Céline Gerard

Loïc Signor

Ludovic Thilly

Celine Gerard

Olivier Castelnau

Keywords: size effects, polycrystalline nickel microwires, cold-drawing, electropolishing, high energy XRD, micro-texture, microstructure modeling, CPFE simulations

Polycrystalline metallic microwires produced by cold-drawing exhibit significant mechanical strength that make them ideal candidates for reinforcement of composites. Previous studies on polycrystalline pure nickel wires have indicated a significant size dependence of their yield and tensile strength as well as their ductility. The aim of this study is to understand these size effects by in-situ X-ray diffraction (XRD) analysis and crystal plasticity finite element (CPFE) simulations. In-situ monotonous and cyclic tensile tests under synchrotron radiation were carried on microwires with diameters ranging from 100 to 40µm. The commercially obtained 100µm as-drawn wires exhibit a core-shell architecture with <111> fiber texture dominant in core and heterogeneous dual fiber texture <111> and <100> in the shell. Reduction of specimen size by electropolishing leads to wires having a homogeneous microstructure, whereas reduction of specimen size by further cold drawing leads to wires with a sharper texture while retaining the core-shell architecture. The yield and tensile strength of the electropolished wires increase with decreasing diameter, whereas the ductility decrease with decreasing diameter. In the case of cold-drawn wires, the yield and tensile strength, and also the ductility was observed to increase with decreasing diameter. The XRD analysis indicates successive yielding of grain families under iso-strain condition. The gradient in the texture of the microwire was seen to activate deformation mechanisms which are not seen for microwires with homogeneous texture. To understand the influence of different microstructural parameters, and notably the influence of crystallographic texture, 3D representative microstructure was generated and CPFE simulations were carried out. The simulated average behavior of different grain families (<111>, <100>) agrees well with the experimental results. The CPFE simulations indicate heterogeneity in the stress field across the microstructure in the presence of a gradient in crystallographic texture. We show that the microstructure engineering of micro-texture components (singleor dual-texture) and their spatial spread (homogenous or architectured) can be used as design guidelines for obtaining optimal microstructure in accordance with a desired set of mechanical properties.

Abstract

Les microfils métalliques polycristallins produits par étirage à froid présentent une résistance mécanique significative en faisant des candidats idéaux pour les renforts de composites. Des études antérieures sur des fils de nickel polycristallin pur ont montré une dépendance importante par rapport à la taille de la limite d'élasticité et de la résistance à la traction, ainsi que de la ductilité. Le but de cette étude est de comprendre cet effet de la taille dans les microfils de nickel pur polycristallin par analyse de diffraction des rayons X in-situ (DRX) et simulations de la plasticité cristalline par éléments finis (CPFE). Des essais de traction monotone et cyclique in-situ sous rayonnement synchrotron ont été réalisés sur des microfils de diamètres allant de 100 à 40µm. Les fils étirés à 100 micromètres obtenus dans le commerce présentent une architecture coeur-coquille avec une texture de fibre <111> dominante dans le coeur et une texture à double fibre hétérogène <111> et <100> dans la coquille. La réduction de la taille de l'échantillon par polissage électrolytique conduit à des fils ayant une microstructure homogène, tandis que la réduction de la taille de l'échantillon par un étirage à froid supplémentaire conduit à des fils avec une texture plus intense tout en conservant l'architecture coeur-coquille. La limite d'élasticité et la résistance à la traction des fils électropolis augmentent avec la diminution du diamètre, tandis que la ductilité diminue avec la réduction du diamètre. Dans le cas des fils étirés à froid, on observe que la limite d'élasticité et la résistance à la traction, ainsi que la ductilité, augmentent avec la diminution du diamètre. L'analyse DRX indique une plasticité successive des familles de grains sous iso-déformation. Nous avons observé que le gradient de la texture du microfil active des mécanismes de déformation qui ne sont pas observés pour les microfils à texture homogène. Pour comprendre l'influence de différents paramètres microstructuraux, notamment l'influence de la texture cristallographique, une microstructure représentative 3D a été générée et des simulations CPFE ont été réalisées. Le comportement simulé moyen des différentes familles de grains (<111>, <100>) concorde bien avec les résultats expérimentaux. La simulation CPFE indique une hétérogénéité du champ de contrainte à travers la microstructure en présence d'un gradient de texture cristallographique. Nous montrons que la micro-texture (texture simple ou double texture) et leur dispersion spatiale (homogène ou architecturée) peuvent être utilisées comme stratégie de conception pour obtenir une microstructure optimale en fonction de l'ensemble désiré de propriétés mécaniques.

Mots-clés: effets de taille, polycristallin microfils de nickel, étirage à froid, électropolissage, DRX à haute énergie, microtexture, modélisation de la microstructure, simulations CPFE.

Introduction

Size effects on the mechanical behavior of metallic materials have been investigated since the mid 20th century. For instance, a classical reference is the work of Hall and Petch in the 1950s on the grain size effect (intrinsic size effect). The miniaturization of the materials at the end of last century has seen different trends in size effects upon the reduction of specimen's size (extrinsic size effect). The race to miniaturization has often met with a trade-off between the strength and ductility of the material. In the last decades, development of different kinds of structures (multi-phase or multi-alloy composite materials) has resulted in very interesting mechanical properties. Owing to the computer revolution, the development of Micro-Electro-Mechanical Systems (MEMS) and Nano-Electro-Mechanical Systems (NEMS) has accelerated. Several different geometries with the characteristic dimension of less than 100µm are used within the context of MEMS such as micro-screws, micro-springs, microwires, micropillars, etc. Nanocrystalline materials turned out to be an ideal candidate at such scale due to their higher strength. However, the usage of these materials is rather limited in the industry, due to the lower ductility in tensile conditions. Novel types of nano-dispersed and/or a multi-gradient based materials have shown extraordinary tensile ductility, but the conception of such materials at the industrial scale is very challenging. With reduction of specimen size, a change in the mechanical properties results from the interaction of different characteristic length scales [1]. Over the years, different trends (strengthening or softening) in size effect have been seen at the micron scale and the understanding of these effects can lead to the development of materials with light weight and high strength. effect. Early work of Rubenstein [5] on Ni microwires in the same size range indicated no strengthening when the wire diameter is reduced by electropolishing, whereas a beneficial size effect was observed for wires further thinned down by cold drawing. The conflicting trends in size effect on mechanical properties for the electropolished cold drawn nickel wires require further investigation.

In the current thesis, we focus on the investigation and fundamental understanding of such size related effects in the micron regime. The choice to work with FCC nickel crystal and cold-drawn microwire is motivated by the previous study on polycrystalline Ni microwires at IISc. Also, experiments on nickel at nanoscale have revealed the effect of intrinsic size, i.e. the reduction of internal size (or microstructure size [6]) and recently, experiments and simulations on thin nickel sheets have been carried out to characterize the interplay between extrinsic and intrinsic size effects [START_REF] Keller | On the origin of the stress decrease for nickel polycrystals with few grains across the thickness[END_REF][START_REF] Keller | TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section[END_REF]. Additionally, experiments on micro-and nano-crystalline Ni have also revealed contradictory strength increase or decrease upon external size reduction [START_REF] Jang | Size-induced weakening and grain boundary-assisted deformation in 60 nm grained ni nanopillars[END_REF][START_REF] Rinaldi | Sample-size effects in the yield behavior of nanocrystalline nickel[END_REF]. Another essential consideration that adds value to the current study is that the size dependence of the wires makes them an ideal candidate for reinforcement of metal matrix composite [START_REF] Cottrell | The ultimate mechanical properties of solids[END_REF].

Methodology

The main objective of this thesis is to address the underlying size effects reported on nickel microwires. To reach this goal, complex in-situ tests were carried out at room temperature on these microwires under high-energy X-ray beams to gain insights into internal deformation mechanisms. Subsequently, crystal plasticity finite element (CPFE) simulations were performed to get a better understanding of the local deformation fields. Finally, experiments and simulations were compared.

In-situ X-Ray diffraction

In-situ X-ray diffraction (XRD)/neutron studies for polycrystalline wires processed by severe plastic deformed (SPD) have been successfully performed previously at Institut Pprime [START_REF] Thilly | Evidence of internal bauschinger test in nanocomposite wires during in situ macroscopic tensile cycling under synchrotron beam[END_REF][START_REF] Thilly | A new criterion for elasto-plastic transition in nanomaterials: Application to size and composite effects on cu-nb nanocomposite wires[END_REF][START_REF] Dubois | Cu-nb nanocomposite wires processed by severe plastic deformation: Effects of the multi-scale microstructure and internal stresses on elastic-plastic properties[END_REF][START_REF] Vidal | Size effect in the plasticity of multiscale nanofilamentary cu/nb composite wires during in-situ tensile tests under neutron beam[END_REF]. It was shown that the diffraction peaks can be followed during deformation to provide information on the evolution of microstructure (including dislocation storage) and to detect elastic-plastic transition and load transfer among different grain families [6,[START_REF] Thilly | A new criterion for elasto-plastic transition in nanomaterials: Application to size and composite effects on cu-nb nanocomposite wires[END_REF]. In the current study, in-situ XRD tests were chosen to discriminate the contribution of internal microstructure and external size on the observed mechanical properties of the polycrystalline nickel microwires. A combination of in-situ tests (monotonous, cyclic tensile, strain rate jumps and stress drops) under high energy X-rays were carried out on several microwires thinned • In Part B, an introduction presents firstly the modeling strategy as well as the main underlying assumptions, in view of the experimental results. (it comprises of Chapter 4 and Chapter 5).

-Chapter 4 discusses the methodology employed in the generation of representative microstructure to be used for CPFE simulation in Chapter 5. Owing to the complex microstructural information from Chapter 3, only the most influential microstructural features were introduced in the generated microstructures. Their representativity regarding those of the actual microwires is also discussed.

-Chapter 5 details the technique and strategy employed for the crystal plasticity finite element simulation of different wires. A brief review of crystal plasticity models from literature along with the choice of model and the parameter identification is discussed. Then, the results obtained using representative microstructures of actual wires are described. Further, conceptual models were also explored to highlight the effect of certain microstructural features.

• Part C contains the Chapter 6, which presents the comparison between results from experiments and simulations. The effect of certain microstructural features on the mechanical properties is also discussed. A discussion in view of the current results and the literature is also provided.

Chapter 1

Literature Review

Introduction

Micro-Electro Mechanical Systems (MEMS) are becoming more widely used with the scale reduction currently ongoing in the microelectronics industry and the associated development of very small devices. The length scale of MEMS spans between a few tens and a few hundreds of micrometers. The application of small-scale materials is vast, with a set of properties like increased strength and ductility, making them ideal in the fields of automotive, electronics and aviation [START_REF] Pelleg | Mechanical properties of materials[END_REF]. At micron scale, the mechanical properties of materials start to deviate from bulk-like behavior [START_REF] Zhu | Micrometre-scale plasticity size effects in metals and ceramics: theory and experiment[END_REF]. The associated size effects occur because of constraints in the microstructure and/or specimen dimension, as demonstrated since the 1950s [1]. Hence, the understanding of the complex material features is required in achieving a desired mechanical behavior. Given the context of this work, two effects, the size and architecture effects are considered here.

1. Size effects can be broadly classified into two types and the interaction between the two: intrinsic (associated with microstructure refinement) and extrinsic (associated with sample size reduction).

• The yield strength of polycrystalline metals increases with grain size reduction, according to the Hall-Petch relation [START_REF] Hall | The deformation and ageing of mild steel: Iii discussion of results[END_REF][START_REF] Petch | The cleavage strength of polycrystals[END_REF]. This regime is seen to be valid from ∼ 20nm to coarse grains. At smaller (nano) scale, the interaction between the dislocations and the grain boundaries plays an important role in influencing the mechanical properties and leads to a deviation from the Hall-Petch behavior. The various behaviors departing from the Hall-Petch relation are illustrated in Figure 1.1.

That is, at nanoscale, the material dependency on the grain size breaks down into several possible behaviors [START_REF] Misra | Structural metals at extremes[END_REF]. With the decrease of grain size the grain boundaries influence dominates, leading to strengthening via an Orowan type mechanism [START_REF] Orowan | discussion in symposium on internal stresses[END_REF].

Another mechanism where the crystals strength is proportional to the inverse of the grain size, approaching the theoretical strength is seen in whiskers [3,[START_REF] Powell | Elastic strength of tin whiskers in tensile tests[END_REF][START_REF] Brenner | Tensile strength of whiskers[END_REF][START_REF] Phani | Tensile strength of sic whiskers[END_REF][START_REF] Hashishin | Morphology and tensile strength of titanium nitride whiskers[END_REF]. Size independent and softening behavior are also seen at few tens of nanometers, also called the inverse Hall-Petch effect [START_REF] Misra | Structural metals at extremes[END_REF][START_REF] Chokshi | On the validity of the hall-petch relationship in nanocrystalline materials[END_REF].

Figure 1.1: The evolution of the yield strength σ y is illustrated for different microstructure regimes (grain size 'd'). Figure redrawn from [START_REF] Misra | Structural metals at extremes[END_REF].

• The strength of single-crystalline materials increases with a decrease of specimen size in the micrometer regime [3,[START_REF] Jang | Size-induced weakening and grain boundary-assisted deformation in 60 nm grained ni nanopillars[END_REF][START_REF] Pelleg | Mechanical properties of materials[END_REF][START_REF] Brenner | Tensile strength of whiskers[END_REF][START_REF] Phani | Tensile strength of sic whiskers[END_REF][START_REF] Hashishin | Morphology and tensile strength of titanium nitride whiskers[END_REF][START_REF] Louchet | Hall-petch law revisited in terms of collective dislocation dynamics[END_REF][START_REF] Greer | Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients[END_REF][START_REF] Richter | Ultrahigh strength single crystalline nanowhiskers grown by physical vapor deposition[END_REF][START_REF] Uchic | Sample dimensions influence strength and crystal plasticity[END_REF][START_REF] Kiener | A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples[END_REF][START_REF] Ng | Breakdown of schmidâs law in micropillars[END_REF][START_REF] Ng | Stochastic nature of plasticity of aluminum micro-pillars[END_REF]. Some well-documented experiments on extrinsic size effect in metals in multi-micrometer regime can be found in [5,[START_REF] Brenner | Tensile strength of whiskers[END_REF][START_REF] Ghosh | Size effects on strength in the transition from single-topolycrystalline behavior[END_REF][START_REF] Miyazaki | Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes[END_REF][START_REF] Fleck | A phenomenological theory for strain gradient effects in plasticity[END_REF][START_REF] Stolken | A microbend test method for measuring the plasticity length scale[END_REF][START_REF] Kim | Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale[END_REF][START_REF] Kim | Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale[END_REF][START_REF] Kim | Crystallographic orientation and size dependence of tension-compression asymmetry in molybdenum nano-pillars[END_REF], as well as at micron and sub-micron scale [START_REF] Rinaldi | Sample-size effects in the yield behavior of nanocrystalline nickel[END_REF][START_REF] Keller | Hall-petch behaviour of ni polycrystals with a few grains per thickness[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF].

• Literature related to experimental studies on interaction of extrinsic and intrinsic size effects usually deals with multi-or poly-crystalline samples, where the strongest coupling between the two size effects is generally observed. In multi-crystalline metals (with only a few grains across thickness), the specimen size (t) and the grain size (d) result in coupled effects, which in turn control the strength of the material [START_REF] Ghosh | Size effects on strength in the transition from single-topolycrystalline behavior[END_REF]. Among the studies on size effect, some of the studies considered possible interaction between grain size and specimen size reduction [START_REF] Rinaldi | Sample-size effects in the yield behavior of nanocrystalline nickel[END_REF][START_REF] Ghosh | Size effects on strength in the transition from single-topolycrystalline behavior[END_REF][START_REF] Miyazaki | Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes[END_REF][START_REF] Kim | Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale[END_REF][START_REF] Kim | Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale[END_REF][START_REF] Kim | Crystallographic orientation and size dependence of tension-compression asymmetry in molybdenum nano-pillars[END_REF][START_REF] Keller | Hall-petch behaviour of ni polycrystals with a few grains per thickness[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF][START_REF] Chen | Specimen size and grain size effects on tensile strength of ag microwires[END_REF], whereas others did not [5,[START_REF] Brenner | Tensile strength of whiskers[END_REF][START_REF] Fleck | A phenomenological theory for strain gradient effects in plasticity[END_REF][START_REF] Stolken | A microbend test method for measuring the plasticity length scale[END_REF].

2. Recently, a strong interest in architectured materials was seen owing to their ability to overcome the shortcomings of metallic materials, especially the strength-ductility synergy [START_REF] Lu | Making strong nanomaterials ductile with gradients[END_REF][START_REF] Lu | Stabilizing nanostructures in metals using grain and twin boundary architectures[END_REF]. Also, at small scales, an increase in strength of the material is usually accompanied by the loss of ductility [START_REF] Koch | Ductility of nanostructured materials[END_REF][START_REF] Wang | High tensile ductility in a nanostructured metal[END_REF][START_REF] Tsuji | Strength and ductility of ultrafine grained aluminum and iron produced by arb and annealing[END_REF][START_REF] Valiev | Nanostructuring of metals by severe plastic deformation for advanced properties[END_REF]. The desire to reach higher strengths in material has led to a stronger demand in architecturing/engineering microstructures to achieve strength-ductility synergy. Architectured materials here refer to a combination of different materials or spatial arrangement of material features. Several experimental approaches have been investigated to establish a framework in terms of manufacturing and behavior of such architectured materials [START_REF] Lu | Making strong nanomaterials ductile with gradients[END_REF][START_REF] Lu | Stabilizing nanostructures in metals using grain and twin boundary architectures[END_REF][START_REF] Koch | Ductility of nanostructured materials[END_REF][START_REF] Wang | High tensile ductility in a nanostructured metal[END_REF][START_REF] Tsuji | Strength and ductility of ultrafine grained aluminum and iron produced by arb and annealing[END_REF][START_REF] Valiev | Nanostructuring of metals by severe plastic deformation for advanced properties[END_REF][START_REF] Zhu | Nanostructured metals: retaining ductility[END_REF][START_REF] Ma | Eight routes to improve the tensile ductility of bulk nanostructured metals and alloys[END_REF]. Figure 1.2 illustrates the definition of architectured material as an intermediate scale lying between the microstructure and superstructures.

Figure 1.2: Definition of architectured materials: a strategy of designing multifunctional material through hybrid and graded materials. Figure taken from [START_REF] Bouaziz | Heterogeneous and architectured materials: a possible strategy for design of structural materials[END_REF].

The purpose of this Chapter is not to review the vast literature related to size and architecture effects (and the related deformation mechanisms in polycrystals), but to provide an insight into different trends of mechanical behavior seen at a scale relevant to the current study. It should be noted that the length scale of interest in this thesis is in micron/sub-micron, hence, review and discussion of 100µm < grain size < 100nm will be limited. Also, the size effects as a result of external stress-strain gradient (i.e. micro-torsion, indentation and bending) are not reviewed here (see Fleck et al. [START_REF] Fleck | A phenomenological theory for strain gradient effects in plasticity[END_REF] and Chen et al. [START_REF] Chen | Size effects in thin coarse-grained gold microwires under tensile and torsional loading[END_REF] for micro torsion of copper wires, Stölken and Evans [START_REF] Stolken | A microbend test method for measuring the plasticity length scale[END_REF] for micro bending on thin nickel foils). First, the section 1.2 gives a brief summary of size effects in single, multi-and poly-crystalline regimes, where specifically the grains and specimen size effects on the plastic flow and yield strength of the material are discussed. Subsequently, the section 1.3 provides an overview of the different architecture effects, followed up with review of the recent and old studies carried out on nickel microwires and related understanding of deformation mechanisms.

Size effects

In this section the effect of size reduction on the mechanical properties of materials is briefly discussed. Generally, the strength of a material increases with decreasing dimensions (external or internal dimensions, i.e. extrinsic or intrinsic), with a decrease in ductility. Decreasing the dimension can be achieved intrinsically by decreasing the grain size in polycrystalline material ( [START_REF] Hall | The deformation and ageing of mild steel: Iii discussion of results[END_REF][START_REF] Petch | The cleavage strength of polycrystals[END_REF], [START_REF] Lloyd | Particle reinforced aluminium and magnesium matrix composites[END_REF]) or extrinsically by decreasing the specimen size in case of a single/multi-/polycrystal ( [START_REF] Kim | Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale[END_REF], [START_REF] Volkert | Size effects in the deformation of sub-micron au columns[END_REF], [START_REF] Fleck | A phenomenological theory for strain gradient effects in plasticity[END_REF]). The strengthening/softening behavior at sub-micron/nano scale are indeed supported by experimental evidences. Generally, in the case of whiskers (Brenner [3]) and micro-pillars (Greer et al. [START_REF] Kim | Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale[END_REF][START_REF] Kim | Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale[END_REF][START_REF] Kim | Crystallographic orientation and size dependence of tension-compression asymmetry in molybdenum nano-pillars[END_REF]), a higher strength and reduced ductility are seen with reduction of external size. However this reduction in ductility with an increase in strength is not evident in all materials at small-scales. Size effects (any changes in extrinsic or intrinsic parameters) are predominant at micron and nano scale of the materials. Additionally, understanding how extrinsic and intrinsic size effects interact with each other and how such interaction leads to enhancement/reduction of material performance is of prime importance to tailor material's response to specific service conditions. Two prominent trends have been seen across literature when it comes to size effect, i.e. 'smaller is stronger', which suggest that the size effect has beneficial effect on mechanical properties of the material and 'smaller is weaker', which suggest that the size effect results in softening of the material behavior. Over the course of time, many different theories have been proposed to understand the size dependent deformation at micron and nano scale. Many of these theories are reviewed extensively in the literature, more precisely in the reviews by Greer et al. [START_REF] Greer | Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect[END_REF], Geers et al. [START_REF] Geers | Size effects in miniaturized polycrystalline fcc samples: strengthening versus weakening[END_REF] and Arzt [1]. Within the context of this thesis, the definition and classification of size effect are categorized into three regimes: the first one being extrinsic (specimen size effect on single/poly-crystals), then intrinsic (grain refinement in polycrystal) and the third one being the interaction of extrinsic and intrinsic size effect in polycrystalline regime, as illustrated in Figure 1.3. Furthermore, the strengthening/softening observed at smaller scales (in microwires, microfilms, micropillars and whiskers) are reviewed briefly.

Extrinsic size effect

Extrinsic size effects are more influential in the single/multi-crystalline regime, i.e. a regime where no or very few grain boundaries exist such that there is no barrier to the mobile dislocations before they reach the surface. Extrinsic size effects have been more commonly observed in thin films [START_REF] Keller | On the origin of the stress decrease for nickel polycrystals with few grains across the thickness[END_REF][START_REF] Keller | TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section[END_REF][START_REF] Keller | Effect of stress path on the miniaturization size effect for nickel polycrystals[END_REF], wires [2,4,[START_REF] Chen | Size effects in thin coarse-grained gold microwires under tensile and torsional loading[END_REF][START_REF] Yang | Cyclic loading behavior of micro-sized polycrystalline copper wires[END_REF][START_REF] Chen | Tensile deformation of silver micro-wires of small thickness-tograin-size ratios[END_REF][START_REF] Khatibi | Tensile properties of thin cu-wires with a bamboo microstructure[END_REF][START_REF] Lederer | Size dependency of mechanical properties of high purity aluminium foils[END_REF][START_REF] Liu | Size effects in the torsion of microscale copper wires: Experiment and analysis[END_REF][START_REF] Tabata | The effect of specimen diameter on tensile behaviors of aluminum thin wires[END_REF], pillars [START_REF] Jang | Size-induced weakening and grain boundary-assisted deformation in 60 nm grained ni nanopillars[END_REF][START_REF] Greer | Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients[END_REF][START_REF] Greer | Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect[END_REF], single crystals in the micron regime [START_REF] Jang | Size-induced weakening and grain boundary-assisted deformation in 60 nm grained ni nanopillars[END_REF][START_REF] Pelleg | Mechanical properties of materials[END_REF][START_REF] Brenner | Tensile strength of whiskers[END_REF][START_REF] Phani | Tensile strength of sic whiskers[END_REF][START_REF] Hashishin | Morphology and tensile strength of titanium nitride whiskers[END_REF][START_REF] Louchet | Hall-petch law revisited in terms of collective dislocation dynamics[END_REF][START_REF] Greer | Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients[END_REF][START_REF] Richter | Ultrahigh strength single crystalline nanowhiskers grown by physical vapor deposition[END_REF][START_REF] Uchic | Sample dimensions influence strength and crystal plasticity[END_REF][START_REF] Kiener | A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples[END_REF][START_REF] Ng | Breakdown of schmidâs law in micropillars[END_REF][START_REF] Ng | Stochastic nature of plasticity of aluminum micro-pillars[END_REF], and whiskers [START_REF] Powell | Elastic strength of tin whiskers in tensile tests[END_REF][START_REF] Brenner | Tensile strength of whiskers[END_REF][START_REF] Phani | Tensile strength of sic whiskers[END_REF].

Tensile strength of whiskers with few micron thickness was first reported by Brenner in the 1950's [3,[START_REF] Brenner | Tensile strength of whiskers[END_REF]. Experiments on whiskers by Brenner [3], Hashishin et al. [START_REF] Hashishin | Morphology and tensile strength of titanium nitride whiskers[END_REF], Phani [START_REF] Phani | Tensile strength of sic whiskers[END_REF] and Powell et al. [START_REF] Powell | Elastic strength of tin whiskers in tensile tests[END_REF] on iron, copper, silicon carbide, titanium and silver whiskers, reported strengthening with decrease of thickness, i.e. 'smaller is stronger' associated to high scatter in strength. The surface effect and batch dependence were proposed to explain this phenomenon. The similar trend of 'smaller is stronger' is reported for most of the single/multi-and nanocrystalline micropillars [28, 30, 38-40, 55, 56, 65, 66]. One of the explanation for such size effects in pillars was proposed by Greer and Nix [START_REF] Greer | Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients[END_REF] with the so-called 'dislocation starvation' mechanism: the dislocations are thought to escape the micropillar before they interact with another dislocation and multiply, and once the pillar is free of dislocations, a higher stress is required to nucleate a new dislocation, hence the strengthening. In contrast other theories have also been proposed to address the strengthening in micro-pillars upon reduction in diameter, such as the 'exhaustion hardening' and 'source truncation' by Dimiduk et al. [START_REF] Uchic | Sample dimensions influence strength and crystal plasticity[END_REF], Parthasarathy et al. [START_REF] Rao | Estimating the strength of single-ended dislocation sources in micron-sized single crystals[END_REF][START_REF] Parthasarathy | Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples[END_REF] and the 'weakest link theory', in polycrystalline regime, by Rinaldi et al. [START_REF] Rinaldi | Sample-size effects in the yield behavior of nanocrystalline nickel[END_REF].

For thin films in the multi-crystalline regime, irrespective of the surface of the specimen (penetrable or impenetrable surface), it was shown that the yield strength scales inversely by the specimen thickness [1]. Keller and Hug [START_REF] Keller | On the origin of the stress decrease for nickel polycrystals with few grains across the thickness[END_REF][START_REF] Keller | TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section[END_REF] have carried out extensive experiments on thin nickel films to study the extrinsic size effect. They have investigated the thickness (t) over grain size (d) ratio and its effect on the mechanical behavior. Based on their work it is evident that for nickel thin films, the number of grains across thickness plays a major role in determining the mechanical properties of the specimen. Three domains of behavior were characterized with respect to different t/d ratios, i.e. microstructure with t/d < 1 (single crystalline), 1 < t/d < 4 (multi crystalline) and t/d > 4 (polycrystalline) regimes. Figure 1.4 illustrates the different regimes of deformation as a function of t/d ratios.

Figure 1.5, shows the evolution of true-stress from tensile test at a strain of 10% for various t/d ratios. The inset shows the microstructure at different t/d ratios and their intragranular stress variation marked by dashed black lines. They reported that the decrease in overall stress in the multi-crystalline regime (1 < t/d < 4) is the result of surface effect, which reduces the intragranular stress for the grains near the surface thus resulting in a stress gradient. The gradient in intragranular stress was almost absent in the case of single-and poly-crystalline regime. In the polycrystalline regime, no major influence of specimen thickness is observed, indicating external size effect comes into play only when the number of grains across thickness is reduced below a critical limit of 4. Their study, with the interaction of inter and intragranular stresses, indicates the delay in the activation of multiple and cross-slip as a possible reason for the observed softening in the multi-crystalline regime. Experimental observations by other researchers on copper sheets (Molotnikov et al. [START_REF] Molotnikov | Size effect on the tensile strength of fine-grained copper[END_REF]), polycrystalline aluminium, copper, copper at 13% of Al and iron (Miyazaki et al. [START_REF] Miyazaki | Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes[END_REF]) have revealed the similar softening trend upon reduction of thickness below a critical limit. In the case of microwires in multi-crystalline regime, discordant results have been observed [2,4,5,[START_REF] Chen | Tensile deformation of silver micro-wires of small thickness-tograin-size ratios[END_REF]. The experimental results for microwires with less than 5 (or more in some case) grains across thickness have shown similar kind of trend as the thin plates [START_REF] Chen | Size effects in thin coarse-grained gold microwires under tensile and torsional loading[END_REF][START_REF] Yang | Cyclic loading behavior of micro-sized polycrystalline copper wires[END_REF][START_REF] Khatibi | Tensile properties of thin cu-wires with a bamboo microstructure[END_REF][START_REF] Liu | Size effects in the torsion of microscale copper wires: Experiment and analysis[END_REF][START_REF] Tabata | The effect of specimen diameter on tensile behaviors of aluminum thin wires[END_REF][START_REF] Wang | Tensile deformation behaviors of pure nickel fine wire with a few grains across diameter[END_REF]. Experimental studies by Yang et al. [START_REF] Yang | Cyclic loading behavior of micro-sized polycrystalline copper wires[END_REF], Liu et al. [START_REF] Liu | Size effects in the torsion of microscale copper wires: Experiment and analysis[END_REF] and Miyazaki et al. [START_REF] Miyazaki | Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes[END_REF] on copper microwires reported a decrease in flow stress with decrease in wire diameter for a few grains across thickness (t/d ≤ 3). The findings of Chen et al. [START_REF] Chen | Tensile deformation of silver micro-wires of small thickness-tograin-size ratios[END_REF] on silver microwire indicate an increase in yield stress with decrease of grains across thickness below the critical t/d ratio of 3. Lederer's [START_REF] Lederer | Size dependency of mechanical properties of high purity aluminium foils[END_REF] work on pure aluminium foils at elevated temperatures revealed the same effect as [START_REF] Chen | Tensile deformation of silver micro-wires of small thickness-tograin-size ratios[END_REF], but it was proposed that the probable cause of such strengthening with decrease in thickness was the formation of the oxide layer near the surface, which further retards the dislocation escape. Another study on cold rolled thin aluminium sheets by Janssen et al. [START_REF] Janssen | An experimental assessment of grain size effects in the uniaxial straining of thin Al sheet with a few grains across the thickness[END_REF] reported that the flow stress increases strongly when the t/d is less than the critical t/d of 3. Since there was no elevated working temperature as in the case of Lederer et al. [START_REF] Lederer | Size dependency of mechanical properties of high purity aluminium foils[END_REF], no oxide layer was observed: the observed strengthening was thought to be a result of presence of grain boundaries parallel to the specimen surface which impede grain rotation and impart more constraint on the grains. The cases where an increase in strength was observed [START_REF] Rinaldi | Sample-size effects in the yield behavior of nanocrystalline nickel[END_REF][START_REF] Chen | Tensile deformation of silver micro-wires of small thickness-tograin-size ratios[END_REF][START_REF] Lederer | Size dependency of mechanical properties of high purity aluminium foils[END_REF][START_REF] Tabata | The effect of specimen diameter on tensile behaviors of aluminum thin wires[END_REF] Figure 1.5: Tensile true stress at 10% strain for various t/d ratios. Inset shows the microstructure corresponding to various t/d ratios with a vertical dashed line profile indicating the state of intragranular stress (in this case: t-varying, d-constant) [START_REF] Keller | TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section[END_REF] upon reduction of thickness were mostly associated with the presence of oxide layer, except for the case of whiskers [3]. In the current thesis, the effect of oxide layer is not of interest as it occurs mostly at elevated temperature, but more detailed analysis of oxide layer and its effect on the strength of material can be found in [START_REF] Lederer | Size dependency of mechanical properties of high purity aluminium foils[END_REF]. The understanding for such strengthening behavior at micron scale seems to be majorly dependent on the microstructure and the experimental conditions.

Most of the studies discussed above concluded that strengthening or softening of the mechanical behavior at lower thickness or diameter is only applicable when the number of grains across the thickness/diameter is less than a critical t/d ratio. In the polycrystalline regime, the material properties were seen to be rather independent from specimen size reduction. However none of the studies considered all the microstructural parameters. For example, the effect of crystallographic texture upon reduction of specimen size in the polycrystalline regime is not often addressed in the literature. Indeed, depending on the processing, texture gradient can be introduced across specimen's thickness and lead to different mechanical properties in the different regimes.

Chen et al. [START_REF] Chen | Size effects in thin coarse-grained gold microwires under tensile and torsional loading[END_REF] study on gold microwire briefly discussed the effect of such texture differences on the mechanical properties at smaller scale. A small variation of yield stress in the polycrystalline regime upon diameter reduction was reported. However the impact of macro-and micro-texture on the observed extrinsic size effect was not quantified. In the case of nickel microwires, recently Warthi et al. [2] reported a 'smaller is stronger' size effect in the polycrystalline regime with no gradient in texture across the wire. So far, no conclusion has been reached regarding the influence of gradients in texture to the observed extrinsic size effect.

Intrinsic size effect

Intrinsically, there are many ways through which a metal can be strengthened. One of the simplest and well understood method among these is the grain size refinement. By refining the grain size, one introduces many grain boundaries, which act as barrier and also source for dislocations. Such strengthening by microstructure refinement with constant specimen size is referred to as intrinsic size effect or Hall-Petch effect. Strengthening by refinement of grain size in the micron regime has resulted in materials with higher strengths, but with increasing strength, a limited ductility is usually observed (less than 5% tensile elongation [START_REF] Raeisinia | Modelling the effect of grain size distribution on the mechanical response of metals[END_REF]). The study reported in [START_REF] Raeisinia | Modelling the effect of grain size distribution on the mechanical response of metals[END_REF] suggests that the limited ability to sustain work hardening is the main reason for reduced elongation. Different microstructural constraints present at the scale of the grains are shown in Figure 1.6. Different behavior is observed when the microstructural parameters of the grain and the characteristic length overlap [1].

The mechanical properties of a material can be enhanced by microstructural constraints. Internal properties of the material such as grain size have noteworthy effect on the yield and fracture strength of material. Hall [START_REF] Hall | The deformation and ageing of mild steel: Iii discussion of results[END_REF] and Petch [START_REF] Petch | The cleavage strength of polycrystals[END_REF] have established the effect of grain size on the yield strength for iron, which is represented as:

σ y = σ o + k * d -1/2 (1.1)
where k is Hall-Petch slope, σ y is the yield stress, σ o is the lattice friction stress and d is the grain size. Generally referred to as the Hall-Petch relationship, it states that yield stress is inversely proportional to the square root of the grain size. Such Hall-Petch behavior has been widely observed for different metals, BCC metals [START_REF] Cracknell | Frictional forces on dislocation arrays at the lower yield point in iron[END_REF], FCC metals [START_REF] Armstrong | The plastic deformation of polycrystalline aggregates[END_REF][START_REF] Phillips | The strain dependence of the flow stress-grain size relation for 70: 30 brass[END_REF]. In the case Figure 1.6: Microstructural constraints present in a grain. Some of the internal characteristic of grain size parameters: D-grain size, δ b grain boundary width, δ width of magnetic domain, L obstacle spacing, R obstacle radius, d dislocation loop diameter, w spacing between partial dislocation [1].

of FCC metals, the Hall-Petch relationship is found to be valid for a wide range of grain size [START_REF] Gertsman | The study of grain size dependence of yield stress of copper for a wide grain size range[END_REF] (down to 1µm) in copper. The Hall-Petch relationship is usually defined for an average grain size and hence by refining the grain distribution, the mechanical response of the material can be improved. The different mechanisms responsible for the observed strengthening are briefly reviewed here. It is also worth noting the inverse Hall-Petch effect [START_REF] Chokshi | On the validity of the hall-petch relationship in nanocrystalline materials[END_REF], where further refinement of grain size leads to a softening of the material. In the case of pure nickel, the transition grain size where strength inverts is predicted at about 16nm [START_REF] Volkert | Size effects in the deformation of sub-micron au columns[END_REF]. Hence, in the present work this regime is not considered, but the details can be found in [START_REF] Meyers | Mechanical properties of nanocrystalline materials[END_REF].

Dislocation pile-up model [START_REF] Li | The role of dislocations in the flow stress grain size relationships[END_REF][START_REF] Li | Petch relation and grain boundary sources[END_REF] was proposed to explain the Hall-Petch behavior in materials. The model states that the bigger the grain size, bigger is the driving force on the dislocations to traverse the grain boundaries. In the case of smaller grains, the pile ups are containing less dislocations leading to an increase of stress required to move a dislocation, thus the strengthening. The other model proposed to explain the Hall-Petch behavior is the slip distance theory [START_REF] Conrad | Effects of grain size on the dislocation density and flow stress of niobium[END_REF], which is based on the distance a dislocation has traveled within the grain. Refining grain size reduces the average distance a dislocation travels. Ashby [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF] and Nye [START_REF] Nye | Some geometrical relations in dislocated crystals[END_REF] explained the Hall-Petch behavior in terms of statistically stored dislocations (SSD) and geometrically necessary dislocations (GND). The assumption is that the strength of the material is enhanced when dislocations are trapped randomly by other dislocations or by grain boundaries during deformation. Asbhy [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF] referred such trapped dislocation within the grain as SSD, which act as obstacles and cause further hardening (forest hardening [START_REF] Taylor | The mechanism of plastic deformation of crystals. part i.âtheoretical[END_REF]). However, SSD were not sufficient enough to explain the hardening and hence the GND were thought to contribute to the additional hardening by increasing the density of immobile dislocations (appearing when a grain undergoes non-uniform strain). The illustration of the GND required to maintain lattice continuity can be seen in Figure 1.7. Another general intrinsic size effect in materials is observed by the introduction of second phase particles. The introduced particles within the grain act as obstacles for dislocations and retard their motion. For a plastic event to take place, a dislocation has to bow out or shear these particles, resulting in strengthening of material properties. For example the Orowan type hardening [START_REF] Orowan | discussion in symposium on internal stresses[END_REF] was experimentally observed and reported by Lloyd [START_REF] Lloyd | Particle reinforced aluminium and magnesium matrix composites[END_REF]. Since the present work deals with pure nickel with no second phase particles and particle interaction will not be addressed here (see [1,[START_REF] Callister | Fundamentals of materials science and engineering: an integrated approach[END_REF] for more details).

Interplay of different size effects

In the study of size effect, the interaction between the specimen and grain size effects are not usually addressed. Such interactions are observed to be the strongest in the single-/multicrystalline regime (with few grains across thickness), i.e. the specimen size (t) and the grain size (d) result in a coupled effect which in turn controls the strength of the material.

One of the early reported analysis by Armstrong [START_REF] Armstrong | On size effects in polycrystal plasticity[END_REF] hints on the coexistence of extrinsic and intrinsic size effect i.e. a dependence of flow stress on both grain size (d) and specimen size (t). Similar dependence of flow stress on the extrinsic and intrinsic size was reported for Al films on Si substrate [START_REF] Venkatraman | Separation of film thickness and grain boundary strengthening effects in al thin films on si[END_REF]. In both of the reported studies, the dependency of the grain size effect (d -1 or d -1/2 ) was difficult to separate as only few grain sizes were investigated. The study [START_REF] Venkatraman | Separation of film thickness and grain boundary strengthening effects in al thin films on si[END_REF] separates the size effect on flow stress by assuming the dependency can be explained as a simple sum of extrinsic and intrinsic size effect (equation 1.2).

f low stress ∝ 1 t + 1 d , (1.2)
A recent study [START_REF] Chen | Specimen size and grain size effects on tensile strength of ag microwires[END_REF] on silver microwire in the multi-crystalline regime reported a failure stress dependency on the intrinsic, extrinsic size effect and the t/d ratio, thus:

f ailure stress ∝ σ (t) + σ (t/d) + k * d -1/2 (1.3)
Though such interaction among different size effects are not often addressed in literature. In the poly-crystalline regime such interaction or coupling of different size effects may be difficult to address due to the superimposing effects [START_REF] Chen | Deformation behavior of thin metallic wires under tensile and torsional loadings[END_REF]. Some of the superimposing effect that could result in an apparent size effect includes: influence of deformation texture, influence of initial dislocation density and influence of strain rate sensitivity.

The Table 1.1 shows some of the studies on the size effects observed over the years in the micron and sub-micron regime.

Author Material (Geometry) t/d regimes Trend in sc, mc and pc regime (in parenthesis the type of size effect)

Observation

Rubenstein [5] Ni (microwires, recrystallized and electropolished, coarse grains: 170µm, fine grains: 20µm, diameter: 76 to 10µm) CG: 0.06-0.44 FG: 0.5-3.8 sc: not applicable mc: smaller is stronger (extrinsic) pc: not applicable An increase in proportional limit stress and decrease in elongation are seen for decrease of diameter in both coarse and fine grains.

Rubenstein [5] Ni (microwires, cold-drawn and electropolished, diameter: 76 to 10µm) ≫ 20 sc: not applicable mc: not applicable pc: no strong changes (extrinsic) The tensile strength of cold-drawn and electropolished microwire exhibited a weak dependency to the specimen diameter.

Rubenstein [5] Ni (microwires, cold-drawn, diameter: [START_REF] Dimiduk | Size-affected single-slip behavior of pure nickel microcrystals[END_REF][START_REF] Frick | Size effect on strength and strain hardening of small-scale [1 1 1] nickel compression pillars[END_REF], Cu [START_REF] Jennings | Microstructure versus size: mechanical properties of electroplated single crystalline cu nanopillars[END_REF], Au [START_REF] Greer | Nanoscale gold pillars strengthened through dislocation starvation[END_REF], Ag [START_REF] Ardell | Precipitation hardening[END_REF].

Architecture effect

In this section, the effect of microstructure architecture on the mechanical properties is briefly reviewed. The architecture effect has led to the development of materials with tailored strength and ductility. In literature, architecture effect has been examined in several different composites and structures from single-phase to multi-phase metals and includes: microstructure gradient in single-phase or multi-phase or multi-component or diffusion-based alloys/composites/biological materials. In the context of current work, only the architecture effect related to single phase metallic materials is reviewed.

By definition, architectured materials are a combination of different materials or spatial arrangement of material parameters to achieve a target behavior. A review by Ma and Zhu [START_REF] Ma | Towards strength-ductility synergy through the design of heterogeneous nanostructures in metals[END_REF] has shown that the strength-ductility synergy has been achieved with structural design such as bi/multi-modal grain size [START_REF] Wang | High tensile ductility in a nanostructured metal[END_REF][START_REF] Prasad | Microstructural evolution and mechanical characteristics in nanocrystalline nickel with a bimodal grain-size distribution[END_REF][START_REF] Witkin | Al-mg alloy engineered with bimodal grain size for high strength and increased ductility[END_REF][START_REF] Dapeng | Ods ferritic steel engineered with bimodal grain size for high strength and ductility[END_REF][START_REF] Wang | A novel process to obtain ultrafine-grained low carbon steel with bimodal grain size distribution for potentially improving ductility[END_REF][START_REF] Zhu | Modelling the plastic deformation of nanostructured metals with bimodal grain size distribution[END_REF][START_REF] Zhao | High tensile ductility and strength in bulk nanostructured nickel[END_REF], harmonic structures [START_REF] Sawangrat | Harmonic-structured copper: performance and proof of fabrication concept based on severe plastic deformation of powders[END_REF][START_REF] Sekiguchi | New microstructure design for commercially pure titanium with outstanding mechanical properties by mechanical milling and hot roll sintering[END_REF][START_REF] Orlov | Obtaining copper with harmonic structure for the optimal balance of structure-performance relationship[END_REF], lamellar structures [START_REF] Wu | Heterogeneous lamella structure unites ultrafine-grain strength with coarse-grain ductility[END_REF], dispersed nanodomains [START_REF] Wu | Nanodomained nickel unite nanocrystal strength with coarse-grain ductility[END_REF] and hierarchical structures [START_REF] Liddicoat | Nanostructural hierarchy increases the strength of aluminium alloys[END_REF][START_REF] Wei | Evading the strength-ductility trade-off dilemma in steel through gradient hierarchical nanotwins[END_REF][START_REF] Lu | Gradient nanostructured materials[END_REF]. The Figure 1.8 shows the synergistic strength and ductility plot of conventional and architectured metals. A review on these different types of architecture in metal can be referred in [START_REF] Ma | Towards strength-ductility synergy through the design of heterogeneous nanostructures in metals[END_REF]. The plotted architecture response of the material corresponds to the single phase metals. For the different materials appearing in the plot the reader is referred to the review article [START_REF] Ma | Towards strength-ductility synergy through the design of heterogeneous nanostructures in metals[END_REF]. Figure taken from [START_REF] Ma | Towards strength-ductility synergy through the design of heterogeneous nanostructures in metals[END_REF].

Architecture effect

Recently [START_REF] Fang | Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper[END_REF], a spatial gradient in grain size by surface mechanical grinding on copper has shown excellent tensile strength and strain hardening abilities. The grain size gradient from surface ranges from tens of nanometers to a few hundred micrometers in the center of the specimen. The results suggest that gradient in grain size leads to additional strain hardening, thus a delayed onset of strain localization. This intentional heterogeneity in the material introduces different, soft and hard, phases leading to plastic deformation in orderly manner. This has also been shown in the case of steel with nanograin gradients [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF]. It was seen that the plasticity sets in the coarse grains first and then propagates to the smaller grains at higher stress. Such gradients in microstructure are seen to introduce heterogeneity in the stress and strain fields resulting in the release of intergranular stresses among the neighbors, thereby delaying the strain localization [START_REF] Zeng | Multiscale modeling and uncertainty analysis of mechanical behavior of nanostructural metals[END_REF]. The Figure 1.9 illustrates the synergistic process of achieving higher strength and ductility with gradient nanograin (GNG) specimens. Different processing routes [START_REF] Thevamaran | Dynamic creation and evolution of gradient nanostructure in single-crystal metallic microcubes[END_REF][START_REF] Hughes | Microstructure evolution, slip patterns and flow stress[END_REF][START_REF] Hughes | Exploring the limit of dislocation based plasticity in nanostructured metals[END_REF][START_REF] Le | Influence of grain size in the near-micrometre regime on the deformation microstructure in aluminium[END_REF] have been proposed to overcome the limitation of having gradient grain size only on the surface by mechanical grinding and also to have more well-mixed and controlled volume fraction of gradient grains. Figure 1.9: Illustration of synergistic approach for strength-ductility. The blue curve indicates the classical banana shaped curve for conventional metals. The red line indicates the strengthductility synergy with gradient nano grains (GNG) [START_REF] Lu | Making strong nanomaterials ductile with gradients[END_REF].

Apart from having gradients in microstructure, a novel class of architecture has been shown by Wu et al. [START_REF] Wu | Nanodomained nickel unite nanocrystal strength with coarse-grain ductility[END_REF], with nanodomain nickel, where a 'self-dispersion strengthening' has been carried out without introducing a second phase. The microstructure includes numerous single-crystal nanodomains of smaller misorientation (<15°with the coarse grain matrix) with 7nm average size spread out in a coarser grain, equaling to 3% of total volume (refer to Figure 1.10 inset). The tensile test results indicate a higher tensile strength, strain hardening and ductility than the homogeneous 18nm grain nickel specimen as shown in Figure 1.10. The higher mechanical properties of nanodomain nickel were explained to be primarily due to the nanodomains increasing the dislocation pinning resistance and also allowing for enough space in the coarser grain for the dislocation to multiply. This indicates that one can fine-tune the mechanical properties by not only blocking the dislocations but also allowing them to multiply in-spite of the blocking. The strength-ductility synergy obtained by such nanodomain nickels is extraordinary, but attaining microstructure with controllable nanodomains is still very challenging. The desire to achieve higher strength and ductility has been realized with the help of gradient microstructures. The important point is that such heterogeneity in the microstructure introduces large strain gradients [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF]. The most common process of achieving a heterogeneous microstructure involves SPD process [START_REF] Tsuji | Strength and ductility of ultrafine grained aluminum and iron produced by arb and annealing[END_REF][START_REF] Valiev | Nanostructuring of metals by severe plastic deformation for advanced properties[END_REF][START_REF] Estrin | Extreme grain refinement by severe plastic deformation: A wealth of challenging science[END_REF]. The obtained material usually exhibits a very complex residual stress state and a preferred texture. The ability of having a more controlled thermomechanical process provides a unique opportunity to obtain heterogeneous microstructure in a single phase material.

Previous studies on nickel microwire

The studies on microwires are of particular interest because of their strength at lower sizes makes them an excellent candidate for reinforcement in composite materials [START_REF] Cottrell | The ultimate mechanical properties of solids[END_REF]. The Figure 1.11 shows the various extrinsic and intrinsic size effect observed in nickel at micron and sub-micron scale. The size dependency in nickel microwires in the range of 10 to 250µm diameters were first reported by Rubenstein [5] in the late 1960's. The tensile tests were carried out on polycrystalline nickel microwires obtained using four types of processing methods: initial cold-drawn and electropolished wires, cold-drawn and recrystallized wires, recrystallized and electropolished wires, further cold-drawn wires. The dependency of tensile strength and ductility on the size varied according to the type of condition the wires were processed. The yield and tensile strength of the cold-drawn wires showed an inverse square root dependency on the wire diameter, i.e. the 'smaller is stronger' effect. The cold-drawn and electropolished wires indicated a weak dependency on the wire diameter with 'smaller is weaker' effect, refer to Figure 1.11(a). While the cold-drawn and recrystallized wire showed no dependency of the strength on the wire diameter, but an increase in proportional limit stress was reported with decrease of wire diameter. For all the four conditions, the ductility of the wire was seen to decrease with decrease in wire diameter. However the results were reported without considering the underlying micro-texture effect as a result of the cold-work.

Recently, tensile tests on commercially cold-drawn and electropolished nickel microwires [2], showed a size effect, i.e. 'smaller is stronger' trend was seen when the wire was thinned down to 20µm by electropolishing from an initial cold drawn 100µm wire. The reported size effect was significant as the smallest wire of 20µm was seen to approach the theoretical strength of the crystal. A strong increase in tensile strength along with a decrease in tensile ductility upon reduction of wire diameter was observed. The fracture surface of the larger wires indicated a cup and cone like surface, whereas the smaller wires (< 50µm) showed a knife-edge fracture surface. Nano-indentation carried out across the section of the largest wire indicated a constant hardness across the wire diameter and hence the observed strengthening upon reduction of diameter was explained as the result of interaction of different characteristic length scales. Such strengthening due to external size reduction in poly-crystalline regime is surprising considering the trends observed in literature. The wires also exhibited prominent shear bands near the fracture surface that were considered to have a role in the higher strength in lower diameter wires. Another series of tensile tests were carried out on cold-drawn and electropolished nickel microwires [4], procured from the same commercial source as [2]. The initial cold-drawn wire showed a comparable strength to the previous study [2], whereas upon electropolishing, a different trend was seen and the smaller wires indicated a significant scatter in the failure stress with no noticeable dependency to the external size. Presence of shear bands were also seen, but a more finer analysis of the fracture surface with FIB-EBSD revealed that the shear bands did not traverse through the specimen thickness. Figure 1.12 shows the sectional EBSD map of fractured region for the 96µm wire. The characterization of the fracture surface revealed extensive fragmentation and rotation of grains from the initial <111> orientation. A increase in grain rotation was reported from the center of the wire to the surface. Similar sectional EBSD map of finer wires revealed grain fragmentation and no grain growth at the fractured region. These two different trends at the same scale indicate an intrinsic parameter at play, which strongly controls the behavior of microwires upon electropolishing.

Summary

During the last few decades size effects have been observed and repeatedly reported for different geometries (wires, films, pillars, whiskers, plate, etc.) at micron and submicron scales. Literature in the field of multi-crystalline samples is contradictory with two prominent observations: the so-called 'smaller is stronger' [START_REF] Chen | Specimen size and grain size effects on tensile strength of ag microwires[END_REF] and 'smaller is weaker' [START_REF] Keller | Effect of stress path on the miniaturization size effect for nickel polycrystals[END_REF][START_REF] Yang | Cyclic loading behavior of micro-sized polycrystalline copper wires[END_REF]. A systematic classification of these effects is provided by Janssen et al. [START_REF] Geers | Size effects in miniaturized polycrystalline fcc samples: strengthening versus weakening[END_REF], who reports possible competition between microstructural constraints, strain gradients, constraints on the surface layer and statistical effects. Experimental observations by other groups on face-centered cubic (FCC) metal thin films [START_REF] Keller | On the origin of the stress decrease for nickel polycrystals with few grains across the thickness[END_REF][START_REF] Keller | TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section[END_REF][START_REF] Chen | Size effects in thin coarse-grained gold microwires under tensile and torsional loading[END_REF][START_REF] Keller | Effect of stress path on the miniaturization size effect for nickel polycrystals[END_REF] indicate a 'smaller is weaker' effect. A more recent study on cold rolled and annealed Ni sheets revealed a complex behavior with the strength increasing and then decreasing when the t/d ratio is less than five [START_REF] Ghosh | Size effects on strength in the transition from single-topolycrystalline behavior[END_REF]. In microwires with few grains across thickness, the effect of specimen diameter was reported to be significant on the properties of the material: in the case of t/d smaller than five, microwires behave as thin plates and exhibit a 'smaller is weaker' trend [START_REF] Kiener | A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples[END_REF][START_REF] Chen | Size effects in thin coarse-grained gold microwires under tensile and torsional loading[END_REF][START_REF] Khatibi | Tensile properties of thin cu-wires with a bamboo microstructure[END_REF][START_REF] Liu | Size effects in the torsion of microscale copper wires: Experiment and analysis[END_REF][START_REF] Tabata | The effect of specimen diameter on tensile behaviors of aluminum thin wires[END_REF], except the case of silver microwires [START_REF] Chen | Specimen size and grain size effects on tensile strength of ag microwires[END_REF].

In the present study, we focus on nickel microwires processed by severe drawing. The literature on Ni and size effects is rather extended but one can refer to the work of Greer et al. [START_REF] Jang | Size-induced weakening and grain boundary-assisted deformation in 60 nm grained ni nanopillars[END_REF], Rinaldi et al. [START_REF] Rinaldi | Sample-size effects in the yield behavior of nanocrystalline nickel[END_REF] and Sun et al. [START_REF] Sun | Dynamic recovery in nanocrystalline ni[END_REF] on nanocrystalline (NC) Ni, and the work of Keller et al. [START_REF] Keller | On the origin of the stress decrease for nickel polycrystals with few grains across the thickness[END_REF][START_REF] Keller | TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section[END_REF][START_REF] Keller | Hall-petch behaviour of ni polycrystals with a few grains per thickness[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF][START_REF] Keller | Effect of stress path on the miniaturization size effect for nickel polycrystals[END_REF] and Ghosh et al. [2,4,[START_REF] Ghosh | Size effects on strength in the transition from single-topolycrystalline behavior[END_REF] on multi-and poly-crystalline Ni to gain insight into the diversity of observed intrinsic and extrinsic size effects. Regarding extrinsic size effects, studies on SPD-produced and annealed Ni thin films [START_REF] Ghosh | Size effects on strength in the transition from single-topolycrystalline behavior[END_REF][START_REF] Keller | Hall-petch behaviour of ni polycrystals with a few grains per thickness[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF], SPD-produced and annealed Ni microwires [5,[START_REF] Wang | Tensile deformation behaviors of pure nickel fine wire with a few grains across diameter[END_REF] indicate different trends in mechanical properties with reduction of specimen size. For example, annealed thin sheets with polycrystalline microstructure (with more than 20 grains across thickness) do not exhibit dependence with respect to specimen thickness, indicating that extrinsic size effect comes into play only when the number of grains across thickness is reduced below a critical value of four [START_REF] Ghosh | Size effects on strength in the transition from single-topolycrystalline behavior[END_REF][START_REF] Keller | Hall-petch behaviour of ni polycrystals with a few grains per thickness[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF]. It seems, that the polycrystalline materials show no dependency on the sample size in micron regime, whereas grain refinement (intrinsic size effect) can result in change of properties. It is also mentioned that the studies on nickel in the polycrystalline regime does not address systematically the superimposition effect of texture or dislocation density.

Studies on architecture effect [START_REF] Meyers | Mechanical properties of nanocrystalline materials[END_REF][START_REF] Kumar | Mechanical behavior of nanocrystalline metals and alloys1[END_REF][START_REF] Zhao | The mechanical properties of multi-scale metallic materials[END_REF] have shown a way to fine tune the mechanical properties by introducing grain size gradient in polycrystalline materials. Severe plastic deformation (SPD) processing techniques applied to metals result in ultra-fine grain (UFG) architecture with grain size ranging between ∼ 100nm and 1µm, that can exhibit high strength and high ductility. Most SPD-related studies deal with intrinsic size effects and possible impact of microstructure architecture such as bimodal grain size distribution [START_REF] Wang | High tensile ductility in a nanostructured metal[END_REF][START_REF] Wang | Enhanced tensile ductility and toughness in nanostructured cu[END_REF], where the fine nano-grains provide high tensile strength and the coarse grains provide ductility.

Recent tensile tests on commercially available Ni microwires by Warthi et al. [2] and Sreenivas et al. [4] have demonstrated a significant extrinsic size effect when the wires are thinned down by electropolishing from an initial cold drawn 100µm wire. The tensile strength of thinnest electropolished wires (in [2]) was seen to approach the theoretical strength and to be much higher than nanocrystalline Ni, whereas [4] reported a huge scatter in tensile strength at lower diameters. As a summary, these studies have shown that cold drawn Ni microwires seem to be sensitive to extrinsic size effect, with increasing tensile strength and reduction of ductility when reducing their diameter by electropolishing, i.e. without changing their microstructure. The following sums-up on size and architecture effects in the different t/d regimes:

• single-crystalline regime: affected by extrinsic size effect and strongly depends on the surface effect followed often by a 'smaller is stronger' trend;

• multi-crystalline regime: interplay of extrinsic and intrinsic size effect plays an important role on the dependency of flow stress. Also the variability in the observed trend may depend on the crystallographic orientation of the grains across thickness;

• poly-crystalline regime: affected by intrinsic size effect, architecture effect and the possible superimposition of texture or dislocation density resulting in an 'apparent extrinsic size effect'.

The objective of this work is thus to understand the strengthening and reduction of ductility observed in nickel microwires with reduction in diameter, by electropolishing and further cold drawing, via an original combination of experiments (high-energy synchrotron XRD) and simulations (CPFEM), and compare with existing literature data and derived models.

Chapter 2

Experimental techniques

2.1 Material description, preparation and characterization

Polycrystalline Nickel microwires

In order to study the fundamental aspect of size effects in nickel microwires [2,4], polycrystalline nickel microwires were obtained from the same commercial source, Alfa Aesar (AA), as in the previous study [2,4] at IISc. Nickel microwires of 100µm diameter in cold-drawn state and 500µm diameter in annealed state, labeled as 'AA100' and 'AA500' hereafter, were purchased from AA in the form of coiled spool. The details about the thermo-mechanical history and the drawing strain of the wires are not available. The material used in this study is high purity Ni with main impurities indicated in A series of wires with different reduced diameters were produced by electropolishing (EP) and cold-drawing the AA100 wires at Department of Materials Engineering -IISc. Characterization of the samples was carried out by SEM and EBSD techniques, which are briefly discussed below.

Characterization technique

Characterization of material and its properties such as grain size and texture distribution provide very important information for establishing the microstructure-property relationship and multiple techniques exist for the said characterization. In this thesis, characterization of the nickel microwires was carried out by scanning electron microscopy (SEM) (secondary electron imaging), electron back-scatter diffraction (EBSD) and X-Ray diffraction (developed in section 2.3). In this section only two techniques will be discussed: SEM imaging and EBSD, both were used for 2D characterization of the microwires.

Scanning electron microscopy (SEM)

Surface topography, defects, and the fractured surfaces can be characterized on a nanometer/ micrometer scale by SEM. A brief overview of SEM used in the scope of characterization of materials can be referred here [START_REF] Joy | Scanning electron microscopy for materials characterization[END_REF] and a detailed history on its development can be referred here [START_REF] Grundy | Electron microscopy in the study of materials[END_REF].

The two major components of the SEM are: the electron emission column and the electron detectors with the control console. During SEM, a fine beam of electrons are accelerated from the filament source and directed at the material via the electron column. The electron beam direction is controlled by scan coils for scanning across the sample. The interaction of the beam with the surface of the material results in a wide range of emissions such as secondary electrons, back-scattered electrons, Auger electrons, X-rays, etc (Figure 2.1). Detectors are used for the collection and conversion of these emissions into an electrical signal, which is later processed to obtain digital images. A secondary electron detector (SED) is used for producing specimen topography. A backscattered electron detector (BSD), Energy-dispersive (EDXS) and wavelength-dispersive (WDXS) X-Ray spectrometers are used to resolve material composition.

Experimental conditions for secondary electron imaging: The measurements on nickel microwires, such as diameter quantification, surface defects, and fracture surface, were carried out on JEOL field emission gun (FEG) SEM (model JSM-7001F) at Institut Pprime, refer Figure 2.2. The range of operating voltage used for characterization and imaging was 10 -15 kV (current of 8 nA) with the chamber pressure of 2.8 × 10 -4 (Torr/ Pa). In the current work, only secondary electron imaging function of the SEM was carried out by JEOL SEM. A specific sample holder on which the microwire was mounted (detailed in section 2.2.1) was then inserted into the chamber and attached to the SEM stage by a double-sided carbon tape. For the secondary electron imaging, the working distance between the sample surface and the polar piece was ∼ 10mm. For each sample, the astigmatism correction/ calibration was carried out. The characterization of the microwire by SEM was carried out before and after the in-situ deformations.

Electron backscatter diffraction (EBSD)

EBSD provides quantitative information on the microstructural aspects of the materials such as crystallographic texture, grain boundary character, grain size and orientations as well as the phase identification. An EBSD pattern collection with different required components is illustrated in Figure 2.3. Similar to SEM, when an electron beam of a specific voltage interacts with the material surface, electron diffraction occurs spherically around the interaction. The diffraction pattern can be recorded by putting a phosphor screen close to the surface of the specimen. The spatial and angular resolution of EBSD is dependent on the resolution of the SEM. Ideally, a 70°tilt is maintained for the sample towards the detector for better acquisition of diffracted electrons. A CCD camera is placed behind the phosphor screen to record the converted light, which corresponds to the diffracted electrons. Specific software is used in the analyses of the EBSD patterns: the recorded patterns are composed of Kikuchi bands (Figure 2.3 (5)) that are analyzed and indexed by doing the best fit to resolve the phase and orientation.

Experimental conditions for EBSD: Sample preparation for EBSD characterization is a very important step. Ideally the surface should be flat and highly polished. Therefore, the EBSD analysis was carried out at dual-beam SEM Focused Ion Beam (FIB) workstation using FEI Nanolab Helios G3 CX at Institut Pprime (Figure 2.4). A FIB consisting of a beam of Ga+ ions was used to remove/ sputter the material locally from the specimen surface: an alternative to mechanical polishing. A detailed explanation on the usage of FIB in material science can be referred to [START_REF] Cox | Focused ion beam materials science applications[END_REF]. For EBSD mapping the surface of the specimen has to be planar and because of the small diameters of the nickel wires, an FIB source is more suitable. The FIB at Institut Pprime is equipped with an electron emission column also with several detectors for data collection. The microwire is mounted on a 'finger' shaped cantilever geometry, as shown in Figure 2.5. The 'finger' holder has two knife edges (facet) with angles specific for EBSD acquisition (Figure 2.5(c)) and FIB milling (Figure 2.5(b)). In the current study, to protect the surface, an initial layer of platinum, referred to as cap material is deposited on the surface normal to the ion beam via a gas-injection. The cap material mills at a slower rate than the material of interest, thereby, improving the surface of the material by eliminating the 'curtaining' or 'waterfall' effect. These curtaining effects produce vertical streaks caused by rough surfaces and can significantly affect the EBSD indexing of patterns [START_REF] Orloff | High-resolution focused ion beams[END_REF]. The milling of the surface is initially carried out at moderate currents to make the surface planar. This is followed up with milling at a very low current to obtain a smooth surface with minimum damage underneath. The finger holder is then rotated 180°, which orients the sample with an angle of 70°between the electron beam and surface normal, because of the pre-tilt provided by the knife edges. The working distance for EBSD is usually between 5-20mm. EBSD characterization was carried out both in longitudinal and cross-sectional direction of the microwire.

Material preparation and characterization

This section details the preparation of different series of microwires for in-situ deformation tests. From the commercially procured 'AA100' and 'AA500' microwires, several other microwires were produced by electropolishing and cold-drawing process. These processed microwires are classified into three batches as electropolished (EP) series, cold-drawn (AA) series and lab-drawn (LD) series of microwires. Figure 2.6 summarizes the list of sample diameter prepared and retained for in-situ testing with their naming convention that will be followed throughout this manuscript.

Commercial 100µm wire (AA100)

The as-received microstructure of the AA100 microwire was characterized by EBSD. The cross-sectional and longitudinal surface of the microwire was initially cut and polished by dual-beam FIB with a very low current. Several EBSD complete cross-sectional mappings were performed on sections taken few meters apart in length to ensure the representativeness of grain size and texture distribution. The EBSD acquisition was done with 50nm step size to have a good resolution of the sub-micron grains and the subsequent analysis was carried out by TSL OIM T M software to compute the micro-texture, grain size as well as the distribution of grain boundary misorientation. A low tolerance angle of 2 • and minimum grain size of 25 pixels were chosen for the cleanup of EBSD data. A fine analysis regarding the impact of these parameters on the microstructural statistics of these microwires has been carried out and are reported elsewhere [START_REF] Rouault | Characterization of nickel microwires by FIB-EBSD[END_REF]. The macro volume fractions of texture components in the microwire have been characterized by the XRD pole figures and are addressed in section 2.3.5.

From the AA100 wires, with diameter of 103µm ± 1 (error bars corresponds to standard deviation of diameter between different samples), two series of wires with varying diameters were obtained by further electropolishing (labeled as 'EP series') and cold-drawing ( labeled as 'AA series') respectively.

Thinning down AA100 microwires by electropolishing (EP series): In the EP series, several wires of 70µm, 50µm and 40µm diameter were produced by electropolishing, labeled respectively as EP70 (diameter: 69µm ± 1.5µm), EP50 (diameter: 49µm ± 1.5µm) and EP40 (diameter: 40µm ± 2.5µm). It should be noted that the diameter and error value corresponds to the mean diameter and standard deviation between the different samples and are not related to the diameter variation along one single wire. The electropolishing was carried out with an electrolyte having a volumetric ratio 9:1 of ethanol to perchloric acid under a potential of 3.3V, at a temperature of 250K. Two aluminium plates interconnected by aluminium rods were used as cathode. The wire was mounted horizontally in between the aluminium plates, on polymer slabs, to minimize the impact of temperature gradient and to obtain uniform diameter. The wire along with the aluminium plates was then immersed in the temperature controlled electrolyte, with positive terminal of power supply attached to the aluminium plates and the negative terminal attached to the wire. As current is applied, the surface of the wire oxidizes and dissolves into the electrolyte. The diameter reduction was monitored by a stop clock and a smooth surface was obtained by achieving an optimum compromise between applied voltage and current with periodic stirring of the electrolyte. A schematic of the electropolishing setup developed in the laboratory at IISc is shown in Figure 2 It is noteworthy to mention that at such scales, certain artifacts can be observed as a result of EP, an example being roughness of surfaces (one such case is reported in Appendix A.1). The surfaces of the electropolished wires were checked along the entire gauge length of 6mm using JEOL FEG-SEM. Only specimens with a smooth surface and uniform diameter having a variation of ±1.5µm or less along the gauge length were selected for the in-situ tests. The SEM micrographs of AA100 wire ( Thinning down AA100 microwires by cold-drawing (AA series): A second series of wires, labeled 'AA' series, were thinned down from the initial AA100 wire by cold-drawing. Comparable to the 'EP series', several wires of 70µm, 50µm and 40µm diameter were produced by further cold-drawing the AA100 wire, respectively labeled as AA70 (diameter: 67.5µm ± 0.5µm), AA50 (diameter: 47.5µm ± 0.5µm) and AA40 (diameter: 37.5µm ± 0.5µm). The cold drawing was carried out using an instron machine at IISc lab as shown in Figure 2.9. The setup consists of a die resting block, which restricts the die movement and a 'three jaw' grip to hold the wire parallel to the drawing axis. The die used for drawing is made upon polycrystalline diamond and has a fixed die angle of 13°. The stationary grip with one end of the wire should be in line with the drawing die axis to avoid any artifacts in texture distribution. One end of the AA100 wire is thinned down by immersing the wire in concentrated nitric acid solution for a few seconds at 330K, to make it pass through the inner die cavity. Once through, the reduced end is attached to the stationary grip and a constant displacement of 8mm/s is applied to the die resting block. Consequently, a decrease in diameter is achieved as the wire passes through the die with a relative increase in length resulting in the volume remaining constant. The wire was subjected to several similar passes to achieve the target diameters of 70µm, 50µm, and 40µm from the initial 100µm. In order to avoid failure of wires during drawing, it was made sure that the area reduction during each pass remained less than 30% [START_REF] Kalpakjian | Manufacturing engineering and technology[END_REF]. Hence, the die sequence (AA100 (103µm) → 85µm → 70µm → 60µm → 50µm → 40µm) used to obtain the target diameter was selected based on the constraints of the area reduction allowed at each step, i.e, not exceeding 30%. Several samples of 70µm, 50µm and 40µm diameters were taken to carry out the in-situ tests. It is important to mention here that the wire drawing was carried out at room temperature with no intermediate stress relief or annealing treatments between passes. A lubricant (machine grade oil) was used during the drawing process for the wires to have a better surface finish.

The smallest diameter wire produced by cold-drawing i.e, AA40, has been characterized by EBSD. Cross-sectional and longitudinal EBSD maps were performed on the wire to compute the micro-texture, grain size as well as the distribution of grain boundary misorientation. The EBSD acquisition was done with a smaller step size of 20nm to have a good resolution of the sub-micron grains and an identical data cleanup and analysis used for AA100 wires was employed for drawing statistics.

Commercial 500µm wire (AA500)

A second set of annealed nickel microwires of 500µm diameter, labeled as 'AA500', were procured from AA (details regarding the annealing treatment were not made available). The wire was procured and characterized by EBSD at IISc. The AA500 wire was never used for any of the in-situ tests. The wire was drawn to a smaller diameter wire comparable to that of AA100 wires, which was used for in-situ testing.

Thinning down AA500 microwires by cold-drawing (LD series): From the initial AA500 wire, a 100µm wire labeled as 'LD100' (diameter: 98.5µm ± 0.5µm), was produced by cold-drawing. The drawing of AA500 was carried out using same technique and under same conditions as mentioned in Subsection 2.1.3.1. Several different passes were done to achieve the target diameter of 100µm from the initial 500µm. The selected die sequence is as follows: AA500 (500µm)→ 300µm → 200µm → 100µm. The subsequent drawing using the aforementioned die sequence leads to a drawing/ deformation strain of 3.2. The SEM micrograph of LD100 wire is shown in The texture analysis using EBSD and high energy XRD was carried out on the LD100 wire. EBSD acquisition was done with 50nm step size and an identical data cleanup strategy as AA100 was employed in calculating the statistics regarding the grain size and micro-texture distribution.

Samples selection and overview

The sample selection criteria which include several ex-situ tests and characterization by optical microscopy and SEM before and after in-situ testing is schematized in Figure 2.12. Figure 2.12: Various steps of nickel microwire processing, characterization and mounting. Bad surface here corresponds to non-smooth surface or a larger diameter variation along gauge length.

Mechanical testing 2.2.1 Sample holder

Adaptable and robust sample holder was designed at Institut Pprime in collaboration with IISc. The sample holder has two lateral metallic bars, which keeps the two grips in line thereby maintaining the gauge length of 6mm while mounting and handling prior to actual testing (2.13(a)). For the tests, the whole assembly along with the sample is mounted on a micro tensile machine (MTM) and the lateral bars are removed before the start of the test. The samples tested were produced in India (at IISc laboratory) and were tested at SLS (Switzerland) and SOLEIL (France) synchrotron. A set of 40 microwire holders were produced to optimize the time and to carry out more tests at synchrotrons. Before mounting, the microwires were cleaned for a few minutes in ethanol using ultrasonic cleaner (cold bath). Every sample was mounted with the assistance of an optical microscope and high magnification camera to achieve a good alignment within the sample holder. Figure 2.14 (a) is a capture of a live image from DinoCAM camera, illustrating horizontal and vertical assistance lines superimposed on the image to help align the microwire in grips. The ends of the mounted microwire are manipulated with tweezers to bring them in line with the tensile axis. Once the alignment is done, the microwire is then glued with a cyanoacrylate-based super glue (commercial name: Loctite), monitoring their alignment via live feed while doing so. One end of the wire is also glued with a patch of conductive colloidal graphite to avoid charge build-up during SEM. The mounted microwire with the sample holder is then imaged with SEM every 500µm along the gauge length. One such stitched SEM image taken every 500µm along the gauge length of EP70 wire is shown in Figure 2.14 (b). This alignment procedure results in more reproducible data during mechanical testing (i.e, less scatter). The axis offsets across two grips, characterized by optical microscope, having a maximum of ±40µm sample misalignment with the axis was retained for in-situ tests.

Micro tensile machine (MTM) at MS and DiffAbs beamline

To carry out mechanical tests on nickel microwires, specific micro tensile machines (MTM) are used at the MS beamline and DiffAbs beamline. The technical drawings of the MTM used at MS and DiffAbs beamline are shown in Figure 2.15. The MTMs were mounted on the goniometer at both the MS and DiffAbs beamline. During the in-situ tests, the sample holder (with sample) was mounted on the MTM and the load was applied via a stepper-motor that controlled the displacement of the sledge at one end of the grip. The displacement/ steps' size used during the tests were 180nm/s at MS and 50nm/s at DiffAbs. The force measurement during loading was done via load cell (Transduce Techniques MLP50 at MS and Futek LCM300 at DiffAbs), which was connected to one end of the grip. The sample elongation was calculated from the changes in distance of the grips. Although, a CCD camera was used to measure the displacement on the sample at DiffAbs beamline, the image quality was not optimum due to sample movement and long shutter time. Hence, DIC data is not presented in the main text but is included in Appendix A.2. The integration of proportional integral derivative (PID) controller with the MTM at MS beamline via a LabView script provides additional freedom for performing tests like stress-drop and strain rate jump tests. The PID with MTM calculates the average stress values of the specimen dynamically during deformation and this provides a more rapid feedback to control and stop the machine at a particular stress level.

The PID integration was not done at DiffAbs beamline and hence, only tensile and tensile cyclic tests were carried out. More details regarding the MTM and its specifications can be found here (MS: [START_REF] Brandstetter | Deformation mechanisms of nanocrystalline nickel studied by in-situ x-ray diffraction[END_REF], DiffAbs: [129]).

Stress and strain calculation

The engineering stress and strain have been calculated with the following relation:

ε eng = △L L 0 , △L = L -L 0 (2.1)
σ eng = F A 0 , A 0 = πr 2 (2.2)
where L 0 is the initial gauge length (6mm), △L is the difference between the actual current length (L) and the initial length (L 0 ). F is the measured force from the load cell, and A 0 is the initial cross-section area of the microwires, defined by the radius of each wire (quantified with SEM measurements). The conversion of engineering stress-strain to true stress-strain is done via the standard equations defined by,

ε = ln(1 + ε eng ) (2.3) σ = σ eng (1 + ε eng ) (2.4)
The true stress-strain (σ and ε) are referred to as applied stress-strain in the current work and the plotted stress-strain curves correspond to true stress-strain unless otherwise mentioned. Since the computed true stress-strain values are valid only until necking (failure stress), only data points until the onset of necking have been considered and presented.

Tensile and cyclic tensile testing

Monotonous and cyclic tensile tests were carried out at both (MS, DiffAbs) beamlines at room temperature. The data collected at DiffAbs beamline was with faster acquisition and hence, more XRD data points were obtained for the same duration of test. The faster acquisition time and the high X-Ray flux made it possible to conduct continuous uni-axial tensile and cyclic tests.

• MS beamline: Tests were conducted on AA100 and EP series (EP70, EP50, EP40) wires at a constant strain rate of 3 × 10 -5 s -1 . In-situ tests were performed at least three times for monotonous tensile tests and twice for cyclic tests for each wire dimension to ensure reproducibility of the results.

• DiffAbs beamline: Tests were conducted on AA100, EP series (EP70, EP50, EP40), AA series (AA70, AA50, AA40) and LD100 wires at a constant strain rate of 8.3 × 10 -6 s -1 .

In-situ tests were performed at least three times for monotonous tensile tests and twice for cyclic tests for each wire dimension to ensure reproducibility of the results. At the beginning of the test, samples were pre-strained, to stresses lower than 100 MPa, to align them with respect to the X-ray beam. This pre-straining ensures minimal vertical displacement of the illuminated volume during the test. Hence, the presented stress-strain curve in Figure 2.16 has initial values of stress and strain higher than zero. The recording of diffraction pattern was started after the initial pre-straining. In the absence of pre-straining, the vertical movement of sample during initial deformation can cause shifts in peak position and may introduce errors (see Appendix A.3 for more details). Figure 2.16 presents in a superimposed way the monotonous true stress-true strain and cyclic (load-unload) true stresstrue strain plots for two AA100 wires tested at DiffAbs beamline, each data point corresponds to a recorded XRD pattern. It should be noted that the machine compliance contribution has not been removed but is expected to be reduced for smaller diameter wires as the forces applied are very small. Digital image correlation (DIC) study was carried out ex-situ on the EP series of wires and the corrected slope for smaller diameter wires were not much different from the uncorrected stress-strain data from the machine, refer Appendix A.2 for more details.

Stress drop tests

Due to the extended close-to-zero hardening regime observed in AA100 wires (see Chapter 3), the stress drop and strain rate sensitivity tests were conducted only for the AA100 wires at MS beamline (thanks to the PID integrated MTM). Two stress drop tests were carried out in the macro-plastic region defined by the 0.2% strain criterion which is met at a stress of around 850MPa for AA100 wires. One example of the stress drop test is shown in Figure 2.17 (each data point corresponds to the recorded XRD patterns).

Figure 2.17: Stress drop tests for one AA100 microwire. Top inset shows stress drop test for one stress ratio defined by a pre-defined stress σ 0 and the current unloaded stress σ r . Bottom inset shows the evolution of macroscopic applied strain during the creep period.

The stress drop tests were conducted by straining the microwires up to a pre-defined stress (σ 0 ) at a constant strain rate of 3 × 10 -5 s -1 and then dropping the stress suddenly to a new lower level (σ r ) and staying at the new level for a creep period of 60 minutes. After this period, Experimental techniques constant strain rate straining can be resumed up to the pre-defined stress, if necessary. In terms of analysis, only the evolution of FWHM and the inelastic strain during the 60min creep period is of interest. The inelastic strain is calculated from the macroscopic stress-strain curve by subtracting the contribution of elastic strain from total strain using the following relation:

ε inelastic = ε total - σ E app (2.5)
where E app is the apparent elastic modulus which includes the contribution of machine. The relative stress reduction ratio is defined as R = σ r σ 0 : for a large stress reduction, R is very small. Stress drop tests allow studying the deformation mechanism responsible for the changes in FWHM in the macro-plastic regime by suppressing dislocation slip. A more elaborate procedure of such stress drop tests on ED NC Ni can be found in reference [START_REF] Sun | Dynamic recovery in nanocrystalline ni[END_REF].

Strain rate jump tests

Strain rate jump tests were carried out at MS beamline only on the AA100 wires. As shown in Figure 2.18, a method of sudden increase and decrease of strain rate in the macro-plastic regime is employed to calculate the strain rate sensitivity index 'm'. The strain rate was sequentially modified to values between 5 × 10 -5 s -1 and 1 × 10 -3 s -1 , and sufficient time in-between to avoid any transient effect. The strain rate sensitivity index is calculated with the following equation:

m = ln(σ A /σ B ) ln(ε B /ε A ) (2.6)
where σ A and σ B are the respective stress level at strain rates εA and εB . The analysis of the strain rate sensitivity index provides information on the nature of deformation. Higher values of m (> 0.3) are considered as footprint of superplastic behavior. A strain rate sensitivity index of nearly zero indicates rate-independent plastic flow. A detailed study on strain rate sensitivity for micro-(> 1µm), ultrafine (100 -1000nm) and nano-grain (< 100nm) Ni can be found in references [START_REF] Van Petegem | Microstructure and deformation mechanisms in nanocrystalline ni-fe. part ii. in situ testing during x-ray diffraction[END_REF][START_REF] Schwaiger | Some critical experiments on the strain-rate sensitivity of nanocrystalline nickel[END_REF].

Figure 2.18: Continuous stress-strain curve for AA100 microwire with different strain rates in the macro-plastic regime. Inset shows the magnified section the curve where the effect of strain rate changes can be seen.

X-Ray powder diffraction 2.3.1 Principle

The fundamental principle of X-ray powder diffraction is that the scattered X-rays from the crystal planes, the atoms and their cloud of electrons, are generated when Bragg's condition (Eq:2.7) is satisfied. This one states that the interaction of monochromatic X-ray beams with the crystal planes interact constructively to produce scattered X-ray beam when,

λ = 2d hkl sinθ hkl (2.7)
where λ the wavelength of the radiation used, d hkl the lattice/ inter-planar spacing of planes with the Miller indices (hkl) of appropriate lattice planes and θ hkl is the diffraction angle between the diffracted X-rays and the crystal planes. The 2θ variable comprises the information of powder diffraction that occurs in all direction effectively into one dimension.

There are two basic methods of generating diffraction by satisfying Bragg's condition. The monochromatic method and the Laue method. In the current thesis, the monochromatic method is employed. A fixed wavelength λ is used (as a result of using monochromatic radiation), thus the Bragg's condition is satisfied by rotating the crystal (θ ).

The material being used is pure nickel, for which the lattice spacing (d) between planes can be calculated from the lattice cell constant of nickel (3.5239 Å [START_REF] Davey | Precision measurements of the lattice constants of twelve common metals[END_REF]). Also it is worth mentioning that the crystallites in the material under investigation has an asymmetric shape (needle like geometry) and has a very strong preferred orientation. This strongly affects the data acquisition time. The procedure for analyzing XRD data and the specific interest of such analysis is elaborated more in subsection 2.3.4.

X-Ray source

In the current work, only synchrotron X-ray sources are employed during testing. The strength of the synchrotron source lies in the following reasoning: choice of wavelength from a continuous X-Ray spectrum, high energy X-Ray beam for better statistics (more intense peaks, better signal to noise ratio) and time-resolved abilities to carry out in-situ continuous deformation with faster acquisition time, the intensity of the incident beam is well concentrated into a well defined dimension. Two synchrotron sources were employed during this study: Swiss Light Source (SLS), Paul Scherrer Institut, Switzerland and SOLEIL, France.

In-situ synchrotron XRD experimental setup

All in-situ tests were performed under high-energy synchrotron XRD (DiffAbs and MS beamlines) at room temperature. For better interpretation of data from beamlines, the sample to detector distance, beam wavelength and also in some cases the tilt of detector relative to the beam has to be calibrated. Before the in-situ tests the diffraction pattern of Lanthanum hexaboride (LaB 6 ) is recorded to calibrate the detector tilt and sample to detector distance. The procedure of calibration with PyFAI [START_REF] Kieffer | Pyfai, a versatile library for azimuthal regrouping[END_REF] and Fit2D [START_REF] Hammersley | Fit2d: an introduction and overview[END_REF] is detailed more in Appendix A.3. The major differences between the two series of experiments (conducted at two different beamlines) lie in the incident X-Ray beam energy (MS: 26 keV; DiffAbs: 19 keV), the type of detectors (MS: 1D microstrip detector MYTHEN [START_REF] Bergamaschi | The mythen detector for x-ray powder diffraction experiments at the swiss light source[END_REF] and area detector Pilatus 6M [START_REF] Rajendran | Radiation damage in room-temperature data acquisition with the pilatus 6m pixel detector[END_REF]; DiffAbs: area detector XPAD S140 [START_REF] Boudet | Xpad: a hybrid pixel detector for x-ray diffraction and diffusion[END_REF]), the detector acquisition time (MS: 10-30 seconds; DiffAbs: 1-3 seconds) and beam dimensions (MS: 200µm high × 600µm wide, DiffAbs: 250µm high × 250µm wide). More details on the beamline can be found here (MS: [START_REF] Willmott | The materials science beamline upgrade at the swiss light source[END_REF][START_REF] Patterson | The materials science beamline at the swiss light source: design and realization[END_REF], DiffAbs: [START_REF] Mocuta | Fast pole figure acquisition using area detectors at the diffabs beamline-synchrotron soleil[END_REF]). The experimental setup of each beamline are briefly described below.

Material Science (MS) beamline at SLS

The first experimental testing campaign on nickel microwires was carried out at MS beamline in 2016. The experimental setup at the MS beamline of SLS is shown in Figure 2.19. To provide additional degree of freedom, the 1D microstrip detector (MYTHEN [START_REF] Bergamaschi | The mythen detector for x-ray powder diffraction experiments at the swiss light source[END_REF]) along with the MTM is attached to the goniometer, which allows for rotation. The MTM has fixed position and angle during the experiments. To record additional diffraction geometry of the material simultaneously during experiments, a 2D area detector (Pilatus 6M [START_REF] Rajendran | Radiation damage in room-temperature data acquisition with the pilatus 6m pixel detector[END_REF]) was installed at 1m from the MTM. Both the detectors allow continuous recording of X-Ray diffraction patterns. During the experiments, the sample holder (and sample) was mounted on the MTM, the incident X-Ray beam of 600µm × 200µm dimension was aligned to the center of the microwire. As can be seen from the Figure 2.19, the diffracted beam is then recorded with the 1D microstrip detector having a 2θ range of 120°and an angular resolution of 0.0039°, simultaneously a part of the Debye-Scherrer rings are also recorded using the area detector. The acquisition time used for both the detectors was 10 seconds per pattern (one full spectrum) for the bigger diameter (AA100) wire and 30 seconds per pattern for the smallest (EP40) wire. For more details on the detector, refer to [6,[START_REF] Bergamaschi | The mythen detector for x-ray powder diffraction experiments at the swiss light source[END_REF].

DiffAbs beamline at SOLEIL

The second experimental campaign was carried out at DiffAbs beamline in 2017. Figure 2.20 shows the experimental setup in two configurations used at DiffAbs beamline of SOLEIL, France. At DiffAbs, only one detector was used to record diffraction pattern. An area detector XPAD S140 [START_REF] Boudet | Xpad: a hybrid pixel detector for x-ray diffraction and diffusion[END_REF] was used in a configuration to record only the reflections of planes perpendicular to the wire axis (see Figure 2.20(a)). The detector is mounted on an arm connected to the 6-axis gyroscope, which allows to record different diffraction geometry. In the current work, the in-situ tests were carried out continuously and two different tilts (δ ) angle configuration were used. The first angle configuration (δ = 90°, Figure 2.20 (a)) involved recording only axial [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections. In the second angle configuration (δ = 0°, Figure 2.20 (b)) involved recording only transverse [START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections. The second angle tilt configuration was only used at the maximum and minimum load of each cycle during the cyclic tests.

During the experiments, the sample holder (and sample) was mounted on the MTM, the incident X-Ray beam of 250µm × 250µm dimension was aligned to the center of the microwire. As can be seen from the Figure 2.20(a), a part of the Debye-Scherrer rings of specific grain families is then recorded with the XPAD S140 detector. Thanks to the very short read-out time (2 ms) of the detector, the acquisition time was decreased to 1 second per pattern for the bigger diameter (AA100, LD100) wire and 3 seconds per pattern for the smallest (EP40, AA40) wire.

Diffraction geometry at MS and DiffAbs beamline

The nickel microwires under study are highly textured materials with preferred <111> and <100> oriented grains (also called 'grain families') along the tensile axis. Hence, for the in-situ tests only the evolution of these grain families has been followed. The corresponding transverse and axial (hkl) reflections of these grain families are illustrated in Figure 2.21. The blue vector corresponds to the diffraction vector associated with planes perpendicular to wire axis (labeled axial (hkl) reflections) and the red vector corresponds to the diffraction vector associated with the planes parallel to wire axis (labeled transverse (hkl) reflections). It is mentioned that the nickel microwires used here are polycrystalline and have tens of thousands of grains across the cross-section, with average grain size being less than 1µm. During in-situ test, it is certain that at any given point during deformation, a large number of grains are being illuminated that fulfills the Bragg's condition. At MS and DiffAbs beamline only a part of the Debye-Scherrer rings of these grain families were recorded using the area detector (MS: Pilatus 6M, DiffAbs: XPAD S140). The recorded Debye-Scherrer rings here corresponds to the reflection of planes perpendicular to the wire axis and the calculated lattice strains corresponds to axial strains. The advantage of recording axial reflection is that here each axial reflection corresponds to the respective texture component of the grain families (refer to blue planes in Figure 2.21). An example 2D pattern of AA100 wire at MS and DiffAbs beamline is shown in Figure 2. 22 (a, b). At the DiffAbs beamline alongside the axial (hkl) reflections, the transverse (hkl) reflections associated to the textured grains were recorded only for the cyclic tensile tests at the minimum and maximum loads of each cycle with the same 2D detector (the sample was rotated 90°to record the transverse (hkl) reflections, see Figure 2.20(b)). Conversely, at the MS beamline, the transverse (hkl) component of the textured grains were continuously recorded simultaneously for all the type of tests with a 1D microstrip detector. In this geometry, the observed peaks corresponds to the transverse reflection (refer to red planes in Figure 2.21). As can be seen from Figure 2.21, the transverse reflection [START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF] can arise from grains with <100> axial texture or <111> axial texture. When analyzing such diffraction peak one should thus remember that it includes the averaged behavior of two different grain families. At MS beamline, thanks to the large 2θ (120°) range offered by the 1D microstrip detector, both positive and negative reflections of the <111> and <100> oriented grains (i.e, -60°to +60°) were recorded. The presented results are the arithmetic average of positive and negative reflection. An example of the recorded peak by the microstrip detector for AA100 wire is shown in Figure 2.22 (c).

Analysis and interpretation of XRD data

The 1D pattern recorded with MYTHEN detector for each experiments are available as intensity over diffraction angle (2θ ) for each recorded spectrum. The 1D pattern recorded at MS beamline has both positive and negative reflections in the same spectrum. Each spectrum is cut out into a positive and negative spectrum and they are treated individually before averaging. For the patterns (axial reflections) recorded with 2D detector, where a part of the Debye-Scherrer rings is recorded, a preliminary process of detector calibration by a standard material (Lanthanum hexaboride powder) and flat field recording is carried out for correction with PyFaI [START_REF] Kieffer | Pyfai, a versatile library for azimuthal regrouping[END_REF] and Fit2D [START_REF] Hammersley | Fit2d: an introduction and overview[END_REF] software. In order to evaluate the peak profiles, the rings are processed by caking along angle ψ (refer to Figure 2.23). Because of preferred orientation, regions of high intensity appear along the rings and the caking angle is defined to include the high intensity segments of the rings (here △ψ = 5°). The integration along ψ yields 1D diffraction intensity pattern with respect to 2θ (refer to Figure 2.23). The 1D pattern is then fitted with a split Pearson VII function to resolve parameters related to the shape of the peak, the peak position (2θ ) and the peak width or Full Width Half Maximum (FWHM) (Equations 2.8 and 2.9). Each peak is evaluated separately and a single peak is described by the following equations:

I(2θ ) = I max × 1 + 2 1 M r -1 × (10 -α + 1) 2 × θ -θ hkl FW HM -M r , i f θ ≥ θ hkl (2.8) I(2θ ) = I max × 1 + 2 1 M l -1 × (10 -α + 1) 2 × θ -θ hkl FW HM -M l , i f θ <θ hkl (2.9)
where θ is the diffraction angle, θ hkl is the peak maximum angle of the corresponding (hkl) reflection, I max the maximum peak intensity or peak height, FWHM the peak width, α the logarithmic asymmetry parameter, M r and M l are the right and left decay component, the value of which gives to Pearson VII a Gaussian or Lorentzian character. A detailed information regarding the peak fitting analysis procedure can be found in paper [6]. Peaks of {111}, {200} and {220} are fitted separately for the transverse diffraction pattern recorded by 1D detector and peaks of {111} and {200} are fitted separately for the axial diffraction pattern recorded by area detectors.

In the current thesis, we have monitored the changes in peak position and peak broadening during deformation. Following the peak profile changes during deformation provides us information on the microstructure evolution. The Table 2 2.2: Internal stresses and their influence on peak profile [START_REF] Sun | Nanocrystalline metals: transient testing during in situ x-ray diffraction and molecular dynamics[END_REF].

Lattice strain evolution: X-Ray diffraction probes the changes in the lattice spacing during deformation and these changes can be monitored for selected grain families. The lattice strain ε hkl is represented in microstrain units by the following relation:

ε hkl = -cot(θ hkl )△θ hkl × 10 6
(2.10)

where △θ hkl is the difference of peak position calculated from the current θ hkl and the initial recorded position. In the plot of lattice strains vs applied stress, the elastic deformation regime is indicated by the linear behavior of the lattice strain (illustrated in Figure 2.24), whereas a deflection from linearity indicates the onset of plastic deformation. For a tensile deformation, a negative deviation from linearity of a particular (hkl) reflection is related to the grains that are plastifying, whereas a positive deviation from linearity is indicative of elastic load takeover or 'load-transfer' from the plastic grains to the still elastic grains [START_REF] Van Swygenhoven | In-situ mechanical testing during x-ray diffraction[END_REF].

Figure 2.24: Schematic presentation of lattice strain (peak shift) and FWHM (peak broadening) with respect to applied stress. The elastic regime is represented by the linear behavior, red marks the macro yield point.

FWHM evolution: Additional information on the microstructure evolution can be obtained from the FWHM analysis. In the current thesis, the evolution of peak broadening is defined as FWHM. The FWHM here is presented in terms of scattering vector 's', calculated with the following relation:

δ s hkl = 2 × cos(θ hkl ) × FW HM hkl λ (2.11)
where FW HM hkl is the measured FWHM in radians and λ is the wavelength of X-rays used.

The FWHM in initial state can result from intergranular strains due to difference in the average strains of different grains and/or intragranular strains due to the presence of dislocations within grains and/or intragranular inhomogeneous elastic strain field. During in-situ deformation, when dislocation density increases, the FWHM is expected to increase (refer to the illustration in Figure 2.24). A decrease in FWHM can also occur as a result of recovery of defects (also internal stresses) by grain boundary (GB) mediated mechanisms [START_REF] Van Petegem | Creep in nanocrystalline ni during x-ray diffraction[END_REF]. Another mechanism that can cause the reduction of FWHM include changes in coherent scattering length as a result of grain size changes during deformation [START_REF] Van Petegem | Creep in nanocrystalline ni during x-ray diffraction[END_REF]. The analysis of lattice strain and evolution of FWHM during deformation provides the possibility to follow the evolution of microstructure (including dislocation storage) and to detect elastic-plastic transition within different grain families [START_REF] Thilly | A new criterion for elasto-plastic transition in nanomaterials: Application to size and composite effects on cu-nb nanocomposite wires[END_REF][START_REF] Van Swygenhoven | In-situ mechanical testing during x-ray diffraction[END_REF]. In this thesis, the in-situ XRD data interpretation is based on the relative changes of the measured values and not the absolute values.

XRD texture analysis

It is assumed that the fiber texture of cold-drawn nickel microwires under study have rotational symmetry along the fiber axis as a result of the drawing process. Hence, only one quadrant of the pole figure was constructed at the DiffAbs beamline for AA100, EP40, AA40 and LD100 wires, whereas on the intermediate wire diameters (EP70, EP50, AA70, AA50) a single fiber texture plot (FTP) was carried out, which is essentially a slice from the pole figure. The texture analysis was made possible at DiffAbs beamline due to the additional degree of freedom provided by the sample stage; the diffraction spectrum were recorded with XPAD S140 area detector. In the pole figure analysis: the sample was tilted (δ ) from 0°to 90°with a step of 1°, and the for every δ angle, the sample was also rotated along the tensile axis (φ ) from -190°t o -90°with a step of 0.5 • . The configuration of the sample at δ = 90°, represents the lattice planes oriented perpendicular to wire axis, and δ = 0°, corresponds to lattice planes oriented parallel to wire axis. A schematic of nickel microwire diffraction geometry with tilt and axis angle is shown in The rotation symmetry of the fiber texture around the fiber axis is confirmed by carrying out a φ scan, in which the sample is rotated along the tensile axis and the pole density intensity plot is reconstructed by moving the sample from δ = 90°to δ = 0 • with step of 1°. Figure 2.26 shows the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF], [START_REF] Schmid | Kristallplastizit˜it[END_REF] and [START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF] pole density intensity vs δ plot for AA100 wire. As can be seen for different φ angle (-180°, -135°, -90 • ), the pole density intensity remains rather close, which confirms the rotational symmetry of the fiber texture.

The FTP analysis may misrepresent the true texture in the case of non-ideal fiber texture. The type of texture analysis carried out on the microwires is summarized in Table 2.3.

Series

Sample ID Average diameter (µm) Type of texture analysis

Commercial wire AA100 103 ± 1 δ = 0°-90°, △φ = 100°E P40 40 ± 2.5 δ = 0°-90°, △φ = 100°E P series EP50 49 ± 1.5 δ = 0°-90°, △φ = 0°E P70 69 ± 1.5 δ = 0°-90°, △φ = 0°A A40 37.5 ± 0.5 δ = 0°-90°, △φ = 100°A A series AA50 47.5 ± 0.5 δ = 0°-90°, △φ = 0°A A70 67.5 ± 0.5 δ = 0°-90°, △φ = 0°L D series LD100 98.5 ± 0.5 δ = 0°-90°, △φ = 100°T
able 2.3: Summary of texture analysis carried out for various diameters of nickel microwire (the error bars correspond to standard deviation and reflects the diameter difference between different samples).

The volume fraction for the radial pole density plots are calculated using the procedure described in [START_REF] Cullity | Elements of x-ray diffraction[END_REF], with the following relation:

V <111> V <100> = 4
3 area of curve corresponding to [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection area of curve corresponding to (200) reflection (2.12)

Chapter 3

Experimental results

This chapter details the results of EBSD and in-situ XRD characterization of three batches of nickel microwires (EP series, AA series, LD wires), as described in Chapter 2. In the current work:

• The first series of tests were carried out at SLS (MS beamline) on commercial and electropolished nickel microwires (EP series) obtained from the same commercial source as Warthi et al [2] at a strain rate of 3 × 10 -5 s -1 (unless otherwise mentioned).

• A second series of tests was carried out at SOLEIL (DiffAbs beamline) on EP series, AA series and LD100 microwires at a strain rate of 8.3 × 10 -6 s -1 (unless otherwise mentioned).

As already discussed in Chapter 2, two different MTMs were used for the series of tests. For a meaningful comparison of results across different diameters, only one series of results will be detailed here. In this chapter, the described results correspond to tests conducted at DiffAbs beamline, unless otherwise mentioned. The results of SLS are detailed in Appendix B and comparison is made wherever required in the text.

Microstructure of Ni microwires

This section details the EBSD characterization of three batches of nickel microwires (EP series, AA series, LD wires). Several EBSD cross-sectional mappings were performed on sections taken few meters apart in length to ensure the representativeness of grain size and texture distribution. The analysis of cross-sectional EBSD maps revealed the microstructure of the wire to consist of equiaxed ultrafine grains in the range of 400nm to a few micrometers. The analysis of local regions in cross-sectional and longitudinal EBSD map revealed the range of grain size from 400nm to 1.5µm in the core. The aspect ratio, grain length along the wire axis to grain diameter along the cross-section, ranges from 5-33. In case of the shell, the grain size ranges from 300nm to 1.5µm and the aspect ratio from 3-20. The EBSD longitudinal and cross-sectional maps and their associated pole figures are representative of the wire microstructure as shown by the good agreement with macroscopic XRD pole figures. Additional cross-sectional and longitudinal EBSD maps and their local analysis are presented in Appendix B. 111), ( 200), ( 220) pole figures from EBSD (pole intensity relative to normal of wire axis).

EP series (EP70, EP50, EP40): Homogeneous reduction of wire diameter by electropolishing leads to a decrease in the shell volume fraction. The smallest diameter studied here is 40µm, where the shell is expected to be completely removed. The expected architecture of these electropolished diameters is illustrated in Figure 3.1(a) by dashed circles. The high energy XRD pole figures of the smallest wire obtained by electropolishing (EP40) are shown in Figure 3.3. The absence of intermediate orientations as well as a strong <111> fiber texture with a very minor <100> component can be observed from the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] pole figures. The analysis of the XRD pole figures of the EP40 wire indicates a 95% volume fraction of <111> and a mere 5% volume fraction of <100> oriented grains. For the intermediate diameters EP70 and EP50, XRD radial texture analysis was carried out for calculation of volume fraction of <111> and <100> texture components and can be found in Table 3.1. The gradual decrease in volume fraction of <100> component with electropolishing is in line with the micro-texture observations by EBSD.

Comparing the macroscopic XRD pole figures of AA100 from Figure 3.1(c) with that of EP40 from Figure 3.3, it is clear that with electropolishing the heterogeneous shell volume fraction is removed and the scatter of texture along the fiber axis is also markedly reduced. AA100 wire has more inhomogeneous microstructure because of the presence of distinct core and shell, whereas for the EP40 wire the inhomogeneity is removed by electropolishing the shell. 200), ( 220) pole figures of 40µm microwire (EP40) from high-energy X-Ray diffraction.

AA series (AA70, AA50, AA40): Different diameter microwires were obtained by colddrawing the AA100 microwire. The analysis of cross-sectional EBSD maps revealed that the wire is composed of equiaxed ultrafine grains with size ranging from 250nm to 2µm. Preliminary investigation revealed that the texture components in the wire have correlation with their spatial location along the wire cross-section, as was observed in the case of AA100 wire. The cross-sectional EBSD map along with the EBSD and high energy XRD pole figures are presented in Figure 3.4. A 'core-shell' architecture is evident from the cross-sectional EBSD map of AA40 wire. Individual local analysis of the cross-sectional map of core and shell of AA40 wire shows a gradient in grain size with core having grains in the size range of 400nm to 2µm. For the shell this range is from 250nm to 700nm.

The dashed black circle (8µm radius) in Figure 3.4(a) corresponds to 40% of the diameter of the AA40 wire. The 'core' of AA40 wire, marked by the innermost circle of 8µm radius, exhibits a strong <111> fiber texture, whereas the 'shell' exhibits a dual texture with majority of <111> oriented grains and a minor <100> oriented fraction of grains. The EBSD pole figures from The analysis of longitudinal EBSD map of AA40 wire revealed highly elongated grains/fibers with major <111> and minor <100> texture components respectively along the wire axis (Figure 3.5). The available longitudinal map of AA40 wire indicates a very high aspect ratio.

Comparing the macroscopic XRD pole figures of AA100 from Figure 3.1(c) with those of AA40 from Figure 3.4(c), it is clear that with further cold work, the scatter of texture is reduced along the fiber axis. AA100 wire has more intermediate orientations in the shell, and the grain size range is uniform across the cross-section, whereas for the AA40 wire the grain sizes are heterogeneous across the cross-section. LD series: The LD100 wire has been cold-drawn at IISc from the AA500 wire to a drawing strain of ~3. The texture analysis using EBSD and high energy XRD was also carried out on the LD100 wire (Figure 3.7). The analysis of cross-sectional EBSD maps revealed the microstructure of the wire to consist of equiaxed ultrafine grains with sizes ranging from 400nm to 1.7µm. 111), ( 200), ( 220) pole figures from high-energy X-Ray diffraction.

As was observed in case of AA100 wire, the texture components in LD100 wire also show strong correlation with spatial location along the wire cross-section. According to the inverse pole figure (IPF) map shown in Figure 3.7(a), the micro-texture of LD100 wire exhibits a 'core-shell' architecture, with 'core' having a dual fiber texture (<111> and <100>) with <100> as major component as illustrated by the innermost circle of 20µm radius. The 'shell' exhibits a dual texture with majority of grains having <111> and <100> orientations, as well as several intermediate orientations. The EBSD pole figures from Figure 3.7(b) and high energy XRD pole figures from Figure 3.7(c) indicate the major fiber texture component being <111> and a minor <100> texture along with a fewer intermediate orientations. At global level, the analysis of the XRD pole figures of the LD100 wire indicates a 77% volume fraction of <111> and 23% volume fraction of <100> oriented grains. Individual local analysis of cross-sectional EBSD map of core and shell shows grain in the core having sizes ranging of 500nm to 1.7µm, whereas the shell has slightly smaller grains with sizes ranging from 400nm to 1.5µm. The statistics above have been drawn from two complete cross-sectional EBSD maps distant from few meters.

XRD texture analysis

For all the microwires (AA100, EP series, AA series, LD100), the radial pole density intensity vs δ angle (δ is defined in Chapter 2, section 2.3.5) was carried out to calculate the volume fraction of <111> and <100> oriented grains. Figure 3.8 shows the intensity vs 90°-δ (the tilt angle) profile for all microwires. An angular spread of 10 • is taken to calculate the volume fraction of EP70, EP50, AA70, AA50 wires from the FTP slice, whereas for the AA100, EP40, AA40 and LD100 the volume fraction was calculated by integrating over the reconstructed pole figure with an angular width of 10°. The calculated volume fractions are listed in Table 3.1. 200) pole density for EP series of wires. b, e: [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] for AA series of wires. c, f: ( 111) and ( 200) for LD100. The ( 111), [START_REF] Schmid | Kristallplastizit˜it[END_REF] pole intensity of AA100 wire is plotted in all the subplots for reference. The intensity counts are normalized with the maximum intensity.

Series

Sample

Summary

The microstructure evolution for different batches is summarized as follows:

• AA100 microwire: Commercially procured cold-drawn architectured nickel microwire with an average diameter of 103µm.

-The wire presents a core-shell architecture with the core (represented by 20µm radius from the center) consisting of majorly <111> fiber textured grains and the shell having a dual fiber <111> and <100> texture as well as significant intermediate orientations. The grain size follows a log-normal distribution i.e having average grain size of ∼ 1µm along the cross-section and highly elongated grains along the wire axis. The core of the AA100 microwire is never exactly at the center along the depth (based on three cross-sectional EBSD maps) but shows deviation of less than 10µm to the left or right alternately.

• EP series: Series of 70, 50 and 40µm wires obtained by electropolishing AA100 wires.

-Different diameters of wires leading to different ratios of the core-shell architectured are obtained by electropolishing the AA100 wires. The shell is gradually removed with the reduction of the wire diameter; EP40 wire has the shell component almost completely removed, such that this smallest wire has majorly <111> fiber texture.

The average grain size along the cross-section for electropolished wires of various diameters remains relatively close to ∼ 1µm.

• AA series: Series of 70, 50 and 40µm wires obtained by cold-drawing the AA100 wire.

-Different diameters microwires were obtained by drawing the AA100 wires resulting in microwires having the core-shell architecture with different texture fraction and a differing grain sizes in the core and shell. Analysis of cross-sectional EBSD maps of AA40 wire shows that the core has an average grain size of ∼ 1µm, whereas the shell shows an average grain size of ∼ 0.4µm.

• LD100 wire: 100µm nickel microwire drawn from an initial 500µm annealed wire in the lab, to a drawing strain of ∼ 3.

-The lab drawn microwire presents a core-shell architecture with 'core' (same definition as AA100) having dual fiber <111> and <100> texture with <100> as major component and shell exhibiting a dual fiber <111> and <100> texture as well as significant intermediate orientations. The grain size follows a log-normal distribution i.e having average grain size of ∼ 1µm along the cross-section and highly elongated grains along the wire axis.

A summary of the microstructural characteristics of the extreme diameter wires of the three batches is presented in Table 3

Mechanical properties of nickel microwires

In this section, changes in mechanical properties of the microwires upon diameter reduction are detailed for all batches of nickel microwires and are presented in the following sequence:

1. EP series (commercial and electropolished): The electropolished wires (EP70, EP50, EP40) are presented along with AA100 (cold drawn commercial wire). The interest of this comparison is to see the effect of electropolishing of a cold drawn architectured wire on its mechanical properties.

AA series (commercial and further cold drawn):

The drawn wires (AA70, AA50, AA40) are presented with AA100, to study the effect of drawing.

LD series (cold drawn):

The cold drawn wire (LD100) will be presented along with AA100 to study the effect of different architectures on microwires of similar diameter.

EP series: Figure 3.9 shows the yield stress and tensile strength of EP series of wires with an inset showing the tensile stress-strain curve of one wire in each diameter. As can be seen in Figure 3.9, the yield stress (definition of yield stress used in the present study is based on the XRD analysis and is presented in section 3.3) and tensile strength of the microwire increases with decreasing wire diameter due to electropolishing. A noticeable increase in strength and decrease in uniform elongation are seen when the wire diameter approaches 50µm (refer to Figure 3.9 inset). Here, the percentage of uniform elongation is taken as the measure of ductility.

The difference between the values of yield stress and tensile strength decreases with decrease in wire diameter and becomes zero in case of the 40µm wires. Results from the monotonous tensile tests show an average uniform elongation of 1.2% before necking in case of AA100 wires, whereas for the EP40 wires uniform elongation is zero as the necking occurs immediately after yielding. In other words, EP40 wires do not exhibit any plateau, in contrast to AA100 wires. AA series: Figure 3.10 is similar to Figure 3.9 but for AA series. It shows that the yield stress and tensile strength of the microwire increase with decreasing wire diameter by drawing. The increase in stresses for wires with diameters from 70µm to 40µm is gradual on contrary to that of electropolished wires. Also, a strong increase in uniform elongation is seen for the cold drawn wires (refer to Figure 3.10 inset). Monotonous tensile tests on AA40 wires show an average uniform elongation of 1.83% before necking, which is almost 53% larger than that of AA100 microwires and almost 240% increase than that of the electropolished wires of similar diameter. Also, AA40 wires exhibit a pronounced plastic plateau. LD100: Figure 3.11 shows the typical stress-strain curve of AA100, EP40, AA40 and LD100 microwires and the effect of architecture on the mechanical properties. It can be clearly seen that the two 100µm wires (LD100 and AA100) wires have different uniform elongation. Monotonous tensile tests on LD100 wires show an average uniform elongation of 1.88% before necking, which is almost 57% larger than that of the AA100 microwire. The tensile strength of LD100 microwire was comparable to the AA100 wires. Also, a significant difference in uniform elongation can be seen for the two 40µm wires (EP40 and AA40), refer to Figure 3.11. A summary of the mechanical properties of the three batches of wire is presented in Table 3

In-situ characterizations of deformation mechanism in

Ni microwires

This section details the results obtained by in-situ monotonous tensile, cyclic tensile, stress drop and strain rate jump deformation tests conducted on the three batches of nickel microwires. A first series of 13 tests were performed at SLS on the AA100 and EP series only, whereas a total of 32 tests were performed at SOLEIL (at least 3 tensile tests and 1 cyclic test per diameter from all the three batches). For the monotonous tensile and cyclic tensile tests, only the SOLEIL data are presented. The SLS results on the EP series can be referred to in Appendix B. The stress drop and strain rate jump tests were only carried out at SLS and are also reported here.

In-situ monotonous tensile test

The presented tensile tests under high energy XRD were performed at a strain rate of 8.3 × 10 -6 s -1 . In the following section the in-situ monotonous tensile test data will be presented into four sub-plots as follows:

• The top plot shows the true strain-true stress curve (inverted representation compared to traditional stress-strain curve), where each data point corresponds to a recorded diffraction pattern.

• The two middle plots show respectively the axial lattice strains derived from ( 111) and [START_REF] Schmid | Kristallplastizit˜it[END_REF] axial reflections in microstrain units and their deviation from linearity, as a function of applied stress. Deviation from linearity for the lattice strains is calculated by carrying out linear fit for XRD data points below 450 MPa (elastic regime) and the second middle plot corresponds to the difference between the linear fit and the actual data.

• The bottom plot presents the variations of FWHM in scattering vector, for ( 111) and ( 200) axial reflections, with respect to applied stress.

AA100 wires

Evolution of lattice strain and peak broadening during in-situ tensile deformation for the AA100 wire is shown in Figure 3.12. Analysis of lattice strain deviation from linearity indicates that, up to an applied stress of 450MPa (marked by the first vertical dash line, at corresponding applied strain of ∼ 0.3%), both <111> and <100> grain families deform elastically. Then [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] axial strain exhibits a negative slope change that can be understood as the footprint of first plastic events, inducing a load transfer from <111> grains to <100> grains as confirmed by the positive slope change in [START_REF] Schmid | Kristallplastizit˜it[END_REF] axial reflection. Above 450MPa, i.e. during the early stages of plasticity (or micro-plastic regime), a decrease in FWHM for the <111> grain family is seen. At higher stress of about 650MPa (marked by the second vertical dash line at corresponding applied strain of 0.55%), a decrease in FWHM is also seen for <100> grain family. Above 830MPa (third vertical dash line at a corresponding applied strain of 0.9%), the macro-plastic regime is characterized by an increase in FWHM in both grain families.

Figure 3.12: XRD peak analysis of AA100 wire (data points before the onset of necking are only presented). Top plot (a) corresponds to monotonous tensile strain-stress data, middle plots (b, c) corresponds to the evolution of axial ( 111) and ( 200) elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plot (d) corresponds to the evolution of the ( 111) and ( 200) Full Width Half Maximum (FWHM) versus applied stress (shaded zones represent the error bar). The vertical dashed lines in the plots represent different stress levels corresponding to the evolution of FWHM (see text).

Three distinct regions for the AA100 wire can be identified based on the evolution of FWHM with respect to applied stress. Regime I is defined as the range where there is minimal or no changes in the FWHM behavior with applied stress for both [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections: regime I corresponds to the elastic regime [0-450MPa]. The first vertical line indicates the end of regime I and the start of regime II associated first with the decrease of FWHM for [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection (sub-regime II´) and second with the decrease of FWHM for ( 200) reflection (subregime II´´), at second vertical line. Sub-regime II´marks the start of microstructural changes in <111> family of grains only [450-650 MPa]; sub-regime II´´is characterized by microstructural changes in both grain families and corresponds to the rounding of the macroscopic stress-strain curve [650-830MPa]. Regime II (sum of sub-regimes II´and II´´) is thus defined as the stress range where the effective load transfer takes place between the grain families, marked by the reduction in FWHM and the deviation of lattice strains from linearity. Regime III starts with the increase in FWHM for both reflections (third vertical line) [>830MPa]: this regime is associated to significant plastic deformation in all major grain families and a macroscopic yield criterion can be defined based on the stress at which regime III starts. This criterion has been applied to obtain the data presented in Figure 3.9 and 3.10 and Table 3.3.

EP series

The Figure 3.13 shows the XRD peak analysis of AA100, EP70, EP50 and EP40 wires. The observed different deformation regimes for EP series of wires with respect to AA100 wires are:

• Regime I (elastic behavior in all grains) extends to the same stress value (about 450MPa) for AA100, EP70 and EP50 microwires but extends to a larger value (about 700MPa) for EP40 microwires.

• Regime II (micro-plasticity): Interesting features are observed in regime II with reduction of wire diameter: first, regarding the lattice strain deviation from linearity, the [START_REF] Schmid | Kristallplastizit˜it[END_REF] lattice strain exhibits a positive slope change in AA100 microwire and a negative slope change in EP40 microwire. As explained previously for the AA100 microwires, this suggests a strong load transfer between <111> grains and <100> grains in the presence of 'core-shell' microstructure while this load transfer disappear for the EP40 microwires, where architecture is absent. In the case of EP70 wire, a stronger deviation of [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection is seen to occur right after the end of sub regime II ′ i.e. the start of microplasticity in <100> grains. Whereas for the EP50 wire, the load transfer (lattice strain deviation) is not seen until the end of sub regime II ′′ . Second, regarding the FWHM behavior, the extension of sub regime II´decreases with decreasing wire diameter and cannot be observed for the EP40 microwires: in the latter case, only regime II´´is seen, with decrease of FWHM for both [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and ( 200) reflections.

• Regime III (macro-plasticity), associated to FWHM increase for all reflections, starts at similar applied stress for AA100 and EP70 microwires (about 830MPa), shifts to about 960MPa for EP50 microwires and is not seen for EP40 microwires. The regime III (homogeneous deformation) is not reached in EP40 because of early onset of strain localization resulting in failure. Hence the yield stress and tensile strength of the EP40 wires overlap in Figure 3.9, indicating that the current definition of yield stress defines the yield as the lower limit for the EP40 wires and is expected to increase had the wire not failed sooner due to strain localization. The behavior of <111> grain family is rather similar in all wires: this can be easily understood as the majority of <111> grains are located in the center of the microwires. As the wire diameter is reduced, the macroscopic behavior of the wire seems to be majorly governed by the behavior of <111> grains.

AA series

For the cold drawn series of wires, similar analysis of lattice strains and FWHM is carried out and the subsequent analysis is shown in Figure 3.14. The observed deformation regimes for AA series of wires with respect to AA100 wires are:

• Regime I (elastic behavior in all grains) extend from about 450MPa for AA100 to a remarkable stress value of 800MPa for AA70, 975MPa for AA50 and 1050MPa for AA40 wires.

• Regime II (micro-plasticity): Interesting features are observed in regime II with reduction of wire diameter: Regarding the lattice strains deviation from linearity, the (200) lattice strain exhibits a positive slope change in all the wires, indicative of the load transfer across all diameter values. This agrees well with the previous result that a load transfer occurs between <111> grains and <100> grains in the presence of 'core-shell' microstructure. We recall that the AA series also exhibit a core-shell architecture. Regarding the FWHM behavior, for the AA70 wire it is seen to decrease simultaneously for both <111> and <100> grains at about 725MPa, thus shows only the presence of sub-regime II ′′ . For the smaller diameter wires, AA50 and AA40, the changes in FWHM are absent, indicating the absence of regime II.

• Regime III (macro-plasticity), associated to FWHM increase for all reflections, starts at an applied stress of 830MPa for AA100 and at a higher stress of 930MPa for AA70, 945MPa for AA50 and 1050MPa for AA40 wires. For AA50 and AA40 wires after regime I, there is only regime III i.e. no distinct micro-plastic regime is evident. The behavior of both <111> and <100> grain family changes with decreasing diameter. 111) and ( 200) elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots corresponds to the evolution of the ( 111) and ( 200) Full Width Half Maximum (FWHM) versus applied stress, the shaded zones represent the error bar. The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text). tensile strain-stress data, middle plots corresponds to the evolution of axial ( 111) and ( 200) elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots corresponds to the evolution of the ( 111) and ( 200) Full Width Half Maximum (FWHM) versus applied stress, the shaded zones represent the error bar. The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text).

LD series

The Figure 3.15 shows the XRD peak analysis of AA100 and LD100 wires. The comparison between the two similar diameter wires is carried out, as they both present similar macroscopic volume fraction of <111> and <100> oriented grains and similar average grain sizes across the cross-section, the main difference being the architecture. The observed deformation regimes for LD100 wires with respect to AA100 wires are:

• Regime I (elastic behavior in all grains) extends to an applied stress level of about 450MPa for AA100 and is smaller for LD100 wires (340MPa).

• Regime II (micro-plasticity): A very interesting regime II is seen for LD100 wires. The start of regime II, indicate by the first vertical line, occurs simultaneously for both <111> and <100> grain families i.e. the sub regime II ′ is absent in LD100 wires. Following which the ∆FW HM of ( 200) reflection becomes very negative in LD100 wire compared to AA100 wire. This is reflected, for the (200) reflection of LD100 wires, by a significant increase in lattice strains. The sub regime II ′′ starts earlier, at about 340MPa, for LD100 wire compared to the AA100 wire (680MPa).

• Regime III (macro-plasticity), associated to FWHM increase for all reflections, starts at an applied stress of 830MPa for AA100 and at a higher stress of about 900MPa for LD100 wires. The Regime III for <111> and <100> grains in LD100 does not occur simultaneously as seen for AA100 wires. Hence, the regime III in LD100 wire can be decomposed into two sub regimes, III ′ and III ′′ . The sub regime III ′ marks the macro-plasticity in <111> grains, indicated by increase in FWHM while the <100> still indicates a decrease in FWHM. In sub regime III ′′ , both the grain families have attained macroplasticity indicated by the increase in FWHM for both the reflections. The lattice strain deviations, associated to load transfer, in LD100 wire continue to evolve strongly in regime III. The yield stress in LD100 wire is defined by the start of the regime III.

Summary

The analysis of in-situ tensile deformation on different batches of nickel microwire gives an insight into the internal deformation of these microwires.

• Commercially procured AA100 microwires exhibit three distinct deformation regimes: Regime I (elastic), regime II (micro-plastic) and regime III (macro-plastic). Regime II marks the effective load transfer regime, where the microstructural changes in <111> was seen first and then in the <100> grains. 111) and ( 200) elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots correspond to the evolution of the ( 111) and ( 200) Full Width Half Maximum (FWHM) versus applied stress (the shaded zones represent the error bar). The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text).

• For the EP series of wires, with reduction of wire diameter, the load transfer diminishes in the micro-plastic regime. For the smaller wire, EP40, the sub regime II ′ is not present indicating the onset of micro-plasticity at the same stress level for both <111> and <100> grain family. Also with decrease in diameter, the macro-plastic regime (regime III) diminishes.

• For AA series of wires, with reduction of wire diameter, the micro-plastic regime disappears. In the case of the smaller wires (AA50 and AA40), regime II is not present and a strong load transfer was seen in regime III with an increase in FWHM.

• For LD series: the LD100 wire indicates the presence of new sub regime in macroplasticity regime. The regime III was sub-divided into regime III ′ and regime III ′′ due to the different behavior of <111> and <100> grains.

The different deformation regimes observed for different wires are summarized in Table 3

Load-unload cyclic tensile tests

The evolution of lattice strains and FWHM are investigated further by carrying out a series of load-unload cycles under high energy XRD. A corresponding cyclic curve superimposed on the tensile curve for AA100 is shown in Chapter 2 (Figure 2.16). Load-unload tensile tests have been carried out at least once for each wire diameter. For each sample at the least 10 cycles have been carried out with the maximum stress of the first cycle being ~400MPa. The recorded XRD reflection presented here corresponds to the axial component of the wire. Though transverse reflections were also recorded at the maximum and minimum load of each cycle, they are not presented here.

For simplicity and clarity reasons, we propose to directly define four distinct regimes based on the evolution of FWHM with load-unload cycles for the nickel wires. They are labeled as α, α ′ , β and γ, and schematized in Figure 3.16. The definition of these regimes is as follows.

1. Regime α: ∆FW HM is seen to decrease with loading and increase with unloading, such that there is no net changes or a net decrease in FWHM at the end of the loadunload cycle, refer to Figure 3.16(b).

2. Regime α ′ : ∆FW HM is seen to increase with loading and decrease with unloading, such that there is no net changes in FWHM at the end of the load-unload cycle, refer to Figure 3.16(c).

3. Regime β : ∆FW HM is seen to increase with loading and decrease with unloading, such that there is a net decrease in FWHM at the end of the load-unload cycle, refer to Figure 3.16(d).

4. Regime γ: ∆FW HM is seen to increase with loading and decrease with unloading, such that there is a net increase in FWHM at the end of the load-unload cycle, refer to Figure 3.16(e).

AA100 wires

Figure 3.17 shows the evolution of lattice strain with time during the cyclic test of AA100 in both grain families (( 111) and (200) reflection); the most interesting information comes from Figure 3.18 where ∆FW HM is plotted with time. The observed regimes are:

• Regime α, which marks the net decrease in FWHM is seen for both the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections. For [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection the regime can be seen up to four load-unload cycles (maximum applied stress of 600MPa), whereas it is seen up to six load-unload cycles in the case of ( 200) reflection (maximum applied stress of 700MPa). For the same load-unload cycles the lattice strains of both reflections hardly show any changes in the unloaded states. It should be also mentioned that the cyclic test of AA100 wire was started at a stress level of 50-100MPa and each unloaded state corresponds to an applied stress of 100MPa.

• Regime β , which is characterized by an increase in ∆FW HM upon loading and a decrease upon unloading, such that there is net decrease of ∆FW HM at the end of the cycle and is observed for both the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections. For (111) reflection the regime seems to appear towards the end of cycle 4 and extends until the end of the test (maximum applied stress of 900MPa), whereas for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection, this regime starts at cycle 7 and is seen until the end of cycle 9 (maximum applied stress of 800MPa). The magnitude of net decrease in ∆FW HM is different for reflections, i.e. the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] shows a continuous net decrease in ∆FW HM at the end of each load-unload cycle, whereas the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection rather shows very small variation. It should be mentioned that the transition from regime α to regime β is not very clear. For the applied stress range of regime β , the changes in the slope of lattice strain cannot be clearly seen from Figure 3.17, but changes in the lattice strain at unloaded states is evident (with >0 lattice strain for <200> and <0 lattice strain for <111> grains). These changes indicate the development of intergranular strains and are the footprint of micro-plasticity.

• Regime γ, marks a regime where a net increase in ∆FW HM is seen as a sign of macroplasticity. For the applied cycles (stopped before wire breaking), regime γ is not seen for the (111) reflection, whereas for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection a net increase in ∆FW HM is seen at the end of cycle 10. The changes in the state of lattice strain of (200) reflection at the end of load-unload cycle is similar to that of regime β .

EP series

For clarity only the EP40 wire from the EP series will be detailed here. The observations of this wire are compared with AA100 behavior. Figure 3.19 shows the load-unload test and evolution of axial lattice strains and Figure 3.20 shows the load-unload test with evolution of ∆FW HM for EP40 microwire. From the comparison between EP40 and AA100 wires, the following observations are reported:

• Regime α for (111) reflection extends to higher applied stress of 900MPa in EP40 wire (i.e. 7 cycles), whereas it was limited to 600MP in AA100 wire (i.e. 4 cycles). For the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection, the regime α is seen until 800MPa in the case of EP40 wire and 700MPa in the case of AA100 wire. The resolution of regime α is not so clear in the case of [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection in EP40 wire, the noisy data can be explained by the very low diffracting volume fraction of <100> grains. For the same load-unload cycles the lattice strains of (200) reflection hardly show any changes in the initial state upon unloading. Conversely for the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection, the change in state of lattice strain upon unloading is evident. It should be also mentioned that the cyclic test of EP40 wire was started at a stress level of 50-100MPa and each unloaded state corresponds to an applied stress of about 100MPa.

• Regime β (micro-plasticity): For the EP40 wire, the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection shows the start of regime β at 800MPa, whereas it sets in later at 925MPa for the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection. In the case of AA100 wire, the regime β is seen to occur first in [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection at about 650MPa and then the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection at about 750MPa. In this regime, the lattice strain of (111) reflection indicates a change in the state of strains upon unloading.

• Regime γ (macro-plasticity), marked by a net increase in ∆FW HM, is not seen for both the ( 111) and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections in EP40 wire i.e., from tensile tests it has been seen that the wire necks before reaching a regime of homogeneous deformation. It can also be seen in the load-unload test that the FWHM of ( 111) and ( 200) reflections do not saturate, contrary to what has been observed for AA100 wires.

AA series

For clarity only the AA40 wire from the AA series will be detailed here. The observations of this wire are also compared with AA100 behavior. Figure 3.21 shows the evolution of axial lattice strains and Figure 3.22 shows the load-unload test and evolution of FWHM for EP40 microwire. A discontinuity between cycle 6 and cycle 7 (for Figure 3.21 and 3.22) is due to the technical problem with the machine resting block and the corresponding changes reflected in the lattice strains and FWHM are due to relaxation of the sample for ~20 minutes. From the comparison between AA40 and AA100 wires, the following observations are reported:

• Regime α is not seen in the AA40 wires, instead regime α ′ is seen. Regime α ′ shows an increase in ∆FW HM with loading and a decrease in ∆FW HM with unloading, such that the resulting net ∆FW HM is zero. Regime α ′ is seen for both the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections in AA40 wire, which extends up to 900MPa for [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection and 750MPa for [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection. For the same load-unload cycles the lattice strains of both reflections hardly shows any changes in the initial state upon unloading. It should be also mentioned that the cyclic test of AA40 wire was started at a stress level of about 100MPa and each unloaded state corresponds to an applied stress of about 50MPa. • Regime β (micro-plasticity): For the AA40 wire, the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection shows that the regime β sets in at 800MPa, whereas it starts at 950MPa for the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection. In the case of AA100 wire, the regime β is seen to occur first in [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection at about 650MPa and then the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection at about 750MPa. This is similar to what has been observed for EP40 wires i.e. the micro-plasticity starts in the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection first and then in the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection. In this regime, the state of lattice strain after unloading remains the same for both the ( 111) and ( 200) reflections.

• Regime γ (macro-plasticity) is only seen for [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection in AA40 wire i.e., an increase in ∆FW HM is seen in the macroplastic regime. Similar to AA100 wire, regime γ is not seen for the (111) reflection, whereas for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection a net increase in ∆FW HM is seen at the end of cycle 11. The changes in the state of lattice strain of [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection at the end of load-unload cycle is similar to that of regime β . • The regime α, which marks a net decrease or no changes in ∆FW HM is seen for both the ( 111) and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections in LD100 wire. The regime extends up to 6 load-unload cycles (a maximum applied stress of about 750MPa) for the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection, whereas for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection it extends for the whole test (applied stress of about 950MPa). Two behaviors are seen in regime α for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection: First, the ( 200) reflection shows no net changes in ∆FW HM until the applied stress of 650MPa; for the same stress range hardly any changes can be seen in the initial state of ( 200) lattice strains upon unloading. Secondly, the ( 200) reflection shows a net decrease in ∆FW HM for the whole test; in this range of applied stress, the lattice strain of ( 200) reflection indicates a strong change in the unloaded states, indicating the development of intergranular strains. It should be also mentioned that the cyclic test of LD100 wire was started at a stress level of about 100MPa and each unloaded state corresponds to an applied stress of about 100MPa. • Regime β (micro-plasticity): For the LD100 wire, the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection shows no sign of regime β for the current loading, whereas it sets in at an applied stress of 800MPa for the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection. The regime β in [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection extends up to an applied stress of about 900MPa. In this regime, the lattice strain of (111) reflection indicates a change in the unloaded states.

• Regime γ: The recovery of FWHM disappears for (111) reflection, and an increase in ∆FW HM is seen at the final cycle, whereas the regime is not seen/achieved for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection in the macro-plastic stresses.

Summary

Several distinct regimes of deformation have been identified with the evolution of FWHM during the cyclic tensile tests: They are labeled as regime α ′ (elasticity), regime α (elasticity), regime β (micro-plasticity) and regime γ (macro-plasticity). The summary of different regimes observed in different wires is as follows:

• Commercially procured AA100 microwire: For the current loading, the (111) reflection exhibit two distinct regimes (α and β ), whereas the (200) reflection exhibits three regimes (α, β and γ). The regime β , micro-plasticity, was seen to observe in [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection at first and then in [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection. The corresponding changes in the state of lattice strains upon unloading in the regime β indicates the build-up of intergranular strains.

• The EP40 wire shows only the presence of two distinct regimes, α and β , for both [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and ( 200) reflections. On contrary to AA100, the regime β is seen to set in first for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection and then later in the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection. The corresponding changes in the state of lattice strains upon unloading in the regime β was only observed for the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection.

• The AA40 wire shows the presence of three distinct regimes (α ′ , β and γ). Regime α ′ is seen for both the ( 111) and ( 200) reflections, whereas regime γ is seen only in [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection. Regime β onset in the ( 111) and ( 200) reflection is similar to that of EP40 wires. In regime β , no significant changes in the lattice strains at unloaded states are seen for both reflections.

• The LD100 wire also shows the presence of three distinct regimes (α, β and γ). For the [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection all three regimes are seen along the loading contrary to the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection where only one regime (α) is present. The regime α in the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection exhibits two trends with no net changes in ∆FW HM upon unloading in the initial 4 cycles and a continuous net decrease in ∆FW HM for the rest of the cycles. This is followed by a strong change in the state of lattice strains upon unloading.

The different deformation regimes observed for different wires are summarized in Table 3.5.

Regime Definition AA100 EP40 AA40 LD100 (111) [START_REF] Schmid | Kristallplastizit˜it[END_REF] [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] [START_REF] Schmid | Kristallplastizit˜it[END_REF] [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] [START_REF] Schmid | Kristallplastizit˜it[END_REF] [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] [START_REF] Schmid | Kristallplastizit˜it[END_REF] α

Elasticity/Microplasticity Table 3.5: Definition of regimes based on the evolution of FWHM with time for nickel microwires wire during in-situ cyclic tensile tests.

The transverse reflections [START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF] corresponding to <111> and <100> textured grains and (200) corresponding to <100> textured grains were also recorded at the maximal and minimal applied stress of each cycle. This provides access to transverse lattice strain of the grains family. The curves presenting the transverse data and subsequently the Poisson ratio calculated as the ratio of transverse to axial lattice strains are also presented in Appendix B section B.4.1.

Stress drop test

Stress drop tests are conducted to investigate the mechanisms responsible for deformation in the constant plateau. These tests have been conducted and studied extensively by Helena Van Swygenhoven's group on the NC nickel [START_REF] Sun | Dynamic recovery in nanocrystalline ni[END_REF][START_REF] Sun | Nanocrystalline metals: transient testing during in situ x-ray diffraction and molecular dynamics[END_REF] to study the deformation mechanisms responsible for the underlying strength. In-situ stress drop tests have been carried out only on the AA100 microwires with stress drop ratio ranging between 0.48 and 0.90. Figure 3.25 shows one of the stress drop test carried out on AA100 wire at SLS. Figure 3.26 shows the evolution of inelastic strains and FWHM of ( 111) and ( 200) axial reflections during a creep period of 60 minutes. For all stress drop ratios, a continuous increase in inelastic strain with creep time is observed as shown in Figure 3.26(a). Also, an immediate decrease in FWHM for both the grain families is seen at the beginning of creep for all stress drop ratios i.e. the FWHM decreases irrespective of the magnitude of the stress drop, refer to Figure 3.26(b, c). The FWHM still continues to decrease over time but at a relatively slow rate. The decrease in FWHM for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection is larger than the one for [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection at all stress drop ratios.

Strain rate jump test

The strain rate sensitivity of Ni microwires was probed by carrying out a series of increase and decrease of strain rate during the continuous tensile test. Hence the strain rate jumps are carried out in the macro-plastic regime of AA100 wire, which is possible here due to the presence of a nearly zero hardening regime. The strain rate sensitivity index calculated from the stress-strain curve in Figure 3.27 ranges from: m(a,b)= 0.00502, m(b,c)=0.00638, m(c,d)=0.0062, m(d,e)=0.00491, averaged to 0.0056 ± 0.00077. Figure 3.27: Continuous stress-strain curve for AA100 microwire with different strain rates in the macro-plastic regime. Inset shows the magnified section the curve where the effect of strain rate changes can be seen.

Postmortem by SEM

The Figure 3.28 shows the SEM montage of different nickel microwires (AA100, EP40, AA40 and LD100), their initial surface before in-situ deformation and one end of the fractured surfaces. The fracture surfaces of other wires in the EP and AA series are presented in Appendix B. The AA40 and LD100 microwires presented in Figure 3. 28(c andd) exhibited a uniform elongation to failure of about 1.8%, whereas the EP40 microwires failed at 0.5%. The tested wires failed by ductile fracture and exhibited a typical cup and cone type fracture during continuous monotonous deformation. Throughout the entire gauge length of the microwire, several surface features were observed which included surface cavities, extrusions and intrusions similar to persistent slip bands, refer to Figure 3.29.

Figure 3.29 (a) shows the typical feature observed on the monotonously tested microwires, the band like structure involving the linkage of surface cavities is periodically present on the

Discussion

Elementary deformation mechanisms in nickel: A study on nickel with microstructure made of NC, UFG or coarse grains (CG) suggested a strain rate dependency of flow stress only in NC regime [START_REF] Van Petegem | Microstructure and deformation mechanisms in nanocrystalline ni-fe. part ii. in situ testing during x-ray diffraction[END_REF]: strain rate sensitivity index 'm' of Ni ranges from 0.02 to 0.04 for NC and tends to zero for CG and UFG. The strain rate dependency index for the current Ni microwires is 0.005; hence, this very low value agrees well with literature data on bulk coarse grain Ni. Moreover, the low strain rate sensitivity index measured from strain rate jump tests indicates that plasticity proceeds via dislocation-based mechanisms rather than grain boundary sliding mechanisms. This is further complemented by the stress-drop tests carried out on AA100 wires. In the case of NC nickel [START_REF] Sun | Dynamic recovery in nanocrystalline ni[END_REF], four distinct regimes have been identified based on the evolution of inelastic strains and FWHM at different stress drop ratios. For large relative stress reduction ratio R (or small stress drops), where the applied stress is kept well above the internal stress, dislocations will continue to nucleate and/or propagate, causing a forward strain with positive changes in FWHM. For smallest relative stress reduction ratio R (large stress drops), a negative strain and continued reduction of FWHM are seen as a result of backward motion of dislocations due to high internal stresses. For intermediate relative stress reduction ratios, different cases are observed: a) positive strain accompanied by negative evolution of FWHM, b) transient decrease of inelastic strain followed by an increase accompanied by continuous decrease of FWHM. All the regimes characterized by a decrease of FWHM are associated with mechanisms involving grain boundary accommodation which result in relaxation of internal stresses. The stress drop tests carried out here on nickel microwires indicate that the inelastic strain always remains positive (for all stress drop ratios) with immediate reduction of FWHM that continues to diminish until the end of the creep period. The continued reduction of FWHM suggests that inhomogeneous strains decrease via grain boundary mediated processes that reduce the internal stresses in the plastic regime (refer to Figure 3.26). A very low measured strain rate sensitivity index indicates that the Ni microwires deform only by dislocation-based mechanisms (and not by some sort of grain boundary sliding). Hence, the observed increase of inelastic strain, accompanied by reduction of FWHM can be attributed to a combination of movements of dislocations and their absorption at grain boundary, resulting in a sort of 'cleaning-up' process of the grain interior with respect to dislocation content. This clean-up process can also be attributed as the primary mechanism responsible for the decrease of FWHM upon loading in the regime I and α from the monotonous and cyclic tensile test.

Deformation of the polycrystalline aggregate in nickel microwires: The directional Young's modulus (calculated with respect to single crystal elastic constant given in [START_REF] Hellwege | Landolt-bornstein tables[END_REF]) of Ni ranges from 131 GPa for loading in <100> direction to 288 GPa for <111> direction. The slope (machine contribution is not removed, but is assumed to be constant or negligible for the different tests) of applied stress-strain curves (refer to Figure 3.11) increases with reduction in wire diameter (for both EP40 and AA40), which is attributed to the increase in volume fraction of <111> fiber texture. The volume fraction trend agrees well with the slope calculated with DIC ex-situ tests on the AA100 and EP40 wires, presented in Appendix B.

Plastic deformation in CG crystalline metals usually occurs by crystallographic slip, along {111} <110> slip systems in the case of FCC materials like Ni. According to the Schmid law, during a tensile test, <100> oriented single crystal (whose Schmid factor is equal to 0.408) should yield before <111> oriented single crystal (Schmid factor equal to 0.272). In the Ni microwires under study, all the grains are highly aligned and elongated along the tensile axis with two dominant orientations, <111> and <100>. These two major grain families can be seen as the two 'phases' of a unidirectional composite material where each 'phase' exhibits different elastic and plastic properties. Under iso-stress condition which is assumed within the Sachs model, yielding of <100> grains would occur first because of their high Schmid factor. Conversely, <111> grains would yield first in the case of iso-strain condition (Taylor model) due to higher Young's modulus. Experimentally, it was observed in the present study that <111> grains yield first. This suggests that the polycrystalline aggregate behaves more like a unidirectional composite in iso-strain mode, with the yield stress of the microwire being controlled by the volume fraction of <111> grains due to high Young's modulus.

If we follow the evolution of lattice strain with respect to applied stress from Figure 3.13(a), it can be seen that the <111> oriented grains plastify first (indicated by the sub regime II ′ , which marks the microstructural changes in <111> grains); this is followed by an effective load transfer towards the <100> oriented grains in the case of AA100 wire, which deteriorates with decreasing diameter for the EP series; delayed for the AA series and is prolonged in the case of LD100 wires. Under higher stress, plasticity sets in <100> oriented grains (indicated by the sub regime II ′′ , which marks the microstructural changes in <100> grains). With the reduction of shell volume fraction by electropolishing, the volume fraction of <100> grains is also reduced. This result in a microwire with high overall volume fraction of <111> grains, leading to a less effective global load transfer. In the case of AA series an opposite trend is seen, refer to Figure 3.14, i.e. with decrease of wire diameter by cold-drawing, the effective load transfer regime is delayed leading to higher strength (i.e. delayed onset of plasticity) and an extended homogeneous deformation regime is present alongside.

For the AA100 and EP series, in-situ monotonous and cyclic tensile tests indicate a decrease of FWHM in the micro-plastic region (regime II and β ). This decrease can be attributed to the 'cleaning-up' process. The cleaning up process happens during the unloading segment, resulting in a net decrease of FWHM. Such mechanisms is not surprising in microstructure that has been obtained by severe drawing: a lot of dislocation segments are bowing out of grain boundaries and are rather unstable towards applied stress. Similar behavior has been already observed in SPD-processed metallic wires [START_REF] Thilly | A new criterion for elasto-plastic transition in nanomaterials: Application to size and composite effects on cu-nb nanocomposite wires[END_REF]. A study by Thompson [146] on high pressure torsion (HPT) nickel and Wilcox et al. [START_REF] Wilcox | The role of grain size and shape in strengthening of dispersion hardened nickel alloys[END_REF] on drawn nickel indicate the formation of dislocation cells with dislocation sources being present near cell wall or grain boundaries.

For the AA series, in-situ monotonous and cyclic tensile tests indicate an extended regime I and regime α ′ in the smaller cold-drawn wire suggesting a stable microstructure with very few 'loose dislocations'. This is also indicated by the delayed load transfer and hence delayed onset of plasticity. The high strength is attributed to the formation of stable cell structures during cold drawing and higher volume fraction of <111> grains. For the AA40 wire, a higher ductility is observed and this could be attributed to the strong presence of load transfer in regime g i.e. the homogeneous deformation regime. Whereas the regime II deterioration with decrease of wire diameter i.e. the recovery (reduction) in FWHM is no longer observed for the smaller diameter wires.

For the LD100 wires, in-situ monotonous and cyclic tensile tests indicate a strong load transfer in the micro-and macro-plastic regimes with higher lattice strains achieved in [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections. Such higher load sharing ability for [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection has already been observed in the case of NC nickel [START_REF] Sun | Nanocrystalline metals: transient testing during in situ x-ray diffraction and molecular dynamics[END_REF]. The yield stress and tensile strength of LD100 wires are slightly higher than that of the AA100 wires, whereas an extended average uniform elongation region is seen for LD100 wires. These differences are attributed to the changes in global volume fraction of major texture components and their spatial arrangement. The LD100 wire also exhibit prolonged load sharing ability of <100> oriented grains in the macro-plastic regime, which seems to play a significant role in providing additional ductility. This prolonged load sharing is attributed to the spatial arrangement of major <100> grains in the core of the microwire.

The load transfer between different grain families can be seen as a mechanism for release of intergranular stresses between neighboring grains (represented by the changes in FWHM), thereby delaying the onset of strain localization. The volume fraction and spatial spread of <100> oriented grains in both the core and the shell of the microwire seems to affect its ductility.

Table 3.6 provides links between the various deformation regimes observed in monotonous and cyclic tensile tests into three categories: elastic, micro-and macro-plastic. Effect of microstructure (grain size, shape and arrangement): Previous study on SPD nickel samples suggests that elongated grains have no considerable effect on the tensile strength and elongation to failure at room temperature [START_REF] Rathmayr | Extrinsic and intrinsic fracture behavior of high pressure torsion deformed nickel[END_REF]. The strength is rather governed by the average grain size perpendicular to the tensile axis. In the present study also, the influence of grain aspect ratio on the deformation mechanism seems rather limited, although this influence can be indirectly seen with respect to iso-strain mode resulting in early yielding in <111> grains. Other studies have shown that having a multi-modal grain distribution or having a gradient in grain size from the surface to the core can result in material with a more optimum combination of strength and ductility [START_REF] Lu | Making strong nanomaterials ductile with gradients[END_REF][START_REF] Wang | High tensile ductility in a nanostructured metal[END_REF][START_REF] Fang | Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper[END_REF][START_REF] Wang | Enhanced tensile ductility and toughness in nanostructured cu[END_REF]. In the current study, the variation of grain size along the cross-section of the AA40 microwire suggests a gradient in grain size from core to shell, whereas for AA100, EP series and LD100 wires no strong grain size gradient is observed. The macroscopic tensile strength of EP40 and AA40 wires are very similar, indicating that the varying grain size in core and shell along with the architecture plays an important role in ductility. In the case of LD100 wires, no strong gradient in grain size is observed, a core-shell architecture with major <100> texture in the core exhibit higher amounts of axial lattice strains and higher average uniform elongation; this suggests that the core-shell architecture seems actually to have the strongest effect on the mechanical properties.

Regimes

Conclusions

In the present study, the effect of diameter reduction on the mechanical properties of colddrawn nickel microwires by electropolishing and drawing has been analyzed. The following conclusions can be drawn. AA100 microwire 1. The commercially procured AA100 microwires exhibit duplex fiber texture (25% of <100>, 75% of <111>) with core-shell architecture: core with <111> oriented grains and shell with <111> and <100> oriented grains. The average tensile strength of this wire is around 885 MPa with an elongation to failure of 1.2%.

2. The low strain rate sensitivity index and the stress drop tests indicate that the deformation in these microwires takes place by dislocation-based mechanisms. They also show that dislocation recovery at grain boundaries leads to decrease of internal strain resulting in prolonged uniform strain regime (regime III/γ).

3. The evolution of lattice strains and FWHM with respect to applied stress indicate successive yielding of grain families in the microwire with <111> oriented grains reaching plasticity first (sub-regime II ′ ). Thereafter, plasticity sets in <100> oriented grains (subregime II ′′ ) resulting from the effective load transfer between <111> and <100> oriented grains.

4. Three distinct deformation regimes have been identified based on the evolution of FWHM with respect to applied stress in monotonous test: Elastic regime (regime I), micro-plastic (regime II) or effective load transfer regime and macro plastic regime (regime III).

EP series

1. Three diameter microwires with different architecture were obtained by electropolishing the AA100 wire, with the smallest diameter of 40µm having no architecture (95% of <111>, 5% of <100> oriented grains). The tensile strength of the EP40 wire is 25% higher than the AA100 wire with an average of about 1110 MPa and a uniform elongation of 0.5%, which is 60% lower than the AA100 wire.

2. The evolution of lattice strains and FWHM with respect to applied stress indicates that plasticity sets in during the load transfer regime and in the absence of <100> grains, the microwire fails before reaching a state of homogeneous deformation due to strain localization.

3. Two distinct deformation regimes were observed in the EP40 wires based on the evolution of FWHM with respect to applied stress: Elastic (regime I and α) and micro-plastic regime (regime II ′′ and β ).

AA series

1. Three diameter microwires with a 'core-shell' architecture were obtained by cold-drawing the AA100 wire, with the smallest diameter of 40µm having a volume fraction of 86% of <111>, 14% of <100> oriented grains. The tensile strength of the AA40 wire is 30% higher than the AA100 wire with an average of about 1146 MPa and a uniform elongation to failure of 1.8%, which is 53% higher than the AA100 wire.

2. The evolution of lattice strains and FWHM with respect to applied stress indicates a stable microstructure with no 'free' dislocations (regime I or α ′ ) and a higher strength is observed due to delayed load transfer. A strong load transfer is seen in the macro plastic regime resulting in a higher ductility.

3. Two distinct deformation regimes were observed in the AA40 wires based on the evolution of FWHM with respect to applied stress in monotonous test: Elastic regime (regime I) and macro-plastic regime (regime III).

LD100 microwire

1. A lab drawn 100µm wire with a 'core-shell' architecture was obtained by cold-drawing a 500µm annealed wire. The LD100 wire exhibits a core-shell architecture with major <100> texture in the core and a dual (<111>, <100>) texture in the shell. The global volume fraction is 77% of <111> and 23% of <100> oriented grains. The tensile strength of the LD100 wire is 5% higher than the AA100 wire with an average of about 935 MPa and an elongation to failure of 1.88%, which is 57% higher than the AA100 wire.

2. The evolution of lattice strains and FWHM with respect to applied stress indicates an effective load transfer regime which extends from micro-plastic regime (regime II ′′ ) to macro-plastic regime (regime III ′ and III ′ '). The [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection shows a higher amount of axial lattice strain, this can be attributed to the spatial arrangement of <100> textured grains both in the core and shell of the microwire. A strong load transfer seen in the micro as well as macro-plastic regime results in a higher ductility.

3. Cyclic tensile test shows that the [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection exhibits regime α for the whole test, while the (111) reflection has already reached macro-plasticity. The monotonous tensile test indicates that macro-plasticity does not occur simultaneously for [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection in regime III. Macro-plasticity is achieved first in the ( 111) reflection (regime III ′ ) and then starts in [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflection (regime III ′′ ).

It is clear from the results that the 'apparent extrinsic size effect' is a result of changes in crystallographic texture upon reduction of specimen size. A direct influence of microwire's architecture on the strength and ductility was observed, which establishes that the effective load transfer within the microwire, as a result of specific microstructure architecture, provides a feasible way to tune the mechanical properties (strength and ductility). This architecture effect should play important role in developing microstructures with superior mechanical properties. Hence, coexistence of <111> and <100> grains in addition to microstructure architecture (core-shell architecture) can probably be considered as the tuning parameters for optimizing the combination of strength and ductility.

Part B: Numerical simulation

The microwire characterization and XRD analysis on the different microwires indicate that the observed mechanical size effect is a result of texture superimposition effect i.e. an architecture effect. The XRD analysis indicated that the texture and especially, the architecture of the microwires have a strong effect on the mechanical properties of the microwires. To extend the understanding of the in-situ test results and to evaluate the individual contribution of texture and architecture, full field CPFE simulations were performed and are presented in Chapter 5. These computations require the generation and meshing of polycrystalline aggregates which are sufficiently representative of the different microwires studied in Chapter 3.

A first simulation study on microwires based on the experimental results is carried out. A specific strategy is tailored to study the impact of one among the many microstructural feature i.e. the architecture. Separating the contribution of superimposition of the crystallographic texture and architecture from the pure size related effect, is one of the major focus of the numerical campaign. The three different components involved in the modeling strategy are illustrated in Figure PB.1.

1. The first step in the numerical strategy involves the generation of a representative microstructure by taking into account the anisotropic grain shape. To consider the different effect of crystallographic texture/architecture, only one type of microstructure is used to represent the different wires.

2. The second step involves representing the crystallographic texture and the architecture of the wire on the generated microstructure in step 1. This is carried out by a proposed texture simplification approach to generate/select a representative texture, such that the final microstructure could be considered as a 'reduced', but representative, model of the wire.. Both step 1 and step 2 are developed in Chapter 4.

3. The next step involves the choice of crystal plasticity constitutive model and the identification of material parameters. The principal objective of the simulations is not to consider the pure effect of size, but the effect of texture/architecture on the behavior of these microwires. As an first approach, a non size dependent constitutive model is desired. The choice of model and the results of simulations are detailed in Chapter 5. Chapter 4

Representative microstructure generation

Introduction

The representative microstructures have been developed using an in-house code: S2M, which was developed at Institut Pprime, to account for the anisotropy of the grain shape. At the start of the project, the available version of S2M was not able to describe the elongated grains and presented numerous limitations in terms of generating representative statistics and optimization of computation time. Significant improvements and developments have been carried out as a part of this work. An ellipsoid packing algorithm is now integrated into the code to describe the anisotropic grain shapes. The integrated developments are applicable to a broad range of microstructures. The aim of this chapter is not to describe thoroughly each of the features but the ones that were used with respect to their applicability to the nickel microwires. The outline of the chapter is as follows.

• After a brief overview of the tools for generation of microstructure (section 4.2), S2M code and improvements brought in, especially to account for the morphological anisotropy are presented in section 4.3.

• The main modeling assumptions for the application of S2M to different nickel microwires studied are discussed in section 4.4.

• Finally the generated aggregates used for FE simulations are presented in section 4.5.

Overview of microstructure generation techniques

This section provides a brief state-of-art regarding the techniques available for generation of the microstructure. The motivation for generation of representative microstructure in the materials community is to explain in details the microstructure-property relationship [START_REF] Groeber | Digital representation of materials grain structure[END_REF].

Modeling a representative microstructure in three dimensions has importance in materials science applications. In literature, many different ways have been detailed for generating a representative microstructure, of which several are not appropriate in terms of explaining microstructure-property relationship. The two major techniques commonly used for generation of representative microstructure are discussed here. The major difference lies in the collection of experimental data as well as reconstructing it. The main details of these techniques are as follows.

1. Reproducing experimental microstructure by 3D FIB EBSD (a destructive technique) or by Diffraction Contrast Tomography (DCT a non-destructive technique): the data processing and parameter correlation by complete analysis of 3D data give a much finer picture of the microstructure-property relationship and the subsequent generated microstructure are referred here as 'realistic microstructure'. The main problem with this analysis lies in the time to extract and clean up the data. For example, in the case of a heavily deformed material with thousands of grains across thickness, it is very difficult and time consuming to use this technique of characterization to get any meaningful description of the representative microstructure.

2. Microstructure generation by simple tessellations and shapes using Voronoi-Delaunay, Voronoi-Laguerre polyhedra or Johnson-Mehl, referred here as 'synthetic microstructure': since, the microstructural features are simplified, a very simple descriptor is often used for the generation of microstructure. This method works well in the case of an isotropic microstructure with no complex correlation of microstructural features. Recently the Voronoi-Laguerre [START_REF] Lavergne | Effects of grain size distribution and stress heterogeneity on yield stress of polycrystals: A numerical approach[END_REF] and Johnson-Mehl techniques have been used to describe more controlled distribution of grain morphological parameters [START_REF] Altendorf | 3d reconstruction of a multiscale microstructure by anisotropic tessellation models[END_REF].

• A sub-class to synthetic microstructure, termed here as 'semi-synthetic microstructure' was also developed over the last decade. The originality of this technique is to take into account one of the experimental surfaces by constraining it on top of the synthetic microstructure, i.e. a synthetic microstructure is generated from one experimental surface. This modification allows for the possibility to have direct comparison of actual experimental surface deformation with the surface of the 3D microstructure.

These techniques have been described in detail in the context of grain scale modeling for polycrystalline microstructure and an extensive comparison of these techniques can be referred here [START_REF] Simonovski | Grain-scale modeling approaches for polycrystalline aggregates[END_REF].

Experimental microstructures

In this section, the 'image based models' are briefly reviewed. In these 'image based models', the grain geometry and texture are extracted from experimental surface and underlying volume using methods like FIB serial sectioning [START_REF] Groeber | 3d reconstruction and characterization of polycrystalline microstructures using a fib-sem system[END_REF] or XRD contrast tomography (DCT) [START_REF] Johnson | X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. ii. the combined case[END_REF]. However, treating an enormous amount of complex experimental data can be difficult, limiting the application of this technique to only specific cases. Serial sectioning method is often used in the context of extracting the true 3D microstructural features of the materials for subsequent finite element models. In this method, EBSD is first carried out on the surface of the material being characterized, then a thin layer of the material is removed by FIB to characterize the layer underneath. This process is carried out for a limited depth to have enough grains in the volume for characterization. The extracted 2D EBSD maps are then stacked and analyzed for grain size distribution, orientation and crystallographic texture. The treatment of data is often difficult due to experimental difficulties and limitations [START_REF] Groeber | A framework for automated analysis and simulation of 3d polycrystalline microstructures.: Part 1: Statistical characterization[END_REF]; over the last decade, many dedicated software are developed to treat and analyze microstructure data, especially the one developed by BlueQuartz software called 'Dream3D' [START_REF] Groeber | Dream. 3d: a digital representation environment for the analysis of microstructure in 3d[END_REF].

Dream3D is an open source software that provides a complete and mostly automated characterization of 3D microstructure generated by serial sectioning. The software also provides the possibility to generate a representative microstructure with correlation of experimental statistics. More information on how the data is treated, characterized and correlated can be found here [START_REF] Groeber | Dream. 3d: a digital representation environment for the analysis of microstructure in 3d[END_REF][START_REF] Groeber | A framework for automated analysis and simulation of 3d polycrystalline microstructures. part 2: Synthetic structure generation[END_REF][START_REF] Chan | Synthetic three-dimensional voxel-based microstructures that contain annealing twins[END_REF][START_REF] Brahme | 3d reconstruction of microstructure in a commercial purity aluminum[END_REF][START_REF] Rollett | Modeling polycrystalline microstructures in 3d[END_REF]. The material being characterized is being destroyed as a part of the technique and the time required to prepare/characterize the 3D microstructure is important. The diffraction computed tomography [START_REF] Johnson | X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. ii. the combined case[END_REF], 3D XRD microscopy [START_REF] Poulsen | Three-dimensional X-ray diffraction microscopy: mapping polycrystals and their dynamics[END_REF] and Differential aperture X-ray microscopy [START_REF] Larson | Three-dimensional x-ray structural microscopy with submicrometre resolution[END_REF][START_REF] Yang | Differential-aperture x-ray structural microscopy: a submicron-resolution three-dimensional probe of local microstructure and strain[END_REF] are alternative techniques to characterize the experimental material without destroying it. The DCT has also been employed to monitor the crack initiation and growth [START_REF] Ludwig | New opportunities for 3d materials science of polycrystalline materials at the micrometre lengthscale by combined use of x-ray diffraction and x-ray imaging[END_REF][START_REF] Herbig | 3-d growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phase-contrast x-ray tomography[END_REF]. DCT is based on XRD to reconstruct gain shape and orientations from projections. These non-destructive techniques require a very intense energy source of X-rays, typically at synchrotron, to characterize the materials. The 3D reconstructions from experimental material often have lot of artifacts like missing data, drift in EBSD data, surface grooves, etc., resulting in a very complex workflow for preparation of the obtained microstructure for FE simulations. However one of the main advantages of these techniques is that the data obtained represent the experimental statistics without any bias or assumptions [START_REF] Groeber | Development of an automated characterization-representation framework for the modeling of polycrystalline materials in 3D[END_REF]. It is possible to correlate several different morphological parameters to achieve a better understanding of the microstructure. As an example, N-point correlation functions can be used to describe parameters that correlate the features of microstructure with its spatial arrangement (more details in [START_REF] Groeber | Digital representation of materials grain structure[END_REF]). The experimental reconstructed volume provides abundant amount of information on the microstructure and there are no limits for the parameters that can be characterized.

Synthetic microstructures

The use of Voronoi polyhedra is one of the most common techniques in material science for generating microstructure. The Voronoi tessellations have been successfully applied in materials science for the study of mechanical properties of polycrystals [START_REF] Cailletaud | Some elements of microstructural mechanics[END_REF][START_REF] Kovač | Modeling elasto-plastic behavior of polycrystalline grain structure of steels at mesoscopic level[END_REF], for modeling crack initiations and propagation [START_REF] Simonovski | Automatic parallel generation of finite element meshes for complex spatial structures[END_REF][START_REF] Musienko | Simulation of inter-and transgranular crack propagation in polycrystalline aggregates due to stress corrosion cracking[END_REF][START_REF] Kamaya | Simulation for intergranular stress corrosion cracking based on a three-dimensional polycrystalline model[END_REF]. The Voronoi polyhedras are cell structures represented by a set of convex polygons. The Voronoi diagram is constructed from random seeds or points in 3D and a specific convex geometry is obtained by making perpendicular lines between the neighboring points. Aurenhammer [START_REF] Aurenhammer | Voronoi diagramsâa survey of a fundamental geometric data structure[END_REF] has provided a very detailed review on these diagrams and they are considered to be one of the most efficient and practical geometries for simulations. Generally, a Voronoi polyhedra can represent an isotropic shape very well. Two Voronoi tessellation techniques are often used in literature: Delaunay tessellation [START_REF] Calvo | The extended delaunay tessellation[END_REF] and Laguerre tessellation [START_REF] Lyckegaard | On the use of laguerre tessellations for representations of 3d grain structures[END_REF]. The Voronoi-Delaunay tessellations are widely used in the case of equiaxed and constant grain size range, whereas the Voronoi-Laguerre or 'power tessellation' can be used to represent more disperse structures. A detailed analysis of both of these methods in modeling material structure can be found in [START_REF] Fritzen | Periodic three-dimensional mesh generation for crystalline aggregates based on voronoi tessellations[END_REF]. Both the Delaunay and Laguerre tessellation schemes can describe equiaxed microstructures and are limited to dispersion characterized by Gaussian cell size. Anisotropy of the morphology has also been addressed by considering a merged version of Laguerre and Johnson-Mehl tessellation [START_REF] Altendorf | 3d reconstruction of a multiscale microstructure by anisotropic tessellation models[END_REF]. Several modifications have been done on these tessellations over the years to take into account the log-normal or gamma distributions and one of the interesting tools that allows for meshing of anisotropic geometries is an open source software called 'Neper' [START_REF] Quey | Large-scale 3d random polycrystals for the finite element method: Generation, meshing and remeshing[END_REF]. Neper allows for the use of Voronoi polyhedra and different schemes to generate different types of polycrystalline microstructures: microstructures with a disperse grain size and shape are constructed based on Laguerre tessellation allowing for the possibility to generate anisotropic microstructures. Figure 4.2 shows different microstructures generated by Voronoi polyhedras using Neper [START_REF] Quey | Large-scale 3d random polycrystals for the finite element method: Generation, meshing and remeshing[END_REF]. In addition, this analytical model allows for the introduction of experimental distribution to generate microstructure. The grain boundaries generated by Voronoi polyhedra have convex shape, thus limiting their ability to describe properly the important details of grains. In the laboratories, due to the relative ease, the characterization of the material has been usually done in 2D using EBSD. With the advent of FIB and lab X-ray tomography, the characterization of materials in 3D has become very accessible. Still, for materials with heterogeneous microstructure, the 3D data presents a complex and time-consuming process. In the literature, several sub-classes of 'synthetic microstructure' exist and the most common ones use 2D data to generate equivalent 3D statistics with some assumptions. Here we detail the generation of representative microstructure from one or several orthogonal EBSD maps. This method is a trade-off between accuracy and computation cost.

The important step in generating a microstructure is the characterization and sampling of representative grain statistics which often result in stereo-logical problems when representing 3D information obtained from 2D data. Rollet et al. [START_REF] Saylor | Statistically representative three-dimensional microstructures based on orthogonal observation sections[END_REF] described a technique for generating 3D representative microstructures with statistical information obtained from orthogonal EBSD maps. Ellipsoid shape distribution was used to represent the anisotropic grain shape and orientations. Figure 4.3 shows the orthogonal EBSD maps used for the generation of representative 3D morphological descriptors. The 2D characterization of these orthogonal maps is carried out by measuring their respective aspect ratio, area fraction, as well as major axis orientation of the fitted ellipse. The number of microstructural parameters that can be correlated with this approach are limited to only grain size and shape and other parameters such as number of neighbors and the connection between different morphological descriptors cannot be described [START_REF] Groeber | A framework for automated analysis and simulation of 3d polycrystalline microstructures.: Part 1: Statistical characterization[END_REF][START_REF] Groeber | A framework for automated analysis and simulation of 3d polycrystalline microstructures. part 2: Synthetic structure generation[END_REF]. In literature, this method has usually been applied for the determination of some properties such as yield or texture in case where the grain morphology details could be avoided [START_REF] Groeber | Digital representation of materials grain structure[END_REF]. There are two major steps for generating a synthetic microstructure: first, the generation of equivalent microstructure features from input distribution and, second, placement of these features in an optimized way to fill a user defined volume. A detailed study on the comparison between the extrapolated 3D data from 2D EBSD maps and the true 3D statistics from serial sectioning was done by Groeber [START_REF] Groeber | Development of an automated characterization-representation framework for the modeling of polycrystalline materials in 3D[END_REF] which shows the extrapolated values to match quite well with the true 3D statistics in cases where the grains were represented by ellipsoids. A similar methodology with different strategy was proposed by St. Pierre et al. [START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF]. The binning of 2D information and respective sampling was based on the extrapolated volume of the grains and not on their shape. Also the experimental EBSD surface was reproduced on top of the generated 3D digital microstructure to compare the simulated surface with the experimental surface. This technique first introduced by Zeghadi et al. [START_REF] Zeghadi | Ensemble averaging stress-strain fields in polycrystalline aggregates with a constrained surface microstructure-part 1: Anisotropic elastic behaviour[END_REF][START_REF] Zeghadi | Ensemble averaging stress-strain fields in polycrystalline aggregates with a constrained surface microstructure-part 2: Crystal plasticity[END_REF] for isotropic grains and texture was modified by St. Pierre et al. [START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF] to take into account the anisotropic grain morphology. As can be seen from

Meshing voxelized microstructures

Meshing microstructure is an important step for finite element simulations. The generated microstructures from the image-based or ellipsoid-based techniques are voxel based. The meshing of the microstructure starts with the characterization of the surface and microstructural features by 3D spline and lines. The extraction of these features is usually done by algorithms that define the iso-surface, i.e. marching cube [START_REF] Lorensen | Marching cubes: A high resolution 3d surface construction algorithm[END_REF], multi-material marching cube [START_REF] Wu | Multiple material marching cubes algorithm[END_REF], marching tetrahedra [START_REF] Treece | Regularised marching tetrahedra: improved iso-surface extraction[END_REF], etc. The outputs of these extractions are in the form of an unstructured mesh. This is followed up by meshing of volume and extracted surfaces for which several software and libraries exist. It is very important to consider the parameters such as mesh triangle quality and mesh resolution during this step. A complete study on surface extraction and volume meshing of a microstructure can be found in [START_REF] Sintay | Testing the accuracy of microstructure reconstruction in three dimensions using phantoms[END_REF].

Several different studies have been conducted for generation of mesh from voxelated microstructure. The objective is not to review each of these techniques, but to highlight the one which works fairly well in the context of this work. A voxel-based mesh, where each voxel is assigned a hexahedral element with 8 nodes, can be obtained from experiments or from numerically generated microstructure. Voxel-based mesh is better in term of quality and is one of the simplest methods for mesh generation. Nevertheless this method introduces artifact at the grain interfaces, the so-called 'stair-stepped' effect, which has no physical meaning. A detailed analysis of voxel based mesh and its application to finite element (FE) and fast Fourier transform (FFT) can be referred in [START_REF] Lewis | Two-and three-dimensional microstructural characterization of a super-austenitic stainless steel[END_REF]. In certain cases a CAD-based technique can be used to fit a polynomial/spline to the interfaces or grain boundaries and hence, a smooth representation of the surface can be achieved with this meshing technique. However, this technique is prone to artifacts such as overlaps and gaps at the interface. Details regarding the techniques can be found in [START_REF] Bhandari | 3d polycrystalline microstructure reconstruction from fib generated serial sections for fe analysis[END_REF][START_REF] Ghosh | Cad-based reconstruction of 3d polycrystalline alloy microstructures from fib generated serial sections[END_REF], for instance. Other meshing techniques such as marching cube [START_REF] Lorensen | Marching cubes: A high resolution 3d surface construction algorithm[END_REF], line tension based smoothing [START_REF] Vollmer | Improved laplacian smoothing of noisy surface meshes[END_REF] are also used for meshing voxelated microstructure and are extensively reviewed in [START_REF] Groeber | Digital representation of materials grain structure[END_REF].

Microstructure generation

In order to generate representative polycrystalline microstructures of Ni microwires (developed in section 4.4 and section 4.5), the in-house code 'S2M' (Simplification and Modeling of Microstructure) developed at Institut Pprime since 2008 [START_REF] Guéguen | Simulations 3d d'agrégats polycristallins reconstruits par approche type cao. In 10e colloque national en calcul des structures[END_REF] was used. As a part of this work, S2M has been significantly improved and modified especially to take into account the anisotropy in grains of the nickel microwires.

Section 4.3.1 describes briefly the previous version of S2M, operative at the beginning of this thesis, which was able to generate an equiaxed microstructure with one constrained face. Some of the limitations associated include inability to specify input distribution for subsequent generation of representative statistics. For instance, the procedure of generation of statistics from EBSD map was limited by the number of bins and was only able to generate face constrained microstructures. Accordingly, the modifications and improvements corresponding to the current version of S2M are then described in 4.3.2.

Presentation of the previous version of S2M

S2M was developed with the aim of generating digitally representative 3D microstructures to carry out FE simulations. The methodology of S2M is based on the semi-synthetic microstructure generation following the one proposed by St. Pierre et al. [START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF]. However, this first version of S2M (written in Matlab) was only based on the placement of spheres to represent the grains, hence not suitable to model elongated grains. It allowed for only one possible workflow, which included necessarily a constrained top surface from an experimental EBSD map. The general process of generating a microstructure from an EBSD map, illustrated in Figure 4.5, can be divided into the following steps.

Input

The only input for this version of S2M is a 'grain file' (.gfi extension) generated using EBSD orientation imaging microscopy (OIM T M ) software. This file includes different information pertaining to each grains in the EBSD map: average crystallographic orientation (Euler angles), centroid coordinates, area, equivalent diameter, ellipse semi-axes, aspect ratio, neighbors and average misorientation. The morphological descriptors related to the ellipse description were not used in this version.

Definition of simulation box and input for constrained surface

The spheres representing the grains in EBSD map are defined and placed in the simulation box. The simulation box has the same dimensions in the plane as that of the EBSD map and a user-defined depth. The intersection between a placed sphere and the top plane (face) of the simulation box has the same area and center coordinates as that of the corresponding grain defined by the gfi file. Two cases are possible: first, it is assumed that the spheres are cut perfectly along their mid-plane, so that the diameter of the sphere is equal to the equivalent diameter of the corresponding grain in the EBSD map. Second, a random height between the sphere center and the top surface is defined so that the actual sphere diameter is equal or larger than the equivalent diameter from the EBSD map. This random height (subsequently the diameter) has an allowable limit defined by the largest grain observed in the EBSD map. This limit exists to avoid generating very large spheres. The latter case has been applied in the example shown in Figure 4.5(b).

Generation of representative spheres

The distribution of the diameter of the spheres placed at the constrained top surface is stored in four bins. Based on the average diameter of the distribution and an estimate of the empty volume of the simulation box, the number 'N' of spheres required to fill the volume is determined. Then, a list of 'N' diameters is randomly generated to match the input diameter distribution classified in four bins.

Placement of generated spheres

For each generated spheres in the list, random center coordinates within the bounds of the simulation box are defined. A user-defined overlap among spheres is permitted in order to achieve a more close packing. If a sphere with the current set of coordinates does not satisfy this overlapping limit, then a new random set of coordinates are generated. This process is continued until the sphere is placed in the box. A maximum number of iterations N iter (=250 by default) is defined. If a coordinate cannot be found after N iter attempts, then the next sphere in the list is considered. It should be mentioned that the larger spheres in the distribution are attempted to be placed first in order to obtain a more efficient filling. Figure 4.5(b) shows the result of sphere placement step.

Voxel assignment

The simulation box is then discretized into equal spaced elements or voxels. The label of the sphere is assigned to voxels which are within the non-overlapped region of the sphere. Then, voxels which belong to overlapped or empty regions are assigned with the label of the closest sphere (minimum point-sphere distance). A grain is defined by a set of connected voxels with the same label. The resulting 3D labeled image is shown in 4.5(c). This tessellation technique (that is very similar to Johnson-Mehl tessellation) leads to grains which are possibly concave with non-planar grain boundaries. These features are reinforced due to the permitted overlaps in spheres.

Assignment of crystal orientation

The final step is the generation and assignment of crystallographic orientation. It can be done in two ways: either by generation of random orientations leading to an isotropic texture or by assigning orientations from the list of Euler angles in the gfi file of the surface EBSD map.

The previous version of S2M included several limitations. The main one was the impossibility of the sphere model in representing the anisotropic grain morphologies and orientations. For instance, it can be clearly seen in Figure 4.5 the grain 7 of the EBSD map (Σ3 twin) is not properly described. Then, the input distribution was limited to EBSD based data, and only constrained experimental surface was possible. The packing of sphere was also not optimized. The number of bins (only 4) might not be sufficient in terms of capturing distributions such as log-normal or gamma. Assignment of voxels to grains was also not optimized. The Matlab version of the tool was not versatile and included only one process flow.

New version of S2M with ellipsoids implementation

A new version of S2M, written in python, has been initiated by M. Gueguen et al. [START_REF] Guéguen | S2M: Simplification and Modeling of Microstructure[END_REF]. Objectoriented approach has been implemented to enable more versatility and multiple workflows. However this python version of the code still contained many bugs at the start of this thesis and only sphere model was implemented. Hence, as a part of this work, the python code has been thoroughly corrected and improved by the addition of ellipsoid based modeling.

The object-oriented approach now enables more freedom in terms of manipulation of input data, e.g. generation of statistics through probability density functions. An improvement of the texture module has been added to take into account the ideal fiber texture. Many visualization and analysis tools have been integrated alongside.

The current python version of S2M now contains the basic tools which allow the generation of a relatively wide range of polycrystalline microstructures, not only limited to the Ni microwires. In order to illustrate in a general way the new developments and issues related to ellipsoids, a microstructure different from the present study has been chosen as example (Figure 4.6).

Microstructure generation with ellipsoids

The ellipsoid-based modeling follows the same main steps as that of sphere-based modeling. Some steps have been modified or included to improve the efficiency as well as the versatility of the microstructure generation. For the example provided in Figure 4.6, the top surface of the simulation box is constrained to match an input EBSD map (Figure 4.6(a)). However, it should be mentioned that the current version of S2M is also able to generate polycrystals without constrained surface. The main steps are described below.

Defining the simulation box

In the case of a constrained (top) surface, the length and width of the simulation box are usually taken the same as that of the EBSD map (this is the case in the chosen example, refer to Figure 4.6). However different dimension can also be defined. Moreover the relative location of the EBSD map with respect to the simulation box can be defined. This enables for instance to select a region of interest within a large EBSD map. The height of the box is user-defined depending on the desired volume or number of grains.

Input data for constrained face

Similar to the previous version, a gfi file should be provided. This file must contain the same information as described in sphere model, i.e. average crystal orientation, center coordinates, area, and also the characteristics of the equivalent ellipse. This includes the major and minor semi-axes, labeled as 'a' and 'b', as well as the angle between the ellipse major axis and the horizontal axis of the map.

Generation and placement of constrained ellipsoids

In the case of constrained experimental surface, the ellipsoids representing the EBSD map are first defined and placed in the simulation box. For the sake of simplicity, no stereological corrections (of little interest for the present study) has been included. Thus it is assumed that the major and minor semi-axes of the equivalent ellipse in EBSD map are equal to the principal semi-axes, 'a' and 'b' of the corresponding ellipsoid (refer to

Generation of representative ellipsoids

Different methods and workflows have been implemented to build statistically representative set of ellipsoids in terms of distribution of volume, dimensions (a, b, c) and aspect ratios (b/a, c/a). Probability density function (e.g. log-normal, normal, beta, etc.) can be used for random generation of the different parameters based on the statistics derived from 3D characterization techniques [START_REF] Groeber | Digital representation of materials grain structure[END_REF] (refer to section 4.2.2).

Binned distribution can be built from one gfi file (possibly different from the one of the constrained surface) or several (e.g, orthogonal sections). Generation of 3D statistics from 2D data has been addressed in similar context in literature ( [START_REF] Brahme | 3d reconstruction of microstructure in a commercial purity aluminum[END_REF][START_REF] Rollett | Modeling polycrystalline microstructures in 3d[END_REF][START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF]). St. Pierre et al. [START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF] used one EBSD map to define the representative ellipsoid distribution and a volume distribution with aspect ratio was used as a binning parameter, whereas Saylor et al. [START_REF] Rollett | Modeling polycrystalline microstructures in 3d[END_REF] and Brahme et al. [START_REF] Brahme | 3d reconstruction of microstructure in a commercial purity aluminum[END_REF] used orthogonal maps to generate a distribution of ellipse semi-axes and the true ellipsoid statistics were obtained by stereological formulation. The main assumption of these methods is that the grains of interest should be represented well by the ellipsoids, i.e. the best fit of the 2D EBSD grain is an ellipse.

In the current example only prolate spheroids, i.e. ellipsoids with revolution symmetry about its major axis (b = c), are considered. The major semi-axis 'a' is furthermore parallel to the top surface. The distribution of ellipsoids volume here are described using 6 bins. The characteristics of ellipsoids, i.e. max and min aspect ratio, principal semi-axes and morphological orientations distribution within each bin are recorded. If a bin has only one ellipsoid, a variation of ±15% is added to the corresponding values of grain aspect ratio. A random ellipsoid from a volume bin is generated following the probability distribution and the generated ellipsoids is verified by comparing its aspect ratio with the binned ellipsoids to avoid generation of unrealistic ellipsoids. This strategy is similar to that of the one used in [START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF].

Then, a preliminary number 'N' of ellipsoids required to fill the volume is calculated as the ratio between available volume of the simulation box and the mean ellipsoid volume from the input distribution. The available volume of the simulation box in the case of constrained surface refers to the volume from which the volume contribution of constrained ellipsoids are subtracted. N ellipsoids are generated from the volume bins to match the input distribution.

The number of generated ellipsoids might be not sufficient to achieve the satisfying close packing, since some ellipsoids will not be fully included in the simulation box (refer to Figure 4.6(d)). Hence an additional safety number of ellipsoids following the same distribution of 'N' ellipsoids are generated. The output of this step is a set of ellipsoids, N sa f ety (corresponding to 10% of the simulation box volume), is generated [START_REF] Groeber | Digital representation of materials grain structure[END_REF].

Placement of generated ellipsoids

The workflow is globally similar to the sphere model but the check and control of ellipsoids overlapping is more complex. Indeed, quantitative estimation of the overlapped volume can be time consuming but a simple binary intersection test is relatively easy and fast. The following strategy is carried out if a certain amount of overlapping is permitted. In the event of a first ellipsoid already being placed and a second one is attempted to be placed: the intersection check is performed with a reduced, or shrinked, ellipsoids (Figure 4.8), whose semi-axes has been decreased by a user-defined factor (in this example, it is 1/3). If the reduced ellipsoids do not intersect, then the placement of the second ellipsoid is validated. The reduction factor controls the amount of possible overlap and can be defined individually for all the principal semi-axes.

To improve ellipsoid packing, especially in the case of large aggregates (in terms of number of grains), a sub-box methodology has also been implemented. Simulation box is divided into many regular boxes, where each box can accommodate a generated grain of average volume. The sub-box strategy allows for a more controlled generation of microstructure, i.e. one could control the spatial placement of big and small ellipsoids in the case of a bi-modal size distribution. This method is also efficient in terms of computational cost, as the intersection check is carried out between a smaller set of the ellipsoids from the neighboring boxes. Several different algorithms exist in literature to control the placement of ellipsoids in volume: 'subset minimization' by Saylor et al. [START_REF] Rollett | Modeling polycrystalline microstructures in 3d[END_REF], but this technique suffers from the optimization of final subset leading to unrealistic overlap towards the end. Also the 'gravity fall' by Wang et al. [START_REF] Wang | A packing generation scheme for the granular assemblies with 3d ellipsoidal particles[END_REF] works quite well and has an optimal packing of ellipsoids in the volume, but the method changes the orientation of the ellipsoids during placement, which in most of the cases can lead to unrealistic grain morphologies.

Voxel assignment

The simulation box is then discretized into regular grid of voxels. First, the label of a given ellipsoid is assigned to voxels which belong to the non-overlapped region of the ellipsoids. This first step of voxelization ensures a filling of 65-70% of the total volume of simulation box (Figure 4.6(e)). Then, the assignment of the remaining voxels (within empty or overlapped regions) is carried out using a nearest neighbor search algorithm, called K-D tree [START_REF] Maneewongvatana | Analysis of approximate nearest neighbor searching with clustered point sets[END_REF]. This method is almost 10 times faster than point-ellipsoid distance calculation. The method uses a binary tree, where each node represents an axis aligned hyper-rectangle. By assigning these free voxels to their nearest neighbors, a filled volume is obtained, as shown in Figure 4.6(f).

Assignment of crystal orientation

In the current example, random generation of orientation is carried out to obtain an isotropic texture: Euler angles φ 1 and φ 2 are selected randomly within the range [0, 2π], while the cosine of Φ is selected between -1 and 1. It should be mentioned that it is also possible to generate an ideal fiber texture for the desired poles. The model that has been implemented in S2M to generate ideal fiber texture is detailed in section 4.5.3.1. Tools for visualization of 3D ellipsoids, grain boundary pixels, view of sectional ellipsoids and also, analysis of texture have been implemented, i.e. pole figures (part of the library has been imported from pymicro [START_REF] Proudhon | pymicro: A python package to work with material microstructures and 3d data sets[END_REF]), orientation and misorientation distribution plots.

Validation and limitation of S2M

In this section, distribution of different microstructural attributes of the generated grains are compared to the target, or input, distribution. This is intended to illustrate some capabilities of S2M as well as some limitations. But it should be emphasized that the given example, in Figure 4.6, was chosen relatively small for the sake of clarity and is thus not well-adapted for such comparison and validation. Indeed the number of grains is too small. However it allows for discussing some important and general features and issues related to the method.

First, it can be clearly seen, though qualitatively, that the use of ellipsoids drastically improves the description of elongated grains at the constrained EBSD surface (refer to Figure 4.6(f and h)). Following [START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF], a more qualitative comparison between sphere and ellipsoid model is provided in Figure 4.9, showing histogram of grain area at the top surface. Both sphere and ellipsoid models are found to reproduce satisfactorily the experimental distribution. This indicates that other morphological indicators (for example aspect ratio, refer to Figure 4.10) need to be used to assess the representativity of the generated microstructure. Similarly, the distribution of grain area in several cross-section can be compared to the experimental one from the constrained EBSD surface to assess the representativity of the microstructure (Figure 4.11). The distribution of grain area shows a rather good match with the experimental distribution. The noticed discrepancies may be attributed to the small size of the aggregate (sampling effect and/ or bias due to the grains affected by the simulation box bounds). Figure 4.11: Comparison of sectional area of the grain taken at various sections normal to Z-axis at 0%, 20%, 40%, 60%, 80%, 100% of the box height (100% corresponds to the top surface). The presented data is normalized and is for all the grains (including the border grains).

More generally, the distribution of 3D descriptors is described here and tracked during the different steps of the aggregate generation. Statistics are provided for all the 174 grains as well as for inner grains only, i.e. grains whose shape is not affected by the simulation box boundary (Figure 4.12). Figure 4.13 shows the distribution of the three principal semi-axes (a, b and c) of the ellipsoids. Figure 4.14 shows the distribution of aspect ratio ( b a , c a ), Figure 4.15 indicates the volume and equivalent size. Input distributions are depicted in red. Blue bars correspond to the distribution related to the ellipsoids that has been placed in the simulation box. Green bars correspond to distribution related to the equivalent ellipsoids of the voxelized grains, obtained by moment invariant analysis (referred to as 'voxel distribution'). The second order moments are calculated for each grains by summing the contribution of the voxels belonging to that grain. The eigenvalues and eigenvectors of these moments provide the principal semi-axes of the ellipsoid (for formulation refer to [START_REF] Groeber | Development of an automated characterization-representation framework for the modeling of polycrystalline materials in 3D[END_REF]). The discrepancies between the input and placed distribution are related to the non-placement of some ellipsoids. It could be noticed that few larger ellipsoids are not successfully placed. This is also the case for smaller ellipsoids since they are attempted to be placed at the end of the placement process, i.e. with lower probability of finding a empty space in the simulation box. The differences between placed and voxel distributions result from the voxel assignment to the ellipsoids: the presence of overlapping regions tends to decrease the grain size while assignment of voxels from empty volume tends to enlarge the grains, refer to the steps in Figure 4.6(e-f). This is also reflected in the voxel distribution of ellipsoids principal semi-axes in Figure 4.13. In the case of grains that belong to the boundaries, the actual size of a voxelized grains should decrease compared to the size of the initial ellipsoid. It should be underlined that detailed understanding and quantification of such effects are beyond the scope of the present study. This would require systematic studies on large-scale aggregates (at least with few thousands of grains) to analyze such distortion of the distributions and eventually optimize the ellipsoid generation step to achieve a better match with the input distribution.

Application to Ni microwires

In this section, the applicability of S2M with implementation of ellipsoids is discussed in order to generate statistically representative microstructures of Ni microwires. The microstructural characterization of the wires from previous chapter have indicated the primary role of crystallographic texture and the architecture (core, shell) on their mechanical properties.

First, the statistics of different microstructural attributes from the experimental data presented in Chapter 3 are briefly described (in section 4.4.1). Then, the main assumptions made to generate the microstructures used for FE simulation (Chapter 5) are presented and discussed (in section 4.4.2).

Summary of microstructure characteristics

4.4.1.1 Crystallographic texture XRD texture measurement has been performed on the three series on wires (EP series, AA series and LD series), as described in Chapter 2. For simplicity, we will consider only four types of wires: AA100, EP40, AA40 and LD100.

For example, EBSD results on AA100 wire reveal the presence of core-shell architecture. The core and shell regions of the AA100 microwire are characterized on the EBSD map with dash lines, refer to

Morphological parameters

.17 and Table 4.2 provides the main statistics obtained, from two cross-sectional and one longitudinal EBSD maps, on AA100 microwire. In the cross-section, the grain size follows a log-normal distribution (Figure 4.17(a)) ranging from sub-micrometer size to about 10µm. The arithmetic average of the grain size having an area fraction of 0.05 or higher is about 1.8µm with no significant difference between the core and shell. The average value of the distribution is found to be ∼ 1µm, by fitting a log-normal distribution to the grain size distribution vs area fraction. The grain size in core and shell distributions are very comparable. Grains in the cross-section are rather equiaxed with a mean aspect ratio of ~0.8 (refer to Figure 4.17 In longitudinal section of AA100 wire, the grains are very elongated along the wire axis. The major semi-axis of equivalent ellipse exhibits a wide scatter ranging from few micrometers to about 50µm (with longest grains mostly observed in the core). The transverse grain size, obtained using linear intercept method, is ∼ 1µm with smaller grains observed in shell. The corresponding aspect ratio mostly ranges between 0.05 to about 0.4 with more elongated grains in the core of the wire.

It should be noted that the longitudinal section cuts the grains at different location across the wire diameter and hence the changes in aspect ratio and grain size are to be considered with caution. In general, the grain size and shape statistics from longitudinal map are noisy and very sensitive to the clean-up parameters of the EBSD data. This may be due to the presence of significant orientation gradient along the wire axis. Moreover, larger map should be considered to obtain a more representative number of 'full' grains along the tensile axis. For the EP40 microwire produced by electropolishing the AA100 wires, the grain size distribution is similar to that of AA100 (reflected in the 'core' of the AA100 microwire analysis). For the AA40 microwire, which has been produced by cold-drawing the AA100 wire, analysis of cross-sectional EBSD maps indicates that the grain size follows a log-normal distribution and the core has an average grain size of ∼ 1µm, whereas the shell shows an average grain size of ∼ 0.4µm. For the LD100 microwire produced by cold-drawing from another batch of annealed 500µm nickel microwires, the grain size distribution is relatively close to that of the AA100 wires (log-normal distribution with an average of ∼ 1µm).

Architecture

Modeling assumptions

Previous chapters have shown that different wires exhibit important changes in texture. Strong differences are also seen between the 'core' and 'shell' regions. Conversely, regarding the morphological parameters, no significant differences have been noticed between the different wires (except in the case of AA40 wires) and also between the core and shell regions.

Experimental results suggest that the texture and architecture of the wire have a major influence on their mechanical properties. The assumptions made for the generation of aggregate used in the next chapter arise from a compromise between the representativity of the microstructure and the cost and quality of computational results that depend on the number of considered grains and the mesh density. For these reasons and in order to evaluate the sole influence of crystallographic texture and architecture, it has been chosen to use a relatively simple morphological description, while retaining the elongated nature of the grains.

Moreover, despite differences between the different wires and the core-shell region, the same microstructure morphology was used to represent all the wires. In addition, it is clear that the current choice of number of grains (developed in section 4.3) considered in the simulation will be several order of magnitude smaller than the actual number of grains in the wire. But the spatial assignment of the orientation will attempt to reproduce the architecture so that the generated aggregate could be considered as a 'reduced', but representative, model of the wire. It should be emphasized that these choices are reasonable since no size effect will be included in the simulation, rather the interest is to study the influence of texture and architecture.

Grain morphology description by S2M

Accordingly, aggregates are generated using S2M following these assumptions:

• All generated ellipsoids are identical and are essentially prolate spheroids (i.e. a ≥ b= c) with their major axis perfectly aligned with the wire axis.

• The minor semi-axis b = c is set to be equal to 0.5µm, such that 2b = 2c = 1µm, corresponds approximately to the average parameter of the log-normal fit of the grain size distribution (refer to Figure 4.17(a)).

• The aspect ratio, b/a, is set to 0.1, which leads to a major semi-axis a = 5µm. Thus, grain size in the axial direction will be about 10µm that is significantly lower than the most elongated grains observed experimentally. However it has been shown that the effect of the aspect ratio at room temperature on mechanical properties tends to saturate below 0.1 [START_REF] Delannay | Modelling the combined effect of grain size and grain shape on plastic anisotropy of metals[END_REF].

Representativity of crystallographic texture

Sufficient number of grains, thus orientations, should be considered to properly represent the actual crystallographic texture of the wires and, if necessary, their core/shell architecture. The number of grains required to describe the texture has been quantified with the pole figure analysis. Texture has been generated by sampling from cross-sectional AA100 EBSD map. The comparison between of experimental pole figures and the sampled texture for 200, 1000 and 5000 orientation sets is shown in Figure 4.18. Qualitatively, the orientation sets of 1000 and 5000 grains seem to describe the fiber texture around the wire axis. Also qualitative analysis of the texture indicates that the 200 orientation set is insufficient to describe the experimentally observed fiber texture around the ( 111) and ( 200) poles ( A quantitative analysis is carried out for the 1000 and 5000 orientation sets and are presented in Figure 4.19, 4.20 and 4.21. The analysis tries to assess the representativeness of fiber texture. For example in the case of (111) pole figures, the Figure 4.19 shows the variation in intensity along the ring at 70°from the pole center. As can be seen, the variation in the intensity of the fiber along the fiber axis is quite well captured with some under-representation between 160-280°by 1000 orientation sets. Similarly for the [START_REF] Schmid | Kristallplastizit˜it[END_REF] pole, the corresponding ( 111) reflection ( refer to Figure 4.20) and the variations in fiber texture around the (200) fiber axis by 1000 orientation set is seen to follow the EBSD profile. Qualitatively, more number of orientation sets are required to match the intensity of the [START_REF] Schmid | Kristallplastizit˜it[END_REF] grains. This difference in intensity is a direct result of the choice of volume fraction of different grain families in the generated orientation sets, which is different from the area fraction observed with the EBSD maps. This is explained in more details in sub-section 4.5.2.1. The corresponding [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection from the [START_REF] Schmid | Kristallplastizit˜it[END_REF] pole is well matched, see Figure 4.20. This under-representation of the (200) texture variation for the 1000 orientation set can be understood with respect to the number of orientations selected. 5000 orientation set seems to define these variations of intensity along the fiber axis quite well. However, the use of 5000 grains aggregate which provide a quite good description of texture (Figure 4.18(d)) could be computationally expensive especially for FE parametric studies. Thus, 1000 grains aggregate appears to be an acceptable compromise between the computation cost and representative texture (Figure 4.18(c)).

Dimension of the simulation box

The dimension of the simulation box should be defined so that the 1000 grain microstructure (with assigned orientation) is representative or defines a 'reduced' model of a given wire. Regarding this issue, one important criterion is the number of grains along the tensile direction. Three full grains may be considered as a minimum number of grains required along the tensile direction. This will average to four grains if the contribution of border grains are to be considered. This will result in a microstructure with an average of 250 grains across a cross-section. In the case of an experimental core-shell architecture (AA100 for example), the core has an area of about ∼ 25% of the total cross-sectional area. It should be mentioned that the definition of core on the EBSD map is done manually by a quasi circle. In the case of a perfect core-shell defined by circle of 20µm radius, the core should occupy an area of about 15 of the total cross-sectional area. For this area, the digital microstructure should have the number of grains in the core close to 40 -50. It is clear that the current configuration should be considered as a minimum number of grains. This also motivates the use of at least 1000 grains.

Generated aggregate for FE simulations 4.5.1 S2M settings, morphology and mesh

The dimensions of the simulation box are 15 × 15 × 35 µm 3 , corresponding to 151 × 151 × 351 voxels. 1200 similar ellipsoids (principal semi-axes: a = 5µm, b = c = 0.5µm) were generated and 994 were placed in the simulation box with N iter = 250 and an acceptable overlap of 1/3 for all the principal semi-axes. The packing of ellipsoids with allowed overlap can be seen in Figure 4. 22(a andc). The resulting voxel maps are shown in Figure 4. 22(b andd). The voxel size of 0.1µm ensures an acceptable number of voxels in the grain semi-axes direction and subsequently a number of finite elements depending on the meshing method. The voxelization step leads to the addition of 2-3 voxels in the vicinity of the ellipsoids. This results in an increase of 2-3 voxels of the semi-axes a and b, and a smaller increase for semi-axis c may be due to overlap. A small scatter in the final distribution arises as a result of voxelization. If all the grains in the simulation box are included for statistics, the distortion of distribution as a result of border grains is evident from the left tail of the distributions of semi-axes and volume. Similarly mean aspect ratio also increases slightly during the voxelization step ( The generated microstructure can then be directly meshed within S2M using hexahedral elements assigned to each voxel. Structured mesh using hexahedral elements would require large number of elements per grain to respect the grain boundaries especially in the case of anisotropic grain shape. Neper has been used to provide an unstructured conforming mesh of the Voronoi-Laguerre tessellation on the voxel image generated by S2M. Tessellation often introduces smaller edge lengths, which requires a local refining of the mesh, leading to higher number of elements. Local refinements are avoided due to modifications of the small edges by Neper without compromising the grain shape. A detailed description of Neper and its application can be found in [START_REF] Quey | Large-scale 3d random polycrystals for the finite element method: Generation, meshing and remeshing[END_REF]. The advantage of Neper is that several algorithms are carried out in parallel to select the mesh with highest overall quality. The output mesh file can then be directly imported to the FE software ZéBuLoN Z-set [START_REF] Besson | Object-oriented programming applied to the finite element method part i. general concepts[END_REF].

Examples of obtained meshes are shown in Figure 4.26 performed on a 177 grain microstructure (used later in Chapter 5 for mesh convergence study). Total number of nodes and elements of the corresponding meshes are reported in Table 4.3. Voxel-based mesh is composed of about 10 6 nodes, while it is about 10 5 for the Neper mesh with the highest mesh density (labeled as 'fine mesh'). Figure 4.26: Different mesh density generated with Neper on a 177 grain microstructure (a) hexahedral mesh with an average of 4000 elements per grain, labeled as 'image mesh', (b) tetrahedral mesh with an average of 200 elements per grain, labeled as 'coarse mesh', (c) tetrahedral mesh with an average of 400 elements per grain, labeled as 'intermediate mesh', (d) tetrahedral mesh with an average of 3000 elements per grain, labeled as 'fine mesh'. (e, f) shows the difference between voxel-meshed grain and tetrahedral-mesh grain (fine mesh). Colors do not represent texture. For the 994 grain microstructure, the voxel based mesh is composed of about 3 × 10 6 nodes. Using Neper, a mesh setting corresponding to the label 'intermediate mesh' as for 177 grains is employed. This leads to 1 × 10 5 nodes and 6 × 10 5 elements, with an average of ~600 elements per grain.

Aggregate with representative texture

The assignment of crystallographic orientations to the 994 grains of the above explained generated microstructure is then carried out so that the 'reduced' 994 grains model has a texture and an architecture representative of:

• AA100 microwire • EP40 microwire • AA40 microwire • LD100 microwire
Experimental texture information related to these microwires are detailed in Chapter 3. In section 4.5.2.1, sampling of experimental texture and assignment of crystal orientation are described in details for the case of AA100 microwires. Then, the characteristics of the assigned textures for the 4 types of wires are presented in the following sections.

Experimental texture sampling and assignment

Here a quantification of the EBSD texture is presented, following which texture statistics have been quantified for all the wires. The pole figures of 'full experimental EBSD' for the AA100 core-shell architecture wire is shown in The full experimental EBSD includes contributions from very small grains: hence, in order to remove such grains from calculation, a filter of mean area fraction is applied, i.e. only the grain having an area fraction equal or higher than the mean area fraction of the grains are kept.

The subsequent texture is referred to as 'simplified experimental EBSD', as shown in Figure 4. 27 (c,d).

It should be noted that the separation into core and shell grains in the EBSD map is done manually. We recall that the transition from core to shell is not always sharp. The core is thus defined by the circular region of diameter 40µm (Figure 4.16(a)). This also corresponds to the smallest diameter of the electropolished wire (EP40) which exhibits a high <111> fiber texture. Also, the core of the AA100 microwire is never exactly at the center along the depth and shows deviation of less than 10µm to the left or right alternately. These simplified EBSD textures are then used for assigning orientations to the digital microstructure. Orientations are divided into three classes based on their misorientation from a given direction (<111>, <100>, <110>). As an example this is shown for the core of AA100 microwire in Figure 4.28. The AA100's 'core' pole figure ( In order to be consistent with the definition of grain families as in XRD, a 10 degree misorientation filter was applied to the EBSD orientations from Figure 4.28, such that each grain family is split into two more sub-groups: orientation having less than 10 degree of misorientation with the ideal direction and the orientations having misorientation of more than 10 degree. This is shown in Figure 4.29 for <111> texture component. Similar splitting has been carried out for other grain families (<100> and <110>) from the 'core'. The area fraction of each orientation of sub-classes calculated from EBSD maps is reported in Table 4.4. Similar statistical analysis has been carried out on EP40, AA40 and LD100 microwires.

We recall that, <111> volume fraction deduced from XRD performed on EP40 wire (assumed to be the 'core' of AA100 wire) is about 95% while the corresponding area fraction from the simplified experimental EBSD map is only 75%. XRD volume fraction data should be more reliable and representative than the EBSD data from one or two cross-sections. Thus, XRD data has been chosen as target for the texture assignment. Because of the mismatch between the XRD and EBSD data, there is a mismatch between the area fraction from EBSD and the digital microstructure. This is due to the fact that the core of the microwire is not always in line with the wire axis. Table 4.4 provides the complete statistics of the simplified experimental texture (SET) and the assigned experimental texture (AET). The area ratio of the shell to the core has been evaluated to ∼ 4.2 using the cropped area of the core and shell crops of EBSD map, performed manually. If one considers that the core-shell architecture perfectly follows the circular region of 40µm diameter core in 100µm diameter wire, the corresponding area ratio is calculated to ∼ 5.2 (Figure 4.16(a)). Similarly, the grains corresponding to the core in the 994 grains reduced model of AA100 wire have been selected to obtain an area ratio of about 4.7, which lies between the two estimates (Figure 4.30(a)). Core of the digital microstructure contains 182 grains and the shell region includes 812 grains.

AA100 texture assignment (labeled as AA100-DMAT)

The AA100 texture assignment has been described in the previous paragraph. The resulting volume and area fraction for each orientation of sub-classes were performed. A Euler angles triplet is chosen randomly from the list of Euler angles defining the core from the 'SET' with the goal of matching the volume fraction or area fractions detailed in Table 4.4. The Euler angles are then assigned to the corresponding core grains in the digital microstructure. Similarly the shell grains of the microstructure are also assigned Euler angles from the list of Euler angles defining the shell in 'SET'. The 'AET' of 994 grains are detailed in Table 4 The AA40 microwire has been obtained by cold-drawing the AA100 wires resulting in microwires with different grain sizes and volume fraction, while still retaining the initial core-shell architecture. Similar to AA100, here a 40% diameter of the 40µm microwire is observed to be the core. Hence the definition of core-shell follows a similar area ratio as that of the AA100 wires, refer to Chapter 3 for corresponding EBSD map. In-terms of global texture, only the texture of whole wire calculated from XRD are available (Table 4.1) and no distinction of core-shell texture volume fraction could be made. The assigned texture was generated to match the XRD calculated volume fractions. The pole figures of the assigned texture follows the probabilities coming from XRD (macro) and EBSD (micro) of AA40 wires (for pole figures refer to Appendix C).

LD100 texture assignment (labeled as LD100-DMAT)

A similar analysis as that of AA100 is carried out for the lab drawn LD100 microwires. Pole figures of the assigned texture following the probabilities from XRD and EBSD data for LD100 wires are presented in Appendix C. It is reminded again that the architecture for the LD100 wires is somewhat inverted when compared to AA100 wires (refer to Chapter 3 for EBSD maps). The XRD volume fractions of the wire are comparable to that of AA100 wires (Table 4.1). Table 4.5 provides the volume and area fraction coming from XRD and EBSD analysis. The analysis of different sub-classes of orientation is done exactly the same way as for AA100 microwires. 4.5: 'Simplified experimental texture' data, labeled as 'SET', from LD100 wire. For SET, the volume fraction data comes from XRD texture analysis and the area fraction data is from EBSD map. Alongside, the texture volume fraction of the 'assigned experimental texture' (AET) on the 994 grain aggregate is also presented. The subsequent area fraction of AET is the average over several cross-sections in the digital microstructure. △g refers to misorientation angle.

Table 4.5 provides the statistic of the simplified experimental EBSD (SET) and the assigned experimental texture (AET). Here the XRD volume fraction of the core alone is not available, hence for the assigned texture, the EBSD core area fraction is matched. Thus, the generated microstructure has a global volume fraction that follows the XRD calculated volume fraction and, locally in the core, the volume fraction is close to the EBSD calculated area fraction. 4.37 shows the misorientation distribution of the texture from EBSD and 3D digital microstructure. Globally the micro texture of the assigned texture matches well with the experimental EBSD microtexture and also the global volume fraction of the texture as calculated from XRD are also conserved. Table 4.5 shows the volume fraction of assigned texture component (AET), the global volume fraction matches well with the global XRD volume fraction. The presented area fraction in Table 4.5 is an average of several cross-sections taken from the digital microstructure.

Aggregate with ideal texture/architecture

Alongside experimental texture, the role of architecture will be further studied with the ideal texture generators. Ideal textures are sampled and assigned to the 994 grains microstructure.

Ideal fiber texture generation

Several different models exist for generating axial fiber textures depending on the materials. In the current version of S2M a model based on the work of Garbacz and Grabski [START_REF] Garbacz | Modelling of csl boundaries distribution in polycrystals[END_REF], modified by Lisa Chan [START_REF] Chan | Synthetic three-dimensional voxel-based microstructures that contain annealing twins[END_REF] is integrated. It is stated that, for the fiber textures, any deviation from the ideal <hkl> or fiber direction (described by a misorientation angle ϕ, see Figure 4.38(a)) is described by the normal distribution.

P(φ ) = 1 σ √ 2π exp - (ϕ -µ) 2 2σ 2 (4.1)
where µ is the mean value of the misorientation angle ϕ, in degrees for a given fiber axis. In the case of fiber textures, µ is set to zero. σ is the standard deviation that specifies the spread of texture around the mean with a normal distribution (

Virtual texture generation

Apart from the 4 experimental cases, few other conceptual architecture with ideal texture were also generated to study the effect of architecture and volume fraction of texture components on the mechanical properties. The generation and assignment of texture was carried out in a similar strategy explained for the experimental microstructures.

For instance, Figure 4.39 shows a virtual microstructure of an ideal <111> fiber texture in the core and an ideal <100> fiber texture in the shell so that texture is composed of 75% of <111> and 25% of <100> (ideal fiber texture generated with σ = 3, corresponding to a scatter of ∼ 10 • ). Other virtual microstructures will be studied in Chapter 5.

Conclusion

The in-house code S2M has been upgraded with ellipsoid morphology to represent the anisotropic grain shapes that are observed experimentally. The tool generates 3D representative microstructure with 2D EBSD map/analysis input. These EBSD maps serve as input distribution for sampling and generating more representative distribution of grains. S2M is a versatile tool and a number of add-on exist that can further improve its efficiency. Microstructures can be generated with correlation with their spatial dependency, i.e a microstructure with spatial gradient in grain size or crystallographic texture.

In the present study, it has been chosen to simplify the morphological description of microstructure in order to focus on the effects of the crystallographic texture and architecture. The assigned experimental texture was sampled from the simplified EBSD texture. The texture matching has been limited to orientation and misorientation distribution from the EBSD as well as global volume fraction calculated from XRD. The texture is assigned to the generated microstructure by selecting an Euler angle at random from the list of Euler angles obtained from the EBSD maps. Based on the probability of the texture depending on its spatial location, the Euler angles are assigned to the grains that satisfy the corresponding spatial location in the digital microstructure. This way the assigned microstructure has a texture that resembles that of the experimental one with the same architecture. The final assigned texture matches qualitatively well with the experimental texture (pole figure andarchitecture).

The notion of 'reduced' model is employed in current study to be representative in terms of the architecture of the wire considered. The selected 994 grain model shows a reasonably good fit with the experimental texture. Four digital microstructure with assigned texture (DMAT) have been generated, labeled as AA100-DMAT, EP40-DMAT, AA40-DMAT and LD100-DMAT, respecting the experimental texture distribution. In addition, conceptual architectures have been described by ideal fiber texture components. These generated microstructures were then used as inputs for CPFE simulations (developed in the next chapter).

Chapter 5

Crystal plasticity finite element simulations

Introduction

CPFE method is used to complete and extend the understanding of heterogeneous deformation in nickel microwires. As detailed before, the grains in the microwires present a specific elongated geometry: in the cross-section the grains size is of the order of magnitude of ∼ 1µm, while in the longitudinal direction they are well aligned with wire axis and can be as large as ∼ 50µm. Previous studies [2,4] on nickel microwires indicate the presence of an apparent size effect, i.e. increase in strength with reduction of wire diameter, which was later revealed in this work to be also related to an 'architecture effect' (refer to Chapter 3).

In-situ XRD analysis (Chapter 3) on all the series (EP, AA and LD series) of nickel microwires indicates a heterogeneous behavior for the <111> and <100> grains. Results also reveal the onset of plasticity in <111> grains at lower strains, following which <100> grains plastify. Thus, the FE results will be analyzed in-terms of grain families, i.e. grains grouped together based on their small misorientation from the ideal crystallographic directions of <111> and <100>. The simulated microstructures will be evaluated regarding their macroscopic behavior, and we will also perform a local analysis of the stresses and strains in core and shell part of the architecture. The objective of the simulation is to better understand the texture/architecture effect, as suggested by the experimental results in Chapter 3, on the mechanical properties of nickel microwires.

The outline of the chapter is as follows:

• a short review about the polycrystalline micro-mechanical modeling with a brief discussion on the reasoning behind the choice of crystal plasticity constitutive equations used in this study is provided in section 5.2;

• section 5.3 describes the constitutive law, material parameters identification, boundary conditions and microstructure mesh used for CPFE simulations;

• section 5.4 details the results of CPFE simulations on AA100-DMAT, EP40-DMAT, AA40-DMAT and LD100-DMAT.

• section 5.5 provides the additional investigation to understand the influence of architecture on the mechanical properties.

Overview of polycrystalline micro-mechanical models

The behavior of single crystal or grains in polycrystals is generally anisotropic elastically and plastically. These anisotropies along with the spatial variability of mechanical properties in polycrystal (i.e. morphological and crystallographic texture) lead to heterogeneities in local mechanical fields (stress, strain). The modeling of single crystal and polycrystal behavior is addressed in the next section. Some studies devoted to pure nickel in literature are also discussed.

Single crystal

The small strain assumption will be considered for single crystals in our study i.e. the definition of strain is considered in its additive decomposition form as:

ε = ε e + ε p (5.1)
where ε e and ε p are respectively the elastic and plastic components. At room temperature, the plastic deformation in pure nickel takes place primarily by dislocation slip and twinning.

Elasticity

The anisotropic linear elastic behavior is described by three independent elastic constants C 11 , C 12 and C 44 , in the case of cubic materials (the corresponding elastic matrix in Voigt notation is provided in equation 5.2). The degree of elastic anisotropy for cubic metals can be quantified by Zener ratio 'A' [START_REF] Zener | Theory of the elasticity of polycrystals with viscous grain boundaries[END_REF], which a dimensionless number (refer to equation 5.3). Zener ratio corresponds to the ratio between the maximal and the minimal directional shear moduli. It equals unity in case of isotropy. Nickel has a Zener ratio of 2.43, calculated from single crystal elastic constants [START_REF] Hellwege | Landolt-bornstein tables[END_REF]. In the current work, the nickel microwires have fiber textures with major components as <111> and <100>. The Young's modulus in nickel has directional dependency with <111> oriented grains having the highest modulus of 288 GPa and the <100> oriented grains have the lowest modulus of 131 GPa (whose ratio is close to 'A'). In the case of anisotropic materials, especially for FCC metals, the effect of cubic anisotropy has been investigated and was found to affect the stress heterogeneities and subsequent yielding [START_REF] Sauzay | Cubic elasticity and stress distribution at the free surface of polycrystals[END_REF][START_REF] Brenner | Elastic anisotropy and yield surface estimates of polycrystals[END_REF].

C i j =           C 11 C 12 C 12 0 0 0 C 12 C 11 C 12 0 0 0 C 12 C 12 C 11 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44           , (5.2)
A = 2C 44 C 11 -C 12
(5.3)

Visco-plasticity

Plasticity is induced by the glide of dislocations on specific planes of close packed atoms called 'slip planes'. In FCC metals at room temperature, the dislocation glide occurs on four octahedral planes of {111} family with three <110> directions in each plane, thus 12 slip systems. Schmid law [START_REF] Schmid | Kristallplastizit˜it[END_REF] provides a formulation to identify the activated slip systems under the external load.

The resolved shear stress (RSS) computed using Schmid law governs the yielding (criterion) and also the evolution of plastic slip (flow rule). Conventional single crystal plasticity laws are based on continuum mechanics, which relies on a set of constitutive equations that defines elastic-plastic response at the scale of grains. Crystal plasticity effectively takes into account the microstructural anisotropy. The constitutive equations of deformation are defined at the grain (slip system) level. The plastic strain rate ε pg is thus defined as the sum of deformation resulting from the contribution of the 12 octahedral slip systems (<110>{111}).

ε p = 12 ∑ s=1 m s : γs , (5.4)
where γs is the inelastic flow rate on slip system (s). The orientation tensor m s is related to the slip system (s).

m s = 1 2 (l s n s + n s l s ) , (5.5)
where the variables n s and l s are the slip plane normal and the slip direction vector for a

given slip system (s). The resolved stress τ s for a particular slip system 's' is related to the stress tensor (σ ) as:

τ s = σ : m s , (5.6)
To formulate a behavior law at the scale of slip systems, two class of models can be generally found in literature:

• The first one is based on phenomenological approach (Kocks [START_REF] Kocks | Laws for work-hardening and low-temperature creep[END_REF], Peirce et al. [START_REF] Peirce | An analysis of nonuniform and localized deformation in ductile single crystals[END_REF],

Hutchinson [START_REF] Hutchinson | Bounds and self-consistent estimates for creep of polycrystalline materials[END_REF], Rice et al. [START_REF] Rice | Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity[END_REF], Méric-Cailletaud (MC) [START_REF] Méric | Single crystal modeling for structural calculations: part 1âmodel presentation[END_REF][START_REF] Méric | Single crystal modeling for structural calculations: Part 2âfinite element implementation[END_REF]), which describes the strain hardening as a function of history of slip accumulation. The state of the material is described using critical resolved shear stress (CRSS) i.e. γs = f (τ s ). Phenomenological internal variables are introduced to describe hardening using a formalism similar to the classical continuum visco-plasticity.

• The second class of models, called the physics based models, introduces internal variables such as dislocation density (Mecking and Kocks [START_REF] Beaudoin | Development of localized orientation gradients in fcc polycrystals[END_REF], Estrin and Mecking [START_REF] Estrin | A unified phenomenological description of work hardening and creep based on one-parameter models[END_REF][START_REF] Estrin | Local strain hardening and nonuniformity of plastic deformation[END_REF], Tabourot [START_REF] Tabourot | Generalised constitutive laws for fcc single crystals[END_REF] or Teodosiu et al. [START_REF] Teodosiu | A physical theory of the finite elastic-viscoplastic behaviour of single crystals[END_REF]), which relates the hardening to the strength of interaction between slip systems and the total dislocation density. The state of the material is described in terms of CRSS and the evolution of dislocation densities, as described in [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF][START_REF] Arsenlis | Modeling the evolution of crystallographic dislocation density in crystal plasticity[END_REF][START_REF] Arsenlis | On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals[END_REF][START_REF] Ma | A dislocation density based constitutive model for crystal plasticity fem including geometrically necessary dislocations[END_REF].

It should be noted that in the physics based models, the required parameters are numerous and especially the interaction matrix are not readily available in the literature for some materials. A detailed overview of CPFE formulation with their application in the field of material science can be found in [START_REF] Roters | Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications[END_REF].

Size dependent models

Classical crystal plasticity models discussed before are size independent. Size effect in literature has been addressed with models using gradient based approach (Fleck et al. [START_REF] Fleck | Strain gradient plasticity[END_REF]), or by GNDs [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF] and also by the inclusion of material's curvature into the constitutive equations of flow stress (Forest et al. [START_REF] Forest | Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multi-phase materials[END_REF]). In literature, a phenomenological way of including the grain size effect at the slip system level, i.e. CRSS, by a Hall-Petch relationship has also been considered [START_REF] Lavergne | Effects of grain size distribution and stress heterogeneity on yield stress of polycrystals: A numerical approach[END_REF][START_REF] Weng | A micromechanical theory of grain-size dependence in metal plasticity[END_REF][START_REF] Berbenni | Impact of the grain size distribution on the yield stress of heterogeneous materials[END_REF]. Contrary to classical visco-plastic hardening models, the physics based models includes constitutive equation with an additional internal state (dislocation density) to account for hardening related to size effect, i.e. at micron scale, the strain gradient induced as a result of size effect can be modeled with GNDs and the interaction of dislocations with SSDs. Over the last decade, several non local formulations that introduce size dependence in backstress have been developed (Tabourot et al. [START_REF] Tabourot | Generalised constitutive laws for fcc single crystals[END_REF], Evers et al. [START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF][START_REF] Evers | Non-local crystal plasticity model with intrinsic ssd and gnd effects[END_REF][START_REF] Evers | Scale dependent crystal plasticity framework with dislocation density and grain boundary effects[END_REF], Schwartz et al. [START_REF] Schwartz | Fatigue crack initiation modeling of 316ln steel based on non local plasticity theory[END_REF][START_REF] Schwartz | Numerical approach of cyclic behaviour of 316ln stainless steel based on a polycrystal modelling including strain gradients[END_REF]).

Polycrystal

The choice of a model for polycrystals is thus motivated in-terms of capturing the anisotropic behavior of the grains as well as the local heterogeneities i.e. intra-and inter-grains response.

It is thus important to establish a relation between the microstructure and its properties for accurate prediction of the mechanical behavior. Two approaches are classically used in literature to establish such relations. They are classified as crystal plasticity mean field (homogenization) and full field (finite element) approach.

Mean field models

The homogenization class of models as initially proposed by Sachs [START_REF] Sachs | Zietschrift verein[END_REF], Cox and Sopwith [START_REF] Cox | The effect of orientation on stresses in single crystals and of random orientation on strength of polycrystalline aggregates[END_REF] and Taylor [START_REF] Taylor | Plastic strain in metals[END_REF] describes the anisotropic behavior of the polycrystal under simplified assumptions. Since then, more sophisticated models have been elaborated by Bishop and Hill [START_REF] Hill | The elastic behaviour of a crystalline aggregate[END_REF][START_REF] Hill | Continuum micro-mechanics of elastoplastic polycrystals[END_REF], Kocks [START_REF] Kocks | Laws for work-hardening and low-temperature creep[END_REF], Asaro & Needleman [START_REF] Lemonds | A numerical study of localized deformation in bi-crystals[END_REF], Kröner [START_REF] Kröner | The statistical basis of polycrystal plasticity[END_REF] and others. In short, this class of models assumes that each grain family behaves within a polycrystal as an inclusion within an homogenized equivalent medium exhibiting the effective behavior of the polycrystal.

In the mean-field approach, only information pertaining to the volume fraction of the phases and its distribution are necessary. Hence they induce very less computational cost, as the mechanical properties are calculated analytically. The two extreme assumptions for stress and strain fields are given by Taylor [START_REF] Taylor | Plastic strain in metals[END_REF] and Sachs [START_REF] Sachs | Zietschrift verein[END_REF] corresponding respectively to iso-strain and iso-stress conditions. Both of these extreme assumptions do not account for the grain morphology and the local neighborhood effect and in general the Taylor model does not satisfy the equilibrium and the Sachs model do not satisfy the compatibility conditions between the grains. The compatibility and the equilibrium conditions are satisfied in the self-consistent scheme introduced by Kröner [START_REF] Kröner | Initial studies of a plasticity theory based upon statistical mechanics[END_REF], where the inclusions are treated as isolated medium within a homogenized matrix having the overall stiffness of the aggregate. However, only the mean stress/strain states per phase, corresponding to a set of grains with some crystallographic orientation, are obtained using such approaches. Thus the local interaction between neighboring grains are not well captured, or only in the average sense. A plastic accommodation factor was introduced by Berveiller and Zaoui (BZ) [START_REF] Berveiller | An extension of the self-consistent scheme to plasticallyflowing polycrystals[END_REF] in the self-consistent scheme. The formulation of BZ model is only valid for proportional loading path and the elastic anisotropy cannot be represented. Some other models have been developed to account for the elastic anisotropy, one can refer to the initial work of Doghri and Delannay [START_REF] Delannay | Prediction of tension-compression cycles in multiphase steel using a modified incremental mean-field model[END_REF][START_REF] Doghri | Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms[END_REF].

Full field models

The second approach of full field finite element considers both long range and short range interactions in grains and the respective mechanical fields are calculated for each element.

The CPFE method has evolved for many applications since the first simulation by Peirce et al. [START_REF] Peirce | An analysis of nonuniform and localized deformation in ductile single crystals[END_REF]. CPFE simulations in literature have been successfully applied for both micro and macro-mechanical problems. With the ability to resolve inter-and intra-grains response, CPFE methods are gaining interest in the field of MEMS. CPFE provides a mean to simulate various boundary conditions, thereby could be used to interpret some of the experimental results at small scales.

In the context of current study, a full field FE model that can explicitly consider the crystallographic orientations and the interaction among grains (inter and intra grain response) is more appropriate. Such full field FE simulations has already been realized to obtain local micro-mechanical behavior at the scale of grains [START_REF] Barbe | Intergranular and intragranular behavior of polycrystalline aggregates. part 2: Results[END_REF]. The major advantage of full field approach is that it takes into account the spatial location of the grain and their interaction with respect to the other grains.

Studies on pure Ni

Very few simulation studies, with mean-field and full-field approaches, have been carried out on pure nickel in literature. A recent study [START_REF] Keller | Kocks-mecking analysis of the size effects on the mechanical behavior of nickel polycrystals[END_REF] on pure nickel with extended two-internal variable Kocks-Mecking (KM) formulation [START_REF] Kubin | Evolution of dislocation densities and the critical conditions for the portevin-le chatelier effect[END_REF] takes into account the size effect and free surface effect. The model has been applied to polycrystalline, multi-crystalline and singlecrystalline nickel samples and was shown to describe very well the grain size effect and the miniaturization effect (reduction of specimen size). The results from KM modeling were comparable to the strain gradient CPFE results. The size effect is included in the two-internal variable KM model by introducing two dislocation densities i.e., the forest dislocation density (statistically stored dislocations) and the mobile dislocation densities. This model was further extended by considering the evolution of dislocation mean free path with strain. Keller et al. [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF] have carried out full field FE simulations using physics based model to study the reduction of size in polycrystalline and single crystalline thin nickel films. Experimentally, in the multi-crystalline regime, a 'smaller is weaker' size effect was seen. A single crystal strain gradient model proposed by Evers et al. [START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF][START_REF] Evers | Non-local crystal plasticity model with intrinsic ssd and gnd effects[END_REF][START_REF] Evers | Scale dependent crystal plasticity framework with dislocation density and grain boundary effects[END_REF] was used to study the extrinsic size effect. The study also discusses the influence of grain size and crystallographic orientation on the observed softening effect. The softening mechanical response upon the reduction of size was attributed to the surface effects, which were seen to affect the strain hardening characteristics. This model was developed in the framework of describing non-linear scale dependent behavior of FCC polycrystals and takes into account the SSD and GND, and their evolution as well. However, the Evers model has been shown only to work well in the case of equiaxed grains. The material parameters required to be identified for this model are not available in literature and hence, Keller et al. [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF] adjusted their material parameters from the material parameters of copper and aluminium. The applicability of the model itself in the case of nickel microwires can be computationally demanding, especially when the grains are elongated.

Renner et al. [START_REF] Renner | Sensitivity of the residual topography to single crystal plasticity parameters in berkovich nanoindentation on fcc nickel[END_REF] have carried out crystal plasticity simulation on pure nickel using the phenomenological model. The anisotropy of polycrystalline nickel at grain scale was carried out using Méric-Cailletaud (MC) single CP model [START_REF] Méric | Single crystal modeling for structural calculations: part 1âmodel presentation[END_REF]. This study highlights a way to identify the interaction matrix coefficients using inverse identification by FE. The material parameters required to be identified in general are the viscosity and hardening parameter. It should be also mentioned that Renner et al. [START_REF] Renner | Sensitivity of the residual topography to single crystal plasticity parameters in berkovich nanoindentation on fcc nickel[END_REF] used the MC model in the large deformation framework.

These studies provide a basis for the choice of model and also the possibility to borrow some material parameters for the current study. In the case of [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF], only few tens of grains were used for simulating the response with a size incorporated model. Adapting a size effect based or physics based model will lead to very high computational cost in the case of microstructure with high number of grains, and moreover the primary objective of current simulation are to study the effect of architecture.

Summary

Microwires produced by severe cold drawing have specific microstructural features (grain size and shape, texture), which play an important role in the observed mechanical behavior. Incorporating these features into model will help understanding and isolating the contribution of each feature on the observed mechanical response, which is difficult to discriminate with experimental techniques. Classical crystal plasticity models have constitutive equation with no length scale coupling and hence does not deal with the effect of specimen or grain size and shape.

In the present study, the considered model should include the specificities of the observed deformation mechanism, i.e. dislocation slip. Hence, a phenomenological constitutive model for its obvious advantages of lower computation run time was chosen.

To model the constitutive behavior of nickel microwires, a classical elasto-viscoplastic constitutive law such as MC single crystal model that takes into account the crystallographic orientation of the grains is chosen (similar formulation to the ones used by [START_REF] Zeghadi | Ensemble averaging stress-strain fields in polycrystalline aggregates with a constrained surface microstructure-part 1: Anisotropic elastic behaviour[END_REF][START_REF] Barbe | Intergranular and intragranular behavior of polycrystalline aggregates. part 2: Results[END_REF][START_REF] Renner | Sensitivity of the residual topography to single crystal plasticity parameters in berkovich nanoindentation on fcc nickel[END_REF][START_REF] Gérard | Mesures de champs et identification de modèles de plasticité cristalline[END_REF]). The constitutive equations of the model along with the identification of material parameters are detailed in section 5.3. Full field CPFE simulations are carried out on the aggregates developed in Chapter 4 under the small strain assumption.

Crystal plasticity finite element strategy

This section describes the different components of CPFE model. We recall here again the strategy employed for the finite element framework as illustrated in parameters identification are detailed. A brief discussion on the effect of mesh density is also provided.

Boundary conditions

The generated polycrystalline aggregates are 'reduced' models of the experimental microwires. Hence, the following boundary conditions (Figure 5.2) are used for the simulation of a tensile test.

• The bottom face of the microstructure (Face 5) is fixed along with the tensile axis i.e.

u z = 0.

• A homogeneous displacement (velocity: 50nm/s) corresponding to a strain rate of ε = 0.0015 s -1 is imposed on the top face (Face 6) of the microstructure i.e. u z = U(t).

• The other lateral faces 1-4 are free surfaces. The above mentioned boundary conditions are used during both the identification of material parameters and the tensile test simulations.

Constitutive model

This section describes the MC elasto-viscoplastic single crystal model. The MC model has been developed as an extension to the classical crystal plasticity theory [START_REF] Hill | Constitutive analysis of elastic-plastic crystals at arbitrary strain[END_REF]. It has been widely used [START_REF] Gérard | Mesures de champs et identification de modèles de plasticité cristalline[END_REF][START_REF] Barbe | Etude numérique de la plasticité d'agrégats polycristallins[END_REF][START_REF] Zeghadi | Effet de la morphologie tri-dimensionnelle et de la taille de grain sur le comportement mécanique d'agrégats polycristallins[END_REF][START_REF] Guilhem | Étude numérique des champs mécaniques locaux dans les agrégats polycristallins d'acier 316L sous chargement de fatigue[END_REF] for modeling the viscoplastic response of a single crystalline and polycrystalline aggregates. The theory and implementation of the model in finite element can be found in [START_REF] Méric | Single crystal modeling for structural calculations: part 1âmodel presentation[END_REF][START_REF] Méric | Single crystal modeling for structural calculations: Part 2âfinite element implementation[END_REF]. The model is presented below under small strain assumptions.

In the MC model, the slip rate γs on a slip system is related to the resolved shear stress by a Norton power law, with Schmid law used as yield criterion:

γs = |τ s -χ s | -r s K n sign(τ s -χ s ), (5.7)
where n and K are related to the viscosity, χ s and r s define the kinematic and isotropic hardening on the slip system. The kinematic and isotropic hardening are non-linear and are defined as follow:

χs = c γs -dx s νs , (5.8)
r s = R 0 + Q ∑ r h rs 1 -e -bν r with νr =| γr |, (5.9)
where R 0 is the initial critical resolved shear stress, ν r is the cumulated plastic strain, h sr is hardening matrix that takes into account interactions between slip systems. Material dependent parameters c, d, b and Q have to be identified. The hardening matrix (h sr ) is a (12 x 12) matrix defined in equation 5.10. Hardening matrix is defined by six independent parameters (h 1 , h 2 , h 3 , h 4 , h 5 , h 6 ) in the case of FCC metals: h 1 defines the self hardening of the slip system, h 2 defines the co-planar interaction between the slip system, h 3 defines the Hirth locks; h 4 defines the collinear interactions, h 5 defines the glissile junctions and h 6 defines the Lomer locks.

[h] =                          h 1 h 2 h 2 h 4 h 5 h 5 h 5 h 6 h 3 h 5 h 3 h 6 h 1 h 2 h 5 h 3 h 6 h 4 h 5 h 5 h 5 h 6 h 3 h 1 h 5 h 6 h 3 h 5 h 3 h 6 h 4 h 5 h 5 h 1 h 2 h 2 h 6 h 5 h 3 h 6 h 3 h 5 h 1 h 2 h 3 h 5 h 6 h 5 h 5 h 4 h 1 h 5 h 4 h 5 h 3 h 6 h 5 h 1 h 2 h 2 h 6 h 5 h 3 h 1 h 2 h 3 h 5 h 6 h 1 h 5 h 4 h 5 Sym h 1 h 2 h 2 h 1 h 2 h 1                          (5.10)
The FE software, Z-set [START_REF] Besson | Object-oriented programming applied to the finite element method part ii. application to material behaviors[END_REF], used in the current work has already the following viscoplastic law implemented.

Parameters identification

This section details the choice of material parameters for the elasto-viscoplastic law described in section 5.3.2. In general, the material coefficients that need to be identified are: elasticity (isotropic or cubic elasticity) parameters, viscosity parameters (K, n), plasticity parameters (R 0 , Q, b, c, d) and the hardening matrix (h sr ).

All the coefficients cannot be identified solely from the tensile experiments conducted in the present study. Moreover, the loading here considered for the simulation is limited to monotonic tensile tests, hence kinematic hardening (χ) is not taken into account. Viscosity and hardening matrix coefficients were taken from Renner et al. [START_REF] Renner | Sensitivity of the residual topography to single crystal plasticity parameters in berkovich nanoindentation on fcc nickel[END_REF] study on nickel that uses the same set of constitutive equations. Regarding the elasticity, the single crystal stiffness matrix (C 11 = 248 GPa, C 12 = 153 Gpa, C 44 = 116 GPa) components was taken from literature [START_REF] Hellwege | Landolt-bornstein tables[END_REF]. The remaining parameters were identified by fitting the monotonous tensile curve using an inverse identification approach. It is mentioned that only AA100 monotonous tensile test result is considered for identification. The Table 5.2 presents the material parameters taken from literature.

Regarding the hardening matrix, the following classification of the components was proposed based on experimental results by Franciosi et al. [START_REF] Franciosi | The concepts of latent hardening and strain hardening in metallic single crystals[END_REF]: (5.11) This has been further evolved based on the dislocation dynamic simulations ( [START_REF] Fivel | Three-dimensional modeling of indent-induced plastic zone at a mesoscale1[END_REF][START_REF] Delaire | Plastic heterogeneities of a copper multicrystal deformed in uniaxial tension: experimental study and finite element simulations[END_REF][START_REF] Devincre | Physical analyses of crystal plasticity by dd simulations[END_REF][START_REF] Madec | Des intersections entre dislocations à la plasticité du monocristal CFC: étude par dynamique des dislocations[END_REF][START_REF] Madec | The role of collinear interaction in dislocation-induced hardening[END_REF]), in the case of physics based models. The identification of interaction matrix by FE simulation [START_REF] Gérard | Mesures de champs et identification de modèles de plasticité cristalline[END_REF][START_REF] Gérard | Hardening description for fcc materials under complex loading paths[END_REF] on the MC law has shown a different order of classification of the hardening matrix components. In the work of Renner et al. [START_REF] Renner | Sensitivity of the residual topography to single crystal plasticity parameters in berkovich nanoindentation on fcc nickel[END_REF], several classification of hardening matrix have been followed to identify the material parameters. In the current work, a hardening matrix coming from Renner et al. [START_REF] Renner | Sensitivity of the residual topography to single crystal plasticity parameters in berkovich nanoindentation on fcc nickel[END_REF] and further supported by the work in [START_REF] Gérard | Modeling of latent hardening produced by complex loading paths in fcc alloys[END_REF] is used. It exhibits high values for collinear interaction and hardening coefficients due to other types of interaction were considered to be unity, as presented in Table 5.2.

h 1 < h 4 = h 3 = h 2 < h 5 < h 6
The identification of remaining material coefficients was carried out with the tensile test results of AA100 wires in three steps.

Pre-identification

Final set (refined with FE (BZ model) model on anisotropic microstructure)

R 0 (MPa) Q (MPa) b R 0 (MPa) Q (MPa) b 290 20 1 300 20 5
Table 5.3: Isotropic hardening parameters identification.

Material parameters related to strain hardening (hardening matrix, K, n) have a major influence on the mechanical properties of nickel [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF]. Identification of the CP parameters is very difficult, especially with limited experimental data, and in the current study the results are not intended to be quantitatively predictive but more to be seen as a parametric study to assess the role to texture and architecture.

Influence of mesh density

This section details the influence of mesh refinement on the mechanical properties. A 177 grain microstructure (detailed in Chapter 4) corresponding in the present study to 7 × 7 × 20µm is used. The microstructure has been meshed with linear tetrahedral elements using Neper [START_REF] Quey | Large-scale 3d random polycrystals for the finite element method: Generation, meshing and remeshing[END_REF]. Three different mesh densities, labeled 'coarse' (∼ 200 average elements per grain), 'intermediate' (∼ 400 average elements per grain) and 'fine' (∼ 3000 average elements per grain), were generated and used for the analysis. The degrees of freedom of the aggregate range from 26928 for the coarse mesh to 306120 for the fine mesh. The characteristics of these meshes are detailed in Table 4.3 (Chapter 4).

The tensile test simulations until an applied strain of 1.1% were carried out with the material properties described in section 5.3.3 and boundary conditions described in section 5.3.1. The macroscopic stress-strain response in the tensile directions is presented in Figure 5.5(a). In the current case, a softer tensile behavior is seen with increasing number of finite elements, see for example the behavior of fine mesh in Figure 5.5(a). This soft tensile behavior can be explained by the behavior of linear elements used, i.e. in general a constant strain or stress is assumed in linear elements. A grain may be subjected to complex multiaxial loading as a result of its neighbor, and the heterogeneous response is not properly resolved in the case where the grains have fewer elements and hence the response of these grains with few elements may appear stiffer, leading to higher stresses.

For each of these simulations, the apparent Young's modulus is calculated from the ratio of macroscopic stress to macroscopic strain in the tensile direction. Figure 5.5(b) shows the Young's modulus as a function of degree of freedom for each mesh refinement. The 'coarse' mesh shows an accuracy of ∼ 1% and the 'intermediate' mesh indicates an accuracy of 0.6%, while the 'fine' mesh indicates an accuracy of ∼ 0.2%.

CPFE results on DMAT

As indicated in Chapter 4, a microstructure has been generated with different assigned experimental textures. A 994 grain microstructure, (with average of 4 grains along the wire axis Z) with experimental AA100, EP40, LD100 and AA40 textures, labeled as AA100-DMAT, EP40-DMAT, AA40-DMAT and LD100-DMAT respectively are used for FE tensile simulations (Figure 5.7). The simulations were performed until a macroscopic strain of ∼1.2%, corresponding to the average strain attained experimentally by the AA100 wires. The results are discussed in-terms of the global response of the FE aggregate. Then a local comparison of the architecture (core-shell) is also presented along with the average response of major grain families. It is also mentioned that the presented average of stress and strain corresponds to the volume average quantities.

Simulations on AA100-DMAT

The results obtained for AA100-DMAT, representing a reduced model of the AA100 wires, are explained in detail in this section. The AA100 wires are the reference wires from which miniaturization by electropolishing and further cold-drawing is carried out experimentally. Thus simulation of the AA100-DMAT is analyzed in detail in comparison to the other architectures. For instance, the role of material elasticity is only carried out and presented for AA100-DMAT aggregates. In the following section the macroscopic behavior and stress-strain heterogeneity are compared with isotropic and cubic elasticity, then the architecture analysis is carried.

Note: Initially, before well defining a texture assignment strategy (as in Chapter 4), a more simple and different texture assignment strategy was used, in particular with less constraints (regarding the misorientation within grain families). The strategy of assignment of texture to the aggregate is similar to the one explained in Chapter 4. The investigation of isotropic and cubic elasticity is carried out with the texture assigned using old method. Later a more refined strategy as proposed in Chapter 4 was used and the subsequent microstructure generated AA100-DMAT is used for the architecture analysis section.

Macroscopic behavior and stress-strain heterogeneity

Figure 5.8(a) shows the cross-section of the AA100-DMAT, with the region corresponding to the 'core', is marked by a black closed boundary. Figure 5.8(b, c) shows the contour of axial stress (σ 33 ), at a macroscopic strain of 0.8%, for the case of isotropic elasticity (Figure 5.8(b)) and cubic elasticity (Figure 5.8(c)) for the respective cross-section in Figure 5.8(a). The axial stress contour in grains indicates intergranular heterogeneity throughout the cross-section, which seems to follow the texture component i.e. grains with orientations closer to the {111} family (blue grains in Figure 5.8(a)) exhibit higher axial stress, whereas grains with orientation closer to {100} family (red grains in Figure 5.8(a)) presents lower axial stresses. Figure 5.8(d) presents the average macroscopic response of aggregate simulated with both isotropic and cubic elasticity.

It can be seen from Figure 5.8(d), that both isotropic and cubic elasticity results are in rather good agreement with the experimental behavior of AA100 wire. The presented experimental AA100 wire curve corresponds to true stress-strain curve calculated with DIC technique during ex-situ tests. Only data until the start of necking is presented for the experimental curve. Macroscopically, similar elastic response is obtained in both cases, whereas at the elasticplastic transition differences can be clearly seen. Aggregate with isotropic elasticity is seen to yield first and this corresponds well with the experimental results. In the case of aggregate with cubic elasticity, a small difference in behavior in comparison to the experimental result can be seen. The elastic slope obtained from the cubic elasticity is in good agreement with the isotropic case and experiments, indicating that the number of grains/orientations considered can represent well the elastic behavior. At first, qualitatively the macroscopic results of the isotropic elasticity is seen to be more representative with the experimental result. However, in the plastic regime (axial strain of > 0.7%), qualitatively the macroscopic response and the trend in heterogeneity in the stress field is not so different for both isotropic and cubic elasticity. In order to understand the differences between the isotropic and cubic elasticity at the macroscale, further post processing is carried out at the grain level. Figure 5.9 shows the average response of all the 994 grains for isotropic and cubic elasticity. In the case of isotropic elasticity, the average stress and strain in all the grains are similar in the elastic regime (< 500MPa) as can be seen from the Figure 5.9(a). While in the case of cubic elasticity ( Figure 5.9(b)), a variation in the stress is seen to follow the Young's modulus i.e. the <111> grains (blue color) present higher Young's modulus and hence more rigidity, while the <100> grains (red color) present a lower Young's modulus and hence less rigidity. For all the other orientations, the Young's modulus lies between these two family of grains. Macroscopically both the isotropic and cubic elasticity present similar average response in the elastic regime, whereas at the scale of grains the heterogeneity in the stress levels due to elasticity are more visible. After the elastic limit, it can be seen that both isotropic and cubic elasticity show a similar scatter in the average stress levels (500-1300MPa). Qualitative analysis on the behavior of grains, from Figure 5.9, reveals that the average behavior of grain families is not the same for isotropic and cubic elasticity, i.e. in the case of isotropic elasticity, most of the <100> grains are seen to plastify first and then the <111> grains. A reverse behavior is seen in the case of cubic elasticity with more of <111> grains plastifying first. Figure 5.10 show the average stress-strain data of all the 994 grains for isotropic and cubic elasticity at four integration times corresponding to the deformation levels of 0.1%, 0.2%, 0.4% and 0.9%. The response of all grains at time step t 1 and t 2 in the case of cubic elasticity indicates a behavior more closely associated to an iso-strain behavior, i.e. all the grains in the aggregate experience same state of deformation. Based on the response of the grains at different deformation level, three regimes are differentiated. The first regime is elastic regime, associated to integration time steps t 1 and t 2 where very little or no scatter in strains is seen. At integration time t 3 , some grains are seen to yield (rounding of the macroscopic curve) and this can be associated to micro-plasticity. The last regime, macro-plasticity can be associated to a time step (t 4 , for instance), where all the grains have attained plasticity. The following observations are made in the three regimes.

1. For isotropic elasticity (Figure 5.10(a)), no change in the average stress and strain of grains is seen in the elastic regime (integration time t 1 and t 2 ). The heterogeneity in stress is visible at t 3 , whereas the strain variation across each grain still appears low at t 3 . In the macro-plastic regime (t 4 ) the distribution of stress and strain is seen to disperse with some grains attaining average axial stress lower than the stress at t 3 .

2. For cubic elasticity (Figure 5.10(b)), the average state of stress and strain of grains in the elastic regime indicates an uniform deformation (iso-strain mode). In the microplastic regime (t 3 ), some grains have attained plasticity but the dispersion in the strain distribution remains rather moderate, thus, close to uniform deformation. In the macroplastic regime, the average axial strain and stress are seen to disperse and are comparable to the isotropic elasticity case.

For the t 4 time step, the stress and the strain dispersion are almost similar with few grains reaching higher values of stress and strains in the case of cubic elasticity. For both the major grain families <100> and <111>, the strain ranges from (0.6% -1.5%), while the stress distribution in <100> grains ranges from (500-900MPa) and (900-1300MPa) in <111> grains.The major differences between the isotropic and cubic elasticity occur at elastic and micro-plastic regimes.

At the elastic-plastic transition t 3 , the macroscopic response of cubic elasticity overshoots the experimental result. This can be attributed to the higher stresses in the <111> family, which occupies a volume fraction of 75%. This indicates that the material parameter identification needs to be improved; in terms of crystallographic orientations this could also mean that the considered 1000 grains/orientations may not be sufficient in representing the elastic-plastic transition of AA100 wires.

Figure 5.10: Volume average of stress-strain for each grain plotted at four integration time (t 1 , t 2 , t 3 and t 4 ) corresponding to the deformation levels of 0.1%, 0.2%, 0.4% and 0.9%, (a) isotropic elasticity, (b) cubic elasticity, the color coding follows IPF relative to the tensile axis.

A comparison of the grain averaged stress and strain distribution at micro-and macroplasticity for isotropic and cubic elasticity case is provided in Figure 5.11. In the micro-plastic regime, at time step t 3 , for isotropic elasticity the average axial stress ranges from (585-870MPa), whereas for cubic elasticity the average axial stress shows a bi-modal distribution centered at 529MPa and 870MPa. In the case of axial strains, the isotropic elasticity indicates a range of (0.34%-0.39%), while the cubic elasticity shows a range of (0.32%-0.42%). In both cases, the stress distribution at t 4 disperses and exceeds the minimum and maximum stresses attained at t 3 . It can be seen from Figure 5. 11(c,d) that in the macro-plastic regime, the stress and strain distributions are more or less similar for both isotropic and cubic elasticity. The average axial strains at t 4 presents a wide scatter (0.56%-1.54%) in comparison to the average axial strains at t 3 .

In this chapter, all the x-axis of the presented histogram plot corresponds to the bin intervals (minimum and maximum) and the bars of the histograms are aligned to the minimum value of the bin class. Whenever a value is mentioned in the text, it corresponds to the minimum values of the bin. Stress-strain curves averaged per orientation families are shown in Figure 5.12 in order to describe more globally the onset of plasticity. The grains are separated based on their misorientation from the ideal <111> and <100> orientations and their volume average behavior is plotted. The solid lines indicate the average response of the grains with less than 10°of misorientation from perfect orientation, and dashed line indicate the average response of the grains with more than 10°of misorientation from perfect orientation. Two behavior can be clearly identified.

1. A difference in average behavior at the mesoscopic scale can be clearly seen. In the case of isotropic elasticity, the average behavior of <100> grains indicate that a majority of the <100> yields first and then plasticity sets in the <111> grains. While, for the cubic elasticity case, an inverse trend is seen with the <111> grains plastifying first, and then the <100> grains. This is related to the iso-strain field in the elastic regime with anisotropic crystal plasticity. The <111> grains experience higher stress due to high stiffness leading to yielding first despite a low Schmid factor.

2. In the plastic regime, the <100> grains have reached a zero hardening plateau, whereas the <111> grains hardening increases.

3. The difference in axial stress between the two sub-class of <111> grains is important i.e. <111> grains with less than 10°misorientation have higher axial stresses than the <111> grains with more than 10°misorientation. Whereas, the same is not true for <100> oriented grains. Moreover, the <100> grains with more than 10°of misorientation yields before the <100> grains with less than 10°of misorientation.

The case of cubic elasticity is consistent with what has been observed experimentally regarding the yielding of grain families. The results highlight the importance of cubic elasticity in representing the elastic and micro-plastic regime. Figure 5.13 presents the axial stress cross-sectional contour maps for the case of isotropic and cubic elasticity. The axial stress contour map presents heterogeneities across the crosssection, and qualitatively, the heterogeneities seem to be larger for the core of the aggregate especially during the micro-plastic regime t 3 . The next section presents a detailed analysis of the architecture and the resulting heterogeneities in stress and strain fields. From this point on, only simulations with cubic elasticity will be discussed.

Architecture analysis

For the architecture analysis, the aggregate AA100-DMAT generated in Chapter 4 is considered. shows the contour of axial stress (σ 33 ), at a macroscopic strain of 0.8%, for the respective section in Figure 5.14(a). From Figure 5.14(b), it can be observed that the axial stress distribution in the 'core' is rather uniform with mostly 'red' color regions corresponding to a stress of ∼1100MPa. Whereas the axial stress contour in the 'shell' region indicates a strong heterogeneity throughout, which seems to follow the texture component i.e. grains with orientations closer to the {111} family exhibit higher axial stress, whereas grains with orientation closer to {100} family show a mix of 'blue' and 'red'.

The clustering of grains with close orientations results in a 'chain' of hotspots (high stress) as can be seen across the cross-section. Regions of low and hotspots can also be identified at specific locations throughout the cross-section.

Figure 5.14(c) presents the average stress-strain curve for 'core' and 'shell' region. From Figure 5.14(c), some observation regarding the architecture can be deduced:

• Both core and shell volume average response indicate fairly simultaneous yielding at ∼0.3% axial strain.

• The average behavior of the core and shell regions of the wire is different. This is attributed to the effect of texture.

• The shell is composed of 812 grains, whereas the core has 182 grains. Hence, the average behavior of the full aggregate follows the behavior of the shell.

Figure 5.15(a) show the average stress-strain data of all the 994 grains at four integration time corresponding to the deformation levels of 0.1%, 0.2%, 0.4% and 0.9%. The distribution of average axial stress and strains at 't 3 ' and 't 4 ', categorized according to the architecture, is presented in Figure 5.15(b-e). For the grains in the shell, a bi-modal distribution of axial stresses can be observed for both 't 3 ' (with centered on 569MPa and 865MPa) and 't 4 ' (with centered on 643MPa 1040MPa). While for the grains in the 'core', only one peak is observed ('t 3 ' 924MPa, 't 4 ' 1040MPa). In the case of average axial strains, the differences are not significant and thus the strain in core ranges from ('t 3 ' 0.33\%-0.38\%, 't 4 ' 0.62\%-1\%) and for shell it ranges from ('t 3 ' 0.3%-0.41%, 't 4 ' 0.52%-1.29%). The heterogeneous axial stress (bi-modal distribution) maps can be related to the presence of hard and soft grains.

Figure 5.15: (a) Volume average of stress-strain for each grain plotted at four integration time (t 1 , t 2 , t 3 , t 4 ) corresponding to the deformation levels of 0.1%, 0.2%, 0.4% and 0.9%, the color coding follows IPF relative to the tensile axis. Histograms of distribution of average axial stresses of all grains, core grains and shell grains at time 't 3 ' (b) and 't 4 ' (d). Histograms of distribution of average axial strains of all grains, core grains and shell grains at time 't 3 ' (c) and 't 4 ' (e).

The Figure 5.16 shows the longitudinal cross-section map used for local heterogeneity analysis. The planes are selected such that in an architecture aggregate, the mid-plane includes both core and shell region, whereas the top-plane only includes the shell region. The heterogeneity in behavior can also be seen locally with the longitudinal cross-sections, presented in Figure 5.17. The Figure 5.17(a) shows the extract of a cross-section parallel to loading axis 'Z', taken at top of the simulation box (top-plane). The cross-section is divided into 20 slabs along the 'X' direction and then the average of the axial stresses are calculated for each slab. The average response of each slab is then represented by scatter points and the cubic spline fitted curve is provided as a guide to eye. This gives the evolution of the mean axial stress profile along X direction for four different level of macroscopic deformation (E 33 = 0.1%, 0.2%, 0.4%, 1.2%). This corresponds to different regimes in the stress-strain curve i.e. elastic regime at E 33 = 0.1% and 0.2% and micro-plastic regime when E 33 = 0.4% and macro-plastic regime when E 33 = 1.2%. Figure 5.17(b) corresponds to the cross-section parallel to the previous section and is taken at the middle of the simulation box (mid-plane), thus including both core and shell regions. The observations are as follows.

1. Elastic regime: At a strain of 0.1% and 0.2%, the evolution of mean axial stress profile along the 'X' axis are heterogeneous. This heterogeneity can be attributed to the crystallographic texture i.e. hard and soft grains.

Figure 5.17: (a) (left) Longitudinal cross-section of AA100-DMAT microstructure at the top of the microstructure (Y= 15µm), with color corresponding to the texture in the wire axis, (right) distribution of average axial stress profile along 'X' axis for the respective cross-section at various macroscopic strains (0.1%, 0.2%, 0.4%, 1.2%). (b) (left) Longitudinal cross-section of AA100-DMAT microstructure at the midsection of the microstructure (Y= 7.5µm), with color corresponding to the texture in the wire axis, (right) distribution of average axial stress profile along 'X' axis for the respective cross-section at various macroscopic strains (0.1%, 0.2%, 0.4%, 1.2%). The solid lines in plot are the result of fit of data with cubic spline interpolation.

2. Micro-and macro-plastic regime: At strains of 0.4% (transition regime) and 1.2% (plastic regime), on the macroscopic stress-strain curve, both core and shell have yielded. The profile of mean axial stress along the X direction is further developed and higher mean axial stresses are observed for the region corresponding to the core (Figure 5.17(b)). In the pure shell region (Figure 5.17(a)), a heterogeneous stress distribution is seen. This heterogeneity can be associated to the dual fiber texture in the shell.

3. The local heterogeneity in the axial stresses for the core and shell corresponds well with the global heterogeneous behavior shown in Figure 5.15(b-e).

Figure 5.18 shows the average response of all the <111> and <100> grains, alongside with the average behavior of the grain families separately in the core and the shell. Most of the <111> grains with less than 10°of misorientation are located in the core (see the SST in Figure 5.18), hence the core exhibits higher axial stresses, whereas the shell has contribution from both <111> and <100> grains. No strong spatial dependence is seen for the behavior of <100> grains. It should also be mentioned that the interpretation of results of the core region may not be representative, owing to its very few number of grains.

Figure 5.18: The response of two major grain families <111> and <100>, along with the mean behavior of these grains when present in core and shell. The grains which are present in the core are marked in black in the SST and the shell grains are marked in magenta. The number in the legend corresponds to the effective number of grains in each grain family.

Summary

The CPFE simulations on AA100-DMAT with isotropic and cubic elasticity indicate that the choice of elasticity model has a strong effect on the behavior of grains and also on the elasticplastic transition. Among the three defined regimes of elasticity, micro-and macro-plasticity, the effect of elasticity was prominently seen in elastic and micro-plastic regimes.

• In elastic regime, the isotropic elasticity indicated constant average stress and strain in the grains, whereas cubic elasticity resulted in a iso-strain like deformation with less/no changes in average strain distribution of grains and a scatter in average stress distribution which seems to depend on the crystallographic orientation relative to the tensile axis.

• In micro-plasticity regime, the average behavior of grain families reveals different trends.

In the isotropic elasticity the <100> grain family is seen to yield first and then the <111> grain family reach plasticity. While, in the cubic elasticity, a quasi iso-strain deformation mode is still seen with <111> grain family yielding first followed by <100> grain family.

• In macro-plastic regime, the stress and strain distribution were comparatively similar for both isotropic and cubic elasticity. In the case of cubic elasticity, few grains were seen to exhibit higher axial strains than the rest of the comparable distribution ('hotspots').

Architecture analysis on AA100-DMAT indicated that the presence of core and shell regions leads to heterogeneity in the stress field. In this case, the core was seen to exhibit high axial tensile stress (∼ 1100MPa) and the shell was seen to exhibit heterogeneous stress distribution with bi-modal distribution (centered at ∼ 650MPa and ∼ 1050MPa).

The AA100-DMAT texture/architectures are generated and assigned using two different approaches, one with least constraints that were used for elasticity calculation (in section 5.4.1.1) and the improved texture assigned aggregate used for architecture analysis (in section 5.4.1.2). Although there are no major differences in behavior as a result of the strategy used, only in the macro-plastic regime the effect can be seen in the extreme values of strain distribution. For instance, at time step t 4 , the texture generated using old strategy results in some extreme strain values that are not reached with the newer texture generation strategy. Effectively, its too early to say that the constraints during generation of texture (old and new strategy) can introduce such effects, more realizations are required to assess the distribution.

Simulations on EP40-DMAT

As a reminder, for the EP40-DMAT, the core texture of AA100 wires has been assigned to the 994 grain microstructure. This model does not exhibit any architecture, as presented in Figure 5. 19(a). The FE simulations on EP40-DMAT were carried out with the same material parameters identified for AA100-DMAT. The reason being that EP40 was produced from AA100 wire by electropolishing. shows the contour of the axial stress (σ 33 ), at a macroscopic strain of 0.5%, for the respective section in Figure 5. 19(a). The axial stress contour indicate that the distribution of stresses is rather homogeneous. This can be attributed to the presence of one major grain family in EP40-DMAT i.e. it has almost 95% of <111> fiber texture and 5% volume fraction of <100> texture. It can be seen from Figure 5.19(c), that the elastic slope attained for the CPFE global average is in good agreement with the EP40 experimental results. The CPFE average shows a softer tensile response. This discrepancy in results and the comparison with other wires are elaborated more in Chapter 6. It should also be mentioned that the EP40 microwires failed at lower strains, whereas the CPFE simulation are carried out until 1.2% strain.

Figure 5.20 shows the average response of all the 994 grains: a similar heterogeneous behavior as that of AA100-DMAT is also observed at the scale of grains. Qualitatively, there is less scatter in the strain distribution in the macro-plastic regime (the extreme values) in comparison to the AA100-DMAT (Figure 5.9(b)). The average axial strain achieved in each grains is smaller in comparison to the AA100-DMAT. In Figure 5.20 no clear trend could be seen regarding the onset of plasticity in regards to the grain orientations probably because of the low representativity of the <100> grains with respect to major <111> family. show the average stress-strain at four integration time corresponding to the deformation levels of 0.1%, 0.2%, 0.35% and 0.55%. The distribution of average axial stress and strains at 't 1 ' and 't 2 ' still follows an iso-strain deformation. The distribution of average axial stress and strains at 't 3 ' and 't 4 ' are presented in Figure 5.21(b-e). A majority of grains exhibits an axial strain close to 900MPa (at t 3 ) and 1000MPa (at t 4 ) but maximum values attained by some grains can be much larger (1006 to 1063MPa at t 3 and 1128 to 1192MPa at t 4 ). The axial stress contribution from the <100> grains is very low in view of their small volume fraction. The grain average axial strains at t 3 and t 4 ranges from ('t 3 ' 0.32%-0.41%, 't 4 ' 0.45%-0.73%). The t 3 state of EP40-DMAT is comparable to the core of the AA100-DMAT (Figure 5.15(b, c)).

Figure 5.21: (a) Volume average of stress-strain for each grain plotted at four integration time (t 1 , t 2 , t 3 , t 4 ) corresponding to the deformation levels of 0.1%, 0.2%, 0.35% and 0.55%, the color coding follows IPF relative to the tensile axis. Histograms of distribution of average axial stresses of all grains, core grains and shell grains at time 't 3 ' (b) and 't 4 ' (d). Histograms of distribution of average axial strains of all grains, core grains and shell grains at time 't 3 ' (c) and 't 4 ' (e). f misorientation with the grain family, and dashed line indicate the average response of the grains with more than 10°of misorientation with the grain family. The average behavior of the <111> grain family is similar to that of AA100-DMAT, while the <100> grain family shows a lower average axial stress in the macro-plastic regime in comparison to the AA100-DMAT. The difference can be attributed to the low volume fraction of <100> grains and also with a sort of 'proximity effect' since the <100> grains are mainly isolated in a <111> grain environment. The longitudinal cross-sectional analysis at different location, similar to the Figure 5.17 is reported here for EP40-DMAT. Though the experimental strain for EP40 wires is limited to 0.5-0.6%, we have carried out deformation up to strains of 1.2% for all the microstructures. The observations are as follows:

1. Elastic regime: At a strain of 0.1% and 0.2% both the top and mid cross-section show a small/no changes in mean axial stress gradient along X. The homogeneity in stress field can be related to the presence of mostly one grain family.

(extended plastic regime), the gradient in the mean axial stress remains same. The small gradient along the profile can be associated to the presence of the few <100> grains. ), with color corresponding to the texture in the wire axis, (right) distribution of axial stresses for the respective cross-section at various macroscopic strains (0.1%, 0.2%, 0.4%, 1.2%).

Summary

The CPFE simulation with cubic elasticity on EP40-DMAT indicates a discrepancy regarding elastic limit value. The heterogeneity in the stress and strain field are comparatively lower for EP40-DMAT with respect to AA100-DMAT. The effect of texture can also be seen, i.e. with reduction of <100> texture, only one peak can be clearly seen in the axial stress distribution corresponding to the <111> texture. Local cross-sectional analysis indicates almost no/less gradient in the axial stress field along the cross-section.

Figure 5.24(a) shows the cross-section of the AA40-DMAT, with region corresponding to the 'core' is marked by a black closed boundary. Figure 5.24(b) shows the axial stress (σ 33 ) contour, at a macroscopic strain of 0.8%, for the respective section in Figure 5.24(a). The axial stress contour indicates higher heterogeneity in the shell region. It can be seen from Figure 5.24(c), that the CPFE response does not corresponds to the macroscopic experimental behavior. However, the elastic slope of the CPFE results are well correlated with the experimental result of AA40 microwire: this suggests that the observed discrepancy in the elastic limit can be related to material parameter being used. The analysis corresponding to the grain family and architecture are similar to that of AA100-DMAT. Hence, they are not presented here. The discrepancies along with the comparison with other wires will be discussed in Chapter 6.

Simulations on LD100-DMAT

The characterization of LD100 wires indicate that the grain size are in the same range as AA100 and the XRD volume fraction of both of these wires are rather similar. The difference for both of these wires majorly lie in the architecture. However, the LD100 microwires present an architecture: we recall that the texture in the core and shell is somewhat inverted compared to the AA100. In view of this the FE simulations on LD100-DMAT were carried out with the same material parameters identified for AA100-DMAT. Hence, only architecture related analysis will be presented for the case of LD100-DMAT.

Figure 5.25(a) shows the cross-section of the LD100-DMAT, where region corresponding to the 'core' has been marked by a black closed boundary. Figure 5. 25(b) shows the axial stress (σ 33 ) contour plot, at a macroscopic strain of 0.8%, for the respective section in Figure 5. 25(a). Similar to AA100-DMAT, a heterogeneous axial stress field is observed in the macroplastic regime. Due to the non-availability of DIC-corrected data for the LD100 wire, the comparison of macroscopic response of the CPFE results are not carried out. The 'core' section of the aggregate presents a softer tensile response (regions colored by blue), contrary to AA100-DMAT where the core exhibited higher axial stresses, as presented in Figure 5.25(c). 5.27(a) shows the average stress-strain data of all 994 grains at four deformation levels (0.1%, 0.2%, 0.4% and 1.2%). The strain range of grains (0.58%-1.2%) at t 4 (1.2% deformation) is comparatively similar to that of AA100-DMAT, except for some grains in AA100-DMAT that present higher values. The distribution of axial stress and strain of the grains categorized based on the architecture (core-shell) is presented in Figure 5.27(b, c) for time t 3 , and for t 4 in Figure 5. 27(d, e). A bi-modal axial stress distribution is seen for both core (centered at (t 3 ) 527MPa and 824MPa; centered at (t 4 ) 587MPa and 994MPa) and shell regions (centered at (t 3 ): 527MPa and 824MPa; centered at (t 4 ): 587MPa and 994MPa). The distribution of axial stresses presents bi-modal distribution for both core and shell, contrary to AA100-DMAT, where the bi-modal stress distribution is only seen for the shell. The distribution of axial strain ranges from: core (t 3 : 0.32%-0.4%; t 4 : 0.73%-1.1%) and shell regions (t 3 : 0.31%-0.41%; t 4 : 0.58%-1.25%).

Figure 5.27: (a) Volume average of stress-strain for each grain plotted at four integration time (t 1 , t 2 , t 3 , t 4 ) corresponding to a deformation level of (0.1%, 0.2%, 0.4%, 0.9%), (b) histograms of distribution of average axial stresses of all grains, core grains and shell grains at time 't 4 ', (c) histograms of distribution of average axial strains of all grains, core grains and shell grains at time 't 4 '. The longitudinal cross-section profiles similar to the ones carried out for AA100-DMAT are presented in Figure 5.29. The observations are as follows:

1. Elastic regime: At a strain of 0.1% both cross-sections show a rather homogeneous stress profile along the 'X' axis, with a smaller gradient between the core and shell for the midsection. At elastic strains of 0.2%, changes along the stress profile in X can be seen, especially for the midsection where the difference between the core and shell becomes obvious.

2. Plastic regime: At strains of 0.4% (micro/macro-plastic transition) and 1.2% (extended plastic regime), an increase in gradient along the stress profile can be seen. As for the top cross-section, the average axial stresses seems to present a heterogeneity of the order of ±100MPa along X. For the mid cross-section, a clear difference between the core and shell region can be observed from the axial stresses. At deformation of 0.4% (corresponding to t 3 ): the average axial stress profile from the cross-section is qualitatively similar to the distribution of axial stress for the whole aggregate.

Summary

The CPFE results on LD100-DMAT firstly indicate heterogeneity in the axial stress contour along the cross-section as a result of the specific architecture. Specifically a softer tensile response, owing to the <100> texture, is seen in the core of the aggregate. Architecture analysis on LD100-DMAT indicates that both core and shell stress distributions exhibit a bi-modal distribution centered on ∼ 587MPa and ∼ 994MPa.

Investigation of influence of architecture

The previous section reported the simulation results on the effect of experimental texture and architecture. With changes in wire microstructure, both the texture and architecture vary, hence separating their individual contribution on the tensile properties has been attempted in the following section. Two approach are presented to address this effect.

1. Experimental texture with conceptual architecture using AA100-DMAT (remark: done using the old texture assignment).

2. Conceptual architecture with ideal fiber texture (as presented at the end of Chapter 4).

CPFE results on influence of AA100 architecture

This section investigates the role of architecture in the case of AA100 wire. To achieve this, one set of orientation was generated using a reduced texture. Two DMAT were generated, labeled as AA100-DMAT and AA100-DMAT-1, such that AA100-DMAT takes into account both the experimental texture and architecture i.e. core and shell, while the other, AA100-DMAT-1, only presents experimental texture and the texture is assigned randomly to the microstructure such that there is no architecture. Figure 5.30(a) shows the cross-section of the AA100-DMAT, with experimental architecture, where the region corresponding to the 'core' is marked by a black closed boundary. Figure 5.30(b) shows the cross-section of the AA100-DMAT-1, with no-architecture and hence the notion of core and shell architecture does not exist in this microstructure. Still, the core region is marked on no-architecture microstructure (AA100-DMAT-1) to have better comparison with architecture microstructure. It is reminded again that both the aggregates have the same set of Euler angles.

Figure 5. 30(c, d) shows the contour of axial stress (σ 33 ), at a macroscopic tensile strain of 0.8%, for the respective cross-section in Figure 5.30(a, b). In the macro-plastic regime, irrespective of the architecture, a global heterogeneity in the axial stress can be clearly seen. This could be a direct result of the volume fraction being used (∼ 75% of <111> and ∼ 25% of <100>), such that any random arrangement of crystallographic orientations in a highly textured material leads to some sort of clustering and thus, the heterogeneity. Despite the heterogeneities in both cases: the shell region in the case of architecture exhibit more heterogeneities (because of the <111> + <100> texture in shell) and in the no-architecture case, these heterogeneities are observed everywhere. It can be clearly seen that the core-shell has an impact on the way heterogeneities are distributed. Figure 5.30(e, f) shows the macroscopic response of the aggregate along with the experimental result of AA100 wires. Macroscopically, both architecture (Figure 5.30(e)) and no-architecture (Figure 5.30(f)) cases have similar response and also has good agreement with experimental results. This suggests that the architecture itself does not have any important effect on the macroscopic yield of the material. However, the local average response of the core and shell of these microstructure do indicate differences. In the case of architecture aggregate, as expected, the average response of the core exhibits higher axial stress, whereas the shell exhibits a softer axial response. In the case of no-architecture aggregate, despite the heterogeneity in the axial stress field, the average response of the core and shell are very similar as expected, since 'core' and 'shell' do not exists in this second case. 5.31(c)) cases, qualitatively the axial strain distributions are considerable different at grain scale in both the cases. Figure 5.31(b, d) shows a classification of <111> and <100> grain families and their average behavior. The solid lines indicate the average response of the grains with less than 10°of misorientation with the grain family, and dashed line indicates the average response of the grains with more than 10°of misorientation with the respective grain family. The average tensile behavior of <100> grains with more than 10°of misorientation is slightly softer in the case of core-shell architecture. No major difference are observed on the onset of plasticity in grain families between architecture and no-architecture case. Figure 5.32: Volume average of stress-strain for each grain plotted at four integration time (t 1 , t 2 , t 3 , t 4 ) corresponding to deformation levels of 0.1%, 0.2%, 0.4% and 0.9% (a) architecture (b) no-architecture; histograms of distribution of average axial strains of all grains, core grains and shell grains at time 't 4 ' (c) architecture (d) no-architecture; histograms of distribution of average axial stresses of all grains, core grains and shell grains at time 't 4 ' (e) architecture (f) no-architecture. Figure 5.32(a,b) shows the average stress-strain data of all the 994 grains at four integration time steps corresponding to deformation levels of 0.1%, 0.2%, 0.4% and 0.9%, for architecture and no-architecture cases. For both cases, the state of stress and strain in the elastic regime indicate an iso-strain like deformation (integration time t 1 and t 2 ). In the micro-and macroplastic regime (t 3 and t 4 ), the average axial stress and strain are seen to disperse. The distribution in the scatter of axial stress and strains at 't 4 ' in the case of architecture is presented in Figure 5.32(c, e). The axial strains are widely distributed from 0.55% to 1.6% and show small difference between the core and shell. On the other hand, the axial stress shows a variation in core and shell, with shell exhibiting a bi-modal stress distribution centered on ∼ 700MPa and ∼ 1050MPa, whereas the core indicate a strong peak at ∼1050 MPa. In the case of no-architecture aggregate (Figure 5. 32(d,f)), the axial strain dispersion is slightly lower (from 0.48% to 1.4%) than what is observed in the architecture case. The axial stress distribution for the no-architecture case indicates no distinguishable difference between core and shell and presents a bi-modal stress distribution centered on ∼ 670MPa and ∼ 1000MPa.

Figure 5.33 shows the average response of the <111> and <100> grain families, alongside with the average behavior of the sub-families according to their position in the core or in the shell. The <111> grains in the core in case of architecture (Figure 5.33(a)) exhibit higher axial stresses, whereas in the no-architecture case, there is no strong difference in the behavior of the <111> grains in the core and in the shell. The higher axial stresses for the <111> grains in the core, in the case of architecture, can be attributed to the clustering of <111> grains.

Figure 5.33: The response of two major grain families <111> and <100>, along with the mean behavior of these grains when present in core and shell (a) architecture (b) no-architecture. The number in the legend corresponds to the effective number of grains in each grain family.

Summary

CPFE analysis on AA100-DMAT (architecture) and AA100-DAMT-1 (no-architecture) highlighted the effect of architecture. Presence or absence of architecture has no effect on the macroscopic response of the aggregate (i.e. macroscopic stress and strain), while it does affect the intergranular stress and strain distributions. In the macro-plastic regime, the presence of architecture influences the strain distribution, particularly the extreme values: for instance at time step t 4 , architecture case show grain average strain reaching up to 2% for some grains, while for the same deformation level, the grain average strain in no-architecture case indicate maximum strains of 1.7% only.

CPFE results on conceptual microstructures

To further aid in the understanding on the influence of architecture on the stress and strain of grain families, CPFE simulation are carried out on few conceptual models with only two set of grain families <111> and <100>. These conceptual architectures were generated with same global volume fraction as AA100-DMAT. The objective is to study the influence of different architectures on the global behavior. Four different architectures (Figure 5.34) with 75% of <111> and 25% of <100> volume fractions are generated with the strategy detailed in section 4.5.3.1 (Chapter 4) with a texture spread of ∼ 10°misorientation from the ideal pole axis.

a. Homogeneous core and homogeneous shell, labeled as case I: Figure 5.34(a) shows a microstructure that has a single fiber texture in the core i.e. all the <100> grains are located in the core and its immediate vicinity. Then all the <111> grains are placed i the shell, globally respecting the '75% <111> + 25% <100>' condition.

b. Homogeneous core and heterogeneous shell, labeled as case II: Figure 5.34(b) shows a microstructure that has a single fiber texture in the core i.e. the core is filled only with <111> grains and the remaining ones are placed randomly in the shell. The other grains in the shell are defined as <100>, again satisfying the global texture distribution (75% -25%).

c. Heterogeneous core and heterogeneous shell, labeled as case III: Figure 5.34(c) shows a microstructure that has a heterogeneous distribution of <100> and <111> texture in both core and shell i.e. no distinct architecture.

d. Heterogeneous core and homogeneous shell, labeled as case IV: Figure 5.34(d) shows a microstructure that has a heterogeneous dual fiber texture in the core and a more homogeneous single fiber texture in the shell (with similar global texture components as other cases). the core exhibits a softer tensile response and the shell exhibits a stronger tensile response. This can be attributed to the presence of a large fraction of <100> grains in the core. For case IV, the core exhibits higher axial tensile stresses in comparison to the core of case I. This is due to the presence of <111> grains in the core.

2. Case II, Figure 5.35(c), exhibits a stronger tensile response for the core and a softer tensile response for the shell. 1% is presented alongside the volume average stress in each grains at four integration times (t 1 , t 2 , t 3 , t 4 ) corresponding to a macroscopic deformation of 0.1%, 0.2%, 0.4% and 1.1%.

Figure 5.36 shows the cross-section of the four conceptual models with their axial stress (σ 33 ) contour plot, at a macroscopic strain of 0.8%, for their respective section. Figure 5.36(right) shows the average stress-strain data of all 994 grains at four time step corresponding to deformation levels (0.1%, 0.2%, 0.4% and 1.1%). It is clear that the stress-strain 'clouds' are larger for case II and case III, suggesting that heterogeneous texture leads to very strong variations in the stress landscape, while the 'clouds' are smaller in case IV and even smaller in case I.

The distribution of grain average axial stress and strain at three time steps (t 2 , t 3 and t 4 ) corresponding to a macroscopic deformation level (0.2%, 0.4% and 1.1%), for the four cases, is provided in Figure 5.37. The comments made regarding the 'clouds' in Figure 5.36, are directly reflected in the axial stress distribution for the four cases in elastic (t 2 ), micro-plastic (t 3 ) and macro-plastic (t 4 ) regimes.

For the <100> grains, the axial stress distribution ranges from 255MPa to 294MPa. For the axial strains, the case I presents a narrow distribution (0.2% to 0.21%) and case IV (0.19% to 0.22%) in comparison to the other cases (0.19% to 0.23%). These differences are seen to evolve in the same manner in micro-and macro-plastic regimes. At macro-plasticity, the axial stress in grain family has almost the same distribution, whereas the difference in axial strain among the cases remains.

In the case where heterogeneous shell is present, i.e. case II, case III and possibly case IV, the average strains among the grains have much wider distribution. This can be reasoned in-terms of number of grains i.e. shell region of the aggregate has more number of grains and a heterogeneity in the shell can lead to a more dispersion of strains. This suggest that the average axial stress of grains are not affected much by their location whereas the same is not true for grain average strains.

Summary

Four conceptual architectures have been investigated with CPFE simulations. They reveal that any presence of heterogeneity (<100> + <111> texture) within the architecture i.e. a heterogeneous core or a heterogeneous shell can result in a heterogeneous strain distribution in the macro-plastic regime. Moreover, any heterogeneity in the shell has an important influence on the whole distribution because of the large fraction. Figure 5.37: Histograms of distribution of average axial stresses of all grains for four cases at macroscopic strain of (a) 0.2%, (b) 0.4%, (c) 1.1%; Histograms of distribution of average axial strains at macroscopic strain of (d) 0.2%, (e) 0.4%, (f) 1.1%.

Conclusion

CPFE simulations were carried out with experimental texture and architecture to investigate their respective influence on the mechanical behavior of nickel microwires. The conclusions for different aggregates are as follows:

AA100-DMAT: The AA100-DMAT exhibits the architecture and texture of commercially procured AA100 microwires (i.e. 25% of <100>, 75% of <111>). The average response of the aggregate matches well with the experimental curves. A local analysis of grains classified by their texture indicates that plasticity first sets in <111> oriented grains, which is in line with the XRD results. The impact of material parameters identification can also been seen via some of the discrepancies in the results. FE results indicate that a distinct core and shell behavior is present in the wire, with core having a more homogeneous state of axial stresses, whereas the shell exhibits a heterogeneous stress distribution. Also the average tensile strains were observed to have a wider strain distribution in the shell compared to the core. These gradient in stresses and strain could be a direct result of the architecture itself.

EP40-DMAT: The EP40-DMAT, which is basically the 'core' of AA100-DMAT exhibits a softer tensile response in comparison to the experimental behavior. This indicates that the electropolished wires are very sensitive to the texture volume fraction and distribution. FE results indicate the absence of pronounced gradient in axial stress and strain field.

AA40-DMAT: The simulation results on AA40-DMAT, with material parameter identified from AA100 wires, was not able to represent the experimental response. Further studies are required to take into account systematically the microstructural features of AA40 wires.

LD100-DMAT: The LD100-DMAT aggregate with core-shell architecture exhibits a gradient in axial stresses and strains. Because of the presence of dual texture in both core and shell (<100> contribution in core is higher and <111> contribution in shell is higher), a heterogeneous stress and strain distribution is seen for both the core and the shell. The average response of <100> grains is softer compared to the same grains in AA100-DMAT aggregate.

CPFE simulation on AA100-DMAT with and without architecture presents a interesting way to decouple the effect of architecture from the effect of texture. Analysis of such cases indicates that architecture hardly has any effect in the elastic and micro-plastic regimes, whereas in the macro-plastic regime the architecture influences the extreme strain distributions. Additional CPFE simulations on conceptual architectures reveal strong heterogeneity at the grain scale as a result of the architecture. These CPFE simulations indicate that the global volume fraction controls the strength of the material while the architecture plays an important role at least in the distribution of average tensile stresses and strains at grain scale. In the absence of architecture the average stress and strain distributions are very narrow. Therefore, the architecture itself has no effect on the macroscopic yield stress of the material but can be expected to have a significant effect on the ductility. This effect of architecture and texture are further commented in Chapter 6 with possible guidelines to optimize the behavior of microwires.

Part C: Comparison and discussion

Chapter 6

Comparison of results and discussion

In this chapter, a general discussion on the behavior of nickel microwires is made based on the comparison of experimental and simulation results. The Figure 6.1 illustrates the synergistic approach followed in the current work with the primary focus being the characterization of texture/architecture and its effect on mechanical behavior. Representative models of the nickel microwires were generated with the information from EBSD and XRD (Chapter 4). Additional information from the mechanical tests and the average behavior of the major grain families along with the grain deformation mechanism (Chapter 3) helped in the choice of constitutive laws for the CPFE simulations (Chapter 5), i.e. so-called 'DMATs'. The simulations were then performed to investigate microwires behavior both at the macro and mesoscale. It is reminded here that the constitutive laws used for the CPFE simulations do not include size effect. The objective of the simulations was to decouple and identify the effect of texture and architecture on the mechanical behavior of DMATs. This has been systematically carried out in Chapter 5. Chapter 6 brings together the important results to provide meaningful discussion towards the goal of proposing guidelines for materials with better properties. The outline of the current chapter is thus as follows.

• In section 6.1, the question of the definition of elastic-plastic transition is addressed. The relevance of simulations regarding the definition of the micro-plastic regime identified experimentally is discussed.

• Section 6.2 discusses the role of texture and architecture on the macro-plasticity regime of the DMATs and provides a comparison with experiments.

• The different trends in size effects observed in nickel microwires over the years are then discussed in view of the possible texture and architecture related effects revealed in the present study. First, the sub-section 6.1.1 highlights the comparison between the simulated and experimental tensile curves in the loading range of interest (typically < 0.2% plastic strain). The possible sources of observed discrepancies are discussed. The definition of micro-plastic regime for simulations is discussed in sub-section 6.1.3. In sub-section 6.1.4, the influence of texture and architecture on the micro-plastic regime is discussed. • The experimental AA100 and simulation results of AA100-DMAT with cubic elasticity show some discrepancy at the elastic-plastic transition. In the case of EP40-DMAT, the macroscopic response of the aggregate is close to the data scatter range (this scatter corresponds to failure stress from 4 tensile tested EP40 wires). However, for the AA40-DMAT, the yield stress and the macroscopic response is visibly different from the experimental one. The Figure 6.4 presents data corresponding to the 0.2% yield criterion from simulated and experimental macroscopic curves and also the yield criterion from FWHM (start of regime III). In the case of AA100 wires, the experimental yield from FWHM predicts a lower yield stress than the 0.2% yield from the simulation. However, the 0.2% yield from simulation shows a good agreement with the 0.2% yield from the experiments. For EP40 wires, the range of yield stress corresponding to the different samples is provided (range marked by an arrow). The 0.2% yield calculated from the simulated macroscopic curve is lower than the experimental scatter of yield calculated from FWHM. We also recall that the 0.2% criterion cannot be applied to EP40 wires, as they fail at lower strains (~0.15% plastic strain), hence the presented value in Figure 6.4 is an extrapolation of stress had the wire not failed. The deliberate choice of including the extrapolated value is made because the 0.2% yield criterion is not very far from the failure plastic strain. It can be seen that for the experiments, the conventional 0.2% yield is at higher stress than the one calculated from the evolution of FWHM. In the case of AA40 wires, the difference between the 0.2% yield from simulation and experimental yield criteria (both 0.2% yield and FWHM) is larger. For the LD100-DMAT, the yield stress by 0.2% strain criterion is seen to correspond well with the yield stress calculated with FWHM. In all the case, the experimental 0.2% yield criterion predicts yield stress higher than the ones calculated with FWHM criterion. This indicates that the 0.2% yield criterion is an upper bound to the actual yield defined by the FWHM evolution. Some of the discrepancies observed between the experimental and simulation results are discussed below.

Comparison of experiments and simulated tensile curve

AA100-DMAT and AA100

The material parameters for the simulation have been identified with the AA100 tensile curves. This led naturally to a relatively good agreement of macroscopic behavior in elastic and plastic regimes for AA100-DMAT and AA100. However, at the elastic-plastic transition, the stresses are higher when cubic elasticity is used. The reason for this overestimation in simulation can be attributed to the material parameters identification, where the influence of all material parameters was not analyzed. For example, the viscosity parameters (K and n) and kinematic hardening contribution were not considered. A more systematic study is required to assess their effect on the elastic-plastic transition.

EP40-DMAT and EP40

The FE simulation on EP40-DMAT, in Figure 6.3(b), indicates a softer tensile response compared to the experimental curve. The discrepancy in the results could be attributed to the use of material parameters identified from AA100 wire. Another way to approach this problem would be to carry out the initial identification process using the experimental results of EP40 wires rather than AA100wires. The difficulty is experimental scatter (shown by the red arrow in Figure 6.3(b)) related to EP40 wires, thus requiring either to average parameters obtained from identification from individual stress-strain curves or identify parameters from the average stress-strain response.

The EP40-DMAT was assigned a volume fraction as calculated from the XRD i.e. 95% <111> and 5% <100> fiber textures. It can be discussed that the experimental scatter in strength for the EP40 wires is a result of variable texture volume fraction along the length of the wire. In order to explore the effect of texture on the mechanical behavior of the EP40 wire, one additional CPFE simulation was carried out on a microstructure assigned with 100% volume fraction of <111> fiber texture, labeled as EP40-DMAT-1. Figure 6.5 shows the macroscopic behavior of AA100-DMAT, EP40-DMAT, and EP40-DMAT-1 superimposed on the experimental AA100 and EP40 tensile stress-strain curves. The effect of texture in the absence of architecture (we recall that EP40 is only made of 'core') induces a noticeable change in the distribution of stress and strain in the EP series. In the absence of <100> grains, the aggregate shows a higher and sharper yielding. The presence/absence of <100> fiber texture (as small as 5% volume fraction) and the sharpness of <111> texture result in a yield stress difference of about 100 MPa.

AA40-DMAT and AA40

AA40-DMAT was simulated with material parameters identified for AA100-DMAT. However, the AA40 wires were produced by further drawing the AA100 wire, i.e. the microstructural state of AA40 wires is modified compared to one of AA100 wires, as was shown with in-situ XRD results. Hence, a re-identification of the material parameters is required to properly account for the modified microstructure. For instance, it is anticipated that the yield values of the grain families are different, as a direct result of the new microstructural state (for example, increased dislocation density). To that end, a re-identification process was carried out using the same procedure described in Chapter 5, and indeed the affected parameters include the plasticity parameters (R 0 and b), as presented in Table 6.1. Further study should now be performed with these new parameters.

Identification on

Identification on AA100-DMAT AA40-DMAT

R 0 (MPa) Q (MPa) b R 0 (MPa) Q (MPa) b 300 20 5 350 20 1
Table 6.1: Material parameters identification for AA40-DMAT.

LD100-DMAT and LD100

In the case of LD100-DMAT, no direct comparison with the experimental macroscopic behavior could be done in the absence of the DIC-corrected curve. Moreover, the LD100 wires are prepared with a different thermomechanical history than the AA100 wires, thus it will be necessary to carry out the identification process on this wire separately. Nevertheless, the AA100 material parameters were used because of the similar global volume fraction of texture components and similar macroscopic stress-strain response, thus giving an opportunity to observe that similar macroscopic properties can be related to different internal mechanisms.

Definition of micro-plastic regime

For a better comparison of data corresponding to the experimental regimes, it is important to define the micro-plasticity regime in simulations. As a first approach, Figure 6.6 shows the definition of regimes in CPFE simulation. The start of micro-plastic regime is defined based on the linear deviation of the macroscopic response of the aggregate and the end of micro-plastic regime is defined as the conventional 0.2% yield criterion. The end of the elastic regime from experiments (transition between regime I and II) and simulations for different wires are provided in Table 6.2. The onset of micro-plastic regime in EP40-DMAT simulation is seen to agree with the case of EP40 wires (mostly single fiber texture). In the case of AA100-DMAT and LD100-DMAT, the value is higher than that of the experimental one. This confirms that the criterion used in simulations to define the onset of micro-plastic regime is an upper bound for the actual micro-plastic regime. In the case of AA40 wires, experimentally the micro-plastic regime is absent, while the AA40-DMAT shows a reduced value of stress that can be attributed to the discrepancies with the material parameters used.

Sample ID Experiments

(MPa) The higher values in simulation for both the onset and end of micro-plastic regime indicates the need for an alternative definition regarding the regimes in the simulation.

Simulation (MPa) AA100 ~450 ~600 EP40 ~700 ~700 AA40 ~1050 ~750 LD100 ~340 ~600

Onset of plasticity in grain families

Experimentally, the average behavior of each grain family can be followed with XRD and the results from Chapter 3 indicate that the two major grain families in the microwire deform in a iso-strain like mode. The analysis of FWHM indicated that the microstructural changes start first in <111> grain family and then following a load transfer, plasticity sets in the <100> grains. CPFE simulations with isotropic elasticity indicated a better description of the macroscopic experimental curve, but more detailed analysis in terms of grain families showed that being macroscopically representative does not necessarily represent the underlying microscale deformation. Indeed, in the case of isotropic elasticity, the <100> grains were seen to attain plasticity first. However, the CPFE simulations with cubic elasticity exhibited iso-strain like mode with the <111> grain family attaining plasticity first and followed by the <100> grains. Figure 6.7(a, c) shows the average behavior of <111> and <100> grain families in AA100-DMAT (Figure 6.7(a)) and EP40-DMAT (Figure 6.7(c)). Figure 6.7(b, d) shows the deviation of linear behavior plotted with respect to average macroscopic stress of the whole aggregate (black curve). It can be seen from Figure 6.7(c) that for AA100-DMAT, the deviation in linearity (micro-plasticity) starts in <111> family of grains and then in the <100> family of grains. The behavior of grain families in the case of AA100-DMAT shows a good agreement with the experimental behavior of AA100 wires. For the EP40 wires, experimentally it was seen that both the grain families attained plasticity at the same time, whereas in simulations (EP40-DMAT) the simultaneous yielding is not clear in the current plot, refer to Figure 6.7(b, d). Difference in the average behavior of <100> grains between the AA100-DMAT and EP40-DMAT are observed and can be attributed to the lower volume fraction of <100> grains in EP40-DMAT. This definition of yield by grain families in simulation could be used as an alternative way to define the onset and end of micro-plastic regime. Further work is required to address questions on what criteria should be used for the definition of micro-plastic regime in simulation.

Discussion on micro-plastic regime

Influence of texture on the micro-plastic regime: experimentally and also in simulation, a change of texture volume fraction results in changes of yield stress. Simulations were performed to asses the role of texture in the case of a non-architectured microstructure. The CPFE simulations on AA100-DMAT, EP40-DMAT, and EP40-DMAT-1 can shed some light onto the influence of texture in micro-plasticity regime. Figure 6.8(a, b, c) shows the average stress-strain data of all the 994 grains at four deformation levels (0.1%, 0.2%, 0.35% and 0.55%) for AA100-DMAT, EP40-DMAT and EP40-DMAT-1. As the global volume fraction of <111> texture changes, differences in axial stress can be clearly seen. Qualitatively, it can be seen that the absence of <100> or intermediate orientations leads to a narrow average tensile strain distribution, for instance at t 3 in the EP40-DMAT-1 (Figure 6.8(c)). c,d) shows the distribution of axial stress and strains at t 3 and t 4 for AA100-DMAT, EP40-DMAT, and EP40-DMAT-1. The axial strains are distributed from 0.4% to 0.7% at t 4 for AA100-DMAT, whereas the distribution is narrower (0.5% to 0.6%) in the case of EP40-DMAT-1. For axial stress, the distribution at the time of yield t 4 is wider (520-1125 MPa) for AA100-DMAT and much narrower and higher (920-1125 MPa) for the EP40-DMAT-1. These differences in stress and strain distribution grow with the decrease of <100> and the intermediate texture components. Influence of architecture on the micro-plastic regime: the case of AA100-DMAT with and without architecture was carried out and presented in Chapter 5. Figure 6.10 presents the stress-strain distribution of all the grains at a macroscopic deformation of 0.4% (corresponds to the time step t 3 in Figure 5.32, chapter 5), which lies in the micro-plastic regime. It is seen that in the micro-plastic regime the axial strains and stress distribution, for the AA100-DMAT with and without architecture, show very small differences in both stress and strains. This suggests that in microstructure with same of set of texture, the presence of architecture does not add any significant heterogeneity in the stress-strain field and has negligible effect on the micro-plasticity. Figure 6.10: Histograms of distribution of average axial strains of all the grains for architecture and no-architecture case at time 't 3 ' (b). Histograms of distribution of average axial stresses of all the grains for architecture and no-architecture case at time 't 3 ' (d).

However, it is reminded that the AA100-DMAT includes an experimental dual texture with majority of grains having <111> and <100> orientation, as well as several intermediate orientations. Simulations on conceptual architectures, with only ideal <111> and <100> fiber texture with less than 10°misorientation among grains in same grain family, indicate that there is a influence of architecture in the micro-plastic regime, refer to Chapter 5 (Figure 5.37-time step t 3 ). This suggests that architecture plays a significant role when there is larger fraction of highly misoriented grains. The sole influence of architecture on the micro-plastic regime in the presence of strong and weak texture requires further investigation.

Macro-plastic regime and failure

The current CPFE simulations cannot predict damage or failure. However, the stress and strain distributions in the macro-plastic regime already give an information on the heterogeneity of the fields. Experimentally, the access to the heterogeneity of intergranular strains requires in-depth XRD profile analysis that was not within the scope of this study. However, this type of information is easily accessible via CPFE, as another added value.

Influence of texture on the macro-plastic regime: experimental results on EP40 wires suggest that the macro-plastic regime is never reached, and the wires fail before entering into a regime of homogeneous deformation. This early onset of strain localization can be attributed to the lack of load-transfer among the grains, that can be seen as a mechanism for release of intergranular stresses. The influence of texture is similar to what was seen in the micro-plastic regime. The Figure 6.11(a, b, c) shows the average stress-strain data for all the 994 grains at 0.1%, 0.2%, 0.35% and 1.2% deformation. Only the behavior at macro-plasticity (i.e. the time step t 5 ) corresponding to a deformation level of 1.2% will be discussed here. It is reminded that the time step t 5 is never reached experimentally for the EP40 wires and is included for comparison. The effect of texture can be seen at time step t 5 : with removal of <100> texture from the global volume fraction, the heterogeneity in the average axial strain decreases. In the case of AA100-DMAT, at t 5 the whole aggregate has an average strain of 1.2%, while internally some grains have strains as low as 0.6% and as high as 1.9%. This dispersion is seen to decrease with reduction of <100> texture component. This suggests that in the absence of dual texture component, all the grains in the aggregate exhibit high and narrow distributed axial strains, whereas in the presence of dual texture component, the grains in the aggregate exhibit a wide distribution of axial strains. It can be reasoned that the local stress gradients achieved in the vicinity of <111>/<100> textured grains occur with higher probability and near surface in the case of EP40 wires, which may play a key role in promoting the early onset of strain localization. These heterogeneities occur in the presence of different grain family and also within a single grain family due to texture spreading. In gradient nano-grains structures, such heterogeneities in the strain field have been shown to be associated with the release of intergranular stresses and the increase of ductility [START_REF] Zeng | Gradient plasticity in gradient nano-grained metals[END_REF]. Influence of architecture on the macro-plastic regime: the case of AA100-DMAT with and without architecture, along with the four conceptual architectures explored the influence of architecture on the macro-plastic regime. In the case of experimental texture, AA100-DMAT, the presence of architecture leads to a wider distribution of strains in comparison to microstructure with no-architecture (refer to time step t 4 in Figure 5.32, Chapter 5). Moreover, the influence of architecture in macro-plasticity can be clearly seen in the case of conceptual architectures, where having an architecture with dual texture component was shown to result in a larger distribution of strains too (refer to time step t 4 in Figure 5.36, Chapter 5).

Discussion on 'size effects' in nickel microwires

The different trends observed upon extrinsic size reduction in the polycrystalline nickel microwires are reported here. It should be noted that only nickel microwires in their cold-drawn polycrystalline state are considered for comparison, other studies on nickel microwires in their annealed state or with less than 20 grains across thickness are not compared here. Figure 6.12(a) presents the plot of normalized tensile strength versus the external wire diameter and Figure 6.12(b) presents the plot of normalized ductility versus external wire diameter. Each study has been normalized with the reference being the average behavior of the starting diameter, respectively. The literature presents two kinds of size reduction processes of polycrystalline nickel microwires: decreasing diameter by electropolishing and decreasing diameter by further cold-drawing.

Two characteristic features are observed in literature during reduction of size of the microwires:

• it leads to an increase in strength and decrease in ductility [2,5].

• it leads to a decrease in both strength and ductility [4,5].

In the current study, reduction in size of the wires by electropolishing leads to an increase in strength and decrease in ductility. Moreover, a reduction in size by cold-drawing led to an increase in strength and ductility. A systematic analysis of these results indicates that they are not due to 'classical' size effects, but rather to superimposition of texture and architecture effects, leading to an apparent size effect. This study thus highlights the crucial importance of good knowledge of the initial microstructure.

Conclusion

The aim of the current research was to understand the 'size effects' in metallic microwires. Pure nickel was chosen as the material of interest due to the previous studies reporting a variable trends in 'size effect' [2,4,5]. Complex in-situ tests (monotonous, cyclic tensile, strain rate jumps and stress drop) were successfully performed at room temperature on these microwires (for the first time) under high-energy X-ray beams to gain insights into deformation mechanisms. In the present study, three batches (EP series, AA series, and LD series) of nickel microwire have been analyzed for the effect of diameter reduction.

The commercially procured microwires, AA100, exhibit duplex fiber texture (25% of <100>, 75% of <111>) with unexpected core-shell architecture: core with <111> oriented grains and shell with <111> and <100> oriented grains. The in-situ strain rate jump and stressdrop tests on AA100 wires indicated that the deformation in nickel microwires proceeds via dislocation-based mechanisms. Stress drop tests showed that grain boundaries play a significant role in the first stages of plastic deformation (dislocations sinks). The in-situ monotonous and cyclic tensile tests on the commercially procured AA100 wire revealed different regimes of deformations: regime I (elastic), regime II (micro-plastic) and regime III (macro-plastic). The micro-plasticity was achieved in <111> grain family first and then in the <100> grain family, with an effective load transfer between the <111> and <100> grain families. While the macro-plasticity was seen to occur simultaneously for both grain families.

The first series of reduced diameter wires were produced by electropolishing (EP series). This resulted in the loss of AA100's initial core-shell architecture, i.e. the shell fraction diminished with reducing diameter (EP40: 5% of <100>, 95% of <111>). An increase in strength with a reduction in ductility was observed upon reduction of wire diameter. In-situ tests indicated that with the reduction in the size of AA100 wire by electropolishing, the regime III (macro-plasticity) was not achieved in the smallest electropolished wire (EP40), as the wire fails before reaching regime III. For the EP40 wire, the micro-plasticity was seen to achieve simultaneously in both the grain families with little or no load transfer.

The second series of reduced diameter wires were produced by further cold-drawing the AA100 wires (AA series). The characterization of reduced wire indicated the retention of the initial core-shell architecture with duplex fiber texture although with changes in global volume fraction (AA40: 14% of <100>, 86% of <111>). An increase in strength and ductility was observed upon reduction of wire diameter. In-situ tests indicated the absence of regime II (micro-plasticity) in smaller diameter wires (AA50 and AA40). The load transfer between the <111> and <100> grain families was seen to occur in regime III (macro-plasticity).

The third series of lab drawn 100µm wires (LD100) was produced by cold drawing an annealed 500µm wire (LD series). The LD100 wires exhibit duplex fiber texture (23% of <100>, 77% of <111>) with core-shell architecture: core with major <100> oriented grains and shell with <111> and <100> oriented grains. The architecture for the LD100 wires is somewhat inverted when compared to AA100 wires. The strength obtained for LD100 wires are comparable to that of the AA100 wire, whereas a ∼ 60% increase in ductility is seen in comparison to the AA100 wires. In-situ tests indicated the presence of all regimes (I, II and III) as was seen in AA100 wires. The micro-plastic regime was seen to be attained simultaneously in both (<111>, <100>) grain families, while the macro-plasticity was seen to occur in <111> grain family first and then in the <100> grain family. The load transfer between the <111> and <100> grain families was seen both in micro-and macro-plastic regimes.

Through the in-situ studies on three series of nickel microwires, it was showed that the microwire's architecture has a direct influence on the observed strength and ductility, which establishes that the effective load transfer within the microwire, as a result of specific microstructure architecture, provides a feasible way to tune the mechanical properties (strength and ductility).

As a first step in understanding such strength-ductility variations, CPFE simulations were carried out to understand separately the role of texture and architecture. To this goal, 3D reduced but representative microstructures (DMATs) of the AA100, EP40, AA40, and LD100 wires were generated using an in-house code modified during this work to take into account the anisotropic grain shape and experimental fiber texture.

At the macroscopic scale, the simulation results were in good agreement with the experimental ones. The response of grain families was also well captured in simulation, i.e. the initiation of plasticity in <111> grain family first and then in <100> grain family. CPFE simulation revealed heterogeneity in stress and strain field across the cross-section of the microstructure. This heterogeneity was strong in the case of core-shell architecture (AA100-DMAT) and was absent in the case of no-architecture (EP40-DMAT). Finally, we developed a synergistic approach between experiments and simulations to investigate the beneficial effect of texture/architecture. By performing simulations on conceptual architectures, a more general conclusion regarding the role of texture and architecture has been reached.

• Texture affects both micro-and macro-plasticity. A strong dual texture even in a random arrangement, i.e. no-architecture, can lead to wider heterogeneity in the strain field and lead to increased ductility. Moreover, a comparatively weaker texture with intermediate texture component can improve ductility by introducing architecture.

• Architecture has the strongest effect on the intergranular strain distribution when the involved dual texture has sharp distribution.

Finally, in conclusion to the performed work, it can be said that the architecture effect plays an important role in developing microstructures with superior mechanical properties. The insights from the present study may contribute meaningfully to the overall study and understanding of the role of texture and its arrangement, the architecture, with respect to mechanical properties in FCC metals.

Perspectives

In the current work, interesting results have been seen regarding the deformation of nickel microwires in the presence of different/no architecture. CPFE simulations suggested that microstructure with heterogeneous core and heterogeneous shell perform better in terms of ductility. Reverse engineering should allow to find the optimal architecture and realizing it experimentally will provide the additional validation for the CPFE model and will demonstrate its ability to fine-tune existing microwires for higher ductility or strength.

A more refine analysis of the grains and its neighbors from the already available data can provide more information regarding the load transfer aspect in the micro-and macro-plastic regime. To investigate the pure-size related effect in these microwires, it would be interesting to investigate different regimes (single crystalline, multi-crystalline and polycrystalline) within the microwires. This can be done experimentally with several heat treatments. Also, a strain gradient CPFE model with size effect formulations, similar to the one used by Keller et al. [START_REF] Keller | Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals[END_REF] on thin nickel sheets could be interesting in the single and multi-crystalline regime. Some of the questions that require continued research and more investigation into this new kind of strength-ductility synergy are:

• In a fiber textured polycrystalline material, to what degree of scatter in texture (<10°or >10°misorientation) controls the macroscopic strength and the load sharing abilities of the material?

• What definition, among many, of micro-and macro-plasticity regime on the simulated curves agrees well with the experimental ones? For instance, defining a probabilistic yield stress criterion, proposed in [START_REF] Brenner | Elastic anisotropy and yield surface estimates of polycrystals[END_REF], and can be adapted here for the volume fraction of grains achieving a given level of cumulative plastic slip.

• What is the influence of architecture on the micro-and macro-plastic regime in the presence and absence of fiber texture?

• Is there an optimal core to shell ratio for strength-ductility improvement?

• What is the influence and role of residual stresses on mechanical properties?

Apart from texture and architecture, several other parameters such as grain size, shape, and their gradient may also have an important effect on mechanical properties. A simulation study [START_REF] Zeng | Gradient plasticity in gradient nano-grained metals[END_REF] on gradients in nano-grained structures has shown that a gradient in grain size from the surface to the core of the material leads to heterogeneous stress and strain distributions. Investigating the individual and interplay of different parameters contribution on the mechanical properties could be very interesting. In order to facilitate such simulation studies, a representative microstructure is the first step. The cold-drawn polycrystalline microwires have grains in the order of tens of thousands and are highly textured and elongated in the wire axis. This makes it difficult to generate an experimental microstructure with the existing 3D characterization techniques. Semi-synthetic microstructures with bi-or multi-modal grain size distribution, bamboo microstructures and grains having different elongation based on their spatial location can be generated with the current version of S2M, refer to Figure 7.1. New advances in S2M are under progress, including the addition of a faster library to mesh a voxelated microstructure by multi-material marching cube without any significant modification of grain boundaries. The sub-box based packing of ellipsoid developed during this thesis allows for complex microstructure generation taking into account their local neighborhood. The ellipsoid packing and texture assignment still needs optimization and there is a scope for greater development of the tool in general in view of the material science application.

A.2 In-situ DIC measurements

Digital image correlation (DIC) was also carried out at DiffAbs beamline, SOLEIL using a CCD camera (Bassler dart series). The same DIC strategy, as in ex-situ tests, was attempted during in-situ deformation. As can be seen from

A.3 Procedure for calibration and analysis

The calibration of XRD synchrotron data has been carried out to be consistent in the interpretation and analysis of 2D XRD data. The parameters requiring calibration include wavelength of the X-rays, distance between the sample and detector and the detector plane tilt with respect to direct beam. The following procedure was used to calibrate the detector before analysis of XRD data.

• Wavelength: A fixed monochromatic wavelength was used for the experiments at both beamlines.

• Sample to detector distance and detector tilt: The pattern for standard material (Lanthanum Hexaboride LaB 6 ) was collected at the beamline. The collected patterns were loaded in PyFAI software to determine the beam center using circle coordinate, refer to In this thesis, single peak analysis method is used for analysis of diffraction data. As the name suggests, here only one peak is considered at a time. In single peak analysis, basically a function is used to fit a reflection (XRD pattern). The interplanar spacing can be calculated by Bragg's law using the diffracted peak positions and wavelength of the X-Rays used. Decomposing a powder diffraction pattern by single peak analysis yields components of specific reflection i.e, Peak height, peak widths (FWHM), integrated intensity, shape factors of line fitting functions. A Pearson VII split fitting functions is employed in this work to carry out line profile analysis.

A.3.1 XRD error source

The error sources in X-Ray diffraction can lead to non-negligible peak shape or broadening changes. One non negligible sources is the sample displacement in the beam. The diffractometer might not be able to detect the diffracted X-Rays if the sample is not aligned properly or if the volume being probed is not constant. The vertical sample displacement in the beam during mechanical loading can cause non physical peak broadening and peak position changes. The errors introduced in the peak position due to a sample displacement of 50µm at SLS has been calculated and is shown in

B.1.2 Local EBSD maps of AA500 and LD100 wires

The several cropped cross-sectional analysis of AA500 wire using EBSD shows a more homogeneously grained microstructure across the diameter of the wire with an average grain size of about 9.5µm, as can be seen from Figure B.3. The texture analysis along the crosssectional EBSD map also shows a preferred texture, markedly the <111> and <100> oriented grains, being present in these annealed wires. In literature, annealing of ED NC nickel with columnar grains was shown to have a more stable <110> texture in the growth direction, contrary to the <111> texture which is usually observed in NC nickel upon annealing [START_REF] Klement | Effect of annealing on microstructural development and grain orientation in electrodeposited ni[END_REF]. The initial <100> and <111> texture in the annealed AA500 wire could be a result of the drawing strains that was previously applied. The texture components in LD100 wire exhibits a dual fiber texture (<111> and <100>) in the center of wire with major <100> grains. The outer radius of the wire exhibits a dual texture with majority of grains having <111> and <100> orientations, as well as several intermediate orientations. The differences in grain size for the AA500 and LD100 wire are in the order of 10.

B.3 SLS results:

A summary of mechanical properties of the EP series of wires (AA100, EP70 and EP50) tested at SLS are presented in Figure B.10. The proportional limit corresponds to the stress where a deviation from linearity of the macroscopic stress-strain curve is observed. The presented yield stress corresponds to the value of stress at the classical 0.2% strain. For EP50 wires this criterion is not applicable as the wire breaks at lower strains. Hence, a different yield criteria was suggested based on the macro plasticity of major grain families in the microwire (presented in detail in Chapter 3). The first XRD tests were carried out first in 2015 (Soham Mukherjee is acknowledged for his participation) and at SLS in 2016 (Steven Van Petegem and Nicola Casati are acknowledged for their participation). The obtained results from SLS do not have a clear trend regarding the effect of specimen size/architecture on the mechanical properties. The scatter in the results could be attributed to the surfaces generated by the electropolishing technique. These initial tests and their analysis have led to improvements in sample preparation and handling. More number of tests were carried out at SOLEIL synchrotron with improved processing and handling of microwires and their results are discussed in Chapter 3. [START_REF] Schmid | Kristallplastizit˜it[END_REF] reflections followed with a negative slope change for [START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] reflection indicating a load transfer, this is also evident in the EP50 wires. The FWHM behavior seen for the axial reflection follows the same evolution as that of the SOLEIL results for AA100 wire. A recovery followed by an increase in FWHM is seen in the case of AA100 wires, whereas a reduction in FWHM is seen in the case of EP50 wires. A direct comparison of SLS and SOLEIL data can only be made qualitatively as the beam characteristics and the sample preparation techniques were quiet different. The fracture mode and surface of these wires are rather similar. Previous studies on these nickel microwires reported a different fracture behavior for smaller wires of 30µm or below. In this study no such difference can be observed in the case of 40µm wires. Fracture surface dimensions characterization has been carried out with ImageJ software. A simple edge filter followed by profile distance analysis is used to calculate the thickness of the fractured region.

C.1 Aggregate with representative texture

This section shows the corresponding pole figures of the assigned texture for AA100-DMAT, EP40-DMAT, AA40-DMAT and LD100-DMAT aggregates sampled from experimental EBSD texture as described in section 4.5.2. Top plots correspond to monotonous tensile strain-stress data, middle plots corresponds to the evolution of axial ( 111) and ( 200) elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots corresponds to the evolution of the ( 111) and ( 200 For SET, the volume fraction data comes from XRD texture analysis and the area fraction data is from EBSD map. Alongside, the texture volume fraction of the 'assigned experimental texture' (AET) on the 994 grain aggregate is also presented. The subsequent area fraction of AET is the average over several cross-sections in the digital microstructure. △g refers to misorientation angle. 166

Figure 1 . 3 :

 13 Figure 1.3: Size effect definition in the framework of this thesis.

Figure 1 . 4 :

 14 Figure 1.4: Different regimes of behavior commonly observed in thin films as a function of different t/d ratios. Here, 'd' is the grain size and 't' is the specimen thickness/diameter. Figure redrawn from [67].

Figure 1 . 7 :

 17 Figure 1.7: Schematic of a) uniform deformation, b) deformation causing voids and overlaps, c) and d) voids and overlaps corrected by GND's [79].

Figure 1 . 8 :

 18 Figure 1.8: Yield strength-ductility synergy for metals. The shaded region in the figures corresponds to the ductility-strength trade-off of conventional metals with homogeneous nanostructures. The values are normalized with their respective coarse-grain counterpart.The plotted architecture response of the material corresponds to the single phase metals. For the different materials appearing in the plot the reader is referred to the review article[START_REF] Ma | Towards strength-ductility synergy through the design of heterogeneous nanostructures in metals[END_REF]. Figure taken from[START_REF] Ma | Towards strength-ductility synergy through the design of heterogeneous nanostructures in metals[END_REF].

Figure 1 . 10 :

 110 Figure 1.10: True stress-strain curve of nickel crystal. The different curves are plotted for different grain sizes with A) 27µm, B) 1µm, C), D) 200nm, E) 18nm, and F) nanodomain nickel [106].

Figure 1 . 11 :

 111 Figure 1.11: Extrinsic and intrinsic size effect related studies on nickel crystal in the micron and sub-micron regime (nc: nanocrystalline, sc: single-crystalline, mc: multi-crystalline, pc: poly-crystalline).

Figure 1 . 12 :

 112 Figure 1.12: Orientation deviation map for <111> grains from the tensile/wire axis. The sections represent the FIB-EBSD of the fracture surface of the 96µm wire. Figure take from [4].

Figure 2 . 1 :

 21 Figure 2.1: Schematics of SEM electron column (1) electron gun, (2) electron beam, (3) anode, (4) magnetic lens, (5) scanning coil, (6) sample. Inset shows the primary excitation volume and the different signals emitted upon interaction of primary beam with sample surface.

Figure 2 . 2 :

 22 Figure 2.2: JEOL SEM JSM-7001F setup at Institut Pprime.

Figure 2 . 3 :

 23 Figure 2.3: Illustration of different component required for EBSD pattern collection: (1) SEM column (electron gun), (2) electron beam, (3) sample at 70°tilt, (4) diffraction cones, (5) phosphor screen (with superimposed Kikuchi band), (6) CCD camera.

Figure 2 . 4 :

 24 Figure 2.4: FEI Nanolab Helios G3 CX workstation at Institut Pprime.

Figure 2 . 5 :

 25 Figure 2.5: Illustration of EBSD 3D sample holder: Finger geometry during (a) loading, (b) 16°tilt for FIB milling, (c) 180°rotation for EBSD pattern collection.

Figure 2 . 6 :

 26 Figure 2.6: Processing and characterization of nickel microwires for in-situ testing.

  .7.

Figure 2 . 7 :

 27 Figure 2.7: Schematic presentation of EP setup: 1. Methanol at -24 • C (cooled with liquid nitrogen), 2. Electrolyte (concentrated perchloric acid 10% to ethanol 90%), 3. Aluminium plates used as cathode, 4. Nickel microwires to be polished are used as anode.

  Figure 2.8(a)) and the electropolished wires are shown in Figure 2.8(b-d).

Figure 2 . 8 :

 28 Figure 2.8: SEM micrographs: (a) AA100, (b) EP70, (c) EP50, (d) EP40.

Figure 2 . 9 :

 29 Figure 2.9: (a) Wire drawing setup at material science laboratory (IISc), (b) illustration of drawing process: 1. Die resting block (moving end), 2. Die with a fixed die angle, 3. Stationary grip to hold the wire, 4. Initial wire, 5. reduced diameter wire

Figure 2 . 10 :

 210 Figure 2.10: SEM micrographs: (a) AA100, (b) AA70, (c) AA50, (d) AA40.

  Figure 2.11.

Figure 2 .

 2 Figure 2.11: SEM micrograph of laboratory cold-drawn 100µm wire.

Figure 2 .

 2 13(b) shows one such assembly with 10 microwire holders.

Figure 2 .

 2 Figure 2.13: (a) Microwire holder ('v': V-shape groove with 300µm width and 1.5mm length). Two lateral bars are in place to keep the sample from moving during handling. The inset shows the stitched SEM images of the wire. (b) Assembly of microwire holders

Figure 2 . 14 :

 214 Figure 2.14: Electropolished 70µm wire in sample holder (a) DinoCam live feed, (b) stitched SEM image, (c) a high magnification SEM image. Red lines plotted on the live image feed provides horizontal and vertical references for alignment of microwires in grip before gluing.

Figure 2 . 15 :

 215 Figure 2.15: Technical drawing of micro tensile machine at (a) MS beamline [6, 128], (b) DiffAbs beamline [129]

Figure 2 . 16 :

 216 Figure 2.16: Monotonous and cyclic load-unload tensile curves for AA100 microwires. The inset shows the stress-controlled load-unload test. A cycle here refers to one load (green) and one unload (red) segments, each cycle ending with tensile stress of 100MPa to avoid bending and movement of wire in the beam.

Figure 2 . 19 :

 219 Figure 2.19: High energy (26 keV) in-situ XRD setup at MS beamline. The setup includes (1) incident X-Ray beam, (2) diffracted X-Ray beam, (3) 1D XRD detector, (4) 2D XRD detector, (5) MTM, (6) fixed grip of MTM, (7) moving grip of MTM, (8) Ni microwire mounted on specific holder.

Figure 2 . 20 :

 220 Figure 2.20: High energy (19 keV) in-situ XRD setup at DiffAbs beamline (a: sample holder at δ = 90°for recording axial reflection, b: sample holder at δ = 0°for recording transverse reflections). The setup includes (1) incident X-Ray beam, (2) diffracted X-Ray beam, (3) 1D XRD detector, (4) 2D XRD detector, (5) MTM, (6) fixed grip of MTM, (7) moving grip of MTM, (8) Ni microwire mounted on specific holder.

Figure 2 .

 2 Figure 2.21: X-Ray diffraction of nickel microwire with major texture components. Both axial and transverse (hkl) reflections were recorded at MS beamline. At the DiffAbs beamline, only the axial (hkl) reflections were recorded (axial reflections are depicted in blue while transverse one are in red).

Figure 2 . 22 :

 222 Figure 2.22: Recorded diffraction pattern: (a) 2D XRD pattern of axial reflection recorded by PILATUS 6M at MS beamline and its corresponding integrated 1D pattern for the defined caking angle(ψ), (b) 2D XRD pattern of axial reflection recorded by XPAD-S140 at DiffAbs beamline and its corresponding integrated 1D pattern for the defined caking angle(ψ), (c) 1D XRD pattern of transverse reflection recorded by MYTHEN at MS beamline and its corresponding intensity vs 2θ plot.

Figure 2 . 23 :

 223 Figure 2.23: Treatment of 2D XRD data using PyFAI.

Figure 2

 2

Figure 2 . 25 :

 225 Figure 2.25: Diffraction geometry for texture analysis and with tilt angles. Configuration at DiffAbs beamline for texture measurement (tilt angle δ ranges from 0 • to 90 • with step a of 1 • and φ ranges from -190 • to -90 • with step a of 0.5 • ).

Figure 2 . 26 :

 226 Figure 2.26: Pole density intensity (a. (111), b. (200), c. (220)) as a function of δ angle for various φ angle (-180°, -135°, -90°) for AA100 wire.

3. 1 . 1

 11 Starting from commercial 100µm wire AA100 wires: An example of cross-sectional EBSD map as well as pole figures obtained using both EBSD and high energy X-Ray diffraction are shown in Figure3.1. As can be seen from the inverse pole figure (IPF) map shown in Figure3.1(a), the micro-texture of AA100 wire exhibits a 'core-shell' microstructure, hereafter referred to as 'core-shell' architecture, with the 'core' having a strong <111> fiber texture (marked by the innermost circle of 20µm radius). The 'shell' exhibits a dual texture with majority of grains having <111> and <100> orientation, as well as several intermediate orientations. The EBSD pole figures from Figure3.1(b) and XRD pole figures from Figure3.1(c) indicate dual fiber textures in the microwire with grain fiber axis being <111> and <100>. The angular width of these texture components represents the degree of scatter in the texture. The volume fractions of <111> and <100> texture components have been calculated from the XRD pole figures with 10°angular width. The analysis of the XRD pole figures indicates 75% vol. of <111> and 25% vol. of <100> oriented grains. The analysis of longitudinal EBSD map confirms that the wire has elongated grains/fibers with major <111> and minor <100> texture components along the wire axis, as shown in Figure3.2.

Figure 3 . 1 :

 31 Figure 3.1: Texture analysis of 100µm Ni microwire (AA100). (a): Cross-sectional EBSD map (IPF relative to the wire axis); the black dashed circles correspond to the different diameters obtained by EP (indicated values are the corresponding radii). (b): (111), (200), (220) pole figures from EBSD. (c): (111), (200), (220) pole figures from high-energy X-Ray diffraction.

Figure 3 . 2 :

 32 Figure 3.2: Texture analysis of 100µm Ni microwire (AA100). (a): Longitudinal EBSD map (IPF relative to the wire axis); the black dashed lines correspond to the core and shell defined previously based on cross-sectional EBSD map. (b): (111), (200), (220) pole figures from EBSD (pole intensity relative to normal of wire axis).

Figure 3 . 3 :

 33 Figure 3.3: (111), (200), (220) pole figures of 40µm microwire (EP40) from high-energy X-Ray diffraction.

  Figure 3.4(b) and XRD pole figures from Figure 3.4(c) indicate the major fiber texture component being <111> and a minor <100> texture along with a fewer intermediate orientations. The analysis of the XRD pole figures of the AA40 wire indicates a 86% volume fraction of <111> and 14% volume fraction of <100> oriented grains. For the intermediate diameters AA70 and AA50, XRD radial texture analysis was carried out for calculation of volume fraction of <111> and <100> texture components and can be found in Table 3.1.

Figure 3 . 4 :

 34 Figure 3.4: Texture analysis of cold-drawn 40µm Ni microwire (AA40). (a): Cross-sectional EBSD map (IPF relative to the wire axis) (b): (111), (200), (220) pole figures from EBSD. (c): (111), (200), (220) pole figures from high-energy X-Ray diffraction.

Figure 3 . 5 :

 35 Figure 3.5: Texture analysis of 40µm Ni microwire. (a): Longitudinal EBSD map (IPF relative to the wire axis); the black dashed lines correspond to the core and shell defined previously based on cross-sectional EBSD map. (b): (111), (200), (220) pole figures from EBSD (pole intensity relative to normal of wire axis).

3. 1 . 2

 12 Starting from commercial 500µm wire AA500 wire: The microstructure analysis of the AA500 wire by longitudinal and crosssectional EBSD map shows that the wire comprises of equiaxed grains (Size: 9.3 ± 0.5µm) in both directions with a strong <100> texture and a weak <111> texture along the wire axis, refer to Figure3.6. A more local analysis of the inner and outer region of the wire indicates a homogeneous microstructure i.e. no architecture (for more details refer to Appendix B section B.1.2). The effect of drawing strain on the ultimate tensile strength of these microwires have been characterized by Abhinav Arya from Atul Chokshi's group at IISc and is reported in Appendix B.

Figure 3 . 6 :

 36 Figure 3.6: EBSD map of commercial 500µm annealed nickel microwire (a): Cross-sectional EBSD map (IPF relative to the wire axis) (b): Longitudinal sectional EBSD map (IPF relative to the wire axis). The following EBSD map of AA500 wire is provided by Abhinav Arya from Atul Chokshi's group at IISc.

Figure 3 . 7 :

 37 Figure 3.7: Texture analysis of lab drawn 100µm Ni microwire (LD100). (a): Cross-sectional EBSD map (IPF relative to the wire axis); the black dashed circles here are only plotted for comparison with AA100 wire (b): (111), (200), (220) pole figures from EBSD. (c): (111),[START_REF] Schmid | Kristallplastizit˜it[END_REF],[START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF] pole figures from high-energy X-Ray diffraction.

Figure 3 . 8 :

 38 Figure 3.8: Pole density intensities as a function of 90°-δ angle. a, d: (111) and (200) pole density for EP series of wires. b, e: (111) and (200) for AA series of wires. c, f: (111) and (200) for LD100. The (111),[START_REF] Schmid | Kristallplastizit˜it[END_REF] pole intensity of AA100 wire is plotted in all the subplots for reference. The intensity counts are normalized with the maximum intensity.

Figure 3 . 9 :

 39 Figure 3.9: Effect of diameter on yield stress and tensile strength of EP series wires. Inset corresponds to typical tensile stress-strain curves of AA100, EP70, EP50 and EP40 microwires. The black dashed line serves as a guide to the eye (tensile strength data).

Figure 3 . 10 :

 310 Figure 3.10: Effect of diameter on yield stress and tensile strength of AA series wires. Inset corresponds to typical tensile stress-strain curves of AA100, AA70, AA50 and AA40 microwires. The black dashed line serves as a guide to the eye (tensile strength data).

Figure 3 .

 3 Figure 3.11: A typical tensile stress-strain curves of extreme diameter wires AA100, EP40, AA40 and LD100 microwires.

Figure 3 . 13 :

 313 Figure 3.13: XRD peak analysis of Ni microwires, a: AA100, b: EP70, c: EP50, d: EP40. Top plots correspond to monotonous tensile strain-stress data, middle plots corresponds to the evolution of axial (111) and[START_REF] Schmid | Kristallplastizit˜it[END_REF] elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots corresponds to the evolution of the (111) and (200) Full Width Half Maximum (FWHM) versus applied stress, the shaded zones represent the error bar. The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text).

Figure 3 . 14 :

 314 Figure 3.14: XRD peak analysis of Ni microwires, a: AA100, b: AA70, c: AA50, d: AA40. Top plots correspond to monotonoustensile strain-stress data, middle plots corresponds to the evolution of axial (111) and (200) elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots corresponds to the evolution of the (111) and (200) Full Width Half Maximum (FWHM) versus applied stress, the shaded zones represent the error bar. The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text).

Figure 3 . 15 :

 315 Figure 3.15: XRD peak analysis of Ni microwires, a: AA100, b: LD100. Top plots correspond to monotonous tensile strain-stress data, middle plots corresponds to the evolution of axial (111) and (200) elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots correspond to the evolution of the (111) and (200) Full Width Half Maximum (FWHM) versus applied stress (the shaded zones represent the error bar). The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text).

Figure 3 . 16 :

 316 Figure 3.16: Schematics of evolution of ∆FW HM with time in (b) regime α, (c) regime α ′ , (d) regime β , (e) regime γ. Green color marks the loading segment and red color marks the unloading segment.

Figure 3 .

 3 Figure 3.17: Load-unload test on AA100 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 .

 3 Figure 3.18: Load-unload test on AA100 microwire. (a) Applied stress with respect to time, (b) Evolution of FWHM of (111) reflection with time. (c) Evolution of FWHM of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 .

 3 Figure 3.19: Load-unload test on EP40 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 .

 3 Figure 3.20: Load-unload test on EP40 wire. (a) Applied stress with respect to time. (b) Evolution of FWHM of (111) reflection with time. (c) Evolution of FWHM of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 .

 3 Figure 3.21: Load-unload test on AA40 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. A discontinuity between cycle 6 and cycle 7 is due to the technical problem with the machine resting block and the corresponding changes reflected in lattice strains are due to relaxation of the sample for ~20 minutes. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 .Figure 3 .

 33 Figure 3.22: Load-unload test on AA40 microwire. (a) Applied stress with respect to time, (b) Evolution of FWHM of (111) reflection with time. (c) Evolution of FWHM of (200) reflection with time. A discontinuity between cycle 6 and cycle 7 is due to the technical problem with the machine resting block and the corresponding changes reflected in FWHM are due to relaxation of the sample for ~20 minutes. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 .

 3 Figure 3.23: Load-unload test on LD100 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 .

 3 Figure 3.24: Load-unload test on LD100 microwire. (a) Applied stress with respect to time, (b) Evolution of FWHM of (111) reflection with time. (c) Evolution of FWHM of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle.

Figure 3 . 25 :

 325 Figure 3.25: Stress drop tests for one AA100 microwire. Top inset shows stress drop test for one stress ratio defined by a pre-defined stress σ 0 and the current unloaded stress σ r . Bottom inset shows the evolution of macroscopic applied strain during the creep period.

Figure 3 . 26 :

 326 Figure 3.26: Stress drop tests on AA100 microwires for various stress drop ratios. (a) Inelastic strain versus time. (b) Evolution of FWHM for the creep period of 60 minutes for <111> textured grains. (c) Evolution of FWHM for the creep period of 60 minutes for <100> textured grains.

Figure 3 .

 3 Figure 3.28: SEM micrographs of (top) the initial and (bottom) fracture surface of nickel microwires (a) AA100, (b) EP40, (c) AA40, (d) LD100.

Figure 3 .

 3 Figure 3.29: SEM micrographs of nickel microwires exhibiting typical features (a) AA70 wire monotonously deformed, (c) EP50 wire monotonously deformed, (b, d) EP40 cyclically deformed.

Figure PB. 1 :

 1 Figure PB.1: Strategy employed in the current work for the numerical framework.

Figure 4 . 1 :

 41 Figure 4.1: Image based modeling techniques for characterization of experimental microstructure (a) 3D FIB EBSD by serial sectioning (image from[START_REF] Groeber | 3d reconstruction and characterization of polycrystalline microstructures using a fib-sem system[END_REF]), (b) DCT for reconstruction of grain shape and orientations (from[START_REF] Johnson | X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. ii. the combined case[END_REF]).

Figure 4 . 2 :

 42 Figure 4.2: Various polycrystal morphologies generated by Neper using Voronoi-Laguerre tessellation. (a) Microstructure representing a recrystallized thin sheet. (b) Microstructure representing a polycrystal with different morphological texture. (c) Microstructure with mixed grain shape. (d) Microstructure with a set of truncated octahedras. Figure taken from [176].

Figure 4 . 3 :

 43 Figure 4.3: Orthogonal EBSD observation area for deformed polycrystalline aluminium [159].

Figure 4 . 4 ,

 44 the grain boundaries and grain shapes are not well represented by Voronoi tessellation, whereas the ellipsoids model captures the anisotropic grain morphology quite well. In the present work, a generation technique developed from the model by St. Pierre et al. [178] has been developed. The subsequent steps involved in generation of the microstructures are detailed in the subsection 4.3.2.

Figure 4 . 4 :

 44 Figure 4.4: 153 grain EBSD map for grade 702 Zr (a) experimental EBSD surface, (b)representative microstructure generated using Voronoi-Delaunay tessellation, (c) representative microstructure generated using ellipsoids[START_REF] St-Pierre | 3d simulations of microstructure and comparison with experimental microstructure coming from oim analysis[END_REF]

Figure 4 . 5 :

 45 Figure 4.5: Generation of representative 3D microstructure with experimental surface using S2M (constrained face is highlighted in red).

Figure 4 . 6 :

 46 Figure 4.6: Integration of ellipsoids in S2M: (a) Experimental IPF map of EBSD data, (b, c) placement of ellipsoids at the constrained top surface of the simulation box, (d) filled microstructure with ellipsoids in the simulation box, (e) voxelized top surface after assignment of voxels in non-overlapped volume of ellipsoids (empty and overlap regions are depicted in light green), (f) voxelized top surface after voxel assignment to nearest ellipsoids, (g) imposed surface for the digital microstructure with respective sphere morphology, (h) corresponding voxelized surface.

Figure 4 . 7 )

 47 , which consequently lie in the constrained top surface. Moreover, the third semi-axes 'c' is assumed to be equal to 'b' (spheroid geometry). The corresponding results are shown in Figure4.6(b, c).

Figure 4 . 7 :

 47 Figure 4.7: Geometric definition of an ellipsoid; a, b and c denote the three principal semi-axes, such that a ≥ b ≥ c.

Figure 4 . 8 :

 48 Figure 4.8: Illustration of intersection check for ellipsoid: A cross-section of two ellipsoid are indicated with two configuration, dotted line indicates reduced, or shrinked, ellipsoids. (a) The placement of ellipsoid 2 is accepted since the two reduced ellipsoids do not intersect. (b) In the case of a low reduction factor, the two reduced ellipsoids intersect thus the placement of ellipsoid 2 is rejected.

  Figure 4.10 clearly indicates that the aspect ratio of the grains on surface are well matched by the ellipsoidmodel. In the current chapter, all the x-axis of the presented histogram plot corresponds to the bin intervals (minimum and maximum) and the bars of the histograms are aligned to the minimum value of the bin class.

Figure 4 . 9 :

 49 Figure 4.9: Comparison of sectional area of the experimental surface reconstructed by spheres and ellipsoids.

Figure 4 . 10 :

 410 Figure 4.10: Comparison of aspect ratio (b/a) of the experimental surface reconstructed by spheres and ellipsoids.

Figure 4 .

 4 Figure 4.12: A 174 grain digital microstructure generated with S2M (a) All grains, (b) inner grains for which the shape is not modified by the simulation box boundary. Colors do not represent texture.

Figure 4 . 13 :

 413 Figure 4.13: Distribution of the principal semi-axes (in µm) (a) semi axis 'a', (b) semi axis 'b', (c) semi axis 'c'. Red indicates the input distribution, blue the placed distribution and green the voxel distribution from moment invariant analysis. Statistics on the left are provided for all grains and on the right for the inner grains.

Figure 4 . 14 :

 414 Figure 4.14: Distribution of the aspect ratios of ellipsoids (a) b/a, (b) c/a. Red indicates the input distribution, blue the placed distribution and green the voxel distribution from moment invariant analysis. Statistics on the left are provided for all grains and on the right for the inner grains.

Figure 4 . 15 :

 415 Figure 4.15: Distribution of (a) volume ratio, (b) equivalent size ratio, the values are normalized with the average value of the distribution. Red indicates the input distribution, blue the placed distribution and green the voxel distribution from moment invariant analysis. Statistics on the left are provided for all grains and on the right for the inner grains.

Figure 4 .

 4 [START_REF] Pelleg | Mechanical properties of materials[END_REF]. XRD results indicate the presence of two main fiber components with ∼ 75% of <111> and ∼ 25% of <100>.

Figure 4 . 16 :

 416 Figure 4.16: EBSD analysis of 100µm Ni microwire. (a): cross-sectional EBSD map (IPF relative to the wire axis); the black dashed circles correspond to the different diameters obtained by EP. (b) Longitudinal EBSD map (IPF relative to the wire axis); the black dashed lines correspond to the core and shell defined in (a).

  Figure 4.17 and Table4.2 provides the main statistics obtained, from two cross-sectional and one longitudinal EBSD maps, on AA100 microwire. In the cross-section, the grain size follows a log-normal distribution (Figure4.17(a)) ranging from sub-micrometer size to about 10µm. The arithmetic average of the grain size having an area fraction of 0.05 or higher is about 1.8µm with no significant difference between the core and shell. The average value of the distribution is found to be ∼ 1µm, by fitting a log-normal distribution to the grain size distribution vs area fraction. The grain size in core and shell distributions are very comparable. Grains in the cross-section are rather equiaxed with a mean aspect ratio of ~0.8 (refer to Figure4.17(b)).

Figure 4 .

 4 Figure 4.17: (a) grain size distribution in the core and shell of the AA100 microwire from cross-sectional EBSD map (b) aspect ratio of the grains on the cross-sectional EBSD map (c) grain size distribution in core and shell of the AA100 microwire from longitudinal EBSD map (d) aspect ratio of the grains in the longitudinal section of EBSD map. Red color indicate distribution from core (defined as 40µm diameter from center on the EBSD map), blue represents shell distribution and green represents distribution from core and shell.

Figure 4 .

 4 18(a, b)).

Figure 4 .

 4 Figure 4.18: (111), (200), (220) Pole Figures from (a) experimental data (EBSD), (b) 200 orientation set assigned on a digital microstructure, (c) 1000 orientation set assigned on a digital microstructure, (d) 5000 orientation set assigned on a digital microstructure. Pole Figures were generated with Dream3D software.

Figure 4 . 19 :

 419 Figure 4.19: Integrated pole density with 10°angular width for (111) pole (65°-75°from pole center) along the fiber axis ′ φ ′ . The 1000 and 5000 orientation refers to the sets of orientation assigned for generated microstructure.

Figure 4 . 20 :

 420 Figure 4.20: Integrated pole density with 10°angular width for (200) pole (50°-60°from pole center) along the fiber axis ′ φ ′ . The 1000 and 5000 orientation refers to the sets of orientation assigned for generated microstructure.

Figure 4 .

 4 Figure 4.21, shows the variation of intensity along the (220) pole. The corresponding (111) reflection in Figure 4.21 is well described by both 1000 and 5000 orientation sets.

Figure 4 . 21 :

 421 Figure 4.21: Integrated pole density with 10°angular width for (220) pole (30°-40°from pole center) along the fiber axis ′ φ ′ . The 1000 and 5000 orientation refers to the sets of orientation assigned for generated microstructure.

Figure 4 .

 4 Figure 4.22: A 994 elongated grain microstructure generated with S2M (a, c) cross-sectional and longitudinal cut of ellipsoids placed in the simulation box: filled ellipsoids indicate the geometry of the ellipsoid intersecting the selected plane, dotted and solid line ellipse around the filled ellipse shows the true size of the ellipsoid if it were to be cut at the center, dotted line indicate that the center of the ellipsoid in above the current section and the solid line indicate that the center of the ellipsoid is underneath the current plane, (b, d) corresponding voxelized cross-section of the placed ellipsoids. Colors do not represent texture.

Figure 4 .

 4 Figure 4.23, 4.24 and 4.[START_REF] Hashishin | Morphology and tensile strength of titanium nitride whiskers[END_REF] show the distribution of the semi-axes, aspect ratio, volume and equivalent size in a similar manner as presented in Figure4.13, 4.14 and 4.15. Since a unique ellipsoid morphology is generated, the target distribution (red bars) is defined by a unique class similar to the distribution for placed ellipsoids (blue bars), even if some of the generated ellipsoids were not successfully placed. The voxelized image is then analyzed with moment invariant analysis to compute the properties of equivalent ellipsoids for each voxels of grain. The corresponding distribution are plotted in green.

Figure 4 . 23 :

 423 Figure 4.23: Distribution of the principal semi-axes (in µm) (a) semi axis 'a', (b) semi axis 'b', (c) semi axis 'c'. Red indicates the input distribution, blue the placed distribution and green the voxel distribution from moment invariant analysis. Statistics on the left are provided for all grains and on the right for the inner grains.

Figure 4 .

 4 24). The voxel distribution (green bars) indicate that the voxelization of a constant statistic distribution results in a distribution close to a Gaussian one, evident from the volume of the voxelized grains (Figure 4.25).

Figure 4 . 24 :

 424 Figure 4.24: Distribution of the aspect ratios of ellipsoids (a) b/a, (b) c/a. Red indicates the input distribution, blue the placed distribution and green the voxel distribution from moment invariant analysis. Statistics on the left are provided for all grains and on the right for the inner grains.

Figure 4 . 25 :

 425 Figure 4.25: Distribution of (a) volume ratio, (b) equivalent size ratio, the values are normalized with the average value of the distribution. Red indicates the input distribution, blue the placed distribution and green the voxel distribution from moment invariant analysis. Statistics on the left are provided for all grains and on the right for the inner grains.

Figure 4 .

 4 27.

Figure 4 .

 4 27 (a) shows the pole figure of AA100 microwires 'core' and Figure 4.27 (b) respectively the pole figures of 'shell'.

Figure 4 . 27 :

 427 Figure 4.27: AA100 pole figures of (a) full experimental EBSD 'core' (~4000 grains), (b) full experimental EBSD 'shell', (~20000 grains) (c) simplified experimental EBSD 'core' (~1300 grains), (d) simplified experimental EBSD 'shell' (~10000 grains)

Figure 4 . 28 :

 428 Figure 4.28: AA100 pole figures of (a) simplified experimental EBSD 'core' (~1300 grains), (b) <111> grains from (a) (~975 grains), (c) <100> grains from (a) (~312 grains), (d) <110> grains from (a) (~13 grains)

Figure 4 .

 4 28 (a)) has been split into three sub-classes of orientations based on their minimum misorientation with one among the three (<111>, <100> and <110>) poles.

Figure 4 .

 4 28 (b) shows the pole figure of all the grains in the core, which has minimum misorientation with[START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] pole direction. Similar pole figures are shown for[START_REF] Schmid | Kristallplastizit˜it[END_REF] pole direction in Figure4.28 (c) and for[START_REF] Evers | Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation[END_REF] in Figure4.28 (d). Similar splitting of texture component has been carried out for shell and is not shown here.

Figure 4 .

 4 Figure 4.29: AA100 pole figures of (a) <111> simplified experimental EBSD 'core' (~975 grains), (b) grains from (a) having <10°misorientation with perfect <111> fiber texture (~852 grains), (c) grains from (a) having >10°misorientation with perfect <111> fiber texture (~123 grains).

  .4.

Figure 4 .

 4 Figure 4.30: 994 grains microstructure with assigned texture (a) view of the cross-section with core-shell architecture, (b) IPF map with location of 994 grains, (c) IPF map with location of 182 'core' grains, (d) IPF map with location of 812 'shell' grains. Colors indicate IPF colormap for texture in the wire direction.

Figure 4 .

 4 Figure 4.30 shows a slice of 3D microstructure with assigned texture component in the core and shell regions.Figure 4.30(b, c, d) show respectively the orientations assigned to all the grains, to grains in the core and grains in the shell respectively. Full pole figures are reported in Appendix C.Figure4.31 shows the misorientation distribution of the texture from EBSD and 3D digital microstructure. A reasonably good fit is seen for the case of the whole assigned texture (, i.e. core-shell). However a non-negligible mismatch can be noticed in the core (Figure4.31(c)).

Figure 4 .

 4 Figure 4.30 shows a slice of 3D microstructure with assigned texture component in the core and shell regions.Figure 4.30(b, c, d) show respectively the orientations assigned to all the grains, to grains in the core and grains in the shell respectively. Full pole figures are reported in Appendix C.Figure4.31 shows the misorientation distribution of the texture from EBSD and 3D digital microstructure. A reasonably good fit is seen for the case of the whole assigned texture (, i.e. core-shell). However a non-negligible mismatch can be noticed in the core (Figure4.31(c)).

Figure 4 .

 4 Figure 4.30 shows a slice of 3D microstructure with assigned texture component in the core and shell regions.Figure 4.30(b, c, d) show respectively the orientations assigned to all the grains, to grains in the core and grains in the shell respectively. Full pole figures are reported in Appendix C.Figure4.31 shows the misorientation distribution of the texture from EBSD and 3D digital microstructure. A reasonably good fit is seen for the case of the whole assigned texture (, i.e. core-shell). However a non-negligible mismatch can be noticed in the core (Figure4.31(c)).

Figure 4 . 31 :

 431 Figure 4.31: Distribution of (a) misorientation for grains in 3D generated microstructure and simplified EBSD map, (b) misorientation for grains in the 'shell' of 3D generated microstructure and EBSD map, (c) misorientation for grains in the 'core' of 3D generated microstructure and EBSD map.

4. 5

 5 .2.3 EP40 texture assignment (labeled as EP40-DMAT) EP40 microwires are electropolished 40µm wires produced from AA100 microwires, i.e. the texture of the electropolished EP 40 microwires are similar to the texture of the AA100's core. Assignment of orientation is performed from the simplified EBSD list for AA100 core only (Figure4.27(c)) and is matched with the global volume fraction of EP40 wire analyzed by XRD. The assigned texture and their respective pole figures are provided in Appendix C.

Figure 4 .

 4 Figure 4.32 shows a slice of 3D microstructure with assigned texture component. EP40 microwires have no architecture in terms of texture, with no core/shell distinction.

Figure 4 .

 4 Figure 4.32: 994 grains microstructure with assigned texture (a) 994 grains aggregate with no architecture, (b) IPF map with location of 994 grains. Colors indicate IPF colormap for texture in the wire direction.

Figure 4 .

 4 Figure 4.33 shows the misorientation distribution of the texture from the EBSD map for the core of AA100 and 3D digital microstructure. Considering 994 grains for just the core of the microstructure leads to a higher mismatch between the EBSD and assigned data. This is due to the imposed XRD volume fraction.

Figure 4 . 33 :

 433 Figure 4.33: Distribution of misorientation for grains in 3D generated microstructure and 'core' of simplified EBSD map of AA100 wire

Figure 4 .

 4 34(a) shows the slice of a 3D microstructure with assigned texture component in the core and shell region.

  Figure 4.34(b) shows the shell microstructure and the core marked by the black boundary and their respective texture component.

Figure 4 .

 4 Figure 4.34: 994 grain microstructure with assigned texture (a) 994 grain aggregate with core-shell architecture, (b) IPF map with location of 994 grains, (c) IPF map with location of 182 'core' grains, (d) IPF map with location of 812 'shell' grains. Colors indicate IPF colormap for texture in the wire direction.

Figure 4 .

 4 Figure 4.35 shows the misorientation distribution of the texture from EBSD and 3D digital microstructure. Globally the micro texture of the assigned texture matches well with the experimental EBSD microtexture and also the global volume fraction of the texture as calculated from XRD are also respected.

Figure 4 . 35 :

 435 Figure 4.35: Distribution of (a) misorientation for grains in 3D generated microstructure and simplified EBSD map, (b) misorientation for grains in the 'shell' of 3D generated microstructure and EBSD map, (c) misorientation for grains in the 'core' of 3D generated microstructure and EBSD map.

Figure 4 .

 4 [START_REF] Fleck | A phenomenological theory for strain gradient effects in plasticity[END_REF] shows a slice of 3D microstructure with assigned texture component in the core and shell region.

Figure 4 .

 4 36 (b) shows the shell microstructure and the core marked by the black boundary and their respective texture component.

Figure 4 .

 4 Figure 4.36: 994 grain microstructure with assigned texture (a) 994 grain aggregate with core-shell architecture, (b) IPF map with location of 994 grains, (c) IPF map with location of 182 'core' grains, (d) IPF map with location of 812 'shell' grains. Colors indicate IPF colormap for texture in the wire direction.

Figure

  Figure 4.37 shows the misorientation distribution of the texture from EBSD and 3D digital microstructure. Globally the micro texture of the assigned texture matches well with the experimental EBSD microtexture and also the global volume fraction of the texture as calculated from XRD are also conserved. Table4.5 shows the volume fraction of assigned texture component (AET), the global volume fraction matches well with the global XRD volume fraction. The presented area fraction in Table4.5 is an average of several cross-sections taken from the digital microstructure.

Figure 4 . 37 :

 437 Figure 4.37: Distribution of (a) misorientation for grains in 3D generated microstructure and simplified EBSD map, (b) misorientation for grains in the 'shell' of 3D generated microstructure and EBSD map, (c) misorientation for grains in the 'core' of 3D generated microstructure and EBSD map

Figure 4 .

 4 38(b)).

Figure 4 .

 4 Figure 4.38: (a) A method for generation of fiber texture, (b) for various σ (1 to 15), a probability density function defining the sharpness (redrawn from [158]).

Figure 4 . 39 :

 439 Figure 4.39: Example of architecture generated with ideal fiber texture with homogeneous core-homogeneous shell. (a) An IPF cross-section of texture along the tensile axis. (b) An IPF cross-section of texture along the transverse direction. (c) SST for (a).

  Figure PB.1.

Figure 5 . 1 :

 51 Figure 5.1: Strategy employed in the current work for the finite element framework

Figure 5 . 2 :

 52 Figure 5.2: Boundary conditions applied to the microstructure (Z axis corresponds to the tensile axis).

1 .

 1 The isotropic hardening parameters (R 0 , Q, b) were firstly estimated from the macroscopic tensile test response of nickel microwires. The tensile test curve is at first fitted with an homogenization scheme of Berveiller-Zaoui (BZ) model. The BZ model was simulated with Young's modulus (˜234GPa), Poisson ration (0.3) and experimental texture reduced to ~200, ∼1000 and ∼5000 orientations and is presented in Figure5.3. The next two steps correspond to CPFE simulation with MC material law with material parameters from the BZ model.

Figure 5 . 3 :

 53 Figure 5.3: Tensile test simulations up to 1.1% axial strains for different number of orientations using BZ homogenization method.

Figure 5 .

 5 Figure 5.4 shows the results of identification. A difference at the elastic plastic transition can be observed in the case of BZ model and the CPFE with cubic elasticity. This difference can be attributed to the manner the parameters are identified and also the lack of sufficient number of DIC-corrected experimental curves for the AA100 wires. The identified parameters from step 1 and 3 are presented in Table5.3.

Figure 5 . 4 :

 54 Figure 5.4: Stress-strain curves for AA100 microwire and also simulated tensile response of 177 grain microstructure.

Figure 5 . 5 :

 55 Figure 5.5: (a) Macroscopic stress-strain response of three different mesh density aggregates, (b) effect of number of degrees of freedom on the apparent Young's modulus.

Figure 5 . 6 :

 56 Figure 5.6: FE microstructure with different mesh densities: (a) coarse mesh, (b) intermediate mesh, (c) fine mesh. The centered plots corresponds to the microstructure with imposed texture and the colors corresponds to the texture in the wire axis (for colored standard stereographic triangle refer to next figure), on the right the tensile axial stresses at 0.8% strain are shown.

Figure 5 . 7 :

 57 Figure 5.7: Digital microstructures with assigned textures (DMAT) used for FE simulations (a) AA100-DMAT, (b) EP40-DMAT, (c) AA40-DMAT, (d) LD100-DMAT.

Figure 5 . 8 :

 58 Figure 5.8: (a) Cross-section of AA100-DMAT microstructure with color corresponding to the texture in the wire axis. Contours of axial tensile stresses at the macroscopic tensile strain of 0.8% (b) isotropic elasticity, (c) cubic elasticity. Macroscopic tensile stress-strain curve of the AA100 and AA100-DMAT with isotropic and cubic elasticity.

Figure 5 . 9 :

 59 Figure 5.9: Average behavior of each of the 994 grains (a) isotropic elasticity, (b) cubic elasticity, the color coding follows IPF relative to the tensile axis.

Figure 5 . 11 :

 511 Figure 5.11: Histograms of distribution of (a) grain averaged axial stresses at time 't 3 ', (b) axial strains of all grains at time 't 3 ', (c) axial stresses at time 't 4 ', (d) axial strains of all grains at time 't 4 '.

Figure 5 . 12 :

 512 Figure 5.12: Average behavior of each of the grain family <111> and <100> separated based on the misorientation (a) isotropic elasticity, (b) cubic elasticity. The numbers in the legend correspond to the effective number of grains in each grain family.

Figure 5 . 13 :

 513 Figure 5.13: Axial stress (σ 33 ) contour at time 't 3 ' (a) isotropic elasticity, (b) cubic elasticity. Axial stress (σ 33 ) contour at time 't 4 ' (c) isotropic elasticity, (d) cubic elasticity.

Figure 5 .

 5 Figure 5.14: (a) Cross-section of AA100-DMAT microstructure with color corresponding to the texture in the wire axis. (b) Contours of axial tensile stresses at the macroscopic strain of 0.8%. (c) Macroscopic tensile stress-strain curve of the AA100 and AA100-DMAT.

Figure 5 .

 5 Figure 5.14(a) shows the cross-section of the AA100-DMAT, where region corresponding to the 'core' is marked by a black closed boundary.Figure 5.14(b) shows the contour of axial stress (σ 33 ), at a macroscopic strain of 0.8%, for the respective section in Figure 5.14(a). From Figure 5.14(b), it can be observed that the axial stress distribution in the 'core' is rather uniform

Figure 5 .

 5 Figure 5.14(a) shows the cross-section of the AA100-DMAT, where region corresponding to the 'core' is marked by a black closed boundary.Figure 5.14(b) shows the contour of axial stress (σ 33 ), at a macroscopic strain of 0.8%, for the respective section in Figure 5.14(a). From Figure 5.14(b), it can be observed that the axial stress distribution in the 'core' is rather uniform

Figure 5 . 16 :

 516 Figure 5.16: Two longitudinal cross-sections of AA100-DMAT.

Figure 5 .

 5 Figure 5.19: (a) Cross-section of EP40-DMAT microstructure with color corresponding to the texture in the wire axis. (b) Contours of axial tensile stresses at the macroscopic strain of 0.5%. (c) Macroscopic tensile stress-strain curve of the EP40 and EP40-DMAT.

Figure 5 .

 5 Figure 5.19(b) shows the contour of the axial stress (σ 33 ), at a macroscopic strain of 0.5%, for the respective section in Figure 5.19(a). The axial stress contour indicate that the distribution of stresses is rather homogeneous. This can be attributed to the presence of one major grain family in EP40-DMAT i.e. it has almost 95% of <111> fiber texture and 5% volume fraction of

Figure 5 . 20 :

 520 Figure 5.20: Average behavior of each of the 994 grains, with color corresponding to the texture in the wire axis.

Figure 5 .

 5 Figure 5.21(a) show the average stress-strain at four integration time corresponding to the deformation levels of 0.1%, 0.2%, 0.35% and 0.55%. The distribution of average axial stress and strains at 't 1 ' and 't 2 ' still follows an iso-strain deformation. The distribution of average axial stress and strains at 't 3 ' and 't 4 ' are presented in Figure5.21(b-e). A majority of grains exhibits an axial strain close to 900MPa (at t 3 ) and 1000MPa (at t 4 ) but maximum values attained by some grains can be much larger (1006 to 1063MPa at t 3 and 1128 to 1192MPa

Figure 5 .

 5 Figure 5.22 shows a classification of <111> and <100> grain families and their volume

Figure 5 . 22 :

 522 Figure 5.22: Average behavior of each of the grain family <111> and <100> separated based on the misorientation. The number in the legend corresponds to the effective number of grains in each grain family.

Figure 5 .

 5 Figure 5.23: (a) (left) Longitudinal cross-section of EP40-DMAT microstructure at the top of the microstructure (Y= 15µm), with color corresponding to the texture in the wire axis, (right) distribution of axial stresses for the respective cross-section at various macroscopic strains (0.1%, 0.2%, 0.4%, 1.2%). (b) (left) Longitudinal cross-section of EP40-DMAT microstructure at the midsection of the microstructure (Y= 7.5µm), with color corresponding to the texture in the wire axis, (right) distribution of axial stresses for the respective cross-section at various macroscopic strains (0.1%, 0.2%, 0.4%, 1.2%).

Figure 5 .

 5 Figure 5.25: (a) Cross-section of LD100-DMAT microstructure with color corresponding to the texture in the wire axis. (b) Contours of axial tensile stresses at the macroscopic strain of 0.8%. (c) Macroscopic tensile stress-strain curve of LD100-DMAT.

Figure 5 .

 5 Figure 5.26 shows the average response of all the 994 grains: a similar heterogeneous behavior as that of AA100-DMAT is also observed at the scale of grains. The extreme values

Figure 5 . 26 :

 526 Figure 5.26: Average behavior of each of the 994 grains, with color corresponding to the texture in the wire axis.

Figure

  Figure 5.27(a) shows the average stress-strain data of all 994 grains at four deformation levels (0.1%, 0.2%, 0.4% and 1.2%). The strain range of grains (0.58%-1.2%) at t 4 (1.2% deformation) is comparatively similar to that of AA100-DMAT, except for some grains in AA100-DMAT that present higher values. The distribution of axial stress and strain of the grains categorized based on the architecture (core-shell) is presented in Figure5.27(b, c) for time t 3 , and for t 4 in Figure5.27(d, e). A bi-modal axial stress distribution is seen for both core (centered at (t 3 ) 527MPa and 824MPa; centered at (t 4 ) 587MPa and 994MPa) and shell regions (centered at (t 3 ): 527MPa and 824MPa; centered at (t 4 ): 587MPa and 994MPa). The distribution of axial stresses presents bi-modal distribution for both core and shell, contrary to AA100-DMAT, where the bi-modal stress distribution is only seen for the shell. The distribution of axial strain ranges from: core (t 3 : 0.32%-0.4%; t 4 : 0.73%-1.1%) and shell regions (t 3 : 0.31%-0.41%; t 4 : 0.58%-1.25%).

Figure 5 . 28 :

 528 Figure 5.28: Macroscopic tensile stress-strain curve of AA100-DMAT and LD100-DMAT.

Figure 5 .

 5 Figure5.28 shows the macroscopic average stress-strain curve of the AA100-DMAT and LD100-DMAT aggregate. It can be seen that the macroscopic behavior of the LD100-DMAT aggregate is similar to that of AA100-DMAT aggregate. The difference lies in the average behavior of core and shell, which are inverted here (Figure5.25(c)).The longitudinal cross-section profiles similar to the ones carried out for AA100-DMAT are presented in Figure5.29. The observations are as follows:

Figure 5 .

 5 Figure 5.29: (a) (left) Longitudinal cross-section of LD100-DMAT microstructure at the top of the microstructure (Y= 15µm), with color corresponding to the texture in the wire axis, (right) distribution of axial stresses for the respective cross-section at various macroscopic strains (0.1%, 0.2%, 0.4%, 1.2%). (b) (left) Longitudinal cross-section of LD100-DMAT microstructure at the midsection of the microstructure (Y= 7.5µm), with color corresponding to the texture in the wire axis, (right) distribution of axial stresses for the respective cross-section at various macroscopic strains (0.1%, 0.2%, 0.4%, 1.2%).

Figure 5 .

 5 Figure 5.30: Cross-section of AA100-DMAT microstructure with color corresponding to the texture in the wire axis (a) core-shell architecture, (b) no-architecture. Contours of axial tensile stresses at the macroscopic tensile strain of 0.8% (c) core-shell architecture, (d) noarchitecture. Macroscopic tensile stress-strain curve of the AA100 and AA100-DMAT (e) core-shell architecture, (f) no-architecture.

Figure 5 . 31 :

 531 Figure 5.31: Average behavior of each of the 994 grains (a) architecture (c) no-architecture, average behavior of each of the grain family <111> and <100> separated based on the misorientation (b) architecture (d) no-architecture. The number in the legend corresponds to the effective number of grains in each grain family.

Figure 5 .

 5 Figure 5.31(a, c) shows the average response of all the 994 grains. In both architecture (Figure5.31(a)) and no-architecture (Figure5.31(c)) cases, qualitatively the axial strain distributions are considerable different at grain scale in both the cases. Figure5.31(b, d) shows a classification of <111> and <100> grain families and their average behavior. The solid lines indicate the average response of the grains with less than 10°of misorientation with the grain family, and dashed line indicates the average response of the grains with more than 10°of misorientation with the respective grain family. The average tensile behavior of <100> grains with more than 10°of misorientation is slightly softer in the case of core-shell architecture. No major difference are observed on the onset of plasticity in grain families between architecture and no-architecture case.

Figure 5 . 34 :

 534 Figure 5.34: Different architectures generated with ideal fiber texture (a) case I, (b) case II, (c) case III, (d) case IV. An IPF cross-section of texture along the tensile axis and its SST along with the transverse direction is provided.

Figure 5 .

 5 Figure 5.35(a) shows the macroscopic response of the four aggregates. It can be seen that microstructures with same volume fraction of texture and different architecture can result in same macroscopic behavior (no noticeable difference on the yield). The AA100 wire mechanical curve is included for a general macroscopic comparison as globally the four ideal cases and the AA100 wire have the same volume fraction but different sharpness in texture. The difference in strength for the ideal cases and the AA100 wire indicates that the presence of intermediate texture components of <111> and <100> can have significant effect on the tensile properties.Figure 5.35(b, c, d) indicates the core and shell behavior of the ideal texture aggregates and the following observations are made.

  Figure 5.35(a) shows the macroscopic response of the four aggregates. It can be seen that microstructures with same volume fraction of texture and different architecture can result in same macroscopic behavior (no noticeable difference on the yield). The AA100 wire mechanical curve is included for a general macroscopic comparison as globally the four ideal cases and the AA100 wire have the same volume fraction but different sharpness in texture. The difference in strength for the ideal cases and the AA100 wire indicates that the presence of intermediate texture components of <111> and <100> can have significant effect on the tensile properties.Figure 5.35(b, c, d) indicates the core and shell behavior of the ideal texture aggregates and the following observations are made.

1 .

 1 Case I and case IV, Figure 5.35(b), both exhibit a distinct core and shell behavior, where

3 .

 3 Case III, Figure5.35(d), exhibit no difference in tensile response for the core and shell.

Figure 5 .

 5 Figure 5.35: (a) Macroscopic tensile stress-strain curve of four cases with the mean response of AA100 for comparison, (b) macroscopic tensile stress-strain curve of case II, (c) Macroscopic tensile stress-strain curve of cases a and d, (d) macroscopic tensile stress-strain curve of case III.

Figure 5 . 36 :

 536 Figure 5.36: Different architectures generated with 75% of <111> and 25% of <100> ideal fiber texture (a) case I, (b) case II, (c) case III, (d) case IV. An axial stress contour map at a macroscopic deformation of 1.1% is presented alongside the volume average stress in each grains at four integration times (t 1 , t 2 , t 3 , t 4 ) corresponding to a macroscopic deformation of 0.1%, 0.2%, 0.4% and 1.1%.

Figure 6 . 1 :

 61 Figure 6.1: Illustration of information flow between models and experiments.

Figure 6 . 2 :

 62 Figure 6.2: Schematic presentation of regimes definition in XRD experiments (based on FWHM evolution).

Figure 6 .

 6 Figure 6.3 shows the macroscopic response of the (a) AA100 microwire and AA100-DMAT, (b) EP40 microwire and EP40-DMAT, and (c) AA40 microwire and AA40-DMAT. For LD100 microwire, comparison of the macroscopic stress-strain curves is not presented due to the non-availability of DIC-corrected data. The following observations can be made:

Figure 6 . 3 :

 63 Figure 6.3: Macroscopic tensile stress-strain curve of (a) AA100 with AA100-DMAT, (b) EP40 with EP40-DMAT (the red arrow corresponds to data scatter from 4 tensile tests), (c) AA40 with AA40-DMAT.

Figure 6 . 4 :

 64 Figure 6.4: Yield stress of extreme wires AA100, EP40, AA40 and LD100 with different criteria. The arrow corresponds to data scatter from 4 tensile test for EP40.

Figure 6 . 5 :

 65 Figure 6.5: Macroscopic tensile stress-strain curve of the AA100 and EP40 with AA100-DMAT, EP40-DMAT and EP40-DMAT-1. The corresponding SST of the microstructure is shown below the strain axis. The black arrow corresponds to data scatter from 4 tensile test for EP40.

Figure 6 . 6 :

 66 Figure 6.6: Schematic presentation of regimes definition in CPFE simulations.

Figure 6 . 7 :

 67 Figure 6.7: Average behavior of the grain family <111> and <100> separated based on the misorientation (a) AA100-DMAT (c) EP40-DMAT. The number in the legend corresponds to the effective number of grains in each grain family. Deviation of average stress from linearity (b) AA100-DMAT (d) EP40-DMAT, plotted with respect to average macroscopic stress of the whole aggregate.

Figure 6 . 8 :

 68 Figure 6.8: Volume average of stress-strain for each grain plotted at four integration time (t1, t2, t3, t4) (a) AA100-DMAT (b) EP40-DMAT (c) EP40-DMAT-1. The color coding follows the SST shown as inset in the sub figures.

Figure 6 .

 6 Figure 6.9(a, b, c, d) shows the distribution of axial stress and strains at t 3 and t 4 for AA100-

Figure 6 . 9 :

 69 Figure 6.9: Histograms of distribution of average axial stresses and strains of all grains in AA100-DMAT, EP40-DMAT and EP40-DMAT-1 at integration time (a, b) t 3 and (c, d) t 4 .

Figure 6 . 11 :

 611 Figure 6.11: Volume average of stress-strain for each grain plotted at four integration time (t1, t2, t3, t5) (a) AA100-DMAT (b) EP40-DMAT (c) EP40-DMAT-1. The color coding follows the SST shown as inset in the sub figures.

Figure 6 .

 6 Figure 6.12: (a) Normalized tensile strength versus wire diameter. (b) Normalized uniform tensile strain (ductility) versus wire diameter. The strength and ductility are normalized by the average properties of the starting diameter, respectively for each study.

Figure 7 . 1 :

 71 Figure 7.1: Different types of microstructure generated with S2M (a) bi-modal grain distribution with bigger grains in core and smaller grains in shell, (b) core exhibit higher elongation grains and shell exhibit lower elongation grains, (c) bamboo microstructure. Colors do not represent texture.

  Figure A.2(a), the wire was marked with patches of non metallic paint along the gauge length to create difference in contrast for DIC software to track. The sample holder was tilted continuously during the in-situ tests to record diffracting vector, as a result of this movement and shutter time being too long, most of the captured images were noisy. This introduces additional difficulties in DIC calculation. The DIC corrected plots for the AA100 and EP series are shown in Figure A.2(b).

Figure A. 2 :

 2 Figure A.2: (a) In-situ DIC setup on AA100 wire, (b) In-situ DIC corrected data of AA100 and EP series.

Figure A. 3 .

 3 Manually the circle fit on the LaB 6 reflections was verified before proceeding with the calculation. The beam center and detector tilt are then calculated and refined using the module in PyFAI.

Figure A. 3 :

 3 Figure A.3: Calibration of beam characteristics with PyFAI software.

Figure A. 4 .

 4 The computed strain errors for a 50µm vertical displacement are rather small. The pre-straining procedure should lead to minimal vertical displacements during continuous deformation ad hence negligible influence on the XRD results.

Figure A. 4 :

 4 Figure A.4: Error calculation for sample vertical displacement of 50µm in the beam (calculated error is for MS beamline).

Figure B. 1 :

 1 Figure B.1: Texture analysis of AA100 microwire. (1) schematic presentation of (a): core and (b): shell in longitudinal section, (2) respective longitudinal EBSD map associated to (a): 'core' (IPF relative to the wire axis); (b): 'shell' (IPF relative to the wire axis) and its corresponding IPF intensity.

Figure B. 2 :

 2 Figure B.2: EBSD scan on the cross section of the AA100 wire, (a) full 100µm (b)outer shell of 10µm (c) inner shell of 20µm (d) core 40µm and their corresponding IPF intensity (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc)

Figure B. 3 :

 3 Figure B.3: EBSD scan on the cross section of AA500 wire (a) near periphery, (b) region between center and periphery, (c) center and their corresponding IPF intensity (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc).

Figure B. 4 :

 4 Figure B.4: EBSD scan on the longitudinal section of the (a) AA500 wire, (b) LD100 wire and their corresponding IPF intensity with misorietation between grains (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc).

Figure B. 5 :

 5 Figure B.5: EBSD scan on the cross section of the (a) AA500 wire (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc), (b) LD100 wire and their corresponding IPF intensity

Figure B. 6 :

 6 Figure B.6: EBSD scan on the cross section of the LD100 wire, (a) full 100µm (b) outer shell of 10µm (c) inner shell of 20µm (d) core 40µm and their corresponding IPF intensity (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc)

Figure B. 7 :

 7 Figure B.7: Effect of drawing strain on tensile strength of nickel microwires (analysis carried out and plotted by Abhinav Arya from Atul Chokshi's group at IISc)

Figure B. 8 :

 8 Figure B.8: Ex-situ mechanical test conducted on AA100 and EP series

  Figure B.9(b) shows the corrected stress-strain curve for the tensile test carried out on AA100 and EP series of wires. The corrected slope agrees well with the volume fraction calculation from high energy XRD. By comparing Figure B.8 with Figure B.9(b), it can be seen that for the smaller wires (EP40), the contribution from machine compliance is almost negligible, as the applied load was very small.

Figure B. 9 :

 9 Figure B.9: (a) Ex-situ DIC setup on AA100 wire, (b) Ex-situ DIC corrected data of AA100 and EP series with their corresponding slope

Figure B. 10 :

 10 Figure B.10: Effect of diameter on yield stress and tensile strength of Ni microwires. The presented results are from the SLS beamtime and the data corresponds to AA100, EP70 and EP50 wires

Figure B. 11 :

 11 Figure B.11:The XRD data analysis of (a) AA100 wire, (b) EP50 wire with respect to applied stress. Top plot corresponds to continuous tensile strain-stress data, middle plots corresponds to the evolution of average axial[START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF],[START_REF] Schmid | Kristallplastizit˜it[END_REF] and (220) elastic lattice strains, bottom plot corresponds to the evolution of the (111), (200) and (220) Full Width Half Maximum (FWHM) versus applied stress. The presented reflections corresponds to axial reflections.

Figure B. 12 :

 12 Figure B.12: Poisson ratio of EP series of wires. Top plots corresponds to Poisson ratio for <111> textured grains corresponding to the transverse (220) reflection and axial (111) reflection, bottom plot corresponds to the <100> textured grain response calculated with (200) transverse reflection and (200) axial reflection.

Figure B. 13 :

 13 Figure B.13: Poisson ratio of AA series of wires. Top plots corresponds to Poisson ratio for <111> textured grains corresponding to the transverse (220) reflection and axial (111) reflection, bottom plot corresponds to the <100> textured grain response calculated with (200) transverse reflection and (200) axial reflection.

Figure B. 14 :

 14 Figure B.14: Poisson ratio of LD series of wires. Top plots corresponds to Poisson ratio for <111> textured grains corresponding to the transverse (220) reflection and axial (111) reflection, bottom plot corresponds to the <100> textured grain response calculated with (200) transverse reflection and (200) axial reflection.

  .

Figure B. 15 :

 15 Figure B.15: SEM micrographs of initial and fracture surface of nickel microwires (a) AA100, (b) EP70, (c) EP50, (d) EP40.

Figure B. 16 :

 16 Figure B.16: SEM micrographs of initial and fracture surface of nickel microwires (a) AA100, (b) AA70, (c) AA50, (d) AA40.

Figure B. 17 :

 17 Figure B.17: SEM micrograph of initial and fracture surface of LD100 nickel microwire.

  Figure B.18 shows an example of such analysis on AA100 microwire.

Figure B. 19 :

 19 Figure B.19: Fracture surface measurements on (a) EP series, (b) AA series, (c) LD series.

Figure C. 2 :

 2 Figure C.2: Pole figures of assigned texture for AA100-DMAT from simplified experimental EBSD texture (a) <111> pole, (b) <110> pole, (c) <100> pole, (d) SST. Each scatter point represent a set of orientation, pole figures are shown for a list of 994 orientations. Colors indicate IPF colormap for texture in the wire direction.

Figure C. 3 :

 3 Figure C.3: EP40 pole figures of assigned texture for EP40-DMAT from simplified experimental EBSD 'core' texture (a) <111> pole, (b) <110> pole, (c) <100> pole, (d) SST. Each scatter point represent a set of orientation, pole figures are shown for a list of 994 orientations. Colors indicate IPF colormap for texture in the wire direction.

Figure C. 4 :

 4 Figure C.4: Pole figures of assigned texture for AA40-DMAT from simplified experimental EBSD texture (a) <111> pole, (b) <110> pole, (c) <100> pole, (d) SST. Each scatter point represent a set of orientation, pole figures are shown for a list of 994 orientations. Colors indicate IPF colormap for texture in the wire direction.

Figure C. 5 :

 5 Figure C.5: Pole figures of assigned texture for LD100-DMAT from simplified experimental EBSD texture (a) <111> pole, (b) <110> pole, (c) <100> pole, (d) SST. Each scatter point represent a set of orientation, pole figures are shown for a list of 994 orientations. Colors indicate IPF colormap for texture in the wire direction.

  ) Full Width Half Maximum (FWHM) versus applied stress, the shaded zones represent the error bar. The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text). . . . . . . . . . . . . . . 91 3.15 XRD peak analysis of Ni microwires, a: AA100, b: LD100. Top plots correspond to monotonous tensile strain-stress data, middle plots corresponds to the evolution of axial[START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and[START_REF] Schmid | Kristallplastizit˜it[END_REF] elastic lattice strains in microstrain unit and their deviation from linearity versus applied stress, bottom plots correspond to the evolution of the[START_REF] Wu | Extraordinary strain hardening by gradient structure[END_REF] and[START_REF] Schmid | Kristallplastizit˜it[END_REF] Full Width Half Maximum (FWHM) versus applied stress (the shaded zones represent the error bar). The vertical dashed lines in the plots represent different stress level corresponding to the evolution of FWHM (see text). . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.16 Schematics of evolution of ∆FW HM with time in (b) regime α, (c) regime α ′ , (d) regime β , (e) regime γ. Green color marks the loading segment and red color marks the unloading segment. . . . . . . . . . . . . . . . . . . . . . . 95 3.17 Load-unload test on AA100 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle. . . . . . . . . . . . . . . 97 3.18 Load-unload test on AA100 microwire. (a) Applied stress with respect to time, (b) Evolution of FWHM of (111) reflection with time. (c) Evolution of FWHM of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19 Load-unload test on EP40 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle. . . . . . . . . . . . . . . 3.20 Load-unload test on EP40 wire. (a) Applied stress with respect to time. (b) Evolution of FWHM of (111) reflection with time. (c) Evolution of FWHM of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21 Load-unload test on AA40 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. A discontinuity between cycle 6 and cycle 7 is due to the technical problem with the machine resting block and the corresponding changes reflected in lattice strains are due to relaxation of the sample for ~20 minutes. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle. . . . . . . . . . . . . . . . . . . . . . . . . . 3.22 Load-unload test on AA40 microwire. (a) Applied stress with respect to time, (b) Evolution of FWHM of (111) reflection with time. (c) Evolution of FWHM of (200) reflection with time. A discontinuity between cycle 6 and cycle 7 is due to the technical problem with the machine resting block and the corresponding changes reflected in FWHM are due to relaxation of the sample for ~20 minutes. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle. . . . . . . . 3.23 Load-unload test on LD100 wire. (a) Applied stress with respect to time. (b) Corresponding evolution of axial lattice strains of (111) reflection with time. (c) Evolution of axial lattice strains of (200) reflection with time. Green color marks the loading segment and red color marks the unloading segment, the vertical black dashed line indicate a complete cycle. . . . . . . . . . . . . . . 6.10 Histograms of distribution of average axial strains of all the grains for architecture and no-architecture case at time 't 3 ' (b). Histograms of distribution of average axial stresses of all the grains for architecture and no-architecture case at time 't 3 ' (d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11 Volume average of stress-strain for each grain plotted at four integration time (t1, t2, t3, t5) (a) AA100-DMAT (b) EP40-DMAT (c) EP40-DMAT-1. The color coding follows the SST shown as inset in the sub figures. . . . . . . . . 6.12 (a) Normalized tensile strength versus wire diameter. (b) Normalized uniform tensile strain (ductility) versus wire diameter. The strength and ductility are normalized by the average properties of the starting diameter, respectively for each study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Different types of microstructure generated with S2M (a) bi-modal grain distribution with bigger grains in core and smaller grains in shell, (b) core exhibit higher elongation grains and shell exhibit lower elongation grains, (c) bamboo microstructure. Colors do not represent texture. . . . . . . . . . . . . . . . . A.1 Artifacts of (a) electropolishing, (b) cold-drawing. . . . . . . . . . . . . . . A.2 (a) In-situ DIC setup on AA100 wire, (b) In-situ DIC corrected data of AA100 and EP series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.3 Calibration of beam characteristics with PyFAI software. . . . . . . . . . . . A.4 Error calculation for sample vertical displacement of 50µm in the beam (calculated error is for MS beamline). . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Texture analysis of AA100 microwire. (1) schematic presentation of (a): core and (b): shell in longitudinal section, (2) respective longitudinal EBSD map associated to (a): 'core' (IPF relative to the wire axis); (b): 'shell' (IPF relative to the wire axis) and its corresponding IPF intensity. . . . . . . . . . . . . . . B.2 EBSD scan on the cross section of the AA100 wire, (a) full 100µm (b)outer shell of 10µm (c) inner shell of 20µm (d) core 40µm and their corresponding IPF intensity (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3 EBSD scan on the cross section of AA500 wire (a) near periphery, (b) region between center and periphery, (c) center and their corresponding IPF intensity (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc). . B.4 EBSD scan on the longitudinal section of the (a) AA500 wire, (b) LD100 wire and their corresponding IPF intensity with misorietation between grains (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc). . . . . . B.5 EBSD scan on the cross section of the (a) AA500 wire (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc), (b) LD100 wire and their corresponding IPF intensity . . . . . . . . . . . . . . . . . . . . . . . . . . B.6 EBSD scan on the cross section of the LD100 wire, (a) full 100µm (b) outer shell of 10µm (c) inner shell of 20µm (d) core 40µm and their corresponding IPF intensity (EBSD map provided by Abhinav Arya from Atul Chokshi's group at IISc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.7 Effect of drawing strain on tensile strength of nickel microwires (analysis carried out and plotted by Abhinav Arya from Atul Chokshi's group at IISc) . B.8 Ex-situ mechanical test conducted on AA100 and EP series . . . . . . . . . B.9 (a) Ex-situ DIC setup on AA100 wire, (b) Ex-situ DIC corrected data of AA100 and EP series with their corresponding slope . . . . . . . . . . . . . . . . . B.10 Effect of diameter on yield stress and tensile strength of Ni microwires. The presented results are from the SLS beamtime and the data corresponds to AA100, EP70 and EP50 wires . . . . . . . . . . . . . . . . . . . . . . . . . B.11 The XRD data analysis of (a) AA100 wire, (b) EP50 wire with respect to applied stress. Top plot corresponds to continuous tensile strain-stress data, middle plots corresponds to the evolution of average axial (111), (200) and (220) elastic lattice strains, bottom plot corresponds to the evolution of the (111), (200) and (220) Full Width Half Maximum (FWHM) versus applied stress. The presented reflections corresponds to axial reflections. . . . . . . . B.12 Poisson ratio of EP series of wires. Top plots corresponds to Poisson ratio for <111> textured grains corresponding to the transverse (220) reflection and axial (111) reflection, bottom plot corresponds to the <100> textured grain response calculated with (200) transverse reflection and (200) axial reflection. . . . . . B.13 Poisson ratio of AA series of wires. Top plots corresponds to Poisson ratio for <111> textured grains corresponding to the transverse (220) reflection and axial (111) reflection, bottom plot corresponds to the <100> textured grain response calculated with (200) transverse reflection and (200) axial reflection. . . . . . B.14 Poisson ratio of LD series of wires. Top plots corresponds to Poisson ratio for <111> textured grains corresponding to the transverse (220) reflection and axial (111) reflection, bottom plot corresponds to the <100> textured grain response calculated with (200) transverse reflection and (200) axial reflection. . . . . . B.15 SEM micrographs of initial and fracture surface of nickel microwires (a) AA100, (b) EP70, (c) EP50, (d) EP40. . . . . . . . . . . . . . . . . . . . . .List of Tables1.1 Summary of various studies on size effects (sc: single crystalline, mc: multi crystalline, pc: polycrystalline). . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Impurity content in Ni microwires . . . . . . . . . . . . . . . . . . . . . . . 2.2 Internal stresses and their influence on peak profile [141]. . . . . . . . . . . 2.3 Summary of texture analysis carried out for various diameters of nickel microwire (the error bars correspond to standard deviation and reflects the diameter difference between different samples). . . . . . . . . . . . . . . . . . . . 3.1 Characteristics of nickel microwires (the error bars on diameter correspond to standard deviation and reflect the difference in diameter between different samples). Volume fractions are calculated from XRD pole figures with 10°a ngular width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Microstructure summaries for extreme wire diameters. *Volume fractions are calculated from XRD pole figures with 10°angular width. . . . . . . . . . . 3.3 Characteristics of nickel microwires. A minimum of three wires has been deformed under X-Rays: error bars correspond to the data scatter. . . . . . . 3.4 Definition of regimes for nickel microwires wire during in-situ monotonous tensile tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Definition of regimes based on the evolution of FWHM with time for nickel microwires wire during in-situ cyclic tensile tests. . . . . . . . . . . . . . . . 3.6 Comparison of deformation regimes of the monotonous and cyclic tensile test. 4.1 Microstructure summary for extreme wire diameters. Homogeneous and heterogeneous refers to uniformity and heterogeneity with respect to crystallographic texture. *Volume fractions are calculated from XRD pole figures with 10°a ngular width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 OIM analysis of AA100 microwire from EBSD data, the average and standard deviation presented in the table are calculated for grains having an area fraction of 0.05 or higher. The provided statistics comes from two cross-sectional and one longitudinal EBSD maps. (1) circular crop of 40m diameter from the center of the EBSD map, (2) shell corresponds to the region not included in (1). (3) Core corresponds to the 40µm height in the longitudinal EBSD map, generally corresponding to the 40m diameter in cross-sectional EBSD map. (4) Shell corresponds to the region not included in (3). For clarity refer to Figure 4.16. 144 4.3 Statistics on different mesh generated with Neper on a 177 grain microstructure. Coarse, intermediate and fine mesh refers to the mesh setting used in the generation of mesh elements. . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.4 Simplified experimental texture data from AA100 wire. For 'Simplified experimental texture' (SET), the volume fraction data comes from XRD texture analysis and the area fraction data is from EBSD map. Alongside, the texture volume fraction of the 'assigned experimental texture' (AET) on the 994 grain aggregate is also presented. The subsequent area fraction of AET is the average over several cross-sections in the digital microstructure. △g refers to misorientation angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 4.5 'Simplified experimental texture' data, labeled as 'SET', from LD100 wire.

Table 1 .

 1

	Size effect occurs when t/d is less	than 15
	sc: not applicable	mc: smaller is weaker	(extrinsic)	pc: no strong changes	(extrinsic)
	3-56
	Ni	(microwires, diameter:	1000µm, grain size:	288 to 18µm)
	Wang et al. [69]

1: Summary of various studies on size effects (sc: single crystalline, mc: multi crystalline, pc: polycrystalline).

Table 2

 2

	.1.

Table 2 .

 2

1: Impurity content in Ni microwires

Table

			.2 provides a classification of stress
	types and their influence on peak profile.
				Influence on peak profile
	Internal stress types	Definition	Peak	Peak
	σ I , Type I	Macrostress	Homogeneous stress	position √	broadening
			over a large number of
	σ II , Type II	Intergranular	crystal domains Average stress variation	√	√
	σ III , Type III	microstress Intragranular	between grains Inhomogeneous stress		√
		microstress	within a grain

Table 3 .

 3

		ID	Average	Volume	Volume
			diameter (µm)	fraction of	fraction of
				<111> grains	<100> grains
	Commercial wire	AA100	103 ± 1	0.75	0.25
		EP70	69 ± 1.5	0.83	0.17
	EP series	EP50	49 ± 1.5	0.90	0.10
		EP40	40 ± 2.5	0.95	0.05
		AA70	67.5 ± 0.5	0.81	0.19
	AA series	AA50	47.5 ± 0.5	0.83	0.17
		AA40	37.5 ± 0.5	0.86	0.14
	LD series	LD100	98.5 ± 0.5	0.77	0.23

1: Characteristics of nickel microwires (the error bars on diameter correspond to standard deviation and reflect the difference in diameter between different samples). Volume fractions are calculated from XRD pole figures with 10°angular width.

Table 3 .

 3 .2. 2: Microstructure summaries for extreme wire diameters. *Volume fractions are calculated from XRD pole figures with 10°angular width.

	Sample ID	AA100	EP40	AA40	LD100
	Average	103 ± 1	40 ± 2.5	37.5 ± 0.5	98.5 ± 0.5
	diameter (µm)
	Origin	Commercial	Electropolished	Cold drawn from	Cold drawn from
		cold-drawn	from AA100	AA100	AA500
	Core-shell	Yes	No	Yes	Yes
	architecture
	Texture of core Major <111> Major <111>	Major <111>	<111> + <100>
			(EP40 ≈ core of		with major
			AA100)		<100>
	Texture of	<111> +		<111> + <100>	<111> + <100>
	Shell	<100>
	Global volume	75%	95%	86%	77%
	fraction of
	<111> grains*
	Global volume	25%	5%	14%	23%
	fraction of
	<100> grains*
	Mean grain	∼ 1µm	∼ 1µm	Core: ∼ 1µm	∼ 1µm
	size of the			Shell: ∼ 0.4µm
	distribution

Table 3 . 3

 33 .3.

	Series	Sample ID	Yield stress	Failure stress	Uniform
			range (MPa)	(MPa)	elongation (%)
	Commercial wire	AA100	820 ± 7	885 ± 12	1.2 ± 0.17
		EP70	850 ± 26	895 ± 30	0.82 ± 0.09
	EP series	EP50	915 ± 90	940 ± 119	0.61 ± 0.07
		EP40	1050 ± 56	1050 ± 56	0.54 ± 0.08
		AA70	953 ± 21	992 ± 12	1.35 ± 0.33
	AA series	AA50	1003 ± 15	1073 ± 42	1.55 ± 0.38
		AA40	1082 ± 28	1146 ± 3	1.83 ± 0.21
	LD series	LD100	885 ± 5	935 ± 9	1.88 ± 0.08

: Characteristics of nickel microwires. A minimum of three wires has been deformed under X-Rays: error bars correspond to the data scatter.

Table 3 .

 3 .4. 4: Definition of regimes for nickel microwires wire during in-situ monotonous tensile tests.

	Regime		I	II		III
	Sub regime	-	II ′	II ′′	-
	Associated reflection (111), (200)	(111)	(200)	(111), (200)
	AA100		Yes	Yes	Yes	Yes
		EP70	Yes	Yes	Yes	Yes
	EP series	EP50	Yes	Yes	Yes	Yes
		EP40	Yes	No	Yes	No
		AA70	Yes	No	Yes	Yes
	AA series	AA50	Yes	No	No	Yes
		AA40	Yes	No	No	Yes
	LD100		Yes	No	Yes	Yes
						(sub-regimes
						III ′ and III ′′ )

Table 3 .

 3 6: Comparison of deformation regimes of the monotonous and cyclic tensile test.

	identified		Deformation regimes
	from tests	Elasticity Micro-plasticity Macro-plasticity
	Monotonous	I	II ′ and II ′′	III ′ and III ′′
	Load-unload cycle	α and α ′	β	γ

Table 4 .

 4

	1.

Table 4 .

 4

1: Microstructure summary for extreme wire diameters. Homogeneous and heterogeneous refers to uniformity and heterogeneity with respect to crystallographic texture. *Volume fractions are calculated from XRD pole figures with 10°angular width.

Table 4 .

 4 2: OIM analysis of AA100 microwire from EBSD data, the average and standard deviation presented in the table are calculated for grains having an area fraction of 0.05 or higher.

	Grain size	Grain
	(µm)	aspect ratio

The provided statistics comes from two cross-sectional and one longitudinal EBSD maps. (1) circular crop of 40µm diameter from the center of the EBSD map, (2) shell corresponds to the region not included in (1). (

3

) Core corresponds to the 40µm height in the longitudinal EBSD map, generally corresponding to the 40µm diameter in cross-sectional EBSD map. (4) Shell corresponds to the region not included in

(3)

. For clarity refer to Figure

4

.16.

Table 4 .

 4 3: Statistics on different mesh generated with Neper on a 177 grain microstructure. Coarse, intermediate and fine mesh refers to the mesh setting used in the generation of mesh elements.

	177 grains	Coarse	Intermediate	Fine mesh
		mesh	mesh
	Simulation box		71 x 71 x 201
	dimension
	Elements		1,013,241
	(hexahedral mesh)
	Nodes (tetrahedral	8,976	14,776	102,040
	mesh)
	Elements	46,374	78,139	569,151
	(tetrahedral mesh)

Table 4 .

 4 4: Simplified experimental texture data from AA100 wire. For 'Simplified experimental texture' (SET), the volume fraction data comes from XRD texture analysis and the area fraction data is from EBSD map. Alongside, the texture volume fraction of the 'assigned experimental texture' (AET) on the 994 grain aggregate is also presented. The subsequent area fraction of AET is the average over several cross-sections in the digital microstructure. △g refers to misorientation angle.

	Architecture
	Core-shell	Core	Shell

Table

			Architecture
			Core-shell	Core	Shell
		<111>	77%	-	-
	Volume fraction	<100>	23%	-	-
		<110>	-	-	-
		<111>	60%	43%	58%
	Area fraction	<100>	38%	56%	37%
	SET	<110> 111>	2% 57%	1% 90%	5% 55%
	△g < 10°< <100>	40%	60%	37%
		<110>	0%	0%	0%
		111>	43%	10%	45%
	△g > 10°< <100>	60%	40%	63%
		<110>	100%	100%	100%
		<111>	76%	41%	87%
	Volume fraction	<100>	24%	59%	16%
		<110>	-	-	-
		<111>	74%	44%	79%
	Area fraction	<100>	26%	56%	21%
	AET	<110> 111>	-57%	-87%	-53%
	△g < 10°< <100>	47%	56%	38%
		<110>	-	-	-
		111>	43%	13%	47%
	△g > 10°< <100>	53%	44%	62%
		<110>	-	-	-

Table 5 .

 5 1 presents some of the elements of mean-field and full-field approaches.

	Parameters	Full-field	Mean-field
	Computational run time	High	Very low
	Pre-and post-processing	High	Very low
	Non linear behavior	Accurate estimate Coarse estimate
	Microtexture/ local grain neighborhood effect	Yes	No

Table 5 .

 5 1: Features of mean-field and full-field approaches.

Table 5 .

 5 3. As a final step of the identification process, FE simulation on microstructure with 177 elongated grains (experimental texture reduced to 177 orientations) is carried out with the material parameters refined in step 2. The refined parameters obtained here are used for FE simulation of the ∼1000 grain aggregate. 2: Parameters taken from literature[START_REF] Renner | Sensitivity of the residual topography to single crystal plasticity parameters in berkovich nanoindentation on fcc nickel[END_REF].

	Elasticity			Viscosity
	C 11 (GPa)	C 12 (Gpa)	C 44 (GPa)	K (MPa.s 1/n )	n
	248	153	116	8		7
	Hardening matrix (h rs )
	h1	h2	h3	h4	h5	h6
	1	1	1	89	1	1

Table 6 .

 6 2: End of elastic regime from experiments and simulationsThe end of the micro-plastic regime from experiments (transition between regime II and III) and simulation for different wires are provided in Table6.3. As commented before, these values of stress from the 0.2% yield criterion for simulations corresponds to an upper bound for experimental values defined from the evolution of FWHM.

	Sample ID Experiments	Simulation
		(MPa)	(MPa)
	AA100	~830	~880
	EP40	~1050	~980
	AA40	~1050	~950
	LD100	~875	~880

Table 6 .

 6 3: End of micro-plastic regime from experiments and simulations

Table C .

 C 1: Statistics for 177, 997 and 4967 grains (tetrahedral mesh is from Neper); for bigger aggregate with 4967 grains such mesh has not been carried out due to limitations with Neper.

		177 grains	994 grains	4967 grains
	Simulation	71*71*201 151*151*351 351*351*351
	box dimension
	Elements	364,170	3,252,261	-
	(tetrahedral
	mesh)
	Nodes	102,040	566,839	-
	(tetrahedral
	mesh)
	Elements	1,013,241	8,003,151	43,243,551
	(hexahedral
	mesh)

  5.1 Features of mean-field and full-field approaches. . . . . . . . . . . . . . . . . 178 5.2 Parameters taken from literature [240]. . . . . . . . . . . . . . . . . . . . . 185 5.3 Isotropic hardening parameters identification. . . . . . . . . . . . . . . . . . 186 6.1 Material parameters identification for AA40-DMAT. . . . . . . . . . . . . . 239 6.2 End of elastic regime from experiments and simulations . . . . . . . . . . . . 240 6.3 End of micro-plastic regime from experiments and simulations . . . . . . . . 241 C.1 Statistics for 177, 997 and 4967 grains (tetrahedral mesh is from Neper); for bigger aggregate with 4967 grains such mesh has not been carried out due to limitations with Neper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

Crystal plasticity finite element simulations 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Overview of polycrystalline micro-mechanical models . . . . . . . . . . . . 5.2.1 Single crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1.1 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . .

Plastic regime: Between the strains of 0.4% (mico/macro-plastic transition) and 1.2%

Acknowledgements

thankful to Girish for helping me out in settling at the IISc campus. I wish to express my gratitude to Soham (Post doc) for an extended support during the initial to thank Mikael GUEGUEN (ENSMA), my deepest gratitude to Mahak for proof reading my abstracts, thesis, and article and for also being a source of musical accompaniment and inspiration during the final year of the PhD.

Support agencies: Thanks are also due to the Indo-French Centre for Promotion of Advanced Research (CEFIPRA) (under project 5408-1), LABEX INTERACTIFS (reference ANR-11-LABX-0017-01) and European Structural and Investment Funds (ERDF reference: P-2016-BAFE-94/95) for their financial support without which I would not have been able to carry out the different aspects of the thesis. ix

observations. I am very XRD data processing.

List of Abbreviation

Simulations on AA40-DMAT

The FE simulation on AA40-DMAT has also been performed with the same material parameters as that of AA100-DMAT. The microstructure analysis of AA100 wire using EBSD techniques is detailed in this section. Analysis of the EBSD map according to its spatial location further provides information that agrees well with the macroscopic high energy XRD pole figures. The analysis of longitudinal EBSD map for AA100 shows that the 'core' of the microwire has majorly <111> oriented grains cross along the length of the microwire, as shown by the IPF intensity plots in shows that there is a marked presence of dual fiber texture in the outer shell and this duality of the texture diminishes as we move towards the core of the microwire. This also indicates that for an electropolished wire of 70µm, already a significant portion of the <100> texture has been removed. The grain size analysis for these regions indicates a more homogeneity spatially with size ranging from 400nm to a few micrometers, whereas for the texture components a heterogeneity linked to spatial location in wire is observed. Upon electropolishing, the microstructure of the target diameter wire has a very different internal microstructure in comparison to the microstructure of AA100 wires. [START_REF] Petch | The cleavage strength of polycrystals[END_REF] shows the profile of fracture surface for different series of wires. The wire cross section is observed to be uniform almost 'x' distance away from the fractured end. Where 'x' corresponds to the diameter of the microwires. For example the EP40 and AA40 wires show a huge variation in elongation to failure, whereas the necking zone of both of these wires is almost similar. The analysis revealed that the shape of the necking zones are similar for all the wire diameters and also, the length of the necking zone of the wires are seen to increase with increasing diameter (marked by dashed lines in the figure).

Appendix C

Microstructure generation

Several different microstructure were generated (~100 to ~5000 grains) with S2M and meshed using Neper and are presented in