The effect of macrozones in Ti-6Al-4V on the strain localisation behaviour. Physical Sciences

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1 The effect of macrozones in Ti-6Al-4V on the strain localisation behaviour A thesis submitted to The University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences 2014 David Lunt School of Materials 1

2 Table of Contents List of Figures... 7 List of Tables Abbreviations DECLARATION COPYRIGHT STATEMENT Acknowledgement Chapter 1 Introduction Project Aims and Objectives Project Aim Project Objectives Chapter 2 Literature Review Titanium Applications of Titanium Alloys Alloying elements Classification of titanium alloys α alloys Near-α alloys α+β alloys Near-β and β alloys Microstructure Texture Development

3 Ti-6Al-4V Mechanical Properties Deformation Crystal structures and deformation mechanisms in α-titanium Slip in α-titanium Schmid Factor Statistical analysis of deformation behaviour in CP, α and α+β Titanium alloys Macrozones Definition Formation of Macrozones Characterisation of Macrozones Macrozone Formation at Various Thermo mechanical Processing Conditions Fatigue Behaviour Dwell Fatigue Stroh pile-up Fatigue Crack Propagation in a Macrozone Region Proposed Studies Chapter 3 Experimental Methods Material

4 3.2 Metallographic Preparation Optical Microscopy Micro hardness Test Scanning Electron Microscopy (SEM) Electron Back Scatter Diffraction (EBSD) Operating parameters Micro and macrotexture scanning conditions EBSD post processing Digital Image Correlation (DIC) Speckle patterns Experimental Analysis Speckle Patterns Gold Remodelling Experimental set-up Microscale DIC Systematic errors in microscale DIC HR-DIC Systematic errors in HR-DIC DIC Software Settings Microscale DIC software settings HR-DIC software settings Slip Trace Analysis

5 3.7.1 Slip Trace angle criteria Slip Trace CRSS and Schmid factor criteria An example of applying Schmid factor and CRSS criteria Multiple different slip traces within a single grain Chapter 4 Material Characterisation Optical Analysis Volume fraction and grain size analysis Qualitative macrozone analysis No-macrozone condition Intermediate-macrozone condition Strong-macrozone condition EBSD material characterisation No-macrozone condition Intermediate-macrozone condition Strong-macrozone condition EBSD orientation maps and normalised pole figures for all conditions Publication 1 Microscopic strain localisation in Ti-6Al-4V during uniaxial tensile loading Publication 2 Slip band characterisation of Ti-6Al-4V with varying degrees of macrozones Publication 3 Analysis of slip activity and nanoscale strain mapping in Ti-6Al- 4V with varying degrees of macrozones

6 Publication 4 Strain behaviour of Ti-6Al-4V with macrozones during fatigue and dwell fatigue loading Chapter 5 Summary and Conclusions Chapter 6 Future Work References

7 List of Figures Figure 1- a) Comparison of density with other metals b) Comparison of specific strengths for different metals and alloys [2] Figure 2- a) HCP phase b) BCC phase [7] Figure 3- Phase diagram for location of different types of alloys [15] Figure 4- Typical thermo mechanical processing route for producing bimodal titanium alloys [15] Figure 5- Crystallographic textures formed in Ti-6Al-4V at different deformation temperatures for unidirectional rolling and forging [1] Figure 6- Slip systems of HCP phase [7] Figure 7- Schematic of Schmid factor calculation method [20] Figure 8- CRSS for slip with basal and prismatic and <c a> type slip in single crystals of Ti-6.6Al in terms of temperature [7] Figure 9- Global Schmid factor analysis for active grains calculated through slip trace analysis in terms of (a) prismatic and (b) basal activated grains for Ti-6Al-4V [21] and basal, prismatic, pyramidal and and twin activated grains for (c) Ti- 5Al-2.5Sn [16], [25] and (d) CP-Titanium [16] Figure 10- Macrozone in a hot rolled Ti-6Al-4V alloy [45] Figure 11- Burgers Orientation Relationship [49] Figure 12- Comparison of a (a) heat tint correlated map to an (b) EBSD map Figure 13- Preferential orientation of HCP unit for Ti-6Al-4V UD rolled plate [13] 46 Figure 14- Orientation distribution of two directions in an IMI834 forging [43] Figure 15- The effect of increasing the peak hold time (dwell period) Figure 16- Fatigue Performance in an IMI834 alloy subjected to a 2 minute dwell period [55]

8 Figure 17- a) Stroh model for planar slip [63] b) Alternative model [11] Figure 18- Effect of Crack Coalescence in Ti-6Al-4V macrozone material [3] Figure 19- Schematic of DIC referencing technique Figure 20- Schematic diagram of the key components of an EBSD acquisition system [71] Figure 21- Schematic diagram of the DIC procedure showing that the original and deformed images are divided into pairs of sub-regions and the displacement of features within the sub-regions is then used to compute the local strain [75] Figure 22- Microscale DIC speckle patterns for (a) Strong-macrozone condition, (b) intermediate-macrozone condition and (c) No-macrozone condition Figure 23- Apparatus for gold remodelling procedure [83] Figure 24- An example of a gold speckle pattern on Ti-6Al-4V no-macrozone condition at (a) 10000X and (b) 20000X magnification Figure 25- Frequency analysis to determine error from imaging for microscale DIC Figure 26- Systematic error distributions associated with HR- DIC for (a) maximum shear strain and (b) strain in the loading direction in terms of (i) normalised frequency distributions, (ii) overlap of the sub regions and (iii) the linear pixel sub region size Figure 27- Values of maximum shear strain calculated for 5% macroscopic strain for the no-macrozone condition using different sub-region size and overlaps: (a) 24x24 pixels 2 with 0% overlap, (b) 8x8 pixels 2 with 0% overlap and (c) 4x4 pixels 2 with 25% overlap Figure 28- Angle mismatch criteria for (a) Strong-macrozone condition and (b) Nomacrozone condition

9 Figure 29- Slip trace analysis of a grain having faint slip traces as shown by the (a) maximum shear strain map and comparing the slip traces to (b) all possible slip traces for this grain Figure 30- Slip trace analysis of a grain having multiple slip systems as shown by the (a) maximum shear strain map and comparing the slip traces to (b) all possible slip traces for this grain and (c) the predicted slip traces Figure 31- (a) No-macrozone condition, (b) intermediate-macrozone condition and (c) Strong-macrozone condition Figure 32- Orientation coordinate system for (a) No-macrozone condition, (b) Intermediate-macrozone condition and (c) Strong-macrozone condition Figure 33-Etched micrographs of (a) No-macrozone condition (b) Intermediatemacrozone condition and (c) Strong-macrozone condition Figure 34- Polarised light micrographs of the no-macrozone condition in the ND-TD, ND-FD and TD-FD plane on a(a), (c) and (e) macroscale and (b), (d) and (f) microscale, respectively Figure 35- Polarised light micrographs of the intermediate-macrozone condition in the ND-TD, ND-RD and TD-RD plane on (a), (c) and (e) a macroscale and (b), (d) and (f) a microscale, respectively Figure 36- Polarised light micrographs of the strong-macrozone condition in the ND- ND II, ED-ND and ED-ND II plane on a(a), (c) and (e) macroscale and (b), (d) and (f) microscale, respectively Figure 37- (i) EBSD orientation maps and (ii) (0002) and pole figures of the no-macrozone material in terms of (a) macrotexture and (b) microtexture in the ND- FD plane

10 Figure 38- (i) EBSD orientation maps and (ii) (0002) and pole figures of the intermediate-macrozone condition material in terms of (a) macrotexture, (b) microtexture and (c) macrotexture across 4x1mm 2 in the ND-TD plane Figure 39-(a) Matrix stitch of the regions analysed in terms of microtexture for the intermediate-macrozone condition in the ND-TD plane. (b)- (e) EBSD microtexture orientation maps and (0002) and pole figures in the macrozone and nomacrozone regions Figure 40- (i) EBSD orientation maps and (ii) (0002) and pole figures of the strong-macrozone condition material in terms of (a) macrotexture, (b) microtexture and (c) microtexture in a macrozone region in the ED-ND plane Figure 41- (i) EBSD orientation map and (ii) (0002) and pole figures of the strong-macrozone condition material in terms of (a) microtexture in the ND-ND II plane Figure 42- EBSD orientation maps of (a) no-macrozone (b) intermediate-macrozone and (c) strong-macrozone materials in terms of (i) macrotexture maps with a 10µm step size, (ii) microtexture maps with a step size of 0.5µm and (iii) microtexture {0001} and pole figures Figure 43- Bright and dark field TEM of dislocations with a Burgers vector

11 List of Tables Table 1- Slip systems in hcp α-titanium [7] Table 2- Summary of fatigue and dwell fatigue tests of Ti-6246 alloys with different degrees of texture [58] Table 3- Microscope operating parameters for the ECCI technique Table 4- Microscope operating parameters for EBSD Table 5- Schmid factors and angles for each possible slip system with likely slip systems highlighted in red for grain shown in Figure Table 6- Schmid factors and angles for each possible slip system with likely slip systems highlighted in red for grain shown in Figure

12 Abbreviations BCC BSE CRSS DaVis DDS DIC EBSD ECCI ESU GND HCP HCF HR-DIC LCF SEM TEM VCHF XR Body Centred Cubic Backscattered Electron Critically Resolved Shear Stress La Vision Digital Image Correlation Software Microtester Software Digital Image Correlation Electron Backscatter Diffraction Electron Channel Contrast Imaging Effective Structural Unit Geometrically Necessary Dislocation Hexagonal Close Packed High Cycle Fatigue High Resolution Digital Image Correlation Low Cycle Fatigue Scanning Electron Microscopy Transmission Electron Microscopy Very High Cycle Fatigue Cross Rolled Strong-macrozone Intermediate-macrozone No-macrozone Material with soft oriented macrozone regions Material with hard oriented macrozone regions Material with no-macrozone regions 12

13 The effect of macrozones in Ti-6Al-4V on the strain localisation behaviour Abstract of thesis submitted by David Lunt to the School of Materials, The University of Manchester for the Degree of Doctor of Philosophy 2014 Ti-6Al-4V is the most widely used titanium alloy and is typically used in stages of gas turbine engines, due to its high strength-to-weight ratio, corrosion resistance and high strength at moderate temperatures. However, the alloy is susceptible to the development of strong textures during thermomechanical processing that leads to a preferred crystallographic orientation. These are referred to as macrozones and are thought to develop during the β to α phase transformation, as a result of the retention of large prior β grains during processing and variant selection. Macrozones are clusters of neighbouring grains with a common crystallographic orientation that may act as one single grain during loading and have been shown to cause scatter in the fatigue life. The focus of the current work was based on the analysing the strain behaviour of soft, hard and no macrozones within the microstructure, during various loading conditions. The local strain behaviour was studied at a micro and nanoscale, using the digital image correlation (DIC) technique, which utilises microstructural images recorded during mechanical loading. On a microscale, the no-macrozone and strongmacrozone condition loaded at 0 exhibited homogeneous strain behaviour. The strong-macrozone condition loaded at 45 and 90 to the extrusion direction, respectively, developed pronounced high strain bands correlating to regions that were favourably oriented for prismatic and basal slip, respectively. Characterisation of the slip bands provided a detailed understanding of the deformation behaviour at the nanoscale and the slip system was subsequently determined for each grain using slip trace analysis. Prismatic slip was the dominant slip system in all conditions, particularly in the soft-oriented macrozone regions of the strong-macrozone condition loaded at 45. Shear strains of 10 times the applied strain were observed. Further investigations on the strong-macrozone condition loaded at 45 to ED during standard and dwell fatigue demonstrated early failure in the dwell sample, with higher strain accumulation for dwell. 13

14 DECLARATION I declare that no portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning; 14

15 COPYRIGHT STATEMENT i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright ) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the Intellectual Property ) and any reproductions of copyright works in the thesis, for example graphs and tables ( Reproductions ), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see in any relevant Thesis restriction declarations deposited in the University Library, The University Library s regulations (see and in The University s policy on Presentation of Theses 15

16 Acknowledgement My greatest thanks go to my supervisor Professor Michael Preuss for his guidance and encouragement throughout the project. I would also like to thank my second supervisor Dr Joao Quinta da Fonseca for his support, valuable input and enthusiasm he has shown towards the subject area I would like to thank Dr Dave Rugg of Rolls-Royce for his continued support, information and supplying material for this investigation. I am also grateful to Dr Adrian Walker of Rolls-Royce for his advice on the subject of dwell fatigue during the latter stages of the project. I would like to thank Dr Claire Hinchliffe for her advice and guidance on the formal aspects of completing a PhD. I would like to thank to Dr Rebecca Sandala for introducing me to the basic understanding of DIC when I initially began the project and also her assistance in setting up the tensile testing facilities. Numerous members of staff at the University of Manchester have helped me to carry out experimental work. I would particularly like to thank Ken Gyves, Michael Faulkner and Dave Strong for their help in the experimental aspects of the project. Also, thanks go to Dr Jonathan Duff for his invaluable help in training me on how to use the optical microscope and fatigue testing rigs, which have been a core part of the project. I would like to thank all of the friends I have made during my time in Manchester and Sheffield particular those from the Advanced Metallic Systems CDT and from the Material Science Centre in offices E30, D10 and C7, whose friendship, humour and encouragement have made it such an enjoyable environment to work in. I would also like to thank all my family especially my parents, partner Rachel and daughter Ava-Rose who have supported throughout and I dedicate this work to them. 16

17 Chapter 1 Introduction The mechanical properties of titanium alloys can be tailored to make them suitable for use in a range of industries including for aerospace, biomedical and energy applications. This is due to the range of mechanical properties that can be achieved through changes in the thermo mechanical processing stages [1]. Changes that can be made to the thermo mechanical processing stages include different temperatures, cooling rates, strain rates and types of deformation, which result in a variety of different microstructures that affect the materials response to factors such as stress and strain concentrations, and crack initiation and propagation. Titanium alloys are important for aerospace applications as they have a high strength to weight ratio and are able to be operated at elevated temperatures. They are also suitable for use in the biomedical industry due to their biocompatibility and for use in energy applications it is due to their corrosion resistance over a range of temperatures. The alloy to be investigated in this dissertation is Ti-6Al-4V, which is an α+β alloy and is the most widely used titanium alloy, it is typically used in stages of gas turbine engines [2]. This alloy can exhibit variations in microstructure and texture due to the amount, temperature and nature of the deformation applied to the material during processing. This variation in texture can lead to localised regions that are highly textured, creating regions within the microstructure containing grains with a similar crystallographic orientation that may result in differences in the strain behaviour. The resultant strain heterogeneity could cause localised areas within the material that have high strain accumulation, leading to an increased probability of early crack initiation. The localised regions also create a high crack density increasing the likelihood of subsequent crack propagation and/or coalescence. This can induce 17

18 scatter in the fatigue life due to slight variations in the size of the localised regions [3]. These regions of grains with the same crystallographic orientation are known as macrozones and are typically produced during the forging process. The macrozones also result in reduced lifetime in rotating components used in aircraft when they are subjected to dwell fatigue [4] [6]. The effect that these macrozone regions have on the failure of the material in terms of strain heterogeneity at low and high spatial resolution will be investigated with regard to tensile and single cycle fatigue behaviour on a low and high resolution scale to identify the deformation mechanisms. A comparison of the strain behaviour of materials exhibiting favourably oriented macrozones, unfavourably oriented macrozones and a material with a weak texture exhibiting no-macrozones was of particular interest. A statistical approach was taken to study the relation between the location and orientation of macrozones and areas of heterogeneous strain and whether there is a greater degree of localised strain in the macrozone conditions as the greater the degree of heterogeneous behaviour the greater the likelihood of cracks initiating. The strain behaviour was studied for each material condition using the Digital Image Correlation (DIC) technique. This involved both optical microscopy based Digital Image Correlation and High Resolution Digital Image Correlation (HR-DIC) on SEM images to provide an understanding of the strain progression and areas of intense heterogeneous strain behaviour in comparison to the local strain. The technique for both DIC methods will involve the comparing of images before and after deformation. Comparison with Electron Back Scatter Diffraction (EBSD) analysis for both resolutions gave a more detailed prediction of the likely slip system that is most dominant in the macrozone regions. Through correlating with HR-DIC 18

19 slip trace analysis was performed utilising the information provided by the EBSD data to give a more accurate prediction of the slip system within each individual grain. Transmission Electron Microscopy (TEM) studies are then performed for single slip trace cases to validate the slip trace analysis results. Slip reversal was then studied within two of the microstructures through single cycle fatigue testing to investigate the impact of macrozones on this mechanism. It is then possible to use these results to predict the effect of macrozones on the fatigue behaviour. 1.1 Project Aims and Objectives Project Aim The summarised aim of the project is to investigate the effect macrozones in the microstructure have on the deformation mechanisms of the titanium alloy Ti-6Al-4V. The effect of macrozones during tensile and fatigue loading was investigated by conducting experiments on three different material conditions at the same loading conditions exhibiting different degrees of macrozones. They had approximately the same primary alpha volume fraction and grain size. The differences in microstructure are that the materials contain soft and hard macrozones and no-macrozones, respectively. The findings of this work will support future decisions on whether it is necessary to eliminate these features from the microstructure during the thermo mechanical processing or if the material is limited to use in certain loading conditions or up to specific stress conditions Project Objectives The main objectives of the study are highlighted below, detailing the initial research and more detailed experimental analysis. The literature review in Chapter 2 provides a detailed overview of the critical literature and establishes the current advances of 19

20 research in the project field and gives an understanding of where the project focus has been. Chapter 3 gives a detailed insight into the experimental techniques that have been utilised during the project and the limitations of these techniques. In Chapter 4 the characterisation of the as received materials is given in terms of microstructure and texture through a range of techniques with a particular focus on optical and electron microscope techniques. EBSD will be utilised to give a more detailed understanding of the starting textures to allow critical loading conditions for experiments to be defined. Chapter 5 is a paper providing a summary of the strain accumulation and heterogeneity in the different materials through the use of optical microscopy based DIC on a microscale during in-situ uniaxial tensile testing. The effect of macrozones loaded at 0, 45 and 90 to the extrusion direction for the strong-macrozone material is summarised. Chapter 6 is a paper looking at the effect of macrozones on the slip mechanisms and strain heterogeneity through the use of HR-DIC during ex-situ uniaxial tensile testing, critically assessing the soft macrozone condition in the extreme loading condition and comparing this to the hard and no-macrozone conditions. Chapter 7 is a paper that uses the slip trace analysis technique to determine the activity of the relative slip systems for the strongmacrozone and no-macrozone materials in detail and how this impacts the mechanical behaviour of the alloys. Chapter 8 is a paper investigating single cycle Tension-Compression behaviour through experiments on the critical loading directions compared to the reference alloy to understand the strain development when loading and unloading through the use of HR-DIC and the impact this may have on the fatigue properties of the materials. It also investigates the low-cycle fatigue (LCF) behaviour for the strong-macrozone condition loaded at 45 at high stresses, where the material appeared to exhibit reduced performance when a dwell 20

21 period was introduced into the loading cycle Chapter 9 summaries the findings from the different length scales and loading conditions studied in the papers and gives suggestions for future work. 21

22 Chapter 2 Literature Review The literature review gives an overview on titanium alloys, looking at different alloying elements and thermo mechanical processing routes to give the alloy various properties and textures. The chapter then focuses on the slip behaviour in α+β titanium alloys and the impact of loading direction and grain orientation on the deformation behaviour. There is an emphasis on studying the current known impact of macrozones on the slip, fatigue and dwell fatigue behaviour and details on why more research is required to understand the factors that are not yet fully understood. 2.1 Titanium Titanium is the fourth most abundant metal in the Earth s crust after Aluminium, Iron and Magnesium [7] and is therefore not in short supply but the difficulty with the metal is that it is never discovered in its pure state [2]. Titanium in its raw state is predominantly found as two main mineral sources, which are rutile (TiO 2 ) and ilmenite (FeTiO 3 ), and is extracted from these two ores mainly through the Kroll process. The Kroll process involves reacting titanium oxide with chlorine to make titanium chloride (TiCl 4 ) and then reducing with magnesium in an inert gas atmosphere to form pure titanium. The result of the process is a product known as titanium sponge due to the porous nature of the product that is produced [7]. Even though this process was invented in the 1940s and is expensive, it is still the dominant processing method for the production of titanium. The demand for titanium increased after the Second World War when there was increased use of the alloy in the aerospace industry particularly for use in the airframes and engines. This is due to the key properties of the alloy, which are its 22

23 high strength to weight ratio and the maintenance of specific strength at elevated temperatures up to 565 [8] Applications of Titanium Alloys Titanium alloys are used in a range of industries including for aerospace, biomedical and energy applications [2], [7]. The importance of the alloy in terms of the aerospace applications is most important for this research. Titanium alloys have been used in aero applications for over 50 years due to their high strength to weight ratio and suitability for use at moderate operating temperatures. They are used in rotating components such as compressor discs and blades [8] that are subjected to high stresses resulting in low cycle fatigue loading [9] [11]. In Figure 1 the relative advantages of titanium compared to the other abundant metals is clear, with the high specific strength in comparison to the relatively low density [12].Titanium alloys are used over other more cost effective materials such as steel, due to the significant weight saving that is required in the increasing demand to reduce the overall weight of the aircraft to improve efficiency. The advantages of titanium alloys over lighter aluminium alloys are that they have superior high fatigue strength, corrosion resistance and higher operating temperature capability meaning they are more suitable for aero engine applications [2]. However, there is an ever increasing demand from the designers for materials with increasing operating temperatures with no loss in performance from the material to continually improve the overall engine efficiency. The current alloy is unable to operate at these conditions but the significant cost increase of metal matrix composites means this is unlikely in the near future [9], [13]. 23

24 Figure 1- a) Comparison of density with other metals b) Comparison of specific strengths for different metals and alloys [2] The capabilities of the current titanium alloys used in the aero engines have almost reached the maximum in their current condition [9]. One aspect that is open to improvement is the scatter in the fatigue life of the components during dwell fatigue, for particular microstructures and loading directions. This needs to be reduced to increase/maximise the life of these materials. If the cold dwell debit issue is addressed, this will provide savings in terms of the cost of replacing and maintaining old components. This could be provided by gaining a more detailed understanding of the deformation behaviour of the alloys in terms of texture and damage accumulation with a focus on critical grain orientations and combinations. 2.2 Alloying elements Titanium is a metal that can have more than one crystal structure depending on the temperature and conditions at which the material is processed. It undergoes an allotropic phase transformation at a temperature of Above this temperature, which is referred to as the β transus, the crystal structure is Body-Centred Cubic (BCC) and below the β transus temperature the crystal structure is Hexagonal Close Packed (HCP) [14]. The BCC phase is often referred to as the β phase and the HCP is referred to as the α phase. By adding alloying additions to titanium the β transus temperature is altered. Alloying elements that stabilise α increase the β transus 24

25 temperature and alloying elements that stabilise β reduce the β transus temperature. An example of α and β stabilisers are Aluminium and Vanadium, respectively. Figure 2- a) HCP phase b) BCC phase [7] 2.3 Classification of titanium alloys There are three main categories of titanium alloy, which are α, α+β and β titanium alloys, and two other categories of titanium alloy, which are near α and near β. The α and near α alloys consist predominantly of the α phase at room temperature as this is the low temperature phase of titanium. α+β titanium alloys consist of mostly α with some β at room temperature, but adjustments to the processing and cooling conditions can lead to higher volume fractions of β than in the α and near α alloys. Theoretically if β alloys that have been quenched from above the β transus the microstructure can consist of 100% martensitic β at room temperature [8], [14]. Figure 3 indicates the different alloy classifications with the near α and near β alloys positioned on the boundaries of the α and β alloy, respectively [12], [15]. The different alloy classifications are described separately in more detail below. 25

26 Figure 3- Phase diagram for location of different types of alloys [15] α alloys α alloys only contain alpha stabilising elements such as aluminium or oxygen and these elements increase the beta transus temperature. This means that the alpha phase is more stable at increasing temperatures and as the alloys only have alpha additions no beta phase is retained at room temperature. An example of an alpha alloy is Ti- 5Al-2.5Sn [16]. These alloys have good creep and corrosion resistance but reduced strength as the alloy cannot be strengthened using traditional heat treatment [12] Near-α alloys Near-α alloys contain predominantly titanium with alpha stabilisers and small amounts of beta stabilisers. This results in some retained beta in the microstructure at room temperature. Examples of near alpha alloys are Ti-6242 [17] and IMI834 [18]. Near-α alloys are predominantly used in high temperature applications due to their 26

27 good creep resistance properties and high strength capability compared to the α alloys due to the small amounts of beta within the microstructure [12] α+β alloys α+β titanium alloys contain a combination of alpha and beta stabilising elements such as both aluminium and vanadium. This means that the volume fractions of the alpha and beta elements will directly impact on whether alpha or beta is more stable at a particular temperature. These alloys can be more easily tailored to produce the desired properties as a result of having both alpha and beta additions. The most common α+β titanium alloy is Ti-6Al-4V Near-β and β alloys β alloys only contain beta stabilising elements such as vanadium or molybdenum and these elements decrease the beta transus temperature, making the beta phase more stable at lower temperature. Fully β alloys contain 100% retained beta at room temperature whereas the near-β alloys do not have sufficient β stabilising elements to retain all of the beta on cooling. The retained β in these cases is metastable beta, but second phase precipitates can be formed with further heat treatments and provide the near-β alloys with higher strengths [12]. The main properties of beta alloys are that they can be hardened, are easily forgeable and are suitable for cold forming. However, they have lower creep resistance and reduced tensile ductility after aging compared to α+β titanium alloys [12]. 2.4 Microstructure Microstructure is controlled through thermo mechanical processing. This is the process of converting a cast ingot into the required shape of the end product through 27

28 first producing shapes such as forged bars in the primary processing stage and then processing to the desired product through final machining. The typical processing route for producing α+β titanium alloys involves four processing stages, which are homogenization, deformation, recrystallisation and aging at low temperatures. The steps that will be discussed here are viewed as the critical steps in producing the desired microstructure. A fully lamellar microstructure can be produced through β recrystallisation, i.e. heating above the β transus, but keeping the temperature within 50 of the β transus to control the grain size. On cooling from the recrystallisation temperature, the cooling rate is crucial in the control of the α colonies, i.e. the size of the α lamellae and size of the α colonies [7]. A slow cooling rate will produce α lamellae with a larger width in comparison to narrower α lamellae in a material that has been water quenched. A fully equiaxed microstructure is achieved through homogenisation of the alloy above the β transus, followed by a deformation stage to break up the α lamellae that are formed on cooling from the homogenisation temperature. The alloy is then recrystallised below the β transus, followed by cooling at a sufficiently low rate to ensure that only primary α are able to grow and no secondary α is able to form within the β grains. As a result of applying a sufficiently slow cooling rate, the α grains are larger in a fully equiaxed microstructure than a bimodal microstructure and the β phase is located at the triple points of α grains because no lamellae have been able to form [7]. 28

29 Figure 4- Typical thermo mechanical processing route for producing bimodal titanium alloys [15] Materials with a bimodal microstructure consist of equiaxed primary α grains and secondary α colonies that have formed on transformation from β. They appear as secondary α laths in a β grain [14]. A bimodal microstructure is produced by following a similar thermo mechanical processing route to that used to produce a fully equiaxed microstructure, except that at the recrystallisation stage a faster cooling rate, in the order of /min, is applied. If a slow cooling rate is applied then this will result in large primary α grains and a coarse secondary α colony within one β grain, i.e. a colony is defined as α lamellae being in one direction only. A high cooling rate produces smaller α p grains and fine α lamellae within the prior β grains. Figure 4 is an example of the thermo mechanical processing route that is required to produce an α+β titanium alloy with a bimodal microstructure Texture Development Crystallographic textures in titanium alloys can develop during the deformation stage of the processing route; the nature of the texture is dependent on the type, amount and the temperature of deformation [2]. Figure 5 indicates the four separate temperature regions for unidirectional rolling and forging indicating the typical 29

30 textures produced for each deformation method respectively. At low deformation temperatures below the transformation temperature a high volume fraction of the α phase is present during the deformation process. Therefore a basal texture is developed for the forging process and a basal/transverse texture is developed for unidirectional rolling. Similarly, at high deformation temperatures there is a large volume fraction of the β phase present during deformation. As a result of this a typical β texture is developed, which is a cubic texture. On cooling from the β phase region a transformation from β to α occurs at the β transus. On this transformation, it has been suggested that only one of the six β phase planes are selected by the α phase to satisfy the Burgers relationship [7]. This results in the development of a transverse texture in the case of unidirectional rolling. At an intermediate temperature range between the low temperature deformation and the β transus deformation temperature, a weak α texture is developed. This is due to the deformation temperature occurring above the α phase region, resulting in a decrease in the intensity of the α texture. Figure 5- Crystallographic textures formed in Ti-6Al-4V at different deformation temperatures for unidirectional rolling and forging [1] 30

31 Ti-6Al-4V Ti-6Al-4V is an α+β alloy, containing 6% aluminium as an alpha stabiliser and 4% vanadium as a beta stabiliser and consists of both alpha and beta at room temperature. Through changes in the thermo mechanical processing route, three different distinct types of microstructure can be produced due to the phase transformation that occurs, which are fully lamellar, fully equiaxed and bimodal Mechanical Properties A key microstructural feature for the α+β alloy that has a significant effect on the mechanical properties of bimodal titanium alloys is the α s colony size. The α s colony size is determined by the magnitude of the cooling rate from the β transus and the prior β grain size. For example, a high cooling rate will produce a small α colony size and therefore give a small effective slip length. The role of the slip length on one of the fatigue mechanisms is that with increasing slip length, the crack propagation rate also increases. Another important feature for alloys with a bimodal microstructure is that the element partitioning effect increases with increasing α p content, causing a reduction in strength in the α s colonies of a bimodal microstructure as opposed to fully lamellar. This reduction in strength in the α s colonies means that there is a tendency for fatigue cracks to initiate in the α s colonies rather than the α p grains of an alloy with a bimodal microstructure [1], [2], [14]. 2.5 Deformation A metal will begin to deform elastically when a certain load has been applied to the material. Elastic deformation is when a material can deform and after loading will return to its original shape. The point when a material is unable to return to its original shape after loading is defined as the yield point. After yield, the material will 31

32 continue to deform plastically and this involves the breaking of atomic bonds through the movement of dislocations. Dislocations tend to occur along the densest plane of atoms as this is the lowest energy state for the movement of dislocations [19], [20]. This movement of dislocations along a specific crystallographic plane is known as slip and the plane along which the slip occurs is the slip plane. Slip occurs as the result of a reaction to the applied local shear stress [19] Crystal structures and deformation mechanisms in α-titanium Alloys with a HCP crystal structure exhibit anisotropic behaviour due to the anisotropic nature of the crystal structure. This results in titanium alloys containing the α phase having a variation in elastic modulus that is dependent on the angle between the c-axis of the crystal and the stress axis. The relationship between the stress axis and the c-axis shows that when the c-axis is parallel to stress axis the elastic modulus is at its maximum. When the c-axis is perpendicular to the stress axis the elastic modulus is at its minimum [7] Slip in α-titanium There are two slip directions that can be activated in α grains in an α+β titanium alloy, they are the three directions and the slip direction. The more easily activated slip direction is the direction for α+β titanium alloys. This is an type Burgers vector and can be found along the basal plane, the three prismatic planes and the six pyramidal planes. The slip direction is a type Burgers vector and is more difficult to activate in α+β titanium alloys, due to the higher stress required for activation. For slip to occur in this direction it will occur along the planes for 1 st order pyramidal slip and 32

33 occur along the planes for 2 nd order pyramidal slip [2], [7]. The slip planes and directions are shown in Figure 6 and summarised in Table 1. From the table it can be observed that there are only four independent slip systems in terms of the two most easily activated slip systems for Ti-6Al-4V alloys in basal and prismatic slip, respectively. This means that according to Von Mises criteria, where 5 independent slip systems must be activated to accommodate standard plastic strain [20], these 4 independent slip systems alone are not sufficient. Therefore, according to this theory, one of the other 3 slip systems, that require a higher stress, must also be activated for plastic strain to be accommodated. In regions containing macrozones, more concentrated, localised, plastic deformation (slip) has been observed compared to similar sized areas within the same microstructure that have a weak microtexture. The main slip modes that have been activated in the macrozone regions are primarily basal and prismatic slip [3], [21]. The slip traces occur mostly in the α p grains and the path of the traces tends to be continuous through neighbouring grains that have the same crystallographic orientation [21]. This is despite going from an α p grain to a β grain that contains α s lamellae, suggesting that only the orientation provides an obstacle to the path of the slip traces. In a random orientation there are more slip traces on the prismatic plane than the basal plane [22], and this is contributed to the slightly lower CRSS for prismatic slip. The effect of having grains with the same orientation is likely to result in creating a high density of slip along the same slip directions and planes and therefore the same slip system. 33

34 Figure 6- Slip systems of HCP phase [7] Table 1- Slip systems in hcp α-titanium [7] Slip Burger s Slip Plane Slip Number of Slip Systems System Vector Direction Total Independent Basal (0001) 3 2 Prismatic 3 2 Pyramidal st order 6 5 Pyramidal 2 nd order 6 5 Pyramidal 34

35 2.5.2 Schmid Factor The critically resolved shear stress is the component of a shear stress on a certain slip plane, resolved in the direction of slip, which is required to cause slip on a certain grain. The Schmid factor is the ratio of applied stress to the resolved shear stress and is equal to cos (λ) cos (φ) and is maximum at 0.5 and minimum at 0. Figure 7- Schematic of Schmid factor calculation method [20] There is normally a strong correlation between a high Schmid factor, which is related to the resolved shear stress acting along the slip direction, and areas where slip occurs on the prismatic plane [3], [4], [23]. But in the case of slip occurring on the basal plane there often appears to be a requirement for a high tensile stress perpendicular to the basal plane combined with a moderate to high Schmid factor [23]. For type slip there is a general requirement for a high Schmid factor for this type of slip combined with a low Schmid factor for basal and prismatic slip, meaning a likelihood that the majority of grains will deform by either basal and/or prismatic slip and relatively few will deform by slip. Figure 8 shows that there is a significant difference in the CRSS required to activate slip compared to 35

36 basal and prismatic slip across any temperature [7]. Preuss et al [24] showed that when this data was presented as ratios of basal/prismatic to slip for single crystal Ti-6.6Al, the room temperature ratio of the basal/prismatic to was ~3:1, decreasing below room temperature and increasing above it. The stress required to activate basal slip is slightly higher than that required for prismatic slip but the difference in stress becomes negligible at high temperatures and at room temperature the ratio of prismatic to basal slip is often assumed to be 1:1 [21]. Figure 8- CRSS for slip with basal and prismatic terms of temperature [7] and <c a> type slip in single crystals of Ti-6.6Al in Statistical analysis of deformation behaviour in CP, α and α+β Titanium alloys Deformation behaviour can be predicted within a microstructure using Schmid factor criteria and the likely slip system can be stated but this does not take into account the 36

37 neighbouring grain interactions and how this impacts on the local stress state. Therefore slip trace analysis is a technique that has been developed to study the likely slip system that is active within each grain by comparing micrographs of the slip traces with before and after deformation EBSD data. It gives a statistical analysis of the likely slip systems for a particular microstructure and this can then be used to analyse the impact on the mechanical performance. The technique utilises the EBSD information by using the orientation data (i.e. Euler angles) and the known slip systems for α-titanium. The relative slip angles and Schmid factors for all slip systems and the values are then cross correlated with the experimental results to identify the most likely slip systems. One issue with the technique for α-titanium alloys is that there are grains where more than one theoretical slip system may align with the experimental slip traces. More criteria are then used to predict the most likely slip system. The general criteria that are used in the literature are Schmid factors and CRSS and therefore do not provide a definitive solution. This technique has been used by [16], [25] for CP-Ti and α-titanium alloys and by Bridier et al [21] for a Ti-6Al-4V alloy with a duplex microstructure. The results have also been used to predict CRSS ratios for the α-titanium alloy Ti-5Al-2.5Sn [26]. The slip trace analysis results for CP, Ti-5Al-2.5Sn and Ti-6Al-4V completed by separate authors are summarised in Figure 9. The Ti-6Al-4V with a bimodal microstructure exhibits a higher density of grains that have deformed by prismatic slip compared to basal slip as can be seen from Figure 9a and Figure 9b. Figure 9c shows that for Ti-5Al-2.5Sn, a higher density of grains deform by basal slip, although prismatic slip is still the dominant deformation system. The increase in the number of grains that deform by basal slip is also related to the starting texture of the material, which exhibits a weak fibre texture with grains oriented at 30 to the normal direction that promotes the 37

38 likelihood of basal slip [25]. The alloy exhibits a small fraction of grains (~10%) that deform by alternative slip systems to basal and prismatic slip. This percentage of grains that deform by non-basal and non-prismatic slip systems is higher for CP-Ti and is approximately 20% of the total active grains, observed in Figure 9d. There are significantly more grains that deform by prismatic compared to basal in the CP- Titanium alloy. Li et al [16] observe that the increase in prismatic slip is likely to be due to the reduction in the c/a ratio in the non-alloyed material. All the materials exhibit an increase in the density of grains that deform by prismatic slip above Schmid factor ratios of 0.4, indicating that favourably oriented grains for this slip system will deform by this mode. A similar trend is observed for basal slip in terms of increasing density of grains above 0.4 Schmid factor, but all authors have stated that through statistical analysis they were able to show that in grains favourably oriented for both basal and prismatic slip, i.e. Schmid factors greater than 0.4 for each slip system, that prismatic slip was the dominant slip system. This shows a greater likelihood of prismatic slip. Li et al [16], [25] estimated the CRSS values for each slip system using the data from the slip trace analysis for both the CP-Titanium and the Ti-5Al-2.5Sn alloy to statistically analyse the different slip systems at different strains for the same temperatures conditions and then use this to deduce the CRSS ratios relative to basal slip. As can be observed qualitatively from the slip trace analysis technique the basal to prismatic slip ratio was lower for CP-Titanium at 0.28 compared to 0.81 for Ti-5Al-2.5Sn at room temperature. However, this may also be influenced by the initial starting texture of the alloy, which exhibited a high density of grains favourably oriented for basal slip as a result of the fibre texture. When predicting the CRSS ratios for different materials it is essential that the starting texture is taken into account to provide a balanced comparison. Another problem 38

39 with the method may be the relatively high CRSS values for other slip systems that are above 6:1 compared to the typical ratio of 3:1. The reasoning behind this could be attributed to the relatively low number of grains activated by these slip systems in the data sets that have been analysed. Overall, the combination of the two methods to validate the deformation mechanisms appears to give a strong agreement with the current literature on this topic. Figure 9- Global Schmid factor analysis for active grains calculated through slip trace analysis in terms of (a) prismatic and (b) basal activated grains for Ti-6Al-4V [21] and basal, prismatic, pyramidal and and twin activated grains for (c) Ti-5Al-2.5Sn [16], [25] and (d) CP-Titanium [16] 39

40 2.6 Macrozones In some of the literature the macrozones may be referred to as microtextures [27] [29] or Effective Structural Units (ESUs) [30] Definition A macrozone is a set of neighbouring individual constituents (i.e. grains) with a common/similar crystallographic orientation that could potentially create regions within a microstructure that have a very large effective grain size [3], [23], [27] [46]. Macrozones are also often referred to as microtextures as this is the extent of short range crystallographic commonality [30] in a material while across a component the degree of texture could be almost random. In other words a material with a low macrotexture may still contain specific regions with a high degree of texture, therefore giving the material a heterogeneous microstructure and potentially heterogeneous mechanical properties. Macrozones have been identified in several materials, after they have been thermo mechanically processed through rolling [27], [45] and forging [3], [44]. Figure 10 depicts a macrozone in a hot rolled titanium alloy with a strong band of basal texture of approximately 70µm in width. Figure 10- Macrozone in a hot rolled Ti-6Al-4V alloy [45] 40

41 2.6.2 Formation of Macrozones The formation of macrozones is reported to be due to the orientation of the prior β grains within the microstructure and a result of variant selection [29], [47], [48]. It is also suggested that if secondary α (α s ) and some primary α (α p ) maintain crystallographic coherency with the β grains this can result in the formation of macrozones [29]. The phase transformation from β to α, that occurs on cooling from the β phase, is shown in Figure 11 and occurs according to the Burgers orientation relationship, which is given by and [49]. This means that there are 12 possible α variants from a single β grain because there are 6 different planes and each plane contains two directions. Figure 11- Burgers Orientation Relationship [49] The formation of α p grains in a titanium alloy occurs due to deformation and spheroidisation of initial α s lamellae within the microstructure [50] and the α s colonies that form are a result of the β transformation upon cooling from the β phase field as discussed in [28]. It has been reported that during the formation of α p grains that the spheroidisation process eliminated the crystallographic coherency 41

42 between prior β grains and the α p grains [51]. This would imply that the presence of a macrozone with similarly oriented α p grains is not a result of the Burgers relationship. But it has been exhibited that the spheroidised α p grains that form from the broken down α lamellae, appear to maintain a common c-axis within a colony of α lamellae [6]. This gives α p grains with a common c-axis orientation that will be similarly oriented as they have formed from α lamellae from the same colony. The size of the macrozones containing similarly oriented α p grains in many cases is not limited to the size of a former α colony. This suggests that there are several commonly oriented colonies of α lamellae within a prior β grain before deformation occurs. It also suggests there are commonly oriented prior β grains before the transformation from β to α that occurs on cooling from the homogenisation temperature. This would provide the possibility for the large macrozones within a microstructure that have been reported. The α s texture evolution, which causes the formation of macrozones, is due to the phase transformation on cooling relating to the Burgers relationship. This factor alone would still produce an almost random macrotexture and a low degree of microtexture as there are still 12 possible variants available on the formation of each α grain. This gives rise to the theory that variant selection is taking place during the transformation from β to α, which is shown by the local texture sharpness that occurs when the α s lamellae are analysed separately from the α p grains [28], [44], [46], [48] Characterisation of Macrozones It is of importance to be able to quantify the scale of macrozones in a given material on a large scale, so that the magnitude of this feature within the microstructure is known and to enable models to be made to investigate the actual effect they have on the mechanical properties. On a small scale, EBSD is the accepted method of 42

43 identifying texture variations on a material because it is an accurate method and gives detailed grain by grain information. On a macroscale, a larger step size could be implemented to gain information on several macrozones across a material. The problem with this is that it would still be costly in terms of machine time as a large number of macrozones would need to be indexed in order for any statistical analysis to be deemed acceptable [52]. Faster techniques are also required to characterise the macrozone content within a material. This is of particular importance to an industry environment, where the EBSD equipment may not be readily available. A common method to provide qualitative information on the microstructure for titanium is the use of polarised light as this allows for the identification of macrozones within the microstructure and is a quick and reliable method [7]. It allows for macrozone identification because α titanium is optically anisotropic, so polarized light can be used to provide the relative orientation of the α grains. When observing the microstructure under polarised light if is often difficult to detect the low angle grain boundaries. One method that can be used to give an indication of texture within a material is heat tinting. This is shown in Figure 12 where a heat tint colour map and an EBSD map of the same region are shown. Heat tinting is the oxidation of titanium in air and on a polished sample an oxidation film will form on the surface of the sample when the sample is heated to approximately [2]. When an optical light source is shone onto the surface of the sample the inner and outer layers of the oxidation film will reflect different colours [53], and these colours that are reflected are used to provide information about the microstructural features of the material. The technique involves converting the colour image to a grey scale image and then through correlation with an EBSD map of the same region, the heat tint colour can be linked 43

44 to the EBSD map colour. Figure 12a shows the heat hint map that has been converted to grey scale and then correlated and this is compared with the Figure 12b of the EBSD map. The macrozone regions are clearly observed but the extra information from the non-macrozone regions may be misleading. This method will not provide detailed information on the microstructure but will provide a faster initial analysis of the macrozone content [54]. Figure 12- Comparison of a (a) heat tint correlated map to an (b) EBSD map Another method that can be used to characterise macrozones is through ultrasonic attenuation inspection [39], [40]. This method involves analysing the ultrasonic signal to assess how the ultrasonic response correlates to macrozone location within the microstructure [39]. It has been found in these papers that in a titanium alloy, exhibiting large regions with macrozones, the ultrasonic response indicates a low signal to noise ratio but in a material with similar grain size containing less macrozone content there is a much higher signal to noise ratio Macrozone Formation at Various Thermo mechanical Processing Conditions The presence of macrozones has been reported by several authors mainly in two specific titanium alloys, which are Ti-6Al-4V and IMI834. The thermo mechanical processing routes for the alloys are different throughout the literature, and therefore there are variations in the size and orientation of the macrozones. 44

45 Bantounas et al [10] reported macrozones in Ti-6Al-4V uni-directional (UD) rolled plate, cross rolled (XR) plate and forged bar. For the forged bar material the microstructure contained elongated primary alpha grains stretched along the extrusion direction with an aspect ratio of 1:6 and a primary alpha volume fraction of 76%. The microstructure of the materials was bimodal for the plate material specimens with a primary alpha volume fraction of approximately 80%. In the case of the forged bar material there were macrozones of 70µm in length and 5µm in width in the extrusion direction, the orientation of the macrozones in this plane were macrozones with their c-axis oriented perpendicular to the extrusion direction. Within the macrozones there were small grain-to-grain misorientations. At the boundaries of the macrozone region there were high angle grain boundaries, due to the different orientations of the grains in the macrozone and non-macrozone regions. The UD plate exhibited neighbouring macrozones of greater than 150µm length along the transverse plate direction, with two macrozone orientations being observed. These orientations were macrozones with their c-axis parallel with the transverse direction neighbouring macrozones with their c-axis aligned with the rolling direction. The XR plate exhibits fewer macrozones than the other two materials but there were bands with similarly oriented grains, where within these bands the orientation of the basal plane is perpendicular to the transverse direction. These macrozone bands were separated by regions with a random orientation. Britton et al [45] also studied Ti-6Al-4V material which exhibited a macrozone region neighboured by a similarly sized region that had a random orientation in comparison. The material was UD rolled bar and the macrozone studied was approximately 70µm in width and runs parallel to the rolling direction though the material, extending for several centimetres in that direction. The macrozone was oriented with the c-axis 45

46 perpendicular to the rolling direction and the study revealed that in the macrozone region there is a greater number of Geometrically Necessary Dislocations (GNDs). For a UD rolled Ti-6Al-4V Bache et al [13] also found that the c-axis was also preferentially oriented perpendicular to the rolling direction, as shown schematically in Figure 13, and showed a texture of 19 times random. Figure 13- Preferential orientation of HCP unit for Ti-6Al-4V UD rolled plate [13] Le Biavant et al [3] studied fatigue crack initiation in a bimodal Ti-6Al-4V billet with a microstructure containing 50% primary alpha and 50% secondary alpha. Through etching of the samples in a 0.5% hydrofluoric acid solution a ghost structure was revealed that through EBSD was confirmed to be the macrozone regions, and these regions were approximately 100 times the typical grain size. These regions were reported to stretch over areas of 1mm 2 and the texture in these regions was strong. The orientation of the macrozones exhibits primary alpha grains with their c- axis perpendicular to the extrusion direction, which is in agreement with the work by Bantounas et al in the investigation of the texture of their forged bar specimen. 46

47 Another titanium alloy that has been studied and was shown to contain a large degree of macrozone regions is IMI834. Germain et al (2007) [28] studied the macrozone regions in an IMI834 billet with a bimodal microstructure containing 30% primary alpha grains surrounded by secondary alpha lamellae. The material was studied in the billet plane and the macrozone regions appear as bands that stretch along the billet direction for several millimetres. The primary alpha grains within the macrozone regions were found to have an orientation with their c-axis near a radial direction of the billet. But in different macrozones there is a significant difference in the main orientation of primary alpha grains within each macrozone and this is not consistent with data on similar materials. This can be attributed to the differences in parameters in the processing of the materials. It was also found that when the contribution of the primary and secondary alpha grains to the overall texture in each macrozone was separated, the transformed secondary alpha tends to favour an orientation similar to the main orientation of the primary alpha. Therefore the sharp local textures is a result of both having similar orientation in each macrozone. Uta et al [43] studied the texture heterogeneities in an IMI834 forged bar with a 30% primary alpha volume fraction. It is reported that in this material there are millimetre large macrozones that appear cylindrical in shape and stretch along the extrusion direction. These macrozones have two distinct orientations stretching along the extrusion direction, as shown in Figure 14. These orientations are macrozones with their c-axis parallel to the extrusion direction and macrozones with their c-axis perpendicular to the extrusion direction, similar to the results for Ti-6Al-4V reported by Bantounas et al and for IMI834 by Germain et al (2005) [48]. 47

48 Figure 14- Orientation distribution of two directions in an IMI834 forging [43] 2.7 Fatigue Behaviour Fatigue and dwell fatigue are the most widely investigated failure mechanisms for materials containing regions with macrozones. Fatigue is when a material experiences localised and progressive damage when subjected to cyclic loading. It is particularly applicable to Ti-6Al-4V as materials used in the aerospace industry are likely to experience Low Cycle Fatigue (LCF) and High Cycle Fatigue (HCF) during service [2]. LCF is when fracture occurs at relatively low number of loading cycles and the material is subjected to mostly plastic strains due to the high stresses that are applied for this condition. In comparison, HCF is when fractures occurs at a relatively large number of cycles and low stresses resulting in the material being subjected to primarily elastic strains. The typical process for fatigue in titanium is crack initiation in a region caused by localised strain concentrations, cyclic plastic strain to cause plastic yielding; this then creates persistent slip bands due to repeated slip in favourably oriented grains. For crack propagation there are two stages of crack growth development, Stage I is the crystallographic crack propagation stage 48

49 and Stage II is the non-crystallographic crack propagation stage. In stage I the persistent slip bands develop into an initiated crack along a high shear stress plane. The crack will usually propagate until it reaches a microstructural feature such as a high angle grain boundary. Stage II crack propagation will occur when there is an increase in stress in the region, near the crack tip, that could be created by an increased applied load, which induces slip along a new direction. In stage II, the crack grows from the grain boundary in a direction that is perpendicular to that of the applied stresses. Final fracture as a result of fatigue loading occurs when the crack continues to grow, until overloading of the material takes place and causes failure of the material. The microstructural properties that strongly influence the fatigue properties are in the case of bimodal titanium alloys α p grain size, α s lamellae width and α p content Dwell Fatigue In this section the current opinion in the literature of the effect of macrozones during fatigue and dwell fatigue loading will be reported, with the key findings that are relevant to the project being highlighted. These types of loading are described in 2.7 Fatigue. Dwell fatigue loading is when a peak hold is introduced to the loading cycle rather than continuous cycling. Significant research has been carried out on dwell fatigue in titanium alloys and has shown a reduction in fatigue life at temperatures below 300C and for this reason it is often also referred to as cold dwell fatigue. Bache et al [55] have shown in Figure 15 that the effect of increasing the peak hold time reduces the cycles to failure exponentially. Relatively short hold periods have little effect on the fatigue life but hold periods greater than 10 seconds have a significant impact on reducing the fatigue life. The generally accepted peak hold time for observation of 49

50 the dwell effect during testing is a 2 minute dwell and it can be observed that this appears to be the dwell period at which the dwell effect is almost at its maximum. Figure 15- The effect of increasing the peak hold time (dwell period) It has been shown in the literature that there are two particular alloys containing macrozones that appear to be susceptible to early failure during dwell fatigue loading [4], [6], [11], [55] [57], which are Ti-6242 and IMI834. There has been a detailed study into the Ti-6242 alloy by the Federal Aviation Authority on the issue of cold dwell debit [58]. This summary of the fatigue and dwell fatigue performance of Ti alloys with different degrees of texture is shown in Table 2. It particularly highlights the impact of microtexture on the dwell effect, with a significant increase in the dwell life debit in a material with a high microtexture. The dwell debit is the ratio of cycles to failure for the standard to dwell fatigue specimens. The maximum local texture intensity for a low microtexture material is 6 compared to 18 for a high 50

51 microtexture material at comparative stress levels of 95% of the yield stress. Even when loaded to 90% of the yield stress, the high microtexture condition displays greater dwell debit (15) compared to the low microtexture material at higher stresses. This does indicate that the dwell debit effect for the high microtexture material reduces with reduced stress. It should therefore be noted that much of the current testing and experiments around this issue have been at high stress levels, close to the yield stress. The reason for this is likely to ensure that the dwell effect was observed and could then be evaluated, but the in-service operation of these alloys is more likely to be at lower stress levels. This is critical because the actual impact at lower and operational stress levels is more important to the industry. The high microtexture material also shows significantly fewer cycles to failure at these stress levels with 1303 cycles compared to 8803 cycles for low microtexture material in Table 2. As expected there is greater plastic strain accumulation for each material condition at higher stress levels, but key for this project is that there is higher strain accumulation in the dwell condition and in the high microtexture material compared to the low microtexture material. This reduction in fatigue life for certain components means that for the aerospace industry they have to be conservative in their life estimations of the components that are sensitive to this type of early failure. In terms of fine grained bimodal Ti-6Al-4V, this particular condition is regarded as being insensitive to dwell fatigue loading [11], but a coarser grained microstructure of the alloy has been shown by Evans [59] to be susceptible to dwell fatigue. 51

52 Table 2- Summary of fatigue and dwell fatigue tests of Ti-6246 alloys with different degrees of texture [58] Material Load σ max / Dwell time Plastic N f (cycles) Dwell Ratio σ YS (minutes) strain- Life failure Debit (ε pl f) Ladish Pancake 1 (low microtexture) Ladish Pancake 1 (low microtexture) Ladish Pancake 2 (high microtexture) Ladish Pancake 2 (high microtexture) Ladish Pancake 2 (high % % % % % % % % % microtexture) Ladish Pancake 3 (βforged) Ladish Pancake 3 (βforged) Retired impeller (α/β forged Retired impeller (α/β forged % % % % % % % % IMI834 forged bar stock was found to be sensitive to dwell fatigue when a dwell period of 2 minutes was applied to fatigue specimens of the alloy [55]. When the dwell loading was applied to the alloy it resulted in significant reductions in the number of cycles to failure in comparison to tests performed under cyclic loading 52

53 without a dwell period at applied stresses above 0.75 of the ultimate tensile strength, see Figure 16. This trend was observed for both bar and disc material with the dwell period having an increased impact to applied stress to ultimate tensile stress levels of less than 0.7 in the disc material. These tests are once again at relatively high stress levels and are therefore more likely to produce the dwell debit effect. The fracture surface of the test specimens were studied and revealed that the formation of quasi cleavage facets was orientated perpendicular to the main tensile direction and the plane of these facets was predominantly on the basal plane. This crack initiation on the basal plane means that slip is required to occur on this plane even though the plane may not be most favourably oriented for slip in regard to the shear stress, i.e. the highest Schmid factor may not be for basal slip. This mechanism of shear stress transfer onto unfavourably oriented grains is described by the Stroh-pile up model. Figure 16- Fatigue Performance in an IMI834 alloy subjected to a 2 minute dwell period [55] Stroh pile-up One possible explanation behind the transfer of shear stress onto planes that are not favourably orientated for slip is the Stroh pile-up model [60]. The model proposes the idea of having neighbouring strong and weak grains, where a strong (hard) grain is a grain unfavourably oriented for slip and a weak (soft) grain is a grain favourably 53

54 oriented for slip. A hard grain would typically be a grain aligned with the c-axis parallel to the loading direction. In comparison, a soft grain has the c-axis aligned perpendicular to the loading direction as the crystal can be deformed easily by prismatic slip [18], [61], [62]. The model describes that dislocation pile-up occurs within the weak grain, which is favourably oriented for basal slip, and is at the grain boundary of the neighbouring strong grain. The original model proposes that this induces a shear stress in the strong grain and causes a slip band to form, which then results in the formation of a fatigue crack as a result of the applied fatigue loading as shown in Figure 17a. In order to describe the anisotropic behaviour of titanium alloys on a microscopic scale an adapted model was proposed by Bache and Evans [11]. This model still uses the idea of strong and weak grains. The model proposes that a fixed stress is applied to a neighbouring strong and weak grain combination and, that despite having slightly different yield properties, they will have a similar value of strain as they are restricted. This restricted value of strain results in lower stress on the weak grain and increased stresses at the boundary with the strong grain as shown in Figure 17b. Therefore it is predicted that the weak grain is likely to redistribute the resultant extra stress onto the strong grain causing preferential failure in the strong grain. This will be due to an initiating crack along the boundary induced by the resultant stress concentration. 54

55 Figure 17- a) Stroh model for planar slip [63] b) Alternative model [11] Fatigue Fatigue loading experiments were performed on Ti-6Al-4V alloys containing different degrees of macrozones that are described in Macrozone Formation at Various Thermo mechanical Processing Conditions. In materials containing macrozones, the loading direction relative to the primary texture component had an important role in the life of the component [1]. Le Biavant et al [3] reported a scatter in fatigue life caused by macrozones with a different dominant orientation resulting in variations of up to 15%. Slip was seen to be continuous between primary and secondary alpha grains. The cracks were located on either the basal or prismatic plane and initiated either along intense slip bands or at the intersection of two planes. The slip system on which cracks initiated was strongly dependent on the resolved shear stress. If the resolved shear stress was above 200MPa cracks initiated on the basal plane and if below this stress the cracks would initiate on the prismatic plane [3]. It was observed in a Ti-6Al-4V alloy that the most critical damage mode leading to fracture was cracking on the basal plane [22], as slip occurred on both the basal and prismatic planes similar to Le Biavant et al. Cracks initiated on the basal planes, unless slip was difficult on this plane, and in these cases cracks initiated on prismatic 55

56 planes. The Schmid factor for each slip system was used to attempt to correlate a relationship between high Schmid factor and crack formation on a particular plane. For prismatic planes there is a strong correlation between high Schmid factor and location of crack initiation sites but for the basal planes only a moderate Schmid factor was required and was in combination with a high tensile stress perpendicular to the basal plane, which is a result of the Stroh pile-up model described for dwell fatigue. It has also been reported by Bantounas et al [27] that macrozones oriented with their c-axis between of the loading direction faceted crack growth occurs with little resistance to propagation whereas when the basal plane is perpendicular to the loading direction the macrozones act as barriers to crack growth. Bache et al [64] have investigated the effect of Effective Structural Units (ESUs) in titanium alloys where clusters of facets within a 200µm diameter were observed with a near basal plane orientation. The fatigue behaviour of macrozone and nonmacrozone variants was compared. Materials with fine equiaxed, coarse equiaxed and macrozone grain structure were subjected to LCF loading and it was observed that the macrozone variant was between the coarse and fine grained microstructures on the S-N curve. There was a large scatter in the cycles to failure for the macrozone variant attributed to the material having various ESU sizes throughout the microstructure. For example a small ESU size by this theory is likely to result in a better fatigue life than a sample containing large ESUs because it will respond to the applied loading in the manner of a finer grained material. Similarly in a nickel-base superalloy with clusters of grains that are similar to ESUs [65] there were a higher density of crack initiation sites than in a region that did not contain any ESU features. The fatigue cracks in the nickel-base superalloy grew in clusters of grains that were misorientated by less than 20 with the crack initiation grain. In 56

57 comparison, in grains with misorientations greater than 20 the crack growth was arrested. The macrozones for the high microtexture Ti-6242 material in Table 2 are approximately 500μm and exhibit significant dwell debit emphasising the impact of large macrozones on reducing the fatigue life [58] Crack Propagation in a Macrozone Region In the literature it is reported that sudden crack propagation occurs in a region containing a macrozone. The reason for this has been attributed to the effect of crack coalescence within neighbouring grains [3]. This is described as the process when cracks initiate at approximately the same time period for similarly oriented grains because the cracks are likely to form at similar loading conditions due to the grains having a common orientation. When grains with this common orientation are part of the same macrozone, the cracks that have formed are expected to be closer together than in a random microstructure and the grains in this region are likely to be separated by low angle grain boundaries. Therefore there are fewer obstacles to propagation. This results in crack coalescence because the small cracks will propagate through grain boundaries and when they meet a neighbouring crack they will coalesce. The likelihood of neighbouring cracks meeting is increased in a macrozone region because there is often an increased crack density. This effect was observed by Biavant et al [3] and is exhibited in Figure 18 It is clear that the two cracks that have initiated in separate macrozones have approximately the same crack growth rate until a sudden increase in crack length in macrozone 2. A possible reason for an increase in the crack propagation rate is due to common grain orientation in neighbouring grains resulting in low angle grain boundaries between similarly oriented grains. But this does not appear to have occurred as the sudden increase in crack length is non-linear. This does not suggest that there is an easier propagation 57

58 route as a result of the nature of the local microstructure. Hence, crack coalescence is likely to have occurred in this case. However crack coalescence was not observed by Szczepanski et al [51] but the experiments preformed in this case were Very High Cycle Fatigue tests. This means that the very low stress used in the experiments is likely to result in a lower crack density within a macrozone and the probability of crack coalescence occurring is reduced. Figure 18- Effect of Crack Coalescence in Ti-6Al-4V macrozone material [3] 2.8 Proposed Studies The current literature on the effect of macrozones on the mechanical properties in titanium alloys has demonstrated that these regions reduce the fatigue life of the material during dwell fatigue loading. The main focus in the literature has been on post mortem studies of the crack initiation sites and there is conflicting opinion on the reason for the reduced life as a result of a dwell period at peak load. The experimental studies behind the combination of hard and soft regions are limited in 58

59 terms of providing any confirmation for the proposed models that have been developed. This project will study the deformation mechanisms on a microscale and nanoscale on materials with different degrees of macrozones to link the deformation behaviour to the crystallographic orientations. The deformation mechanisms will be analysed through surface strain measurements using the Digital Image Correlation technique at different length scales. This will allow an understanding of the strain accumulation to be gained on a macrozone to macrozone scale as well as sub grain to sub grain scale. The deformation will be observed during tensile studies and an attempt made to link this to the underlying fatigue behaviour. 59

60 Chapter 3 Experimental Methods This section describes the material provided and the experiments that were conducted at the University of Manchester. It also gives detailed descriptions of the experimental analytical tools used in the characterisation of the materials. The pattern applications for DIC will be reviewed and the appropriate errors associated will be calculated. 3.1 Material Three different product forms of Ti-6Al-4V alloy were provided by Rolls-Royce, which are a medium forging, uni-directional rolled plate and a blade bar that were labelled as no-macrozone, intermediate-macrozone and strong-macrozone conditions from here on, respectively. The microstructure of the three products is equiaxed consisting of α p grains with β at the triple points. 3.2 Metallographic Preparation Samples were taken from several sections of each of the materials to allow for comparison of the microstructure of the same material in different regions and in the 3 different possible directions, to enable the key directions for analysis to be determined. This also helped to confirm whether the microstructure of the sample is homogenous or whether it varies throughout the thickness and length of the materials, as this will affect the materials response during mechanical testing. In order to prepare the three materials for optical microscopy and EBSD analysis, the three product forms were first sectioned using a Struers Accutom 5 cutting machine to provide samples of the required dimensions. The cutting occurred under water cooling and the feed rate and cutting speed were controlled to ensure localised overheating did not occur. The feed rate was set at 1.1mm/min and a cutting speed of 60

61 4000rpm. The cut samples were then mounted in Bakelite to enable subsequent grinding and polishing to be performed. The first stage in preparing the material for microscopy is water cooled grinding on SiC papers, which was conducted on four SiC papers from grit 320 up to grit The samples were then mechanically polished on a cloth with diamonds of first 6μm, then 1μm and finally a 1/4μm, with the surface being observed after each polishing step to ensure that sufficient polishing time had been spent at each stage. Each of the 3 materials required different polishing times due to the variations in microstructure. The next stage in preparing the samples was to polish them on a synthetic cloth with colloidal silica (OPS polishing) for one hour and then etch until the microstructure was visible under the optical microscope. Etching of the alloy was performed using Kroll s reagent, for which the chemical composition is as follows: 100ml water, 1ml hydrofluoric acid and 2ml nitric acid. Typical etching time when the sample is going to be OPS polished again is seconds. This process of OPS polishing and etching is conducted three times per sample and then a final OPS step is performed to allow for microscopic analysis. For tensile test specimens, the same procedure was repeated and after EBSD analysis the sample was then OPS polished again for 10 minutes and etched. This re-etching of the test specimens was performed until there were sufficient micro structural features to enable Digital Image Correlation (DIC) to be possible. 3.3 Optical Microscopy Optical microscopy was performed using a Zeiss Axio (Scope.A1) microscope with a differential interference contrast and cross polarised light filter. The samples were initially analysed after etching to allow for grain size and α p volume fractions to be estimated using the linear intercept and point counting methods, respectively. Then, 61

62 after the final stage of OPS polishing analysis was undertaken using a cross polarised light and/or differential interference contrast filter to provide qualitative information on the orientations of the grains. When analysing under polarized light a clear image of the microstructure should be obtained, as this will indicate that the sample has been prepared suitably for EBSD. Polarized light also allows for the identification of macrozones within the microstructure because α titanium is optically anisotropic [66]. Hence, polarized light can be used to provide the relative orientation of the α grains. This means that an approximate estimate can be made of the size of macrozones within the microstructure. Once the macrozones had been identified under this condition the sample was marked with micro hardness indents, the indents provide reference points for possible macrozones that have been identified to enable these regions to be easily located when analysing the samples using EBSD. 3.4 Micro hardness Test Micro hardness indents were made on particular samples as reference points to enable the regions for DIC and EBSD to be easily identified. A unique grid was applied to each sample with a single large indent at the edge of the sample with two smaller indents spaced 1mm and 2mm vertically from the edge, respectively. A further smaller indent was made 1mm horizontally from the central indent as shown in Figure

63 Figure 19- Schematic of DIC referencing technique 3.5 Scanning Electron Microscopy (SEM) An SEM provides us with, typically, a more detailed set of information on a higher magnification scale and is used in combination with the initial information that can be gathered from an optical microscope. Different imaging modes are available and enable a variety of different aspects of grains to be imaged such as slip traces and secondary alpha phases. Electron Channel Contrast Imaging (ECCI) was used in combination with DIC analysis to observe the slip traces and to then predict the likely deformation system. ECCI images are produced by channelling down the crystal planes of a particular grain. The defects or deformation such as slip traces can be observed through variations in the grey scale across single grains. There will be observable changes in grey scale, where there are dislocations in the crystal compared to the non deformed regions of the grain, if the crystal planes aligned with the beam. Tilting the sample 1 or 2 gives increased BSE signal [67], [68]. However, it is difficult to show detailed information using ECCI on more than a few grains in a single micrograph because the technique involves aligning the beam down a particular crystal plane to produce maximum BSE intensity and several crystal orientations will have different plane alignments at the same tilt angle [67]. For this analysis regions of grains are imaged, with some grains displaying clearer slip traces as the alignment of the beam with the orientation favoured certain grains. 63

64 From these micrographs using ECCI the slip traces are in some cases clearly observed as they have sharp changes in grey scale from the rest of the grain or in other grains shown as faint lines that have similar grey scale the whole grain. The microscope operating parameters used for the ECCI technique are summarised in Table 3, and these provided the best results in terms of observing slip traces within single grains. Table 3- Microscope operating parameters for the ECCI technique Operating Voltage 8kV Spot Size Working Distance <5mm Magnification >1000X Electron Back Scatter Diffraction (EBSD) EBSD is a method that is used to provide detailed information on the orientations of individual grains across a sample through electron diffraction within a SEM [69] [73]. The samples for this purpose need to be prepared with a flat and deformation free surface. On analysing samples in an SEM the sample is first roughly focussed then tilted to 70 and then finely focussed to the optimum working distance for the microscope. The sample is tilted as this reduces the path length that the diffracted electrons have to travel to reach the EBSD detector thus increasing the number of electrons that hit the detector and a typical tilt angle of greater than 70 is used [74]. The astigmatism correction is then applied and the EBSD detector is inserted and the patterns are analysed and refined appropriately [70] [73]. The patterns are produced because the electron beam is diffracted by the crystal onto a phosphor screen (detector). The diffracted electrons that hit the detector cause the phosphor screen to fluoresce and form a pattern on the screen that is linked to a CCD camera. This 64

65 pattern provides detailed information on the structure of the crystal and its orientation [74]. The diffraction pattern for the crystal is then analysed using computer software by identifying the Kikuchi bands in the pattern and using this to determine the underlying crystal structure. Figure 20 outlines the procedure that is followed when collecting the EBSD data including the processing steps that are initially required in the computer software. These include frame average, which is the number of iteration points at a single location, and then the background noise must be subtracted from the patterns to give clear Kikuchi bands. The pattern is then indexed to give the crystal structure at that location and once all patterns for a single map have been indexed the pattern is often displayed as a complete EBSD map. Figure 20- Schematic diagram of the key components of an EBSD acquisition system [71] Operating parameters In this section the key operating parameters for both the microscope and the computer software used to capture the diffraction patterns will be discussed in regard to the parameters used and the impact of these on the results that are gathered. EBSD 65

66 was conducted in a Sirion FEG SEM and a CamScan Maxim 2500FEG SEM with a NordLYS detector. Both machines are equipped with HKL EBSD system to enable data acquisition and processing. A Quanta 650 FEG SEM was also used for EBSD analysis, which is equipped with Aztec acquisition software that typically achieves higher indexing rates as a result of the different algorithm for pattern recognition that is implemented in the software. The probe current for the analysis was approximately set at 5nA on all microscopes and a high probe current increases the number of electrons that will be diffracted, thus increasing the quality of the EBSD patterns, which in turn will increase the indexing rate [71]. However, increasing the current will increase the beam size and thus reduce the spatial resolution. An accelerating voltage of 20kV is typically used for titanium alloys and this was used in this research. Increasing the parameter has a similar impact to that of the probe current where increasing the voltage negatively impacts on the spatial resolution but increases the indexing by providing higher contrast patterns. At low accelerating voltages it may be difficult to produce suitable EBSD patterns. In terms of spot size, increasing this parameter will improve weak diffraction patterns thus increasing indexing. In this analysis the patterns were generally strong. Therefore, the spot size was optimised to provide the maximum spatial resolution. The working distance is variable for each microscope system and is optimised for that equipment to provide the best results [71], [72]. For the microscopes used the working distances are 13-15µm, 24-27µm and 11-13µm for the Sirion, CamScan Maxim 2500 and Quanta 650 FEG SEM, respectively. The magnification is dependent on the type of scan that is being performed in terms of micro and macrotexture and the higher the magnification the higher the indexing rate and the lower the magnification the lower the indexing rate. Step size is generally 66

67 microstructure specific and also depends on the features within the microstructure such as twins. A fine step size will produce higher indexing rates than a large step size as features such as grain boundaries and surface damage will have less impact on the patterns away from these features. The operating parameters for EBSD acquisition for the individual microscope are summarised in Table 4. Table 4- Microscope operating parameters for EBSD Microscope FEI Sirion Quanta 650 FEG SEM CamScan Maxim 2500 Operating Voltage 20kV 20kV 20kV Spot Size Working Distance 13-15μm 11-13μm 24-27μm Software HKL Aztec HKL The software parameters that were used to determine the orientation of the individual points are described in terms of timing per frame, frame averaging and the number of Kikuchi bands as these are the three main parameters that impact the results. The timing per frame is optimised depending on the background and the pattern quality and is typically as low as possible to increase the acquisition rate. Using longer frame times than required is generally time wastage as this will not improve the quality of the pattern captured if the time per frame is set correctly. Frame averaging can be used if the quality of the patterns is uncertain as it is likely to provide a more reliable result and will increase the overall indexing rates. The pattern qualities only required a maximum frame average of 2 frames in this work. The maximum/minimum number of Kikuchi patterns used to determine the solution of the pattern for each acquisition point should ensure that the resultant crystal for the point is correct in almost all cases. If this parameter is too low then it will result in an incorrect interpretation of many of the points and the overall EBSD results would be 67

68 questionable. Typically in this work the minimum/maximum number of bands was 4/6 as this is sufficient to ensure the higher reliability in the results Micro and macrotexture scanning conditions Both macrotexture and microtexture scans are required to provide information on the local and overall textures. Therefore two types of scanning technique within the EBSD and SEM are utilised, a beam scan and a beam and stage scan. A beam and stage scan is required when the macrotexture of the samples is being analysed as the EBSD maps will cover a large area to give an idea of the overall texture. The use of the movement of the stage results in a well focussed image at each new position but this takes longer than beam scanning. For the materials provided a step size that is equal to or double the grain size (i.e. approximately 5-10µm) is used to analyse the texture. A beam scan is typically used when the microtexture of the sample is being analysed to assess the level of texture on a smaller scale look at the actual scale relative to the microstructure. The beam scan disables the operation of the microscope meaning only the software is able to move the beam and this means that for high magnification the technique is fast as there is no move of the stage but covering large areas will reduce the resolution at the edge of the scan. This means that detailed information on the grains can be gathered, such as grains size, orientation analysis and neighbouring grain effects [72]. For a microtexture scan a step size of 1/10 of the grain size is typically used. In the present case this translated to a step size of 0.5μm, to allow for identification of the local texture. On the strongmacrozone sample where macrozones had been identified under polarized light and micro hardness indents applied to the sample for identification purposes, a large region of the sample was analysed micro texturally. This was to give a detailed insight into the relative macrozone texture across a large region of the condition. 68

69 EBSD post processing EBSD post processing is required to remove anomalies from the results that have been produced by incorrect interpretation of the patterns by the software. These are often single points within a complete grain or at grain boundaries where the patterns incorrectly indexed. These are removed by using the wild spikes function, which will replace these points with a non-indexed point. Once all these points have been removed the rest of the map is interpreted as reliable. Therefore, the next step is to replace the non-indexed points with likely solutions for their crystal orientation. This is determined by interpolating the results from the neighbouring points and the HKL software has a scale of 1 to 8 neighbours to provide the solution to the non-indexed points. In this work a minimum of 6 neighbours are required for a solution to be provided. Otherwise the point is left as a non-indexed point. This is sufficient to keep the reliability of the maps. This extrapolation is required as it enables grain boundaries to be quickly recognised when comparing the results from EBSD and DIC. 3.6 Digital Image Correlation (DIC) Displacement mapping techniques are being used more prominently to study the surface deformation of different materials. The information provides a more detailed understanding of the strain behaviour during various loading conditions by tracking the displacement of features through in-situ and ex-situ imaging of the sample surface. One of the most widely used methods for computing the deformation behaviour of the materials by calculating the displacement vectors of features is Digital Image Correlation (DIC) [75] [88].The main principles of the DIC technique are that it requires an image before and after deformation, and the surface of the sample must exhibit a set of features that will remain unaffected by the strain during 69

70 deformation. The two images are then separated into sets of sub regions with unique features, also called speckles, within each matching sub region from before and after deformation. The displacement vectors for the pixels for each individual sub region are then calculated by tracking the features during deformation and correlating relative to the first image taken before deformation. The displacement map for the whole image can then be calculated by combining the information gathered from the single sub-regions. This also means that if multiple images are taken with increasing load that the overall strain progression can be recorded as long as the increasing strain images are correlated back to the first image. The single sub regions should contain distinct regions from sub-region to sub-region to ensure that during image processing identical sub regions in terms of features are correlated relative to each other. If the features cannot be distinguished from each other it is likely that the software may wrongly correlate features that are not in identical positions within the same and/or different sub regions. This will create inaccuracy in the correlation and give incorrect strain measurements. This relationship of distinguishable features is shown schematically in Figure 21 [75], where the whole image before and after deformation has been broken down into the same sub regions in terms of position. The features in the figure can clearly be distinguished from one and other and this allows for the displacement of the speckles to be calculated. The tracking of features from the same sub region before and after deformation gives the relative displacement of the features and across the entire region gives a full set of displacement vectors for this area. Once the displacement vectors have been calculated for the whole image these are differentiated to give an overall strain map in the appropriate direction or the total strain for all directions can be computed [75], [77], [78]. 70

71 Figure 21- Schematic diagram of the DIC procedure showing that the original and deformed images are divided into pairs of sub-regions and the displacement of features within the sub-regions is then used to compute the local strain [75] The local strain in the x and y directions are calculated using Equation 1 and Equation 2, respectively, where u and v are the displacement vectors and x and y are the distances the features are apart in the relevant directions [75]. These are used to determine the relevant strains in terms of the loading direction. Equation 1 Equation 2 For the microscale and High Resolution DIC (HR-DIC) the strain results are presented in terms of maximum shear strain, as this will take into account the contribution of all in-plane strain tensors. The maximum shear strain (τ max ) is calculated using Equation 3, where ε xy is the in-plane shear strain and is calculated using Equation 4 [83]. By resolving the deformation in terms of maximum shear for 71

72 the HR-DIC it provides a good representation of the strain associated with slip traces. This also helps to reduce the uncertainty of having no information on the out-ofplane deformation using 2D DIC [81], [83]. Equation 3 Equation 4 The out-of-plane motion is calculated using Equation 5, where ΔZ is the out-of-plane translation and Z eff is the effective distance between the microscope lens and the sample [89]. It could also be described as a method of determining the error in 2D DIC, as it suggests that by reducing the distance between the lens and the sample the contribution of the out-of-plane motion will increase. [89] Equation 5 One factor that is not taken into account by Equation 5 is focus adjustment, which is used in both the microscale DIC and HR-DIC and this ensures that the sample surface is at approximately the same position throughout to keep this factor constant. This will apply for the microscale DIC as the main detail that impacts on the out-ofplane plastic strain. But for the HR-DIC it is likely that the maximum and minimum heights of single traces will not be constant. This means that there is likely to be an increased error as the focus is likely to be at the centre of the slip trace height. Therefore, there will be points within the slip trace that decrease Z eff further and increase the contribution of the out-of-plane motion. The effect of the out-of-plane 72

73 motion has been reduced as much as possible using the techniques described above and is factored into the interpretation of the results Speckle patterns DIC requires a random pattern on the surface of the sample in order for displacement correlations to be computed to determine strain measurements [75], [77], [85]. The size of the individual features in an overall pattern determines the strain resolution that can be achieved in terms of the length scale. A number of patterns have been applied to specimen surface to determine the strain in the microstructure using the DIC method including using features of the microstructure by etching the sample surface [75], spraying a coating on to the sample [88], using FIB indents to replicate a random pattern [80] and by using vapour assisted remodelling of thin films [83], [90], [91]. The ranges of patterns that can be achieved enable strain to be determined on the macroscale and microscale, to capture both grain-to-grain and sub-grain behaviour. The largest feature determines the maximum resolution that can be gained from a certain pattern. Therefore, a random speckle pattern with a uniform size distribution is desired to allow the software to distinguish between features [92]. FIB indents have been applied as a grid on titanium alloys by Littlewood et al [80] and the resolution of this pattern allowed for grain-to-grain deformation to be studied. Heterogeneous strain behaviour was observed under tensile, fatigue and dwell fatigue loading and regions of low strain neighbouring grains that were heavily deformed. The limitation of this study was that it did not provide sufficient information of the nature of the slip behaviour to be proven, but did demonstrate the heterogeneous nature of the deformation in HCP titanium and quantified strain in soft and hard grains, respectively. 73

74 The gold remodelling technique has been used on austenitic stainless steel to produce particles of various sizes depending on the polishing method involved [83]. The size of the particles and suitability for different magnifications varies with OPS-colloidal silica polishing time and the thickness of the initial gold layer. The study showed that without OPS polishing only small speckles were produced and these were difficult to image due to the low backscattered signal, unless a 70μm thickness of gold was applied. Very high magnification images were required to provide strain mapping information in this condition. When an OPS polish greater than 10 minutes was applied to the sample surface speckles were produced that provided a pattern suitable to be used at a lower magnification. This magnification meant that a bigger region of interest could be covered in less time providing a more detailed understanding of the deformation behaviour over a larger length scale. High resolution strain maps have been acquired using a Scanning Electron Microscope (SEM) to provide detailed information on the deformation in this alloy [83], including the capture of fine slip traces within single grains, by capturing Backscatter Electron Images (BEI) at high magnification. This enabled full field strain mapping at increasing degrees of plastic strain. Overall, fine speckle patterns provide a finer resolution than coarse speckle patterns and a desired feature size for DIC is typically between 2x2 pixels 2 and 4x4 pixels 2 [75]. To produce a full field strain map across a region it is required that the pattern is uniform in terms of feature size across the whole analysed region. This means that the resolution of the strain map will be comparable across the sample. If the speckle pattern was non-uniform in regard to feature size across a sample this would create differences in resolution. For example large speckle features would reduce the resolution and a fine speckle pattern would provide a high resolution pattern suitable 74

75 for observing sub grain deformation. Differences in resolution could also be a result of having a sample with a distribution of features with the same speckle size but uneven spacing between speckles. Therefore some regions would have a greater density of finely spaced features resolving at a high resolution compared to other regions of the sample that are widely spaced but are fine speckles meaning the pattern would be difficult to resolve in the regions between the features Experimental Analysis DIC was performed at different length scales to provide a detailed understanding on the macro and micro strain behaviour, as this will provide information on the macrozone to macrozone effect but also the sub grain strain heterogeneity. For this purpose patterns suitable at different length scales were applied to the surfaces of the samples to enable microscale and HR-DIC Speckle Patterns For optical microscopy the surface of the patterns for the 3 conditions was etched using Kroll s reagent with a solution of 100ml water, 1ml hydrofluoric acid and 2ml nitric acid for seconds because a strong etch provides adequate features for DIC. It should be noted that the freshness of the Kroll s reagent effects the etching time. The Kroll s reagent colours the beta phase of the microstructure dark brown and does not colour the alpha phase. The 3 microstructures consist of primary alpha grains with beta phase at the grain boundaries. Therefore, no sub-grain information will be gathered from this speckle pattern. The differing patterns for the 3 microstructures are shown in Figure 22. The no-macrozone condition and the intermediate-macrozone condition both exhibit similar grains structures in terms of size and shape with the no-macrozone condition having a higher volume of beta clusters in the microstructure. The strong-macrozone condition has grains that are 75

76 elongated but the shape of the grains is not a uniform distribution, therefore this will not cause any problems with the cross correlation procedure for the image correlation by misrecognition of features as they do not appear the same. Figure 22- Microscale DIC speckle patterns for (a) Strong-macrozone condition, (b) intermediatemacrozone condition and (c) No-macrozone condition Gold Remodelling To provide sub-grain resolution a fine speckle pattern is applied to the surface of the sample. The method for applying this pattern to the surface is the gold remodelling technique [83], [93], [94]. To relate the subsequent strain behaviour to the microstructure the specimens are first polished to EBSD quality and then a before deformation EBSD scan of the region is taken. A gold layer of 25-40nm is then applied to the surface of the sample using a sputter coater at a rate of 5-8nm/min. Increasing the thickness of the gold layer appears to initially provide a speckle pattern suitable for lower magnification images, but then as the thickness of the layer increases the gold coating peels away from the surface of the sample. The tensile specimens are placed in a water vaporisation environment to produce a fine speckle pattern. The remodelling occurs by placing the sample on a hot plate at a temperature of between the vapour source and an inverted cup as shown in Figure 23, to allow the vapour to circulate around the system. The gold coating is remodelled in this environment for a period of minutes, with longer remodelling times having shown not to cause significant difference in the developed pattern quality. 76

77 Figure 23- Apparatus for gold remodelling procedure [83] Different material conditions have been shown to produce variations in the remodelled pattern, from a mesh pattern to separated gold speckles. The resolution of the pattern appears to vary from material to material because the variation in patterns means that different magnifications may need to be utilised to provide the optimum conditions for the imaging. Subsequently, when the images are cross-correlated using the DIC technique the sub-grid windows are adjusted to give the same spatial resolution for each material condition. Figure 24 is an example of a typical gold speckle pattern generated on the no-macrozone condition using the gold remodelling technique. Figure 24a shows the typical magnification that images for HR-DIC are captured as this provides gold speckles that are approximately 3x3 pixels 2. The high magnification micrograph in Figure 24b highlights the strong contrast between the gold speckles and the substrate that provides suitable features for the subsequent displacement mapping. 77

78 (a) (b) 1μm 5μm Figure 24- An example of a gold speckle pattern on Ti-6Al-4V no-macrozone condition at (a) 10000X and (b) 20000X magnification Experimental set-up The microscale DIC was performed in-situ using an optical microscope and the HRDIC was performed ex-situ on a Scanning Electron Microscope by loading the sample to specific strain values. The set-up and conditions for the two techniques will be discussed Microscale DIC DIC was conducted on an optical microscope rig using a microtester to perform insitu tensile loading on tensile specimens with 30mm gauge length, 3mm gauge width, 1mm thickness and 10x10mm handles to secure the specimen in place. The microtester was controlled using DDS software connected to a laptop. The images were acquired with a DaVis Axiocam connected to a computer equipped with DaVis 7.2 software to handle and process the images. The images taken were 2048 x 2048 pixels and were acquired at a rate of 1 a second. The microtester was positioned on a height adjustable stage, enabling fine focus adjustment. This meant that it was possible to perform real-time focus adjustment and real-time image capture during interrupted tensile loading [75]. 78

79 The procedure for acquiring the images for DIC was to first measure the sample dimensions and then securing the tensile specimen in place using the grips and placers to stop the specimen from slipping during loading. The sample was initially preloaded to remove the effect of misalignment as this eliminates the rigid body movement. The microtester was then positioned on the optical microscope rig and the microscope stage was used to find the area on the sample for DIC. This area typically involved finding the micro hardness indent that had been applied to the sample and then using the edge of the tensile specimen to line up the x-axis with the bottom of the computer screen. The sample was focussed on to x100 magnification and the sample has been etched to provide the speckle pattern. This typically allows accurate strain mapping values in 0.1% increments, with a constant local contrast and brightness [75]. The light intensity across the region of the sample in view was set at a light intensity to show clear contras between the etched regions and the rest of the microstructure. This was maintained throughout testing to reduce the impact of noise on the results, by limiting the difference in light intensity from one image set to another Systematic errors in microscale DIC The systematic error was assessed to determine the accuracy of the results at increasing strain. To calculate the error in the results a set of images are taken before deformation then the microtester is removed from the rig. The sample is then repositioned on the rig and the region of interest is located and another set of images are taken. The error can be calculated from these images by comparing the two data sets when no there is no stress applied to the material. As a result when the two sets of images are correlated the local strain that is calculated will give the noise and the error in the local strain results when deformation occurs. The error created during 79

80 Normalised Frequency imaging for the microscale DIC for the strong-macrozone condition in all 3 loading directions is shown in Figure 25. The average errors calculated are 0.03%, 0.07% and 0.03% for the strong-macrozone condition loaded at 0, 45 and 90, respectively. This accumulates to an overall average error across the microscale DIC of 0.04%. The local strains in the elastic and plastic region with increasing load will exceed these error values. But for the initial loading increments caution will be taken in the interpretation of the results with the error in the imaging being taken into account degrees 90 degrees 45 degrees Strain (%) Figure 25- Frequency analysis to determine error from imaging for microscale DIC Tensile loading of the samples is then conducted by increasing the load applied to the samples using the DDS software, in increments of 200N up to 1000N and then in increments of 100N up to the point where it can be seen that the yield point has been reached on the load-extrusion curve. The load increments were reduced to 100N steps at 1000N. From preliminary experiments that more information was required at increased applied loads. The values captured in the DDS software were exported to Excel to generate the stress-strain curves for each material. When the load was held for images to be captured at each load value, the time taken was approximately 30s 80

81 each time. The time was taken to refocus the image at x400 zoom and then adjust the light to the correct intensity across the image to reduce the noise. 5 images were acquired at each load and then when the sample was unloaded images were acquired at one/two per second HR-DIC HR-DIC experiments were performed ex-situ on a Kammrath-Weiss 5kN Tension- Compression microtester with the same specimen dimensions as the microscale DIC tensile tests. In-situ testing was not possible as a result of the difficulty imaging the speckle patterns at long working distances. This cannot be reduced because the microtester limits the working distance to a minimum of 20mm. The ex-situ tensile strains were strained to approximately 1%, 3% and 5% overall strain for each material condition and loading direction by measuring the gauge length extension during testing and at each strain step the region of interest was imaged. By doing equal strain increments it was possible to study the strain evolution without the requirement for in-situ testing. The images for DIC were acquired with an FEI Sirion and a Quanta FEG Scanning Electron Microscope (SEM) at magnifications of X1000 and X3000 with horizontal field widths ranging between 20-75μm. Images are taken at a low working distance of approximately 5mm in Back-Scattered Electron (BSE) mode to maximise the high contrast morphology of the gold speckles. The images in the FEI Sirion were acquired in ultra-high definition (XHD) imaging mode at an image size of 3872x2904 pixels 2 and at 4096x3755 pixels 2 for the Quanta 650, with a dwell time of 30μs. The images take ~ 2-4 minutes per image to acquire and the sample was not held at load. Image mosaics of 3x3 and 4x4 images are taken and the image is refocused at each new reference point, only slight readjustment was typically needed. 81

82 The subsequent strain maps were stitched together after processing to give a single large high resolution strain map Systematic errors in HR-DIC The systematic error for the HR-DIC was calculated using a similar method to the one deployed for the microscale DIC. Two separate images are taken on the same region of a sample before deformation and the images are then compared using the DIC technique to calculate the strain in the region. The strain values are defined as the systematic error as a result of the raster scanning process and the detector noise [83]. Figure 26 summarises the systematic error in terms of the correlation software (DaVis) processing parameters and gives an indication of how the strain results were optimised by adjusting these parameters to give the most accurate output, whilst retaining the desired high resolution strain mapping. Figure 26a (i) and b (i) shows the maximum shear strain and strain in the loading direction for different overlap and linear sub region grid sizes in terms of normalised frequency, respectively. As expected, it can be observed that for the maximum shear strain there was a narrow range in the strain values. Interestingly, the 12x12 pixels 2 sub grid size with 0% overlap does not significantly increase the peak value. The peak value was shifted 0.2%, which lies within the acceptable systematic error. With increasing overlap for this grid size the peak systematic error increases along with the maximum shear strain value and is comparable to correlating with a finer grid size. Therefore the error associated with these correlation parameters is not suitable. This is also shown by analysing the data for the strain in the loading direction, which indicates there is a strong peak and small range in strain values for both the 16x16 and 12x12 pixels 2 sub grid size with 0% overlap. Overlaps of 0%, 25% and 50% were used with a constant sub pixel grid size of 12x12 pixels 2 and this is shown in Figure 26a (ii) and b (ii) for 82

83 the maximum shear strain and strain in the loading direction, respectively. The strain that has been evaluated for this parameter is the average strain across the region and the error bars have been calculated using the root mean square (RMS) method. The figures indicate that for the maximum shear strain the average systematic error increases with overlap and the strain in the loading direction is near constant. However, the systematic error increases exponentially with increasing overlap and therefore the minimum overlap will give the most reliable results. Sub region grid sizes of 8x8 pixels 2, 12x12 pixels 2 and 16x16 pixels 2 were used with a constant overlap window of 0% and this is shown in Figure 26a (iii) and b (iii) for the maximum shear strain and strain in the loading direction, respectively. The strain and root mean square values have also been used to evaluate the impact of the sub region grid size. The figures indicate that for the maximum shear strain the average systematic error decreases with increasing sub region pixel size and the strain in the loading direction is near constant for all sub grid sizes. However, the systematic error decreases exponentially with increasing linear sub pixel grid size but the difference in systematic error between sub region pixels sizes of 12x12 pixels 2 compared to 16x16 pixels 2 is minimal. Therefore a sub region pixel grid size of 12x12 pixels 2 is favoured as it provides the maximum resolution in terms of the strain parameter without a significant increase in the systematic error. This is the method that is used to determine the optimal parameters for a particular speckle pattern as these can vary depending on the speckle shape and size. It should be noted that when comparing strain results the patterns are typically resolved to the same spatial resolution rather than the maximum strain resolution that can be achieved. This is to provide an accurate comparison between material conditions because using different spatial resolutions would cause a bias in the results that are reported. 83

84 Figure 26- Systematic error distributions associated with HR- DIC for (a) maximum shear strain and (b) strain in the loading direction in terms of (i) normalised frequency distributions, (ii) overlap of the sub regions and (iii) the linear pixel sub region size Figure 27 highlights the effects of the parameters evaluated in Figure 26 by varying the sub region grid sizes and the overlap for a particular speckle pattern, and also details how the optimal speckle resolution was achieved. Figure 27a-c shows that by reducing the sub grid size the deformation features are resolved at a finer scale and are therefore more apparent. The large sub grid size in Figure 27a provides a good evaluation of the microscopic features but does not provide sufficient information on a nanoscale. However, the fine sub grid size with overlap shown in Figure 27c has over resolved the features and has a greater degree of background noise and this reduces the reliability of the strain mapping. Figure 27b has an intermediate sub grid size with no overlap and provides the required balance between the resolution of the deformation features (i.e. slip traces) and the reliability of the strain measurements by reducing the background noise. It should also be noted that the optimal processing 84

85 parameters enable fine slip traces with low strain heterogeneity to be observed as well as deformation features with high strain heterogeneity. Figure 27- Values of maximum shear strain calculated for 5% macroscopic strain for the no-macrozone condition using different sub-region size and overlaps: (a) 24x24 pixels 2 with 0% overlap, (b) 8x8 pixels 2 with 0% overlap and (c) 4x4 pixels 2 with 25% overlap DIC Software Settings For both microscale and HR-DIC the deformation images were correlated to before deformation images using DaVis software, Version 7.2 was used for microscale DIC and Version 8.3 for the HR-DIC. The parameters were different for the two resolutions because of the etched pattern and the gold speckles Microscale DIC software settings The method for performing DIC using the DaVis software for each load set of 5 images was to calculate an average image and then create a series of averaged 85

86 images from before deformation to maximum load. If necessary, the images were realigned to ensure the matching features are overlaid using the shift correction function manually identifying a point of reference within the software for the shift. The images captured were also reduced to 1000x1000 pixels 2 to reduce the feature size to between 4 and 16 pixels 2. The deformation calculations settings to give the displacement vectors were calculated to relative to the first image. A sub pixel grid size of 32x32 pixels 2 with a 50% overlap was used as the optimal settings, in terms of noise reduction and maximum strain resolution. The overlap maintains the spatial resolution, while allowing a bigger sub-region to be used. The sub grid size in real terms was 36x36µm 2, covering approximately 9 grains for each material. In terms of a macrozones in this study they typically have a width of grains for the strongmacrozone condition and grains for the intermediate-macrozone condition, therefore a single macrozone will overlap several sub-regions. A strain map for each loading increment is generated in relation relative to nondeformed image, so that the evolution of the strain behaviour throughout the experiment can be observed. The raw data values from the DaVis software can be exported to Excel to generate the frequency distributions for the different strain maps that have been produced and to provide a comparison with the strain data from the microtester at each load increment HR-DIC software settings The settings for the HR-DIC were more refined as a result of the fine speckle pattern and the imaging accuracy. The images were made into a dataset for each image section of the matrix ordered from before deformation to final loading stage, and a shift correction was applied to each dataset to align the central features within the set of images. For the deformation calculations, a cross correlation relative to the first 86

87 image was applied and a sub-pixel grid size of between 8x8 and 16x16 pixels 2, dependence on the resolution of the speckle pattern, with a 0% overlap was used. No overlap was required because the fine speckle patterns do not change during deformation and the features remain finely spaced throughout deformation. The high density of speckles within each sub-region means there are sufficient features per sub-region to minimise the sub-region size without overlap. This increases the overall strain resolution that is possible and will accurately maximise the observed strain heterogeneity without the requirement for smoothing of the results. 3.7 Slip Trace Analysis Slip trace analysis is a technique that is utilised to predict the likely deformation systems that are active within a single grain. This prediction is made by comparing the results from the theoretical slip trace analysis with experimental results in the form of ECCI micrographs and/or HR-DIC strain maps. Before deformation EBSD were used to provide the orientation information for each grain. The University of Sheffield Materials Department have developed a Crystal Mathematical Tool, where the Euler angles are input to enable the calculation of Schmid factor and slip trace angles for all theoretical slip systems that are considered. The tool converts all theoretical slip systems, in terms of the slip plane and slip direction, into sample space and then calculates all the possible trace angles and Schmid factors for each system relative to the orientation of the single grain. The theoretical slip angles are cross correlated with the slip angles for individual grains from the experimental results to predict the likely active slip system. The experimental slip traces were measured using ImageJ software where the angles are measured in a range of Two readings were taken within each single grain to provide an average as the angle of the slip traces can differ slightly depending on the location within in the grain. It 87

88 should be noted that the experimentally measured angle are analysed separately from the theoretical data and the initial readings are recorded in a separate spreadsheet to remove the effect of any bias on the results and to ensure that the angles that are matched between the two data sets are reliable. The slip systems that are considered in the analysis are 3 basal, 3 prismatic, 6 pyramidal, 12 1 st order pyramidal and 6 2 nd order pyramidal. Twinning is not included in the analysis as these have not been observed from the strain mapping Slip Trace angle criteria Slip traces were identified from the HR-DIC results for single grains. Correlating the strain map with the raw EBSD data provides information regarding the likely slip system in terms of Schmid factor but does not give any information on the slip angles for each slip system to accurately predict the likely individual slip system. The criteria for determining whether the correct slip system has been identified are initially to ensure that the likely slip systems lie within 5. The mismatch between the theoretical and experimental results for the strong-macrozone condition and nomacrozone condition, respectively, for different angle criteria is identified in Figure 28. It can be observed that all grains lie within ±10 and more than 5 lie within 5. Less than 30 of the identified slip systems lie within 1 of the theoretical slip trace and for both materials over 60 of active grains lies within 3 criteria. It should be noted that in a nickel base superalloy, Knoche found many slip traces did not lie between 10 [95] and this was not a result of large misorientations across a single grain or misalignment between strain and EBSD images. Therefore one explanation for the better alignment in alpha grains in titanium alloys compared to the Nickel base superalloy may be due to the higher number of available slip systems 88

89 associated with the hcp crystal structure. This means that care must be taken in the interpretation of the results and further validation of the slip systems within single grains is required. A further explanation of how the active slip system was chosen in critical cases is described below. Figure 28- Angle mismatch criteria for (a) Strong-macrozone condition and (b) No-macrozone condition Slip Trace CRSS and Schmid factor criteria There are grains where more than one theoretical slip system may lie within 5 of the observed experimental slip trace. In these cases a number of parameters must be used to determine the likely slip system. The two key parameters that are used are CRSS for the slip system type based on historical data and the Schmid factor of the actual slip extracted from the slip trace analysis data. This method is not conclusive and further analysis is needed to determine whether this method is typically the most accurate way of predicting the slip system without the need for more detailed experimental analysis of the samples. This detailed analysis would be in the form of interpretation of diffraction patterns and slip traces within single grains for complex cases using detailed TEM studies. The CRSS parameter is based on literature values from [96], [97]. For this work, a conservative estimate of the CRSS ratio of 1:1:3:3:3 for prismatic: basal: prismatic: pyramidal : 1 st order pyramidal : 2 nd 89

90 order pyramidal was implemented. This is used in combination with the Schmid factor to predict the likely slip system. In cases where more than one slip system lie within 5, if these slip systems are basal and prismatic slip, the slip system with the highest Schmid factor is predicted to be the likely slip system. In cases where the Schmid factors for these two slip systems have similar Schmid factor values, each slip system is equally weighted in terms of the slip trace analysis and they are given a weighting of 0.5 each compared to the typical value of 1 for a definitive slip system. Although this is inconclusive it does provide a satisfactory method of including all grains within the analysis. In cases where the two slip systems that meet the angle criteria are basal or prismatic slip and pyramidal and/or slip a combination of CRSS and Schmid factor criteria is used to predict the slip system. The Schmid factor for the pyramidal and/or slip system is divided by the CRSS ratio taken to be 3 in this analysis, as shown in Equation 6. The normalised Schmid factor is then compared with the other slip systems to predict the likely slip system similar to the method described above for prismatic and basal slip. Once again, if the likely slip system is still not clear weighting criteria is applied. Equation An example of applying Schmid factor and CRSS criteria A detailed example of applying the Schmid and CRSS criteria to a single grain is shown below in Figure 29 for a grain where there are single slip traces that are low in shear strain in Figure 29a but can still be observed. It can be shown from Figure 29b that there are 5 unique slip systems that are a close match when overlaid on the experimental slip trace. To carry out a more detailed analysis of the active slip 90

91 systems all the Schmid factors and slip trace angles are extracted from the Crystal Mathematical Tool and the results for this particular case are shown in Table 5, where the slip systems that are a close match have their Schmid factor highlighted in red. One of the initial slip systems that were observed do not lie within the 5 angle criteria when the actual data values are compared to the experimental slip trace. Therefore there are only 4 unique possibilities in terms of the likely slip system and these are pyramidal, two 1 st order pyramidal and 2 nd order pyramidal. The pyramidal slip system has a Schmid factor of close to zero and is therefore disregarded but the other slip systems cannot be separated using Schmid factor or CRSS criteria as these similar. As a result of this all the systems are given an equal weighting out of 1 with the 1 st order pyramidal given a weighting of 2/3 and 2 nd order pyramidal given a weighting of 1/3. Figure 29- Slip trace analysis of a grain having faint slip traces as shown by the (a) maximum shear strain map and comparing the slip traces to (b) all possible slip traces for this grain 91

92 2 nd order Pyramidal Pyramidal Prismatic Basal 1 st order Pyramidal Table 5- Schmid factors and angles for each possible slip system with likely slip systems highlighted in red for grain shown in Figure 29 Measured angles Slip System Schmid Factor Angle Slip System Schmid Factor Angle Multiple different slip traces within a single grain There are cases where single grains can show numerous slip traces with different angles that are clearly a result of different deformation systems. The slip systems are 92

93 typically two different prismatic slip systems, but if the slip systems are different the weighting criteria is once again applied with each slip system being given an equal rating relative to the grains overall rating of 1. An example of two types of prismatic slip being the active deformation systems within a single grain is shown in Figure 30 and the Schmid factor analysis for the grain is shown in Table 6. A similar method was used to determine that the slip systems were both prismatic as that described for the slip system case above. In this case there are two different slip trace angles to be considered as shown in Figure 30a, where the slip traces in the strain map are compared to all possible slip systems in Figure 30b. This figure shows that there are numerous slip systems that overlay the slip traces but if just the prismatic cases are highlighted, as shown in Figure 30c, then it is evident that both slip traces match well with prismatic slip. However, the likelihood of prismatic slip must be confirmed using the raw data from the slip trace analysis. All possible slip systems that match the 5 angle criteria are highlighted in red in Table 6 and it can be seen that for both slip traces there are several possible slip systems that match. However, for the slip trace that is close to 116, the Schmid factor for prismatic slip is greater than 0.3 and all other possible slip systems are a pyramidal or slip system and therefore required a larger activation stress. Therefore using the normalised Schmid factor equation it can be predicted that the likely slip system is prismatic. For the slip that is near to 54 the Schmid factor for prismatic slip is significantly less and is 0.18, which means the slip system is not favourably oriented. However, all the other slip systems that fit within the angle criteria are once again pyramidal or type slip systems but more importantly have a Schmid factor of less than 0.15 in all cases. As a result of this, it is predicted that the likely slip system is prismatic slip because all other slip systems do not 93

94 appear possible despite the relatively low Schmid factor for prismatic slip. The slip trace angle match is within ±1. This grain is therefore predicted to have two prismatic slip traces. Figure 30- Slip trace analysis of a grain having multiple slip systems as shown by the (a) maximum shear strain map and comparing the slip traces to (b) all possible slip traces for this grain and (c) the predicted slip traces 94

95 2 nd order Pyramidal Pyramidal Prismatic Basal 1 st order Pyramidal Table 6- Schmid factors and angles for each possible slip system with likely slip systems highlighted in red for grain shown in Figure and Measured angles Slip System Schmid Factor Angle Slip System Schmid Factor Angle

96 Chapter 4 Material Characterisation The materials were characterised using the optical and scanning electron microscopes described in the experimental methods. The magnifications and EBSD parameters used to characterise the 3 materials were consistent throughout the current section to give a detailed comparison. The three materials have been provided by Rolls-Royce and are no-macrozones, intermediate-macrozone and strong-macrozone conditions, respectively. The three as received raw materials are shown in Figure 31 and are all Ti-6Al-4V alloys. The no-macrozone material was forged material that had not been exposed to any rolling and the material with intermediate-macrozones was uni-directionally rolled plate material. The material with strong-macrozones originated from extruded bar material intended for blade applications. The respective coordinate systems for the 3 materials are indicated in Figure 32 and these axes are used in the subsequent characterisation of the materials. 96

97 Figure 31- (a) No-macrozone condition, (b) intermediate-macrozone condition and (c) Strong-macrozone condition Figure 32- Orientation coordinate system for (a) No-macrozone condition, (b) Intermediate-macrozone condition and (c) Strong-macrozone condition 97

98 4.1 Optical Analysis The three different alloys have been characterised in terms of grain size and primary alpha volume fraction. These have been determined using the point counting and the linear intercept methods, respectively Volume fraction and grain size analysis The micrographs are presented in the extrusion and rolling direction plane for the etched condition for each material, respectively. The three materials provided all exhibited an equiaxed microstructure consisting of α p grains and small amounts of α s lamellae in the prior β grains at the grain boundaries, as indicated in Figure 33 by the micrographs of the samples after etching. For the no-macrozone condition, the average grain size was 7.0 μm with a volume fraction of approximately 88% for the α p grains and approximately 12 for the remaining β grains and α s lamellae. For the intermediate-macrozone condition, the average grain size was μm with a volume fraction of approximately 93 for the α p grains and approximately 7% for the remaining β grains and α s lamellae. The volume fraction of the α p grains and the average grain size for the strong-macrozone condition were an average grain size of μm and a volume fraction of approximately 91 for the α p grains and approximately 9 for the remaining β grains and α s lamellae. Figure 33-Etched micrographs of (a) No-macrozone condition (b) Intermediate-macrozone condition and (c) Strong-macrozone condition 98

99 The grain size analysis was taken from 2 different samples for each material to quantify the grain size across the materials. The no-macrozone condition had the smallest average grain size and the intermediate-macrozone condition had the largest average grain size. There was a difference of 3µm between the smallest and largest grain size. For the strong-condition the aspect ratio for the elongated grains was around a maximum of 1:3 in the extrusion direction but most grains show an aspect ratio of 2.5 or less. The results for the grain size and volume fraction analysis for each material show that all 3 material conditions exhibit similar microstructures other than the elongated grains in the strong-macrozone condition. This means the impact of these two characteristics on the mechanical performance during experiments will be minimal and mechanical performance can therefore be principally related to the nature of the macrozones in the microstructure Qualitative macrozone analysis The micrographs in Figure 34, Figure 35 and Figure 36 have been captured using polarized light to allow for the identification of macrozones in a microstructure in a qualitative manner for the no-macrozone condition, intermediate-macrozone condition and strong-macrozone condition, respectively. The actual orientations of the individual grains cannot be extracted from the micrographs but clusters and bands of grains with the same orientation will be visible due to the anisotropic nature of α-titanium and this is therefore a usual technique for identifying and measuring the macrozones in each material over a statistically representative region. To identify the macrozones using EBSD would take large amounts of microscope time but would give orientation information, so therefore the polarised technique is used to support and contextualise the information from EBSD rather than replace the technique. 99

100 No-macrozone condition Figure 34a, c and e are low magnification micrographs in each plane, respectively, for the no-macrozone condition and these indicate that there was little or no texture in all three planes because the grain size was observed to be almost the same in each plane and there are no clusters or bands within the micrographs. The high magnification micrographs in Figure 34b, d and f for each of the 3 planes show that there were also no low angle grain boundaries between grains in this material and there are no clusters of small grains with similar shades confirming there are nomacrozone regions. 100

101 Figure 34- Polarised light micrographs of the no-macrozone condition in the ND-TD, ND-FD and TD-FD plane on a(a), (c) and (e) macroscale and (b), (d) and (f) microscale, respectively Intermediate-macrozone condition Figure 35a and b in the ND-TD plane and Figure 35c and d in ND-RD planes on a low and high magnification scale and they show macrozone bands stretching through the microstructure that are parallel to the rolling direction. The low magnification micrographs in ND-TD plane show the macro bands that appear were more than a millimetre in length and were approximately 100µm in width. A similar trend was 101

102 observed in the ND-RD plane, as the macrozones stretch for several millimetres in the rolling direction. But the width of the macrozones were less apparent, with the macrozones appearing to be more broken up in the normal direction and in some cases the macrozone width appears to be single grains. It can also be observed from the high magnification micrographs of both planes that the grain boundaries in the ND-RD plane were more difficult to observe than in ND-TD suggesting that there was a higher density of lower angle grain boundaries on this plane. Figure 35e and f shows the polarised micrographs of the intermediate-macrozone condition in the TD- RD plane on a low and high magnification scale, respectively. These appear to indicate a random microstructure as there were no distinct bands or clusters present in this plane over large regions although small clusters of grains can be seen. 102

103 Figure 35- Polarised light micrographs of the intermediate-macrozone condition in the ND-TD, ND-RD and TD-RD plane on (a), (c) and (e) a macroscale and (b), (d) and (f) a microscale, respectively Strong-macrozone condition From Figure 36 for the blade material bar several pronounced macrozones were identifiable in the microstructure for each direction and had distinct characteristics. Figure 36a and b in the ND-ND II plane shows the region at a low and high magnification, respectively. The low magnification micrographs show macrozones with clusters of approximately 100x100mm 2 and the high magnification micrographs shows the grains within the clusters are common in colour and were therefore likely 103

104 to exhibit similar orientations. Figure 36c and d for the strong-macrozone condition in the ED-ND and Figure 36e and f in the ED-ND II directions shows micrographs on a low and high magnification scale. The macrozones are clearly observed as long vertical bands and for both planes stretch the full length of the micrographs. When analysed over several micrographs it can be seen that the macrozones stretch for several millimetres through the structure which is in agreement with the macrozones observed in [28], [43]. The width of the macrozone regions for this specimen varies between µm. It can be observed in the high magnification micrographs of these regions that the grain boundaries were faint and the grains are similar in colour, suggesting that these were low angle grain boundaries and similar grain orientations, respectively. 104

105 Figure 36- Polarised light micrographs of the strong-macrozone condition in the ND-ND II, ED-ND and ED- ND II plane on a(a), (c) and (e) macroscale and (b), (d) and (f) microscale, respectively 105

106 4.2 EBSD material characterisation The EBSD orientation maps in Figure 40 to Figure 42 have been acquired using macrotexture and microtexture scans with appropriate step sizes and magnifications to allow identification and analysis of the microstructures with a particular emphasis on quantifying the macrozones in each material. The results from the polarised light analysis have enabled particular planes to be focussed on in terms of the macrozones for each condition, respectively, and although macrotexture and microtexture EBSD analysis has been performed on all planes for each material only the planes that will be used in the mechanical performance experiments have been included in the figures No-macrozone condition The EBSD maps for the macrotexture and microtexture of the no-macrozone condition are shown in Figure 37. A combined beam and stage scan with a step size of 10µm was used to analyse the macrotexture and a beam scan with a step size of 0.8µm to analyse the microtexture. It can be observed that the in Figure 37a(i) that on a macrotexture scale there was no clear texture component and this was confirmed by the pole figure in Figure 37a(ii) with a random texture of ~2. The microtexture EBSD map in Figure 37b (i) displays the grains more clearly and it can be seen that there is a weak texture with very few neighbouring grains with a similar orientation. The trend for the pole figures on a microtexture scale was the same as that for the microtexture and is shown in Figure 37b (ii) with maximum texture intensities of 2 times random. This shows that for this condition although there is no clear texture component and that there is similar texture intensity on the macroscopic and microscopic scale, indicating no mesoscopic texture is present. Therefore this material will act as a reference microstructure in terms of mechanical properties and 106

107 scatter in factors such as fatigue life compared to the more clearly defined macrozone materials. Figure 37- (i) EBSD orientation maps and (ii) (0002) and pole figures of the no-macrozone material in terms of (a) macrotexture and (b) microtexture in the ND-FD plane Intermediate-macrozone condition The EBSD maps for the macrotexture of the intermediate-macrozone condition are shown in Figure 38 where a combined beam and stage scan with a step size of 10µm was used to analyse the texture of the intermediate-macrozone condition in the key direction as seen from polarised light microscopy, which is the ND-TD plane. The macrozones within this specimen run parallel to the rolling direction for several millimetres and are approximately 100µm in width, these findings are similar to the results for similar material found by [22]. The regions containing macrozones can be seen in Figure 38a (i) by the large regions that are blue in colour. By examining the pole figure in Figure 38a (ii) it can be observed that in the regions containing macrozones, the c-axis was oriented parallel to the transverse direction. On a microtexture scale in Figure 38b (i) and (ii) with a finer step, the same texture nature was observed but the pole figure indicates a higher intensity. This means the grains within the macrozone will have a strong common orientation. When analysing the 107

108 macrotexture in the intermediate-macrozone condition on a larger scale in Figure 38c(i) and (ii) to give a representation of the overall texture. It can be observed that the overall texture of the sample including the macrozones and the neighbouring regions was 7 times random, the texture in the macrozone region was 14 times random and the texture in a no-macrozone region was approximately 3 times random. This gives an indication of the strength of the texture and that the macrozones bands in this material were separated by similarly sized bands with a random orientation. The EBSD maps for the microtexture of the intermediate-macrozone condition are shown in Figure 39 where a combined beam and stage scan with a step size of 0.5µm was used to analyse the texture within different single macrozones of the rolled plate in the ND-TD plane. A matrix of 6x3 separated grids, shown in Figure 39a, was used to analyse the texture on a microtexture scale to allow detailed information on the actual macrozone bands to be gathered. Each single region covers a region of approximately grains. 4 EBSD maps from the matrix have been selected in Figure 39b-e, to show the different degrees of texture in the macrozone and nomacrozone regions and also to highlight the width of the macrozones. The texture in Figure 39b and c shows a relatively low local intensity with 8-9 times random but no distinct textures and a high likelihood that single large grains are influencing the pole figure intensities. Figure 39d and e indicates the strength of the texture in the macrozone regions with texture intensities at a high of 28 times random and the same texture that was described earlier with a transverse texture. The macrozones are the blue regions in the two figures and Figure 39d displays a very thin macrozone with a width in the normal directions of 25μm but a strong common orientation in the macrozone. This was compared to Figure 39e where the macrozone retains the strong 108

109 texture but in this case has a width of μm in the normal direction. From this the observation can be made that on a microtexture scale the macro bands have a strong texture but are separated by regions with a relatively random orientation, this was likely to lead to areas that exhibit local strain heterogeneity. The scale of the strain heterogeneity is likely to be influenced by the width of the macrozone as this could lead to a greater build up of dislocations at the macrozone boundary if it was favourably oriented for slip. Figure 38- (i) EBSD orientation maps and (ii) (0002) and pole figures of the intermediatemacrozone condition material in terms of (a) macrotexture, (b) microtexture and (c) macrotexture across 4x1mm 2 in the ND-TD plane 109

110 Figure 39-(a) Matrix stitch of the regions analysed in terms of microtexture for the intermediatemacrozone condition in the ND-TD plane. (b)- (e) EBSD microtexture orientation maps and (0002) and pole figures in the macrozone and no-macrozone regions Strong-macrozone condition The EBSD maps for the strong-macrozone condition on a macrotexture and microtexture scale are shown in Figure 40 for the ED-ND plane and on a 110

111 microtexture scale in Figure 41 for the ND-ND II planes and were produced using combined beam and stage jobs. Figure 40a (i) shows the characteristic macro bands observed in the polarised light micrographs for both the ED-ND and ED-ND II planes were also clearly visible in the EBSD map. The macrozones were wider than suggested by optical microscopy as they were approximately 200µm in width but continue to stretch throughout the material in the extrusion direction. The pole figures in Figure 40a (ii) show the strength of the texture in this direction on a macrotexture scale was approximately 16 times random and the c-axis was aligned perpendicular to the extrusion direction as indicated by {0001} pole figure. The {10 0} pole figure indicates that the prismatic planes have a strongly fixed c-axis. This means they had a preferred crystallographic orientation. On a microtexture scale the results are shown in Figure 40b (i) for the ED-ND plane and were produced with a step size 0.1 times the grain size to gather detailed information on the grain orientations. The results are similar to those described on a macrotexture scale, except that within the macrozone bands it can be observed that there were individual grains within the macrozone region that do not have a common orientation and therefore had a significantly higher angle grain boundary. Also the contribution of the macrozone regions to the overall texture was significant and this is shown in Figure 40c (i) where only the texture in the macrozone region will be calculated. The contribution of the macrozone in the ED-ND plane was shown by comparing the pole figures in Figure 40b(ii) and Figure 40c(ii), which compares the microtexture in the overall sample and the macrozone region only, respectively, in terms of the {0001} and pole figures. The texture in the macrozone region only once again shows that the basal plane was perpendicular to the extrusion direction and has a texture of 24 times random. This was in comparison to 12 for the whole sample and 111

112 emphasises the common orientation in the macrozones that can be seen from the micrographs. The macrotexture analysis across the ND-ND II plane indicates that the c-axis was aligned parallel to the extrusion direction but the texture is weaker than the macrotexture observed in the ED-ND plane as it is only 6 times random. The microtexture EBSD map for the strong-macrozone condition in the ND-ND II planes was shown in Figure 41a (i) and a single macrozone cluster was observed and this was similar to those reported in the ND-ND II plane using the polarised light micrographs. The shape of the macrozone is elliptical and often elongated in either the ND or ND II direction. This gives rise to the likelihood that if the macrozones within the material were analysed using 3D EBSD, they would have a straw like appearance along the extrusion direction. 112

113 Figure 40- (i) EBSD orientation maps and (ii) (0002) and pole figures of the strong-macrozone condition material in terms of (a) macrotexture, (b) microtexture and (c) microtexture in a macrozone region in the ED-ND plane 113

114 Figure 41- (i) EBSD orientation map and (ii) (0002) and pole figures of the strong-macrozone condition material in terms of (a) microtexture in the ND-ND II plane EBSD orientation maps and normalised pole figures for all conditions The microtexture for the 3 conditions was compared in the reference plane for DIC analysis; this comparison will be made by normalising the pole figures to the maximum texture value of the material exhibiting the strongest texture. Only the microtexture pole figure was shown in this case as the regions for DIC analysis will 114

115 only cover regions of 500x500µm 2 and this will be one or two macrozones in most cases. The material showing the strongest texture was the strong-macrozone condition with a texture of 15 times random. The analysis in Figure 42 shows the comparative EBSD orientation maps for the 3 conditions with grain boundaries with a misorientation larger than 30 present on the map and pole figures normalised to the maximum of the strong-macrozone condition. As has been described previously for the 3 different materials that the strong-macrozone condition exhibits the strongest overall texture with the c-axis perpendicular to the extrusion direction, the intermediate-macrozone condition exhibits a weaker texture that was significantly different as the material has a strong transverse texture and the no-macrozone exhibited no strong texture component. The additional information that can be gathered from the micro maps was the grain boundary angles in the macrozone and no-macrozone regions, due to the reduced step size providing detailed information on the individual grains. The micro maps were set up to identify grain boundary misorientations of 30 or more. It can be seen clearly that in the location of the macrozone for the strong-macrozone condition in Figure 42a there was a high density of low angle grain boundaries and in the nomacrozone region there was a high density of high angle grain boundaries. A similar relationship is observed for the macro band in the intermediate-macrozone condition in Figure 42b but the macrozone was narrower and there was a greater density of high angle grain boundaries, due to the irregularity of the macrozones. For both processing conditions there was a higher density of high angle grain boundaries in the no-macrozone regions, this means it is likely that the likelihood of slip transfer is reduced. The no-macrozone condition shown in Figure 42c exhibits no distinct 115

116 regions with a high density of low angle grain boundaries and nearly all grains appear to have high angle grain boundaries. In summary the 3 different materials will provide an opportunity to obtain a detailed understanding of the macrozone effect on strain heterogeneity in the material, as the no-macrozone condition will act as the reference material as it has no-macrozones. The plate material (intermediate-macrozone condition) will have hard unfavourably oriented macrozones because the loading direction will be parallel to the c-axis of the macrozones therefore they will be hard oriented for slip. This is likely to initiate strain localisation in the neighbouring regions. Finally, the strong-macrozone condition will have soft favourably oriented macrozones because the loading direction will be perpendicular to the c-axis of the macrozones therefore they will be soft oriented. This will show the effect of strain localisation in the macrozone region. 116

117 Figure 42- EBSD orientation maps of (a) no-macrozone (b) intermediate-macrozone and (c) strong-macrozone materials in terms of (i) macrotexture maps with a 10µm step size, (ii) microtexture maps with a step size of 0.5µm and (iii) microtexture {0001} and pole figures 117

118 Publication 1 Microscopic strain localisation in Ti-6Al-4V during uniaxial tensile loading D. Lunt, J. Quinta da Fonseca, D. Rugg, M. Preuss Note: The material was provided by Rolls-Royce with three distinct microstructures. David Lunt carried out the characterisation of the microstructure and subsequent tensile loading experiments. The initial setting up of the tensile loading experiments and insitu DIC were accomplished together with Rebecca Sandala and Grant Klimaytys. David Lunt wrote the first draft of the proposed publication. Publication prepared for Material Science and Technology 118

119 Microscopic strain localisation in Ti-6Al-4V during uniaxial tensile loading D. Lunt 1, J. Quinta da Fonseca 1, D. Rugg 2, M. Preuss 1 1 Material Science Centre, University of Manchester, Manchester, M13 9PL, UK 2 Rolls-Royce PLC, Elton Road, PO Box 31, Derby, DE24 8BJ, UK Keywords Titanium alloys, Macrozones, Tensile, EBSD, DIC, Plasticity Abstract The titanium alloy Ti-6Al-4V is investigated in terms of the effect of macrozones within the microstructure through cross correlation of local strain measurements and microstructure, using digital image correlation (DIC) and electron backscatter diffraction (EBSD) techniques. Three different product forms of Ti-6Al-4V including strong, intermediate and a no-macrozone condition with a weak texture have been investigated focusing on the impact of the primary macrozone orientation, macrozone dimensions and loading direction. Strain localisation was characterised at the microscale using optical microscopy during in-situ uniaxial tensile loading and analysing the recorded images using digital image correlation. The no-macrozone material and the strong-macrozone condition loaded parallel to the macrozones exhibited homogeneous strain behaviour in both the elastic and plastic strain regions. The strong (soft-orientated) macrozone condition loaded at 45 and 90 and the intermediate (hard-oriented) macrozone materials both exhibited heterogeneous strain behaviour in grains with their c-axis oriented perpendicular to the loading direction. The strong-macrozone material showed a direct correlation between macrozones with their grains favourably oriented for prismatic slip and high strain 1

120 regions when loaded at 45 to the elongation direction. Correlating strain maps to Schmid factor suggested a likelihood of basal slip when loading at Introduction Titanium alloys are widely used in the aerospace industries due to their high specific strength, corrosion resistance, suitability for moderate temperature applications and good fatigue performance [1]. The workhorse alloy for aerospace applications is Ti- 6Al-4V, which is a two-phase, α+β Ti-alloy. During thermomechanical processing below β-transus temperature, a bimodal microstructure is produced as this provides the best balance between fatigue strength and creep resistance in the alloy [2]. However, during the β to α phase transformation it has been demonstrated that as a result of the retention of large prior β grains during processing [3] and variant selection [4], [5] there are large macrozones in the subsequent microstructure and these have been shown to cause scatter in the fatigue life [6]. A macrozone is a set of neighbouring individual grains with a common crystallographic orientation that could potentially create structural regions within a microstructure that are larger than the average grain size [7] [10]. Grain size is a key factor in the mechanical properties of titanium alloys, but microstructures exhibiting macrozones would be expected to behave similar to alloys that have a grain size distribution with several grains at the high end of the distribution. This is because low angle boundaries between similarly oriented grains are more likely to result in easy slip transfer. The common orientation also means that soft or hard oriented macrozones will contain many neighbouring grains where slip occurs more easily or is more difficult, respectively. During plastic deformation a soft oriented region might undergo a greater level of strain than a hard orientated region, which in return 2

121 will carry a higher level of elastic strain [11]. If such regions are very small, i.e. small grain size level, the significant constraint imposed by the hard grain on the soft grain will reduce the level of plastic deformation in the soft grain. Miao et al [12] found that a region in a Ni-based superalloy with large grains in the microstructure exhibited increased strain localisation and a higher density of crack initiation sites than a region in the alloy with a regular grain size distribution. In Waspaloy, fatigue crack initiation was shown in or at grain boundaries of grains that were significantly larger than the average grain size [13]. A similar relationship was observed by Le Biavant et al in titanium alloys with large macrozones up to 1 mm in diameter, that were subjected to fatigue loading [8]. It was observed that there was a high density of crack initiation sites within a single macrozone region and it can therefore be described as deforming as one single unit with less constraint rather than individual grains. Consequently, it is likely that materials containing fine-grained macrozone could potentially display fatigue behaviour closer to a coarsely grained material than a fine-grained one, causing scatter in the fatigue life. Soft oriented grains are favourably oriented for slip and hard grains have an unfavourable orientation. In hexagonal close-packed metals slip occurs along the and the slip directions. The easier slip direction for titanium alloys is the type direction. It can be found on the basal plane, the three prismatic planes and the six pyramidal planes. In titanium alloys, the type Burgers vector is larger than the type meaning slip is more difficult to activate along this direction [14], [15]. Basal and prismatic type slip are regarded as the easier slip modes with the type mode considered to be ~3 times more difficult [16]. 3

122 To study the local strain behaviour the use of digital image correlation (DIC) on microstructural images recorded during mechanical loading is becoming increasingly popular. The DIC technique enables full-field displacement and strain mapping across an imaged region [11], [17] [25]. The principle behind DIC is the tracking of features on 2 images of the same region before and after deformation. The images are divided into sub-regions and then the relative displacement of the features within a single sub region is cross-correlated with respect to an image of the same region at a different loading condition. The displacement vectors for the entire image are then differentiated to give the strain tensors [17]. The resolution of the DIC is affected by a number of factors, which are mainly the resolution of the microscope, image capture settings, speckle pattern size and nature and sub-grid sizes for data processing [11], [17], [21], [23]. Optical microscopy is typically implemented for micro/macroscopic scales while electron microscopy imaging potentially allows strain mapping at the nanometre scale. A potential issue of high spatial resolution strain mapping is the limited number of grains that are studied in such case. This problem becomes particularly apparent when studying macrozones in Ti alloys that typically expand across several hundreds of microns. The benefits of using optical rather than electron microscopy to enable full-field strain mapping through DIC is that simple etching of an polished surface might be sufficient for undertaking successful image correlation and the simple set up allows fast image capture avoiding potential artefacts that might result from slow scanning techniques in an electron microscope. Hence, optical microscopy in combination with mechanical loading seems a suitable tool for mapping strain localisation at a scale that is particularly suitable for enhancing understanding of the effect of macrozones on mechanical performance. 4

123 2. Experimental procedures 2.1 Starting materials The materials used in this study were three different product forms of Ti-6Al-4V, all provided by Rolls-Royce plc. The product forms are defined as strong-macrozone, intermediate-macrozone and no-macrozone materials as they all exhibit different degrees of macrozones and have an equiaxed microstructure. The material with strong-macrozones originated from extruded bar material intended for blade applications while the material with intermediate-macrozones was uni-directionally rolled plate material. The no-macrozone material was forged material that had not been exposed to any rolling. Specimens for tensile testing and microstructural characterization were extracted from the alloys with the aid of electric discharge machining. The recast layer was removed through grinding. The geometry of the tensile specimens was flat with 26 mm in gauge length, 3 mm in gauge width and 1 mm in thickness. The tensile test specimens were hand polished on an OPS cloth with colloidal silica for 3 h after initial polishing to #4000 grit paper. The etching pattern was applied to the sample using Kroll s reagent for approximately 60 seconds. The etched pattern provides the necessary features for successful DIC because of the preferential attack of grain boundaries. The microstructures were studied optically using a Zeiss microscope with a cross-polarised differential interference contrast filter and a polarised prism to estimate the dimensions of the macrozone regions, and to observe whether the pattern applied to the specimen for DIC was suitable. A micro hardness indent grid was applied to each specimen to allow the DIC region to be identified before and after testing, as well as to enable grain orientation mapping by electron backscatter diffraction (EBSD) of the same region. EBSD analysis was performed in 5

124 a field emission gun (FEI Quanta 650) scanning electron microscope (SEM) equipped with an AZtec EBSD system and a Nordlys II detector. EBSD scans were performed at an operating voltage of 20 kv. An area of 4 x 4mm 2 using a step size of 10μm was used for macrotexture analysis. For microtexture scans a step size of 0.5μm and an area of 0.5 x 0.5µm 2 were used. The data (confidence index > 0.1) were analysed using HKL Channel 5 TM software. Due to very small size of the β ligaments between grains the phase was not considered during orientation mapping. 2.2 Local strain measurements In-situ loading experiments were conducted using a Kammrath-Zeiss 5kN microtester installed on an optical microscope with a fixed stage. The microtester was controlled using DDS software and the load data was converted to stress and compared to the strain data at each load step to produce stress-strain curves. The samples were held at each load increment to record images for DIC purposes. The images for DIC were acquired with a DaVis Axiocam connected to a computer equipped with DaVis 7.2 software to handle and process the images. Figure 1 is a schematic of the process used to acquire the strain maps from the raw images and indicates the main processing parameters that were optimised. The images taken were 2032x2032 pixels 2 and were acquired at a rate of 2 per second. At each load increment 15 images were taken and averaged to minimize the error from the CCD camera caused by change in intensity at each pixel over time [17]. The stage of the microtester is height adjustable to allow for real-time focus adjustment and real-time image capture during interrupted tensile loading. The images captured were reduced to 1000x1000 pixels 2 in order to have the desired range of between 4 and 16 pixels 2 for individual features that can be followed by DIC [17]. A sub region grid size of 6

125 32x32 pixels 2 with a 50% overlap was used to gain strain information about the sub regions. The sub region grid size in real terms was 36x36µm 2, equating to a grid containing 9-16 grains that is 3-4 grains wide. In terms of the macrozones in this study they typically have a width of grains for the strong-macrozone condition and grains for the intermediate-macrozone material, meaning that the chosen spatial resolution enables the detection of any heterogeneous strain behaviour related to macrozones. The overlap maintains the spatial resolution, while allowing a bigger sub-region to be used [26]. The images are divided into sub-regions and the relative displacement of features is computed across the whole image. Once the displacements have been computed they can be differentiated to obtain strain values. The resolution of the optical DIC method is limited by the pattern being the etched grain boundaries, i.e. the highest resolution is restricted to single grain boundaries. In reality the resolution of the pattern for this system is approximately 2-3μm, as indicated in Figure 2. In order to study the relationship between crystallographic orientation of macrozones in respect to the loading direction and strain maps during elastic and plastic behaviour, the DIC strain maps were compared with the corresponding orientation maps recorded by EBSD. It should be noted that due to the grains being elongated in the strong-macrozone material, the spatial resolution of the strain maps is worse along the length of the grains, which are usually aligned with the macrozone. After deformation, the samples were OPS polished for 10 minutes to remove the etching pattern used for image correlation purposes. The removal of the pattern reveals the deformed sample surfaces and images were then taken with a Nikon Digital SLR camera with a 100 mm macro lens to show the macro-scale deformation. 7

126 3. Results Optical micrographs were taken for the 3 conditions as shown in Figure 3 and the images were used to deduce the primary volume fractions and grain sizes that are listed in Table 1 together with estimated accuracies. The quantitative analysis of each condition is based on ~ 250 grains. The microstructure for the no-macrozone condition shown in Figure 3a indicates equiaxed grains with the phase concentrated at the grain boundaries and triple points between grains. A similar morphology is observed for the intermediate-macrozone condition in Figure 3b with the only difference being that the phase appears more aligned in terms of the grain boundaries in the intermediate-macrozone condition. The strong-macrozone condition shown in Figure 3c indicates elongated grains particularly within and along the direction of the macrozones. Table 1 shows that primary volume fractions and average grain sizes for the 3 conditions are all comparatively similar (88% and 93% and 7μm and 10μm, respectively). Therefore, it can be assumed that any differences in heterogeneous strain behaviour for the three conditions can be related to the presence or absence of macrozones rather than grain size and volume fraction effects. 3.1 Microstructure and Texture Figure 4 shows macro orientation maps recorded by EBSD with a step size of 10μm and the corresponding and pole figures of the three product forms of Ti-6Al-4V. The no-macrozone material displays a relatively weak texture with a maximum intensity of 5 times random on the pole figure, Figure 4a. Figure 4b shows that the intermediate-macrozone material exhibits dispersed macrozones in the NT-TD plane that stretch for approximately 500μm in length along the transverse direction and are 50 µm in width in the normal direction. The respective pole figures 8

127 show that the primary texture component has the c-axis aligned parallel to TD and the {0002} pole figure intensity is around 8 times random. Further analysis showed that the sporadic macrozones do dominate the observed texture. Hence, in the case when the material were loaded parallel to the transverse direction the macrozones will have their c-axis preferentially parallel to the loading direction and hence the macrozones should appear as hard regions. Figure 4c shows very pronounced macrozones stretching along the extrusion direction (ED) for millimetres and approximately 200 µm in width along the normal direction. The pole figure is strongly dominated by the macrozones with the c-axis aligned perpendicular to ED and the intensity approximately 16 times random. In addition, the pole figure shows that there is a strongly preferred crystallographic orientation of the prismatic planes giving a distinct crystallographic orientation. Figure 4d focuses specifically on the non-macrozone region and highlights the more random nature of the texture (note the different scale bar). Considering this distinct orientation of the macrozones, it is clear that depending on the loading direction the macrozone could either behave like a soft or a hard region. 3.2 Strain Mapping Tensile tests were performed along the forging direction (FD) in the case of the nomacrozone material. For the intermediate-macrozone condition the material was loaded along TD as this allows the impact of hard oriented macrozones to be studied. The strong-macrozone condition was loaded in the ED-ND plane and at 0, 45 and 90 to ED, respectively. Optical micrographs were recorded at progressive strains in the elastic and plastic region, to maximum strains of between 5-10%. Stress-strain curves were constructed 9

128 from each loading experiment by combining load cell data from the micro tester with averaged strain data from the DIC analysis, Figure 5. The maximum tensile strengths and yield strengths for each material are shown in Table 1. Figure 5a and Table 1 demonstrate excellent agreement of the elastic response for the three conditions providing great confidence in the accuracy of the strain analysis. Figure 5b highlights the plastic behaviour and the respective yield points of the different conditions and it can be observed that all conditions appear to show similar work hardening behaviour but have different yield points. The no-macrozone condition and the strong-macrozone condition loaded at 0 are the two softest materials followed by the intermediate-macrozone condition. The strongest response is displayed by the strong-macrozone condition loaded at 45 and 90. Macrographs of the tensile samples with the strong-macrozone after deforming 0, 45 and 90 to the loading direction are shown in Figure 6. The deformation bands on the surface of the samples appear to be always parallel to the macrozones and are comparable in width to the width of the macrozone regions. In all three cases, the deformation bands clearly pass throughout the gauge volume suggesting that each macrozone is deforming as a single structural unit. The shear strain localisation characterised by DIC is related to the microstructure through correlation with basal and prismatic Schmid factor maps computed from EBSD data in Figure 7, ~2.5% applied strain. For the no-macrozone condition it can be observed from the strain map in Figure 7a (i) that the strain behaviour across the entire region is homogeneous at the microscale. Therefore, the prismatic and basal Schmid factor maps in Figure 7a(ii) and (iii) cannot be correlated to any strain pattern. The intermediate-macrozone condition shows some strain hot spots on the 10

129 strain map in Figure 7b (i), which cannot be correlated with the prismatic and basal slip Schmid factor maps in Figure 7b (ii) and (iii). The strong-macrozone condition loaded with the macrozones parallel to the loading direction (0 ) exhibits a similar homogeneous strain pattern as the no-macrozone condition, Figure 7c (i). This is despite the Schmid factor maps, showing a large macrozone region that has grains well orientated for prismatic slip, Figure 7c (ii). In contrast, when the macrozones are loaded at 45, the strong-macrozone material exhibits clear heterogeneous strain behaviour, Figure 7d (i). By correlating the strain map with the Schmid factor maps for prismatic and basal slip in Figure 7d (ii) and (iii), respectively, it can be observed that the well developed strain bands coincide with regions that are well orientated for prismatic but not basal slip, particularly in the case of the strongly developed strain band that stretches across the centre of the strain map. It should also be noted that the bands that show less strain also appear to have a low density of grains that are favourably oriented for prismatic slip. The strong-macrozone material loaded with the macrozones orientated 90 to the loading direction also exhibits heterogeneous strain behaviour and strain localisation within a macrozone region as can be observed from the strain map in Figure 7e (i). There is a single high strain region (band) stretching along ED with a neighbouring region of very low strain. Here, the prismatic and basal Schmid factor in Figure 7e (ii) and (iii) show that the high strain band corresponds to a macrozone favourably oriented for basal slip and unfavourably oriented for prismatic slip. The strain accumulation at progressive loading steps is displayed in Figure 8 in terms of frequency plots for each loading step and the colours of the individual loading steps correspond to approximately the same average strain. Initially, all material conditions and loading directions display similar homogeneous strain behaviour 11

130 during elastic loading resulting in sharp peaks in Figure 8a-e. Once plastic deformation takes place the shear strain distribution widens noticeably but now also significant differences can be seen between microstructures and loading conditions. The no-macrozone condition in Figure 8a shows relatively gradual broadening of the shear strain distributions with increasing overall shear strain. The intermediatemacrozone condition shows a relatively similar behaviour, Figure 8b, although the shear strain distributions seem somewhat wider in the plastic regime than for the nomacrozone region. The strong-macrozone material loaded parallel to the macrozone direction displays again a similar picture but with the sharpest shear strain distributions in the plastic regime, Figure 8c. In the case of the strong-macrozone material loaded at 45 and 90 to the macrozones, Figure 8d and e display very early broadening of the shear strain distribution that develop a very large range in shear strain for each load step as the material is further strained. For instance, the 45 condition displays a shear strain range of approximately 2% at 3.1% average shear strain. The 90 condition develops bimodal shear strain distributions from an average shear strain of 1.5%. The two peaks both have a similar range of strain but the low strain peak has a greater distribution than the high strain peak. The overall strain distribution behaviour for all conditions and loading directions is summarised in Figure 9 at 3% average shear strain. It can be seen that the nomacrozone and strong-macrozone condition loaded parallel to the macrozones show similar peak shapes and heights indicating the homogeneous nature of the strain distributions. The other 3 conditions exhibit wider frequency curves and this highlights the heterogeneous strain behaviour. 12

131 4. Discussion Both the no-macrozone material and the strong-macrozone condition loaded at 0 exhibited homogeneous strain behaviour at the microscale. The intermediatemacrozone condition exhibited some degree of heterogeneous strain behaviour while the strong-macrozone condition loaded at 45 and 90 both displayed pronounced heterogeneous strain behaviour with favourably oriented regions correlating to high strain regions. By comparing these observations with the stress-strain curves presented in Figure 5, it becomes apparent that the materials with the highest yield stress exhibit the strongest heterogeneous strain behaviour while homogenous strain behaviour seems to give the lowest yield stress in the present study. This however is related more to the overall texture of the material and the respective loading direction. The intermediate and strong-macrozone conditions display pronounced basal textures, which soften the intermediate-macrozone condition when loaded along ND and strong-macrozone condition when loaded at 0. In contrast, when the strong-macrozone condition is loaded at 45 or 90, the majority of the grains are rotated from a soft to a hard orientation. Further, the intermediate-macrozone condition displayed a modest level of strain heterogeneity at the microscale, which cannot be correlated to the macrozones within the microstructure. In contrast to the strong-macrozone conditions, the intermediatemacrozone condition display comparatively small and individual macrozones, which do not extend through the thickness of the sample. In addition, the macrozones are orientated in respect to the loading direction that they are hard regions. The strain hot spots that are observed contain several neighbouring grains to the macrozone that have a primary orientation with their c-axis perpendicular to the loading direction, i.e. soft orientation. Hence, while the macrozones, or the regions in-between, cannot 13

132 be directly identified in the strain maps, the macrozones still enhance the heterogeneity of the strain response. For the strong-macrozone condition all three loading directions appear to show distinctive strain behaviour relative to the underlying microstructure. Figure 10 depicts the strain accumulation across the material for 0, 45 and 90 loading conditions to give a representation of when the onset of the heterogeneous strain behaviour begins. The normalised position is the position along the corresponding strain image depicted under the figures. The shear strain lines in Figure 10 were drawn perpendicular to the macrozone direction. Therefore, in the case of the 0 loading condition, the normalised position represents a direction transverse to the loading direction while for the 90 loading condition the direction the line was drawn is parallel to the loading direction. Accordingly, Figure 10a shows almost no shear strain variation during the early stage of plasticity and only some at high average strain levels of 8%. Note that such large overall plastic strain is not observed during typical fatigue loading conditions, which is one of the drivers to understand better strain heterogeneity. For the 45 and 90 loading condition, shown in Figure 10b and c, respectively, a key observation from the high strain macrozone regions are that the trend for strain localisation develops early in the loading regime, i.e. after only very small amounts of plastic strain. Similar observations were made by Littlewood and Wilkinson [11] during strain mapping of Ti-6Al-4V. Therefore, these conditions and their resulting strain localisation are more likely to have a detrimental impact on some fatigue loading conditions. The significant strain variations for the 45 and 90 condition begin at approximately 0.7% and 0.8% average strain, respectively, and the trend then continues to progress and becomes even more pronounced with increasing load/average strain. When loaded into the plastic regime, 1.5% strain, the 14

133 strain behaviour develops a heterogeneous nature. In the case of the 45 loading condition, there is a clear correlation between high strain bands and macrozones with their c-axis oriented perpendicular to the loading direction. This was also observed by Le Biavant et al [8] where macrozones well orientated for slip accommodated significantly plastic strain than the regions in-between. They also found that the strain heterogeneity between the two regions increases with continued loading. In order to relate the crystallographic orientation of the strong-macrozone condition to the strain mapping conditions, the prismatic and basal Schmid factors have been compared across two neighbouring regions that contain differently oriented macrozones for each of the 3 loading conditions, Figure 11. In principle, the strongmacrozone condition shows a strain response not unlike a fibre reinforced composite material. When the loading direction is parallel to the macrozones the two distinct regions have to deform together and consequently, no microscale strain heterogeneity is observed. In addition, by analysing the Schmid factor distributions of the macrozone and non-macrozone regions, it also becomes apparent that all regions are well aligned for prismatic or for basal slip, Figure 11a. Therefore, the macrozone and non-macrozone regions can both be considered soft under this loading condition, which further explains the low strain heterogeneity and low yield stress. In the 45 loading condition the strong-macrozone material exhibits pronounced heterogeneous strain bands that can be related to the macrozone and non-macrozone regions. In Figure 11b, the macrozone region shows a high frequency of grains well aligned for prismatic slip and it is this region that displays the high strain. In contrast, the non-macrozone region exhibits an even distribution of the Schmid factor for prismatic slip while there is a clear trend for grains being well aligned for basal slip. 15

134 Similar observations have been reported previously by Padilla et al for strongly textured Zirconium that was compression tested [19]. Here compressive strain concentrations were observed in the neighbouring grains favourably oriented for prismatic slip. It should be noted that the macrozone region also displays a slightly increased number of grains with a high Schmid factor for basal slip but one would assume that prismatic slip is likely to be the more dominant of the slip systems due to its slightly lower CRSS value [16]. Loading the strong-macrozone condition at 90 results again in pronounced heterogeneous strain behaviour strongly correlated to the macrozone and nonmacrozone region. However, surprisingly, it is now the non-macrozone region that does show high strain, Figure 11c. In contrast, the neighbouring low strain region is favourably oriented for prismatic slip. Closer investigation of the non-macrozone region reveals that it is rather unusual compared to the non-macrozone region shown in Figure 4 as it shows a strong texture with the basal pole tilted by about 45, as illustrated by the {0001} pole figure in Figure 11d. Consequently, the grains are favourably orientated for basal slip while the macrozone is well aligned for prismatic slip. At first glance, this observation seems to contradict the findings for the 45 loading condition. However, the normalised frequency plot for the 90 loading condition shows a very high Schmid factor peak between for basal slip, which suggests that the non-macrozone region does in fact have extremely well aligned grains (and as such is more another macrozone than a non-macrozone). As mentioned earlier, the area studied in this particular tensile sample was unusual in terms of its non-macrozone region. However, it demonstrates that rather than the CRSS of prismatic and basal slip, it is the misorientation within these regions and the level of high Schmid factors that makes them either relative soft or hard. 16

135 The link between the stress strain behaviour and the nature of strain distribution has been highlighted previously. Table 2 summarises the average Schmid factor for prismatic and basal slip across the analysed strain region covering at least 3000 grains. The three conditions that exhibit heterogeneous strain and overall high yield stress show a lower Schmid factor for prismatic than basal slip and in addition the average Schmid factor for both slip modes also tends to be lower compared to the nomacrozone and strong-macrozone at 0 conditions, which display relatively low yield stresses. Both the 45 and 90 loading directions show significant strain localisation at the microscale relative to macrozones and non-macrozone regions and the high strain regions stretch along the entire length of those regions. At a microscale, the strain localisation in the favourably oriented macrozone appears as a single band of high strain covering the entire macrozone region with little difference in strain across the band. It is beyond the remit of the present paper to investigate strain heterogeneity on the nanoscale, which is at a scale that allows the actual slip traces to be resolved. Using the present approach, it has been observed that, depending on the type of microstructural heterogeneity and loading direction, there can be large differences in strain localisation at overall strain levels that are typically observed during for instance low cycle fatigue loading. These strain heterogeneities are likely to create compatibility issues between the two regions that will impact on the fatigue performance of such material. As in the case for the strong-macrozone 45 and 90 loading conditions the boundaries between macrozones and non-macrozones would be subjected to significant stress concentrations and are therefore potential sites for early crack initiation and high crack densities. Wilkinson and Littlewood [11] observed crack formation in a single region where a grain well oriented for slip 17

136 deformed intensely to allow neighbouring unfavourably oriented grains to remain non-deformed. Scaling this up to take into account large favourably oriented macrozones neighbouring poorly oriented regions is likely to create a high density of closely located potential crack initiation sites. On the other hand, a strong macrozone-region might be benign if loaded in a direction that does not create heterogeneous strain between the two different regions. However, such arrangement might still show a more detrimental slip localisation at the nanoscale. 5. Conclusions Strain mapping at the microscale using digital image correlation of optical micrographs study the strain localisation behaviour of three alloys with soft, hard and no macrozones, respectively. This has been correlated with electron backscattered diffraction orientation maps to relate the strain behaviour to the primary orientation of the macrozones within the material in regard to the loading direction. The main conclusions are as follows: There was a clear link between materials with a high yield stress exhibiting highly heterogeneous strain behaviour while homogenous strain behaviour seems to give the lowest yield stress. The heterogeneous strain behaviour was established early in the plastic regime and high strain regions continued to deform more than the low strain regions. Deformation was relatively homogeneous in the no-macrozone condition and the strong-macrozone condition loaded parallel to ED, as the majority of the grains were well aligned for either basal or prismatic slip. The hard-oriented intermediate-macrozone condition showed moderate strain heterogeneity with 18

137 low strain in the macrozone regions. The small strain hot spots corresponded to grains with their c-axis perpendicular to the loading direction. The strain distribution in the strong macrozone condition loaded at 45 and 90 to ED was highly heterogeneous. The macrozone region in the 45 condition showed a clear correlation with high strain bands and macrozones with their c-axis perpendicular to the loading direction and therefore preferentially oriented for prismatic slip. The pronounced high strain band in the strong-macrozone condition loaded at 90 to ED corresponded to a non-macrozone region favourably oriented for basal slip. Further analysis of the non-macrozone region revealed that well aligned grains with a strong texture that had a basal pole tilted by about 45 and gave the non-macrozone region a higher Schmid factor intensity than the macrozone region aligned for prismatic slip. Acknowledgements The authors would like to thank the EPSRC for partially funding the project. David, Michael and Joao are also thankful to Rolls-Royce for funding the project and the provision of materials. 19

138 Reference [1] R. Boyer, Materials Property Handbook: Ti and Ti alloys [2] R. Boyer, An overview on the use of titanium in the aerospace industry, Mater. Sci. Eng. A, vol. 213, no. 1 2, pp , Aug [3] L. Germain, N. Gey, M. Humbert, P. Vo, M. Jahazi, and P. Bocher, Texture heterogeneities induced by subtransus processing of near α titanium alloys, Acta Materialia, vol. 56, no. 16. pp , Sep [4] G. C. Obasi, S. Birosca, J. Quinta da Fonseca, and M. Preuss, Effect of β grain growth on variant selection and texture memory effect during α β α phase transformation in Ti 6 Al 4 V, Acta Mater., vol. 60, no. 3, pp , Feb [5] M. Humbert, L. Germain, N. Gey, P. Bocher, and M. Jahazi, Study of the variant selection in sharp textured regions of bimodal IMI 834 billet, Mater. Sci. Eng. A, vol. 430, no. 1 2, pp , Aug [6] M. Bache, Dwell sensitive fatigue in a near alpha titanium alloy at ambient temperature, Int. J. Fatigue, vol. 19, no. 93, pp , Jun [7] D. Rugg, M. Dixon, and F. P. E. Dunne, Effective structural unit size in titanium alloys, J. Strain Anal. Eng. Des., vol. 42, no. 4, pp , Jan [8] K. Le Biavant, S. Pommier, and C. Prioul, Local texture and fatigue crack initiation in a Ti-6Al-4V titanium alloy, Fract. Eng. Mater. Struct., vol. 25, no. 6, pp , Jun [9] M. G. Glavicic, B. B. Bartha, S. K. Jha, and C. J. Szczepanski, The origins of microtexture in duplex Ti alloys, Mater. Sci. Eng. A, vol , pp , Jul [10] L. Germain, N. Gey, M. Humbert, P. Bocher, and M. Jahazi, Analysis of sharp microtexture heterogeneities in a bimodal IMI 834 billet, Acta Mater., vol. 53, no. 13, pp , Aug [11] P. D. Littlewood and a. J. Wilkinson, Local deformation patterns in Ti 6Al 4V under tensile, fatigue and dwell fatigue loading, Int. J. Fatigue, vol. 43, pp , Oct [12] J. Miao, T. M. Pollock, and J. Wayne Jones, Microstructural extremes and the transition from fatigue crack initiation to small crack growth in a polycrystalline nickel-base superalloy, Acta Mater., vol. 60, no. 6 7, pp , Apr

139 [13] D. L. Davidson, R. G. Tryon, M. Oja, R. Matthews, and K. S. Ravi Chandran, Fatigue Crack Initiation In WASPALOY at 20 C, Metall. Mater. Trans. A, vol. 38, no. 13, pp , May [14] M. Peters and C. Leyens, Titanium and Titanium Alloys [15] G. Lutjering and J. C. Williams, Titanium, 2nd Editio [16] J. C. Williams, R. G. Baggerly, and N. E. Paton, Deformation Behavior of HCP Ti-Al Alloy Single Crystals, no. March, pp , [17] J. Quinta Da Fonseca, P. M. Mummery, and P. J. Withers, Full-field strain mapping by optical correlation of micrographs, J. Microsc., vol. 218, no. April, pp. 9 21, [18] G. Martin, C. W. Sinclair, and R. a. Lebensohn, Microscale plastic strain heterogeneity in slip dominated deformation of magnesium alloy containing rare earth, Mater. Sci. Eng. A, vol. 603, pp , May [19] H. a. Padilla, J. Lambros, a. J. Beaudoin, and I. M. Robertson, Relating inhomogeneous deformation to local texture in zirconium through grainscale digital image correlation strain mapping experiments, Int. J. Solids Struct., vol. 49, no. 1, pp , Jan [20] F. Hild and S. Roux, digital image correlation from displacement measurement to identification of elastic properties, no. June, [21] F. Gioacchino and J. Quinta da Fonseca, Plastic Strain Mapping with Submicron Resolution Using Digital Image Correlation, Exp. Mech., Oct [22] B. Pan, K. Qian, H. Xie, and A. Asundi, Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review, Meas. Sci. Technol., vol. 20, no. 6, p , Jun [23] M. a. Tschopp, B. B. Bartha, W. J. Porter, P. T. Murray, and S. B. Fairchild, Microstructure-Dependent Local Strain Behavior in Polycrystals through In- Situ Scanning Electron Microscope Tensile Experiments, Metall. Mater. Trans. A, vol. 40, no. 10, pp , Aug [24] F. Hild and S. Roux, Comparison of Local and Global Approaches to Digital Image Correlation, Exp. Mech., pp , Mar [25] J. D. Carroll, W. Abuzaid, J. Lambros, and H. Sehitoglu, High resolution digital image correlation measurements of strain accumulation in fatigue crack growth, Int. J. Fatigue, Jun [26] M. A. Sutton, J. J. Orteu, and W. H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements

140 Figures and Captions Figure 1-Flow diagram of the DIC process. 22

141 Figure 2-Schematic of the optical sub-grid resolution 23

142 Figure 3-Optical micrographs of etched microstructure for (a) No-macrozone, (b) Intermediate-macrozone and (c) Strong-macrozone 24

143 Table 1-Mechanical and microstructural properties of Ti-6Al-4V in different product forms Material No-macrozone along LD) (strained Intermediate-macrozones (strained along LD) E (GPa) σ y (MPa) σ max (MPa) Volume fraction of α phase (%) Average α grain size (μm) Aspect ratio of α grains Strong-macrozone (0 ) Strong-macrozone (45 ) Strong-macrozone (90 )

144 Figure 4- IPF maps of Ti-6Al-4V alloy in different product forms (a) No-macrozone, (b) Intermediatemacrozone, (c) Strong-macrozone and (d) the no macrozone regions of the strong-macrozone material. EBSD generated {0001} and pole figures are shown on the right side of each figure. For interpretation of the references to the colour in this figure legend the reader is referred to the web version of this article 26

145 Figure 5- (a) Stress-strain curves obtained from the DaVis strain map data and (b) magnified view around the yield point 27

146 Figure 6-Macro images of plastic deformation after in-situ tensile loading for the Strong-macrozone loaded at (a) 0, (b) 45 and (c) 90 28

147 Figure 7- Correlation of strain to Basal and Prismatic Schmid factor, at ~ 2.5% applied strain, for (a) Nomacrozone, (b) Intermediate-macrozone, and Strong-macrozone loaded at (c) 0, (d) 45 and (e) 90. (i) Shear strain maps corresponding to (ii) Prismatic and (iii) Basal Schmid factor, processed from raw EBSD data with a 0.5µm step size. 29

148 Figure 8-Cumulative frequency plot of the strain progression during in-situ tensile loading for (a) Nomacrozone, (b) Intermediate-macrozone and the Strong-macrozone loaded at (c) 0, (d) 45 and (e)

149 Figure 9- Normalised frequency shear strain distribution plot for each material and loading condition at an average shear strain of 3%. 31

150 Figure 10-Strain accumulation across a macrozone with increasing load for the Strong-macrozone loaded at (a) 0, (b) 45 and (c)

151 Figure 11-Comparison of prismatic and basal Schmid factor in two neighbouring macrozone and nonmacrozone regions when loaded at (a) 0, (b) 45 and (c) 90, with the inset strain maps and EBSD orientation maps. (d)ebsd generated {0001} and pole figures for the non-macrozone region only in the 90 condition. For interpretation of the references to the colour in this figure legend the reader is referred to the web version of this article 33

152 Table 2- Summary of average Schmid factor for prismatic and basal slip for all conditions in DIC region Material Average Schmid Factor ~ no. of grains Prismatic Basal No-macrozone Intermediatemacrozones Strongmacrozone (0 ) Strongmacrozone (45 ) Strongmacrozone (90 )

153 Publication 2 Slip band characterisation of Ti-6Al-4V with varying degrees of macrozones D. Lunt, J. Quinta da Fonseca, D. Rugg, M. Preuss Note: The material was provided by Rolls-Royce with three distinct microstructures. David Lunt carried out the characterisation of the microstructure and optimisation of the gold remodelling technique for titanium alloys along with Albert Smith. David Lunt conducted the subsequent ex-situ tensile loading experiments, SEM imaging, EBSD and DIC analysis. David Lunt wrote the first draft of the proposed publication. Publication prepared for Material Science and Engineering: A 119

154 Slip band characterisation in Ti-6Al- 4V with varying degrees of macrozones D. Lunt 1, J. Fonseca 1, B. Wynne 2, D. Rugg 3, M. Preuss 1 1 Materials Science Centre, The School of Materials, The University of Manchester, M13 9PL, UK. 2 Department of Materials Science and Engineering, Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD, UK. 3 Rolls Royce PLC, PO Box 31, Derby, DE24 8BJ. Keywords Ti-6Al-4V, Macrozones, Strain Heterogeneity, Nanoscale, Digital Image Correlation, Slip Traces Abstract Electron Backscatter Diffraction (EBSD) orientation maps and Digital Image Correlation (DIC) were combined to analyse slip trace formation of Ti-6Al-4V with varying degrees of microstructural inhomogeneity. The focus of the study are three product forms of Ti-6Al-4V that are termed strong-macrozone, intermediatemacrozone and no-macrozone material that were loaded to study the impact of the primary macrozone orientation on strain localisation. Strain localisation was characterised at the nanoscale by a applying a fine speckle pattern to the sample surface using the Gold remodelling technique. All materials exhibited a proportion of 1

155 grains that exhibited high intensity planar slip traces, neighbouring regions within the same grain showed little deformation. In the no-macrozone material the majority of grains deformed but the level of transgranular strain remained relatively constant across the material. For the intermediate-macrozone condition, macrozones with their c-axis parallel to the loading direction resulted in grains that did not deform and the neighbouring grains that had favourable orientations for easy slip showed highly planar strain slip traces. Progressive strain maps of the strong-macrozone condition loaded at 45 to the extrusion direction (ED) showed that a pronounced high strain band develops in the macrozone region. The primary crystallographic orientation of the macrozone had the c-axis perpendicular to the loading direction and the likely activated slip system was prismatic slip. There were higher overall transgranular strains across the macrozone region compared to the neighbouring region, which displays greater misorientation between grains. The 45 loading direction of the strong-macrozone condition produced finer slip trace spacing and more intense strain heterogeneity and increased localised deformation than the no-macrozone condition 1. Introduction It is commonly observed that thermomechanically processing engineering alloys show microstructural inhomogeneity. In Titanium, so-called macrozones have been widely reported for a number of alloys. Macrozones are clusters of grains within a microstructure that have a common crystallographic orientation [1] [5]. This means there are regions within the microstructure that have a stronger texture than the neighbouring regions where there is no common orientation. Various techniques have been used to detect macrozones in the microstructure [6], such as optical 2

156 polarised microscopy and electron backscatter diffraction (EBSD) [7]. The impact of having large regions with a common orientation is that it is likely to have a detrimental effect on the mechanical properties of the alloy [8]. It is thought that macrozones, favourably oriented for slip (i.e. soft regions), will accumulate a high amount of plastic strain to compensate for the no slip condition in the unfavourably oriented hard grains. In metals with an hexagonal close packed structure, the difference in ease of slip depending on the crystallographic orientation can be very pronounced as only prismatic and basal slip are considered to be easy slip modes while slip that involves a component, i.e. slip, is about 3-4 times harder in Ti at room temperature [9]. Consequently, at boundaries to neighbouring regions that are unfavourably oriented for easy slip, stress concentrations will develop, which might lead to a high density of potential crack initiation sites in the hard neighbouring regions, thus causing early failure in the alloy, particularly during low cycle dwell fatigue loading conditions [10], [11]. Eliminating macrozones from the microstructure has been shown to enable a more reliable prediction of the mechanical performance in terms of less scatter in the fatigue life of alloys with the same composition but little texture [3], [12], [13]. Surface strain mapping work at a microscale, i.e. using optical microscopy imaging during tensile loading and digital image correlation (DIC) on the strong-macrozone material showed heterogeneous strain behaviour when the material was loaded at 45 and 90 to the extrusion direction (ED) but not when the loading direction was parallel to the macrozones [14]. As one would expect, microscale high strains were detected in soft oriented macrozone regions and little deformation in regions with hard oriented macrozones when loaded at 45 to ED. The high strain macrozone 3

157 regions had grains predominantly with their c-axis perpendicular to the loading direction, thus making them favourably oriented for prismatic slip [14], [15]. In the case of loading at 90 to ED, an unusual area was strain mapped, which had two neighbouring macrozone regions of different crystallographic orientations rather than a macrozone region neighboured by a non-macrozone region. Here, the more strongly textured region, i.e. less misorientation within the macrozone, displayed high strains despite this region only being favourably orientated for basal slip while the other macrozone region showed very limited strain despite being well orientated for prismatic slip [14]. In order to obtain actual shear strain information from slip lines rather than averaged strain information at the microscale, Gioacchino et al [16] developed a high resolution strain mapping methodology using Scanning Electron Microscopy (SEM) imaging in combination with DIC. The method involves first sputter coating a gold layer onto a finely polished surface followed by gold remodelling [17], [18] to produce a speckle pattern on a sub-micron scale, as the largest feature determines the maximum resolution that can be achieved. The gold speckle patterns form by dewetting of the gold layer when heated and exposed to water vapour to form gold particles on the surface. The gold particles form random pattern morphologies with high contrast to the substrate when imaged by Backscatter Electron Imaging (BEI) and are suitable for DIC to allow full field strain mapping at different amounts of plastic strain. In the present study the high resolution DIC technique was utilised to obtain a sufficiently high spatial resolution to analyse slip band formation when tensile 4

158 loading three different conditions of Ti-6Al-4V with variable degree of macrozone formation. A particular emphasis was placed on examining the role of hard and soft grains/macrozone regions on transgranular slip band formation. The material investigated here is identical with material examined in [14]. 2. Experimental Procedure 2.1 Material The materials used in this study were three different product forms of Ti-6Al-4V, provided by Rolls-Royce plc. The product forms are called here strong-macrozone, intermediate-macrozone and non-macrozone conditions. The strong-macrozone condition was from an extruded bar designed for blade applications, the intermediate-macrozone condition was uni-directionally rolled-plate and the nomacrozone condition was forged material. The conditions exhibited similar primary alpha volume fractions (~85%) and primary alpha grain sizes (~8μm) [14]. Electron discharge machining was used to extract tensile specimens from the as-received materials. The test specimens were plain, flat dog-bone shapes with geometry of 26mm gauge length, 3mm gauge width and 1mm thickness. The tensile test specimens were hand polished on an OPS cloth in diluted colloidal silica with 20% hydrogen peroxide for 3 hours after initial polishing to #4000 grit paper. Ex-situ loading experiments were conducted using a Kammrath-Zeiss 5kN micro tester and backscattered electron images were taken before loading and after the samples were strained to 1%, 2% and 3% for each material condition. The images were taken ex-situ as this enabled better imaging conditions and the elastic strain 5

159 contribution is very small compared to the plastic strain contribution. Figure 1 is a schematic diagram showing the experimental procedure from the initial polishing of the sample surface to EBSD quality, sputtering a thin gold layer on the polished surface, remodelling the gold layer using water vaporisation and repeating until the ideal pattern is produced. The final stage shows the repeat process of imaging and deforming of the sample. To locate the same region after each loading increment, a grid of micro hardness indents was placed around the area of interest. After the samples had been strained to 3% and the patterns had been recorded, the gold speckles were removed by OPS polishing and grain orientation mapping by EBSD was carried out. 2.2 Scanning Electron Microscopy The EBSD analysis was performed in a Field Emission Gun (FEG) (FEI Quanta 650) Scanning Electron Microscope (SEM) equipped with an Aztec EBSD system and a Nordlys II detector. Macro-texture EBSD scans were performed at an operating voltage of 20kV, at a step size of 10μm over an area of 4x4μm 2. Micro-texture scans were taken over an area of 0.5x0.5μm 2 at step size of 0.5μm, to provide a sufficiently detailed grain orientation map for comparison with the 2D strain measurements. Backscatter electron images were acquired of the region of interest using a Sirion FEI SEM with a Schottky FEG and a FEG FEI Quanta 650 SEM. Images were acquired at 20kV with a working distance of less than 5μm, at magnifications giving horizontal field widths ranging from 37.6μm to 74.6μm. The magnification of the images was adjusted according to the size of the speckles for each condition. The images were acquired in ultra-high definition (XHD) imaging mode at a resolution of 6

160 3872x2904 pixels 2 and 4096x3755 pixels 2 for the Sirion FEI SEM and a FEG FEI Quanta 650 SEM, respectively. A scan mode with 30μs dwell time was used and it took 2-4 minutes to acquire an image. No cold creep effect was expected as the experiment is ex-situ and 2 images were taken at each strain increment to minimize the error from the CCD camera [19]. Larger areas were analysed by imaging adjacent regions using mosaics of 3x3 and 4x4 images. 2.2 Gold Remodelling For high resolution strain mapping, a fine speckle pattern was applied to the surface of the sample using the gold remodelling technique. A gold layer of ~25-40nm was sputter coated onto the polished sample at a sputtering rate of 5-8mm/min in an Edwards S150B sputter coater. Subsequently, the specimen was placed on a hot plate and the gold layer was remodelled in a water vaporisation environment in between a beaker with the vapour source (water) and an inverted beaker cover. This allowed the vapour to flow around the system. Samples were remodelled for minutes. The three materials investigated had differences in the morphology of the speckle patterns, but the magnification was adjusted to achieve the optimum imaging conditions for each speckle pattern. 2.3 High Resolution DIC The main principle of DIC is the tracking of features on 2 images from the same region before and after deformation. DIC was performed using DaVis 8 software and images of the same region were correlated at each strain step relative to the nondeformed image. A sub pixel grid size of between 4x4 to 12x12 pixels 2 with a 0% overlap was used to gain high resolution strain information about the sub regions. 7

161 The overlap was not required due to the high quality and accuracy of the pattern. Each image was processed to give the same overall spatial resolution equating to sub grid sizes of 0.38x0.38μm 2. The subsequent strain maps were stitched together after DIC processing to give a single large high resolution strain map. In this project, the DIC results are presented as maps of maximum shear strain as this takes into account all the components of the in-plane strain. The maximum shear strain (ε max ) was calculated using equation 1, where ε xx is the strain in the loading direction, ε yy is the strain normal to the loading direction and ε xy is the in-plane shear strain. Presenting the results as maximum shear strain helps to reduce the uncertainty provided by the lack of out-of-plane deformation data that is not taken into account by 2D DIC [16], [20]. The governing equation is: Equation 1 3. Results 3.1 EBSD characterisation Grain orientation maps at two different magnifications are shown of the different material conditions in Figure 2 together with corresponding and pole figures calculated from the large area maps.. The no-macrozone material exhibits a relatively random distribution of grain orientations with a high density of high angle grain boundary misorientations that can be observed across the various representations in Figure 2a. The maximum texture intensity was identified for the pole figure to be 6 times random, Figure 2a (iii). The grain orientation maps 8

162 of the intermediate-macrozone material are shown in Figure 2b (i) and (ii), respectively. They exhibit macrozones that are narrow and unevenly distributed in the ND-TD plane. Figure 2b (ii) shows a macrozone with dimensions of ~50μm width and 250μm in length along TD. The macrozone region has a high density of low angle grain boundaries and there are also small clusters of neighbouring grains with a different orientation that have apparent low angle grain boundaries. The respective pole figures in Figure 2b (iii) show that the primary texture component has the c-axis parallel to TD and one of the (10-10) normal aligned parallel to RD (outof-plane). The maximum texture intensity in the pole figure is 8. There are also two weaker texture components with their basal pole tilted at 45 between TD and RD. The grain orientation map of the strong-macrozone condition in Figure 2c (i) shows that there are prominent macrozone regions with a common orientation that stretches along ED for several millimetres and are 200µm in width along ND. The grain orientation map in Figure 2c (ii) highlights the high density of low angle grain boundaries in the macrozone region compared to a non-macrozone region where there is a high density of high angle grain boundaries. The (0002) pole figure in Figure 2c (iii) shows a strong texture component with the c-axis aligned parallel to TD (out-of-plane) and little rotation of the c-axis for the prismatic planes indicating a strongly preferred crystallographic orientation too. It is important to note that the texture is strongly dominated by the preferred orientation of the macrozones. 3.2 Mechanical Properties Initial experiments by Lunt et al [14] on the same materials using optical based imaging in combination with DIC demonstrated that the differences in yield strength 9

163 seen in Figure 3 were strongly correlated with the overall texture rather the level of strain heterogeneity. Material with textures that promote prismatic and basal slip showed the lowest yield stress despite also displaying the lowest level of microscale strain heterogeneity. In contrast, materials that displayed high levels of microscale strain heterogeneity was overall less well aligned for prismatic and basal slip and consequently also displayed higher yield stresses. 3.3 Schmid factor analysis No-macrozone and Intermediate-macrozone In the region of the 2D strain and EBSD analysis the Schmid factor distributions were calculated for basal, prismatic and pyramidal slip using the recorded EBSD data and the given loading direction, i.e. along FD in the case of the nomacrozone condition and along TD for the intermediate-macrozone condition. The results of this analysis are summarised in Figure 4. The prismatic slip Schmid factor distribution for the no-macrozone material demonstrates a significant tendency for high prismatic slip Schmid factor values, Figure 4a (i). Figure 4a (ii) shows that the intermediate-macrozone condition is hard oriented in both the macrozone and nonmacrozone regions for prismatic slip. The basal slip Schmid factor distributions for the no-macrozone and intermediate-macrozone conditions are shown in Figure 4b (i) and (ii), respectively. They indicate that the no-macrozone condition also has a high density of grains soft oriented for basal slip but with a lower peak frequency than prismatic slip. The intermediate-macrozone material shows a relatively even but low frequency across the basal slip Schmid factor rang for macrozone and nonmacrozone regions. The slip Schmid factor distribution shows that the no- 10

164 macrozone material also has a high frequency of favourably oriented grains for this type of slip, Figure 4c (i) while the intermediate-macrozone material again shows a relatively even distribution with no significant differences between the macrozone and non-macrozone regions Strong-macrozone condition For the strong-macrozone condition the critical loading direction to promote soft oriented macrozones was again determined through EBSD analysis of a single macrozone region. Figure 5 shows the basal, prismatic and pyramidal Schmid factor distributions when loading 0, 45 and 90 to the extrusion direction. For the 0 loading direction, shown in Figure 5a (i), both the macrozone and nonmacrozone region appear to be well oriented for prismatic slip. Regarding the 45 and 90 loading conditions, the macrozones appear to be well aligned for prismatic slip while the non-macrozone regions are not, Figure 5a (ii) and (iii). The basal slip activity is summarised for the 0, 45 and 90 loading conditions in Figure 5b (i), (ii) and (iii), respectively. Again, the basal slip Schmid factor distribution is similar in the macrozone and non-macrozone regions in the case of the 0 loading condition. For the 45 and 90 loading directions there is increased likelihood of basal slip in the non-macrozone regions compared to the macrozone regions. However, the peak frequency intensities at high Schmid factors are lower for basal slip compared to prismatic slip in the macrozone regions. The slip Schmid factor distribution activities can be seen in Figure 5c (i), (ii) and (iii) for 0, 45 and 90, respectively, and show a very similar trend to the prismatic slip Schmid factor distributions for each loading condition. 11

165 3.4 High Resolution Strain Mapping The effect of the primary macrozone orientation was studied by loading the three material conditions to promote soft and hard oriented macrozones. The nomacrozone condition was used as baseline. The intermediate-macrozone condition was loaded along TD to provide hard oriented macrozone regions with the c-axis preferentially orientated parallel to the loading direction. The strong-macrozone condition was loaded at 45 to ED, as previous studies had shown high strain concentrations in the macrozone region [14]. The Schmid factor analysis presented in Figure 5 also suggests that the greatest difference between macrozone and nonmacrozone regions should be observed when loaded at No-macrozone Figure 6 shows the Schmid factor maps for prismatic, basal and pyramidal slip calculated from EBSD analysis and the corresponding shear strain map obtained by high resolution DIC after 3% plastic deformation for the no-macrozone condition. Each Schmid factor map shows, as one would expect, significant variation of grey levels for neighbouring grains for the two soft slip modes, i.e. prismatic and basal slip. The maximum shear strain map clearly shows the slip band formation that has taken place after 3% plastic deformation. It exhibits several grains with many intense slip traces that reach maximum shear strains of ~ 25%. At the same time, the map also reveals grains that have low strain slip lines or have not deformed at all. The slip lines are typically finely spaced and planar in the deformed grains. Relating the strain localisation to the Schmid factor maps is difficult due to the large number of grains that are favourably oriented for either prismatic and/or basal slip. However, the 12

166 majority of grains that are heavily deformed appear to be favourably oriented for prismatic slip and poorly oriented for basal slip. Grains that have deformed and have a more favourable orientation for basal slip appear to have low peak shear strains in the slip traces suggesting that it is the grains favourably orientated for prismatic slip that accommodate most strain. At this stage, it is also worth pointing out that the majority of grains are favourably oriented for slip according to the Schmid factor analysis. However, it is assumed that due to the relatively low CRSS value of prismatic slip compared to pyramidal slip [9], prismatic slip is dominant Intermediate-macrozone Figure 7 is the same arrangement of representations as in Figure 6 but for the intermediate-macrozone condition. Here, clusters of dark grey to black grains in Figure 7a and b represent the hard macrozone regions, which are separated by single grains favourably orientated for either prismatic or basal slip. The majority of the grains in the macrozone region are also hard oriented for slip. In the nonmacrozone regions the majority of grains are oriented favourably for basal slip although the Schmid factors are not particularly high. The shear strain map in Figure 7d shows a significant number of grains have not deformed while there are individual grains that have accumulated high strain with planar slip traces. It is difficult to distinguish a pattern between favourable orientation for a specific slip system and grains that have deformed heavily. However, there are single grains with distinct slip traces that are well oriented for basal and/or prismatic slip. Typically, the grains exhibiting high shear strain are favourably oriented for either slip mode. The hard oriented macrozones show no strain accumulation and little strain across the 13

167 complete macrozone. This appears to result in greater slip band formation in the neighbouring clusters and as a result there is a distinct pattern of grains either showing very little or very well developed shear strain but no grains that cover a middle ground Strong-macrozone, 45 The shear band evolution of the strong-macrozone condition loaded at 45 is shown in Figure 8 at progressive strains of 1%, 2% and 3%. The two dashed lines frame the region of the soft macrozone. Figure 8a shows that in the strain map for ~ 1% applied strain there are 3 intense regions of high strain, which all appear to show intense and well developed strain bands parallel to ED and much shorter slip traces perpendicular to ED. While two of the intense strain traces are located within the macrozone, one is not. After ~ 2% applied strain, Figure 8b, it can be observed that adjacent strain bands have formed from the two intense strain regions within the macrozone, which start to stretch along the complete macrozone region. At the same time, slip traces in the perpendicular direction stretch from one side of the macrozone to the other one. In contrast, the initial high strain region in the non-macrozone region has not developed further. The shear strain after 3% deformation shows a further progression in the development of slip band formation and shear strain intensification within shear traces with maximum local shear strains of over 30% at the boundaries between the macrozone and non-macrozone region, Figure 8c. Figure 9 again compares the different Schmid factor maps with a high-resolution strain map also recorded for the 45 loading condition. The Schmid factor maps highlight that within the macrozone region, the grains are well aligned for prismatic 14

168 and pyramidal slip but not for basal slip. As for the previous case, presented in Figure 8, there is a distinct trend of the highest shear strain values being located at the macrozone grain boundaries. The grains that accumulated high shear strain in the non-macrozone region after 1% applied strain also display a high Schmid factor for prismatic slip. However, the neighbouring grains are hard oriented for prismatic slip and only favourably oriented for basal slip, which seems to have hindered the spread of further shear band formation similar to the macrozone region. 4. Discussion Whilst it is well known that deformation is highly heterogeneous through shear band formation [21], high resolution strain mapping using DIC opens up the possibility to quantify the level of shear strain during plastic deformation. This in principle enables one to compare the true level of strain heterogeneity for different alloys, microstructures and microstructure inhomogeneity. Previous studies using optically based DIC have concentrated on strain localisation at the microscale, reporting maximum strain concentrations ranging between times the average strain [14], [15], [22] when strain hot spots are compared to the average strain. By utilising the gold remodelling technique to produce nanoscale patterns in combination with SEM imaging in the present work, it is now possible to gain an understanding of the strain concentrations that occur across a single grain and variations in strain across several grains. Figure 10a shows the nanoscale frequency distributions of the maximum shear strain for the two extreme microstructure conditions regarding expected strain heterogeneity, i.e the no-macrozone and strong-macrozone loaded at 45, after 3% plastic deformation. It can be seen that the no-macrozone condition shows slightly 15

169 higher frequency for shear strains below 5% while beyond 5% the strong-macrozone shows consistently higher frequencies. Importantly, the maximum shear strain in the no-macrozone condition is about 25% (8 times the macroscopic strain) while in the strong-macrozone condition loaded at 45 the maximum shear strain reaches almost 35% (11 times the macroscopic strain). The results are in agreement with similar high resolution strain analysis using nanoscale patterns in stainless steel [16], [23] that has also shown peak-to-applied strain ratios of 10. Figure 10b exhibits a representative slip trace spacing analysis across single grains for the no-macrozone and strong macrozone condition loaded at 45. It is important to note that the comparison is carried out on two similarly oriented grains in respect of the loading direction. The strong-macrozone condition exhibits a higher density of slip traces with a fine slip trace spacing of ~0.5μm compared to 1-1.5μm for the non-macrozone material. The strain heterogeneity is also higher in the strong-macrozone material with an average shear strain in slip traces of ~13% and maximum intensity of 18%. This compares to the non-macrozone condition with an average shear strain within slip traces of 8% and a maximum of 17%. The shear strain between slip traces is somewhere between 1-2% in both cases. The contribution of a higher density of slip traces showing increased peak shear strains in the strong-macrozone material loaded at 45, which also happens to display the highest yield strength in Figure 3, is likely to result in increased strain mismatches at the grain boundaries between soft and hard oriented grains/regions. Consequently, reduced ductility or early crack initiation during fatigue loading might be expected. Strain analysis by high resolution DIC of the three material conditions highlights the differences in strain localisation between the three different materials with soft, hard 16

170 and no macrozones, respectively. Previously, optically based DIC [14], [15] on Ti- 6Al-4V has shown that hard oriented macrozones exhibit low strain, with surrounding regions showing high strain accumulation. The high-resolution strain analysis of the intermediate-macrozone material is in agreement with this as there are large concentrations of grains with very little slip band formation corresponding to hard oriented macrozones regions. Single grains in the surrounding, non-macrozone region, oriented for easy slip, deformed by distinct slip traces across the complete grain with different shear strain intensities dependent on the location within the grain. The majority of these grains displayed slip traces being restricted to the single grain. For the no-macrozone and strong-macrozone conditions loaded at 45 to ED there are also regions that show little deformation and these correspond to grains not favourably orientated for type slip. However, these two conditions have a higher density of soft oriented grains than the intermediate-macrozone condition according to Figure 4 and Figure 5, which is also apparent from the higher density of deformed grains when comparing the strain maps. For the no-macrozone condition, the central region of the strain map shows a strong alignment of the slip lines across several grains with only slight changes in slip trace orientation. It is likely that the neighbouring grains were favourably oriented to accommodate slip in this direction. The slip traces within single grains show either planar slip traces or significant curvature of the slip traces across the grain. The highlighted grain in the white box of Figure 6d is an example of a grain that has large slip trace curvature and discontinuation of the slip traces at a grain boundary. It is analysed in more detail in Figure 11. In Figure 11a, the magnified strain map shows the irregular slip trace intensity and the curvature of the slip trace from the top to the bottom of the grain. 17

171 Figure 11b shows that there are large variations in the slip trace spacing and shear strain intensity across the grain with several diffuse slip traces. The relative curvature profile from the top to the bottom of the grain shows a total misorientation of 17 across a 20μm path length that is close to 1 /μm, Figure 11c. The significant lattice curvature is similar to observations made by Gioacchino et al [23] for stainless steel. It was suggested that the curvatures are caused by incompatibilities at grain boundaries that are accommodated by two mechanisms, which are variations of slip intensity or the formation of a secondary slip domain [23]. The current grain appears to deform by reducing the slip intensity from the top to the bottom of the grain, producing a large lattice curvature. Other grains appear to deform by the second mechanism proposed where two slip systems are activated within a single grain and this is highlighted in a red box in Figure 6d. Clearly, this work demonstrates that deformation behaviour is observed in a polycrystalline aggregate, which is unlikely to occur if the grains were deforming as single crystals. For the strong-macrozone condition loaded at 45, the high strain band corresponding to a macrozone is apparent at 2% and 3% strain. It clearly displays a higher transgranular strain than the slip traces observed in the non-macrozone regions. The favourable slip orientations in the macrozone region have lead to a high density of grains accumulating high strain localisation. The macrozone region is favourably oriented for prismatic slip and the high intensity slip traces are parallel to the macrozone length in most grains. The higher overall strain in the macrozone is likely to have occurred through easy slip transfer across low angle grains boundaries. The non-macrozone region has deformed at a reduced rate to accommodate the high strain localisation despite having regions that are favourably oriented for slip. From 18

172 the strain maps for the intermediate and no-macrozone condition it is apparent that there are no apparent high transgranular strains in these materials. Finally, it should be pointed out that the strong-macrozone condition was deliberately strained in a direction for which the macrozone was particularly soft. If the opposite was the case, the material would first of all display a very high yield point. At this stage it is not clear if a neighbouring non-macrozone would in such a case accommodate larger fractions of shear strain considering the large degree of misorientations between grains or if indeed it would be easier to have slip transfer within the macrozone. 5. Conclusions High resolution DIC has been used to observe the strain behaviour at a nanoscale in Ti-6Al-4V with macrozones. The critical loading directions in respect to the primary macrozone orientation for each condition were determined through detailed analysis of the Schmid factor distributions generated from the EBSD data. The no-macrozone condition was used as a baseline material, the intermediate-macrozone condition was loaded parallel to TD to observe hard oriented macrozones and the strong-macrozone condition was loaded at 45 to ED as this loading direction was likely to promote strain heterogeneity. The experiments on the different material conditions indicated that in the nomacrozone condition the majority of grains exhibited high intensity planar slip traces that correlated to grains likely to deform by basal or prismatic slip. The hard oriented macrozones in the intermediate-macrozone condition corresponded to regions with 19

173 little deformation, but single grains that were soft orientated for slip deformed heavily with pronounced slip traces across the grain. For the strong-macrozone material the initial strain hot spots at 1% strain progressed across the macrozone region with increasing applied strain to form a high strain band that correlated to a macrozone region that was favourably oriented for prismatic slip. The high transgranular strain bands were parallel to ED with shorter slip traces perpendicular to ED. The two extreme microstructures showed noticeable differences in strain heterogeneity with the strong-macrozone condition showing a higher density of slip traces with increased maximum shear strains. The nanoscale deformation studies provided a more detailed insight into the actual extent of the strain heterogeneity, with maximum shear strain intensities of ~ 10 times the applied strain. Acknowledgements The authors would like to thank the EPSRC for partially funding the project. They are also grateful to Rolls-Royce for funding the project and the provision of materials. 20

174 Reference [1] I. Bantounas, D. Dye, and T. C. Lindley, The role of microtexture on the faceted fracture morphology in Ti 6Al 4V subjected to high-cycle fatigue, Acta Mater., vol. 58, no. 11, pp , [2] L. Germain, N. Gey, M. Humbert, P. Bocher, and M. Jahazi, Analysis of sharp microtexture heterogeneities in a bimodal IMI 834 billet, Acta Mater., vol. 53, no. 13, pp , Aug [3] K. Le Biavant, S. Pommier, and C. Prioul, Local texture and fatigue crack initiation in a Ti-6Al-4V titanium alloy, Fract. Eng. Mater. Struct., vol. 25, no. 6, pp , Jun [4] D. Rugg, M. Dixon, and F. P. E. Dunne, Effective structural unit size in titanium alloys, J. Strain Anal. Eng. Des., vol. 42, no. 4, pp , Jan [5] E. Uta, N. Gey, P. Bocher, M. Humbert, and J. Gilgert, Texture heterogeneities in alpha/alpha titanium forging analysed by EBSD-relation to fatigue crack propagation., Journal of microscopy, vol. 233, no. 3. pp , Mar [6] A. Moreau, L. Toubal, P. Bocher, M. Humbert, E. Uta, and N. Gey, Evaluation of macrozone dimensions by ultrasound and EBSD techniques, Mater. Charact., vol. 75, pp , Jan [7] D. J. Dingley and V. Randle, Microtexture determination by electron backscatter diffraction, J. Mater. Sci., vol. 27, no. 17, pp , [8] M. R. Bache, W. J. Evans, B. Suddell, and F. R. M. Herrouin, The effects of texture in titanium alloys for engineering components under fatigue, Int. J. Fatigue, vol. 23, pp , [9] J. C. Williams, R. G. Baggerly, and N. E. Paton, Deformation Behavior of HCP Ti-Al Alloy Single Crystals, no. March, pp , [10] M. Bache, A review of dwell sensitive fatigue in titanium alloys: the role of microstructure, texture and operating conditions, Int. J. Fatigue, vol. 25, no. 9 11, pp , Sep [11] V. Sinha, M. J. Mills, and J. C. Williams, Understanding the contributions of normal-fatigue and static loading to the dwell fatigue in a near-alpha titanium alloy, Metall. Mater. Trans. A, vol. 35, no. 10, pp , Oct

175 [12] C. J. Szczepanski, S. K. Jha, J. M. Larsen, and J. W. Jones, Microstructural Influences on Very-High-Cycle Fatigue-Crack Initiation in Ti-6246, Metall. Mater. Trans. A, vol. 39, no. 12, pp , Aug [13] W. Evans, J. Jones, and M. Whittaker, Texture effects under tension and torsion loading conditions in titanium alloys, Int. J. Fatigue, vol. 27, no , pp , Oct [14] D. Lunt, M. Preuss, J. Fonseca, and D. Rugg, The macroscopic impact of macrozones on the strain behaviour of Ti-6Al-4V alloy during uniaxial tensile loading (Not-submitted), pp [15] P. D. Littlewood and a. J. Wilkinson, Local deformation patterns in Ti 6Al 4V under tensile, fatigue and dwell fatigue loading, Int. J. Fatigue, vol. 43, no. 2012, pp , Oct [16] F. Gioacchino and J. Quinta da Fonseca, Plastic Strain Mapping with Submicron Resolution Using Digital Image Correlation, Exp. Mech., Oct [17] Y. Luo, J. Ruff, R. Ray, Y. Gu, H. J. Ploehn, and W. a. Scrivens, Vapor-Assisted Remodeling of Thin Gold Films, Chem. Mater., vol. 17, no. 20, pp , Oct [18] W. a. Scrivens, Y. Luo, M. a. Sutton, S. a. Collette, M. L. Myrick, P. Miney, P. E. Colavita, a. P. Reynolds, and X. Li, Development of Patterns for Digital Image Correlation Measurements at Reduced Length Scales, Exp. Mech., vol. 47, no. 1, pp , Feb [19] J. Quinta Da Fonseca, P. M. Mummery, and P. J. Withers, Full-field strain mapping by optical correlation of micrographs, J. Microsc., vol. 218, no. April, pp. 9 21, [20] H. a. Padilla, J. Lambros, a. J. Beaudoin, and I. M. Robertson, Relating inhomogeneous deformation to local texture in zirconium through grainscale digital image correlation strain mapping experiments, Int. J. Solids Struct., vol. 49, no. 1, pp , Jan [21] M. F. Ashby, The deformation of plastically non-homogeneous materials, Philos. Mag., vol. 21, no. 170, pp , Feb [22] C. Efstathiou, H. Sehitoglu, and J. Lambros, Multiscale strain measurements of plastically deforming polycrystalline titanium: Role of deformation heterogeneities, Int. J. Plast., vol. 26, no. 1, pp , Jan [23] F. Di Gioacchino and J. Quinta da Fonseca, An experimental study of the polycrystalline plasticity of stainless steel, J. Fatigue, no

176 Figures and Captions Figure 1- Schematic of gold remodelling and ex-situ DIC process 23

177 Figure 2- EBSD orientation maps of (a) no-macrozone (b) intermediate-macrozone and (c) strong-macrozone materials in terms of (i) macro-texture maps with a 10µm step size, (ii) micro-texture maps with a step size of 0.5µm and (iii) micro-texture {0001} and pole figures 24

178 Figure 3- (a) Stress-strain curves obtained from the DaVis strain map data 25

179 Figure 4- Likely slip activity for (a) prismatic, (b) basal and (c) slip for (a) no-macrozone and (b) intermediatemacrozone material 26

180 Figure 5- Likely slip activity for (a) prismatic, (b) basal and (c) 90 slip for a macrozone loaded at (i) 0, (ii) 45 and (iii) 27

181 Figure 6-EBSD Schmid factor maps for the no-macrozone condition in terms of (a) prismatic, (b) basal and (c) pyramidal slip at (d) 3% average strain 28

182 Figure 7-EBSD Schmid factor maps for the intermediate (hard-oriented) macrozone condition in terms of (a) prismatic, (b) basal and (c) pyramidal slip at (d) 3% average strain 29

183 Figure 8- Nanoscale DIC strain maps of the strong-macrozone condition loaded at 45 at (a) 1%, (b) 2% and (c) 3% strain 30

184 Figure 9- EBSD Schmid factor maps for the strong-macrozone condition loaded at 45 in terms of (a) prismatic, (b) basal and (c) pyramidal slip at (d) 3% average strain 31

185 Figure 10- Comparison of (a) maximum shear strain frequency and (b) slip trace spacing at 3% overall strain for strongmacrozone and non-macrozone condition 32

186 Figure 11-(a) Maximum shear strain map for an individual grain at 3% strain for the non-macrozone condition, (b) slip trace spacing and (c) misorientation profile across the grain 33

187 Publication 3 Analysis of slip activity and nanoscale strain mapping in Ti-6Al-4V with varying degrees of macrozones D. Lunt, J. Quinta da Fonseca, B. Wynne, D. Rugg, M. Preuss Note: The material was provided by Rolls-Royce with two distinct microstructures. David Lunt carried out the characterisation of the microstructure and strain analysis. David Lunt utilised the user-friendly Crystal Mathematical Tool provided by Brad Wynne s group at the University of Sheffield to perform slip trace analysis. David Lunt wrote the first draft of the proposed publication. Publication prepared for Acta Materialia 120

188 Analysis of slip activity and nanoscale strain mapping in Ti-6Al-4V with varying degrees of macrozones D. Lunt 1, J. Quinta da Fonseca 1, B. Wynne 2, D. Rugg 3, M. Preuss 1 1 Materials Science Centre, The School of Materials, The University of Manchester, M13 9PL, UK. 2 Department of Materials Science and Engineering, Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD, UK. 3 Rolls Royce PLC, PO Box 31, Derby, DE24 8BJ. Keywords Ti-6Al-4V, Macrozones, Nanoscale, Digital Image Correlation (DIC), Slip Trace analysis Abstract The tensile deformation behaviour of Ti-6Al-4V alloys of a no macrozone and softoriented macrozone material were compared using high resolution digital image correlation to study the strain heterogeneity. The active slip system within each grain was determined using slip trace analysis by cross-correlating the theoretical slip trace angles calculated from Electron Back Scattered Diffraction (EBSD) orientation data with experimental slip trace angles measured from nanoscale shear strain maps. Both materials showed a dominance of prismatic: basal: pyramidal of ~60%:30:10% with a single macrozone region in the strong macrozone material showing a higher density of grains deforming by prismatic slip. The shear strain was associated with 1

189 the slip activity by comparing the Schmid factor of the active slip system to the maximum slip intensity. Deformation by prismatic slip demonstrated increase shear strain followed by basal and then slip. The maximum shear strain values in the strong-macrozone condition for prismatic slip were considerably higher than in the no-macrozone material. The validity of the Schmid factor argument for predicting the active slip system in poly crystals was studied through comparing the Schmid factor predicted slip system to the slip trace analysis results with the majority of grains showing agreement, but there were instances where other factors influenced the primary slip system. 1.0 Introduction Thermomechanical processing of + Ti alloys, such as Ti-6Al-4V, has been shown to potentially result in microstructures that contain large regions with a common crystallographic orientation, generally referred to as macrozones, which act as a single structural unit [1] [2]. These regions have been found to have a significant impact on reducing the fatigue life of the alloys [3]. In hexagonal close-packed (hcp) metals slip can occur along the and the directions. In the case of Ti, slip occurs more easily along the direction, which has an type Burgers vector and can be found along the basal plane, the three prismatic planes and the six pyramidal planes. The slip direction has a type Burgers vector that is larger than the type Burgers vector in Ti alloys and therefore is more difficult to activate. For slip to occur in this direction it will occur along the planes for 1 st order pyramidal slip and along the planes for 2 nd order pyramidal slip [4], [5]. The 2

190 ease of slip along a specific slip system is generally related to the corresponding Critical Resolved Shear Stress (CRSS) for that slip system, with a low CRSS meaning easier slip activation. At room temperature, the CRSS ratio for single crystal Ti-6.6Al was shown to be of the order of ~1:3 for basal/prismatic slip to slip [6], [7]. The slip trace behaviour of titanium alloys has been studied by Boehlert et al [8] using EBSD-based slip trace analysis and has shown a similar number of grains with a likelihood for prismatic and basal slip in a Ti-5Al-2.5Sn alloy. The prismatic grains were activated over a greater Schmid factor range and it has been shown for this alloy that the calculated CRSS at room temperature is a ratio of 0.8:1, prismatic to basal slip [9]. Previous studies on the deformation mechanisms of Ti-6Al-4V alloys using slip trace analysis has been performed by Bridier et al [10] and they reported lower resolved shear stresses for basal to prismatic slip. However, there was more prismatic gliding in grains where the Schmid factor for basal and prismatic slip was equal. There is generally a lack of deformation studies on the active slip that compare different microstructures. This is particularly true for Ti alloys with homogeneous (no-macrozone) or heterogeneous (macrozone) microstructures where different levels of strain localisation are to be expected. The importance of characterising slip traces by high resolution 2D deformation studies has been demonstrated recently for stainless steel since both the magnitude and direction of slip are important in understanding how intergranular incompatibility is accommodated [11]. Studies on Ti-6Al-4V have demonstrated that when macrozones are well oriented for basal and/or prismatic slip they accommodated significantly more plastic strain than the regions in-between the macrozones both on a micro [12], [13] and nanoscale 3

191 [14]. The latter compared a no-macrozone and strong-macrozone variant of Ti-6Al- 4V (same material as in the present study) by high resolution digital image correlation (HR-DIC) and it was observed that the strong-macrozone material, with the macrozones loaded at 45, exhibited high transgranular shear strains and high strain heterogeneity in single grains within a macrozone that were well oriented for prismatic slip. This strain behaviour was contributed to the favourable orientation of the prismatic slip system but since Schmid factor analysis simply assumes that the overall loading direction is the same as the loading direction at grain level, detailed analysis is required of the slip traces that form during plastic deformation. In the present study detailed 2D strain maps recorded by HR-DIC are cross correlated with grain orientation maps obtained by electron backscatter diffraction (EBSD) at various degrees of macroscopic strain to quantify the slip behaviour in terms of individual slip systems within single crystals. The strain heterogeneity recorded at individual grain level, presented previously [14], will be related to the active slip system detected using slip trace analysis. 2. Experimental Procedure 2.1 Material The materials used in this study were two different product forms of Ti-6Al-4V, provided by Rolls-Royce plc. The product forms were forged material without macrozones and hot extruded material with strongly developed macrozones. Both materials exhibit similar primary volume fractions (~85%) and primary grain size (~8μm). Flat dog-bone tensile specimens with dimensions of 26mm gauge length, 3mm gauge width and 1mm thickness were electrical discharge machined 4

192 from the as-received materials. The specimens were hand polished on an OPS cloth in dilute colloidal silica for 30 minutes after initial grinding to #4000 grit paper. The test pieces were strained to 3% macroscopic strain using a Kammrath-Weiss 5kN micro tester at a strain rate of about 2 x 10-5 s -1. EBSD analysis was conducted in a Field Emission Gun (FEG) (FEI Quanta 650) Scanning Electron Microscope (SEM) equipped with an Aztec EBSD system and a Nordlys II detector. For high resolution strain analysis the gauge section of the samples were gold sputtered and remodelled in order to a random pattern of gold nanoparticles [14]. Backscattered electron images of the nanoparticles for HR-DIC stain analysis were recorded before and after deformation using a Sirion FEI SEM with a Schottky FEG and a FEG FEI Quanta 650 SEM. Images were acquired at magnifications giving horizontal field widths ranging from 37.6μm to 74.6μm. 2.2 HR-DIC and Slip Trace Analysis HR-DIC provides detailed information on the strain behaviour of the two material conditions relative to each other by comparing images before and after deformation and tracking the displacement using features on the surface. Lunt et al describe the DIC technique and pattern application in more detail in [14] with a particular emphasis on the sub grain shear strain behaviour in regard to transgranular strain and slip traces. Slip trace analysis gives a quantifiable prediction of the overall likely slip activity in a single grain by using the grain orientation information from EBSD analysis and cross correlating it with slip traces quantified by HR-DIC measurements. The processing of the raw EBSD data provides limited information in terms of the active slip system, if this is restricted to correlating the high strain regions with Schmid factor for each slip system. From the EBSD data, the Euler 5

193 angles are extracted for individual grains and used as inputs in the theoretical slip trace analysis. The University of Sheffield Materials Department have developed a user-friendly Crystal Mathematical Tool to predict slip trace angles for every slip system, where the Euler angles and all the planes and directions of each slip system are inputs. The theory behind the implementation of the slip trace analysis technique is covered comprehensively in the literature [10]. The theoretical slip angle predictions are correlated with the slip angles for individual grains from the 2D strain mapping analysis to predict the most likely active slip system. The methodology is summarised schematically in Figure 1, where the processing steps for the correlation between slip trace analysis and HR-DIC are indicated. 3. Results The EBSD orientation maps together with pole figure information for the two product forms are summarised in Figure 2. Figure 2a confirms that the forged material does not contain any macrozones and that the material is only weakly textured. In contrast, the extruded-bar material exhibits very strongly developed macrozones, Figure 2b, that are aligned parallel to the extrusion direction and stretch along for several millimetres and are 200µm in width. The grains in the macrozone have their c-axis primarily aligned perpendicular to the extrusion direction. The (0002) and pole figures in Figure 2b and c indicate that the non-macrozone regions in extruded bar material has a texture that is 2-3 times weaker than in the well developed macrozone regions. In the macrozone region, the grains also seem to have a fixed orientation rather than a fibre texture. It should also be noted that the maximum texture component in the non-macrozone regions is also a basal texture but on a more diffuse scale. 6

194 The 2D strain pattern determined from HR-DIC analysis after deforming both microstructure conditions to 3% macroscopic strain are shown in Figure 3. Both materials displayed slip bands within grains and grains that showed little or no deformation. Another feature of the strain patterns is that intense slip bands are neighboured by regions within the same grain that have almost not deformed at all. Maximum shear strains were about 25% in the case of the no-macrozone condition and closer to 35% for the strong-macrozone condition loaded at 45. The nomacrozone condition in Figure 3a exhibits a high density of grains with observable slip traces but no significant transgranular strains stretching across several grains. In contrast, the strong-macrozone condition loaded at 45 in Figure 3b shows significant transgranular strain with the entire macrozone region deforming at a greater rate than the neighbouring regions. This creates neighbouring structural units that are accumulating strain at different rates. The strain behaviour and shear strain distributions of the different material conditions are summarised in more detail in [13], [14]. 3.1 Accuracy of Slip Trace Analysis Initially, prismatic, basal and pyramidal Schmid factor distributions have been calculated for the area analysed here to predict the likely deformation behaviour of the materials, Figure 4. For the no-macrozone condition, Figure 4a (i), b(i) and c(i) shows that the grain are preferentially orientated for prismatic and pyramidal slip. In case of the strong-macrozone condition loaded at 45, it was important to distinguish between the two different regions. Figure 4a(ii), b(ii) and c(ii) shows that the macrozone region is well aligned for prismatic and pyramidal slip while in the non-macrozone region the Schmid factor analysis suggests a tendency for 7

195 basal and slip. Since in a polycrystalline material the stress direction of individual grains is not necessarily equal the applied stress direction, Schmid factor analysis is not particularly accurate although it might have its value in strongly developed macrozones that could be less constrained. In order to more accurately determine relative slip activities, Electron Channel Contrast Imaging (ECCI) and the 2D strain maps presented in Figure 3 were combined with the grain orientation information available from Figure 2 in order to predict the most likely slip mode for the observed slip traces. ECCI was initially used to undertake an initial assessment of the measured slip trace orientation with the predicted one. ECCI shows a strong contrast between the slip traces and the rest of the grain structure and the results have been combined with the slip trace analysis in Figure 5. Grains A and B are identified in Figure 5a and b through EBSD maps and channel contrast imaging, respectively. The slip traces for the respective grains are shown and the angles are calculated relative to the loading direction (horizontal direction here). Table 1 summarises the slip trace identification for the two grains. In these two cases, grain A is likely to have deformed as a result of prismatic slip with a difference between the theoretical and measured slip angle of 0.8 and a Schmid factor of Grain B is an example of a grain that is likely to have deformed as a result of basal slip with only a 0.4 misalignment and a high Schmid factor for this slip system of These two cases show a likelihood of prismatic and basal slip and are common cases in regards to the close alignment of the theoretical and experimental trace angles and the ease of identification of the active slip system. In general, it was found that an acceptance level not exceeding +/- 2 was sufficient to identify slip traces. Figure 6 shows the angular mismatch for the active slip system between the theoretical and experimental slip traces identified by the use of HR-DIC for the 8

196 macrozone and no-macrozone condition. The experimental slip traces were measured using ImageJ software, where the angles were measured relative to the horizontal with the angles measured between It can be observed for both conditions that an acceptance angle between predicted and measured slip trace orientation of 10 provides a 100% match. However, by reducing the acceptance angle, it is noticeable that the fraction of no matches increases quite dramatically reaching 70-80% no match if using a 1 angle. No significant differences were detected between the two different microstructure conditions. Based on the results shown in Figure 6, an acceptance angle of 5 was deemed to be acceptable for the slip trace analysis, which is slightly higher than for the ECCI analysis. The most likely reason is that short, straight slip trace segments were analysed when using ECCI imaging while the slip traces visualised by HR-DIC displayed some curvature. In cases where more than one slip system lies within the criteria, CRSS and Schmid factor arguments were used to determine the active slip system. In the case when basal and prismatic seemed possible, two slip modes with relatively similar CRSS value [6], the slip system was chosen with the higher Schmid factor. In all cases this meant that the chosen slip mode had a very high Schmid factor while the other slip mode had a distinctively low Schmid factor. It should also be noted that for basal slip the 3 slip systems result in the same overall slip trace angle. Therefore, for basal slip the highest Schmid factor for the 3 systems was taken into consideration as this the most likely slip system. In the case that pyramidal and one of the slip modes was possible, the about 3 times higher CRSS value of slip versus prismatic and basal slip [4] was also taken into consideration by normalising the corresponding Schmid factor for slip with respect to the CRSS ratio. 9

197 3.2 Slip trace analysis Slip activity Slip trace analysis was performed on the overall materials and for the strongmacrozone material, both the overall material and an individual macrozone were analysed. For the overall materials at least 50 grains is the mini number of analysed of grains to give a statistical evaluation. For the no-macrozone condition 66 grains were investigated. For the soft-oriented strong-macrozone condition, 54 grains were analysed in the overall material and 26 grains were evaluated in a single macrozone region. The slip activity based on slip trace analysis is summarised in Figure 7 for the different conditions. For the no-macrozone condition the entire region was analysed and in the strong-macrozone condition the region highlighted with a white box in Figure 3 was used for slip trace analysis. In the case of analysing the no-macrozone condition, 66 grains were identified whereas it was 54 grains for the strongmacrozone condition. The macrozone on its own was also analysed, which was based on 26 grains. The data were shown as Schmid factor distributions for the active slip systems in each condition with binning windows of 0.05, in order to enable comparison between the different conditions. Table 2 summarises the deformation behaviour in terms of number of active grains for each slip system. From the table each material condition shows a trend for the number of active grains of N Prismatic >N Basal >N with an approximate ratio of 60:30:10% for prismatic: basal: slip. Apart from the special case of the macrozone analysed on its own, the slip trace analysis in Figure 7 suggests that slip associated with very low Schmid factors is predominantly prismatic slip. Other slip modes generally require Schmid factors 10

198 in excess of 0.25 with the exception of the macrozone. Focusing on the macrozone, Figure 7c, there is evidence of prismatic and basal slip being very dominant with pyramidal slip being almost completely absent. Considering the texture of the macrozone and loading direction, this observation is expected Shear strain relative to active slip system The great advantage of using HR-DIC for slip trace analysis is that it also provides the actual shear strain associated with each slip trace. Therefore it was possible to plot the shear strain for each slip system as a function of Schmid factor, Figure 8. In order to take into consideration slight differences in macroscopic strain between the two samples, the shear strain was divided by the average strain recorded in this region. This analysis reveals that prismatic slip traces typically display the highest shear strains in both microstructure conditions followed by basal slip. In addition, Figure 8a shows that the spread in normalised shear strain in the no-macrozone material is distinctively narrower than the spread is seen in Figure 8b for the strongmacrozone condition. A closer look reveals that the widening of the spread for the strong-macrozone condition is almost completely a result of a wide normalised shear strain spread from prismatic slip. 4. Discussion The slip traces analysis demonstrates that in principle a very high fraction of slip traces can be associated with one of the established slip modes in Ti when using acceptance angles of either 2 or 5 when using ECCI or HR-DIC for slip trace visualisation. Interestingly, work by Knoche et al using ECCI in combination with EBSD for slip trace analysis in a nickel base superalloy found a significant fraction 11

199 of slip traces that did not meet an acceptance criterion of [15]. Detailed TEM analysis revealed that such discrepancy can be explained by the presence of stepped slip traces within grains making them to appear non-crystallographic on a microscale. While fcc material, such as Nickel, has 12 independent slip mode, it does only provide the {111}<110> slip mechanism. Hence there are fewer possible slip traces to choose from compared to analysing an hcp metal. Therefore, caution may be required in the slip mode identification presented here until further slip trace analysis by TEM analysis has confirmed the findings by ECCI or HR-DIC. Despite such concerns, the trends observed in terms of the active slip systems for the macrozone and no-macrozone condition are similar to those observed by Boehlert, Li et al [8], [16] for CP-Ti and the -Ti-alloy Ti-5Al-2.5Sn. In [8] CP-Ti shows slightly lower basal pyramidal slip and an increased number of grains that deform by twinning and slip compared to the current work. As the starting textures and relative loading directions are different and CP-Ti has a higher propensity for twinning [6] while Al additions promote basal slip, such difference are indeed expected. The work on Ti-5Al-2.5Sn [16]revealed more basal slip activity than in the present case, which again can be related to texture/loading direction but also the before mentioned effect of Al. Bridier et al [10] also carried out slip trace analysis on a Ti-6Al-4V, where prismatic slip was observed to be dominant similar to the present work. Unsurprisingly, the single macrozone in the strong-macrozone region showed a strong dominance of prismatic slip far exceeding what was observed overall despite the non-macrozone region also being fairly well orientated for prismatic slip. An important aspect of the macrozone is clearly, that such a large region with almost a 12

200 single crystallographic orientation will experience relatively little constrain. Interestingly, the macrozone did contain one grain well with a prismatic Schmid factor less than 0.3, which seems to have deformed by pyramidal slip slip, which seems to have been imposed on the grain by the strongly aligned neighbourhood. In the no-macrozone the less pronounced texture means that the strain concentrations within favourably oriented grains are reduced as there these grains are constrained by differently orientated grains. This is shown in Figure 9 where for the no-macrozone condition the Schmid factor of the active slip systems is shown for each individual grain to give an indication of how the material deforms by relating to the strain intensities and the skeleton slip trace schematic. The validity of Schmid s law as a parameter to predict the likely slip system for a single grain is considered by showing the Schmid factor for the active slip system through slip trace analysis and comparing it with the theoretical most likely slip system in Figure 9a and b, respectively. Similar to the findings by Bridier et al [10], the majority of grains support the predictions of the active slip system in a single grain through the Schmid factor alone, but there are notable exceptions where factors such as slip trace alignment appear to have influenced the primary slip system. For instance, the large grain in the top-right corner has Schmid factors of 0.48 for prismatic slip and has heavily deformed according to the strain map in Figure 9c. More importantly, it appears the grain has a significant impact on the slip activity and active slip system of the surrounding regions. The grain directly below, that has also accumulated high strain, has deformed on a prismatic plane with a Schmid factor of 0.35 even though a different prismatic slip system was available with a Schmid factor of The deformation behaviour appears to agree with observations made by Di Gioacchino 13

201 and Fonseca [11] on stainless steel using HR-DIC where the incompatibility between neighbouring grains was compensated through the alignment of the respective slip systems. In the present case, the grain below has deformed along the slip system that has the closest alignment to the grain above minimising the lattice curvature and minimising compatibility issues. Interestingly, this grain also appears to have activated a second slip system, which is the second mechanism that was discussed to overcome the incompatibility at grain boundaries [11]. This is likely to be a result of the high planar strain across the complete neighbouring grain creating large stress concentrations at the grain boundary. These two heavily deformed grains seem to have shielded the two grains below, resulting in relatively low shear strain in those grains. The low strain is expected in one of the grains as it is badly oriented for both prismatic and basal slip but the other grain is a large grain that is particularly well oriented for prismatic slip with a Schmid factor of Only the lower half of the grain has accumulated high strain slip traces and these are more widely spaced than similarly oriented grains. The skeletal map of the slip traces in Figure 9d shows the high level of slip trace alignment that is described above as one of the possible mechanisms for accommodating the potential incompatibility at the grain boundaries as a result of shear strain. This is predominant in the strain region that stretches from top right to bottom left. The three grains that have deformed by pyramidal slip with Schmid factors of 0.33, 0.18 and 0.28 are in strong agreement with this observation. Despite the grains being favourably oriented for prismatic slip with predicted Schmid factors of 0.43, 0.50 and 0.40, respectively, they have deformed by alternative slip systems to align shear bands. This highlights the restrictive nature of the Schmid factor law as it does not take into account the type and severity of the deformation in the neighbouring grains. 14

202 Finally, slip trace analysis based on HR-DIC enables one to consider not only the number of slip traces but their actual contribution to shear strain, as demonstrated in Figure 8. Such analysis highlights that traces based on prismatic slip do shear more than other slip modes. When comparing the two different microstructures, it is particularly striking to see that in the strong-macrozone condition, shear strain based on prismatic slip reaches significantly higher values than in the no-macrozone condition. Clearly, this is related to the ease of prismatic slip transfer in the macrozone, which is not the case for the no-macrozone condition. 5.0 Conclusions The deformation behaviour of Ti-6Al-4V of strong-macrozone and no macrozone conditions has been studied using HR-DIC to gain detailed information on the strain heterogeneity at the nanoscale. Slip trace analysis technique was used to determine the likely deformation mode in each grain by cross correlating the theoretical slip traces calculated from grain orientation information gained through EBSD with the experimentally observed slip traces from HR-DIC. The main conclusions that can be made on the deformation behaviour are: The no-macrozone and strong-macrozone material showed primary deformation was by prismatic slip with a ratio of ~1:0.5:0.1 for prismatic to basal to pyramidal for deformation by each slip mode. Within a single soft oriented macrozone grains the deformation by prismatic slip was far greater than the overall material and this was contributed to the majority of grains in this region being favourably oriented for this slip domain. 15

203 The shear strain intensity in grains that deformed by prismatic slip was noticeably higher than the other slip modes for both material conditions. Although, the maximum shear in the strong-macrozone material was considerably higher than the values for the no-macrozone condition. The validity of Schmid s law for analysing the deformation systems across a large number of grains was assessed and it was concluded that the majority of grains deformed along the predicted slip system. However, incompatibility issues at grain boundaries were generally overcome by neighbouring grains deforming by a slip system that favoured close alignment of the slip traces across the boundary. Acknowledgements The authors would like to thank the EPSRC for partially funding the project. They are also grateful to Rolls-Royce for funding the project and the provision of materials. 16

204 Reference [1] D. Rugg, M. Dixon, and F. P. E. Dunne, Effective structural unit size in titanium alloys, J. Strain Anal. Eng. Des., vol. 42, no. 4, pp , Jan [2] L. Germain, N. Gey, M. Humbert, P. Vo, M. Jahazi, and P. Bocher, Texture heterogeneities induced by subtransus processing of near α titanium alloys, Acta Materialia, vol. 56, no. 16. pp , Sep [3] M. Bache, Dwell sensitive fatigue in a near alpha titanium alloy at ambient temperature, Int. J. Fatigue, vol. 19, no. 93, pp , Jun [4] G. Lutjering and J. C. Williams, Titanium, 2nd Editio [5] M. Peters and C. Leyens, Titanium and Titanium Alloys [6] J. C. Williams, R. G. Baggerly, and N. E. Paton, Deformation Behavior of HCP Ti-Al Alloy Single Crystals, no. March, pp , [7] M. Preuss, J. Q. da Fonseca, V. Allen, D. G. L. Prakash, and M. R. Daymond, Twinning in structural material with a hexagonal close-packed crystal structure, J. Strain Anal. Eng. Des., vol. 45, no. 5, pp , Jul [8] H. Li, C. J. Boehlert, T. R. Bieler, and M. A. Crimp, Analysis of slip activity and heterogeneous deformation in tension and tension-creep of Ti 5Al 2. 5Sn ( wt %) using in-situ SEM experiments, no. September 2012, pp [9] H. Li, D. E. Mason, T. R. Bieler, C. J. Boehlert, and M. a. Crimp, Methodology for estimating the critical resolved shear stress ratios of α-phase Ti using EBSD-based trace analysis, Acta Mater., vol. 61, no. 20, pp , Dec [10] F. Bridier, P. Villechaise, and J. Mendez, Analysis of the different slip systems activated by tension in a alpha+beta titanium alloy in relation with local crystallographic orientation, Acta Materialia, vol. 53, no. 3. pp , Feb [11] F. Di Gioacchino and J. Quinta da Fonseca, An experimental study of the polycrystalline plasticity of stainless steel, J. Fatigue, no. 0. [12] K. Le Biavant, S. Pommier, and C. Prioul, Local texture and fatigue crack initiation in a Ti-6Al-4V titanium alloy, Fract. Eng. Mater. Struct., vol. 25, no. 6, pp , Jun

205 [13] D. Lunt, M. Preuss, J. Fonseca, and D. Rugg, The macroscopic impact of macrozones on the strain behaviour of Ti-6Al-4V alloy during uniaxial tensile loading (Not-submitted), pp [14] D. Lunt, M. Preuss, J. Fonseca, B. Wynne, and D. Rugg, Nano-scale strain mapping of Ti-6Al-4V with varying degrees of macrozones (not-submitted), no. Dic. [15] E.. Knoche, Influence of the precipitate size on the deformation mechanisms in two nickel-base superalloys, University of Manchester, [16] H. Li, D. E. Mason, Y. Yang, T. R. Bieler, M. a. Crimp, and C. J. Boehlert, Comparison of the deformation behaviour of commercially pure titanium and Ti 5Al 2.5Sn(wt.%) at 296 and 728 K, Philos. Mag., vol. 93, no. 21, pp , Jul

206 Figures and Captions Figure 1- Schematic of slip trace analysis process 19

207 Figure 2- EBSD macro texture maps and (0002) and pole figures with 10μm step size for (a) nomacrozone condition, (b) strong-macrozone condition and (c) no-macrozone regions in strong-macrozone condition 20

208 Figure 3- Nanoscale DIC strain maps of (a) the no-macrozone condition and (b) strong-macrozone condition loaded at 45 both at 3% strain 21

209 Figure 4- Schmid factor argument for (a) no-macrozone and (b) strong macrozone loaded at 45 22

210 Table 1-Comparison of slip angle for between measured (channel contrast imaging) and theoretical (slip trace) analysis Grain ID Theoretical trace Measured trace Active slip Schmid angle ( ) angle ( ) system Factor A (Prismatic) (10-10)[-12-10] B (Basal) (0001)[11-20]

211 Figure 5-Comparison of slip angles for (a) EBSD map of the strong-macrozone condition loaded at 45 after deformation and (b) Channel contrast imaging with two highlighted grains A and B 24

212 Figure 6-Angle mismatch between theoretical and experimental slip trace analysis for (a) No-macrozone condition and (b) Strong-macrozone loaded at 45 25

213 Figure 7-Schmid factor distributions for active slip systems calculated by slip trace analysis for (a) No-macrozone (b), Strong-macrozone and (c) Strong-macrozone in the macrozone region only 26

214 Table 2-Summary of deformation behaviour for each material condition Material Number Active slip system Condition of grains analysed Prismatic Basal No-macrozone 66 58% 33% 9% 54 56% 31% 13% (soft oriented) 26 65% 27% 8% Strongmacrozone Strongmacrozone (Macrozone region only) 27

215 Figure 8- Maximum shear to overall strain ratio shown in terms of Schmid factor for each active slip system for (a) No-macrozone and (b) Strong-macrozone condition 28

216 Figure 9- Schematic of the Schmid factors of (a) the active slip systems and (b) theoretical slip system prediction using Schmid factor within single grains for the no-macrozone condition, (c) the respective shear strain map at 3% applied strain and (d) the skeleton map of the slip traces with the grain boundary map processed with 15 grain boundaries 29

217 Publication 4 Strain behaviour of Ti-6Al-4V with macrozones during fatigue and dwell fatigue loading D. Lunt 1, J. Quinta da Fonseca 1, J. Duff 1, D. Rugg 2, M. Preuss 1 Note: The material was provided by Rolls-Royce with two distinct microstructures. Joao Quinta da Fonseca suggested the single cycle tension-compression experiments to simulate the initial fatigue cycles. David Lunt carried out the characterisation of the microstructure and gold remodelling of the fatigue samples. David Lunt conducted the tension-compression experiments, SEM imaging and DIC analysis. Jonathan Duff and PhD student Christopher Evans assisted David Lunt with the setting up and monitoring of the Tension-Torsion rig. David Lunt wrote the first draft of the proposed publication. Publication prepared for Scripta Materialia 121

218 Strain behaviour of Ti-6Al-4V with macrozones during fatigue and dwell fatigue loading D. Lunt 1, J. Fonseca 1, D. Rugg 2, M. Preuss 1 1 Materials Science Centre, The School of Materials, The University of Manchester, M13 9PL, UK. 2 Rolls Royce PLC, PO Box 31, Derby, DE24 8BJ. Keywords Ti-6Al-4V, Dwell Fatigue, Macrozones, Strain Heterogeneity, Digital Image Correlation Abstract The single cycle tension-compression behaviour of Ti-6Al-4V with two different microstructures was investigated using High-Resolution Digital Image Correlation (HR-DIC). Results show full slip trace reversal in the homogenous microstructure with low texture while the microstructure that contains macrozones only displays partial reversal. Further investigations on the microstructure containing macrozones by fatigue and dwell fatigue loading demonstrated early failure under dwell conditions. At 1000 cycles, the average and maximum shear strain for dwell fatigue was twice that in the fatigue specimens. 1

219 Titanium alloys are widely used in the aerospace industry due to their high strength to weight ratio, moderate temperature properties and good fatigue performance during service [1], [2]. However, it has been shown that when a peak stress hold is introduced into the fatigue cycle there is a significant reduction in the fatigue life of the material [3]. Dwell debit has been shown to occur in both strong and weak textured titanium alloys at high stress levels. Titanium alloys with a strong local texture showed an increase in dwell debit of ~ 3 times compared to a weak micro texture variant, at 95% of the yield stress [4]. The impact of micro texture was also predominant at 90% of the yield stress but there was a reduction in the dwell debit for the high micro texture material [4]. To date, the majority of experiments on the issue of dwell fatigue have been carried out at high hold stress levels, near the yield stress. This increases the likelihood of the dwell effect being observed. However, inservice operation of these alloys is more likely to be at lower stress levels closer to the cyclic yield. A macrozone is a set of neighbouring grains that have a common crystallographic orientation [5] [8]. They potentially create regions within a microstructure that are larger than the average grain size and are likely to impact mechanical properties [9]. Macrozones have been shown to reduce the dwell fatigue life in both IMI834 and Ti alloys [3], [4], [10] [14]. The reduction in fatigue life in material with macrozones is of significance to this study, as the material investigated has strong macrozones. Studies by Lunt et al [15], [16] in Ti-6Al-4V with and without macrozones have used the Digital Image Correlation (DIC) technique combined with Electron Backscatter Diffraction (EBSD) to study the strain evolution on a low and high resolution scale. They have shown that macrozones that are oriented well for prismatic or basal slip deform more heavily and accommodate a higher density of 2

220 slip traces with high shear strain than the neighbouring regions. In the present work, High Resolution Digital Image Correlation (HR-DIC) was used to investigate the strain localisation in Ti-6Al-4V alloys with strongly developed macrozones (strongmacrozone condition) and a microstructure without any macrozones (no-macrozone condition) during single tension-compression cycling. In addition, fatigue testing was undertaken with and without dwell load using the strong-macrozone condition loaded at a 45 angle to the macrozones and using HR-DIC to compare strain localisation under the two different loading conditions. The materials used in this study were a no-macrozone and strong-macrozone variant of Ti-6Al-4V, provided by Rolls-Royce. The strong-macrozone material was from extruded bar designed for blade applications and the no-macrozone condition was forged material. The fatigue specimens were extracted from the materials by electric discharge machining. The test specimens for single cycle tension-compression were flat dog-bone shaped with geometry of 26mm gauge length, 3mm gauge width and 1mm thickness. The standard fatigue and dwell fatigue specimens had the same gauge geometry apart from being 4mm thick. All test specimens were hand polished on an OPS cloth in diluted colloidal silica with 20% hydrogen peroxide for 3 hours after initial grinding to #4000 grit paper. EBSD analysis was performed in a Field Emission Gun (FEG) Scanning Electron Microscope (SEM) (FEI Quanta 650) equipped with an Aztec EBSD system and a Nordlys II detector. Macro-texture and micro-texture EBSD scans were performed with a step size of 10μm and 0.5µm, respectively, at an operating voltage of 20kV. High-resolution strain maps were produced by imaging areas before and after deformation and correlating those images by using DIC [17] [19] In order to achieve the required spatial resolution to resolve slip bands, fine speckle patterns were applied to the polished sample surface using 3

221 the gold remodelling technique [15], [19]. Backscattered electron images were taken with a FEG FEI Quanta 650 SEM at 4000X magnification giving horizontal field widths of 37.3μm. The images were acquired at resolution of 4096x3536 pixels, with a dwell period of 30μs. In order to sample a sufficient number of grains, a mosaic of 4x4 images were recorded. The single cycle tension-compression tests were conducted using a Kammrath-Zeiss 5kN micro tester place outside the microscope. Hence, samples were imaged at zero applied stress by using backscattered electrons before mechanical loading, after 1% and -1% macroscopic strain for each condition. Standard fatigue and dwell fatigue experiments were performed on the strongmacrozone condition loaded at 45 using a Zwick-Roell HTM 50B Servo-hydraulic fatigue testing machine with a 100kN load cell. Samples were loaded at 95% of the yield stress taken from previous tensile experiments [16], at an R ratio of 0.1. For the standard fatigue tests, a trapezoid waveform was used with a 4 second cycle time. For the dwell fatigue experiments, a peak stress hold period of 120 seconds was used. Tests were interrupted at 1000 cycles to record images of the region of interest for each sample. Images before and during deformation were processed using DaVis 8 software to provide high-resolution strain maps of the region. The images were processed with an 8x8pixel 2 sub grid giving a sub grid resolution of 70x70 nm 2. The strain mappings results are presented as maximum shear strain, as this takes into account all the components of in-plane strain. Grain orientation maps together with the associated pole figures recorded by EBSD for the no-macrozone and strong-macrozone condition are shown Figure 1. Figure 1a provides evidence of the absence of macrozones and weak texture for the nomacrozone condition. In contrast, Figure 1b visualises the pronounced macrozones along the extrusion direction (ED) with the c-axis of the primary grains in the 4

222 macrozone regions being predominantly orientated parallel to TD. In addition, the pole figure indicates a strong texture component (rather than fibre texture) with one of the prismatic planes being parallel to ED, Figure 1c shows that in the non-macrozone region the texture is much weaker, indicating that the macrozone regions strongly dominates the texture seen in Figure 1b. The loading experiments on the strong-macrozone condition were performed at 45 to the ED, as previous studies had shown that strain heterogeneity is maximised in this condition under such loading condition [15], [16]. The no-macrozone condition was loaded along the former forging direction. Figure 2 shows the shear strain localisation characterised using high-resolution DIC, after 1% tension and 1% compression for the two conditions. The strain maps are plotted at the same magnification but a smaller region was mapped for the nomacrozone condition due to the more homogeneous microstructure compared to the strong-macrozone condition. Figure 2a shows that after 1% tension, the nomacrozone condition exhibits many grains containing several high intensity slip traces. The slip traces are typically planar and evenly spaced. Figure 2b plots the shear strain map of the same region after subsequent 1% compression. Note that in both cases, after 1% tension and compression, the reference image was the image taken before any loading. Figure 2b shows qualitatively that the majority of the high intensity slip traces have fully reversed or show a large reduction in shear strain in the slip traces. The shear strain map for the strong-macrozone condition, Figure 2c, shows that there are two distinct regions with high and low shear strain, respectively. The top left of the strain map is a non-macrozone region correlating with the low strain band. The high strain band in the centre of the strain map is parallel to ED and exhibits many high intensity slip traces perpendicular to the macrozone direction. 5

223 Figure 2d shows that after 1% compression, there is a reduction in strain in both the high and low shear strain bands. Unlike the no-macrozone condition, it appears that the shear strain within majority of the slip traces has not fully reversed with only partial reductions in shear strain. The overall shear strain within single grains has decreased, particularly in the region of the low strain band. Hence, Figure 2 suggests that the two microstructure conditions display different deformation behaviour during reverse loading. Figure 3 shows the shear strain profiles across grains 1 and 2, marked with white dashed lines in Figure 2, after 1% tension and 1% compression. The grains had similar crystallographic orientations. For the no-macrozone condition, shown in Figure 3a, it is clear that the shear strain intensity of the three distinct slip traces developed during tensioning have dropped to low levels, similar to the rest of the grain, after reverse loading. In contrast, Figure 3b shows that for the macrozone in the strong-macrozone condition there is only a slight decrease in the shear strain within the slip trace regions after reverse loading. Hence, the slip traces are still clearly identifiable after compression loading. The strong-macrozone condition loaded at 45 to ED was studied further during standard fatigue and dwell fatigue loading, due to the suspected susceptibility to dwell fatigue in a material with such heterogeneous nature of the strain behaviour [15], [16]. The HR-DIC methodology was once again used to calculate 2D shear strain maps after mechanical loading. The results for both loading conditions after 1000 cycles are shown in Figure 4 and summarised in Table 1. The dwell fatigue specimen failed after 2022 cycles and the standard fatigue specimen did not fail after 5000 cycles. Figure 4a shows the frequency distributions of shear strain for the two loading conditions after 1000 cycles. It can be seen that the standard fatigue specimen shows slightly higher frequencies for shear strains below 2.5% while above 6

224 2.5%, the opposite trend is observed. Most importantly, the maximum shear strain for the standard fatigue specimen was about 15% while for the dwell fatigue loading the maximum shear strain was just short of 25%, respectively. The standard fatigue specimen accumulated an average shear strain of 1.3% compared to 2.5% in the dwell fatigue sample, a ratio of ~1:2 increase in shear strain from the dwell period. Figure 4b compares the shear strains recorded in slip traces across single grains with a common crystallographic orientation, for the two loading conditions. The two loading conditions exhibit similar slip trace spacing of ~0.5-1μm. However, the dwell loading condition shows significantly higher shear strain intensities across the single grain with an average shear strain in the slip traces of ~5% and a maximum intensity of 11%. This compares to an average shear strain in the slip traces of ~ 2% with a maximum shear strain of 3.5% for the standard fatigue loading condition. The shear strain map for the specimen fatigue loaded under standard condition shows many low intensity slip traces with sporadic high strain slip traces, Figure 4c (i). In contrast, Figure 4c (ii) shows more developed slip traces with much higher strain intensities for the dwell fatigue loading condition. Notable differences were observed in the shear strain localisation for the nomacrozone and the strong-macrozone conditions, when a 1% compression cycle was applied. The shear strain in the slip traces for the no-macrozone condition appeared to fully reverse along the same slip plane, while the shear strain in the strongmacrozone condition only showed partial reversal within the slip traces, with compression in the initial low strain regions. It was expected that the slip traces would fully reverse, as in compression the dislocations are likely to follow the easy slip path that has already been established in the tension cycle. An explanation for the observations in the strong-macrozone condition might be that the macrozone 7

225 regions are accumulating significantly more deformation than the neighbouring nonmacrozone regions. Therefore, the macrozone region will have deformed more plastically while the non-macrozone region has accumulated more elastic deformation. This leads to the possibility of easier slip reversal and subsequent compression in the grains in the non-macrozone region. In principle, a similar situation exists in the no-macrozone condition with grains orientated well for plastic deformation and others less so. However, the slip length in the no-macrozone region is greatly reduced due to the high misorientation between neighbouring grains. In other words there is less strain heterogeneity in the no-macrozone condition than the strong-macrozone condition, which has been observed previously by Lunt et al [16]. Hence, the mismatch generated during 1% tensioning is less than in the strongmacrozone condition. The strong-macrozone condition loaded at 45 to ED was studied further under fatigue and dwell fatigue loading, as the impact of micro-texture is known to have a pronounced effect on the dwell life [3], [4], [10] [12], [20]. The fatigue experiments in this study showed early failure under dwell conditions in the single specimen. However, it should be noted that the experiments were at stress levels of ~95% of the yield stress to increase the likelihood of the dwell debit behaviour being observed. The dwell debit cannot be calculated, as the standard specimen did not fail after 5000 cycles and it should be noted that this is single specimen comparison. Dwell debit is the ratio of cycles to failure for standard to dwell fatigue. But previous studies of highly micro-textured titanium alloys subjected to similar stress levels exhibited dwell debits of 18 compared to 6 in a low micro-texture material [4]. Similar dwell debits are expected in the present study and the early failure is likely to be related to the dwell specimens accumulating twice the average shear strain of the standard 8

226 specimens at the same number of cycles. It is thought that the increased average and maximum shear strain intensities in the strong-macrozone condition are likely to result in pronounced high strain bands similar to the strain band in the tensioncompression tests and in previous tensile loading of the strong macrozone at 45 s to ED [15], [16]. In summary, high-resolution strain maps of the no-macrozone condition during tension-compression tests showed pronounced slip traces after tension and full slip reversal after compression. After tension, the strong-macrozone condition loaded at 45 to ED had a distinct high strain band with clear slip traces. However, the compression cycle only showed partial slip trace reversal. Further dwell fatigue studies on the strong-macrozone condition showed early failure and average and maximum shear strains of ~ 2 times compared to the standard fatigue sample. The authors would like to thank the EPSRC for partially funding the project. They are also grateful to Rolls-Royce for funding the project and the provision of materials. 9

227 Reference [1] G. Lutjering and J. C. Williams, Titanium, 2nd Editio [2] M. Peters and C. Leyens, Titanium and Titanium Alloys [3] M. Bache, A review of dwell sensitive fatigue in titanium alloys: the role of microstructure, texture and operating conditions, Int. J. Fatigue, vol. 25, no. 9 11, pp , Sep [4] S. Gosh, M. Mills, S. Rokhlin, V. Sinha, W. O. Soboyejo, and J. Williams, The Evaluation of Cold Dwell Fatigue in Ti-6242, [5] L. Germain, N. Gey, M. Humbert, P. Vo, M. Jahazi, and P. Bocher, Texture heterogeneities induced by subtransus processing of near α titanium alloys, Acta Materialia, vol. 56, no. 16. pp , Sep [6] L. Germain, N. Gey, M. Humbert, P. Bocher, and M. Jahazi, Analysis of sharp microtexture heterogeneities in a bimodal IMI 834 billet, Acta Mater., vol. 53, no. 13, pp , Aug [7] M. G. Glavicic, B. B. Bartha, S. K. Jha, and C. J. Szczepanski, The origins of microtexture in duplex Ti alloys, Mater. Sci. Eng. A, vol , pp , Jul [8] N. Gey, P. Bocher, E. Uta, L. Germain, and M. Humbert, Texture and microtexture variations in a near-α titanium forged disk of bimodal microstructure, Acta Mater., vol. 60, no. 6 7, pp , Apr [9] D. Rugg, M. Dixon, and F. P. E. Dunne, Effective structural unit size in titanium alloys, J. Strain Anal. Eng. Des., vol. 42, no. 4, pp , Jan [10] V. Sinha, M. J. Mills, J. C. Williams, and J. E. Spowart, Observations on the faceted initiation site in the dwell-fatigue tested ti-6242 alloy: Crystallographic orientation and size effects, Metall. Mater. Trans. A, vol. 37, no. 5, pp , May [11] A. Woodfield, M. Gorman, R. Corderman, J. Sutliff, and B. Yamrom, Effect of microstructure on dwell fatigue behaviour of Ti-6242, Titan. 95 Sci. Technol. Proc. eighth Int. Conf. Titan., vol. 2, pp , [12] M. Bache, Dwell sensitive fatigue in a near alpha titanium alloy at ambient temperature, Int. J. Fatigue, vol. 19, no. 93, pp , Jun

228 [13] V. Sinha, M. J. Mills, and J. C. Williams, Understanding the contributions of normal-fatigue and static loading to the dwell fatigue in a near-alpha titanium alloy, Metall. Mater. Trans. A, vol. 35, no. 10, pp , Oct [14] M. E. Kassner, Y. Kosaka, and J. A. Hall, Low-Cycle Dwell-Time Fatigue in Ti-6242, no. September, pp , [15] D. Lunt, M. Preuss, J. Fonseca, B. Wynne, and D. Rugg, Nano-scale strain mapping of Ti-6Al-4V with varying degrees of macrozones (notsubmitted), no. Dic. [16] D. Lunt, M. Preuss, J. Fonseca, and D. Rugg, The macroscopic impact of macrozones on the strain behaviour of Ti-6Al-4V alloy during uniaxial tensile loading (Not-submitted), pp [17] D. Lunt, D; Preuss, M; Fonseca, J; Wynne, B; Rugg, Sub-micron plastic strain mapping of Ti-6Al-4V with varying degrees of macrozones. [18] J. Quinta Da Fonseca, P. M. Mummery, and P. J. Withers, Full-field strain mapping by optical correlation of micrographs, J. Microsc., vol. 218, no. April, pp. 9 21, [19] F. Gioacchino and J. Quinta da Fonseca, Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation, Exp. Mech., Oct [20] L. Toubal, P. Bocher, and A. Moreau, Dwell fatigue life dispersion of a near alpha titanium alloy, Int. J.,

229 Figures and Captions Figure 1- Macro-texture EBSD orientation maps of (a) the no-macrozone condition and the strong-macrozone condition in (b)the macrozone region only and (c) the non-macrozone region only with a 10µm step size and related {0001} and pole figures 12

230 Figure 2- Shear strain maps for the no-macrozone condition at (a) 1% tension and (b) 1% compression and for the strong-macrozone condition loaded at 45 at (c) 1% tension and (d) 1% compression 13

231 Figure 3- Shear strain profiles for (a) line 1 for the no-macrozone condition and (b) line 2 for the strongmacrozone condition loaded at 45 14

232 Figure 4- Fatigue behaviour of the strong macrozone condition loaded at 45 to ED in terms of (a) normalised frequency of the Shear strain values, (b) slip trace spacing across a single grain and (c) strain mapping of the (i) standard and (ii) dwell fatigue experiments 15

233 Table 1- Summary of the shear strain and cycles to failure during fatigue loading of the strong macrozone condition loaded at 45 Dwell Standard Ratio Dwell/Standard Average Strain in loading direction (%) Average shear strain (%) Maximum Shear Strain (%) Cycles to Failure 2022 No failure after 5000 cycles 16

234 Chapter 5 Summary and Conclusions In the present work, the strain localisation behaviour in Ti-6Al-4V alloys with varying degrees of macrozones has been studied. The conditions were characterised using optical and electron microscopy to identify the critical directions to promote soft and hard macrozone responses during loading. The no-macrozone condition exhibited a weak texture and was loaded along FD, to give a reference material to compare to the macrozone behaviour. The intermediate-macrozone condition had macrozones that were narrow and unevenly distributed in the ND-TD plane. The primary texture component of the material had the c-axis parallel to TD. Therefore, the material was loaded along TD to study the effect of hard oriented macrozones. For the strong-macrozone condition, the macrozones were pronounced and stretched along ED. The primary texture component was the c-axis aligned parallel to TD and little rotation of the c-axis for the prismatic planes indicates a strongly preferred crystallographic orientation. Therefore, this material was loaded at 0, 45 and 90 to ED to observe the effect of different degrees of soft-oriented macrozones. Tensile tests were performed on an optical microscope rig to allow the strain behaviour to be characterised using the DIC technique at the microscale. This was related to the underlying microstructure through cross-correlation with EBSD studies of the regions that were deformed. Microscale shear strain maps showed homogeneous strain localisation in the no-macrozone and strong-macrozone condition loaded at 0 to ED. This was strongly linked to the relatively homogeneous orientation distributions of the two conditions, in respect to the loading direction. The intermediate-macrozone condition shows similar behaviour, but slightly wider shear strain distributions at higher applied strain. The sporadic distribution of the macrozone regions was a key factor. The deformation in the strong-macrozone 122

235 loaded at both 45 and 90 was highly heterogeneous with high strain bands strongly correlation with favourably oriented regions. Slip band characterisation studies using HR-DIC were invaluable in providing detailed information on the strain behaviour at the nanoscale. For all materials, deformation occurred by slip with a dominance of planar slip bands with high shear strain intensity. The maximum shear strain in the no-macrozone condition was about 25% (7 times the macroscopic strain) while in the strong-macrozone condition loaded at 45 the maximum shear strain was almost 35% (11 time the macroscopic strain). The no-macrozone condition showed an even distribution of grains that had not deformed to those that had heavily deformed, with the majority of grains showing partial deformation. However, the intermediate-macrozone condition displayed high density of grains that had not deformed as they were hard oriented with respect to the loading direction. These resulted in high deformation in favourably oriented grains with clear high intensity planar slip traces. A single large high transgranular strain band, where the majority of grains were heavily deformed, was apparent in the strong-macrozone condition loaded at 45. This correlated to a macrozone favourably oriented for prismatic slip. Also, the corresponding deformation in the non-macrozone regions was significantly lower. Slip trace analysis was useful in identifying the active slip systems within each grain through correlation of the HR-DIC strain mapping and the EBSD orientation data. This demonstrated that majority of grains deformed by prismatic or basal slip with the ratio of grains that had deformed by the respective slip system of ~1:0.5:0.1 for prismatic: basal: pyramidal slip. Linking the Schmid factor of the active slip system to the shear strain showed that the shear strain on grains deformed by 123

236 prismatic slip reaches significantly higher values than in the no-macrozone condition. There was an increase in scatter in the shear strain intensities for the strongmacrozone material. The two material conditions both demonstrated that prismatic slip domains deform more than the other slip modes. The validity of Schmid s law for analysing the deformation systems in a polycrystalline material was analysed using the slip trace results. For the no-macrozone condition it showed that most grains deformed along the Schmid factor predicted slip system. However, it appeared that grains also would attempt to deform by a slip system that favoured close alignment of the slip traces between grains, to minimize the incompatibility at grain boundaries. In this case, the slip system chosen is not necessarily the one that has the highest Schmid factor. HR-DIC showed significant differences in the slip behaviour during tensioncompression tests strain on the no-macrozone and strong-macrozone loaded at 45 to ED. The no-macrozone condition showed full slip reversal after compression while the strong-macrozone condition only showed partial slip trace reversal with increased compression in the non-macrozone grains. Further dwell fatigue studies on the strong-macrozone condition loaded at 45, showed early failure and average and maximum shear strains of ~ 2 times compared to the standard fatigue sample. The studies have shown that the orientation of the macrozones relative to the loading direction plays an important part in the shear strain localisation within a material. In Ti-6Al-4V alloys, the macrozone region of the soft oriented strong-macrozone condition accumulated significantly higher shear strains than in the hard oriented intermediate-macrozone condition. The high strains in the strong-macrozone condition were predominantly in the macrozone region and decreased at the 124

237 macrozone boundaries, with the majority of the grains in the macrozone region deforming by prismatic slip. The dominant deformation mechanism in the three conditions was shown to be slip with particular high strain concentrations in the strong-macrozone condition. If the strain behaviour observed locally extended across the material, it is likely to result in significant differences in mechanical performance due to the accumulation of high shear. 125

238 Chapter 6 Future Work Based on the dwell fatigue failure when the strong-macrozone condition was loaded at 45 to ED, it is suggested that similar experiments are repeated for the intermediate and no-macrozone materials during both standard and dwell fatigue loading. This will give good representations of the impact of the microstructure on the dwell behaviour, with respect to the local microstructure. It would also be interesting to study whether increasing the length of the dwell periods has a significant impact on the accumulated shear strain intensities. More importantly, the dwell effects at lower peak stresses, close to the typical operating conditions, should be of particular interest and this would provide a better understanding of the local strain intensities at these loads. Also, on the subject of dwell fatigue, it is shown in the current literature that the dwell effect is suppressed at operating temperatures of 300 C. Therefore, it would be of interest to conduct experiments on the materials at this temperature to study the relationship between the strain behaviour and the number of cycles to failure. Studies of the gold patterns used for HR-DIC at these operating temperatures over time scales greater than 24 hours have shown no change in the pattern morphologies. Currently, the slip trace analysis technique is used to predict the likely deformation systems that are active within a single grain by cross correlation with ECCI or HR- DIC, but these findings have not been confirmed yet using Transmission Electron Microscopy (TEM). Confirmation of these predicted slip systems could be determined by extracting TEM foils, using a Focussed Ion Beam (FIB), from individual grains predicted to deform by prismatic, basal and pyramidal slip from slip trace analysis on the HR-DIC samples. Preliminary work has been performed to investigate the active slip systems on electro-polished 3mm discs that 126

239 were extracted from the gauge length of the tensile specimens. The discs were punched at the edge of the gauge length to enable easy identification of the loading direction. The initial results have shown slip traces with a Burgers vector and these slips traces are shown in Figure 43 with an type. Further TEM analysis could be used to identify slip traces from the different slip systems. Figure 43- Bright and dark field TEM of dislocations with a Burgers vector The EBSD data could be used in conjunction with Crystal Plasticity Finite Element Modelling (CPFEM) to predict the strain behaviour of the materials already studied using DIC. The models could then be implemented to predict the material performance under different loading conditions. 127