix J Load − Stress Diagrams (Various Load Ratios) 243

Appendix K Fractured Test Specimens 250

Appendix L Biaxial Testing Data 257

Appendix M Scanning Electron Microscopy Images of Fracture Surfaces 262

List of Figures…………………………………………………………...... Page

Figure 1.1 Schematic process flow diagram for the development of biaxial tensile testing system...... 6 Figure 1.2 Schematic diagram of the system validation process...... 7 Figure 1.3 Schematic diagram of Biaxial Testing and Analysis of biomedical materials...... 8 Figure 2.1 Mechanical properties of common engineering materials compared with those of natural human bone. upper: true stress vs. true strain in the range of 0–0.6; lower: true strain range of 0–0.02 (from Mishuishi, 2013)...... 13 Figure 2.2 Stress-Strain curves for SS304 and SS301 (from NID, 2014)...... 17 Figure 2.3 Stainless Steel bone plate and bone screws...... 19 Figure 2.4 LHD tool geometry (From Talyan 1998)...... 20 Figure 2.5 High rate tensile test done in water and air (from Talyan, 1998)...... 21 Figure 2.6 Forming Limit Diagram SS304 (from Talyan, 1998)...... 21 Figure 2.7 Cracking mode of SS304 under biaxial-tensile cyclic loading (from Zouani, 1999). .. 22 Figure 2.8 Stress-Strain curves for UNS30403 alloy (from Rasmussen, 2003)...... 24 Figure 2.9 Shape and dimensions of the specimen tested, mm (from Zhang, 2007)...... 24 Figure 2.10 SEM micrographs of the surface coating of 304 SS (from Naghib, 2012)...... 25 Figure 2.11 Austenite and Martensite structures of the NiTi compound...... 26 Figure 2.12 Martensitic transfromation (A) and Stress-strain bahavior of the phases of Nitinol (B)...... 27

Figure 2.13 The effect of Nitinol composition on the Ms temperature...... 28 Figure 2.14 Schematic presentation of the stress-strain behaviour of ordinary implant metals. . 29 Figure 2.15 Schematic of the spare memory effect of an SMA showing the unloading and subsequent heating to austenite under no load condition...... 30 Figure 2.16 Stress-strain-temperature data exhibiting the shape memory effect for a typical NiTi SMA...... 31 Figure 2.17 Phase diagram and two possible pseudoelastic loading paths...... 32 Figure 2.18 A typical SMA pseudoelastic loading cycle...... 33 Figure 2.19 Load-extension and engineering stress-strain curve of a ductile metal (a), Expansion of initial part of the curve (b)...... 40 Figure 2.20 Comparison of engineering and true stress-strain curves...... 42 Figure 2.21 Schematic illustration of a multistage tension test (Kim and Yin, 1997; Kuwabara, 2002c)...... 44

Figure 2.22 Growth of flow stresses at 0.2% offset plastic strain σ0.2, with increasing εII...... 45 Figure 2.23 Force balance in hydraulic bulging...... 47 Figure 2.24 The Duncan friction test...... 48 vii

Figure 2.25 Olsen and Erichsen test...... 49 Figure 2.26 Schematic diagram of experimental apparatus for stretch bending test (dimensions: mm) (Kuwabara et al., 2004)...... 50 Figure 2.27 Shapes of specimens and the effect of springback...... 51 Figure 2.28 Uniaxial and biaxial stress states...... 53 Figure 2.29 Biaxial linkage for compression test machine (from Fraunhofer 2005)...... 55 Figure 2.30 Pantograph mechanism for tensile test machine (from Ferron and Makinde, 1988)...... 56 Figure 2.31 Mechanism of Biaxial Holder (from Vezer and Major, 2009)...... 57 Figure 2.32 In-plane biaxial testing system (from Vezer and Major, 2009)...... 58 Figure 2.33 Sketch of the biaxial test apparatus (Makinde et al., 1992) ...... 60 Figure 2.34 Biaxial hydraulic testing machine (Eberhardsteiner 1995) ...... 61 Figure 2.35 Experimental apparatus for the biaxial tensile test (Kuwabara 1998) ...... 62 Figure 2.36 Test Rig for Biaxial Tests (Gozzi 2004) ...... 63 Figure 2.37 Plane biaxial test device for cruciform specimens (Smits 2005) ...... 64 Figure 2.38 Cruciform specimen with actuators: a) four actuators; b) two actuators...... 64 Figure 2.39 Forces on the cruciform specimen: a) ideal situation; b) real situation...... 65 Figure 2.40 Plan view and cross section of the biaxial testing machine (from Merklein, 2008). . 66 Figure 2.41 ADMED planar biaxial test systems (from ADMET, 2014)...... 68 Figure 2.42 Instron planar biaxial cruciform testing system (from Instron, 2014)...... 69 Figure 2.43 Zwick/Roell Biaxial Testing Machines with Electrical and Mechanical Synchronization (from Zwick/Roell, 2014) ...... 70 Figure 2.44 MTS Planar Biaxial Testing Systems (from MTS, 2014)...... 70 Figure 2.45 Stresses on specimens (Geiger et al., 2005)...... 72 Figure 2.46 Proposed geometry for cruciform type specimen (from Ohtake, 1999)...... 73 Figure 2.47 Dimensions (all - inches) of cruciform specimens (from Zidane, 2010)...... 75 Figure 2.48 Cruciform specimen for the biaxial tensile test (from Kuwabara, 1998)...... 76 Figure 2.49 Finite element analysis results of the first principal strain for four cruciform geometries (from Smits, 2006)...... 77 Figure 2.50 Geometry of specimens a) 1; and b) 2 (from Zidane, 2010)...... 78 Figure 2.51 Geometry of specimens a) 3; and b) 4 (from Zidane, 2010)...... 79 Figure 2.52 Equivalent plastic strain and maximal principal strain fields for specimens 1 and 2 (from Zidane, 2010)...... 80 Figure 2.53 Equivalent plastic strain and maximal principal strain fields for specimens 3 and 4 (from Zidane, 2010)...... 81 Figure 2.54 Geometry of the optimized specimen shape (from Zidane, 2010)...... 82

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Figure 2.55 Specimens I and II: transition with chamfer (a) and radius (b) (from Zidane, 2010)...... 83

Figure 2.56 Effect of number of slits N and slit width ws on maximum equivalent plastic strain p ε max applicable to gauge area of cruciform specimen (from Hanabusa, 2013)...... 84

Figure 2.57 Effect of slit width ws and work hardening exponent n on maximum equivalent p plastic strain ε max applicable to gauge area of cruciform specimen. The number of slits is 7. (from Hanabusa, 2013) ...... 85 Figure 2.58 Yield surface for AA6016 alloy: experimental and predicted yield surface by Hill’48, Hill’90 and Yld2000-2d model (from Merklein, 2013)...... 86 Figure 2.59 R-values as a function of the tensile loading axis (from Merklein, 2013)...... 86 Figure 2.60 Yield stress as a function of the tensile loading axis (from Merklein, 2013)...... 87 Figure 3.1 Preliminary Design 1 of Biaxial Testing Machine...... 92 Figure 3.2 Preliminary Design 2 of Biaxial Testing Machine...... 93 Figure 3.3 Interface for the machine control...... 93 Figure 3.4 Final design of Testing System...... 94 Figure 3.5 Support structure for Biaxial Testing System...... 95 Figure 3.6 Main drive unit with motor gearbox...... 96 Figure 3.7 Exploded view of main drive unit...... 97 Figure 3.8 Preliminary Design 1 of Cruciform Specimen...... 99 Figure 3.9 FEA analysis Specimen Design 1...... 99 Figure 3.10 Cruciform Specimen Design 2...... 100 Figure 3.11 FEA analysis Specimen Design 2...... 100 Figure 3.12 Manufacturing drawing of the Specimen Type 1...... 101 Figure 3.13 Manufacturing Drawing for Specimen Type2...... 101 Figure 3.14 Specimen Type 1...... 102 Figure 3.15 EDM processing of the specimen...... 103 Figure 3.16 Proposed System of Grips...... 104 Figure 4.1 The front panel of Controls/Data Acquisition program...... 108 Figure 4.2 Controls of the motors' fine tuning...... 109 Figure 4.3 Data Logging panel of Controls/Data Acquisition program...... 109 Figure 4.4 Block diagram of Controls/Data Acquisition program...... 110 Figure 4.5 Input parameters of the program...... 110 Figure 4.6 Motors Speed Setting and Turning ON code blocks...... 111 Figure 4.7 The Stop Motor/Data Acquisition Block of codes...... 111 Figure 4.8 The Shutdown System codes block...... 112 Figure 4.9 Logging of Data block of codes...... 112 Figure 4.10 Omega LCM 203 Load Cell (from Omega Engineering Inc.)...... 113

Figure 4.11 The SCXI Signal Conditioning Front-End System for Plug-In DAQ Devices (from National Instruments)...... 114 Figure 4.12 SCXI System Configuration (from National Instruments)...... 115 Figure 4.13 Load Cell calibration rig assembly...... 117 Figure 4.14 Correlation between the Load and Force Measured by Load Cells 1 and 2 (loading path)...... 119 Figure 4.15 Correlation between the Load and Force measured by Load Cells 1 and 2 (unloading path)...... 120 Figure 4.16 Bonded Metallic Strain Gauge (from National Instruments)...... 121 Figure 4.17 LVDT assembly for biaxial testing application...... 122 Figure 4.18 Video Extensometer set up over biaxial specimen...... 123 Figure 4.19 Real time video used to set camera over the specimen...... 123 Figure 4.20 Strain measure using Olympus software...... 124 Figure 4.21 Olympus software interpretation of liner distance...... 125 Figure 4.22 Tracking the displacement using Olympus analysis software...... 126 Figure 4.23 Displacement Recording using Olympus software...... 127 Figure 5.1 Uniaxial Testing set up...... 131 Figure 5.2 Standard design for uniaxial specimen...... 131 Figure 5.3 Uniaxial specimens tested on uniaxial machine (a), biaxial system in X (b), and Y (c) directions...... 132 Figure 5.4 The results of uniaxial testing of two specimens...... 133 Figure 5.5 Uniaxial specimen after testing using the biaxial machine...... 133 Figure 5.6 The results of testing uniaxial specimens on the biaxial machine...... 134 Figure 5.7 True stress-strain graph for the specimens tested on uniaxial and biaxial machines...... 135 Figure 5.8 Biaxial specimen after testing CR4 from (Hannon & Tiernan, 2007)...... 136 Figure 5.9 True stress−strain graph − biaxial testing of CR4 from (Hannon & Tiernan, 2007). 136 Figure 5.10 Biaxial specimen used in this study (CR4)...... 137 Figure 5.11 The results of biaxial testing of CR4 (current study)...... 137 Figure 5.12 Aluminium specimen before testing...... 138 Figure 5.13 The results of the biaxial testing of aluminium 1050 H12...... 139 Figure 5.14 The model of biaxial specimen (one quarter)...... 140 Figure 5.15 The meshing applied to the model of the specimen...... 141 Figure 5.16 The visualisation of the test results...... 142 Figure 5.17 True stress−strain graph − stainless steel SS304...... 143 Figure 5.18 Modelled behaviour of stainless steel SS304...... 144 Figure 5.19 Modelling the behaviour of stainless steel SS304 using the constants equation... 145

Figure 5.20 True stress−strain graph − Nitinol...... 146 Figure 5.21 Modelled behaviour of Nitinol...... 146 Figure 6.1 Meshing of biaxial specimen (one quarter) with rectangular elements...... 149 Figure 6.2 Loading simulations - Stainless Steel SS304: (a) 1:0 ratio, (b) 1:1 ratio...... 150 Figure 6.3 Strain distribution under different loading conditions SS304: (a) 1:0 ratio, (b) 1:1 ratio...... 151 Figure 6.4 Load vs strain graph SS304: (a) - loading ratio 1:1.25; (b) - loading ratio 1:20...... 152 Figure 6.5 Loading simulations - Nitinol: (a) 1:0 ratio, (b) 1:1 ratio...... 153 Figure 6.6 Strain distribution under different loading conditions Nitinol: (a) 1:0 ratio, (b) 1:1 ratio...... 153 Figure 6.7 Load vs strain graph Nitinol: (a) - loading ratio 1:1.25; (b) - loading ratio 1:20...... 154 Figure 6.8 Stainless Steel SS304 specimen after testing...... 155 Figure 6.9 Load vs Stress graph SS304...... 156 Figure 6.10 True stress-true strain graph SS304 (biaxial, uniaxial and model)...... 156 Figure 6.11 Stresses in SS304 (X and Y directions) under different loading conditions compared to the von Mises and Hill'48 criterions...... 157 Figure 6.12 Nitinol specimen after testing...... 158 Figure 6.13 Load vs stress graph: Nitinol...... 159 Figure 6.14 Nitinol specimen before (a), during (b) & (c) and after (d) fracturing...... 160 Figure 6.15 True stress-strain graph Nitinol (biaxial and uniaxial)...... 161 Figure 6.16 Stresses in Nitinol (X and Y directions) under different loading conditions compared to von Mises and Hill'48 criterions...... 162 Figure 6.17 SS304 sample (magnification X270)...... 163 Figure 6.18 SS304 sample (magnification X350)...... 164 Figure 6.19 SS304 sample (magnification X900)...... 164 Figure 6.20 Nitinol sample (magnification X100)...... 165 Figure 6.21 Nitinol sample (magnification X400)...... 166 Figure 6.22 Nitinol sample - top surface (magnification X550)...... 166 Figure 7.1 The aluminium (a) and mild steel CR4 (b) specimens before testing...... 171 Figure 8.1 Manufacture of the connection link grove...... 178 Figure 8.2 Proposed system of grips...... 179

List of Tables…………………………………………………………...... Page

Table 2-1 Selected mechanical properties of NiTi...... 28 Table 2-2 Mechanical properties of cold-rolled low-carbon steel sheet used in this study (from Kuwabara, 1998)...... 75 Table 2-3 Stiffness’s of the tested specimens ...... 81 Table 2-4 Optimized geometrical parameters (from Zidane, 2010)...... 83 Table 2-5 Analysis conditions for FEA (from Hanabusa, 2013)...... 84 Table 4-1 Excitation Voltage and current options...... 116 Table 4-2 Load Cells calibration results (loading path)...... 118 Table 4-3 Load Cells calibration results (unloading path)...... 119 Table 4-4 Data Output from the displacement tracking...... 127 Table 5-1 The measurements of the specimens...... 132 Table 5-2 The results testing uniaxial specimens on the biaxial apparatus...... 134

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LIST OF ABBREVIATIONS

A Area m2 a Pressurised area for bulge test m2 d Displacement m d Rate of change E Young’s Modulus N/m2 ε Effective Strain

εz Longitudinal strain

εθ Hoop strain F Force N FE Finite Element FEA Finite Element Analysis FEM Finite Element Method h Bulge height m k Stiffness of the Element L Length m ΔL Change of Length m

Lo Original Length m LVDT Linear Variable Displacement Transducer 2 Pi Pressure inside tube N/m σ Effective stress N/m2 2 σz Longitudinal strain N/m 2 σθ Hoop strain N/m t Thickness m to Initial Thickness m ui Node displacement m UTS Ultimate Tensile Strength MN/m2 V Voltage Volts w Bulge width m

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Declaration

I declare that this thesis has not previously been accepted in substance for any degree and is not concurrently submitted in candidature for any degree.

...... (Uladzislau Ivashyn) (Dr. Peter Tiernan)

Date: ...... Date: ......

Statement

I affirm that the substance of this thesis is entirely the results of my own investigation, unless otherwise stated, and that all sources of information have been properly acknowledged and referenced.

...... (Uladzislau Ivashyn) (Dr. Peter Tiernan)

Date: ...... Date: ......

xiv

Dedication

To my family, in grateful appreciation for their wholehearted support and for their encouragement.

Acknowledgements

I would like to thank to Dr. Peter Tiernan for his excellent help, advice and guidance throughout my research.

A special thanks to the staff of the Design and Manufacturing Technology Department for their support and help throughout this project. Particular, Tom Burns for all the work and helpful advice in design and manufacturing biaxial tensile testing system as well as in manufacturing the cruciform specimens.

A special thanks to Vincent Warfield for his technical advice and expertise as well as Kevin O'Flanagan for electrical installations on biaxial testing system. Thanks to Rose Costello for administrative support and help throughout the study time.

Thanks to all colleagues at the Department and the University of Limerick for making the past few years so enjoyable.

I am grateful to the University of Limerick for the use of its workshops, laboratories and other facilities. I also wish to thank the Irish Research Council (IRC) for their financial support under EMBARK initiative during the course of this research programme and making it all possible.

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Abstract

The tensile test is one of the most commonly used techniques to establish the mechanical properties of a material. The test is accomplished by extending the specimen with known cross sectional area in the direction perpendicular to its cross-sectional area axis. The loading of the specimen is increased until fracture occurs. This simple and accurate method of defining material properties has been the subject of recent research investigations when used to characterise the tensile behaviour of sheet metal. Forming of sheet metal leads to largely anisotropic behaviour of the material under variable loading conditions. It has varying mechanical strength in different directions due to rolling (type of manufacturing process used). The resulting data obtained by the standard tensile test may not be applicable to multi directional forming processes used in biomedical alloys.

Biaxial testing has become an increasingly used common technique to determine mechanical properties of sheet materials. It provides closer approximation of the behaviour of sheet metals (anisotropic materials) during deformation processes used in sheet metal forming. Mechanical loading is applied to a cruciform specimen in two directions simultaneously. One of the aims of this research was to design and build a biaxial planar testing system to study the properties of biomedical materials. A biomedical grade Stainless Steel and Nitinol, near equi-atomic alloy of Nickel and Titanium, were investigated and their tensile properties were established under biaxial loading conditions as well as the mechanisms of their fracture. The goals of this research are outlined in Chapter 1. These goals are followed by hypotheses used in this study.

A comprehensive literature review of four areas: biomedical materials, sheet metal formability, biaxial planar testing and cruciform specimen design was conducted and is presented in Chapter 2. Chapter 3 accounts for the activities necessary to design and manufacture biaxial testing system and cruciform specimens. The biaxial planar testing system was designed, manufactured and assembled at the University of Limerick. Chapter 4 presents the integrations of all the controls and data acquisition components (hardware and software) required for successful testing. Most of the components required for the system were available from the previous research activities in the Department of Design and Manufacturing Technology. Additional items were purchased to satisfy the requirements of the controls and data acquisition system. The biaxial testing system underwent a series of steps to prove its validity. These steps are explained in Chapter 5. The Finite Element Analysis models of Stainless Steel SS304 and Nitinol were developed in ABAQUS software. Stainless Steel SS304 and Nitinol specimens were tested biaxially and also underwent microscopic analysis. Chapter 6 contains the results of biaxial testing of Stainless Steel SS304 and Nitinol, their FEA models and microscopic analysis of the materials. Chapter 7 summarises the experience gained from the project. Conclusions

xvii drawn from the analysis are presented in Chapter 8. Chapter 9 presents a reference list and is followed by Appendices.

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Chapter 1

Introduction

1 Introduction

Research on new materials for biomedical applications has led to exciting scientific developments at the interface between the disciplines of materials science, medicine, chemistry, and biology. Biomaterials have been defined as “nonviable materials used in medical devices, intended to interact with biological systems.” In fact, biomaterials are rarely used as isolated materials but are more commonly integrated into devices or implants. The biological response to the final fabricated biomedical device will ultimately govern its success or failure. The field’s rapid (Patel, 2010).

In modern history, metals have been used as implants for more than 100 years when Lane first introduced metal plate for bone fracture fixation in 1895 (Lane, 1895). In the earliest developments, metal implants faced corrosion and insufficient strength problems (Lambotte, 1909, Sherman, 1912). Shortly after the introduction of the 18-8 stainless steel in 1920s, which had far-superior corrosion resistance to anything in that time, it immediately attracted the interest of the clinicians. Thereafter, metal implants experienced vast development and clinical use. The type of metal used depends on specific implant applications. 304L type stainless steel (304L SS) is still one of the most commonly used alloys in all implants division ranging from cardiovascular to otorhinology. Grade 304 SS is often used as orthopedic implants due to their corrosion resistance, impact resistance, long-term value, strength to weight advantages, hygiene, ease of fabrication and aesthetic appearance.

Nitinol is a nearly equi-atomic alloy of Nickel and Titanium, which possesses the exceptional and unique properties of pseudoelastisity and shape memory. These properties allow the material to undergo large strains and recover completely, and also undergo a deformation at a low temperature and recover its original shape when heated. These properties are the result of a stress- and temperature- induced solid- solid phase transformation within the material, from high temperature parent phase austenite, to the low temperature variant martensite phase. Its properties have promoted its application as actuator, brace wire for teeth, self-expanding stent implants and guidewires for implanting the stent.

A wide range of testing techniques has been applied to discover the mechanical properties of biomedical materials. Uniaxial tensile testing and a combination of biaxial torsion and tensile testing are among those most common tests conducted. One of the aims of this research is to test biomedical materials (304 SS, Nitinol) under biaxial tensile loading to investigate the difference in its behaviour under this type of loading as compared to uniaxial loading. This will provide data for sheet metal forming of these materials.

Sheet metal forming processes are among the most important metal working operations (Green, Neale et al. 2004). These processes account for a sizeable proportion of the manufactured goods made by industrialised countries each year. Frequently, the metals used in these forming processes have limited formability. Thus, a thorough understanding of the deformation processes and the factors limiting the forming of sound parts is important, which contributes to faster product development at a lower cost and with enhanced product quality (Klaus and Gerlach 1998).

In sheet metal forming operations, the amount of useful deformation is limited by the occurrence of unstable deformation, which mainly takes the form of localised necking or wrinkling. Failure by wrinkling occurs when the dominant stresses are compressive, tending to cause thickening of the material. Localised necking occurs when the stress state leads to an increase of the surface area of the sheet at the cost of a reduction in the thickness. Sheet metal used in forming processes is typically accompanied by data that defines the behaviour of the material when it is subjected to mechanical loading. This important data, which usually includes material yield strength, tensile strength and work hardening exponent, is typically obtained from a standard uniaxial tensile test. As most metal forming operations are carried out under biaxial states of stress, the stress–strain formability parameters obtained by uniaxial tensile testing are inadequate for the application to deformation induced under states of biaxial stress (Jones 2001). Consequently, biaxial testing has become of great importance in establishing the formability characteristics of sheet metal where the material is subjected to deformation in more than one plane or axis. Furthermore, many manufacturing materials exhibit anisotropic properties for which in-plane biaxial testing of cruciform (cross-shaped) specimens is important for deriving mechanical properties used in the determination of a material’s formability (Demmerle and Boehler, 1993).

Biaxial tensile testing has become increasingly common in determining the mechanical properties of materials used in aircraft structural components, bridge support sections, machine components, etc. (Jones 2001). In service, these components are normally loaded in more than one direction at once, i.e. biaxially loaded. It has been recognised that limiting the evaluation of a material's mechanical characteristics to uniaxial coupon tests can lead to a misrepresentation of the behaviour of a material in an engineering structure (Green, Neale et al. 2004). However, by the use of more realistic loading during the test, such as the introduction of biaxial loading conditions, leads to a more accurate representation of the expected behaviour of the structure in-service (Ohtake and Rokugawa, 1999).

Among the experimental methods in use, biaxial tensile testing with various types of cruciform specimens has become the most promising method to produce stress states of biaxial tension

3 by changing proportion of load or displacement of two axes (Wu and Wan, 2005). The most important element of a biaxial testing system is the design of the cruciform specimen. To enable the acquisition of full stress–strain curves, the centre section of the specimen must experience elastic and plastic deformation. Although specimens of the cruciform type have been investigated quite extensively, no standard geometry exists for the specimen design (Lin and Ding, 1995).

1.1 Research Objectives

The current research seeks to answer the following questions: 1. Does Nitinol exhibit anisotropic behaviour during biaxial testing? 2. Does the deformation pattern of Nitinol during biaxial testing follow the same path (elastic – plastic – necking – fracture) as during the uniaxial test? 3. Does Nitinol obey Von Mises criterion for multiaxial deformation? 4. What is the fracture mechanism for the biomedical materials SS304 and Nitinol?

The steps below were determined to accomplish the research goals and answer the questions above:  Design, manufacture and commission a Biaxial Tensile Testing rig, to determine the biaxial tensile properties of biomedical materials (304 SS, Nitinol)  Design an optimised cruciform specimen using experimental data and Finite Element Analysis software  Analyse data obtained from Biaxial Testing and compare it with uniaxial tensile testing data for biomedical materials (304 SS, Nitinol)  Use optical and scanning electro-microscopy (SEM) to establish microstructural changes and fracture patterns at strained areas of tested samples.

1.2 Research Hypotheses

The following hypotheses were established to find answers the research questions above:

Hypothesis 1: Nitinol will exhibit anisotropic behaviour during the biaxial testing. Its mechanical properties will be different to the ones determined by uniaxial testing.

Hypothesis 2: The deformation pattern of Nitinol will follow the same path (elastic – plastic – necking – braking) when testing the material biaxially comparing to the path of uniaxial test.

Hypothesis 3: Nitinol does obey Von Mises criterion for multiaxial deformation.

Hypothesis 4: The same fracture mechanisms disclosed in the other metallic materials (crystal structure imperfections, voids and crack propagations) will become evident for Nitinol during biaxial testing.

1.3 Methodology

It was envisaged at the start of the current research programme that planar biaxial testing system would be designed and manufactured. It was required to carry out the biaxial test programme. The limitations of the existing device - attachment to uniaxial tester - designed by Hannon at the University of Limerick in 2007 were outlined by the researcher. One of the recommendations of the previous research team included the development of stand-alone machine to allow for different speeds in the X and Y directions during biaxial testing (Hannon & Tiernan, 2007). Figure 1.1 shows the process flow diagram for the biaxial testing system development.

Figure 1.1 Schematic process flow diagram for the development of biaxial tensile testing system.

A more detailed explanation of the validation technique is presented in Chapter 5. A schematic diagram of the validation process is shown in Figure 1.2.

Yes

Figure 1.2 Schematic diagram of the system validation process.

A schematic diagram of the methodology used during biaxial testing and analysis of biomedical alloys; Stainless Steel SS304 and Nitinol is shown in Figure 1.3.

Figure 1.3 Schematic diagram of Biaxial Testing and Analysis of biomedical materials.

1.4 Thesis Review

This thesis outlines the steps undertaken to achieve the completion of the current study. In Chapter 2, a comprehensive, critical literature review of the subject area is provided to include the overview of the biomedical materials, SS304 and Nitinol. This Chapter reports on the research work carried out to date on the design of a biaxial testing machine and cruciform specimen as well as preliminary finite element analysis on the specimen. Chapter 3 overviews the work carried out on the design and manufacturing of the biaxial testing rig as well as cruciform specimen. Chapter 4 reviews testing system controls and data acquisition. The technique used for testing system validation is described in Chapter 5. The outcomes/results of this research and their analysis are outlined in Chapter 6. Chapter 7 and 8 contain the discussions and recommendations/conclusions, which summarise the outcomes of the current research. Chapter 9 presents all the references used in this thesis. Appendices present the drawings and other research data.

Chapter 2

Literature Review

2 Literature Review

2.1 Biomedical Materials

2.1.1. Introduction

The development of medical devices and systems is essential for improving the quality of life and reducing global healthcare costs. A comprehensive surgical system assisted by tele- operation, imaging, and predictive modelling, as an example, can extend the effective years of skilful doctors and bring time-sensitive treatment to remote sites using high-speed Internet. The global market volume for medical equipment was approximately USD 297 billion in 2012 according to Frost & Sullivan’s survey. Prosthesis is another high-demand item. The global market value of knee and hip prostheses reached EUR 9 billion in 2011 with about 58% of the market in the USA, 23% in Europe, and 19% in Asia–Pacific. This sector will continue to grow as people become more active in sports and live longer. Other bio-implant applications include pacemakers to treat heart disorders – a USD 4.2 billion market in 2008 is expected to grow to a USD 6.1 billion market in 2015 (Mitsuishi, Cao, & Bartolo, 2013) – and deep brain stimulation (DBS), which is a new treatment method for curing Parkinson’s disease (Hur, Harris, & Pharm, 2010). Miniaturising these implants is highly desirable for and critical to improving patients’ quality of life. A miniaturised external artificial kidney that integrates micro-manufacturing and control technologies with biosensors can alleviate the suffering and restore the productivity of an estimated 438 million diabetic adults (7.8% of the world’s adult population) by 2030 (Mitsuishi, Cao, & Bartolo, 2013).

Owing to the nature of the active interaction of medical devices and human systems, the design requirements for biomedical products and systems significantly differ from those for other consumer or commercial products: examples include reliability, corrosion resistance, biocompatibility, customisation, doctor–intuitive interface, and controllability. Advanced manufacturing technologies are needed to achieve these desired attributes at reduced cost, particularly in patient-specific products and for patients in developing countries.

To meet the challenges in biomedical manufacturing, the International Academy for Production Engineering (CIRP) created a collaborative workgroup (CWG) in August 2010 known as ‘Bio- manufacturing’ to address the integration of current manufacturing technologies and the development of new methods. Bio-manufacturing requires expertise in basic manufacturing processes – such as cutting, electro-physical and chemical processes, forming, and abrasive processes – integrated with machine design, surface modification, precision engineering, and 11 metrology under the overarching frameworks of design, life cycle engineering and assembly, production systems, and organisation.

Bio-manufacturing is defined as the application of design and manufacturing technologies to reduce the cost while advancing the safety, quality, efficiency and speed of healthcare service and biomedical science (Mitsuishi, Cao, & Bartolo, 2013).

A large number of CIRP and non-CIRP members actively participated in the collaborative research activities of the CWG and identified the following core themes for bio-manufacturing:

(a) bio-specific design constraints (design strategy, personalised manufacturing, classification, and biocompatibility);

(b) bio-mechatronics (sensors, actuators, systems, and metrology);

(d) bio-design and assembly (modelling, design, and interfaces).

The aims and objects of this research mainly fall into (a) and (c) categories outlined above. Both categories are directly related to the goals of current research. Designers need to have in-depth knowledge of the materials used in bio-engineering. This deeper knowledge of the materials behaviour leads to inventions of new materials which closely meets customers’ requirements.

Bio-fabrication includes the fabrication of natural and artificial body components and the fabrication of biomedical devices that are used in surgery. Bones, artificial joints, and biomaterials are machined, and pacemaker components are stamped or moulded before they are implanted in a human body during a surgical procedure, which may use an endoscope again made through bio-fabrication. The quality of bio-fabrication depends on the combination of a good understanding of material and process mechanics and the availability of advanced machine tools. The demand for bio-fabrication is expected to increase with an ageing society. The demand for less invasive surgical procedures imposes an increasing need for micro- manufacturing capabilities. They are defined as processes that can create features where two dimensions are less than a millimetre in scale. Such examples include parts used for arthroscopy, dental treatment, endoscopy, oncology, orthopaedics, and biomedical implants to cope with vascular diseases (Mitsuishi, Cao, & Bartolo, 2013).

Fabrication of natural materials, including bone and blood clots is a part of bio-fabrication processes. Bone, skin, and tissue are common natural materials that are worked with in surgery. A common feature of these natural materials is a hierarchal structure, which leads to highly anisotropic behaviour. The mechanical properties of bone have been studied from a 12 biomechanical point of view since the second half of the nineteenth century. In Figure 2.1 the mechanical tensile properties of natural human bone are compared with those of typical engineering materials used in biomedical devices. The metallic materials have much greater elongation than natural human bone; the initial elastic modulus of the Ni–Ti smart memory alloy is the closest to that of natural bone. The latest research on bone mechanical properties has focused on analysis of bone substance behaviour at the microscopic level (Mitsuishi, Cao, & Bartolo, 2013).

Figure 2.1 Mechanical properties of common engineering materials compared with those of natural human bone. upper: true stress vs. true strain in the range of 0–0.6; lower: true strain range of 0–0.02 (from Mishuishi, 2013).

Material choices for implantable biomedical products are limited owing to the requirements of biocompatibility and corrosion/fatigue resistance and the difficulties in obtaining regulation clearances. Before proceeding with the discussion on bio-fabrication processes, understanding the material choices available in bio-manufacturing is important. 13

Platinum group metals (PGMs) are a common choice because of platinum’s appropriate ‘charge injection properties’, which are similar to those of gold, another commonly used material in bio- devices. Palladium and rhodium are both considered Pt group metals. PGMs are generally costly: about USD 38/g in 2012. Commercially pure platinum (99.95% Pt) has an ultimate tensile strength (UTS) of 125–240 MPa with an elongation of up to 40% at the annealed stage. Platinum–iridium alloy (Pt–10% Ir) has an UTS of 380–620 MPa, whereas that of platinum– tungsten alloy (Pt–8% W) can reach 895–2070 MPa.

Metal–ceramic alloys are popularly used in dental restoration. Gold–platinum–palladium (Au– Pt– Pd) was the first successfully used alloy. In recent years new alloys have been developed with better mechanical properties and ‘sag resistance’ (i.e. resistance of film to sagging on a surface). Pt alloys are being replaced by new Pt-free alloys owing to the latter’s more economical production and better properties.

Titanium and its alloys are used in joint replacement, spine and trauma systems, dental implants, and pacemaker casings. It is a common material choice for nails and screws to fix artificial bones in surgery because of its favourable biocompatibility, corrosion resistance, and mechanical properties. One of the most commonly used materials for these components is the titanium alloy Ti6Al4V.

Stainless steel – which is known for its strength, hardness, corrosion resistance, and ease of sterilisation – is widely used in arthroscopic, endoscopic, and dental instruments as well as in vascular stents and surgical instruments.

As a degradable implant material, magnesium provides both biocompatibility and sufficient mechanical properties. Previous studies have shown that magnesium, which is an essential element of the human body, is suitable as a degradable biomaterial for use in medical implants. Furthermore, the mechanical properties of magnesium alloys are superior to those of biodegradable synthetic polymers but inferior to those of permanent surgical steel or titanium alloys. The base character of magnesium leads to a low corrosion resistance; it is significantly attacked in saline media, which is a particular environment of the human body. This chemical characteristic enables its use as an absorbable implant material. Magnesium alloy AZ31 has been investigated as a stent material. One challenge with using magnesium alloy implants is slowing down the degradation rate. Researchers have shown that surface modification can alter the corrosion behaviour (Tomac & Tonnessen, 1991) through the use of machining, EDM, or ECM processes.

Biodegradable implants that dissolve in the human body represent an appropriate solution. Polyglycolide (PGA), polylactide (PLA), and polydioxanone (PDA) are synthetic biodegradable

14 polymers that have been clinically used as surgical materials during the last few decades (Denkena & Lukas, 2007). Porous polymer media made of polycarbonate (PC) or polydimethylsiloxane (PDMS) are an effective base for cell cultures owing to their low cost, biocompatibility, and manufacturability.

Shape memory alloys respond to external stimuli with a change in a key material property. Nitinol is a nickel–titanium shape memory alloy used primarily in vascular stents. Nitinol has good electrical and mechanical properties, long fatigue life, and high corrosion resistance. In particular, nitinol is both self-expanding and crush-recoverable (i.e. it fully recovers its shape after being crushed flat). At the target site, nitinol stents are released from the delivery system and elastically expand until they contact the vessel wall. Nitinol is also used in catheters and endoscopic guide wires to make them more steerable by altering the tool’s stiffness during procedures.

Understanding the behaviour of both natural and artificial materials under combined loading conditions is critical to process planning and surgery planning. Human bone, as an example, is a one-direction reinforced composite material that has anisotropic characteristics that will respond to machining differently depending on the cutting direction and process planning. In addition, surface interactions of natural material with artificial materials (e.g. bonding between living tissues and biomaterials) over various length scales need to be understood to design the properties and surface textures of bio-devices.

Investigation of the properties of biomaterial materials have not been extensively investigated in terms of their process capabilities and interfacial behaviour with other engineering materials or natural materials compared to traditional engineering materials. Different loading conditions and loading sensitivities may be needed for this material class in the standard testing apparatus (Mitsuishi, Cao, & Bartolo, 2013).

2.1.2. Stainless Steel 304/304L. Properties

Stainless steels are iron-base alloys containing 10.5% or more chromium by mass. They have been used for many industrial, architectural, chemical and consumer applications for over a half century.

Stainless steel is the most common alloy (a mixture or solid solution of two or more metals) used for surgical instruments. These alloys are used for manufacturing surgical instruments because they have specific properties that make them more useful than pure metals. There are

15 several types of stainless steel alloys and understanding their characteristics is critical to determine how they can be used. Stainless steels are normally grouped in three types:

• Austenitic – Austenitic steels are alloys containing chromium and nickel (and sometimes manganese and nitrogen). The most familiar stainless steel is Type 304, sometimes called T304. The high chromium content of austenitic stainless steel enables it to resist oxidation (scaling) and corrosion, and makes it more malleable and workable;

• Ferritic – Ferritic steels contain ferrite, iron and chromium. They are less ductile (able to be moulded or shaped) than austenitic steels and cannot be hardened by heat;

• Martensitic – Martensitic steels contain a small amount of carbon and they can be tempered, hardened and sharpened. Martensite gives steel great hardness, but it also reduces its toughness and makes the steel brittle. This type of stainless steel is used when sharp cutting edges are required (Pagounis & Lindroos, 1998).

The most widely used of the austenitic grades, 304 offers good corrosion resistance to many chemicals and industrial atmospheres. It has a nominal composition of 18% chromium and 8% nickel (NID, 2014). Generally considered non-magnetic, it can become slightly magnetic when cold-worked. 304 is non-hardenable by heat treatment. In 304L, the carbon content has been lowered to 0.03% max. for corrosion resistance at heat affected zones from welding (Alro, 2014).

Austenitic stainless steels also possess a unique combination of properties that makes them useful at cryogenic (very low) temperatures. These steels have low temperature tensile strengths that reduce strains and ruptures, while their toughness is only slightly degraded. This property is useful for surgical interventions that use low-temperature action on the tissue being dissected and for the forging stage of instrument manufacturing. Figure 2.2 shown Stress-Strain curves for Type 304 and Type 1 stainless steels.

Figure 2.2 Stress-Strain curves for SS304 and SS301 (from NID, 2014). 2.1.2.1. Production of Stainless Steel

A major advantage of stainless steels and the austenitic grades, in particular, is their ability to be fabricated by all the standard manufacturing techniques. The common austenitic grades can be folded, bent, cold- and hot-forged, deep drawn, spun, and roll-formed. The first (forming) stage of instrument manufacture may be done manually or mechanically. Hot operations such as rolling, extrusion and forging are among the methods which result in finished or semi-finished parts.

The mechanical properties of stainless steels serve as an indication of their relative formability at ambient or room temperature. Annealed austenitic grades are typically having low yield strengths, high tensile strength and high elongation. Some of these alloys work harden to a high degree, which further increases their strength properties. The ferritic alloys have much lower ductility than the austinitic types and are closer to carbon steels with the respect to mechanical properties; and they do not work harden significantly during cold forming. Because of the excellent mechanical properties stainless steels has exceptional cold-forming characteristics.

The weldability of various grades of stainless steels varies considerably. Nearly all can be welded, and the austenitic grades are some of the most readily welded of all metals. Examples of welded instruments include Frazier suction tips, Deaver retractors with formed handles, and some orthopedic reamers. Inspection of all welded points is essential to ensure the weld is of high quality to prevent instrument failure during a surgical procedure.

During the manufacturing process, stainless steels are often heat-treated by methods that depend upon the type of stainless steel and the reason for the treatment. Annealing, hardening and stress-relieving restore desirable features such as corrosion resistance and ductility to 17 metal that were altered by fabrication. While austenitic stainless steels cannot be hardened by thermal treatments, they do harden rapidly by cooling to sub-zero temperatures.

The desirable corrosion-resistant surfaces of stainless steel surgical instruments can only be achieved if appropriate cleaning and finishing operations are carried out after the fabrication process is completed. The presence of any iron, cast iron, mild steel, carbon steel, or low alloy steel particles on the surface of stainless steel will promote pitting corrosion at the points where the “free” iron and stainless steel meet. This potentially serious problem most often occurs from the contamination caused by scraping the instrument with carbon steel tools or fixtures, or from grinding and polishing tools. Passivation creates a protective film on the surface of steel. This process involves the removal of free iron by immersing the steel in an oxidant such as nitric acid or citric acid solution.

2.1.2.2 Applications of SS304

The stainless steel family offers a remarkable and extremely versatile range of engineering materials. They are widely used in the medical device sector.

Stainless steels have been long established in medical device applications, it is important to distinguish between stainless steels used for implant applications and commercial grades [eg 1.4305 (AISI 303), 1.4301 (AISI 304) and 1.4401 (AISI 316)] used for other medical devices (eg dental scalers, dental explorers, dental and surgical forceps, kidney dishes, theatre tables, etc).

ISO 7153-1 specifies stainless steels for surgical and dental instruments. It should be stressed that the grades specified in ISO 7153-1 are generic and represent typical, readily available, commercial steel compositions (ie not specifically prepared for surgical applications). This standard also provides an indication of typical applications for each grade.

Martensitic stainless steel [eg grades 1.4006 (AISI 410), 1.4021 (AISI 420), 1.4028 (AISI 429) and 1.4125 (AISI 440C)] is used extensively for dental and surgical instruments. These stainless steels can be heat treated (hardened and tempered) to develop a wide range of mechanical properties (high hardness for cutting instruments and lower hardness with increased toughness for load-bearing applications).

Austenitic stainless grades AISI 303, AISI 304, AISI 316 and their derivatives are also used for medical devices (Figure 2.3). Grade AISI 303 stainless steel is used where its free-machining properties enhance the ease of manufacture (eg medical devices with screw threads, with drilled and/or tapped holes). Handles of multi-part dental instruments are often manufactured in grade 1.4305 (AISI 303), where its lower corrosion resistance is not a disadvantage. Grade

1.4301 (304) and its derivatives are used where good corrosion resistance and moderate strength are required (eg dental impression trays, hollowware, retractors, guide pins, theatre tables and storage cabinets), while grade 1.4401 (AISI 316) and its directives may be used for dental explorers and vaginal probes (Newson, 2003).

Figure 2.3 Stainless Steel bone plate and bone screws.

Appropriate material selection is critical for the most cost-effective instruments. The material must perform as intended, and it must also be one that can be fabricated economically. Historically, stainless steel (type 304) has been used for the tubular components of dental and surgical instruments. This alloy has worked well for instruments designed for use in confined spaces; however, it has some drawbacks that limit its usefulness (Pagounis & Lindroos, 1998). These include loss of strength during welding and poor edge retention, wear resistance and galling resistance.

Interest in metal release from medical devices in contact with body fluids and human tissue has tended to remain an academic issue, which has mainly concerned surgeons when their patients have exhibited allergies attributable to specific metals (eg nickel). As a consequence, test methods for such studies have not been refined and remain to be validated. In addition, the quality of papers on the subject is variable and a frequent criticism of such studies is that test materials are not adequately characterised. For these reasons, it is difficult to provide typical values for metal release from materials in contact with body fluids and human tissue. However, test results indicate that metal release from metallic materials in contact with body fluids/human tissue is greater than that for drinking water. The ongoing EU Risk Assessment of nickel has required a greater understanding of these interactions and the proposed European New

Chemicals Policy will require still more data. In response, research on stainless steels in contact with body fluids has commenced (Newson, 2003).

2.1.2.3 Previous Research on Formability of Stainless Steels

The forming behaviour of austenitic steels (Types 201, 301 and 304) was investigated by Talyan in 1998. The ability to form sheet metal (formability) is controlled by the materials resistance to strain localisation and fracture and ability to distribute strain over an arbitrary tool surface. Thus, formability represents a complex interaction of mechanical properties, surface properties and configuration, and applied rates and temperature (Talyan, Wagoner, & Lee, 1998).

The Limiting Dome Height (LHD) testing system shown in Figure 2.4 was used to evaluate the accuracy of numerical simulations and to estimate formability under the conditions approximating those found in forming operations.

Figure 2.4 LHD tool geometry (From Talyan 1998).

The austenitic steels were tested at 10-1/s immersed in water at 21°C and in air in order to distinguish the effect of strain rate and temperature rise. The water improved heat transfer from the specimen. The results of the LHD tests are shown in Figure 2.5.

Figure 2.5 High rate tensile test done in water and air (from Talyan, 1998).

Forming Limit Diagrams (FLD) were constructed for different grades of stainless steel including Type 304 as shown in Figure 2.6.

Figure 2.6 Forming Limit Diagram SS304 (from Talyan, 1998). 21

In 1999 team of researchers from Ecole Polytechnique de Montreal, Canada investigated "Fatigue Life Parameters for Type 304 Stainless Steel under Biaxial-Tensile loading at elevated temperatures" (Zouani, Bui-Quoc, & Bernard, 1999). The aim of their research was to examine the behaviour of mechanical components subjected to cyclic loading conditions. A focus was placed on localisation of critical stress areas of the specimen under biaxial loading.

Results of this research included analysis of the failure mechanism. Some images of the tested components are shown in Figure 2.7. The photos were obtained during the examination of the specimen cross section after fracture.

Figure 2.7 Cracking mode of SS304 under biaxial-tensile cyclic loading (from Zouani, 1999). 22

The research group concluded that micro cracks initiated in the direction perpendicular to the major normal strain and the main crack propagated in the circumferential direction (Zouani, Bui- Quoc, & Bernard, 1999).

Researchers from the University of Sydney investigated "Full-range stress-strain curves for stainless steel alloys" in 2003. According to the author, the research is useful for the design and numerical modelling of stainless steel members and elements which reach stresses beyond the 0.2% proof stress in their ultimate limit state. In this stress range, current stress–strain curves based on the Ramberg–Osgood expression become seriously inaccurate principally because they are extrapolations of curve fits to stresses lower than the 0.2% proof stress. The extrapolation becomes particularly inaccurate for alloys with pronounced strain hardening (Rasmussen, 2003).

A new expression for simulation of full stress-strain curve was proposed as shown in Equation 2.1.

휎 휎 푛 + 0.002 ( ) 푓표푟 휎 ≤ 휎0.2 퐸0 휎0.2 휀 = { 푚 Eq. 2-1 휎− 휎0.2 휎− 휎0.2 + 휀푢 ( ) + 휀0.2 푓표푟 휎 > 휎0.2 퐸0.2 휎푢− 휎0.2

where ε, ε0.2 and εu are strain, 0.2% strain and ultimate strain respectively, E0 - Young’s modulus, σ, σ0.2 and σu - stress, 0.2% proof stress and ultimate strain respectively, parameter (n), which determines the sharpness of the knee of the stress–strain curve, is determined using the Equation 2-2.

풍풏 (ퟐퟎ) 풏 = Eq. 2-2 풍풏 (흈ퟎ.ퟐ⁄흈ퟎ.ퟎퟏ)

Exponent m is determined using Equation 2-3.

흈ퟎ.ퟐ 풎 = ퟏ + ퟑ. ퟓ Eq. 2-3 흈풖

Young's Modulus E0.2 is determined as a slope to strain-stress graph at 0.2% strain using Equation 2-4.

푬ퟎ 푬 = Eq. 2-4 ퟎ.ퟐ ퟏ + ퟎ.ퟎퟎퟐ풏⁄ 풆 23

In the design of stainless steel structures, it has become industry practice to use the 0.2% proof stress (σ0.2) as the equivalent yield stress (Rasmussen, 2003).

Comparative analysis of the test data and two simulations are shown in Figure 2.8.

Figure 2.8 Stress-Strain curves for UNS30403 alloy (from Rasmussen, 2003).

Zhang in 2007 investigated multiaxial creep-fatigue life using cruciform specimens (Zhang, Harada, Ozaki, & Sakane, 2007). The research group used cruciform specimens made from Type 304 stainless steel heat treated at 745 °C for 1 hour. The shape and dimensions of the specimen used are shown in Figure 2.9.

Figure 2.9 Shape and dimensions of the specimen tested, mm (from Zhang, 2007).

Naghib and the other researchers investigated the bioactivation of 304 Stainless Steel through 45S5 Bioglass Coating for Biomedical Applications (Naghib, Ansari, Pedram, Moztarzadeh, & Mozafari, 2012). Micrographs obtained by the research group are shown in Figure 2.10.

Figure 2.10 SEM micrographs of the surface coating of 304 SS (from Naghib, 2012).

The Figure 2.10 shows the SEM micrographs of the surface of 304 SS coated by 45S5 bioglass using both melting (A) and sol–gel techniques (B) after 14 days immersion in simulated body fluid (SBF). The difference between the hydroxyapatite (HA) layers formed on the coatings produced by two different techniques could be clearly defined. The HA layer formed on the coating produced by sol–gel technique showed more perfect and homogeneous surface, whereas a porous and a heterogeneous surface in micro-scale was formed on the other specimen (Naghib, Ansari, Pedram, Moztarzadeh, & Mozafari, 2012).

2.1.3. Nickel Titanium (Nitinol).

Nickel titanium, also known as Nitinol or NiTi, is a metal alloy of nickel and titanium, where the two elements are present in nearly equal atomic percentages.

The term Nitinol is derived from its composition and its place of discovery: (Nickel Titanium Naval Ordnance Laboratory). William Buehler along with Raymond Wiley discovered its properties during research at the Naval Ordnance Laboratory in 1962 (Gall and Sehitoglu 2001).

While the potential applications for Nitinol were realised immediately, practical efforts to commercialise the alloy did not take place until a decade later. This delay was largely due to the extraordinary difficulty of melting, processing and machining the alloy. Even these efforts encountered financial challenges that were not overcome until the 1990s, when these practical difficulties finally began to be resolved (Hane and Sheild 1999).

Nitinol can exist in a two different temperature-dependent crystal structures (phases) called martensite (lower temperature) and austenite (higher temperature or parent phase) as presented in Figure 2.11. Several properties of austenite NiTi and martensite NiTi are notably different (Lagoudas 2008).

Figure 2.11 Austenite and Martensite structures of the NiTi compound.

When martensitic NiTi is heated, it begins to change into austenite Figure 2.12a. The temperature at which this phenomenon starts is known as the austenite start temperature (As). The temperature at which this phenomenon is complete is known as the austenite finish temperature (Af). When austenite NiTi is cooled, it begins to change into martensite. The temperature at which this phenomenon starts is known as the martensite start temperature

(Ms). The temperature at which martensite is again completely reverted is known as the martensite finish temperature (Mf) (Buehler and Wang 1967).

Composition and metallurgical treatments have a dramatic impact on the aforementioned transition temperatures. From the point of view of practical applications, NiTi can have three different forms: martensite, stress-induced martensite (superelastic), and austenite. When the material is in its martensite form, it is soft and ductile and can be easily deformed. Superelastic NiTi is highly elastic, while austenitic NiTi has high mechanical strength and is hard (similar to titanium) Figure 2.12b. The NiTi material has all these properties, their specific expression depending on the temperature at which it is used.

Figure 2.12 Martensitic transfromation (A) and Stress-strain bahavior of the phases of Nitinol (B).

A) Martensitic transformation and hysteresis (= H) upon a change of temperature. As = austenite start, Af = austenite finish, Ms = martensite start, Mf = martensite finish and Md = Highest temperature to strain-induced martensite. Grey area = area of optimal superelasticity. B) Stress-strain behaviour of different phases of NiTi at constant temperature.

Properties of Nitinol are very sensitive to the Nickel/Titanium ratio in the alloy as well as the presence of other alloying components such as Co, Fe, Nb etc. The sensitivity of Nitinol to the Ni/Ti ratio is presented in Figure 2.13.

Figure 2.13 The effect of Nitinol composition on the Ms temperature.

When Nitinol is below its transformation temperature, it has lower yield strength and can be deformed quite easily into any new shape - which it will retain. However, when the material is heated above its transformation temperature, it undergoes a change in crystal structure which causes it to return to its original shape. If it encounters any resistance during this transformation, it can generate extremely large forces. This phenomenon provides a unique mechanism for remote actuation.

The mechanical properties of NiTi depend on its phase state at a certain temperature (Ohtake, Rokugawa et al. 1999) Figure 2.12b. Fully austenitic NiTi material generally has suitable properties for surgical implantation devices. The common mechanical properties of martensitic and austenitic NiTi are presented in Table 2-1.

Table 2-1 Selected mechanical properties of NiTi.

NiTi Austenitic Martensitic Ultimate tensile strength (MPa) 800 - 1500 103 - 1100 Tensile yield strength (MPa) 100 - 800 50 - 300 Modulus of elasticity (GPa) 70 - 110 21 - 69 Elongation at failure (%) 1 - 20 up to 60

Nitinol has some exceptional properties that are useful for surgical implantation devices. NiTi has an ability to be highly damping and vibration-attenuating below its As temperature. For example, when a martensic NiTi ball is dropped from a constant height, it bounces only slightly over half the height reached by a similar ball dropped above the Af temperature. From the orthopedic point of view, this property could be useful in, for example, dampening the peak 28 stress between the bone and the particular prosthesis. The low elastic modulus of NiTi (which is much closer to the bone elastic modulus than that of any other implant metal) provides benefits in specific applications. NiTi has unique high fatigue and ductile properties, which are also related to its martensitic transformation. These properties are usually favourable in orthopedic implants. Also, very high wear resistance has been reported compared to the CoCrMo alloy (Sekiguchi 1987). NiTi is a non-magnetic alloy. MRI imaging is thus possible. Electrical resistance and acoustic damping also change when the temperature changes.

The material exhibits elastic behaviour until sufficient stress is applied to reach the tensile yield strength, at which point permanent deformation occurs. In the elastic range, the stress/strain ratio determines the elastic modulus. The metal fractures when the stress exceeds the ultimate tensile strength as shown below in Figure 2.14.

Figure 2.14 Schematic presentation of the stress-strain behaviour of ordinary implant metals.

2.1.3.1 Shape Memory Effect.

The unique behaviour of NiTi is based on the temperature-dependent austenite-to-martensite phase transformation on an atomic scale, which is also called thermoelastic martensitic transformation. The thermoelastic martensitic transformation causing the shape recovery is a result of the need of the crystal lattice structure to accommodate the minimum energy state for a given temperature (Otsuka and Ren 2005).

In NiTi, the relative symmetries between the two phases lead to a highly ordered transformation, where the displacements of individual atoms can be accurately predicted and eventually lead to

29 a shape change on a macroscopic scale. The crystal structure of martensite is relatively less symmetric compared to that of the parent phase.

If a single crystal of the parent phase is cooled below Mf, then martensite variants with a total of 24 crystallographically equivalent habit planes are generally created. There is, however, only one possible parent phase (austenite) orientation, and all martensitic configurations revert to that single defined structure and shape upon heating above Af. The mechanism by which single martensite variants deform is called twinning, and it can be described as a mirror symmetry displacement of atoms across a particular atom plane, the twinning plane (Andreasen and Fahl 1987).

While most metals deform by slip or dislocation, NiTi responds to stress by simply changing the orientation of its crystal structure through the movement of twin boundaries.

A NiTi specimen will deform until it consists only of the corresponding variant which produces maximum strain. However, deformation beyond this will result in classical plastic deformation by slip, which is irrecoverable and therefore has no “memory effect”. If the deformation is halted midway, the specimen will contain several different corresponding variants. If such a specimen is heated above Af, a parent phase with an orientation identical to that existing prior to the deformation is created from the corresponding variants in accordance with the lattice correspondences between the original parent phase and each variant. This phenomena is presented below in Figure 2.15. The austenite crystal structure is a simple cubic structure, while martensite has a more complex rhombic structure. This phenomenon causes the specimen to revert completely to the shape it had prior to deformation (Andreasen and Fahl 1987).

Figure 2.15 Schematic of the shape memory effect of an SMA showing the unloading and subsequent heating to austenite under no load condition.

NiTi senses a change in ambient temperature and is able to convert its shape to a preprogrammed structure. While NiTi is soft and easily deformable in its lower temperature form (martensite), it resumes its original shape and rigidity when heated to its higher temperature form (austenite) as shown in Figure 2.16. This is called the one-way shape memory effect. The ability of shape memory alloys to recover a preset shape upon heating above the transformation temperatures and to return to a certain alternate shape upon cooling is known as the two-way shape memory effect. Two-way memory is exceptional. There is also an all-round shape memory effect, which is a special case of the two-way shape memory effect (Shimizu and Tadaki 1987).

Figure 2.16 Stress-strain-temperature data exhibiting the shape memory effect for a typical NiTi SMA.

2.1.3.2 Superelasticity or Pseudoelastisity.

The pseudoelastic behavior of SMAs is associated with stress-induced transformation, which leads to strain generation during loading and subsequent strain recovery upon unloading at temperatures above Af. A pseudoelastic thermomechanical loading path generally starts at a sufficiently high temperature where stable austenite exists, then develops under an applied load to a state at which detwinned martensite is stable, and finally returns to the austenitic phase when returned to zero stress state. An example of this path (a → b → c → d → e → a) is shown in Figure 2.20 as Path 1. Most commonly, a pseudoelastic test is performed at a nominally constant temperature above Af. The loading path for such a test is shown as Path 2 in Figure 2.20. To illustrate the pseudoelastic behavior in greater detail, consideration is given to the thermomechanical loading path (A → B → C → D → E → F → A) in Figure 2.17, which starts at 31 zero stress at a temperature above Af. The corresponding σ-ε experimental data for the loading path is shown in Figure 2.18.

When a mechanical load is applied, the parent phase (austenite) undergoes elastic loading (A → B). At a specific load level, the loading path intersects the surface for initiation of martensitic transformation on the phase diagram. This marks the stress level (σMs) for the onset of transformation into martensite. Note that the stress-induced transformation from austenite to martensite is accompanied by the generation of large inelastic strains as shown in the stress- strain diagram presented in Figure 2.18. The transformation proceeds (B → C), to the stress Mf level (σ ) where the loading path intersects the Mf transformation surface, indicating the end of the transformation.

Figure 2.17 Phase diagram and two possible pseudoelastic loading paths.

The completion of martensitic transformation is indicated by a distinct change in slope on the σ- ε curve, which is associated with the elastic loading of the martensitic phase. A subsequent increase in the stress causes no further transformation and only the elastic deformation of detwinned martensite occurs (C → D). When the stress is released gradually by unloading, the martensite elastically unloads along the path (D → E). At point E, the unloading path intersects the austenitic start surface (at σAs), which causes the martensite to revert to austenite. The process is accompanied by the recovery of the strain due to phase transformation at the end of unloading.

The end of the transformation back into austenite is denoted by the point at which the σ-ε unloading curve rejoins the elastic region of austenite (point F corresponding to stress σAf ). The material then elastically unloads to A. The forward and reverse phase transformation during a

32 complete pseudoelastic cycle results in a hysteresis, which, in the σ-ε space, represents the energy dissipated in the transformation cycle. The transformation stress levels and the size of the hysteresis vary depending on the SMA material and testing conditions.

The detwinned martensite that forms from austenite as a result of the applied stress during Path 1 or 2 presented in Figure 2.17 is one form of stress-induced martensite (SIM). SIM, in general, is martensite that forms from austenite in the presence of stress. There are many thermomechanical loading paths that can result in the formation of SIM.

Figure 2.18 A typical SMA pseudoelastic loading cycle.

Generally, the term pseudoelasticity describes both superelastic behaviour and so-called rubber-like behaviour. The reversible phase transformation (Figure 2.18) caused by a thermomechanical loading path is strictly called the superelastic behaviour. The rubber-like effect is an exclusive behaviour of the martensite phase only and occurs due to the reversible reorientation of martensite. In some cases, aging the martensitic phase can enable the reversal of the martensitic detwinning process upon unloading at temperatures below Mf. The resulting σ-ε curve is similar to the superelastic curve, and this phenomenon is called the rubber-like effect to emphasize the similarities with the nonlinear elastic behaviour of rubber. In SMAs exhibiting the rubber-like effect, the stress required to detwin martensite is very small compared to σMs (Duerig, 1994).

2.1.3.3 Production of Nitinol

Solid NiTi alloys are manufactured by a double vacuum melting process, to ensure the quality, purity and properties of the material. After the formulation of raw materials, the alloy is vacuum induction melted (1400°C). After the initial melting, the alloy transition temperature must be controlled due to the sensitivity of the transition temperature to small changes in the alloy chemistry. This is followed by vacuum arc remelting to improve the chemistry, homogeneity and structure of the alloy. Double-melted ingots can be hot-worked (800°C) and cold-worked to a wide range of product sizes and shapes (Andreasen and Fahl 1987).

Porous NiTi can be made by sintering or using self-propagating high temperature synthesis, also called ignition synthesis. The possibility to make composite SMA products (combination with polymers) was investigated previously (Brailovski and Trochu 1996).

Denkena and Lucas demonstrated that the deep rolling process reduces the corrosion rate by a factor of approximately 100. They also found that a slight difference in the surface finishing has no relevant effect on the corrosion behaviour. They intended to investigate different workpiece materials to detect longer periods of time for corrosion and analyse the influence of surface modification for materials with similar subsurface properties (Denkena & Lukas, 2007).

2.1.3.4 Medical and Non-Medical Applications of NiTi

Superelastic Nitinol is now a common and well-known engineering material used in the medical device industry. While the greater flexibility of the alloy drives many of the applications, there are a large number of lesser-known advantages of Nitinol in medical devices. Several new medical applications will be used to exemplify these points, including the quickly growing and technologically demanding stent applications. Stents are particularly interesting in that they involve new and complex manufacturing techniques, present a demanding and interesting fatigue environment, and most interestingly, take advantage of the thermoelastic hysteresis of Nitinol.

The diversity of (potential) applications using shape memory alloys (SMA), apart from the medical field, becomes quite large. Classic categories such as free recovery, actuators, constrained recovery, pseudo-elasticity or damping require further specifications. For example, micro-actuators, smart materials or active damping, can be all classified as actuator applications, but each of those items demands specific functional performance, dimensions and processing. Furthermore, success for applications can only be realised in so far those materials offer also a price-competitive advantage relative to other functional materials or mechanical 34 designs. This competition requires perfect control of the material performance. It is known that Nitinol alloys can be tuned relatively easy to some specific requirements of the envisaged application: hysteresis, transformation temperatures, damping capacity. At the other side, little is known on recovery stresses, wear resistance, fracture mechanics, fatigue.

Shape memory alloys respond to external stimuli with a change in a key material property. Nitinol is a nickel–titanium shape memory alloy used primarily in vascular stents. Nitinol has good electrical and mechanical properties, long fatigue life, and high corrosion resistance. In particular, Nitinol is both self-expanding and crush-recoverable (i.e. it fully recovers its shape after being crushed flat). At the target site, Nitinol stents are released from the delivery system and elastically expand until they hit the vessel wall. Nitinol is also used in catheters and endoscopic guide wires to make them more steerable by altering the tool stiffness during procedures (Mitsuishi, Cao, & Bartolo, 2013).

2.1.3.5 Previous Research on Nitinol

From the review of the relevant literature, the work of a number of researchers was identified as important to describe.

Duerig and Pelton carried out research on some of the key properties of equiatomic and near- equiatomic titanium-nickel alloys with compositions yielding shape memory and superelastic properties. Alloys containing Nickel and Titanium were studied as a family of alloys with properties that greatly depend on exact compositional make-up, processing history, and small ternary additions. Each manufacturer has its own series of alloy designations and specifications within the TiNi range. A second complication that was acknowledged is that all properties change significantly at the transformation temperatures Ms, Mf, As and Af. Moreover, these temperatures depend on applied stress. Thus, any given property depends on temperature, stress, and history (Duerig and Pelton, 1994).

Ford and White performed extensive and full range mechanical testing of Nitinol alloy wire up to failure over a wide range of testing temperatures. Thermo-mechanical properties were obtained including: initial modulus, secondary modulus, critical martensitic start and finish stresses, plastic flow stress, recovery strain limit, failure stress and plastic modulus. The data was correlated with the Brinson constitutive model modified to account for full range loading. The influence of the initial temperature treatment of the nitinol was shown to be pronounced within the transformation range. Reasonably accurate correlation was obtained with the modified

Brinson constitutive model although there was some discrepancy in critical stress predictions which is partially attributed to experimental scatter (Ford and White, 1995).

Hane and Shield investigated the microstructure in the cubic (B2) to monoclinic (B19) transition in the technologically important Ti±Ni shape memory alloys. Martensitic transformations, the twinned martensite, austenite-martensite, wedge, triangle, and diamond microstructures were studied using a geometrically nonlinear theory. 192 habit planes were found for a particular Ti±Ni alloy, but only 24 had been unambiguously observed in experiments. A complete enumeration of the various microstructures was given, and algorithms were presented so that the calculations can be repeated with different lattice parameters (Hane and Sheild, 1999).

Wang and Yue presented the results of a series of experiments to investigate the superelastic cyclic stress–strain responses of NiTi shape memory alloys under tension–torsion biaxial loading conditions. The uniaxial tension and torsion experiments were also conducted to make comparisons. Experiments were controlled by axial displacement and torsional angle in sine wave form with fixed maximum values. Saturation was reached after 30 cycles. The evolutions of equivalent stress–strain curves as well as the separated tensile and shear stress–strain curves during cycling were analyzed. Results showed that the mechanical responses were significantly affected by the loading path. The stress–strain behaviour under proportional loading was similar to those under uniaxial loading. With the increase of the out-of-phase angle during the non-proportional loading, the special phase transformation exhibition totally disappears in the equivalent stress–strain curves (Wang and Yue, 2009).

Morakabati and Aboutalebi undertook research on hot tensile properties of as cast NiTi and NiTiCu shape memory alloys by hot tensile test at temperature range of 700–1100°C using the strain rate of 0.1/s. The NiTi alloy exhibited a maximum hot ductility at temperature range of 750–1000°C, while the NiTiCu alloy showed it at temperature range of 800–1000°C. It was found that at temperatures less than 750°C, the diffusion-assisted deformation mechanism was inactive leading to semi-brittle type of failure and limited ductility in both alloys. Also it was found that at temperature range of 800–1000°C, dynamic recrystallization was dominant leading to high ductility. Likewise, the fracture surface of the specimens presenting the maximum hot ductility showed an ideal type of ductile rupture in which they gradually pulled out to a fine point. On the other hand, the decline in ductility occurred at the temperatures above 1000°C was attributed to the liquid phase formation leading to interdendritic and intergranular types of fracture (Morakabati and Aboutalebi, 2011).

2.1.4 Summary

Numerous researchers in various machining industries are becoming increasingly interested in applying their technologies in the field of bio-manufacturing. This includes biospecific design constraints, bio-mechatronics, bio-fabrication, and bio-design and assembly.

Current trends indicate that precise machining and control in the micro-/nano-domains, advanced biomaterials, integration of numerous medical subsystems, and personalised applications will be key factors in the future, and the market is rapidly growing owing to rising quality-of-life expectations. Some of these technologies have been intensively studied and such technologies can be expected to bring about major breakthroughs if they are applied properly to medical industries. In particular, personalised medical applications in the future will require high- mix low-volume production, and this change can benefit from previous experiences with such paradigm shifts in other industrial applications.

Promoting of academia–industry and medicine–engineering collaborations will facilitate the entry of machining industry researchers/companies into medical industries. Engineers in biomedical domains require a good knowledge of material and process mechanics and the availability of advanced machine tools. Although current regulatory and cost requirements are very severe, innovations will be brought about by the encouragement of talented individuals to enter the medical industry and multi-disciplinary collaborations (Mitsuishi, Cao, & Bartolo, 2013).

Biomaterials provide an excellent platform for converging innovations in precision engineering, nanotechnology, biotechnology, information technology, and cognitive sciences.

As a result of industry-researchers collaboration the requirements of in depth knowledge of materials properties were outlined. Sheet metal formability analysis provides this data and is discussed in the following paragraph.

This research aims to add to the existing body of knowledge outlined above and provide the information on mechanical properties and pattern of behaviour of Nitinol under biaxial planar loading conditions. Nitinol material in the sheet form was required to carry out experiments.

The material was purchased from Johnson Matthey Company. The Certificate of Conformance indicated that Nitinol material supplied is Superelastic, 1.5 mm +/- 0.015mm Thickness, 115 mm Width, 457 mm +/- 6.35 mm Length, Flat Annealed manufactured per ASTM F 2063-05. Chemical composition: Ni – 56%, Ti – Balance, C - < 0.05%, O - <0.05% and Total All Others (Co, Cr, Cu, Fe and Nb) - < 0.20%. Mechanical Properties: UTS (ksi) – 206, Elongation (%) – 11.1.

2.2. Sheet Metal Formability

2.2.1. Introduction

One of the tasks of the design engineer is to select an appropriate material for a specific design application or product. The properties of the material chosen need to comply with the particular requirements of the process. To meet these requirements, the materials to be used must be selected and specified in most cases, to utilise the material and to enable the product to have the desired form. The designer knows that certain manufacturing processes will have to be employed in many instances and that the selection of a specific material may dictate what processing must be used. On the other hand, when certain processes must be used, the design may have to be modified in order for the process to be utilised effectively and economically. An increasing role is given to the testing of material to establish its properties. In modern manufacturing, materials are more often subject to multiaxial loading. Consequently, it is important to use multiaxial testing processes to find the true material properties under these types of loading. Furthermore, the material and, consequently the testing process should satisfy the particular requirements of the manufacturing process.

While it is common to assume that the various "-ability” terms also refer to specific material properties, they actually refer to the way a material responds to specific processing techniques. As a result, they can be quite nebulous. Machinability, for example, depends not only on the material being machined but also on the specific machining process; the conditions of that process, such as cutting speed; and the aspects of that process that are of greatest interest. Machinabllity ratings are generally based on relative tool life. In certain applications, however, it may be more interesting in how easy a metal is to cut or how it performs under high-speed machining, and less interested to establish the tooling or the resulting surface finish. For other applications, surface finish or the formation of fine chips may be the most desirable feature. As a result, the term machinabillty may mean different things to different people, and it frequently involves multiple properties of a material interacting with the conditions of a process.

In a similar manner malleability, workability and formability all refer to a material's suitability for plastic deformation processing. Since a material often behaves differently at different temperatures, a material with good "hot formability" may have poor deformation characteristics at room temperature. Furthermore, materials that flow well at low deformation speeds may behave in a brittle manner when loaded at rapid rates. Formability, therefore, needs to be evaluated for a specific combination of material processes and process conditions. The results cannot be extrapolated or transferred to other processes or process conditions. Likewise, the

38 weldability of a material may also depend on the specific welding or joining process and the specific process parameters.

Product development cycles are continually being shortened, making the use of traditional empirical approaches for determining optimum forming conditions inappropriate. The goal in manufacturing must be to establish ‘‘prototype-free’’ manufacturing. Accordingly, there is a need for accurate simulation techniques for metal forming using finite element analysis. For accurate and time-effective finite element simulations, it is vital to use accurate phenomenological plasticity models based on anisotropic yield functions (Banabic, 2000). The responses of materials to a variety of loading modes have been of interest for at least a century. Many anisotropic yield criteria and constitutive models have been proposed to date. However, experimental evidence is often lacking, particularly for materials in industrial use.

In sheet or tube forming processes, materials are generally subjected to multiaxial loads. Moreover, metal parts are very often manufactured in two or more forming stages. Therefore, multiaxial and/or multistage loading tests are infinitely preferable for checking the plasticity models to be used in simulations. Servo-controlled testing machines are commonly used for such tests. Although not categorized as multiaxial tests, in-plane compression tests or in-plane stress reversal tests are effective in observing and modelling the strength differential effect and the Bauschinger effect of sheet metals. These tests are also important from the industrial point of view, because such modes of deformation are very common in sheet forming processes, including deep drawing and draw-bending.

When evaluating the mechanical and physical properties of materials, it is important that testing be conducted in a standardised and reproducible manner. ASTM International, formerly the American Society of Testing and Materials, maintains and updates many testing standards, and it is important for the engineer to become familiar with them. For example, ASTM specification E370 describes the "Standard Test Methods and Definitions for Mechanical Testing of Steel Products”. Tensile testing is described in specifications E8 and E83, impact testing in E23, creep in E139, and penetration hardness in E10. Other specifications describe fracture mechanics testing as well as the procedures to evaluate corrosion resistance, compressive strength, shear strength, torsional properties, and corrosion-fatigue.

In addition, it is important to note not only the material being tested but also the location from which the specimen was taken and its orientation. Rolled sheet, rolled plate, and rolled bars, for example, will have different properties when tested parallel to the direction of rolling (longitudinal) and perpendicular to the rolling direction (transverse). This variation of properties with direction, known as anisotropy, may be crucial to the success or failure of a product.

2.2.2. Uniaxial Tensile Testing

Tension tests are used to measure the effect of strain on strength. Sometimes other tests, such as torsion, compression, and bulge testing are used, but the tension test is simpler and most commonly used. The major emphasis is given to the dependence of yield (or flow) stress on strain. The temperature and strain rates influence test results. Normally the strain rate is in the order of 10–2 to 10–3/s and the test temperature is between 18° and 25°C. Measurements are made in a gauge section that is under uniaxial tension during the test.

Initially the deformation is elastic and the tensile force is proportional to the elongation. Elastic deformation is recoverable. It disappears when the tensile force is removed. At higher forces the deformation is plastic, or non recoverable. In a ductile material, the force reaches a maximum and then decreases until fracture. Figure 2.19 outlines schematic tensile load-extension curve.

Figure 2.19 Load-extension and engineering stress-strain curve of a ductile metal (a), Expansion of initial part of the curve (b).

Stress and strain are computed from measurements in a tension test of the tensile force, F, and the elongation Δl. The nominal or engineering stress, S, and strain, ε, are defined as

푺 = 푭 / 푨ퟎ Eq. 2-5 and

풆 = ∆ 풍/ 풍ퟎ Eq. 2-6

where A0 is the initial cross sectional area and l0 is the initial gauge length. 40

Since A0 and l0 are constants, the shapes of the s–e and F– Δl curves are identical. The stress at which plastic flow begins, sy, is called the yield strength, Y, and is defined in terms of the yield force, Fy, as

푭풀 풀 = = 흈풀 Eq. 2-7 푨ퟎ

The tensile strength or ultimate tensile strength, su, is defined as

푠푢 = 퐹푚푎푥/퐴0 Eq. 2-8

The engineering stress-strain curve does not give a true indication of the deformation characteristics of a metal because it is based entirely on the original dimensions of the specimen, and these dimensions change continuously during the test. Also, ductile metal which is pulled in tension becomes unstable and necks down during the course of the test. Because the cross-sectional area of the specimen is decreasing rapidly at this stage in the test, the load required for continuing deformation decreases. The average stress based on original area likewise decreases, and this produces the reduction in the stress-strain curve beyond the point of maximum load. In fact, the metal continues to strain-harden all the way up to fracture, so that the stress required to produce further deformation should also increase. If the true stress, based on the actual cross-sectional area of the specimen, is used, it is found that the stress-strain curve increases continuously up to fracture. If the strain measurement is also based on instantaneous measurements, the curve, which is obtained, is known as a true-stress-true-strain curve.

휺 = 풍풏(풆 + ퟏ) Eq. 2-9

Figure 2.20 Comparison of engineering and true stress-strain curves.

This equation is applicable only to the onset of necking for the reasons discussed above. Beyond maximum load the true strain should be based on actual area or diameter measurements.

휺 = 퐥퐧(푨ퟎ/푨) Eq. 2-10

Figure 2.20 compares the true-stress-true-strain curve with its corresponding engineering stress-strain curve. Strain in the necked region obtained from Equation (2.10) far exceed the engineering strain calculated from Equation (2.6). Frequently the flow curve is linear from maximum load to fracture, while in other cases its slope continuously decreases up to fracture. The formation of a necked region or mild notch introduces triaxial stresses, which make it difficult to determine accurately the longitudinal tensile stress on out to fracture. The following parameters usually are determined from the true-stress-true-strain curve.

Ductility is a measure of the amount that a material can be deformed before failure. There are two common parameters: % elongation and % reduction of area.

% 풆풍풐풏품풂풕풊풐풏 = ퟏퟎퟎ(풍푶 − 풍풇)/풍푶 Eq. 2-11

% 풓풆풅풖풄풕풊풐풏 풐풇 풂풓풆풂 = ퟏퟎퟎ (푨푶 − 푨풇)/푨푶 Eq. 2-12

where Af and lf are the cross-sectional area and gauge length at fracture.

Although standard values of Af and lf are usually used, the % elongation depends on the ratio of the gauge length-to-diameter because the elongation after necking depends on the diameter

42 and the uniform elongation depends on the gauge length. The % reduction of area is much less dependent on specimen dimensions. The % reduction of area in a tension test should not be confused with the reduction of area, r, in a metal working process,

풓 = (푨푶 − 푨)/푨푶 Eq. 2-13 where A is the cross-sectional area after forming.

2.2.3. Multistage Tensile Test

In sheet or tube forming processes, sequential forming operations are often used. In these operations, material elements of the formed parts are generally subjected to strain path change which can, in turn, affect the hardening behaviour, flow rule, and ductility of the elements. Therefore, multistage loading tests are infinitely preferable for measuring the deformation behaviour of the material under multiple strain paths and checking the validity of a given plasticity model to be used in the simulations for sequential forming operations.

Wagoner and Laukonis (1983) performed two-stage tension tests for cold-rolled, aluminium- killed steel sheets. The steel sheets were subjected to plane strain pre strain followed by subsequent uniaxial tension. They found that major differences exist between subsequent tensile tests carried out with the tensile axis collinear with the original principal strain axis and tests with the tensile axis oriented 90˚ to the original principal strain axis.

Coaxial specimens yield at the expected stress (as measured in the continuous plane strain tension test), while non-coaxial specimens yield at stresses as much as 18% higher than expected. Moreover, the abrupt changes in the strain path from plane strain to uniaxial tension reduce the residual total elongation and uniform elongation as well as the deforming gauge length. These effects are enhanced when the major strain axes are non-coaxial.

Kim and Yin (1997) studied the evolution of anisotropy of an IF steel sheet employing two-stage tension tests, in which sheet specimens are subjected to uniaxial tensile loading at an angle to the orthotropic axes. They observed that the orientations of the orthotropic axes change drastically over a few percent of tensile strain. Kuwabara et al. (2002) carried out the same test as Kim and Yin (1997) on an IF steel sheet (0.8 mm thick), to determine whether the same phenomenon can be observed. Figure 2.21 shows the experimental procedure for the three- stage tension test.

Procedure 1: Large specimens, 300 mm wide and 1500 mm long (Figure 2.21a), were cut from an as-received IF steel sheet with its longitudinal direction taken to be parallel to its rolling 43 direction. To enhance the degree of anisotropy, the large specimens were pre strained along the rolling direction by applying εI = 3% tensile strain.

Procedure 2: Medium specimens, 60 mm wide and 200 mm long (Figure 2.21b), were cut from the gauge section of the pre strained large specimens at angles of Ψ = 30˚, 45˚, 60˚, and 90˚ to the first pre straining direction (i.e., rolling direction of the as-received material). The medium specimens are then pre strained along their length by applying εII = 1%, 2%, 3%, 5%, and 9% tensile strain.

Figure 2.21 Schematic illustration of a multistage tension test (Kim and Yin, 1997; Kuwabara, 2002c).

(a) Large specimen (amount of pre strain, εI = 3%). (b) Medium specimens cut from the large specimen (amount of pre strain, εII = 1, 2, 3, 5, and 9%). (c) Small specimens cut from the medium specimens. The dimensions of the specimens in the figure are those adopted by Kuwabara (2002). W is the tensile direction of the medium specimen relative to the direction of the first pre straining (i.e., rolling direction of the as-received material). It is the tensile direction of the small specimen from the direction of the second pre straining (i.e., direction of the axis of the medium specimen).

Procedure 3: Small specimens, 6.25 mm wide and 37.5 mm long (Figure 2.21c), were cut from the gauge section of each pre strained medium specimen at angles of φt = 0˚, 10˚, 20˚, . . . ,170˚

(18 directions) to the direction of the specimen axis. For each medium specimen, 18 data value on the yield stress, σ0.2, i.e., the flow stress at 0.2% offset plastic strain, are obtained.

The results of the research are presented in Figure 2.22.

Figure 2.22 Growth of flow stresses at 0.2% offset plastic strain σ0.2, with increasing εII.

The amount of pre strain applied to the medium specimen shown in Figure 2.21b, measured with uniaxial tension at different angles to the longitudinal direction of the medium specimen (Kuwabara et al., 2002). (a) Measured data for the medium specimen cut from the large specimen with no pre straining (εI = 0%), at an angle of Ψ = 45˚ to the rolling direction. (b–d) Measured data for the medium specimens cut from the 3% pre strained large specimen, at angles of Ψ = (b) 30˚, (c) 60˚, and (d) 90˚ to the direction of the first pre straining, i.e., the rolling direction.

Wu et al. (2005) have shown that the conventional methodology for determining material anisotropy (i.e., on the basis of flow stress measurements) overestimates the pre straining effect; they concluded that the degree of material anisotropy depends on the strain level at which the tensile flow stresses are measured. The experiments carried out using AA6111 alloy 45 demonstrate that pre-straining mainly affects the elastic–plastic transition at yield and that the apparent change in the directionality of the axes of orthotropy is not validated by the r-value measurements.

2.2.4. Biaxial Testing

Many formability tests exist for metallic sheet materials. A given test may correlate well with behaviour in one type of forming process and poorly with the behaviour in another due to the variation of relative amounts of drawing and stretching from test to test and process to process. There are various techniques for testing sheet metals which include the hydraulic bulge test, the biaxial compression test on adhesively bonded sheet laminate specimens, and the biaxial tension and plane strain tension tests using cruciform specimens. Examples of measured yield loci (contours of plastic work) and incremental plastic strain vectors for steel alloys are presented and compared with theoretical predictions based on conventional anisotropic yield functions. The effect of material modelling on the accuracy of spring back simulation for plane strain stretch bending is also discussed.

Hereafter, the three orthogonal axes of anisotropy, x, y, and z, are taken to be the rolling, transverse and through-thickness directions of a sheet material, respectively.

2.2.4.1. Bulge test

Much higher strains are possible in a hydraulic bulge test than in a tension test, so the effective stress–strain relations can be evaluated at higher strains. The sheet is placed over a circular hole, clamped, and bulged outward by the oil pressure, P.

Consider a force balance on a circular element of radius ρ near the pole (Figure 2.23). The radius r of this element is

풓 = 흆∆휽 Eq. 2-14

The vertical component of the force acting on the circumference of this element is

ퟐ ퟐ흅풓풕흈∆휽 = ퟐ흅풕흆흈∆휽 Eq. 2-15

This is balanced by the force of the oil,

ퟐ ퟐ 흅풓 푷 = 흅(흆∆휽) 푷 Eq. 2-16

Figure 2.23 Force balance in hydraulic bulging.

Equating, 2 2 2휋푡휌휎∆휃 = 휋(휌∆휃) 푃 Eq. 2-17 or

흈 = 푷흆/(ퟐ풕) Eq. 2-18

The radial strain, εr, can be used to find the thickness,

풕 = 풕ퟎ 퐞퐱퐩(−ퟐ휺풓) Eq. 2-19

Simultaneous measurement of εr, ρ and P is required to obtain the stress-strain relation.

The hydraulic bulging test is widely used in determining the work hardening characteristics of sheet materials up to plastic strains greater than can be achieved in simple tension (Mellor and Parmar, 1978). Several improvements, including a biaxial extensometer (Johnson and Duncan, 1965) and automated hydraulic bulge testers (Gologranc, 1975; Young et al., 1981) have simplified the experiment. For an accurate determination of biaxial stress–strain curves, the geometry of the bulge must be taken into consideration and the strain rate must be constant during bulging (Ranta-Eskola, 1979). The major limitations are the restricted range of stress states (usually from plane strain to balanced biaxial tension) and being fixed into a specific stress state by the geometry of the die opening (circular or elliptical).

2.2.4.2. Duncan Friction Test

This consists of stretching a strip between two fixed cylinders as indicated in Figure 2.24. The strains in Sections A and B are measured. From these the stresses, σA and σB, and the thicknesses, tA and tB, can be deduced from 풏 흈 = 푲휺 Eq. 2-20 and

푡 = 푡0 exp(휀)

Now FA and FB can be determined as

퐹 = 휎푡푤 where w is the strip width. Finally, the friction coefficient can be found by solving

퐹퐴 휇휋 = exp ( ) for μ. 퐹퐵 2

풏 ퟐ 휺푨 흁 = ( ) 풍풏 [( ) 풆풙풑 (휺푨 − 휺푩)] Eq. 2-21 흅 휺푩

Figure 2.24 The Duncan friction test.

2.2.4.3. Cupping Test

The Swift cup test is the determination of the limiting drawing ratio for flat-bottom cups. In the Erichsen and Olsen tests, cups are formed by stretching over a hemispherical tool. The flanges are very large so little drawing occurs. The results depend on stretch ability rather than draw ability. The Olsen test is used in America and the Erichsen in Europe. Figure 2.25 shows the setup.

The Fukui conical cup test involves both stretching and drawing over a ball. The opening is much larger than the ball so a conical cup is developed.

Figure 2.25 Olsen and Erichsen test.

The cupping tests discussed above are losing favour because of irreproducibility. Hecker attributed this to “insufficient size of the penetrator, inability to prevent inadvertent drawing in of the flange, and inconsistent lubrication.” Hecker proposed the limiting dome height test (LDH) which uses the same tooling (100mm diameter punch) as used to determine forming limit diagrams. The specimen width is adjusted to achieve plane strain and the flange is clamped to prevent draw-in. The limiting dome height (LDH) is the greatest depth of cup formed with the flanges clamped. The LDH test results correlate better with the total elongation than with the uniform elongation. The total elongation includes the post-uniform elongation. A major problem with the LDH test is reproducibility within a laboratory and between different laboratories. Part of the problem may be caused by minor variations in details of the clamping.

Springback denotes the elastic recovery of press-formed parts. It is caused by relief of the resultant moment and resultant force retained in the material directly after press forming.

Accordingly, factors which affect the generation of stress in the material during loading/ unloading influence the springback behaviour of press-formed parts. These factors include the stretching forces applied to the material, the coefficient of friction at the material/die interfaces, the tool temperature, the elastic deflection of the die, the deformation history of the material, the work hardening characteristics, and the Bauschinger effect of the material (Kuwabara, Seki et al. 1999). Therefore, when discrepancy arises in the extent of springback between simulation and observation, it is difficult to trace the reason, particularly in the case of forming parts that have complex geometry. Furthermore, the accuracy of the simulation code itself can be in doubt. It is therefore important to establish a testing method for evaluating the springback- capability of sheet metals that is simple in its testing procedure but accurate enough to test the validity of the material model for a given test material.

Kuwabara et al. (2004) proposed a method for evaluating the springback characteristics of sheet metals based on the plane strain stretch bending test, as shown in Figure 2.26. A sheet specimen is fixed into position on the blank holder, and a blank holding force is applied.

The radius of the punch is 100 mm. The draw height h is measured with a displacement gauge, and the punch force, P, is measured with a load cell. The nominal tensile stress T, applied to the specimen is determined, using the equilibrium equation, as

푻 = 푷/ퟐ풃풕ퟎ 퐬퐢퐧 휽 Eq. 2-22

where b and t0, respectively, denote the initial width and thickness of the specimen. The magnitude of T was varied by changing the blank holding force. The punch head was lubricated using a PTFE sheet of thickness 0.05 mm and machine oil ISO Grade 32. The amount of springback, η, is defined as:

|ퟏ⁄ − ퟏ⁄ | ′ 푹′ 푹 푹 − 푹 ′ 휼 = ퟏ = ′ = 횫푹/푹 Eq. 2-23 ⁄푹 푹 where R (=100 mm) and R', respectively, denote the radius of curvature of the inner surface of the specimen with load and after load removal. R' was measured at the centre of the bent specimen using a dial gauge with a minimum scale value of 1 µm. The length of the measurement section was 20 mm.

Figure 2.26 Schematic diagram of experimental apparatus for stretch bending test (dimensions: mm) (Kuwabara et al., 2004).

Figure 2.27a shows the deformed shapes of stretch-bent specimens after spring back, tested on a high-strength steel sheet JSC340P (Kuwabara, Ikeda et al. 2004). Figure 2.27b shows the amount of spring back, ΔR/R', for the observation and finite element simulations based on von Mises’ and Hill’s quadratic yield functions.

The amount of spring back decreases with increasing tensile stress, falling almost to zero when the tensile stresses are higher than the yield stress of the material. The values calculated using von Mises’ yield function agree more closely with the observations than do those based on Hill’s quadratic yield function. The von Mises yield function accurately predicts the flow stress of the material under plane strain tension; whereas Hill’s quadratic yield function overestimates it. Hill’s quadratic yield function therefore overestimates the bending moment, leading to overestimation of the amount of spring back. It follows from Figure 2.27 that the choice of an appropriate anisotropic yield function is vital for accurate spring back simulation.

Figure 2.27 Shapes of specimens and the effect of springback.

(a) Shapes of stretch-bent specimens after springback. Material: high-strength steel sheet, JSC340P, of thickness 0.7 mm and tensile strength 340 MPa. (b) Effect of nominal tensile stress on the magnitude of springback in the stretch bending test (Kuwabara et al., 2004).

2.2.4.4. Combined tension-torsion test

Tube hydroforming is the process of forming tubular components under hydraulic pressure. This process reduces the weight and cost of and gives greater structural strength and rigidity to automotive body structures. The deformation histories of tubes in tube hydro forming are complex, making it difficult for die designing engineers to predict defects in formed parts, including fracture and springback. For accurate and time-effective finite element simulations, it is vital to use accurate phenomenological plasticity models based on anisotropic yield functions.

Many experimental studies of multiaxial testing of thin-walled tubular specimens loaded in combined tension-torsion or tension–internal pressure modes. Extensive reviews of the early experimental studies have been made by Michno and Findley (1976). Few groups have, however, considered constitutive modelling of the anisotropic plastic deformation behaviour of tubular materials in industrial use.

Kuwabara et al. (2003) designed and built a servo-controlled tension–internal pressure testing machine to investigate the anisotropic plastic deformation behaviour of tubular materials used for hydro forming automotive parts. This machine can apply arbitrary stress or strain paths to a tubular specimen using an electrical, closed-loop control system.

Using this biaxial stress testing machine, Kuwabara et al. (2005) investigated the anisotropic plastic behaviour of an extruded aluminium alloy tube, A5154-H112, for linear and combined stress paths. The researchers verified the validity of conventional anisotropic yield functions by comparing the observed data with theoretical predictions based on the yield functions.

2.2.5 Summary

This section presents the variety of approaches used to describe the formability of metallic materials. Methods used depend on the following parameters:  Type of material;  Manufacturing methods used prior to testing;  Profile of the material (sheet, pipe, etc.);  Further manufacturing processes material needs to undergo.

The current research aims to advance the knowledge in the area of planar biaxial testing. Next section is specifically dedicated to the design and knowledge analysis in the area of in-plane biaxial testing. This type of testing, according to the current author’s opinion, is only one step of advancement from standard uniaxial test, yet it provides significant data on the behaviour of sheet metals. Experimental data obtained could potentially serve the engineers designing biomedical components manufactured from sheet materials.

2.3. Biaxial Planar Testing Systems

2.3.1. Introduction

Another approach to biaxial testing of sheet metals is to use a cruciform specimen and to apply biaxial tension. The biaxial tensile test is used to determine the multiaxial deformation characteristics of materials. This test is used primarily for research and development as it allows defined stress values in the intersection area of the specimen to be set up and investigated.

In the biaxial stress state, forces are working in two directions on an infinitesimal small volume, the third direction is the out of plane direction that is related to the two in-plane directions, similar to the uniaxial stress state as shown in Figure 2.28a. The stresses working on the volume under biaxial stress can be visualised, as shown in Figure 2.28b: forces are acting on the four areas perpendicular on the plane, from which the stresses can be computed dividing the force by the area it is acting on.

Strains in a biaxial deformation can be computed using Equations 2.24 to 2.26. Often, it is more convenient to measure strains, Equations 2.27 and 2.28 are given for calculating stresses from known strains. σ3 = 0 as there is no force acting on the plane. These equations are only valid in the elastic regime, whereas for plastic deformation pure biaxial loading only takes place up to localization.

(a) (b)

Figure 2.28 Uniaxial and biaxial stress states.

휺ퟏ = (흈ퟏ − 흂흈ퟐ)/ 푬 Eq. 2-24

휺ퟐ = (흈ퟐ − 흂흈ퟏ)/ 푬 Eq. 2-25

휺ퟑ = − 흂(흈ퟏ + 흈ퟐ)/ 푬 Eq. 2-26

(휺ퟏ+ 흂휺ퟐ) 흈 = 푬 Eq. 2-27 ퟏ (ퟏ− 흂ퟐ)

(휺ퟐ+ 흂휺ퟏ) 흈 = 푬 Eq. 2-28 ퟐ (ퟏ− 흂ퟐ)

A complicating factor in the biaxial case is to determine the area that the forces are acting on, which makes determining stresses σ1 and σ2 more difficult than for the uniaxial case. Furthermore, during an actual manufacturing process the biggest problem is determining the plastic response. This cannot be described with a set of equations as given above.

An important observation is that real biaxial loading only occurs up to localisation. Due to damage, necking and failure in a material, asymmetry is introduced and the simplified approaches as used in the elasticity regime are not correct anymore. However, the elastic behaviour is important, as this is where the final failure mode is likely to be determined.

Predictive calculations of press loads, strain distributions, failure loci and springback in sheet metal forming operations depend on an accurate knowledge of plastic behaviour under various stress states. For this reason, the development of a general plasticity theory has been pursued for many years. Rigorous experimental investigation however, is also crucial for ensuring that the constitutive model adequately describes the behaviour of the material under a variety of complex loading conditions.

Biaxial testing is required to quantify and clarify the yield criteria and constitutive equations of a particular material. The most common method of biaxial testing employs thin-walled cylinder tubes subjected to axial and/or torsional loads and internal pressure. The disadvantage of this method is that it requires the material to be in the form of a circular tube, so it cannot be applied to rolled sheet materials.

Two of the most appropriate biaxial tests of rolled sheet materials for use in press-stamping are the biaxial tensile test using cruciform specimens and the biaxial compression test using a metal block made by stacking and gluing metal sheets. The disadvantage of the latter is the difficulty in obtaining accurate stress–strain relations at small stains, because of the friction between the test piece and pressure plates.

However, one of the most important problems encountered in the use of cruciform specimens is that of determining the stresses in the gage section of the specimen.

2.3.2. Link attachment mechanics for biaxial testing

In an attempt to reduce the cost associated with building stand-alone biaxial test machines, attachments have been designed for existing machines such as tensile and compression testers for the purpose of biaxial testing. The most common biaxial test setup is that of converting a standard tensile machine.

This is typically achieved by adding an extra actuator to the system such as the addition of a horizontal hydraulic ram to a vertical tensile test machine. The tensile tester is then used to apply the vertical load and this removable attachment can be used to apply the horizontal load. One such device which was designed by Hoferlin et al. (1998). It consisted of a standard tensile test machine with a removable hydraulic actuator attached. Both the vertical and horizontal loading directions contained load cells and an alignment fixture. The horizontal fixture was mounted on low-friction bearings to ensure that the horizontal structure remained aligned with the centre of the specimen during the test. A biaxial test device was developed at the Fraunhofer Institute in Germany by converting a compression tester by a series of linkages (Fraunhofer 2005). This setup developed is presented in Figure 2.29.

Figure 2.29 Biaxial linkage for compression test machine (from Fraunhofer 2005).

This system operated by using four links attached to the cross-head of the compression tester. As the cross-head moved in a downward direction these links converted the movement into horizontal motion in two different directions.

This motion was used to apply the force to the cruciform specimen as shown in Figure 2.29. As in most cases, a load cell was used in each direction to measure the forces and a camera was used to measure specimen elongation. Mohr and Mulalo (2004) have used a compression testing machine to test honeycomb structures under multi-axial loading. This universal biaxial testing device (UBTD) was used to apply combinations of large compressive and shear displacements to the boundaries of a honeycomb specimen.

A further method of transforming a tensile test machine into a biaxial test machine is by the use of links. This method was developed by Ferron and Makinde (1988).

By using eight links it was possible to convert the vertical movement of the cross-head into directional movement of the grippers. This link mechanism is presented in Figure 2.30.

Figure 2.30 Pantograph mechanism for tensile test machine (from Ferron and Makinde, 1988).

After mounting the specimen on the device, the complete system was attached to the testing machine by means of heads H1 and H2 and tested in tension. During the experiment, the displacement of the vertical frame, made up of the four arms, Av assured a decrease in distance between the connecting parts C1 and C2, which in turn produced an adequate displacement of the horizontal frame made up of the four arms, Ah.

Thus, the loading system assured an increase in the distance between the two heads H3 and H4. With this configuration, the increase in the distance between H3 and H4 was equal to the 56 distance between H1 and H2. The specimen, fixed to the four heads H1, H2, H3 and H4 by means of gripping plates, was subject to an equi-biaxial deformation. When a tensile load was applied to the two heads H1 and H2, the vertical arms were subjected to a tensile load while the horizontal arms were under a state of compression. It follows that the equibiaxiality of the specimen deformation is true under the assumption of negligible elastic deformation of the mechanism.

The load on the specimen was measured by two load cells, which were positioned on the heads H1 and H4. One of the main differences with this apparatus was that the device was used on a compression testing machine. Here, a compression force was applied to the heads C1 and C2, which applied the same movement to the grippers as in the previous setup. The pantograph apparatus converted a compression load applied on the two cross-shaped membranes to a biaxial tensile load via the arrangement of eight articulated arms. The strain was measured by the use of a video extensometer.

The biaxial test system developed by Vezer S. and Major Z. (2009) presented in Figure 2.31 consisted of a combination of several existing solutions with some novel features for fixed stretch ratio. In the realised test set-up, the special holders transformed the longitudinal movement of the testing machine to a transverse displacement, resulting in a biaxial stress state in the middle of the specimen. While the bottom section of the fixture with the two vertical shafts was fixed to the load cell of the testing machine, the upper part moved with the hydraulic actuator along the two linear bushings on both sides.

Home position Maximal displacement

Figure 2.31 Mechanism of Biaxial Holder (from Vezer and Major, 2009).

A standard MTS tensile testing machine was used to operate a biaxial frame. An Optical 3D and PCCL measurement tools were used as measuring devices for the strain (Figure 2.32).

Figure 2.32 In-plane biaxial testing system (from Vezer and Major, 2009).

The preliminary experiments showed that the maximum load capacity was sufficient for elastomers but not for cord fibre reinforced composites. Hence a modified version was stiffened and used for composites.

Development of optimised specimen geometry for rubbers and their composites was complicated. Initially, finite element simulation was carried out. To overcome these difficulties, the thickness reduction of the middle area was the preferred solution as it was already tested for metal and composite materials. However, due to the processing options of the elastomers the manufacturing of these types of specimens was extremely difficult.

2.3.3. Stand-alone biaxial testing machines

A biaxial test system, which combined electrical, mechanical and hydraulic elements, was designed by Parsons and Pascoe (1975). The machine consists of four double acting hydraulic cylinders rigidly supported on an octagonal frame which can apply tensile or compressive loads to a cruciform specimen. The maximum load that can be applied in either direction is 200kN. Opposing cylinders are connected to common supply pipes so that the loads exerted by them are equal and opposite. No side load in the plane of the specimen should, therefore, be transmitted to the arms that lie in a perpendicular direction. A load cell is included in each loading direction. The oil pressure in the cylinders was measured by gauges which had electrical contacts used to operate hydraulic valves, thereby reversing the loading direction at predetermined values of load. Microscopes are used to monitor the progress of cracking in the specimens. For tests on metal specimens failure was designated as the stage at which a crack 58 had propagated sufficiently for relative movement of its sides to be detected with a magnification of X75. The only possible load ratios obtainable with this control system were 1/1, 1/0, and 1/-1. Furthermore, the load-time curve had an undesirable saw-tooth shape.

These limitations were overcome by the later addition of a closed-loop control system. Signals of the desired value were obtained from an oscillator with a variable-phase attachment. This allowed any desired phase angle between the horizontal and vertical signals to be maintained. The amplitude and the mean value of each signal were controlled separately.

The experimental work was conducted using a biaxial testing apparatus that was designed and constructed at the Universite de Sherbrooke. The testing apparatus comprised a hydraulic loading system and a closed-loop control system. A detailed description of the apparatus was given in Makinde et al. (1992). Figure 2.33 shows a sketch of the biaxial testing system. A cross-shaped steel slab 152 mm thick constituted the main load frame. It was welded onto an I- beam structure to ensure maximum rigidity. A load train of four linear hydraulic actuators was mounted in a horizontal plane on this frame. Two sets of opposing actuators had a rated capacity of 250kN form two orthogonal loading axes. Hydraulic wedge grips with controllable gripping pressure were installed on each actuator, thereby holding the specimen at the centre of the loading system. Finally, a load cell was included in each direction.

Each loading axis was controlled independently by an electrohydraulic closed-loop channel, which was monitored from an MTS microconsole. A function generator, capable of producing a wide range of waveforms, provided command signals that control the operation of two opposing actuators. This closed-loop system enabled testing to be done in either force or strain control modes. Measurements from load and displacement transducers were transmitted to a personal computer equipped with a 16 bit analog/digital expansion board for data acquisition.

Figure 2.33 Sketch of the biaxial test apparatus (Makinde et al., 1992)

A biaxial extensometer was also designed in-house (Makinde et al., 1992) in order to measure and control strains independently along each loading direction. It consisted of two lightweight frames that were mounted at 90° to each other prior testing, on either side of a specimen. Each frame housed a pair of sliding blocks which moved with friction eliminated as the specimen was deformed. Rounded points in contact with the sample caused the sliding blocks to move, and their relative displacements were measured using linear variable displacement transducers (LVDTs).

Eberhardsteiner (1995) developed biaxial hydraulic testing machine for orthotropic materials. The load carrying system consisted of two welded steel frames. At the frame corners four movable anchorage units were mounted. Each of these anchorage units was used for the attachment of six loading axes. As shown in Figure 2.34, there were 24 hydraulic cylinders in

60 total, each pulling or pushing under approximately 45° towards the borders of the specimen. This test concept allowed the introduction of two independent in-plane displacement components onto the specimen at each individual loading point, and the measuring of two components of the corresponding force by means of load cells integrated in each loading axis. The distance between two neighbouring load application points was 48 mm. It was minimized with respect to the required homogeneity of the displacement distribution in the measuring field of the specimen. The respective distance depended on the width of the loading axes. Therefore, very small cylinders with two pistons in series had to be developed (Eberhardsteiner 1995).

Figure 2.34 Biaxial hydraulic testing machine (Eberhardsteiner 1995)

The load carrying capacity of one loading axis (hydraulic cylinder) amounts to +/-17 kN, and the accuracy of the absolute displacement-controlled cylinder positioning was approximately 3μm. This high positioning accuracy was remarkable, but necessary because of the small displacement increments (10-30/μm) applied to the specimen in one load step.

Figure 2.35 shows the biaxial tensile testing apparatus developed by Toshihiko Kuwabara in 1998. Opposing hydraulic cylinders were connected to common hydraulic lines so that they were subjected to the same hydraulic pressure. The hydraulic pressure of each pair of opposing hydraulic cylinders was servo-controlled independently.

Figure 2.35 Experimental apparatus for the biaxial tensile test (Kuwabara 1998)

Displacements of opposing hydraulic cylinders were equalised using the pantograph-type link mechanism so that the centre of the cruciform specimen was always maintained at the centre of the testing apparatus during biaxial tensile tests. This link mechanism was effective in reducing the production cost of the presented testing apparatus (Kuwabara and Ikeda 1998).

A load cell was included in each loading direction. Biaxial strain components in the gage section of the specimen were measured using biaxial-strain gages. The outputs of loads and strains were monitored continuously using A/D data acquisition and a personal computer.

The biaxial testing rig, presented in Figure 2.36, used for this experimental investigation was a concept with two actuators perpendicular to each other and four arms hinged at the bottom. Makinde et al. (1992) used a test set-up with four actuators but the two actuator concept made the rig self-aligning and the need of synchronising the actuators was avoided. The drawback using hinged arms was that the grips holding the specimen along an arc. The distance from hinge to the specimen was 1000 mm and the total movement in one arm was approximately 3 mm. Granlund (1995) studied the effect of this bending force and found that the bending force introduced into the specimen was very small and could be considered as negligible. This biaxial testing concept had been shown to work well by Granlund (1997), Olsson (2001) and Gozzi (2004).

Figure 2.36 Test Rig for Biaxial Tests (Gozzi 2004)

To enable compression tests, the out-of-plane buckling of the specimen had to be prevented. This was solved by the use of support plates that were clamped around the specimen. The support plates were designed to guide the grips of the rig and thereby enhance the global stability in both the vertical and the horizontal directions. The bolts holding the support plates were equipped with strain gauges to ensure similar conditions, i.e. same clamping force, in all tests. This obviously causes friction between specimen and support plates but to reduce the friction as much as possible a thin teflon film was attached to the plate. This friction, as well as that in the hinges of the rig were measured and included in the evaluation procedure.

The actuators were controlled by an Instron control unit that has the capability to control the two actuators independently. All tests were performed in load control with a constant stress rate of 2.7 MPa/s throughout the test.

The biaxial test rig, as presented in Figure 2.37, developed by A. Smits (2006) at Free University of Brussels had a capacity of 100kN in each perpendicular direction, but only in tension, limiting the experimental results to the first quadrant of the two-dimensional stress space. As no cylinders with hydrostatic bearing were used, failure or slip in one arm of the specimen would result in sudden radial forces, which could seriously damage the servo- hydraulic cylinders and load cells. To prevent this, hinges were used to connect the specimen to the load cells and the servo-hydraulic cylinders to the test frame. Usage of four hinges in each loading direction resulted in an unstable situation in compression and consequently only tensile loads could be applied. The stroke of the cylinders was 150 mm. Applied loading could be static

63 or dynamic up to a frequency of 20 Hz. Each cylinder was independently controlled and any type of loading waveform, including spectral sequences of variable amplitude, could be efficiently introduced using the dedicated software and control system.

Figure 2.37 Plane biaxial test device for cruciform specimens (Smits 2005)

For a symmetric strain distribution – one of the requirements for a successful biaxial test using cruciform specimens – the force P had to be equal and collinear to the force P’ and the force F equal and collinear to F’ (Figure 2.38a). In addition, the forces P and P’ had to be perpendicular to the forces F and F’. In order to maintain the co-linearity to avoid bending moments, which caused a non-symmetric strain distribution in the biaxially loaded zone, the centre of the specimen must remain stationary. An arrangement where two ends of the cruciform specimen were held fixed while the opposite two ends were loaded – as was done in the past with test devices using two actuators – was unsatisfactory in this respect (Figure 2.38b). The displacements Dx and Dy caused bending of the specimen and a non-symmetric strain distribution. Four servo-hydraulic cylinders were used with a control unit to explicitly keep the forces collinear (Figure 2.38a).

Figure 2.38 Cruciform specimen with actuators: a) four actuators; b) two actuators. 64

In an ideal situation, no displacement of the centre point of the specimen was observed (Figure 2.39a). Even when using four actuators, a small displacement occurred and an imbalance arose in the forces and for instance a component Fy was added in the y-direction (Figure 2.39b). Due to the displacement, forces P and P' were no longer equal. However, as four load cells were used, it is possible to measure this small load difference and this was used as a control signal. Nevertheless, using this control procedure made it difficult to load a cruciform specimen uniaxially in this test rig. With the current control configuration, the minimum loading in each direction should be higher than 10kN.

Figure 2.39 Forces on the cruciform specimen: a) ideal situation; b) real situation.

The apparatus developed by Merklein in 2013 belongs to the family of stand-alone machines with an out-of-plane loading system. The machine concept was based on the idea followed by Geiger et al. (2005) of avoiding active control of the loading axes, thus representing a cost savings solution in terms of construction compared to servo controlled stand-alone machines.

Nevertheless, the choice of governing the stress state via the specimen geometry prevented from directly measuring the in-plane reaction forces. This aspect was implemented in this machine, where the load mechanism bore similarities to Hayhurst (1973) with the distinguishing advantage of allowing a discrete setting of a biaxial stress state. The machine developed by Merklein in 2013 was an entirely new development and does not share any hardware component with the machine used by the same main author in Merklein (2008) as the load train, i.e. the way the specimen is loaded, as well as the specimen geometry itself had very different designs.

Figure 2.40 Plan view and cross section of the biaxial testing machine (from Merklein, 2008). where (1) Steel mounting plate; (2) steel base plate; (3) solid round bar ∅ 60 mm; (4) DC motor; (5) worm gear screw jack; (6) lifting screw; (7) top steel plate; (8) bottom steel plate; (9) solid round bar ∅ 30 mm; (10) hollow round bar; (11) specimen; (12) clamping fixture; (13) linear bearing system; (14, 17) pull roads; (15) 50 kN load cell; (16) needle bearing; (18) angle adjustment device.

The assembly shown in Figure 2.40 represented a combination of arms mounted on a frame. Single motor gearbox provided the movement to the frame and subsequently series of arms to simulate biaxial in-plane loading of the specimen. As a result of this arrangement, the screw jack converted the rotary motion of the DC motor into linear displacement of the top steel plate and the kinematic of each clamping fixture is uniquely described by the relation:

푷풚 = 풕풂풏흑 Eq. 2-29 푷풛

66 where ϑ was the current angle. Angle ϑ could be adjusted between 29° and 52° in four uniform steps of 8° by fixing the joint (17) in position A, B, C and D. With the choice of pairwise different angles in the two main direction was thus possible to have different displacement Px and Py which means non-equibiaxial stress states in the specimen center (Merklein & Biasutti, 2013).

2.3.4. Commercial biaxial testing machines

Leading producers of testing equipment responded to the increasing interest to biaxial testing from academic institutions as well as industrial companies by bringing to the market a wide variety of commercial biaxial testing machines. Instron, Zwick/Roell and TMS design their machines to suit the application and the industrial use of specific engineering material such as metal, tissue or composite.

ADMET is a relatively new company in testing systems manufacturing. Founded by Richard Gedney in 1989 Advanced Machine Technology was focused on building software and controllers for material testing equipment manufacturers and resellers, later shortened to ADMET. In 1999, ADMET launched its first testing system eXpert 5600 and over the next decade continued to invest in its product family, launching many product ranges covering tension, compression, flexure and peel/adhesion tests.

Constitutive models were necessary to predict the mechanical behaviour of biological tissues. However, biological materials presented challenges in constitutive modelling due to their complex mechanical behaviour. Their oriented fibrous structures often exhibited pronounced mechanical anisotropy. Due to anisotropy, stress strain data generated from uniaxial tests could not be used to extrapolate to generalised three-dimensional constitutive equations. Since biological tissues were generally considered incompressible, planar biaxial testing allowed for a two-dimensional stress-state that could be used to characterise their mechanical properties and validate the constitutive models (ADMET, 2014).

ADMET planar biaxial testing systems (Figure 2.41) were engineered solutions based on specimen sizes, specimen elongations, test speeds, force capacities, environmental conditions and gripping requirements. Each system came equipped with ADMET’s biaxial version of the MTESTQuattro Materials Testing System.

Figure 2.41 ADMED planar biaxial test systems (from ADMET, 2014).

Established in 1946, Instron manufactures and services materials testing instruments, systems, and accessories, providing the customers with comprehensive solutions for all their research, quality, and service-life testing requirements. Instron machines evaluate the mechanical properties of materials and components using tension, compression, flexure, fatigue, impact, torsion and tests (Instron, 2014).

The Instron planar biaxial cruciform testing systems, shown in Figure 2.42, feature high- stiffness, precision-aligned annular load frames combined with four advanced actuators mounted in-plane and perpendicular to one another. Their controller systems provide translation and deformation control of each axis. These systems are used for large strain field coverage in two-axis tensile, low-cycle fatigue (LCF), high-cycle fatigue (HCF), thermo-mechanical fatigue (TMF), and fracture tests. Console software provides full system control from a PC: including basic waveform generation, calibration, limit set up, and status monitoring. WaveMatrix Dynamic Testing Software is used for synchronised test control of each axis with simple or complex tests being developed from the Graphical method setup screen (Instron, 2014).

Features:  Standard systems feature load capacities ranging up to 250 kN;  8800 Advanced Modal Control Techniques;  Wide variety of options, grips, and accessories available to suit application requirements.

Figure 2.42 Instron planar biaxial cruciform testing system (from Instron, 2014).

Zwick/Roell is the world's leading supplier of materials test machines with over 150 years of history. Their machines are used for R&D and quality assurance in more than twenty industries. As well as standard tensile, compression and flexure tests, Zwick materials testing machines are used for multiaxial tests such as biaxial tensile tests and torsion tests. The company is also the leading supplier of fatigue testing machines, hardness testing equipment, pendulum impact testers and melt index testers.

Zwick/Roell supplies two main biaxial testing machine types as shown in Figure 2.43:  Biaxial testing machines with electrical synchronization;  Biaxial testing machines with mechanical synchronization. Biaxial testing machines with electrical synchronization are used for 2-axis tensile tests on metal specimens. They are equipped with two load frames, angled at 90° to each other and each fitted with two central lead-screws.  Maximum test load 250 kN;  Maximum test speed 40 mm/min;  Lead screws are powered via four maintenance-free AC servo-motors for each loading orientation.  Two testControl measurement and control electronics units used (Zwick/Roell, 2014).

Biaxial testing machines with mechanical synchronisation are used for 2-axis tensile tests on plastic and metal specimens. They are equipped with two load frames, each with two lead screws with left and right-hand threads.  Maximum test load 10 kN.  High test speeds - up to 1 m/min - guarantee high efficiency.  Lead screws are powered via four maintenance-free AC servo-motors.  Two testControl measurement and control electronics units used (Zwick/Roell, 2014).

Figure 2.43 Zwick/Roell Biaxial Testing Machines with Electrical and Mechanical Synchronization (from Zwick/Roell, 2014)

MTS Planar Biaxial Testing System (Figure 2.44) combines modular load frame technology, innovative control methods, advanced alignment techniques and integrated environmental chambers to effectively simulate the mixed mode loading environments of materials and components. The MTS Planar Biaxial Testing System employs multiaxial loading technology to apply and measure in-plane stresses in both the X and Y axes. Key system attributes include:

 A highly stiff frame and large specimen mounting area;  Compact design;  Low friction actuators with hydrostatic bearings;  High lateral stiffness that provides accurate test results and very high frame natural frequency;  Optional over-travel protection in X, Y, Z planes for system protection;  Optional acceleration compensation for high frequency work (MTS, 2014).

Figure 2.44 MTS Planar Biaxial Testing Systems (from MTS, 2014).

The MTS Planar Biaxial Testing System features a highly stiff frame, four actuators and load cells, hydraulic or mechanical grips and fixtures, rubber isolation mounts and an MTS hydraulic power unit (HPU). The system supports 100 KN, 250 KN and 500 KN actuators to perform static testing and dynamic testing to 20 Hz. Users can link basic processes, including function generation, data acquisition, events, and triggers, to conduct tests. Optional system components include a variety of integrated environmental chambers to simulate real world service environments, as well as an advanced alignment system comprised of a special strain- gauged specimen and software to ensure precise system alignment (MTS, 2014).

2.3.5. Summary

In the previous sections various configurations of biaxial test machines were described. They range from attachments for existing testing machines to in-house built and commercial stand- alone units. Each type has advantages and disadvantages associated with it. Attachments, which are placed into tensile testing machines, are more economic and easier to build. The main disadvantage, however, with the attachments or link mechanisms is that only one type of biaxial testing can be performed. The ratio between the movement in X direction and the Y direction is fixed and in most cases Ratio = ε1/ε2 = 1. If a biaxial test has the requirements to have a ratio of X to Y equal to 1/2, the links in the device have to be changed which makes it time consuming and prohibitively expensive. Stand-alone biaxial testing machines can achieve the required ratio changes by programming the speed of motors or hydraulic actuators. These testing devices allow the performance of different biaxial tests at variety of speed ratios and loading conditions in the X and Y directions. The main disadvantage of stand-alone machines is the cost of design and building. One of the aims of the present research is to design and build in-house stand-alone biaxial testing machine. This would avoid the cost of procuring a commercial unit without compromising on the flexibility of testing methods.

Planar biaxial testing requires specially designed cruciform specimen. Various research groups contributed significantly to the area of design and optimisation of cruciform specimen. The outcomes of this work are presented in the following paragraph.

2.4. Design of Cruciform Specimens

2.4.1. Introduction

One of the most challenging aspects of a biaxial testing system is test specimen design. Test specimens can vary from cruciform types to cylindrical tubes as used in the bulge test. To perform a biaxial test on sheet metal, a cross-shaped specimen is typically used (Figure 2.45). The design of the cruciform specimen is the main difficulty that restricts application of the cruciform biaxial tensile test. Although specimens of the cruciform type have been investigated quite extensively, no standard geometry exists (Lin and Ding 1995). The lack of standard specimen geometry makes it difficult to compare test results from different laboratories (Makinde, Thibodeau et al. 1992). Different biaxial tests have been performed in parallel to finite element simulation in an attempt to achieve an optimum specimen design. FEA and other simulation models in sheet metal forming in the automotive industry have proven to be beneficial to reduce tool costs in the design stage and for optimizing current processes (Vegter and van den Boogaard 2006).

Figure 2.45 Stresses on specimens (Geiger et al., 2005).

Depending on the specific theory, which is used to describe the material behaviour, several variables, e.g. tensile strength, anisotropy, yield locus, etc can be taken into account for modelling sheet metal forming. In comparison with parameters that are determined in uniaxial 72 experiments, e.g. uniaxial tensile tests, the yield locus defines a starting point of plastification as a function of the biaxial stress condition (Geiger, Husnatter et al. 2005). The typical force system that acts on the specimen during the test is presented in Figure 2.45. A large range of materials other than metals have been examined using the cruciform specimens. These include cellular tissue and composite materials (Brody and Pandit 2002).

In designing a specimen, it was of great importance to ensure that the majority of deformation at the centre section of the specimen and to avoid stress concentrations in other regions of the specimen (Demmerle and Boehler, 1993). Deformation capacity of sheet metal under uniaxial tension is much less than that under biaxial tension. Rupture consistently occurs on the arms of the specimen. There have been a number of methods employed to prevent this in a cross- shaped specimens. The three main methods are the (i) cut type, (ii) reduced section type and (iii) strip and slot type as proposed by (Ohtake, 1999) and shown in Figure 2.46. The cut type uses large radii at the corner sections of the specimen to cause an increase in the deformation at the centre section of the specimen. From the cross-section of the reduced section, presented in Figure 2.46, the specimen is reduced in thickness to increase the deformation at the center. The strips used in the strip and slot-type specimen reduce the effect of load sharing on the arms. These slits made in each arm, were found to be very effective in causing uniform strain distribution within the gauge section, allowing the biaxial stress components in the gauge section to be easily identified without assuming the effective cross-sectional area (Kuwabara, 1998). These slots are also used to distribute the applied load evenly to the gauge section and also uncouple the two loading axes by allowing more flexibility for the specimen to deform in the two directions (Donne and Trautmann, 2000). This was also shown in a method of gripping the standard square specimens.

Figure 2.46 Proposed geometry for cruciform type specimen (from Ohtake, 1999).

In an attempt to investigate the influence of parameters such as: (i) the rounding radius at the intersection of two arms, (ii) the thickness of the biaxial loaded test zone in relation to the thickness of the arms and (iii) the geometry of the test zone on the aforementioned requirements, finite element simulations have been used by the research group. Afterwards, these numerical results are normally compared with experimental results obtained from biaxial tests on selected cruciform geometries.

The literature on fatigue is replete with attempts made to correlate the fatigue strengths of specimens subjected to different kinds of stress system. These investigations have resulted in theories of failure, which generally have only limited application because of the restricted stress systems on which they are based. Such theories cannot therefore be regarded as well substantiated and practically no information exists as to the behaviour when the biaxial components of stress are not synchronous.

2.4.2. Historic overview of the design of cruciform specimens

Wilson and White (1971) noticed that it was unusual for the most significant stresses to occur on the surface of a body where, provided the surface was not loaded, the stress system was biaxial. It was equally usual in design to use fatigue data obtained under a uniaxial-stress system and this involved using a theory of failure to relate the data to the biaxial state.

A flat-bottomed specimen was, however, preferred since the strain would be uniform over a much greater area. In Zidane’s (2010) investigation, four different specimens with the dimensions shown in Figure 2.47 were considered.

The maximum and minimum thicknesses and the overall diameter of the reduced section were the same for all four profiles as those given for the fully dimensioned section for d/t = 12.5. It was convenient to refer to the specimens by the ratio of the diameter d of the flat-bottomed portion to the minimum thickness t. The d/t ratios considered are thus 12.5, 5, 2.5, and 0.

The specimens were made from mild-steel plate to B.S. 1501-161, Grade 28A. These were initially flame-cut from 100mm thick plate and after stress relief at 600°C for 3 h the cruciform profile and surfaces were milled. The reduced centre section was turned on a lathe with a radiusing attachment and a manual feed and was finally polished with abrasive paper.

Figure 2.47 Dimensions (all - inches) of cruciform specimens (from Zidane, 2010).

Kuwabara conducted a test in 1998 on cruciform specimens. The test material was an as- received cold-rolled low carbon steel sheet 0.8 mm thick. The mechanical properties of the test material were listed in Table 2-2. Figure 2.48 shows the geometry of the cruciform specimen used in this study. The x- and y-axes were taken parallel to the rolling and transverse directions of the specimen respectively, where the origin of the coordinates was at the centre of the specimen. Each arm of the specimen had seven slits 60 mm long and 0.2 mm wide at 7.5 mm intervals, in order to exclude geometric constraint on the deformation of the 60x60 mm square gauge section. The slits were produced by laser cutting (Kuwabara, 1998).

Table 2-2 Mechanical properties of cold-rolled low-carbon steel sheet used in this study (from Kuwabara, 1998).

where, a - approximated using σ=c(α+εp)n; b - measured at uniaxial plastic strain εp=0.05. As preliminary experiments, cruciform specimens with five biaxial strain gauges mounted on the x- or y-axis were stretched under linear loading paths and the development of biaxial strain components at the gauge section was measured. 75

Figure 2.48 Cruciform specimen for the biaxial tensile test (from Kuwabara, 1998).

The objective of the research conducted by Ohtane in 1999 was to obtain fatigue failure criteria for all possible combinations of biaxial stress states in conventional low-strain high-cycle fatigue and for all possible combinations of biaxial-strain states in high-strain low-cycle fatigue. In the conventional fatigue tests, synchronous controlled biaxial stresses should be applied to produce principal-stress ratios at convenient intervals between 1/1 and -1/1. In the high strain fatigue tests, synchronous controlled biaxial strains were applied to produce principal-strain ratios at convenient intervals between 1/1 and -1/1. Before proceeding with the construction of the machine the researcher (Ohtane, 1999) investigated the performance of different cruciform specimens. Elastic finite element analyses and elastic and plastic analyses of cyclically strained specimens with photo-elastic coatings were used to study strain distributions. Number of fatigue tests were conducted in which only one pair of arms of the cruciform was loaded. The findings of these investigations were reported and specimen dimensions were recommended both for stress controlled (elastic) cycling and strain-controlled (plastic) cycling (Ohtane, 1999).

Smits (2006) noticed that successful biaxial strength test with cruciform specimens required the following conditions: (i) maximization of the region of uniform biaxial strain, (ii) minimisation of the shear strains in the biaxially loaded test zone, (iii) minimization of the strain concentrations outside the test zone, (iv) specimen failure in the biaxially loaded test zone, and (v) repeatable results. It was proven extremely difficult to develop cruciform specimens that would simultaneously fulfil all these requirements (Smits, 2006).

Conditions (i) and (ii) were required if strains were measured at the centre of the specimen with a strain gage or extensometer where one average strain value was obtained over their length. This average value should be representative for the whole length of the strain gage or extensometer. The other conditions and their combinations were analysed. Major constraints of optimal design were highlighted. FEA of the specimens used are shown in Figure 2.49.

Figure 2.49 Finite element analysis results of the first principal strain for four cruciform geometries (from Smits, 2006).

Poncelet (2010) carried out research to characterise the mechanical behaviour of materials subjected to biaxial loadings using, various cruciform specimens. Several researchers proposed a cruciform specimen shape with a reduced thickness in the square central and arm slits. An example of such geometry is shown in Figure 2.50a. To study the influence of biaxial loadings on hardening anisotropic materials, Ferron and Makinde (1988) and Demmerle and Boehler (1993) optimized this specimen and obtained a homogeneous stress–strain field over a large part of the square zone. Johnston et al (2002) modified Specimen 1 and added a circular central zone with a smaller thickness (Figure 2.50b).

a b Figure 2.50 Geometry of specimens a) 1; and b) 2 (from Zidane, 2010).

Removing arm slits, Yong (2002) proposed the shape shown in Figure 2.51a. This form was developed to determine the FLD under complex loading paths by numerical finite element simulations. The initial specimen dimensions defined by the author (Yong, 2002) led to a very stiff specimen: the arm width is 90 mm and the central area diameter is 20 mm. However, to the best of the author's knowledge, no experimental results were published to validate this specimen geometry.

Another cruciform specimen geometry (Figure 2.51b) with a reduced thickness in the central area and variable width arms has been proposed by Zhang and Sakane (2007). This specimen was used to realise fatigue tests, i.e. at low strain levels.

Through FE simulations, the efficiency of the four specimen geometries mentioned above were numerically investigated. For that, an equi-biaxial tensile test is simulated by means of the FE software package ABAQUS. Considering the symmetry of the specimen geometry, only one- quarter of the specimen is analysed. For meshing, tetrahedral elements are used and a refined mesh is adopted in the sensitive areas where strain localizations could occur (central zone, intermediate section, fillet, arm slits). Isotropic elasto-plastic behaviour of an aluminium alloy is assumed. The elastic part is described by Hooke’s model with the Young modulus E = 70GN/m2 and the Poisson ratio ν = 0.3. For the plastic part, isotropic von Mises yield criteria are used and the hardening behaviour is described by Ludwick’s law:

풏 흈 = 흈푶 + 푲휺 Eq. 2-30

78 where σ and ε are the equivalent stress and the equivalent plastic strain, respectively, σ0 is the yield stress obtained from a mono-axial tensile test, and K = 553MPa and n = 0.61 are material parameters.

a b

Figure 2.51 Geometry of specimens a) 3; and b) 4 (from Zidane, 2010).

The various geometries suggested (Figures 2.50 to 2.51) were dimensioned with the following rules: (i) the characteristic dimension of the central zone was fixed at a value ranging from 20 to 30 mm. This dimension was mainly imposed by the dynamic acquisition capacities of the camera, (ii) other principal dimensions (width and thickness of the arms, thickness of the central area) were chosen according to either the maximum load capacities of the experimental setup or the maximum stiffness of the sample. The maximum value of the stiffness was defined by the capacities of the experimental device. Consequently, the thickness of the central area and arms were fixed to 1 and 4 mm respectively. For Specimens 2–4, the thickness of the intermediate zone was 2 mm (Zidane, Guines et al. 2010).

Figure 2.52 Equivalent plastic strain and maximal principal strain fields for specimens 1 and 2 (from Zidane, 2010).

To ensure that necking always appeared in the central zone, the design of the cruciform specimens should induce the greatest deformations in the central zone and no strain localis ations in the other areas (arm slits, fillets, etc). Both the equivalent plastic strain and the maximal principal strain in the specimen were observed. In the geometrical singularities (arm slits for example), the observation of the equivalent plastic strain was not sufficient since the major principal strain could reach high values leading to a localization of the deformation (and then fracture) although the equivalent strain was not very high. Figures 2.51 and 2.52 show the distribution of the equivalent plastic strain (PEEQ) and the maximal principal strain fields for Specimens 1–4.

Figure 2.53 Equivalent plastic strain and maximal principal strain fields for specimens 3 and 4 (from Zidane, 2010).

According to Figures 2.52 and 2.53, it was evident that the strain concentration was more homogeneous in the central test section of the specimens with arm slits (Specimens 1 and 2). But, for Specimen 1, the maximum strain value (30%) was observed in the grooves. This phenomenon was less pronounced for Specimen 2 where an intermediate zone was added. For Specimen 3, the maximal principal strain was obtained in the fillet of the arms (25%), whereas in the central zone, the level reached was approximately 15%. For Specimen 4, the highest strain values (maximal principal strain or equivalent plastic strain) are located in the fillet of the arms (Zidane and Guines, 2010).

The results of the FE simulations showed Specimens 2 and 3 as more efficient since they return the maximum values of strain in the central zone. But Specimen 3 is, for all the specimens tested, the stiffest (Table 2-3).

Table 2-3 Stiffnesses of the tested specimens

Specimen 1 2 3 4 Stiffness (kN mm−1) 42 45 62 38

The geometry of the specimen illustrated in Figure 2.50b was considered to be the most effective and the most promising. The positioning of the arm slits permitted to limit the stiffness of the specimen. An optimization could be performed; FE simulations showed notably that the distance between the ends of the arm slits and the edge of the square central zone had a great influence on the level of deformation in the slits and fillets of the arms (Zidane and Guines, 2010).

Thereafter, on the basis of the geometry of Specimen 2, a modified form was proposed and optimized in order to reduce the strain localization in slits.

Figure 2.54 Geometry of the optimized specimen shape (from Zidane, 2010).

The main purpose of the optimisation was to ensure strain localisation at the central point of the specimen and then the onset of necking in this zone. The strain path value at the central point of the specimen was directly linked to the velocity ratio of actuators for the two tested axes. If the strain localization appeared in a different zone, the strain path in this zone would be different from the velocity ratio and then only a partial forming limit curve could be drawn. Thereafter, on the basis of the shape illustrated in Figure 2.54, a modification of the form of the central zone was proposed (Zidane and Guines, 2010). .

(a) (b) Figure 2.55 Specimens I and II: transition with chamfer (a) and radius (b) (from Zidane, 2010).

According to the previous study, two key geometrical parameters were identified for the strain distribution in the specimen. These parameters were the length L between the ends of the slits and the edge of the square central zone and the fillet of arms Rc (Figure 2.54). As previously described, by adjusting these parameters to adequate values, the strain level in slits and fillets of the arms was limited by comparison with the level in the central region of the specimen. This was the first step of the optimisation procedure; the second step consisted in the strain localization at the central point of the specimen for the strain path control. Hereafter, to achieve the procedure, two different shapes were proposed and discussed for the central zone of the specimen. For Specimen I, a chamfer between the flat central circular zone and the intermediate square zone was defined (Figure 2.55a), and for Specimen II, the central point and the intermediate square zone were connected by a curved profile radius (Figure 2.55b).

It was evident from Figure 2.55 that the thickness of the central test section T was also a key parameter for the strain localisation and homogeneity. For Specimen I, the diameter of the flat central test section was noted, Di. A parametric study was carried out and the best set of parameters obtained was given in Table 2-4.

Table 2-4 Optimized geometrical parameters (from Zidane, 2010).

L (mm) Rc (mm) Di (mm) T (mm) Specimen I 4.5 8 10 0.75 Specimen II 4.5 8 - 0.75

A rigorous method, which could be applied in a numerical or experimental approach, was constructed in this part and it was proposed to validate it through an experimental campaign on an aluminium alloy dedicated to sheet forming processes.

Hanabusa (Hanabusa, Takizawa, & Kuwabara, 2013) proposed a method of evaluating stress measurement errors in biaxial tensile tests using a cruciform specimen is proposed in 2013. The cruciform specimen was assumed to be fabricated from a section of uniformly thick flat sheet metal via laser or water-jet cutting and to have a number of parallel slits cut into each of the four arms.

Using finite element analyses with the von Mises yield criterion, the optimum geometry of the cruciform specimen and the optimum strain measurement position necessary to minimize the stress measurement error were determined. Additionally, an experimental validation of the FEA was performed using a sheet material that had been experimentally confirmed to be nearly isotropic. Analysis conditions for FEA are shown in Table 2-5.

Table 2-5 Analysis conditions for FEA (from Hanabusa, 2013).

Stress ratio: sx : sy 1:0, 4:1, 2:1, 4:3, 1:1

Thickness: t0 (mm) 0.6, 1.2, 2.4, 3.6, 4.8 Slit length: L (mm) 15, 30, 45, infinite length (unconstraint along arm edges in transversal direction) Number of slits: N 3, 5, 7, 9

Slit width: ws (mm) 0.2, 0.3, 0.5 Corner radius: R (mm) 0.1, 0.5, 1.0, 3.0 The following conclusions were drawn: (i) the thickness of the test material should be less than 0.08B (B: side length of the gauge area of the cruciform specimen);

(ii) the geometric parameters for the cruciform specimen should be N ≥ 7, L ≥ B, ws ≤ 0.01B, and 0.0034 ≤ R/B ≤ 0.1 (N: number of slits (Figure 2.56)), L: length of slits cut into the arms, ws: slit width (Figure 2.57), and R: corner radius at the junction of the arms to the gauge area);

Figure 2.56 Effect of number of slits N and slit width ws on maximum equivalent plastic strain p ε max applicable to gauge area of cruciform specimen (from Hanabusa, 2013).

(iii) the strain components in the gauge area should be measured on the centerline of the specimen parallel to the maximum force direction at a distance of approximately 0.35B from the center of the specimen. The stress measurement error is estimated to be less than 2% when the optimum conditions above are satisfied.

Merklein in 2013 used the design parameters outlined in Hanabusa research (Merklein & Biasutti, 2013). Feature added to the design of the specimen was the one-sided recess of the testing area. Parts of the outcomes of that research are outlined below.

For the purpose of comparison with analytical yield criteria a set of points belonging to the same contours of plastic work was selected at W0.2%. The equibiaxial yield stress for AA6016 determined in this study was compared with the value taken from an independent source (Butuc, 2003) as shown in Figure 2.58, where the standard deviation for each set of the three experimental repetitions was partially overlapped by the black spot which represented the average experimental result. The resulting calculated difference was in the same range of the differences calculated from the uniaxial tensile test values along the main axes. 85

The yield surfaces for AA6016 were superimposed as shown in Figure 2.58 for different anisotropic yield criteria, which parameter were identified according to the analytical formulations outlined below. As widely known Hill’48 (Hill, 1948) did not properly describe the behaviour of aluminium alloys due to the so-called “anomalous behaviour” underestimating the equibiaxial stress when the R-values are less than 1. Hill’90 (Hill, 1990) and modern yield criteria like the Yld2000- 2d (Barlat, 2003) could model this behaviour, with the latter showing a better proximities to the experimentally obtained nonequibiaxial stresses (Merklein & Biasutti, 2013).

Figure 2.58 Yield surface for AA6016 alloy: experimental and predicted yield surface by Hill’48, Hill’90 and Yld2000-2d model (from Merklein, 2013).

Yld2000-2d criterion showed better prediction of the R-value distribution over the angle of the rolling direction (Figure 2.59).

Figure 2.59 R-values as a function of the tensile loading axis (from Merklein, 2013).

Figure 2.60 Yield stress as a function of the tensile loading axis (from Merklein, 2013).

The predicted yield stresses as a function of the loading axes are shown in Figure 2.60 with Hill’48 overestimating and Hill’90 overlapped to Yld2000-2d matching the experiments. The advanced yield criterion of Yld2000-2d is overall found to be the best match between experimental and predicted values for AA6016.

2.4.3 Summary

Biaxial testing is a relatively new area yet a vast amount of knowledge of this area has been accumulated over the last 50 years. It shows the interest of the manufacturers and consequently the researchers on this testing technique. Biaxial testing proved to be providing useful data, which explains the behaviour of sheet anisotropic materials. This data is later used by manufacturers to predict materials behaviour for various production processes.

Analytical knowledge and experimental data as an outcome of work presented by different research groups was gathered in this part of literature review. The main focus was placed on the design of the cruciform specimen and its optimisation. Various research groups presented different approaches to the design. The specimen designs used for the current research program are described in Chapter 3. The specimens present combination of the features used by other researchers and proved to provide valid data for further analysis.

2.5 Literature Review Summary

The active interaction of human systems and medical devices demands much higher design requirements for biomedical products and systems. These requirements include biocompatibility, corrosion resistance, reliability, customisation, and controllability. Advanced manufacturing technologies are needed to meet these desired requirements. Furthermore, designers need to have in-depth knowledge of the materials used in bio-engineering. This deeper knowledge of the materials behaviour leads to inventions of new materials which closely meets customers’ requirements.

The design engineers are responsible for appropriate materials to be selected for a specific design application or product. Furthermore, the particular requirements of the manufacturing processes used must be met when choosing the material. In modern manufacturing, materials are more often subject to multiaxial loading. In sheet or tube forming processes, for example, materials are generally subjected to multiaxial loads. Metal parts are very often manufactured in two or more forming stages. Therefore, an increasing role is given to the testing of material to establish its properties through multiaxial and/or multistage loading tests. Consequently, it is important to use multiaxial testing processes to find the true material properties under these types of loading. In addition, it is important to note not only the material being tested but also the location from which the specimen was taken and its orientation. Rolled sheet, rolled plate, and rolled bars, for example, will have different properties when tested parallel to the direction of rolling (longitudinal) and perpendicular to the rolling direction (transverse). This variation of properties with direction, known as anisotropy, may be crucial to the success or failure of a product.

Three types of the biaxial testing systems were described in the third section of this chapter. They include: attachments for existing testing machines, in-house-built stand-alone systems and commercial stand-alone units. Each type has advantages and disadvantages associated with it. Attachments, which are placed into tensile testing machines, are more economic and easier to build. The main disadvantage, however, with the attachments or link mechanisms, is that only one type of biaxial testing can be performed. The ratio between the movement in X direction and the Y direction is fixed and in most cases Ratio = ε1/ε2 = 1. If a biaxial test has the requirements to have a ratio of X to Y equal to 1/2, the links in the device have to be changed which makes it time consuming and prohibitively expensive. Stand-alone biaxial testing machines can achieve the required ratio changes by programming the speed of motors or hydraulic actuators. These testing devices allow the performance of different biaxial tests at variety of speed ratios and loading conditions in the X and Y directions. The main disadvantage of stand-alone machines is the cost of design and building. 88

One of the most challenging aspects of a biaxial testing system is test specimen design. Test specimens can vary from cruciform types to cylindrical tubes as used in the bulge test. To perform a biaxial test on sheet metal, a cross-shaped specimen is typically used. The design of the cruciform specimen is the main difficulty that restricts application of the cruciform biaxial tensile test. Although specimens of the cruciform type have been investigated quite extensively, no standard geometry exists. The lack of standard specimen geometry makes it difficult to compare test results from different laboratories. Different biaxial tests have been performed in parallel to finite element simulation in an attempt to achieve an optimum specimen design. FEA and other simulation models in sheet metal forming in the automotive industry have proven to be beneficial to reduce tool costs in the design stage and for optimizing current processes.

The information presented in this chapter (specially, last two section of it) contributed to the body of knowledge required for the successful completion of design and manufacture phase of the current project. The knowledge gained greatly reduced design time and trial and error period. Some of the concepts presented in this chapter were utilised by the author of this research and are discussed in more details in the next Chapter - Design and Manufacture of Biaxial Tensile System.

The literature review outlines that investigations of mechanical properties of Nitinol have not been previously performed under biaxial loading conditions. The aim of this research is to fill the gap and provide numerical date, which indicates the ability of Nitinol to withstand biaxial loading. Comparative analysis of the behaviours of Nitinol and SS304 not only aims to establish the deformation-fracture patterns for both materials but also distinguish the differences.

Chapter 3

Design and Manufacture of Biaxial Tensile System

3 Design and Manufacture of Biaxial Tensile System

3.1. Introduction

The testing system should satisfy the requirements of the testing process. It should also provide precise and accurate results for further analysis. Standard requirements for testing systems are the safety of the operator and durability of the machine. Both criteria were taken into account when designing the current testing system. The system was used to test metallic materials and required sufficient rigidity and strength to withstand the high forces applied during testing (designed for force of 20kN).

Operator’s safety is outlined in the Health and Safety at work Act 2005. The current design must satisfy the requirement of this document. The majority of tensile testing machines operate with very low speeds. This is essential for obtaining valid tensile testing data. High speeds of testing machine would simulate impact or high strain rates. This approach to material testing is outside of the scope of current research. The system design was equipped with the standard features required by Health and Safety regulations for these types of machines: Emergency stop, Main ON/OFF switch and Circuit breakers.

Critical parts of the machine were modelled using CAD software (SolidWorks). Simulation of machine motion was also performed. The requirement for the Factor of Safety to be 3-5 was achieved for the parts. This condition ensures that no plastic deformation occurs in any of the machine components, during machine operation.

The main objectives of the design phase of the current project were as follows: 1. To ensure that the proposed machine design would satisfy the goals of the research project (provide simultaneous planar loadings in X and Y directions). 2. To ensure that sufficient forces could be generated by the machine to plastically deform 304 SS and NiTi cruciform specimens. 3. To identify a method of machine control and data acquisition for biaxial tensile testing.

3.2. Testing system design

As outlined in the previous chapter, there are advantages and disadvantages associated with stand-alone commercial machines and attachment mechanisms for tensile testers. An in-house- built stand-alone concept was chosen as a most economical and efficient combination to provide control of all axis’s of motion. The knowledge accumulated through the review of previous research activities in the area of biaxial testing inspired two preliminary designs, which are described below. Both design ideas were considered simultaneously. Design 1 is presented in Figure 3.1 and includes following features:

Figure 3.1 Preliminary Design 1 of Biaxial Testing Machine.

 Two horizontally mounted supports with provision to bolt the structure to the concrete floor.  Four vertical supports welded to horizontal supports.  Front and back plates 20mm thickness.  Four Motor Gearboxes mounted between the front and back plates.

Other equipment which is not shown on the Figure 3.1 include: 4 Holders mounted to the shafts of the Gearboxes (2 with load cells), 4 inverters to control the Motors and LabVIEW Hardware to control the testing machine and manage data transfer to computer for further analysis.

An alternative Design is presented on Figure 3.2. It includes the following features: a. Welded cruciform base made from I-beam steel profile. b. Four Motor Gearboxes mounted as shown in Figure 3.2. c. Screw transport system attached to the shafts of the Gearboxes. 92

Figure 3.2 Preliminary Design 2 of Biaxial Testing Machine.

Other equipment which is not presented on the Figure 3.2 include: 4 Holders mounted to the sliding mechanisms attached to Screws c (2 with load cells), 4 inverters to control the Motors and LabVIEW Hardware to control the testing machine and manage data transfer to computer for further analysis.

A concept of the interface for the machine control was developed and is shown in Figure 3.3.

Figure 3.3 Interface for the machine control.

Design analyses were based on 2 criteria: fit for purpose and cost effectiveness. Design 1 was economically prohibitive. Purchasing of two plates with 20 mm thickness and laser cutting of it to the required sizes was investigated. The purchase price for it was outside of the budget available. It was concluded to proceed with Design 2 concept.

The concept of Design 2 underwent further development and is shown in Figure 3.4. Four motor gearboxes which were mounted on each end of the structure and the base of the machine are not shown on Figure 3.4. The support structure is shown in Figure 3.5.

The mounting structure supports the driving units. The mounting structure in manufactured from 150 x 150 x 8 mm I-beam. I-beam provides sufficient resistance to simple bending as well as supporting tensile and compressive loading. The design consists of 2 types of beams: 4 beams to form the centre section and 4 end beams (1 at each corner of the square).

Mounting Structure

Figure 3.4 Final design of Testing System.

A major deviation from Design 2 was the introduction of square void area in the centre of the cross shape mounting structure. This design will allow for further development of the current testing rig. The void area could be used for installation of a furnace in the middle of the structure. A furnace would allow for further research on different materials at elevated temperatures.

The cross shape I-beam structure was mounted on top of the support unit shown in Figure 3.5. 50 x 50 x 3 mm hollow square beam was used. 4mm wall thickness of 50 square hollow beam is sufficient for good weldability of the material. Welding was used to join all the parts of support structure. The cross shape I-beam structure was mounted on top of support and welded in position. This design provides a rigid support to the mechanism of tensile testing system assembled on top of this structure.

Figure 3.5 Support structure for Biaxial Testing System.

Heavy duty wheels were attached on each leg of the support structure (not shown on Figure 3.5). This allowed for easy movement of the testing system. The electric control enclosure was bolted to the support structure. Controls and data collection devices were mounted on the main support structure or the table, which holds the main PC unit. This design allowed for easy disassembling and moving of the system to other locations, when necessary.

A key component of the drive system was the HIWIN ball-screw (50mm in diameter with 10mm pitch) shown in Figure 3.6. The system was designed as a working prototype for biaxial testing and allowed for part interchanging with ease. If heavier duty operations for the machine were anticipated, HIWIN ball-screws could be replaced with THK equivalent.

Figure 3.6 Main drive unit with motor gearbox.

Four motor gearboxes FCNDK63/FCNDK30 (600:1 reduction ratio) provided a drive to the system. Four similar type of gearboxes were chosen to minimise discrepancies within the drive mechanism. The same approach was taken when choosing the motors. Four 0.14kW 1500 rev/min TECH motors were used.

Each motor gearbox was mounted on a support plate. Each support plate had 2 round pins manufactured from silver steel. The setup is presented in Figure 3.7 (far right) and Appendix A. The pins served two functions:

 Sliding of motor gearbox function is available for fine adjustment of the griping mechanism. Fine adjustment can be accomplished by manual rotation of ball-screw to reach the required position of the grip.  Torque transmitting function.

Each motor mounting plate was equipped with an additional torque bar. This bar also prevented the mounting plate and motor gearbox from sliding backwards, when under load.

Motor gearboxes were connected to the ball-screws with the aid of star couplings. A star coupling transmits the torque and also prevents the motor gearbox from shock load. Shocks are absorbed by the nylon star insert.

One of the challenges associated with the design of the testing system was to connect the specimen grip to the nut and the ball-screw. As an assembled unit, the nut is capable of withstanding a static force of 131kN (radial bearing withstands 41kN). Furthermore, the nut is limited to support a bending load of 500Nm. The aim of the design was to reduce the bending 96 load element in the system and confine the nut assembly to axial loading conditions only. This goal was achieved by the introduction of the following elements to the system shown in Figure 3.7:

 Saddle - consists of two similar parts mounted on the nut and assembled to the nut with an aid of 8 M10 bolts (4 bolts for each half of the saddle). The two parts of the saddle are bolted together - 2 M10 bolts.  Each side of the saddle has slots to fit two parallel bars 20 x 20 x 540mm. Each bar is bolted to both halves of the saddle by 4 M10 bolts (2 each bar).  The two front ends of the bars are interconnected with an aid of a cross member element of the system. The assembly requires 4 M10 countersink bolts (2 each bar to cross member)  Two load cells and two dummy load cells and bolted to the cross members and the 4 gripers are bolted to them. Biaxial planar systems require only 2 load cells (one on each axis). Two dummy block of the size of the load cell were manufactured to compensate the length differences.

Cross Member Parallel Ball-screw Saddle Top Element Bar (2) and Nut and Bottom

Locator Motor Pins (2) Support Plate

Figure 3.7 Exploded view of main drive unit.

This design allowed minimisation/elimination of bending forces.

The ball-screws are supported by 2 bearings: radial bearing on the testing side and an assembly of a radial and a thrust bearing at the motor side. Bearing housings are bolted (6 M16 bolts per ball-screw) to the base plate. A base plate was bolted (4 M20 bolts) to the cross shape support structure. This assembly mechanism gives the system flexibility and ease in further modernisation. Manufacturing/assembly drawings of the testing system are presented in Appendix A.

Additional challenges to the design were to overcome the flexibility and uncontrolled movement of parallel bars 20 x 20 x 540mm due to their length. Guiding units were designed to solve this problem and provide the parallel bars necessary support. The guiding units consist of 3 elements: a front plate which is attached to the base plate and two guides (left and right) mounted at each side of the front plate. Guiding units (4 - 1 each side of the cross) are assembled using 6 M8 bolts (two different bolt lengths). Parallel bars sliding through the guides were sufficiently lubricated. Further development of the planar biaxial testing system will require more comprehensive guide greasing. Greasing system for guiding units could have 2 grease nipples (one on the top of each guide). A slot delivers grease to 3 sides of the parallel bar, which are in contact with the guiding unit. The parallel bar was also engraved with a sinusoidal shape pattern to increase its ability to hold grease. An experimental model of this system was manufactured but is considered to be outside the scope of this project to machine the components for 4 guiding units. The guiding system in presented in Appendix A p. 194-198.

3.3. Specimen design

The literature review in section 2.4 showed that specimen design is a critical area of research in the field of biaxial testing. Many researchers have contributed to the specimen design optimisation. Numerous requirements of the biaxial testing process included maximisation of test area, reduction of cross-sectional area and simplification of cross section area for further test analysis. Some of these requirements are in contradiction with one another. To date no standard geometry exists and investigation continues.

The following are the objectives of the specimen design phase:

1. To ensure that the proposed specimen will satisfy the goals of the research.

2. To incorporate the experience in the development of cruciform specimen accumulated by other researchers into current research and advance on it.

The proposed cruciform specimen design must satisfy the requirements of biaxial testing system. A literature review of the specimen designs is presented in Chapter 2. Proposed Design 1 is shown on Figure 3.8.

Figure 3.8 Preliminary Design 1 of Cruciform Specimen.

Finite Element Stress Analysis of Specimen 1 is shown on Figure 3.9.

Figure 3.9 FEA analysis Specimen Design 1.

An alternative design for the cruciform Specimen ( Design 2) is presented on Figure 3.10.

Figure 3.10 Cruciform Specimen Design 2.

Preliminary FEA stress analysis on Specimen Design 2 in shown in Figure 3.11.

Figure 3.11 FEA analysis Specimen Design 2.

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Both specimens underwent further development as a part of current research project. Knowledge accumulated in Chapter 2, mainly the research of Hanabusa in 2013, greatly influenced the design of cruciform specimens. The decision was made to proceed with both types of specimens, assigning them designations: Type 1 and Type 2. Type 1 specimen is shown in Figure 3.12. Both specimens were initially cut from aluminium.

Figure 3.12 Manufacturing drawing of the Specimen Type 1.

Specimen Type 2 was inspired by preliminary Design 2 and is shown in Figure 3.13.

Figure 3.13 Manufacturing Drawing for Specimen Type2.

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As a pilot project, the blanks for the two specimen designs (Types 1 and 2) were cut by waterjet. Two types of materials were used for the pilot project: mild steel CR4 and aluminium 1050. Successful testing of these specimens was accomplished. Waterjet technology proved effective in cutting aluminium. Yet its precision would not be sufficient when cutting 1.5 mm thick 304 SS and Nitinol. Slits on the four sides of the specimen as shown in Figure 3.14 were 0.8-1.0 mm. Laser cutting technology was chosen over waterjet cutting. It provided the required precision of 0.2-0.3 mm width of slit and also reduced the cost of manufacturing. The benefit of waterjet technology over laser cutting is the possibility to avoid melting in specimen material. As melting was not happening in the main testing area it was allowable to use laser cutting technology. Laser cutting of specimen blanks was used by many researchers (Hanabusa, 2013; Merklein, 2013). Reduction of slit width also allowed for an increase of the number of slits on each side of the specimen. 7 slits were recommended by Hanabusa in 2013. The slits contribute to even stress/strain distribution in the testing/gauge area.

Figure 3.14 Specimen Type 1.

Blank specimens required further manufacturing: reduction of the thickness of gauge area to obtain the desired shape for testing the material properties. The following manufacturing processes were considered: conventional milling, CNC milling and Electric Discharge Machining (EDM). Conventional machining required more set up work and would not provide the same accuracy and repeatability as CNC milling and therefor was not considered. CNC milling would provide the required repeatability and accuracy as EDM. EDM machining of the blank specimens was the preferred cutting process when considering machining Nickel Titanium, which is a difficult material to machine and special tooling is required. EDM machining of the mild steel was successful and was used for the other testing materials. Two special jigs were 102 designed to allow machining of two different specimen sizes. The EDM process used for machining the Nitinol material is shown in Figure 3.15.

Figure 3.15 EDM processing of the specimen.

A comparative analysis was carried out on the Type 1 Nitinol specimens with the recess in the testing area. Eight (8) out of twelve (12) specimens were recessed using EDM technology, while other four (4) were recessed by CNC machining. This analysis aimed to achieve fracturing in the testing area. Two (2) out four (4) of the specimens, recessed by CNC machining, broke near the grippers. Possible explanation of this type of fracturing could be in work hardening of material during machining. This type of fracturing (at grippers) was not exhibited by the specimens recessed using EDM technology. Manufacturing drawings of the specimens used in this research project can be found in Appendix B.

3.4 System of Grips

The specimen grippers system allowed the specimen to be mounted in the testing machine for biaxial testing. The system as shown in Figure 3.16 consists of the following components:

1. Set of 4 bottom parts to be attached to the transport system of biaxial testing machine. 2. Set of 4 top parts to be mounted over the cruciform specimen and assembled to the Bottom part a by 4 sets of 3xM6 bolts.

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Currently designed specimens reviewed in Chapter 2 contain 3 major areas:

a. testing area (normally squire or circular), b. arms which are next to the testing area and serve for the distribution (slits) and transmission of stress, c. holding area used to mount specimen in the grippers of testing machine.

The proposed system of grips would allow to combine areas (b) and (c) as above. This will be achieved by eliminating part (b). Its function will be provided by specially designed Top and Bottom Grippers which have horizontal grooves. An advantage of this design is minimisation of cost associated with larger specimens. It becomes more important when testing of expensive material, like Nitinol, is required.

Figure 3.16 Proposed System of Grips.

It was decided not to proceed with manufacturing of system of grips. The investigations in the area of plastic deformation of biomedical material showed that superelastic Nitinol would be difficult to control using the proposed system. Further investigations will be required to justify the benefits from the proposed system of grips. Appendix B contains the assembly drawing of the system. 104

3.5 Summary

During the design and manufacturing phase of the project the following aims of the project were accomplished:

 Design of the testing system for planar biaxial testing (Max capacity per axis - 20 kN);  Manufacturing of testing system components and machine assembly;  Design of the cruciform specimen for biaxial testing;  Manufacturing of cruciform specimens from aluminium, mild steel, 304 SS and Nitinol.

Control and data acquisition systems were also developed at this phase of the project. The elements of these systems and their functionality are described in Chapter 4.

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Chapter 4

Testing System Controls and Data Acquisition System

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4 Testing System Controls and Data Acquisition System

4.1. Introduction

The main requirement for the testing system is to acquire precise and accurate data from the biaxial test. Appropriate methods of data acquisition are needed to achieve this goal. The best practice is to have one software program controlling the testing system and data acquisition. The following limitations were identified:

 Olympus software supplied with i-SPEED camera is not compatible with LabVIEW software controlling testing system. An updated version of the software is currently available from Olympus but not with i-SPEED2 camera;  Software packages available from Olympus allow for automatic or manual points tracking during the data analysis phase. The current software which was purchased with i-SPEED2 camera is limited to manual only.

To ensure that the goals of the research were met, the following techniques were applied. First of the limitations stated above brought the requirement for software systems: LabVIEW and Olympus software for i-SPEED2 camera. The LabVIEW program controlled the biaxial tester motion and monitored the applied forces (X and Y directions). Strain/Extension Data was obtained from the analysis of the images captured by high speed i-SPEED2 Olympus camera. Both sets of data required further processing and compiling to a single data set presenting stress/strain or force/extension information. This technique provides valid results.

4.2. LabVIEW control system design

LabVIEW is a reliable programming platform used by the researchers to control testing machinery and collect testing data. LabVIEW programming is based on a graphical programming environment. Coding with LabVIEW involves graphical symbols rather than textual language to describe programming actions. LabVIEW programs are known as virtual instruments (VI's) because of their appearance and operation being very similar to actual instruments. A VI is made up of two parts; a front panel and a block diagram.

The front panel is the user interface of the VI. It usually contains controls such as push buttons, flip switches, etc. and indicators such as gauges and graphs. The other part of a VI is the block diagram. This is where the actual programming is completed using the graphical programming language. The block diagrams contain such items as terminals, which are block diagram 107 representations of items on the front panel. It also contains wires, which indicates the path data takes through the block diagram. There are also a large amount of functions, which are used to perform specific tasks on the data.

The requirements in term of controls and data collection were:  START/STOP functions on each of the four motors driving the ball-screws  Speed/frequency control on all four motors required to achieve desired linear velocity  Fine tuning of the motors if balance error in frequency on different motors is present  Data acquisition from two load cells as well as electrical signal to be supplied to the load cells  Data display showing force information on the graph  Error messaging

The front panel of the controls/data acquisition program is presented in Figure 4.1. The front panel designed in the LabVIEW programming platform is user friendly and allows to control the machine and data acquisition from a single screen.

Figure 4.1 The front panel of Controls/Data Acquisition program.

The fine tuning of each of the motors speeds allows for the fine adjustment of motor frequency – speed. This function gives the operator a possibility to run all four motors at the same speed

108 with high level of precision – 0.01 Hz. The control panel for fine tuning of the motors is presented in Figure 4.2.

Figure 4.2 Controls of the motors' fine tuning.

The data logging screen allows for visual data analysis and is presented in Figure 4.3. The outputs from both load cells are presented and allow for ongoing monitoring of data output.

Figure 4.3 Data Logging panel of Controls/Data Acquisition program. 109

The three interfaces enable the user of the program to fully control the operations required for tensile biaxial testing. The front panel gives the user sufficient controls for all aspects of the testing process. The block diagram of the program, as presented in Figure 4.4, reveals all the connections between the blocks enabling them to complete the tasks required.

Figure 4.4 Block diagram of Controls/Data Acquisition program.

The input of the testing parameters is achieved at the “start-up” block of code shown in Figure 4.5.

Figure 4.5 Input parameters of the program.

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The start-up block of code also contains a time delay of 250ms to allow for efficient operation of the PC processor. All the motors are getting a signal to run at the set speed by code blocks shown in Figure 4.6. These blocks shown are also responsible for switching on the motors.

Figure 4.6 Motors Speed Setting and Turning ON code blocks.

The stop code on the Front Panel allows the user to finish/stop the program at any time during the test cycle. Synchronized stop of all the elements of the program is controlled by the block of code shown on Figure 4.7.

Figure 4.7 The Stop Motor/Data Acquisition Block of codes.

The block of codes called “System Shutdown” ensures that the current software loop is completed. It also contains a code block of the command for Fine Tuning of Motor speeds. This block of codes is presented in Figure 4.8.

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Figure 4.8 The Shutdown System codes block.

Logging of all test data is achieved by running the code block shown at Figure 4.9.

Figure 4.9 Logging of Data block of codes.

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The LabVIEW software records the data from two load cells to a dedicated computer file. The voltage signals from the load cells are passed through series of conditioning devices before being recorded. This process is described in more detail in the following section of this chapter.

4.3. Force measurement

Two Omega LCM 203 load cells, shown in Figure 4.10, were mounted on the testing rig - one on each axis. These load cells were used to measure the magnitude of the force applied to each axis of the test specimen. The upper range of the load cells was deemed higher than the actual load required to break the specimen. Preliminary load calculations were performed and it was determined that the required load was to be lower than 20kN. The Omega LCM 203 Load Cell with the capacity of 20kN was chosen for the testing machine. The load cells were supplied with a stud on each end. This allowed for easy-of-mounting and their alignment. The load cells were positioned next to the grippers. Any elastic deformation of the testing system components mounted after the load cells would not affect the specimen and could be disregarded. The LabVIEW program as outlined in the previous section of this Chapter, recorded the output voltage signals from both load cells at frequency of 60 Hz. Detailed load cell specifications are presented in Appendix E.

Figure 4.10 Omega LCM 203 Load Cell (from Omega Engineering Inc.).

The voltage signals from the load cells are transmitted to the controlling computer through the series of hardware devices. The load cell - PC connection diagram is shown in Figure 4.11.

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Figure 4.11 The SCXI Signal Conditioning Front-End System for Plug-In DAQ Devices (from National Instruments).

All necessary precautions were taken to ensure that the data collected contained minimum noise. The signal wires were coated with conductor-shielded cable to minimise any noise interference that may interfere with the voltage signals. Before acquisition by the PC, all signals were routed through a Signal Condition eXtension Instrumentation (SCXI) unit. The SCXI system is an open system with multiple modules which allows easy connection of sensors. The SCXI systems are ideal for amplifying, filtering, and even isolating the very low-level voltages that load cells generate.

National Instruments modules used in this project are shown in Figure 4.12. The SCXI chassis was calibrated to provide valid input signals to the PC as outlined below. The raw signal was directed from the load cell to the SCXI unit. The signal was then processed before it reached the controlling computer to eliminate noise and amplify the signal. It allows for greater accuracy during the data analysis.

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Signals from Load Cells

Figure 4.12 SCXI System Configuration (from National Instruments).

The main processing carried out on the raw signal is: 1) Amplification 2) Filtering 3) Transducer excitation 4) Isolation

1) Amplification: Most signals generated by transducers are low level, typically of the order of millivolts or milliamps. By amplifying these low level signals, they are protected from noise and interference. The SCXI module can be set to amplify the signal by the gain of 1, 2, 5, 10, 50, 100, 200, 500, 1000 or 2000. To calculate the gain Equation 4.1 was used.

ퟏퟎ (푽) 푻풐풕풂풍 푮풂풊풏 = 풎푽 Eq. 4-1 푳풐풂풅 푪풆풍풍 푶풖풕풑풖풕 ( )× 푰풏풑풖풕 푽풐풍풕풂품풆 (푽) 푽

115 where, 10 (V) is the maximum voltage read by the P.C; Load Cell output - 2mV/V (from the specification sheet of load cell Appendix E); Input Voltage - 5 V (from DAQpad, NI). This calculation resulted in the required gain of 1000. Consequently a total gain of 1000 (100 X 10) was set on SCXI chassis.

2) Filtering: Low-level load cell signals are very susceptible to noise corruption. Therefore, it is very important that measurement instruments are well shielded and have very good low-noise performance. National Instruments measurement products are designed to prevent signal corruption from external noise. For example, the SCXI front-end signal conditioning system consists of fully shielded chassis and modules. Signals are passed along a low-noise analog bus and then to a plug-in data acquisition device via a shielded, twisted-pair cable for the best possible low-noise performance (National Instruments, 2001).

This noise can be produced by AC power lines that are in close proximity to the signal lines. Even though the lines are insulated, it is good practice to further reduce this noise by filtering. There are two types of signal filters on the chassis for low and high frequency signals. The filter used in this operation was a 4 Hz low pass filter, which is suitable for removing the 50/60 Hz power line noise prevalent in most laboratory settings. Two filters are available in the SCXI chassis, both of which were set to filter low or high frequency signals. The low frequency signals were filtered by setting both filters not to pass signals lower than 4 Hz.

3) Transducer excitation: Most sensors such as strain gauges and load cells require an external voltage or current to excite their circuitry so they can measure physical phenomena. The SCXI module can produce two different excitation voltages and currents as shown in Table 4.1.

Table 4-1 Excitation Voltage and current options.

Voltage Mode (V) Current Mode (mA) 3.33 0.15 10 0.45

From the specification in Appendix E, it is evident that the excitation needed was a voltage setting of 10V.

4) Isolation: Isolation is carried out to isolate the transducer from the PC. When a PC is used to measure voltage, large voltage spikes may be present in the signal. The isolation will eliminate damage to the equipment or personnel by these voltage spikes.

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Also, the load cell itself may be exposed to large common-mode voltages. The load cells were mounted in close proximity to the four electric motors. As the biaxial test control unit powered by 380V main electricity the common-mode signal to the measurement device could be several hundred volts. Measurement systems with isolation are built to block these larger common- mode voltage levels, as well as adding system protection to voltage spikes or improper signal connections.

Each of the above settings to achieve the appropriate amplification, filtering, excitation and isolation were completed by setting the position of jumpers in the module of the SCXI chassis. When the SCXI chassis was set up, both load cells were connected.

The load cells required calibration prior to use on the biaxial testing system. The calibration process is used to confirm manufacturer’s parameters for the loading cell. It is also to provide force/voltage ratio which will be used in the LabVIEW program to calculate forces based on voltage output from the load cell.

The Load cell calibration was achieved using a Tinius Olsen uniaxial tensile testing machine. It’s load cell is regularly calibrated/certificated. The data from this load cell was used as a base line for the force readings from the two load cells. Both load cells for the biaxial testing system were mounted in series with the Tinius Olsen load cell. A special jig was designed and machined to allow for simultaneous calibration of the two load cells. The jig consisted of a series of adaptors, which permitted appropriate assembly of three load cells as shown in Figure 4.13.

Figure 4.13 Load Cell calibration rig assembly. 117

A series of readings were recorded in an Excel spreadsheet. The recorded data is presented in the Tables 4-2 and 4-3 as well as Figures 4.14 and 4.15. Initial calibration results showed high percentage of error: Cell 1 - 4.06% average on loading and 4.44% while unloading; Cell 2 - 0.97% on loading and 0.65% - unloading the cell. Correction values were found experimentally for Cell 1 - 210 N and Cell 2 - 60 N. Correction values represent permanent reading error. Percentages of error were significantly reduced with the introduction of correction values: Cell 1 - 0.07%, Cell 2 - 0.05% (loading path). Both values are within the specification of Omega LCM - 203 load cell shown in Appendix F. Load Cells calibration results (loading path) are shown in Table 4-2.

Table 4-2 Load Cells calibration results (loading path).

Load, Force Cell1, Error Cell1, Force Cell 2, Error Cell 2, Step N N % N % 1 0 0 0.00% 0 0.00% 2 990 1011 2.12% 965 -2.53% 3 2050 2085 1.71% 2040 -0.49% 4 3030 3061 1.02% 3041 0.36% 5 3990 4014 0.60% 3993 0.08% 6 5020 5039 0.38% 5018 -0.04% 7 6050 6064 0.23% 6068 0.30% 8 6990 7017 0.39% 6996 0.09% 9 8010 8042 0.40% 8021 0.14% 10 8980 8994 0.16% 8998 0.20% 11 9990 10000 0.10% 10000 0.10% 12 11000 11020 0.18% 11000 0.00% 13 12000 12000 0.00% 12000 0.00% 14 12980 12970 -0.08% 12980 0.00% 15 13990 14000 0.07% 14000 0.07% 16 14990 14980 -0.07% 15000 0.07% 17 16000 16000 0.00% 16000 0.00% 18 17020 17000 -0.12% 17010 -0.06% 19 17980 17950 -0.17% 17980 0.00% 20 18980 18960 -0.11% 18960 -0.11% Average Average Error Cell 1, 0.07% Error Cell 2, 0.05% % %

Calibration results for Load Cells 1 and 2 - unloading paths are presented in Table 4-3.

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Table 4-3 Load Cells calibration results (unloading path).

Load, Force Cell1, Error Cell1, Force Cell Error Cell Step N N % 2, N 2, % 1 0 0 0.00% 0 0.00% 2 18940 18910 -0.16% 18930 -0.05% 3 17930 17910 -0.11% 17910 -0.11% 4 14900 14880 -0.13% 14880 -0.13% 5 11950 11920 -0.25% 11930 -0.17% 6 9940 9922 -0.18% 9925 -0.15% 7 7950 7944 -0.08% 7923 -0.34% 8 5950 5942 -0.13% 5946 -0.07% 9 4000 3989 -0.28% 3993 -0.18% 10 1990 1987 -0.15% 1966 -1.21% 11 990 986 -0.40% 941 -4.95%

Average Average Error Cell 1, -0.15% Error Cell -0.24% % 2, %

The strong linear relationship was detected between the loads measured by both load cells and are presented in Figure 4.14.

Load vs Force Measured by Load Cells 1 & 2 20000 Cell 1: y = 0.9975x + 31.759 18000 16000 14000 12000 Cell 2: y = 0.9999x + 2.2821 10000 8000 CellLoad 1 Cell 1 6000 Force Measured,Force N 4000 CellLoad 2 Cell 2 2000 0 0 5000 10000 15000 20000 Load, N

Figure 4.14 Correlation between the Load and Force Measured by Load Cells 1 and 2 (loading path). 119

A graphical representation of the unloading path of the load cell calibration process is shown in Figure 4.15.

Load vs Force Measured by Load Cells 1 & 2 20000 18000 Cell 1: y = 0.9986x - 1.7739 16000

14000 12000 Cell 2: y = 1.0002x - 19.49 10000 CellLoad 1 Cell 1 8000

6000 Force measured, N measured, Force CellLoad 2 Cell 2 4000 2000 0 0 5000 10000 15000 20000 Load, N

Figure 4.15 Correlation between the Load and Force measured by Load Cells 1 and 2 (unloading path).

Hysteresis parameters were calculated using the Excel Spreadsheet. It was discovered that hysteresis parameters (calculated at 10 kN): Cell 1 - 0.17% and Cell 2 - 0.14% were higher than manufacturer's data for the load cell - 0.1%. However, it was concluded that both load cells provide sufficient accuracy for acquisition of data.

4.4. Displacement measurement

Currently many methods of strain measurement exist for mechanical test systems. Choosing an appropriate system was critical to success of the current project. The following methods were considered as suitable:  Strain gauges  Linear Variable Displacement Transducer (LVDT)  Video tracking (High speed Olympus camera)

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Strain gauges (Figure 4.16) are devices whose electrical resistance varies in proportion to the amount of strain, are most commonly used for measuring strain. It is very important that the strain gauge is properly mounted onto the test specimen so that the strain is accurately transferred from the test specimen, though the adhesive and strain gauge backing, to the foil itself. Careful surface preparation of the specimen is necessary if strain gauges are used for elongation measurement to ensure valid results. The application of strain gauges is a time consuming task, as specimens need to be properly prepared. Furthermore, as testing will involve both plastic deformation and the destruction of the specimen, a new strain gauge will be required for each test. Due to large deformation of the specimen (5-20mm) strain gauges were deemed unsuitable for the current project. Taking all of the above into account the decision was made not to use this method of displacement measurement for the current project.

Figure 4.16 Bonded Metallic Strain Gauge (from National Instruments).

The method using LVDT sensors was investigated to provide a measurement of specimen elongation. The LVDT could be attached to the specimen using brackets. The setup is shown in the Figure 4.17. The LVDT and its assembly could be set up and calibrated using the standard tensile test machine. Problems could arise though when using this setup during biaxial testing. The large elongations recorded during uniaxial testing would not be similar to those noted during biaxial testing. For small elongations the LVDT was found to have insufficient sensitivity. Also this method was only capable of measuring the elongation of the specimen in one direction. Consequently, for biaxial testing, it was concluded that the LVDT method was inadequate.

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Figure 4.17 LVDT assembly for biaxial testing application.

A non-contact method of elongation measurement was deemed necessary, because of this. A video extensometer was used by focusing the camera on the gauge area of the specimen. The setup is presented in Figure 4.18. The specifications of iSPEED 2 camera from Olympus are presented in Appendix F.

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i-SPEED2 Olympus Camera

Cruciform Specimen

Figure 4.18 Video Extensometer set up over biaxial specimen.

Specifically designed markers were placed on the specimen gauge area and the camera was used to record their movement. Real time image mode of the camera allows for precise positioning, focusing and image sharpening before the test (Figure 4.19).

Figure 4.19 Real time video used to set camera over the specimen.

By using the i-Speed (pixel tracking software), the movement of the markers could be converted to linear measurement and hence to elongation of the specimen. This system of video extensometer was developed by Olympus. It consisted of the actual camera and a flat screen 123 control panel to allow for setup prior to testing. It also allowed for the camera to be triggered by an external digital signal to start and finish the recording.

The data recorded by the camera was initially stored onto a memory card, which was then transferred onto the PC. It was necessary to ensure that both the load recorded by the load cells and the elongation recorded by the camera, started recording and continued to record the data at the same instant in time, i.e. that both load and displacements were synchronised.

As previously stated, a digital signal sent from the PC activated the camera to record. This ensured that both the camera and LabVIEW started to record data at the same instant. To ensure that both systems recorded at the same rate, the record time for each were set at 60 Hz. As both system started to record and continue recording at the same rate it can be concluded that the load and the elongation on the specimen at any instant in time correspond to each other.

Uniaxial specimens, manufactured from CR4 mild steel, were tested to prove the system as shown in Figure 4.20. The distance between the centres of two markers was measured prior to testing.

Figure 4.20 Strain measure using Olympus software.

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The distance between the markers, which were marked with red identification points (Figure 4.20), was entered into the Olympus software. It allowed the software to calculate number of pixels per mm as shown in Figure 4.21.

Figure 4.21 Olympus software interpretation of liner distance.

The displacement of two marked points was manually tracked. The position of each point was recorded on every 200th frame starting with the first and including the last frame. The displacement of each point is shown in Figure 4.22. The uniaxial tensile testing machine operates by changing the position of top gripper. This explains the lower displacement of the lower marker compared to the upper point.

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Figure 4.22 Tracking the displacement using Olympus analysis software.

The position of each point was also recorded by the software as shown in Figure 4.23. This data underwent further analysis. The Olympus software allows tracking of 4 points simultaneously, which makes further analysis of biaxial testing data possible. The output of the data is available in the form of text or Excel file. This feature is also shown in Figure 4.23.

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Figure 4.23 Displacement Recording using Olympus software.

Data Output Table is shown below (Table 4-4).

Table 4-4 Data Output from the displacement tracking.

Analysis Data Sheet

Test Data Date: 6/25/2013 Time: 5:25:54 PM File Name: E:\movie\9625550m.avi

Calibration Calibration: 5.1266 Pixels / Millimeter Tilt 0 Degrees Export Units: Millimeters

Tracking Data Frame Time Track Point 1 Track Point 2 x y distance speed x y distance speed 1 0.02 74.51 27.89 79.56 0.00 74.12 70.22 102.10 0.00 200 3.33 74.51 26.72 79.16 0.35 74.12 70.03 101.97 0.06 400 6.67 74.51 25.55 78.77 0.35 74.12 69.83 101.84 0.06 600 10.00 74.51 24.38 78.40 0.35 74.12 69.64 101.70 0.06 800 13.33 74.51 23.21 78.05 0.35 74.12 69.44 101.57 0.06 1000 16.67 74.51 22.04 77.71 0.35 74.12 69.25 101.44 0.06 1200 20.00 74.51 20.68 77.33 0.41 74.12 69.25 101.44 0.00 1400 23.33 74.51 19.51 77.02 0.35 74.12 69.05 101.30 0.06 1600 26.67 74.51 18.14 76.69 0.41 74.12 69.05 101.30 0.00 1800 30.00 74.51 16.78 76.38 0.41 74.12 69.05 101.30 0.00 1883 31.38 74.51 16.19 76.25 0.42 74.12 69.05 101.30 0.00 127

4.5 Summary

Chapter 4 describes the main control and data acquisition components used. The force and displacement measurement techniques used proved to be the most suitable and yet affordable to accomplish the goals of the project. Measurements obtained from the load cells (force) and the Olympus high speed camera (displacement) would require further analysis. The complete evaluation of the results is presented in Chapter 6.

It was outlined in this Chapter how accuracy and precision are important for obtaining reliable data. The following procedure was applied to ensure that this goal was achieved in this project:

 A control program was created to simultaneously start 4 motor gearboxes and run them at the same speed through the test (fine adjustment of motor speed function is available);  Olympus iSPEED camera was started together with LabVIEW program controlling the speed of the motor gearboxes;  Displacement/strain set of data and force/stress set of data were processed separately and subsequently combined to form stress/strain data sets.

It was required to validate the biaxial testing system. The details of the validation process are described in Chapter 5.

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Chapter 5

Test System Validation

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5 Test System Validation

5.1. Introduction

The biaxial testing system underwent a two−step validation process, as described in this chapter. Firstly, testing results from commercially designed and built uniaxial testing system were compared to the results obtained from the system designed for the current research project. Secondly, the results obtained from the biaxial testing system were compared to the results published in the literature. An attempt was made to use similar specimens to avoid bias using this validation technique. This technique provided sufficient evidence of the validity of the results obtained from the biaxial testing system.

5.2. Comparative analysis of uniaxial and biaxial testing for validation purposes

A comparative analysis of uniaxial testing results obtained from the commercially built machine and biaxial planar testing system designed for the current project was performed. Specimens used for this analysis were cut from 2mm-thick CR4 mild steel. The specimens were cut 45° to the rolling direction. International standards ASTM E8 (2011) and ISO 6892-1 (2009) outline the requirement for the specimen geometry. Sub-sized specimens (ASTM, 2011) must be 6.00 mm wide with +/-0.125 mm tolerance. All specimens were machined to these specifications. Specimen geometry was verified by micrometer measurements at three points along specimen width. This method proved that the biaxial testing system is as capable of successfully performing the biaxial testing as commercially available uniaxial testing machines designed by Tinius Olsen, a world leader in the manufacturing of testing systems for various applications. Tensile testing machine specifications can be found in Appendix C. The testing set-up is shown in Figure 5.1.

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Figure 5.1 Uniaxial Testing set up.

A standard uniaxial specimen design, as shown in Figure 5.2, was used for the comparative analysis.

GAUGE LENGTH

Figure 5.2 Standard design for uniaxial specimen.

All six specimens were measured at three different points along the reduced length section. The minimum value for each specimen is recorded in Table 5.1. The specimen is most likely to fracture at that point. The measurements of the specimens are shown in Table 5-1.

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Table 5-1 The measurements of the specimens.

Specimen Thickness Width Gauge Length Tested on No (mm) (mm) (mm) 1 2 5.93 50 Uniaxial Machine 2 2 5.89 50 Uniaxial Machine 3 2 5.92 50 Biaxial Machine - X Direction 4 2 5.91 50 Biaxial Machine - X Direction 5 2 5.92 50 Biaxial Machine - Y Direction 6 2 5.89 50 Biaxial Machine - Y Direction

Table 5-1 shows the variation in the width of the specimens. This variation could be caused by tool wear, variable cutting forces, and the jig or fixture used to manufacture the specimens. The variation of width (+/- 0.02 mm) will result in less than 0.5% inaccuracy during stress and strain calculations. Figure 5.3 shows the specimens undergoing testing on the uniaxial testing machine (a), the biaxial testing apparatus - X direction (b), and Y direction (c).

Figure 5.3 Uniaxial specimens tested on uniaxial machine (a), biaxial system in X (b), and Y (c) directions. 132

Two uniaxial specimens tests were performed on Tinius Olsen testing equipment and subjected to tensile load until the specimen fractured. The stress−strain plots for these tests are shown in Figure 5.4.

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250 ), MPa ), σ

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100 Specimen 1 Engineering Stress ( Stress Engineering 50 Specimen 2 0 0 10 20 30 40 Engineering Strain (ε), %

Figure 5.4 The results of uniaxial testing of two specimens.

Figure 5.5 shows the specimen after being tested using the biaixial testing system.

Figure 5.5 Uniaxial specimen after testing using the biaxial machine.

The following results were obtained from testing uniaxial specimens on the biaxial testing system. Both X and Y directions on the biaxial system were tested, and the results are presented in Figure 5.6.

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), MPa ), 250.0 σ

200.0 Specimen 1 150.0 Specimen 2 100.0 Specimen 3 Engineering Stress ( Stress Engineering 50.0 Specimen 4 0.0 0.0 10.0 20.0 30.0 40.0

Engineering Strain (ε), %

Figure 5.6 The results of testing uniaxial specimens on the biaxial machine.

The summary of the results of tensile testing are presented in Table 5-2.

Table 5-2 The results testing uniaxial specimens on the biaxial apparatus.

Specimen CSA Max Force Tensile Strength Elongation No (mm2) (N) (MPa) (%) 1 11.86 3765 317.5 34.3 2 11.78 3708 314.8 32.3 3 11.84 3718 314.0 32.1 4 11.82 3714 314.2 31.1 5 11.84 3745 316.3 31.3 6 11.78 3695 313.7 34.0

Based on the results of the tests, it is evident that there is a strong correlation between the results obtained from the uniaxial and biaxial testing machines. The results obtained from the biaxial planar testing system were compared to the results from the commercially built uniaxial tensile testing machine. In both cases, the same specimens types were used. The average tensile strength of the specimen tested on the uniaxial machine was 316.1 MPa, whereas the average tensile strength for the specimens tested on the biaxial machine were 314.1 MPa (X

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Direction) and 315.0 MPa (Y Direction) i.e. a 1% variance. True stress and true strain values for each test could also be obtained using the Equations 2.9 and 2.20. The results of these calculations are shown in Figure 5.7.

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300 Specimen 1 - Biaxial 250 Specimen 2 - Biaxial 200 Specimen 3 - Biaxial

True Stress, MPa Stress, True 150 Specimen 4 - Biaxial 100 Specimen 1 - Uniaxial 50 Specimen 2 - Uniaxial 0 0 5 10 15 20 25 30 35 True Strain, %

Figure 5.7 True stress-strain graph for the specimens tested on uniaxial and biaxial machines.

From the stress-strain graph shown in Figure 5.7, it can be concluded that the biaxial testing system can provide accurate and valid results.

5.3. Comparative analysis of biaxial testing results for validation purposes

This part of the chapter aims to compare previously published results to the results of the current research and confirm that the results obtained in this project are valid. Further validation processes will include the results analysis for mild steel CR4 and aluminium.

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5.3.1 Comparison of CR4 mild steel results

Comparative analysis of experimental data was made to provide evidence supporting the validity of the results obtained in this project. A previous research project at the University of Limerick (Hannon & Tiernan, 2007) utilised mild steel CR4 as a base material. Numerous experiments were carried out using various specimen geometry and optimisation of specimen geometry was performed. A mathematical model of the tested material was also validated using the Finite Element Analysis (FEA) package, DEFORM. The specimens used and the results of this study are shown in Figures 5.8 and 5.9, respectively.

Figure 5.8 Biaxial specimen after testing CR4 from (Hannon & Tiernan, 2007).

Figure 5.9 True stress−strain graph − biaxial testing of CR4 from (Hannon & Tiernan, 2007). 136

The specimen type and the results obtained during this study are shown in Figures 5.10 and 5.11, respectively.

Figure 5.10 Biaxial specimen used in this study (CR4).

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True Stress, MPa Stress, True 150.0 Uniaxial 100.0 Biaxial X Direction 50.0 Biaxial Y Direction 0.0 -2 0 2 4 6 8 10 12 14 16 18

True Strain, %

Figure 5.11 The results of biaxial testing of CR4 (current study). 137

Comparative analysis of two sets of data allows one to conclude that:

 both sets of data show similar tensile strength for the tested material (mild steel CR4) 420 − 450 MPa (previous study), 410 − 420 MPa (current project);  both sets of data provide evidence of greater tensile strength compared to the uniaxial testing of the same material;  both sets of data allow the conclusion of major reduction in elongation (from 20 to 30% during uniaxial testing to 7 to15%, while testing biaxially) and;  there is a significant difference between the strain values. The study conducted by Hannon (2007) showed 15% strain, whereas the current study is showing only 7% strain.

Figures 5.8 and 5.10 present the difference between the specimens used. Laser and waterjet technology were used to machine slits in four arms of the current specimens. A conventional milling process was used during the previous study. These relatively new technologies allowed slit reduction from 3 mm in width to 0.3 mm. Total slits' width was reduced from 12 mm to 1.5 mm. This change allowed an increase in testing area thickness from 0.5 mm to 1.2 mm. These major changes in specimen design have been deemed responsible for the discrepancy in strain values between the two studies.

5.3.2 Biaxial Testing of Aluminium 1050 H12

The aluminium specimen (manufacturing grade 1050 H12) shown in Figure 5.12 was tested for calibration purposes only.

Figure 5.12 Aluminium specimen before testing. 138

The results of the test are shown in Figure 5.13.

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60 Uniaxial 40 True Stress, MPa Stress, True Biaxial X Direction 20 Biaxial Y Direction 0 -2 0 2 4 6 8 10 12 14 -20 True Strain, %

Figure 5.13 The results of the biaxial testing of aluminium 1050 H12.

Biaxial testing of the aluminium 1050 H12 specimen showed tensile behaviour similar to that of mild steel, CR4 specimen. The tensile strength of the biaxial specimen in both X and Y directions is greater than the strength of the uniaxial specimen experiencing similar elongation (strain). The uniaxial specimen manufactured from aluminium 1050 H12 experienced greater elongation before fracture (12%) compared to the elongation of the biaxial specimen (both X and Y directions). Elongation of the biaxial specimen was 5% before fracture.

5.4. Validation of ABAQUS Models

Material behaviour during biaxial testing was analysed using ABAQUS, Finite Element Analysis (FEA) software. FEA is a computer simulation technique, which uses material data and predicts the material behaviour during biaxial testing. These predictions were not accounting for the anisotropy of the material. The results of this simulation are to be compared to the experimental data. This technique exhibits the following benefits over traditional design methods:

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 Significantly reduces materials' cost by avoiding excessive design  Allows flexibility and easy management of design changes and design comparison  Facilitates identification and analysis of critical design areas  Requires less prototyping The disadvantage of FEA modeling is that it requires highly trained operators to use the software correctly. Misuse or misinterpreting the software requirements during any of the programming steps can lead to incorrect results and consequently design failures. ABAQUS 6.9 was used to model a tensile test. This software has specific features that allow the comparison of modelled data to experimental results. Three main steps are to be completed during FEA analysis:  Pre-processing of data  Actual machine analysis of data (solving)  Data post-processing or analysis of processed data

The first step of data pre-processing is to create a geometrical model of the part (biaxial specimen) in ABAQUS. This software also allows geometry import into ABAQUS. This option was used, as the model, initially designed in SolidWorks, was successfully imported into ABAQUS later. The design of the specimen is shown in Appendix B. Figure 5.14 shows the model of the specimen.

Figure 5.14 The model of biaxial specimen (one quarter). 140

The next step was to define the properties of the material to be used by the software during the virtual deformation of the specimen. Two types of material were studied, and their modelling is described in the following sections. When a model is assembled in the software, the analysis time frame is assigned. The analysis time frame refers to the type of analysis (static), base units (10 seconds), and time incremental during data analysis (0.01 sec). Load mode allows the selection of the boundary conditions (constraints and maximum elongation/strain), loading conditions (forces: point of application, magnitudes and directions), and temperature conditions. The next step is to select the mesh. The software allows the user to select two different meshing elements − triangle and rectangle. Mesh concentration − the number of meshing elements per mm2 of the part − can also be changed. This feature allows higher mesh concentration and consequently higher precision of the analysis of critical parts of the model. Lower mesh concentration is used in less critical parts of the model, and it saves on computer memory, which is required to store the model and model processing time (solving). Meshing of the specimen is shown in Figure 5.15.

Figure 5.15 The meshing applied to the model of the specimen.

After mesh types are assigned to different parts of the model, a final step must be completed before the model can be processed (solved). This step is known as "assign job"; it allows the user to label the particular configuration of part−properties−load−mesh into one job. Once

141 completed, this job is stored under a specific name and can be retrieved later for post- processing of data. Post-processing of data helps the software user to interpret the results (visualisation mode). Figure 5.16 shows a typical view in visualisation mode.

Figure 5.16 The visualisation of the test results.

The visualisation mode presents specimen information by using colour contours. Each colour represents a different range of stress, elongation or strain in a particular point (node) or area. For the specimen shown in Figure 5.16, the highest stress is present in the gauge area, which is the desired outcome. It predicts the specimen fracture in the testing area during the actual biaxial tensile test. ABAQUS software also allows the user to export the stress−strain graph for specific points (nodes). True stress−strain diagrams for the studied materials SS304 and Nitinol are shown in the following sections.

5.4.1 Modelling Stainless Steel (SS304)

Simulating the elastic behaviour of the material in ABAQUS is a relatively simple task: standard data available for the material (Young's Modulus, Poisson's ratio and elongation) are inputted into the software. Modelling plastic behaviour, however, is a more complex process. It requires 142 that plastic deformation data be inputted into the program. The first step of this process requires uniaxial testing of stainless steel SS304. The true stress−stain diagram, which was obtained through this testing, is shown in Figure 5.17.

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400 True stress, MPa stress, True Specimen 1 - Rolling Direction 200 Specimen 2 - Perpendicular to Rolling Direction 0 0 10 20 30 40 50 60 True strain, %

Figure 5.17 True stress−strain graph − stainless steel SS304.

The following equations were used to calculate the value of true strain (휺푻) and true stress (흈푻):

푻 휺 = 풍풏(ퟏ + 휺) Eq. 5-1

푻 흈 = 흈 (ퟏ + 휺) Eq. 5-2

The data inputted into ABAQUS provide information on the behaviour of SS304. The results of this process are shown in Figure 5.18. The model represents the behaviour of the material under biaxial loading conditions; the loading ratio in X and Y directions is 1:1. The model does not account for anisotropy of the material. This type of material behaviour will require biaxial testing and will be discussed in Chapter 6.

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6 Load, KN Load, 4 Load ratio = 1:1 2

0 0 5 10 15 Strain, %

Figure 5.18 Modelled behaviour of stainless steel SS304.

The cruciform specimen will undergo both elastic and plastic deformation. Elastic deformation of stainless steel SS304 can be modelled by using von Mises yield criterion. Plastic deformation can be modelled using the constants as described in Equation 5-3.

풏 흈 = 푲휺 Eq. 5-3

where K is the strength coefficient (1400 MPa for SS304), ε is the strain, and n (0.44 for SS304) is the strain-hardening exponent.

This model containing strain-hardening constants for elastic-plastic deformation is widely used in the analysis of different materials' behaviour. The results for stainless steel SS304 are shown in Figure 5.19.

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400 True Stress, MPa Stress, True Specimen 1 200 Specimen 2

0 0 10 20 30 40 50 60 True Strain, %

Figure 5.19 Modelling the behaviour of stainless steel SS304 using the constants equation.

5.4.2 Modelling NITINOL

This section contains the details of simulation of the elastic-plastic behaviour of Nitinol using ABAQUS software. The following information on the material is required to complete the elastic behaviour modelling: Young's Modulus, Poisson's ratio and elongation. This information is inputted into the software. Modelling plastic behaviour is provided to be a more complex process. It requires that plastic deformation data be inputted into the program. The first step of this process requires uniaxial testing of Nitinol.

The uniaxial specimens were cut from 1.5 mm thick Nitinol sheets in directions both parallel and perpendicular to the rolling direction. These specimens were tested uniaxially, and the results of the tests are shown in Figure 5.20.

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True Stress, MPa Stress, True 300

200 Specimen 1 - Rolling Direction 100 Specimen 2 - Perpendicular to Rolling Direction 0 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 True Strain, %

Figure 5.20 True stress−strain graph − Nitinol.

ABAQUS prediction of the behaviour of Nitinol under biaxial loading conditions is shown in Figure 5.21.

6 Load, KN Load, 4

2 Load ratio = 1

0 0 1 2 3 Strain, %

Figure 5.21 Modelled behaviour of Nitinol.

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The stress – strain graph, which describes the behaviour of Nitinol, contains the steep upward curve immediately before the fracture of the specimen. It poses limitation to the description of the graph using exponential Equation 5-3.

5.5 Summary

This chapter explained the testing system validation. The validation process showed strong correlation between the results obtained from the commercially built uniaxial testing machine and the biaxial testing system designed for the current research project. The biaxial testing results obtained in previous research (Hannon & Tiernan, 2007), who designed the attachment to uniaxial testing machine, compared to the biaxial testing results performed on the designed stand-alone biaxial testing machine also showed correlation in stress values. Validation of ABAQUS models for both stainless steel and Nitinol were performed and the results of these processes will be used in Chapter 6 in order to compare the biaxial testing results with their models.

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Chapter 6

Results and Analysis

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6 Results and Analysis

6.1. Introduction

This chapter outlines the results obtained from biaxial testing of the biomedical alloys: stainless steel SS304 and Nitinol. The planar biaxial testing method was used. The results were compared to finite element analysis (FEA) predictions of the deformations of these materials, which were described in the previous chapter. Fractured specimens underwent microscopic observations using a scanning electronic microscope (SEM). Mechanical properties of tested materials can be found in Appendix D.

6.2. Finite Element Analysis (ABAQUS)

The major advantages of using FEA modelling and analysis tools for the design process were outlined in the previous chapter. This section, Chapter 6, is intended for a deeper understanding of the biaxial deformation of the material under investigation. Both stainless steel SS304 and Nitinol were modelled under different loading conditions. Loading ratios in X and Y directions changed from 1:1 to 0:1. Five different loading ratios were used: 0:1, 1:20, 1:5, 1:2.5, 1:1.25 and 1:1. This investigation aimed to confirm the optimum loading ratio for biaxial testing and to discover whether tested materials obey the von Mises criterion.

Figure 6.1 Meshing of biaxial specimen (one quarter) with rectangular elements.

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Figure 6.1 shows the meshing which was used for this study. Triangular meshing elements were changed to rectangular (square) elements. These types of elements represent the deformation in the gauge area and the stress distribution under different loading conditions with high accuracy.

6.2.1 Finite Element Analysis of Stainless Steel SS304 Cruciform Specimen

The stainless steel data input into ABAQUS (outlined in the previous chapter) was used to predict the biaxial behaviour of the material. Figure 6.2 shows the results of strain distribution using two loading ratios 1:0 (a) and 1:1 (b). An 8.5 kN load was applied in the X direction for (a), and both X and Y directions for (b). The analysis results for the other loading ratios (1:1.25, 1:2.5, 1:5 and 1:20) are presented in the Appendix G.

(a) (b)

Figure 6.2 Loading simulations - Stainless Steel SS304: (a) 1:0 ratio, (b) 1:1 ratio.

Figure 6.2 (b) shows the highest uniformity of strain distribution in the gauge area achieved at 1:1 loading ratio compared to any other loading ratio. It confirms 1:1 ratio as the optimum loading condition to attain stress/strain uniformity in the gauge area. This loading ratio will be used for the testing program discussed in the following sections of this chapter. Figure 6.3 presents, the strain distribution graphically in the testing area. The loading conditions remained the same (8.5 kN).

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12 6.8 10 6.6 8 6.4

6 % X Direction

y, y, 6.2 4 , % ε y

Y Direction ε 2 6 and x and

ε 0

x 5.8 -1 -0.5 -2 0 0.5 1 ε 5.6 X Direction -4 Y Direction -6 5.4 x/L and y/L -1 -0.5 0 0.5 1 x/L and y/L (a) (b)

Figure 6.3 Strain distribution under different loading conditions SS304: (a) 1:0 ratio, (b) 1:1 ratio.

Figure 6.3 (a) indicates a significant strain difference in X and Y directions by magnitude and type (loading ratio 1:0). While the specimen elongates in the X direction by 9.15 to 10.73% it contracts in the Y direction. The highest amount of shrinkage or contraction occurred in the centre of the testing area - 4.88%, while only being reduced by - 2.60% at the edge of testing area. This type of deformation is also evident in Figure 6.2 (a). Figure 6.3 (b) shows the deformation at a loading ratio 1:1. The strains in the X and Y directions are identical yet the strain along each axis is changing. The smallest strain is reported in the centre of the specimen 5.62%, while the highest value can be observed 78% away from the centre of the specimen 6.55% (X and Y directions + or -). The strain patterns predicted for the other loading ratios (1:1.25, 1:2.5, 1:5 and 1:20) are shown in the Appendix H.

Figure 6.4 shows the load-strain graphs for loading ratios 1:1.25 (a) and 1:20 (b).

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10 6 X Direction 5 8 Y Direction

6 3

Load, kN Load, 4 X Direction kN Load, 2 2 Y Direction 1

0 0 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, % Strain, %

(a) (b)

Figure 6.4 Load vs strain graph SS304: (a) - loading ratio 1:1.25; (b) - loading ratio 1:20.

Figure 6.4 (a), which represents the load-strain relation in the simulated material, shows lower strain in the Y direction. It corresponds to the lower load applied to this axis (loading ration 1.25:1). Figure 6.4 (b) shows that the strain would be negative under certain loading conditions (ratio 20:1). The load/strain graphs for the other loading ratios are shown in the Appendix I.

6.2.2 Finite Element Analysis of Nitinol Cruciform Specimen

Nitinol is a superelastic material, which also exhibits shape memory. One of the aims of the FE modeling is to determine whether Nitinol will behave in a similar way to stainless steel SS304 and many other biomedical materials under biaxial planar loading conditions. Similar to SS304, the uniaxial testing data for Nitinol was input into ABAQUS to provide the basis for virtual simulation of the biaxial testing conditions. Different loading ratios were simulated to investigate the possible responses of the material. The X axis was loaded with 9.1 kN. The load applied to the Y axis was calculated by a division of the X axis load (9.1 kN) by the loading ratios - 1, 1.25, 2.5, 5, 20 and infinity. The results which correspond to the 1:1 and 1:0 loading ratios are shown in Figure 6.5 (a) and (b).

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(a) (b)

Figure 6.5 Loading simulations - Nitinol: (a) 1:1 ratio, (b) 1:0 ratio.

Figure 6.5 shows the difference in strain distribution within the testing area. Figure 6.5 (b), which represents the data for the 1:0 loading ratio confirms non-uniform strain distribution under this loading condition. Figure 6.5 (a) shows two desirable features for biaxial tensile testing:

 Maximum stress/strain in the testing area;  Uniform strain distribution within the testing area.

Further confirmation of a much greater uniformity of strain distribution (load ratio 1:1) in the testing area can be obtained from Figure 6.6 (a) and (b).

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2.2 4 2.18 3 2.16 2.14 2 X Direction 2.12 1 Y Direction 2.1 0 2.08 Strain X and Y, % Y, X and Strain -1 -0.5 0 0.5 1 X Direction -1 2.06 Y Direction % Y, X and Strain 2.04 -2 -1 -0.5 0 0.5 1 -3 x/L and y/L x/L and y/L (a) (b)

Figure 6.6 Strain distribution under different loading conditions Nitinol: (a) 1:1 ratio, (b) 1:0 ratio.

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Figure 6.6 (a) shows the strain distribution in the testing area for the loading ratio 1:1. Strain varies between 2.06 % and 2.20 % (X and Y directions). Figure 6.6 (b) represents strain distribution when 1:0 loading is applied. Strain values vary between 2.61% and 4.04% in the X direction, and between - 1.80% and - 1.02%. Negative strain or contraction in the Y direction confirms that the behaviour of Nitinol is similar to stainless steel SS304 under the same loading conditions (ratio 1:0). The information for the other load ratios (1:1.25, 1:2.5, 1:5 and 1:20) is shown in the Appendix H.

Figure 6.7 shows a strain-load diagram under two loading conditions: 1:1.25 (a) and 1:20 (b).

10 6 X Direction 8 5 Y Direction 4

6 3 4

Load, kN Load, kN Load, 2 X Direction 2 Y Direction 1

0 0 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, % Strain, %

(a) (b) Figure 6.7 Load vs strain graph Nitinol: (a) - loading ratio 1:1.25; (b) - loading ratio 1:20.

A negative strain value can be observed under the 1:20 loading ratio. The load/strain graphs for the other loading ratios are shown in Appendix I.

6.3. Testing results and analysis of material properties

The previous Chapters (3-5) presented the design, manufacture, calibration and validation procedures. The output of these procedures is the testing system. The specimens from both SS304 and Nitinol type of materials were tested and the results were compared to those obtained from the FE modelling, which were discussed previously. The biaxial testing of the biomedical materials was carried out at 21 °C.

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6.3.1 The results of testing stainless steel SS304

The biaxial testing of the stainless steel specimens was performed under the strain condition on the testing machine. The deformation rate induced to the system was 0.086 mm/sec, Each specimen was tested to failure. Figure 6.8 shows a typical fractured specimen after testing.

Figure 6.8 Stainless Steel SS304 specimen after testing.

Figure 6.8 shows fracturing in the testing area in the diagonal direction of the gauge area. Images of the other fractured specimens are presented in Appendix K. Analysis of stress and strain data for this specimen was performed using the Dawicke and Pollock technique (Dawicke and Pollock, 1997). This technique requires the knowledge of stress - load relations. A stress - load diagram for stainless steel SS304 is shown in Figure 6.9.

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Load, kN Load, 4

2 X and Y Directions

0 0 200 400 600 800 Stress, MPa

Figure 6.9 Load vs Stress graph SS304.

The graph shown in Figure 6.9 allowed the calculations of stress corresponding to a particular load obtained from the test machine load cells. The results are shown in Figure 6.10.

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400 Uniaxial X Direction True Stress, MPa Stress, True

200 Uniaxial Y Direction

Exponential Model 0 -10 0 10 20 30 40 50 60

True Strain, %

Figure 6.10 True stress-true strain graph SS304 (biaxial, uniaxial and model).

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Based on the comparative analysis of graphical data in Figure 6.10, it is possible to conclude on the lower strain capacity of stainless steel SS304 under biaxial loading. True strain values are 22 - 23% for biaxial strain versus 50 - 52 % for uniaxial strain. Anisotropic behaviour of the material can also be observed for both uniaxial and biaxial testing methods. Stainless steel exhibits higher yield strength in both the X and Y directions, while tested biaxially.

The von Mises and Hill'48 criterions were used to analyse how the materials respond to different loading conditions. The results of this analysis are shown in Figure 6.11.

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200 , MPa , 2 150 σ von Mises

100 Hill '48

Data 50

0 0 50 100 150 200 250 300 350

σ1, MPa

Figure 6.11 Stresses in SS304 (X and Y directions) under different loading conditions compared to the von Mises and Hill'48 criterions.

Modelled predictions as well as test data correlate well with von Mises and Hill'48 criterions.

6.3.2 The results of testing Nitinol cruciform samples

One of the main difficulties of biaxial testing is the design and manufacture of cruciform specimens. The complex shape of the specimen, which includes many variable parameters, 157 makes the manufacturing process very expensive. The requirements for the specimens were identified in Chapter 2. They include maximisation of the testing area, minimisation of shear strain within the testing area, minimisation of stress concentrations outside the testing area and others (Smith, 2006). Some of constrains of the specimen design faced in this project were the high cost of sheet Nitinol and the testing system capabilities. The width of the plates limited the size of the specimen to 100mm x 100mm. The budget available for the testing system manufacturing allowed for a 20kN pulling capacity of the machine. A greater machine capacity would be needed if the specimen size were increased. Figure 6.12 shows the Nitinol specimen after testing.

Figure 6.12 Nitinol specimen after testing.

Visual observation of the specimen in Figure 6.12 allows for a preliminary conclusion of little (if any) plastic deformation during testing. Multiple fracture lines allow the assumption of different fracture mechanisms of Nitinol compared to stainless steel. These multiple fracture lines were observed in other Nitinol specimens tested. Images of the other fractured specimens are presented in Appendix K.

The Dawicke and Pollock technique (1997) was used to analyse the stress strain data for Nitinol specimens. The knowledge of stress - load relations was required in order to use this technique. Figure 6.13 shows a stress - load diagram for Nitinol.

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Load, kN Load, 4

2 LoadX and Ratio Y Di 1:1rections

0 0 200 400 600 800 Stress, MPa

Figure 6.13 Load vs stress graph: Nitinol.

Nitinol exhibited different fracture patterns, when compared to that of stainless steel. The fracturing of the Nitinol specimen is shown in Figure 6.14 (a-d). While stainless steel developed a single line (diagonal to the testing area) fracture, Nitinol showed multiline fracturing. The lines of the fracture are not diagonal to the testing area. The lines are either parallel or perpendicular to one another, as shown in Figure 6.14 (b). Another difference observed was in the presence of the necking area for stainless steel specimens and minimal to the non-existent necking area in the Nitinol samples. It gives an indication of brittle fracturing for Nitinol. Figure 6.14 (c) shows the presence of a number of Nitinol particles during the fracture.

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(a) (b)

Figure 6.14 Nitinol specimen before (a), during (b) & (c) and after (d) fracturing.

Figure 6.15 shows the results of biaxial testing of the Nitinol specimen. These results in the X and Y directions are compared to uniaxial testing results.

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1000 900 800

700 600 500 400 Biaxial X Direction 300 True Stress, MPa Stress, True Biaxial Y Direction 200 Uniaxial X Direction 100 Uniaxial Y Direction 0 -1 0 1 2 3 4 5 6 7

True Strain, %

Figure 6.15 True stress-strain graph Nitinol (biaxial and uniaxial).

Testing results shown in Figure 6.15 outline the similarities between the biaxial and uniaxial behaviour of Nitinol. Both the biaxial and uniaxial testing of Nitinol specimens showed an upward twist of the diagram before fracture. Similar to stainless steel in both the X and Y directions Nitinol showed smaller strain values (2 - 2.5%) compared to uniaxial testing (5.8 - 6%).

Figure 6.16 shows the response of Nitinol to different loading conditions.

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500

450

400

350

300

250 , MPa , 2 σ 200 von Mises 150 Hill '48 100 Data 50

0 0 100 200 300 400 500

σ1, MPa

Figure 6.16 Stresses in Nitinol (X and Y directions) under different loading conditions compared to von Mises and Hill'48 criterions.

Figure 6.16 shows the correlation between the theoretical values (von Mises and Hill'48 criterions) and experimental data obtained from biaxial testing of Nitinol.

6.4. Microscopic analysis of the specimen (SEM)

Scanning microscopy is a powerful tool available to researchers. It can provide qualitative and quantitative data to the researcher. In this project, qualitative information was sought for, in order to determine the fracturing mechanism for stainless steel and Nitinol. Scanning microscopy can also be used to determine the behaviour of these biomedical materials under biaxial testing (ductile or brittle fracturing). Ductility of the material was investigated by the amount of necking in the fracture area.

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6.4.1 Microscopic analysis of stainless steel SS304

Stainless steel specimens, which underwent planar biaxial tensile testing, were used to obtain samples for scanning microscopy. They were removed from the gauge area of the specimens. Each sample contained the edge where the fracture occurred. This type of sample preparation allowed for visual observation of the fracture surface. Figure 6.17 shows the fracture of a stainless steel specimen under a scanning microscope.

Figure 6.17 SS304 sample (magnification X270).

A magnification of 270X allows observation of the reduction of the cross-section area of the location where fracturing occurred. This area reduction or necking confirms the high ductility of stainless steel observed during the biaxial testing experiment. All microscopic images taken are presented in Appendix M.

Figure 6.18 shows the edge of the stainless steel specimen under 350 times magnification.

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Figure 6.18 SS304 sample (magnification X350).

The number of voids and cavities that can be seen on the image in Figure 6.18 allow for the conclusion of internal imperfections of the material to be the main fracture mechanism. Figure 6.19 shows the observation of these voids and cavities under higher magnification (900 times).

Figure 6.19 SS304 sample (magnification X900).

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6.4.2 Microscopic analysis of Nitinol

Nitinol samples for scanning microscopy were obtained by cutting them out of fractured specimens. These samples were set perpendicular to the table of the scanning microscope in order to observe the fracture. Figure 6.20 shows the fracture of Nitinol specimen under 100 times magnification.

Figure 6.20 Nitinol sample (magnification X100).

The image shown in Figure 6.20 permits the conclusion of a very brittle fracturing of Nitinol under biaxial testing. The edge of the material doesn't demonstrate any sign of necking (plastic deformation or cross-section area reduction). This type of material behaviour corresponds to the data obtained during biaxial testing of the material. Nitinol showed a maximum of 2% of strain in both the X and Y directions. The image of Nitinol fracturing under higher magnification of 400 times is shown in Figure 6.21.

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Figure 6.21 Nitinol sample (magnification X400).

The image in Figure 6.21 demonstrates voids and cavities on the fracture edge of Nitinol. These material imperfections are deemed to be the main cause of Nitinol fracturing under biaxial loading. Figure 6.22 shows the top (surface) view of the Nitinol sample.

Figure 6.22 Nitinol sample - top surface (magnification X550). 166

There are a number of cracks on the surface of the Nitinol specimens, which can be observed on the image shown in Figure 6.22. Most of the cracks are rather parallel or perpendicular to one another. This allows for the conclusion of two major directions of crack propagation. The hypothesis of these directions to correspond to the X and Y loading axis's needs to be further investigated and is not a part of this project. Nevertheless, there is evidence supporting this hypothesis. The image in Figure 6.14 (b) shows multiple fracture lines similar to micro fractures on the surface. All microscopic images taken are presented in Appendix M.

6.5. Summary

This chapter contains the results of a programme of biaxial testing on SS304 and Nitinol. The biaxial behaviour of biomedical materials (stainless steel and Nitinol) was initially modelled using ABAQUS FEA software. The specimens manufactured from both materials were tested using a biaxial system designed and built for this type of experimentation. The results of these tests are presented in this chapter. The conclusions drawn from the results together with recommendations for further research are presented in Chapter 8. Some of the conclusions are based on a microscopic analysis of the stainless steel and Nitinol samples. The results of the microscopic analysis are also contained in this chapter.

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Chapter 7

Discussion

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7 Discussion

7.1. Introduction

This chapter aims to summarise the experience gained from pursuing this research project. Four major areas were reviewed at the initial phase of this project: biomedical materials, sheet metal formability, biaxial testing, and the design of the cruciform specimen. The knowledge gained in these areas was critically important in completing the research project. The design, manufacture, and assembly were the most time and energy consuming tasks, but the reward for them was paid by observation of the testing system successfully performing its function. The testing and analysis phase was the culmination, which delivered the results of this project.

7.2. Biaxial Testing System

The review of formability of sheet metals outlined that the uniaxial tensile testing is the most commonly used method of determining mechanical properties of materials. The properties, which can be determined using this method, include ultimate tensile strength (UST), yield strength, and Young's Modulus. This testing technique also provides information on the ductility of the material. When applied to sheet materials, uniaxial tensile testing proved to be less descriptive comparing to the biaxial testing. Numerous attempts has been made to eliminate the shortcomings of the uniaxial test and close the gap in the knowledge of the material properties. The biaxial tensile test is one of the more recently developed methods. This testing method is considered to produce more relevant data to characterise the behaviour of sheet metal. The biaxial test also shows closer relationship between the testing and manufacturing process when the material is formed in more than one direction.

Various biaxial testing systems were reviewed to determine the most cost effective and efficient method of generating biaxial test. Currently used methods include uniaxial machine attachments, in-house build stand-alone machines and commercially built biaxial testing units. The conclusion was drawn that building the testing system in-house provided the most cost- effective and flexible solution. In-house built machines proved to be more cost effective than commercial units, while offering sufficient accuracy and repeatability. A number of biaxial testing systems were built by previous researchers and this accumulated knowledge was used to design and build the testing system for the current project. Stand-alone units tend to be more expensive than attachments but present with greater flexibility in applying various loading conditions to the cruciform specimen (load ratios in the X and Y directions).

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The apparatus built for this research project allows variable loads to be applied in the X and Y directions. It can also measure forces in both loading directions. The elongation of the specimen is measured by a high speed camera (iSPEED by Olympus). The testing system underwent the calibration and validation process. The biaxial system (both X and Y axes) results were compared to the results obtained from a commercially built tensile testing machine manufactured by Tinius Olsen. The comparative analysis can be found in Chapter 5. The strong correlation between the results allows to validate the testing rig. The biaxial testing system was later used to determine the properties of biomedical materials (Stainless Steel SS304 and Nitinol). The results of the tests were also compared to the modelled behaviour of these materials simulated by FEA software, ABAQUS.

7.3. Optimisation of Cruciform Specimen

The literature review outlines the difficulty related to the design of the cruciform specimen for biaxial testing. Currently, no international standard exists for the specimen design. This causes difficulty with comparative analysis of the results. Design differences make the results of previous research less comparable. Smits (2006) summarised some of the requirements for good specimen design: stress concentration in the test area, uniform stress distribution, etc. (Smith, 2006).

In considering these complications, many design ideas by different researchers were examined. A number of features of the design, such as proportions between the test area, legs of each side and the holding area, the recess of the test area, the size and number of slits in each of four legs, the radii at legs intersection, and the recess radii were investigated. FEA features of SolidWorks software and ABAQUS served as a powerful tool and reduced time to reach a near- optimum specimen design, as well as lowering the cost of the specimen design optimisation process. The stress concentration in the gauge area and exposure of the test area to both elastic and plastic deformations were considered the most important factors at the initial phase of design optimisation.

A design, proposed by Hanabusa in 2013, was considered the most successful and modern attempt in cruciform specimen optimisation, as proven by the experiments. The features of the design presented by Hanabusa were modelled using SolidWorks software and the results correlated well with the main biaxial test requirement, as stated above. Hanabusa also proved that specific test requirements (nearly isotropic tested material, synchronous movement in X and Y directions, and 1:1 motion ratio) would not require the reduction in the gauge area of the

170 specimen. Yet these parameters need much higher control of forces/elongation, which could only be achieved when a hydraulic system is used to operate the tester (actuators, valves etc). This type of system presents much higher cost and would exceed the budget of the present project. Furthermore, the current research aims to study anisotropic behaviour of biomedical materials and therefore requires the reduction of thickness in the gauge area. Other researchers, including Merklein (Merklein, 2013), also used the recess in the gauge area. This approach was taken in the current research.

Some of the ideas modelled in this project were not investigated further due to time/cost constraints. For example, the system of holders shown in Figure 3.16, which was proposed as an attempt to reduce the specimen size, was not manufactured. An alternative specimen design, which is described in Chapter 3 and shown in Figure 3.13, was manufactured only from aluminium and mild steel CR4. Figure 7.1 shows the aluminium (a) and mild steel CR4 (b) specimens before testing.

(a) (b)

Figure 7.1 The aluminium (a) and mild steel CR4 (b) specimens before testing.

The testing process resulted in fracture of these specimens within the gauge area. Yet, the close proximity of the middle slits did not allow for fracture along the cross-shaped recessed area. Further optimisation is required to determine the optimum number of slits and their positions. This alternative gauge area design was not investigated further due time and economic reasons. Some alternative manufacturing processes were considered to reduce the size of the slits. The waterjet technology, when compared to laser cutting, proved itself to be less damaging to the 171 specimen. The legs of the specimen are not heat treated during the waterjet cutting. But the minimal diameter of a water jet is 0.8mm. It increases the size of slits from 0.3mm to the jet diameter. Micro water jetting technology was developed in the recent years. It permits the manufacturing of 0.15mm slits. This technology is still very expensive and was therefore not used. Laser cutting of the specimens was performed by many researchers (Merklein, 2013) and was also used in this project.

7.4. Establishing the Biaxial Tensile Properties of Biomedical Materials

The primary goal of the research was to establish the biaxial tensile properties of metallic biomedical materials. Designers of tools and devices for biomedical application require reliable data, which describes the material properties. These devices, when manufactured and used, are frequently subject to variable multiaxial loading conditions. Biaxial testing will provide the required data for the designers.

Stainless steel is a widely used material in the biomedical industry. The biaxial testing of stainless steel SS304 showed a major reduction in elongation compared to the uniaxial test − from 70% (uniaxial) to 20% (biaxial). The results of the biaxial test of SS304 did not show greater values of the ultimate tensile strength compared to the uniaxial data (this type of behaviour was recorded during mild steel CR4 test). Nevertheless, the yield stress values available from the uniaxial test of SS304 were exceeded during biaxial test.

Nitinol is a relatively modern biomedical material. The biomedical industry has seen a significant increase in usage of Nitinol in the recent years. This is mainly due to the properties of the material, such as shape memory and superelasticity. This project aimed to increase the knowledge in the area of the tensile properties of Nitinol and determine whether they change when tested biaxially, compared to uniaxial testing. The biaxial tensile behaviour of Nitinol was noticeably different to that of the uniaxial behaviour. Nitinol, which elongated up to 15% during the uniaxial test, exhibited brittle material characteristics, when tested biaxially. The elongation reduced to 2 − 2.5%. Yet, the upward direction of the stress−strain curve before the fracture was noticed during both the biaxial and uniaxial tests. No significant increase in either yield or ultimate tensile strength was observed during the biaxial test compared to the uniaxial test. The biaxial tensile strength of Nitinol should be further investigated. An attempt should be made to test a Nitinol cruciform specimen using a larger testing area with reduced thickness, and the same material thickness and bigger gauge area (more powerful testing system with greater pulling capacity will be required).

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7.5 Summary

Chapter 7 summarises the work completed to achieve the goals of this project. Research on biaxial testing systems and cruciform specimens was performed. The design and manufacturing of the biaxial testing system, and the cruciform specimens were based on the knowledge obtained from the literature review. The biaxial system was calibrated and validated before the actual testing process was carried out. The successful performance of the test system allowed for the extraction of data, which underwent further analysis. The conclusions are presented in Chapter 8. Additional investigation on Nitinol properties under biaxial planar loading conditions is recommended to provide a deeper understanding of the materials behaviour.

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Chapter 8

Conclusions and Recommendations

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8 Conclusions and Recommendations

8.1 Introduction

This chapter presents recommendations for future researchers in the area of biaxial testing of biomedical and other metallic materials. The conclusions, drawn from the result of the analysis of testing data, are also outlined.

8.2 Conclusions

The five sections of conclusions are presented below. Each section covers a particular area of the current research project. The first section summarises the accomplishments of the research. The second section is specifically dedicated to the new knowledge generated. The other sections are outlining the conclusions related to the following areas: biaxial testing, cruciform specimen design and testing of biomedical materials.

The accomplishments of the research

 A stand-alone biaxial planar testing system was designed, manufactured and successfully evaluated;  The testing system was effectively used to characterise biomedical materials: stainless steel SS304 and Nitinol;  A cruciform design was optimised to suit the needs of the research and was used for the characterisation of the above stated materials;  Modelling of the biomedical materials in ABAQUS FEA software was completed and utilised for comparative analysis with the biaxial testing data;  Microscopic analysis of SS304 and Nitinol was performed.

New knowledge generated

 The biaxial testing of Nitinol showed a reduction in linear elongation (2 − 2,2%) of the material compared to uniaxial test (6%);  The ultimate tensile strength of Nitinol, obtained during the uniaxial test, was achieved during the biaxial test. The yield stress value calculated from the biaxial testing results was lower than the value observed during the uniaxial test;

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 During biaxial testing, the fracture pattern of the Nitinol specimen corresponded to that of a brittle material. No reduction of the specimen thickness was observed during the microscopic analysis of the fracture. Voids and cavities were detected on the fracture surface of the material. These imperfections deemed to be the main mechanism of material fracturing;  Tested Nitinol specimens exhibited multi-line fracturing in the gauge area, while stainless steel fracturing was single-line, diagonal to the gauge area. This type of Nitinol fracturing also confirms the material's brittle behaviour during the biaxial testing;  Multi-line micro cracks were also observed on the surface of the specimen under the microscope. These lines were rather parallel or perpendicular to one another. Further investigations would be needed to fully understand the formation of these micro cracks.

Biaxial testing

 The most common method used to determine the mechanical properties of the materials is the uniaxial tensile test. Nevertheless, this test fails to provide appropriate data for materials, which undergo multi-axial loading conditions (sheet metals, anisotropic materials, etc.);  The biaxial tensile test provides a much closer approximation of the behaviour of metals in sheet form during various manufacturing processes. The results of the biaxial test could be used to predict the behaviour of sheet metals undergoing forming processes such as pressing, deep drawing and bending;  Stand-along biaxial testing machines have proved themselves to provide researchers with greater flexibility in applying various loading ratios compared to the attachments for uniaxial tensile testing machines;  In-house design, manufacturing and the assembly of testing systems is more cost efficient than procurement of an off-the-shelf test system. This approach was adopted during the current research program;  A newly built machine must be calibrated before any test is carried out. A two-step validation process was used to ensure that the results of the biaxial testing carried out on the system were valid. Successful completion of this process allows one to make a conclusion on the validity of acquired data;  The design of the apparatus must allow for simultaneous data collection of load/stress and extension/elongation for further analysis. Each set of acquired data must be compiled into single file for analysis. Successful completion of this step ensured that valid data is analysed after each testing procedure.

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Cruciform specimen design

 No international standard currently exists for cruciform specimen design. Various attempts have been made to develop such a standard. The difference in the types of specimens used makes comparative analysis of the results a difficult task to accomplish;  Current cruciform specimen design must incorporate the combination of features described by various authors. Testing of the specimens showed that this goal was achieved successfully.

Testing of the biomedical materials (SS304 & Nitinol)

 The biaxial testing of stainless steel SS304 showed that linear elongation of the material is approximately 2.5 times less when compared to the uniaxial test (20 − 25% during the biaxial test, 55% − uniaxial);  The value of the ultimate tensile strength for uniaxial test − stainless steel SS304 (1000 MPa) − was not achieved during the biaxial test (900 MPa). Nevertheless, yield stress during the biaxial test of stainless steel SS304 (400 MPa) was determined to be greater compared to the value obtained from the uniaxial test (320 MPa);  Stainless steel retained its property of ductility throughout the biaxial test. The microscopic analysis of the fracture (SS304) showed the reduction of the specimen thickness at the edge of the fracture. Voids and cavities on the fracture surface allowed for the conclusion of the material's imperfections to be the main mechanism of fracturing under the loading.

8.3 Recommendations

The completion of the current research has opened opportunities to further improve the area of biaxial testing. Some recommendations are outlined below:

1. Upgrade of the testing machine to increase its capacity to 50kN. The testing system would apply this load with a high factor of safety (> 3). The first elements of the system to fail this loading condition are the thrust bearings. Larger bearings must be considered for successful operations of the testing system at 50kN loading. Changing the bearing type would lead to the following:

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 Changing of the housing unit to accommodate the new bearing size or machining of the existing housing units;  Potential additional machining of ball-screw end(s) to suit new bearings and new housing units.

The connection link between the ball-screw nuts and the grippers would require modification to increase the loading characteristics of the system as well as rigidity. Figure 8.1 shows a prototype for heavier connection links. It is also proposed to machine sinusoidal-wave groves on three (at least one) sides of each link as shown in Figure 8.1. These groves should carry grease and reduce the friction between the connection links and the support units.

Figure 8.1 Manufacture of the connection link grove.

2. An upgrade of the high speed camera or its software. New software is available from Olympus, which is compatible with the LabVIEW platform. This software allows users to control start/stop and data acquisition through the same program, which runs the testing machine.

3. A software upgrade to include automatic tracking mode. This will reduce the time taken by the manual tracking of the points on the specimen. 178

4. The currently used griping system will require upgrade for the 50kN loading. The proposal is made to use a dovetail connection as shown in Figure 8.2.

Figure 8.2 Proposed system of grips.

5. Development of the system of grips shown in Figure 3.16 is recommended. This system should reduce the size of the biaxial specimen, which is specifically desirable for expensive materials like Nitinol.

6. Further development of the cruciform specimen design as shown in Figure 7.1 is recommended. The optimisation process outcomes should present with optimum ratios between the cruciform-shaped gauge area and the distance to the slits.

7. Further investigation is required to gain deeper understanding of the fracturing mechanism of Nitinol under biaxial planar loading conditions. The author's recommendations include increasing the size of the gauge area and development of alternative methods of specimen manufacturing.

8. An upgrade of the testing system could include the incorporation of heating elements (furnace). It would allow an investigation of the behaviour of biomedical materials at elevated temperatures.

9. Mathematical modelling of the fracture patterns of the biomedical materials is also recommended.

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8.4 Summary

This chapter outlines the conclusions drawn as a result of the design, manufacturing and analysis processes. The recommendations of the author are also presented. The testing system modifications are proposed. Further optimisation of the cruciform specimen is suggested, as well as additional testing of Nitinol for a deeper understanding of the behaviour of this biomedical material.

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Appendices

186

Appendix A Drawings of the Biaxial Test System

187

188

189

190

191

192

193

194

195

196

197

198

199

200

Appendix B Drawings of the Cruciform Specimens

201

202

203

204

205

206

207

Appendix C Tensile Test Machine Specifications (Tinius Olsen)

208

Table C 1 Tensile Testing Machine Specifications (Part 1)

Table C 2 Tensile Testing Machine Specifications (Part 2)

Load measurement accuracy: +/- 0.5% of indicated load from 2% to 100% capacity; extended range down to 1% capacity with accuracy of 1% of indicated load

Position measurement accuracy: +/- 0.01% of reading or 0.001 mm, whichever is greater

Speed accuracy: +/- 0.005% of set speed

Operating temperature range: 32 to 100 degrees F (0 to 38 degrees C)

Storage temperature range: 14 to 115 degrees F (-10 to 45 degrees C)

Humidity range: 10% to 90% non-condensing, wet bulb method

Power: standard optional voltages 220/240VAC, 50-60 Hz, 2000W; power must be free of spikes and surges exceeding 10% of the nominal voltage

209

Appendix D Mechanical Properties of Tested Materials

210

Mild Steel CR4

Table D 1 Classifications

Table D 2 Compositions

Table D 3 Mechanical Properties

211

Aluminium 1050 H12

Table D 4 Classifications

Table D 5 Compositions

Note: Contains Fe – 0.4% (max); Si – 0.25% (max); Zn – 0.07% (max); Mn, Cu, Mg and Ti – 0.05% (max).

Table D 6 Mechanical Properties

212

Stainless Steel SS 304

Table D 7 Classifications

Table D 8 Compositions

213

Table D 9 Mechanical Properties

214

Nitinol

Table D 10 Classifications

Category Alloy

Class Shape Memory Alloy Common Nitinol, Nickel Titanium, NiTi Names Designation United States: ASTM F 2063

Table D 11 Compositions

Element Weight %

C 0.02 (max)

Co 0.26 – 0.28

Fe 0.03 – 0.05

Ni 49

Ti 51

Table D 12 Mechanical Properties

Properties

Density (x1000 kg/m3) 6.45

Poisson’s Ratio 0.33

Elastic Modulus (GPa/m2) 41 (M) – 75 (A)

2 895 (fully annealed) Tensile Strength (MPa/m ) 1900 (work hardened)

2 70 – 140 (M) Yield Strength (MPa/m ) 195 – 695 (A) 25 – 50 (fully annealed) Elongation (%) 5 – 10 (work hardened)

215

Appendix E LCM 203 Series Load Cell Specifications

216

Table E 1 Specifications

Specifications

Excitation: 10 Vdc, 15 Vdc max

Output: 2 mV/V ±0.25%

Linearity: ±0.15% FSO

Hysteresis: ±0.1% FSO

Repeatability: ±0.05% FSO

Zero Balance: ±2% FSO

Deflection: 0.025 to 0.075 mm (0.001 to 0.003")

Protection Class: IP65

Operating Temp Range: -46 to 107°C (-50 to 225°F)

Compensated Temp Range: 16 to 71°C (60 to 160°F)

Zero: 0.006% FSO/°C Thermal Effects: Span: 0.009% FSO/°C

Safe Overload: 150% of capacity

Ultimate Overload: 300% of capacity

Input Resistance: 360 Ω minimum

Output Resistance: 350 ±10 Ω

Construction: Stainless steel

Electrical: 3 m (10') 4-conductor PVC shielded cable

Mating Connector: PT06F10-6S

217

Figure E 1 Dimensions

218

Appendix F Olympus iSpeed Camera Specifications

219

Table F 1 Camera Dimensions and Features

Dimensions

Size W 106 mm x H 98 mm x L 264 mm

Weight 2 kg

Mechanical connections

Tripod mounting 1 x standard tripod mount (¼” Whitworth thread)

Lens mounting Standard C-mount

Nominal position 17 mm. C-mount can be screwed in 1 Back focus mm and out 3 mm

Accessory mounting 4 x ¼” Whitworth thread fixing holes on the base

Performance

Sensor CMOS

Resolution 800 x 600 active pixels

Operating modes Normal, Timelapse

Maximum: 33,000 fps Frame rate Minimum: 0.0667 fps (4 frames per minute) Maximum for full resolution: 1000 fps

Economy modes 3 each Tall, Wide, Square

220

Table F 2 Controller Dimensions and Features

Dimensions

Size W 273 mm x H 214 mm x D 51 mm

Weight 1.5 kg

A flip-out stand with ratchet positions of -3°, 42°, 87°, Stand 132°, 177°. When in the 177° position, the stand can be used as a hanger

Connector

Type Standard LVDS connector, 26 way MDR

Electrical

Input voltage 5V ±10%, 12V ±10%

Input power <2W, <8W at nominal voltages, derived from camera

Resolution 800 x 600

Brightness 350 cd/m2

221

Appendix G Modelling Specimen Deformation in ABAQUS

222

Figure G 1 Simulation of 8.5 kN load - Stainless Steel SS304 (1:0 load ratio).

Figure G 2 Simulation of 8.5 kN load - Stainless Steel SS304 (20:1 load ratio). 223

Figure G 3 Simulation of 8.5 kN load - Stainless Steel SS304 (5:1 load ratio).

Figure G 4 Simulation of 8.5 kN load - Stainless Steel SS304 (2.5:1 load ratio).

224

Figure G 5 Simulation of 8.5 kN load - Stainless Steel SS304 (1.25:1 load ratio).

Figure G 6 Simulation of 8.5 kN load - Stainless Steel SS304 (1:1 load ratio).

225

Figure G 7 Simulation of 9.1 kN load - Nitinol (1:0 load ratio).

Figure G 8 Simulation of 9.1 kN load - Nitinol (20:1 load ratio). 226

Figure G 9 Simulation of 9.1 kN load - Nitinol (5:1 load ratio).

Figure G 10 Simulation of 9.1 kN load - Nitinol (2.5:1 load ratio). 227

Figure G 11 Simulation of 9.1 kN load - Nitinol (1.25:1 load ratio).

Figure G 12 Simulation of 9.1 kN load - Nitinol (1:1 load ratio). 228

Appendix H Strain Distribution in Testing Area (Various Load Ratios)

229

6.8

6.6

6.4

, %

y 6.2 ε and

6 x ε

5.8 X Direction 5.6 Y Direction 5.4 -1 -0.5 0 0.5 1 x/L and y/L

Figure H 1 Strain distribution in the testing area Stainless Steel SS304 (1:1 load ratio).

5 y, % y, ε 4 x and and x

ε 3

2 X Direction 1 Y Direction 0 -1 -0.5 0 0.5 1 x/L and y/L

Figure H 2 Strain distribution in the testing area Stainless Steel SS304 (1:1.25 load ratio).

230

9 8 7 6

5 y, % y,

ε 4 X Direction 3 x and and x

ε Y Direction 2 1 0 -1 -0.5 0 0.5 1 -1 -2 x/L and y/L

Figure H 3 Strain distribution in the testing area Stainless Steel SS304 (1:2.5 load ratio).

4 y, % y, ε X Direction 2 x and and x

ε Y Direction

0 -1 -0.5 0 0.5 1 -2

-4 x/L and y/L

Figure H 4 Strain distribution in the testing area Stainless Steel SS304 (1:5 load ratio).

231

y, % y, 4 ε X Direction 2

x and and x Y Direction ε 0 -1 -0.5 0 0.5 1 -2

-4

-6 x/L and y/L

Figure H 5 Strain distribution in the testing area Stainless Steel SS304 (1:20 load ratio).

6 %

y, y, X Direction ε 4

and Y Direction

x 2 ε

0 -1 -0.5 0 0.5 1 -2

-4

-6 x/L and y/L

Figure H 6 Strain distribution in the testing area Stainless Steel SS304 (1:0 load ratio).

232

2.22

2.2

2.18

2.16

2.14

2.12

Strain X and Y, % Y, X and Strain 2.1

2.08 X Direction 2.06 Y Direction 2.04 -1 -0.5 0 0.5 1 x/L and y/L

Figure H 7 Strain distribution in the testing area Nitinol (1:1 load ratio).

2.5

1.5

Strain X and Y, % Y, X and Strain X Direction 0.5 Y Direction

0 -1 -0.5 0 0.5 1 x/L and y/L

Figure H 8 Strain distribution in the testing area Nitinol (1:1.25 load ratio).

233

2.5

1.5 X Direction 1 Y Direction

Strain X and Y, % Y, and X Strain 0.5

0 -1 -0.5 0 0.5 1 -0.5 x/L and y/L

Figure H 9 Strain distribution in the testing area Nitinol (1:2.5 load ratio).

3.5

2.5

1.5

1 X Direction 0.5 Y Direction Strain X and Y, % Y, X and Strain 0 -1 -0.5 0 0.5 1 -0.5

-1

-1.5 x/L and y/L

Figure H 10 Strain distribution in the testing area Nitinol (1:5 load ratio).

234

2 X Direction 1 Y Direction Strain X and Y, % Y, X and Strain 0 -1 -0.5 0 0.5 1 -1

-2 x/L and y/L

Figure H 11 Strain distribution in the testing area Nitinol (1:20 load ratio).

2 X Direction 1 Y Direction Strain X and Y, % Y, X and Strain 0 -1 -0.5 0 0.5 1 -1

-2

-3 x/L and y/L

Figure H 12 Strain distribution in the testing area Nitinol (1:0 load ratio).

235

Appendix I Load − Strain Diagrams (Various Load Ratios)

236

6 Load, kN Load,

2 X Direction

0 0 2 4 6 Strain, %

Figure I 1 Load vs Strain diagram SS304, loading ratio 1:0

5 X Direction 4 Y Direction

Load, KN Load, 2

0 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, %

Figure I 2 Load vs Strain diagram SS304, loading ratio 1:20

237

8 X Direction

Y Direction 6

Load, kN Load, 4

0 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, %

Figure I 3 Load vs Strain diagram SS304, loading ratio 1:5

8 X Direction Y Direction

Load, kN Load, 4

0 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, %

Figure I 4 Load vs Strain diagram SS304, loading ratio 1:2.5

238

Load, kN Load, 4

X Direction 2 Y Direction

0 0 0.5 1 1.5 Strain, %

Figure I 5 Load vs Strain diagram SS304, loading ratio 1:1.25

6 Load, kN Load,

2 X and Y Directions

0 0 1 2 3 Strain, %

Figure I 6 Load vs Strain diagram SS304, loading ratio 1:1

239

6 Load, kN Load, 4

2 X Direction

0 0 2 4 6 Strain, %

Figure I 7 Load vs Strain diagram Nitinol, loading ratio 1:1

5 X Direction

4 Y Direction

3 Load, kN Load, 2

0 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, %

Figure I 8 Load vs Strain diagram Nitinol, loading ratio 1:20

240

8 X Direction

Y Direction 6

Load, kN Load, 4

0 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, %

Figure I 9 Load vs Strain diagram Nitinol, loading ratio 1:5

X Direction

6 Y Direction

Load, kN Load, 4

0 -1.5 -1 -0.5 0 0.5 1 1.5 Strain, %

Figure I 10 Load vs Strain diagram Nitinol, loading ratio 1:2.5

241

Load, kN Load, 4

X Direction 2 Y Direction

0 0 0.5 1 1.5 Strain, %

Figure I 11 Load vs Strain diagram Nitinol, loading ratio 1:1.25

6 Load, KN Load, 4

2 X and Y Directions

0 0 1 2 3 Strain, %

Figure I 12 Load vs Strain diagram Nitinol, loading ratio 1:1

242

Appendix J Load − Stress Diagrams (Various Load Ratios)

243

6 Load, kN Load,

4 X Direction

0 0 200 400 600 800 Stress, MPa

Figure J 1 Load vs Stress diagram SS304, loading ratio 1:0

Load, kN Load, 4 X Direction

2 Y Direction

0 0 200 400 600 Stress, MPa

Figure J 2 Load vs Stress diagram SS304, loading ratio 1:1.25

244

Load, kN Load, 4

2 X Direction Y Direction

0 0 200 400 600 Stress, MPa

Figure J 3 Load vs Stress diagram SS304, loading ratio 1:2.5

Load, kN Load, 4

2 X Direction Y Direction

0 0 200 400 600 Stress, MPa

Figure J 4 Load vs Stress diagram SS304, loading ratio 1:5

245

Load, kN Load, 4 X Direction

2 Y Direction

0 0 200 400 600 Stress, MPa

Figure J 5 Load vs Stress diagram SS304, loading ratio 1:20

6 Load, kN Load, 4

2 X and Y Directions

0 0 200 400 600 800 Stress, MPa

Figure J 6 Load vs Stress diagram SS304, loading ratio 1:1

246

6 Load, kN Load, 4

2 X Direction

0 0 200 400 600 800 Stress, MPa

Figure J 7 Load vs Stress diagram Nitinol, loading ratio 1:0

Load, kN Load, 4 X Direction

2 Y Direction

0 0 200 400 600 Stress, MPa

Figure J 8 Load vs Stress diagram Nitinol, loading ratio 1:1.25

247

Load, kN Load, 4 X Direction

2 Y Direction

0 0 200 400 600

Stress, MPa

Figure J 9 Load vs Stress diagram Nitinol, loading ratio 1:2.5

Load, kN Load, 4

X Direction

2 Y Direction

0 0 200 400 600

Stress, MPa

Figure J 10 Load vs Stress diagram Nitinol, loading ratio 1:5

248

Load, kN Load, 4 X Direction

Y Direction 2

0 0 200 400 600 Stress, MPa

Figure J 11 Load vs Stress diagram Nitinol, loading ratio 1:20

6 Load, kN Load, 4

2 X and Y Directions

0 0 200 400 600 800 Stress, MPa

Figure J 12 Load vs Stress diagram Nitinol, loading ratio 1:1

249

Appendix K Fractured Test Specimens

250

Figure K 1 Stainless Steel SS304 Specimen 1

Figure K 2 Stainless Steel SS304 Specimen 2

251

Figure K 3 Stainless Steel SS304 Specimen 3

Figure K 4 Stainless Steel SS304 Specimen 4

252

Figure K 5 Stainless Steel SS304 Specimen 5

Figure K 6 Nitinol Specimen 1

253

Figure K 7 Nitinol Specimen 2

Figure K 8 Nitinol Specimen 3

254

Figure K 9 Nitinol Specimen 4

Figure K 10 Nitinol Specimen 5

255

Figure K 11 Nitinol Specimen 6

Figure K 12 Nitinol Specimen 7

256

Appendix L Biaxial Testing Data

257

450

400

350

300

250

200

150 True Stress, MPa Stress, True X Direction 100 Y Direction 50

0 0.0 2.0 4.0 6.0 8.0 True Strain, %

Figure L 1 Biaxial Testing of Mild Steel CR4.

140

120

100

True Stress, MPa Stress, True X Direction 40 Y Direction 20

0 -1 0 1 2 3 4 5 6 -20 True Strain, %

Figure L 2 Biaxial Testing of Aluminium 1050.

258

1000

900

800

700

600

500

400

True Stress, MPa Stress, True 300 X Direction 200 Y Direction 100

0 -1 4 9 14 19 24 True Strain, %

Figure L 3 Biaxial Testing of Stainless Steel SS304 (Specimen 1).

1200

1000

800

600 X Direction True Strress, MPa Strress, True 400 Y Direction 200

0 0 5 10 15 20 25

True Strain, %

Figure L 4 Biaxial Testing of Stainless Steel SS304 (Specimen 2).

259

1200

1000

800

600

X Direction

True Stress, MPa Stress, True 400 Y Direction

200

0 0 5 10 15 20 25 True Strain, %

Figure L 5 Biaxial Testing of Stainless Steel SS304 (Specimen 3).

900

800

700

600

500

True Stress, MPa Stress, True 400

300 X Direction 200 Y Direction 100

0 0 0.5 1 1.5 2 2.5 3 True Strain, %

Figure L 6 Biaxial Testing of Nitinol (Specimen 3).

260

1000 900 800

700 600 500 400 X Direction

True Stress, MPa Stress, True 300 Y Direction 200 100 0 0 0.5 1 1.5 2 2.5 3

True Strain, %

Figure L 7 Biaxial Testing of Nitinol (Specimen 5).

900

800

700

600

500

400

300 True Stress, MPa Stress, True X Direction 200 Y Direction 100

0 0 0.5 1 1.5 2 2.5 3 True Strain, %

Figure L 8 Biaxial Testing of Nitinol (Specimen 7).

261

Appendix M Scanning Electron Microscopy Images of Fracture Surfaces

262

Figure M 1 Stainless Steel SS304 sample (magnification X270).

Figure M 2 Stainless Steel SS304 sample (magnification X350).

263

Figure M 3 Stainless Steel SS304 sample (magnification X900).

Figure M 4 Stainless Steel SS304 sample (magnification X1500).

264

Figure M 5 Nitinol sample (magnification X100).

Figure M 6 Nitinol sample (magnification X350).

265

Figure M 7 Nitinol sample (magnification X500).

Figure M 8 Nitinol sample (magnification X700).

266

Figure M 9 Nitinol sample − top surface (magnification X450).

Figure M 10 Nitinol sample − top surface (magnification X550).

267