V Venkatraman

A Guitton Taupin

Under

L Decluse

M Ben

Haj Slama

S Bahi

A Guitton

P Wood

N Maloufi

A Rusinek

I N Revision 〈hal-03381828〉

M Taupin

W Vallet

A Guitton Yu

Scripta

W Pi

M Chen

A Vallet

L Guitton

F Guitton

F Schäfer

M Scholz

J Schneider

G Frenzel

N Laplanche

Maloufi

V Taupin

K Venkatraman

A D Rollett

R A Lebensohn

S Berbenni

B Beausir

A Guitton Materialia

Dimensionality reduction using principal component analysis to classify different grain boundary slip transfer regimes in BCC-titanium Ti21S

Presentation of high and medium entropy alloys . . . . . . . . 61 IV.3.2 Links between mechanical response and microstructure . . . . 62 IV.3.2.1 Pop-in load variations with distance from a LAGB . 62 IV.3.2.2 Evolution of microstructures . . . . . . . . . . . . . . 63 V Mesoscale and statistical comparison between polycrystalline plasticity models and experiments 69

all of my colleagues from LEM3 and particularly:

• Stéphane Berbenni I wish also all the best to Adrien Heinzelmeier, Julien Aubourg and Renaud Genin for their on-going doctoral research.

In addition, I would like to thank my colleagues from the IUT de Metz and particularly:

• Nathalie Allain

• Patrice Bourson

• Pierre Pino

• Jérôme Serri

Finally, I want to thank the LabEx DAMAS, the région Grand-Est and the CNRS through the MITI interdisciplinary programs for their financial supports. Critical resolved shear stress of the slip system (α)

Contents

M (α)
Schmid tensor for the slip system (α) B (α) Unit vector along the slip direction of the slip system (α)

N (α)
Unit vector along the normal to the slip plane of the system (α)

V h Complex Fourier coefficients (j)
The j-th wave ε (j) Excitation amplitude of the j-th wave

C (j)
g Amplitude of diffracted j-th wave -→ k (j) 0

Wave vector of the j-th primary wave xi Nomenclature q (j) Attenuation parameter expressing the exponential attenuation of the wave amplitude with increasing depth z N Atom number per unit of volume

Introduction

Developing new materials and understanding how they deform is the main challenge of researchers in order to follow and meet the challenging developments needed by a fast-paced and evolving society. For instance, in the framework of energy cost reductions, increasing mechanical performance of materials is synonymous with continuous improvements of experimental techniques leading to new insights on their fundamental deformation mechanisms, which then leads to design high-performance materials with enhanced properties. Although research in materials plasticity has developed for more than one century, it is fair to say that it still holds many secrets, particularly because of difficulties to extrapolate simplistic models to real samples, far from ideal cases. Cottrell summarized this conflict by qualifying the theory of plastic hardening as "the first problem to be attempted by dislocation theory and may be the last to be solved" [START_REF] Cottrell | Dislocations and Plastic Flow in Crystals[END_REF].

Generally, materials are polycrystalline, i.e. they consist of millions of single crystals called grains. Grains have different orientations of the atom lattice and they are separated from neighboring grains by interfaces called Grain Boundaries (GBs). It is well established that the irreversible (or plastic) deformation of a sample originates mainly from the nucleation and the propagation of more than hundreds of billions per cm 3 of micrometric (even nanometric) linear defects of the regular crystal lattice called dislocations [START_REF] Hirth | Theory of Dislocations[END_REF]. Dislocations move through the grain and interact with each other or with GBs. GBs may act in several ways: sinks, obstacles, traps Introduction and sources of dislocations. Combination of experimental and simulations studies gives valuable insights on the operating mechanisms. Although, there exists a welldeveloped theory for describing the interaction between a single dislocation and a model GB, the response of several real GBs (contained in a real bulk polycrystalline sample) after receiving numerous dislocations is still a major scientific challenge.

The mystery becomes inextricable, when one considers that there are more than hundreds of billions of dislocations per cm 3 of sample interacting together and with billions of GBs. Even more inextricable, if one wants to take into account influence of distribution of GBs, other types of interfaces, grain shape, grain orientation, and defects in the bulk sample i.e. its microstructure. Due to this inherent complexity, materials scientists have to bridge the gap between these two extreme length scales:

sample (or macro-) scale and dislocation (or micro-) scale (Figure 1). It is obvious that these two worlds interact with each other but their connections remain extremely difficult to understand because of need of extrapolations.

Here, the role of micromechanical modeling brings new insight. Such computational schemes need constitutive equations that have to be "fed" with experimental criteria and parameters, capturing important operative mechanisms. However, such valuable experiments are still marginal and all suffer numerous constraints making interpretations unreliable statistically. These obstacles are now close to be overcome, through innovative experimental procedures, made now possible with recent progress in electron microscopy.

Such is the background to the current report. Chapter I summarizes basics of plasticity and the major role of microstructures in deformation mechanims. The example of MAX phases, a promising material for industries, is given, because they show reversible non-elastic phenomena due to the strong anisotropy of their mi-Introduction crostructures. At the end of Chapter I, the influence of strain-path changes on plasticity has been introduced. The development of a miniaturized biaxial deformation rig is reported. Then, Chapter II focuses on the contribution of electron microscopy. Indeed, this is one of the most well-known technique for analyzing defects, thus allowing to understand their response to external solicitations. Two kinds of electron microscopes are generally used and bring complementary information:

at micro/nano-scale, Transmission Electron Microscopy (TEM) and at macro/mesoscopic scale, Scanning Electron Microscopy (SEM). Because SEM can access diffraction contrast on bulk materials with the phenomenon of electron channeling, emphasis is on the Electron Channeling Contrast Imaging (ECCI) and its upgrade, the Accurate ECCI (A-ECCI), developed at LEM3. This leads to Chapter III, where physics of ECCI is presented for optimizing experimental conditions. Then

Chapter IV explores the potentiality of A-ECCI for probing evolution of crystalline The macroscopic stress, Σ, due to the application of F is written as Σ = F S . Moreover, the component of F projected along the slip direction is F cos χ. This latter acts on the slip plane with a section equal to S cos ϕ . Therefore, the Resolved Shear Stress (RSS), τ (α) RSS , for the slip system (α), characterized by the normal to its slip plane (angle ϕ) and its slip direction (angle χ) is given by:

τ (α) RSS = Σ cos ϕ cos χ (I.1)
thus linking the RSS to the applied stress, Σ, through the Schmid factor, m, defined as follows:

m = cos ϕ cos χ (I.2)
Therefore, the system (α) will be active, if the RSS reaches a critical value, the Critical Resolved Shear Stress (CRSS), τ (α)

CRSS . In the general case of a non-uniaxial deformation, τ (α) RSS is linked to the applied stress tensor written in the crystal frame (c), T (c) , through the Schmid tensor (⊗ is the dyadic product):

M (α) = 1 2 B (α) ⊗ N (α) + N (α) ⊗ B (α) (I.3)

I.I.1 From one interface to polycrystals with grain boundaries

τ (α) RSS = T (c) : M (α) (I.4)
where:

• B (α) : unit vector along the slip direction of the system (α);

• N (α) : unit vector along the normal to the slip plane of the system (α).

I.1.1.2 Dislocations

Slip steps on the surface arise from the movement of several micrometric (even nanometric) linear defects of the regular crystal lattice called dislocations [START_REF] Hirth | Theory of Dislocations[END_REF][START_REF] Volterra | Sur l'équilibre des corps élastiques multiplement connexes[END_REF]. Dislocations are characterized by the strain field they produce (given by the Burgers vector labelled -→ b ) and the infinitely thin slip area assimilated by a line named the dislocation line (labeled -→ u ) [START_REF] Burgers | Physics. -Some considerations on the fields of stress connected with dislocations in a regular crystal lattice. I[END_REF]. Therefore, the height H of a surface step is given by (p is the number of dislocations and -→ n the normal vector to the surface):

H = p - → b • - → n (I.5)
Based on the angle between -→ b and -→ u ( -→ b , -→ u ), three types of dislocations are distinguished:

• for -→ b , -→ u = 0°, dislocations are called "screw";

• for -→ b , -→ u = 90°, dislocations are called "edge";

• for other cases, dislocations are called "mixed".

The glide plane, with normal N (α) , is defined by the plane -→ b , -→ u . Note that for screw dislocations, no unique glide plane can be associated. In most cases, -→ b is a complete lattice translation vector of the crystalline network. Therefore, glide of such dislocations, called "perfect", leaves a perfect crystal. Nevertheless, in some materials, dislocations with a Burgers that is a vector different from the crystalline network, can be observed. They are called "partial" and their glide leads to the formation of Stacking Faults (SFs).

Chapter I. Microstructure: a major and complex role in polycrystalline plasticity SFs, as planar defects, can play an important role in plasticity of crystal. Indeed, they are local regions in the crystal where the regular stacking sequence is interrupted [START_REF] Hull | Introduction to Dislocations[END_REF]. Such error in the stacking is associated to a translation vector -→ R between both parts of the crystal.

I.1.2 Plasticity of polycrystal I.1.2.1 Grain boundaries

Polycrystals consist of numerous grains separated by GBs [START_REF] Priester | Les joints de grains -De la théorie à l'ingénierie[END_REF]. According to synthesis and/or machining processes, crystallographic orientations of grains are random or with preferential orientations (i.e. texture). In a polycrystalline sample, each grain has it own orientation with the loading axis. Therefore, one grain will be deformed differently compared to its neighbors [START_REF] Schreiber | Impact of grain boundaries on microstructure evolution during deformation of a magnesium tricrystal[END_REF]. Because of this connection, the grain will undergo loading stress field reduced by the interaction stresses generated by surrounding grains in order to maintain the cohesion of the sample [START_REF] Priester | Les joints de grains -De la théorie à l'ingénierie[END_REF]. Therefore, the yield stress is generally higher in polycrystalline specimens compared to the single crystals [START_REF] Hansen | Hall-Petch relation and boundary strengthening[END_REF]. Note that the interaction stresses are higher close to GBs than inside the grain [START_REF] Priester | Les joints de grains -De la théorie à l'ingénierie[END_REF], so that slip will occur essentially in its center. Moreover, in order to plastically deform a polycrystalline specimen by slip, the Taylor theory says, that minimum five independent slip systems have to be activated in each grain otherwise stress concentrations against GBs will occur, thus leading to cracking [START_REF] Mises | Mechanik der festen körper im plastisch-deformablen zustand[END_REF].

Interfaces, particularly GBs, may act in several ways. The behavior of dislocations reaching a GB depends on the applied stress, the temperature, and, of course, on the GB nature [START_REF] Priester | Les joints de grains -De la théorie à l'ingénierie[END_REF][START_REF] Kacher | Dislocation interactions with grain boundaries[END_REF][START_REF] Heller | Deformation of µmand mm-sized Fe2.4wtwith a high angle grain boundary at room temperature[END_REF].

GBs are described by the misorientation between both adjacent crystals and by the orientation and the position of the GB plane itself. Only five macroscopic parameters are therefore necessary for describing the GB geometry [START_REF] Priester | Les joints de grains -De la théorie à l'ingénierie[END_REF]. It is convenient to categorize GBs according to their misorientation. Low-Angle Grain Boundaries (LAGBs) are those with misorientation less than about 20° [START_REF] Hirth | Theory of Dislocations[END_REF][START_REF] Priester | Les joints de grains -De la théorie à l'ingénierie[END_REF]. They can be described by relatively simple intrinsic dislocation configurations: tilt or twist LAGBs

(Figure I.
2) made up of walls of edge dislocations or screw dislocations respectively.

I.I.1 From one interface to polycrystals with grain boundaries

Mixed LAGBs consist of a wall of edge and screw dislocations. For LAGBs, the misorientation, β, is related to spacing, D, between intrinsic dislocations with -→ b as their Burgers vector [START_REF] Hull | Introduction to Dislocations[END_REF]:

D = -→ b 2 sin β 2 ∼ - → b β (I.6)
From equation I.6, it is clear that high misorientations lead to dislocation spacing reduced to one or two atomic spacing. Therefore, the description of such GB in terms of walls of distinguishable dislocations does not make sense anymore. These High-Angle Grain Boundaries (HAGBs), whose misorientation is greater than about β ≈ 20°, become a region of severe localized disorder [START_REF] Hirth | Theory of Dislocations[END_REF].

Concerning GB energy, its variations with misorientation are shown in Figure other or with GBs, acting in several ways (sinks, obstacles, traps and sources of dislocations), so that they are very important from the mechanical properties point of view [START_REF] Priester | Les joints de grains -De la théorie à l'ingénierie[END_REF]. One of the best-known model based on dislocation pile-up at GBs (described by the Hall-Petch equation [START_REF] Hall | The Deformation and Ageing of Mild Steel: III Discussion of Results[END_REF]) predicts that the yield stress of the sample is inversely proportional to the square root of its grain size. Therefore, such microscopic operating mechanisms have a direct influence on the strategies employed for designing polycrystalline materials [START_REF] Valiev | Paradox of Strength and Ductility in Metals Processed Bysevere Plastic Deformation[END_REF][START_REF] Zhu | Performance and applications of nanostructured materials produced by severe plastic deformation[END_REF][START_REF] Cordero | Grain size effects on plastic strain and dislocation density tensor fields in metal polycrystals[END_REF].

I.1.2.2 Interactions between dislocations and GB

Plastic deformation of polycrystalline materials is strongly influenced by the microstructure, in particular by GBs. Dislocations within a grain and near a GB will interact with the latter, according several scenarios. complex mechanisms include, for instance, dislocation absorption at GB by dislocation dissociation. Moreover, the active mechanism (note that several can be Chapter I. Microstructure: a major and complex role in polycrystalline plasticity activated simultaneously, as well) not only depends on grain misorientation and the GB nature but also on the type of dislocations (i.e. edge, screw or mixed). For example, screw dislocations, can glide through GBs without residual dislocation [START_REF] Bayerschen | Review on slip transmission criteria in experiments and crystal plasticity models[END_REF].

GB can act as dislocation source. Such dislocations remains generally in the vicinity of the GB and they can be emitted in both adjacent grains afterwards.

Concerning slip transfer rules, several criteria were proposed. A comprehensive overview is presented in [START_REF] Bayerschen | Review on slip transmission criteria in experiments and crystal plasticity models[END_REF]. Briefly, they can be classified into two main categories:

• crystallographic criteria such as slip plane normals and slip directions for active slip systems in both adjacent grains [START_REF] Livingston | Multiple slip in bicrystal deformation[END_REF][START_REF] Lee | Prediction of slip transfer mechanisms across grain boundaries[END_REF][START_REF] Luster | Compatibility of deformation in two-phase Ti-Al alloys: Dependence on microstructure and orientation relationships[END_REF][START_REF] Werner | Slip transfer across grain and phase boundaries[END_REF][START_REF] Beyerlein | Structure-Property-Functionality of Bimetal Interfaces[END_REF];

• weight-function-based criteria combined with crystal plasticity output parameters: they are based on the above-factors and they are obtained by the summation over all slip system transmission factors and weighting each one with plastic slips or the Schmid factors [START_REF] Bieler | Grain boundaries and interfaces in slip transfer[END_REF].

I.1.2.3 Micromechanical modeling

It is clear that the response of one grain of interest in a polycrystalline sample cannot be understood individually without taking into account its neighborhood.

Therefore, the stress field inside one grain (σ) is not equal to the macroscopic stress field (T), applied on the sample during the deformation test. Mathematically, the problem consists in calculating this local stress tensor (σ) from polycrystal plasticity models, and then writing it in the crystal frame:

σ (c) = R : σ : R (I.7)
where R and R are respectively the rotation tensor and its transpose, characterizing the sample microstructure. Then, σ (c) can be linked to τ

(α)
RSS by M (α) , written in the crystal frame, as well:

τ (α) RSS = σ (c) : M (α) (I.8)
Note that in the case of a monocrystal or for simple experimental considerations,

I.I.1 From one interface to polycrystals with grain boundaries

one generally supposes that the solicitation experienced by one grain is equal to that experienced by the all specimen:

T = σ (I.9)
Therefore, the influence of the surrounding microstructure and the crystalline anisotropy are considered as negligible.

Two types of dislocation configurations are distinguished, of which both the density evolution and their specific interactions can be modeled [START_REF] Nye | Some geometrical relations in dislocated crystals[END_REF]: Geometrically Necessary Dislocation (GND) densities result in a lattice disorientation of an elementary volume of reference in order to accommodate geometrically the deformation of the specimen (long-range effect). The other type of dislocations is called Statistically-Stored Dislocation (SSD) densities. They do not contribute to lattice disorientation but they can result in pinning of dislocations (short-range effect).

Note that experimentally this distinction is mainly a question of resolution i.e. each dislocation can be seen as GND [START_REF] Ernould | Global DIC approach guided by a cross-correlation based initial guess for HR-EBSD and on-axis HR-TKD[END_REF].

It is obvious that computational schemes need constitutive equations that have to be "fed" with experimental criteria and parameters, capturing the important operative mechanisms [START_REF] Lowe | Modeling Internal Stresses in the Nonelastic Deformation of Metals[END_REF][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] Dillard | 3D quantitative image analysis of open-cell nickel foams under tension and compression loading using X-ray microtomography[END_REF][START_REF] Dierke | Portevin-LeChatelier effect in Al-Mg alloys: Influence of obstacles -experiments and modelling[END_REF][START_REF] Lebensohn | Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper[END_REF][START_REF] Pokharel | Polycrystal Plasticity: Comparison Between Grain -Scale Observations of Deformation and Simulations[END_REF][START_REF] Rollett | Comparison of Gradients in Orientation and Stress between Experiment and Simulation[END_REF]. Experiments at mesoscopic scale, can bring new light both on our knowledge on polycrystal plasticity and models at the grain scale. Indeed, they can feed numerical simulations for predicting mechanical response of polycrystals (strain hardening, ductility etc.), with respect to the evolution of dislocation densities inside the grains and their interactions with GBs.

Modeling tools include for instance Discrete Dislocation Dynamics (DDD), Crystal Plasticity models using Finite Elements or Fast Fourier Transform algorithms (CPFEM, CPFFT), or mean field approaches (e.g. Self-Consistent models like Vis-coPlastic Self-Consistent VPSC, Elasto-ViscoPlastic Self-Consistent EVPSC schemes) [START_REF] Bertin | Frontiers in the Simulation of Dislocations[END_REF]. Recent studies have been carried out, which aim at coupling models (especially CPFFT) to experiments [START_REF] Hansen | An investigation of geometrically necessary dislocations and back stress in large grained tantalum via EBSD and CPFEM[END_REF][START_REF] Zhang | Datasets for multi-scale diffraction analysis (synchrotron XRD and EBSD) of twinning-detwinning during tensile-compressive deformation of AZ31B magnesium alloy samples[END_REF][START_REF] Pi | Modeling uniaxial tensile deformation of polycrystalline Al using CPFEM[END_REF][START_REF] Di Gioacchino | An experimental study of the polycrystalline plasticity of austenitic stainless steel[END_REF]. Such approaches can provide information on textures, GND density patterning, plastic strain localization and transfer across GBs, etc. Among the results, such coupled modeling-experimental methods show importantly, that it is possible to connect the evolution of microstructures to their Chapter I. Microstructure: a major and complex role in polycrystalline plasticity stress-strain state.

Through the previous overview, it is clear that the deformation of materials is a multiscale and a statistically complex problem of neighborhood (Figure I.5).

Multiscale, because we have to be able to understand the plasticity at every scale where it takes place. Complex because the surrounding microstructure influences the response of the grain, and the combination of all grains gives the macroscopic behavior. On one side, the macroscopic response of a sample is known; on the other side, the operating mechanisms within the grain are well characterized. Knowing what happens in between is very challenging. Moreover, we have no idea whether the reported mechanisms are anecdotal or not, because of low statistic of observations. It is true to say that several laws or models were already proposed. In several cases, they have proven their efficiency for predicting, which operating mechanisms will be activated but there are even more cases where they simply do not work. The technological impact of these ternary compounds does not derive from any single property but rather they achieve a unique combination of properties. Indeed, they combine properties of both ceramics (refractory, high stiffness, low density -4.5 g cm -3 for Ti 3 SiC 2 [START_REF] Barsoum | The MAX Phases: Unique New Carbide and Nitride Materials[END_REF] -, low ductility at room temperature) and metals (high thermal and electric conductivity, thermal shocks resistance, mechanical resistance).

Moreover, several composites of MAX phases and metals allow to elabor complex microstructures for optimizing several properties (electricity, hydrogen storage, etc.) [START_REF] Pi | Processing and Mechanical Properties of Ti2AlC MAX Phase Reinforced AE44 Magnesium Composite[END_REF][START_REF] Yu | Frank partial dislocation in Ti2AlC-MAX phase induced by matrix-Cu diffusion[END_REF][START_REF] Yu | Effects of A-site atoms in Ti 2 AlC and Ti 3 SiC 2 MAX phases reinforced Mg composites: interfacial structure and mechanical properties[END_REF]. But before any industrial exploitation, it is crucial to shed new light on comprehension of deformation mechanisms of these promising materials.

I.2.2 Overview of deformation mechanisms of MAX phases

MAX phases exhibit a Brittle-to-Ductile Transition (BDT) around 800 °C which leads to failure after a very limited plastic regime at room temperature [START_REF] Barsoum | The MN+1AXN phases: A new class of solids[END_REF][START_REF] Zhang | Shear fracture behavior of Ti3SiC2 induced by compression at temperatures below 1000°C[END_REF].

A very intriguing behavior is observed, when MAX samples are subjected to loadunload cycles in the elastic regime: reversible hysteretic loops are recorded [START_REF] Barsoum | Fully reversible, dislocation-based compressive deformation of Ti3SiC2 to 1 GPa[END_REF].

These features are illustrated by the compression stress-strain curve shown in Figure nucleate and expand when load is applied and to collapse when load is removed.

This "reversible" dislocation-based micro-mechanism is invoked to explain the abovementioned energy dissipation observed in the elastic regime and the formation of Kink Band (KB) [START_REF] Barsoum | Fully reversible, dislocation-based compressive deformation of Ti3SiC2 to 1 GPa[END_REF][START_REF] Barsoum | Kinking Nonlinear Elastic Solids, Nanoindentations, and Geology[END_REF]. KBs give rise to misorientation of the lattice with a so-called "stovepipe" shape [START_REF] Forest | Modeling slip, kink and shear banding in classical and generalized single crystal plasticity[END_REF][START_REF] Marano | Intragranular localization induced by softening crystal plasticity: Analysis of slip and kink bands localization modes from high resolution FFT-simulations results[END_REF]. For high deformation, KBs lead to buckling and delamination cracks within individual grains [START_REF] Barsoum | Dislocations, kink bands, and room-temperature plasticity of Ti3SiC2[END_REF]. Besides the fact, that IKBs have never been observed, the observation of open-loops at very low stress somehow contradicts this model involving a critical shear stress needed to overcome the energy barrier associated to dislocation nucleation. In addition, a mechanism, based on atomic-scale ripples in basal layers, called "ripplocation" has been recently invoked for explaining kinking in MAX phases, essentially from atomistic simulations [START_REF] Barsoum | Ripplocations: A universal deformation mechanism in layered solids[END_REF][START_REF] Plummer | On the origin of kinking in layered crystalline solids[END_REF].

However, an aspect for understanding the mechanical behavior of MAX phases is that MAX polycrystals, fabricated by powder metallurgy techniques, exhibit very anisotropic microstructure with grains being highly elongated in the basal plane direction [START_REF] Bei | Pressure-enforced plasticity in MAX phases: from single grain to polycrystal investigation[END_REF]. Considering this feature of MAX phases, it has been shown, by in-situ deformation coupled with neutron diffraction and microscopy observations that the MAX polycrystal can be described as an ensemble of soft and hard grains leading to a high local concentration of non-uniaxial stresses at GBs The reversible hysteretic behavior can therefore be explained by this microstructure anisotropy and the associated Bauschinger effect [START_REF] Bauschinger | Changes of the elastic limit and the modulus of elasticity on various metals[END_REF], i.e. within the classical framework of crystal plasticity in polycrystals [START_REF] Guitton | Effect of microstructure anisotropy on the deformation of MAX polycrystals studied by in-situ compression combined with neutron diffraction[END_REF]. In other words, MAX phase deformation mechanisms usually explained by the IKB model -the reversible hysteretic loops observed, when MAX polycrystals are subjected to elastic load-unload cycles -can be as well explained by the complex response of the very anisotropic microstructure that generate strong variations of microstrains in all grains, even in the elastic regime [START_REF] Guitton | Effect of microstructure anisotropy on the deformation of MAX polycrystals studied by in-situ compression combined with neutron diffraction[END_REF].

It is well established that deformation at room temperature involves dislocation movement [START_REF] Barsoum | Kinking Nonlinear Elastic Solids, Nanoindentations, and Geology[END_REF][START_REF] Guitton | Dislocation analysis of Ti 2 AlN deformed at room temperature under confining pressure[END_REF]; these dislocations are a -type basal dislocations ( -→ b = 1 3 1 1 2 0 ) and glide in the basal plane forming large dislocation pile-ups and walls [START_REF] Barsoum | Kinking Nonlinear Elastic Solids, Nanoindentations, and Geology[END_REF][START_REF] Bei | Pressure-enforced plasticity in MAX phases: from single grain to polycrystal investigation[END_REF].

The latter may interact to form pairs of low-angle tilt GB (or kink boundaries) [START_REF] Barsoum | Dislocations, kink bands, and room-temperature plasticity of Ti3SiC2[END_REF]. According to the KB formation model, mechanical properties of MAX phase materials is thus mainly ascribed to basal plane dislocations, which are able to freely glide without dislocation reactions, allowing dislocation wall formation [START_REF] Barsoum | Fully reversible, dislocation-based compressive deformation of Ti3SiC2 to 1 GPa[END_REF].

Out-of-basal-plane dislocations have been observed by TEM in as-grown Ti 4 AlN 3 [START_REF] Joulain | Revisiting the defect structure of MAX phases: the case of Ti 4 AlN 3[END_REF] and in Ti 3 SnC 2 [START_REF] Tromas | Slip line analysis around nanoindentation imprints in Ti 3 SnC 2 : a new insight into plasticity of MAX-phase materials[END_REF]. These dislocations do not play a key role in the plastic deformation at room temperature in standard deformation conditions. On the contrary, numerous dislocation dipoles, alignments, nodes have been observed in room-temperature-deformed Ti 2 AlN [START_REF] Guitton | Dislocation analysis of Ti 2 AlN deformed at room temperature under confining pressure[END_REF]. Such dislocation reactions may result in the formation of dislocation cells, as observed in Figure I.12 [START_REF] Guitton | Dislocation analysis of Ti 2 AlN deformed at room temperature under confining pressure[END_REF]. The presence of dislocation interactions and networks has to be considered in the comprehension of Chapter I. Microstructure: a major and complex role in polycrystalline plasticity the deformation mechanisms. Dislocations were also observed to align along specific directions leading to segments with screw, 30 • , 60 • or edge character, indicative of an elevated lattice friction [START_REF] Guitton | Dislocation analysis of Ti 2 AlN deformed at room temperature under confining pressure[END_REF][START_REF] Gouriet | Dislocation modelling in Ti 2 AlN MAX phase based on the Peierls-Nabarro model[END_REF]. In addition, it has been recently reported that the specific stacking of M 6 X octahedrons and A-element layers is at the origin of non-Schmid effects [START_REF] Zhan | On the non-classical crystallographic slip in Tin+1AlCn MAX phases[END_REF].

At high temperature, it has been observed that out-of-basal-plane dislocations are not anecdotal events and therefore cross-slip plays a key role in the deformation (see Figure I.13) [START_REF] Guitton | Evidence of dislocation cross-slip in MAX phase deformed at high temperature[END_REF]. This increase of available glide systems (basal, prismatic and pyramidal planes) is likely to promote significant ductility at high temperature. These major changes in the plasticity mechanism are expected to play a key role in the appearance of the BDT with temperature notably with respect to the decrease of the yield strength with increasing temperature [START_REF] Guitton | Evidence of dislocation cross-slip in MAX phase deformed at high temperature[END_REF]. Note also that evidences of Adapted from [START_REF] Guitton | Evidence of dislocation cross-slip in MAX phase deformed at high temperature[END_REF].

Chapter I. Microstructure: a major and complex role in polycrystalline plasticity

I.3 Towards the influence of strain-path changes on metal plasticity

I.3.1 Strain-path changes

For some metals, plastic strain increases the stress required to continue the deformation. This phenomenon is called strain hardening. But when deformation is stopped, reversed or continued in other direction, the situation becomes more complex and less predictable. One could expect that a dislocation pile-up created during the first straining direction might partially or fully relax. Subsequent straining in another direction will cause new dislocation pile-ups. Therefore, it has become clear that the strain path can have important influences on the microstructural evolution.

Because the structure-property relation is multiscale, an in-depth understanding requires a multiscale experimental approach. Such was the background of my postdoctoral research. Our main objective was to investigate what happens in metallic materials if the strain occurs in different directions or changes during deformation.

Such questions could not be clarified using previously available methods and are for instance important for the production processes in the automotive sector. Furthermore, the project also developed new methods that can be used to study materials at large-scale facilities, such as the Swiss light source at the PSI.

I.3.2 Development of a novel biaxial machine

Most of the knowledge on mechanical behavior has been derived from conventional uniaxial tests. However industrial production of metallic components consists in many strain-path changes, which modify drastically their mechanical response. In

I.I.3 Towards the influence of strain-path changes on metal plasticity

this framework, in-situ experiments can give valuable insights on deformation mechanisms which could appear or could be modified during strain-path changes.

In-situ mechanical testing under x-ray powder diffraction has become a frequently applied research method to study elastic and plastic anisotropy of metals, the evolution of microstructure and intergranular stresses, load transfer in multiphase materials, mechanical driven phase transformations etc. . . By taking the lattice as a strain gauge i.e. using the position of the Bragg peaks, the evolution of lattice strain is measured for individual grain families averaged over thousands of grains [START_REF] Van Swygenhoven | In-situ mechanical testing during X-ray diffraction[END_REF]. A few decades ago, in-situ mechanical testing was usually performed using optical microscopy. However, the low resolution and the small depth focus Such development was very challenging because of numerous constraints. Finally, it was a success in its own. The proof-of-principle was obtained at the end of my postdoctoral stay. Our in-situ x-ray diffraction experiments revealed that the

I.I.3 Towards the influence of strain-path changes on metal plasticity

developed rig operates successfully [START_REF] Van Petegem | A miniaturized biaxial deformation rig Bibliography for in-situ mechanical testing[END_REF]. This opened up new research frontiers on complex biaxial strain path changes and the continuation of the ERC project of Prof. Helena Van Swygenhoven.

Chapter I. Microstructure: a major and complex role in polycrystalline plasticity

Chapter II

Contribution of electron microscopy

Mechanical tests followed by microstructural investigations provide information to computationally predict mechanical performances of components. Electron microscopy is one of the most well-known techniques for analyzing deformation features of materials for allowing to understand their response to exterior solicitations. Two kinds of electron microscopes are generally used and bring complementary information: at macro/meso-scopic scale, the SEM [START_REF] Reimer | Scanning Electron Microscopy[END_REF] and at micro/nano-scale, the TEM [START_REF] Williams | Transmission Electron Microscopy[END_REF].

II.1 Overview of electron microscopes

II.1.1 Transmission Electron Microscope

The TEM is one of the most well-known techniques for both observing and characterizing dislocations on one hand, at the sub-micron, and on the other hand, at the nano-scale, and more generally deformation defects in electron transparent thin foils (thickness of ≈ 100 nm [START_REF] Ayache | Sample Preparation Handbook for Transmission Electron Microscopy[END_REF]). Preparation of such a thickness is both an art and a science. It needs devising suitable methods, as well as realizing/demonstrating them in a defined process with reproducibility. Also, utmost care is necessary in preparing and handling specimens, as they are extremely thin and hence prone to bending and breaking.

Determining the Burgers vector -→ b of dislocation consists in obtaining two diffracting vectors (or -→ g ) that put the observed dislocations out of contrast by tilting the lamella (necessary and sufficient condition) [START_REF] Williams | Transmission Electron Microscopy[END_REF]. Mathematically, extinction

Chapter II. Contribution of electron microscopy

conditions for a dislocation are given by [START_REF] Williams | Transmission Electron Microscopy[END_REF]:

- → g • - → b = 0 ; - → g • - → b × - → u = 0 (II.1)
The line direction -→ u is defined as the intersection of non-parallel planes containing the dislocation. It can be determined from the observations of the dislocation in different orientations of the thin foil. Note that for a stacking fault with -→ R as fault vector, the extinction condition is [START_REF] Williams | Transmission Electron Microscopy[END_REF]:

- → g • - → R = 0 (II.2)
Such after-deformation or post-mortem comprehensive dislocation studies at microscopic scale bring valuable information for extrapolating to the macroscopic response of materials and they can feed advanced numerical multiscale models [START_REF] Yu | Frank partial dislocation in Ti2AlC-MAX phase induced by matrix-Cu diffusion[END_REF][START_REF] Gouriet | Dislocation modelling in Ti 2 AlN MAX phase based on the Peierls-Nabarro model[END_REF].

Among the difficulties encountered, here is that most of our detailed knowledge has been extracted from post-mortem observations. In-situ mechanical testing combined with TEM is required for studying the instantaneous evolution of defects during exposure to stress. Such an experiment allows capturing footprints of deformation mechanisms responsible for the changing microstructure [START_REF] Legros | In situ mechanical TEM: Seeing and measuring under stress with electrons[END_REF][START_REF] Legros | Dynamic observation of Al thin films plastically strained in a TEM[END_REF][START_REF] Mompiou | In situ TEM observations of reverse dislocation motion upon unloading in tensiledeformed UFG aluminium[END_REF][START_REF] Mompiou | Inter-and intragranular plasticity mechanisms in ultrafine-grained Al thin films: An in situ TEM study[END_REF]. Although various approaches of mechanical testing inside a TEM exist today [START_REF] Legros | In situ mechanical TEM: Seeing and measuring under stress with electrons[END_REF][START_REF] Legros | Dynamic observation of Al thin films plastically strained in a TEM[END_REF][START_REF] Mompiou | In situ TEM observations of reverse dislocation motion upon unloading in tensiledeformed UFG aluminium[END_REF], in-situ TEM mechanical testing is experimentally very tough [START_REF] Yu | In situ TEM nanomechanics[END_REF]. In addition to the difficult control of deformation conditions, the space available is generally less than one centimeter and statistics on physical mechanisms is very weak. TEM needs an electron transparent specimen with a thickness of ≈ 100 nm with a useful field of view of few µm 2 . It is usually said that if one is able to assemble all zones studied by TEM since its development in the forties, they would not even fill a thimble. Therefore, fundamental questions on the representativeness of observed phenomenon must be raised, when extrapolating discussions to a millimeter-size specimen.

II.II.1 Overview of electron microscopes

II.1.2 Scanning Electron Microscope

Unlike TEM described in the previous part, SEM can both image and analyze bulk samples. Various information can be deduced from the analysis of signals (electrons and photons) emitted by the sample through the electron-matter interaction and coming from different depths. The affected volume is called "interaction pear" [START_REF] Reimer | Scanning Electron Microscopy[END_REF].

II.1.2.1 SEM imaging

Information on surface topography is provided by Secondary Electrons (SE), their energy is low. SE detectors are located either in the column or in the chamber.

BackScattered electrons (BSE), with an energy comparable to the primary beam, give crystallographic information and they are linked to the chemistry of the material. They are used to generate orientation or even phase contrast micrographs on mirror polished sample.

II.1.2.2 Electron backscatter diffraction

Electron BackScatter Diffraction (EBSD) is a SEM technique providing quantitative microstructural information on the crystallographic nature of most crystalline materials (metals, minerals, semiconductors, ceramics). It enables to determine crystallographic orientations, grain size, misorientations at GB and the different phases of the material [START_REF] Rollett | Three-Dimensional Characterization of Microstructure by Electron Back-Scatter Diffraction[END_REF][START_REF] Allain-Bonasso | A study of the heterogeneity of plastic deformation in IF steel by EBSD[END_REF][START_REF] Barbier | EBSD for analysing the twinning microstructure in fine-grained TWIP steels and its influence on work hardening[END_REF][START_REF] Kalácska | 3D HR-EBSD Characterization of the plastic zone around crack tips in tungsten single crystals at the micron scale[END_REF] The sample is mounted in the SEM chamber, where the primary beam of electrons is focused on the studied area. The BSEs within the sample will be diffracted, if they are in Bragg incidence with the reflecting planes. For {h k l}, electrons diffract according to two diffraction cones, which are symmetrical with respect to the (h k l) plane. The projection of these cones on the phosphorescent screen of the EBSD camera produces quasi-parallel hyperbolic lines similar to straight lines forming a band of Kikuchi [START_REF] Nishikawa | Diffraction of Cathode Rays by Mica[END_REF]. The median axis of this band corresponds to the trace of the (h k l) plane. The band pattern generates a diagram of Kikuchi, where angles between bands correspond to angles between crystal planes. Thus, automatic indexing of this diffraction pattern enables to determine crystallographic orientation

Chapter II. Contribution of electron microscopy

of grains. It should be noted that the sample is tilted at 70°from the horizontal in order to optimize the BSE yield.

Each point or area of the sample, impacted by the electron beam, produces a Kikuchi pattern related to its crystallographic orientation. Recent cameras and acquisition software allow recording about 1600 points per second, making EBSD the fastest method for determining crystallographic orientation. In terms of resolution, EBSD has a spatial resolution between 20 and 70 nm. This resolution depends on the material and the accelerating voltage of the electrons. For example at 20 kV, it is around 50 nm for steel. Concerning angular resolution, it is approximately 0.05°(Oxford Instruments System). However, EBSD is limited in absolute angular resolution: the orientation of the crystal relative to the optical axis of the microscope is given from 1°to 2° [START_REF] Humphreys | Grain and subgrain characterisation by electron backscatter diffraction[END_REF]. This uncertainty is due to the specific geometry the technique (sample inclination at 70°).

In addition, one of the advantages of EBSD is the measurement of local misorientation, from which it is possible to estimate GND density [START_REF] Ernould | Global DIC approach guided by a cross-correlation based initial guess for HR-EBSD and on-axis HR-TKD[END_REF][START_REF] Kalácska | Comparison of the dislocation density obtained by HR-EBSD and X-ray profile analysis[END_REF][START_REF] Ernould | Integrated correction of optical distortions for global HR-EBSD techniques[END_REF]. The latter can be represented in the form of a map. GND density, ρ GN D , is calculated by:

ρ GN D = Cβ - → b δx (II.3)
where

• C is a constant;

• β is the misorientation;

• δx is the step size used for the mapping.

II.II.2 From electron channeling contrast imaging to accurate electron channeling contrast imaging

II.2 From electron channeling contrast imaging to accurate electron channeling contrast imaging

Full characterization of crystalline defects is not only possible by performing TEM experiments on thin foil samples. SEM can access diffraction contrast on bulk materials with the phenomenon of electron channeling [START_REF] Reimer | Scanning Electron Microscopy[END_REF].

Electron channeling is due to electrons that channel down crystal planes i.e.

paths, where electrons can penetrate to a higher depth before scattering (Figure II.1). Some orientations of the crystal will backscatter more electrons than others, giving rise to orientation contrast. Due to these limitations, the ECP/SACP technique has been over-shadowed by the development of EBSD pattern analysis, which offers high spatial resolution (about 30 nm) and very high data acquisition rates. Nevertheless, EBSD provides orientations on high tilted crystals (about 70°), and does not readily give the orientation with respect to the incident beam, which leads to absolute angular resolution limited to about 1°-2° [START_REF] Humphreys | Grain and subgrain characterisation by electron backscatter diffraction[END_REF]. This makes it difficult to set up specific channeling conditions and thus to observe defects with high contrast and carry out quantitative studies.

Despite this, an alternative approach using EBSD orientation analysis to predict the specimen stage tilts and rotations necessary to bring a crystal into optimum channeling conditions, known as Controlled Electron Channeling Contrast Imaging (cECCI) [START_REF] Gutierrez-Urrutia | Electron channeling contrast imaging of twins and dislocations in twinning-induced plasticity steels under controlled diffraction conditions in a scanning electron microscope[END_REF]. However, due to EBSD uncertainties, the exact deviation from the Bragg condition cannot be assessed and it remains difficult to achieve optimum contrast of defects.

To overcome these challenges, Guyon et can be obtained via specimen stage tilts and rotations allowing to carry out TEM style contrast analysis for dislocation characterization in fine grained bulk materials [START_REF] Mansour | Accurate electron channeling contrast analysis of dislocations in fine grained bulk materials[END_REF][START_REF] Ben Saada | Multiscale approach for analyzing sub-boundaries induced during dislocational creep of uranium dioxide[END_REF]. The first results obtained using this HR-SACPs assisted Accurate-ECCI ECCI is based on the fact that the BSE yield depends on the orientation of the crystal relative to the incident electron beam i.e. optic axis of the SEM [START_REF] Booker | Some comments on the interpretation of the 'kikuchi-like reflection patterns' observed by scanning electron microscopy[END_REF]. That is why, strain and defects, distorting crystal planes, produce changes in BSE intensity (I BSE ), leading to a contrast on a micrograph.

To understand the origin of ECCI contrasts, the dynamical theory of diffraction in 2-wave condition was adapted from the one of TEM [START_REF] Reimer | Scanning Electron Microscopy[END_REF][START_REF] Williams | Transmission Electron Microscopy[END_REF][START_REF] Reimer | Transmission Electron Microscopy[END_REF]. Inside the crystal, electron beams are described by a superposition of Bloch waves. The different inelastic scattering events are divided into two categories: those scattered with angles (with respect to the incident beam) less than 90°(forward scattering) and those scattered at angles higher than 90°(back-scattering) [START_REF] Reimer | Scanning Electron Microscopy[END_REF]. In the multiple scattering model, the back-scattered and forward scattered wave are allowed to interact with each other.

By using the same model based on Bloch waves, simulations of I BSE profiles done by Spencer et al. [START_REF] Spencer | A dynamical theory for the contrast of perfect and imperfect crystals in the scanning electron microscope using backscattered electrons[END_REF] and Wilkinson et al. [START_REF] Wilkinson | Electron diffraction based techniques in scanning electron microscopy of bulk materials[END_REF] and their comparisons with experiments show that such profiles correspond to a white band with dark

Chapter III. Physics of ECCI and optimization of experimental conditions

edges, in the case of a perfect crystal. The same approach was also used by Reimer [START_REF] Reimer | Scanning Electron Microscopy[END_REF][START_REF] Reimer | Kikuchi band contrast in diffraction patterns recorded by transmitted and backscattered electrons[END_REF] for a perfect crystal, where multiple diffusions are treated as incoherent.

III.1 Perfect crystal

In a crystal, the wave function Ψ is a solution of the time-independent equation of Schrödinger [START_REF] Schrödinger | An Undulatory Theory of the Mechanics of Atoms and Molecules[END_REF], where the atomic potential is written as a Fourier series on the nodes, -→ h , of the reciprocal lattice [START_REF] Reimer | Scanning Electron Microscopy[END_REF]:

∇ 2 Ψ + 2m e 2 E - h V h e 2π i -→ h • -→ r Ψ = 0 (III.1)
where:

• m e : mass of an electron;

• E: kinetic energy of an electron;

• -→ r : position vector;

• V h : complex Fourier coefficients.

In the formalism of Bloch waves, Ψ is given by [START_REF] Reimer | Scanning Electron Microscopy[END_REF]:

Ψ ( - → r ) = i ε (j) g C (j) g e 2π i --→ k (j) 0 + -→ g • -→ r e -2πq (j) z (III.2)
where:

• (j) : the j-th wave;

• ε (j) : excitation amplitude of the Bloch wave Ψ (j) ;

• C (j) g : amplitude of diffracted waves with a wave vector

-→ k (j) g = -→ k (j) 0 + - → g ; • -→ k (j)
0 : wave vector of the j-th primary wave;

• -→ g : diffraction vector;

III.III.1 Perfect crystal

• q (j) : attenuation parameter expressing the exponential attenuation of the wave amplitude with increasing depth z .

In order to determine the coefficients of the Bloch function, in equation III.2, the two-beam condition is used i.e. only one set of planes is in channeling condition.

Experimentally, such condition is satisfied when the incident beam is far from any intersections of pseudo-Kikuchi bands [START_REF] Kriaa | Fundamental and experimental aspects of diffraction for characterizing dislocations by electron channeling contrast imaging in scanning electron microscope[END_REF].

The BSE signal of a slice of a thickness d z, located at a depth z, is given by [START_REF] Reimer | Scanning Electron Microscopy[END_REF]:

d η d z = N σ B   Ψ * Ψ +   1 - j |C (j) 0 | 2 e -4πq (j) z     (III.3)
where:

• N : atom number per unit of volume;

• σ B : cross section of backscattering;

• Ψ * Ψ: probability for the Bloch wave to be backscattered at a depth z;

• the last term in parentheses in equation III.3 describes the electrons that are removed from the Bloch wave field by scattering before reaching the slice d z.

The BSE coefficient (η OC ) is proportional to I BSE . It is obtained by integrating the equation III.3 in the total depth of interaction, i.e. between z = 0 and z → +∞.

The subscript OC refers to the total I BSE due to the orientation contrast, while both contributions due to atomic number and surface inclination are not taken into account [START_REF] Reimer | Scanning Electron Microscopy[END_REF]:

I BSE ∝ η OC = N σ B 4π ξ 0      - ω + ξ 0 ξ g 1 + ω 2 - ξ 0 ξ g 2 + ω 1 + ω 2 + (1 + ω 2 ) ξ 0 ξg 2      (III.4)
where:

• ξ 0 and ξ g : absorption lengths;

Chapter III. Physics of ECCI and optimization of experimental conditions

• ξ g : extinction distance;

• ω = sξ g = g(θ -θ B )ξ g : tilt parameter ;

III.III.2 Imperfect crystal

III.2 Imperfect crystal

III.2.1 Planar defects

In addition to dislocations, GBs and SFs play a crucial role in plasticity as well. As first approximation, they can be considered as planar defects.

An interface separates a crystal into two distinct regions. Generally, one defines the upper crystal as fixed and the lower one as shifted by a vector -→ R ( -→ r ) and inclined at an angle β around an axis -→ v . In order to simplify, we restrict our study, on the one hand, to the specific cases of translation boundaries (i.e. β = 0) such as SFs, and on the other and, to flat interfaces (i.e. parallel to a crystallographic plane), such as coherent TBs. Note that a coherent TB can be described as cumulative SFs (each of them translating the crystal of

- → R ) on adjacent planes. Therefore, - → R ( - → r )
is not constant moving away from the TB plane (but constant along it), thus giving a -→ R ( -→ r ) not directly connected to the crystal lattice.

III.2.1.1 Theoretical approach

Let us assume that an isolated inclined planar defect (angle ζ from the surface) separates a perfect upper crystal with a translated lower one, as schematized in

Chapter III. Physics of ECCI and optimization of experimental conditions

Atoms in the lower crystal are translated collectively by a vector -→ R (assumed to be constant along the plane of the defect i.e.

- → R ( - → r ) = - → R
) with respect to the upper crystal. It is convenient to introduce another modified tilt parameter, ω , such as [START_REF] Kriaa | Modelling Electron Channeling Contrast Intensity of Stacking Fault and Twin Boundary Using Crystal Thickness Effect[END_REF]:

ω = ω + ω DP = ω + - → g • - → R ξ g (III.5)
Therefore, ω DP is the tilt parameter due to the translation of the lower crystal with the upper one. Note that ω DP is null in the upper crystal.

For a column localized at a position x, whose inclined planar defect is at a depth z DP , the BSE intensity is given by [START_REF] Kriaa | Modelling Electron Channeling Contrast Intensity of Stacking Fault and Twin Boundary Using Crystal Thickness Effect[END_REF]:

η tot (ω) = z DP 0 ∂η(ω, z) ∂z d z + ∞ z DP ∂η(ω , z) ∂z d z = η sup (ω) + η inf (ω ) = z DP 0 ∂η(ω, z) ∂z d z + ∞ 0 ∂η(ω , z) ∂z d z - z DP 0 ∂η(ω , z) ∂z d z = η sup (ω) + η inf (ω ) -η inf (ω ) (III.6)
where:

• η sup : contribution of the upper crystal with an equivalent thickness of z DP ;

• η inf : contribution of the translated lower crystal with an infinite thickness;

• η inf : contribution of the lower crystal with an infinite thickness;

• η inf : contribution of the lower crystal with an equivalent thickness of z DP .

From Figure III.2, z DP is given by:

z DP = x tan(ζ) (III.7)
where:

III.III.2 Imperfect crystal

• x: abscissa, where I BSE is calculated. Origin is taken at the intersection of the planar defect with the surface;

• ζ: angle between the planar defect and the surface of observation.

The term η sup in equation III.6 is the contribution to I BSE of the upper crystal with a thickness of z DP . By considering equation III.7, all displacement along x leads to an increase of z DP , and then, the thickness of the upper perfect crystal.

Analytically, we can note that η sup is written as:

η sup (ω, z DP ) = z DP 0 ∂η(ω) ∂z d z = η OC (ω) + T (ω, z DP )
with lim

z DP →∞ T (ω, z DP ) = 0 (III.8)
where:

• η OC : BSE coefficient independent of z DP . Its expression is given by equation III.4;

• T : term of the BSE signal dependent on ω and z DP . • -→ g • -→ R = 0: the curve is constant and no contrast is distinguished from the background. Such condition corresponds to the extinction condition of SF.

Note that it is similar to that one in TEM (equation II.2).

III.III.2 Imperfect crystal

It is important to note, that a coherent TB is a particular GB with very low

III.2.2 Dislocations and their configurations

Let us consider a column at the distance x from a dislocation, localized at x = 0, at the depth z = z D , with a line parallel to the surface (Figure III.6).

Chapter III. Physics of ECCI and optimization of experimental conditions

Contrary to SFs, -→ R for dislocations is not constant but it depends on (x, z) [START_REF] Hirth | Theory of Dislocations[END_REF].

Hence, -→ R , at the depth z D can be written in series of Taylor:

- → R (x, z) = - → R (x, z D ) + ∂ - → R (x, z D ) ∂z (z -z D ) (III.
s = s exp + s D with s D = - → g • ∂ - → R ∂z z=z D (III.10)
s exp is the deviation from the exact Bragg position in a perfect crystal and it can be measured experimentally [START_REF] Kriaa | Fundamental and experimental aspects of diffraction for characterizing dislocations by electron channeling contrast imaging in scanning electron microscope[END_REF]. The dot product -→ g • ∂ -→ R ∂z z=z D represents the deviation s D due to the variations of the angle between the primary beam and the

III.III.2 Imperfect crystal

distorted planes around the dislocation core. Far from the dislocation, the crystal is seen as perfect i.e. the deviation s D becomes null. By substituting s by s in equation III. [START_REF] Hirth | Theory of Dislocations[END_REF], we can take into account the effect of the presence of a dislocation line on the intensity profile, given by:

I BSE ∝ N σ B 4π ξ 0      - (s exp + s D (x) z=z D ) ξ g + ξ 0 ξ g 1 + (s exp + s D (x) z=z D ) 2 ξ 2 g - ξ 0 ξ g 2      + N σ B 4π ξ 0    (s exp + s D (x) z=z D ) ξ g 1 + (s exp + s D (x) z=z D ) 2 ξ 2 g + 1 + (s exp + s D (x) z=z D ) 2 ξ 2 g ξ 0 ξg 2    (III.11)
Therefore, with equation III.11, it is possible to study the variations of I BSE with x (distance from the dislocation core).

III.2.2.1 Screw dislocation

At a distance x from the dislocation core (localized at x = 0), crystalline planes are distorted. The displacement field, -→ R screw is given in cartesian coordinates by [START_REF] Hirth | Theory of Dislocations[END_REF]:

- → R screw = - → b 2π tan -1 z -z D x (III.12)
The derivative of -→ R screw respect with the depth z, at the vicinity of the turning point (z = z D ) is given by: contrast. Moreover, when changing from -→ g to --→ g , these extrema are inverted: peak becomes hollow, and vice-versa.

  d - → R screw d z   z=z D =      - → b 2πx 1 + z-z D x 2 2      z=z D = - → b 2πx (III.

III.2.2.2 Edge dislocation

For an edge dislocation parallel to the surface, it is analogous to the case of a screw dislocation. Intensity profiles are similar, as well. However, -→ R edge is written as [START_REF] Hirth | Theory of Dislocations[END_REF]:

- → R edge = - → b β 2π β + sin 2β 2(1 -ν + - → b ∧ - → u 2π 1 -2ν 2(1 -ν) ln |r| + cos 2β 4(1 -ν) (III.14)

III.2.2.3 Extinction conditions

Theoretical calculations allow to demonstrate the extinction conditions well-known in microscopy (equation II.1). Note that such criteria are experimentally applicable for ECCI but they were not proved theoretically. Calculated dislocation intensity Despite this undeniable limitation, ECCI has the major advantage of providing access to a large regions of interest, allowing more statistically relevant studies to be carried out. Some examples will be presented in the following chapters.

Chapter IV

Evolution of crystalline defects close to a real interface

Most of our detailed knowledge on dislocation-interface interactions are extracted from in and/or ex-situ TEM [START_REF] Kondo | Direct observation of individual dislocation interaction processes with grain boundaries[END_REF][START_REF] Kacher | Quasi-four-dimensional analysis of dislocation interactions with grain boundaries in 304 stainless steel[END_REF]. However, these studies have drawbacks, such as areas of observation limited to a few tens of µm 2 and modification of the microstructures due to the preparation of a thin foil [START_REF] Ayache | Sample Preparation Handbook for Transmission Electron Microscopy[END_REF][START_REF] Kohnert | On the use of transmission electron microscopy to quantify dislocation densities in bulk metals[END_REF]. Besides TEM, in-situ mechanical testing coupled with x-ray diffraction (particularly Laue microdiffraction) [START_REF] Maaß | In situ Laue diffraction of metallic micropillars[END_REF][START_REF] Malyar | Dislocationtwin boundary interaction in small scale Cu bi-crystals loaded in different crystallographic directions[END_REF] or with EBSD can provide features of operating mechanisms that can feed full-field models [START_REF] Richeton | Modelling the transport of geometrically necessary dislocations on slip systems: application to single-and multi-crystals of ice[END_REF]. However, both techniques are sensitive to variations of GND density only [START_REF] Van Swygenhoven | In-situ mechanical testing during X-ray diffraction[END_REF] and particularly for Laue microdiffraction, it requires devising techniques for sample preparation [START_REF] Guitton | Picosecond pulsed laser for microscale sample preparation[END_REF]. Therefore, one part of the problem is passed over in silence (i.e. SSD).

It is clear that current techniques have reached their limits. We have to deal with the following conflict: if the technique (Laue or EBSD) is statistically representative, some information will be missing and if the technique allows capturing all the information (TEM), its statistical representativeness will be very low. Therefore, full comprehension of dislocation-interface interactions requires a new experimental approach, in order to study localized deformation in the vicinity of an interface and to characterize evolution of microstructures.

These studies were initiated at the end of the doctoral work of Hana Kriaa linked to the nucleation of dislocations [START_REF] Bahr | Nanoindentation: Localized Probes of Mechanical Behavior of Materials[END_REF]. Proposed mechanisms suggest homogeneous nucleation of dislocations, activation of sources of dislocations, rupture of a surface film or interaction of a film with the underlying dislocation structure. Thus, the pop-in is seen as the event, which marks the sudden transition from an elastic regime to a continuous elastoplastic regime. In addition, the complex interactions of stress fields due to configurations of dislocations and indentation account for the large scatter in the measured value of the pop-in load P [START_REF] Habiyaremye | Influence of the configurations of dislocations on the pop in load during nanoindentation in a CrCoNi medium entropy alloy[END_REF].

The elastic part of the nanoindentation curve i.e. before pop-in, can be described by the Hertz theory of contact [START_REF] Hertz | Ueber die Berührung fester elastischer Körper[END_REF][START_REF] Lawn | Indentation of Ceramics with Spheres: A Century after Hertz[END_REF]. This theory models the elastic contact between a sphere and a plane by assuming elastic deformation and very small penetration depth respect with the contact radius. Therefore, F is related to the penetration depth h as follows [START_REF] Bahr | Nanoindentation: Localized Probes of Mechanical Behavior of Materials[END_REF]:

F = 4 3 E * a 1 2 h 3 2 (IV.1)
where:

• E * : reduced elastic modulus given by:

1 E * = 1 -ν 2 i E i + 1 -ν 2 s E s (IV.2)
with E and ν are the elastic modulus and Poisson's ratio respectively. Subscripts i and s refer to the indenter and the sample respectively.

• a: radius of a spherical indenter.

IV.1.2 Procedure for studying deformation mechanisms in the vicinity of a real GB

The first step consists in selecting the GB of interest and characterizing it by EBSD.

Initial crystalline defects are also characterized by A-ECCI before deformation. Note that in the case of LAGBs, A-ECCI is the most adapted technique for observing them in standard conditions.

As soon as the GB is well characterized, localized deformation tests are performed near the GB by nanoindentation using a Berkovich tip i.e. a triangle-based pyramid. A network of indents can therefore be programmed.

In order to easily localize the indent network, indents are high load (20 mN) are programmed as horizontal and vertical lines at about 100 µm from the network of interest. These indents are clearly visible with SEM. Finally, some indents are observed by A-ECCI. Note that because of low loads, residual indents of interest are very small i.e. about few tens of nm. By following this procedure, it is now possible to link local mechanical properties with the evolution of microstructures near GBs.

In the next parts, we will focus on two cases: Mainly two of them are ordered at room temperature: γ as the major phase and α 2 as a minor phase.

IV.IV.2 Deformation mechanisms near a twin boundary in a

Chapter IV. Evolution of crystalline defects close to a real interface

• The α 2 phase is hexagonal with a DO19 structure. (0 0 0 1) planes have the Ti 3 Al composition but along a normal direction to (1 1 2 0), a substructure appears and it can be defined as a staking of an alternation of Ti planes and TiAl planes;

• the γ phase is tetragonal with a L10 structure. It can be described as a stacking Among these microstructures, FL alloys have the best high temperature performances, whereas DP alloys are suitable for balanced properties between room temperature plasticity and high strength and good creep resistance at high temperature.

IV.IV.2 Deformation mechanisms near a twin boundary in a TiAl alloy

IV.2.2 Deformation mechanisms of TiAl based alloys

In dual phase TiAl alloys, plastic deformation mainly occurs on the {1 1 1} planes of the γ phase [START_REF] Marketz | Deformation mechanisms in TiAl intermetallics-experiments and modeling[END_REF] by dislocation glide and it is strongly related to the ordered In the α 2 phase, the possible slip modes are {1 0 1 0} 1 2 1 0 prism slip, (0 0 0 1) 1 2 1 0 basal slip and pyramidal 1 1 2 6 -slip with very different values of critical shear stress [START_REF] Marketz | Deformation mechanisms in TiAl intermetallics-experiments and modeling[END_REF].

This brief overview shows that deformation mechanisms of TiAl-based alloys are very complex, because many fields of materials science are necessary for exploring their behaviors. The strong interplay between phases, microstructures, crystallography and chemistry forces researchers to carry out studies at different scales for taking advantages of these marvelous compounds.

IV.2.3 Evolution of microstructures near a twin boundary

The region in ) is observed as well. No good channeling conditions were reachable in grain B, so that dislocations were not fully characterized. In many materials, such pile-up areas are associated to canalization of deformation, generally originating in the accommodation of twins [START_REF] Hirth | Theory of Dislocations[END_REF] or KB [START_REF] Bei | Pressure-enforced plasticity in MAX phases: from single grain to polycrystal investigation[END_REF]. Although the accommodation of twins • Under the indent, the [1 1 2] (1 1 1) NT is formed.

IV.IV.2 Deformation mechanisms near a twin boundary in a TiAl alloy

• The stress concentration at the tip of the [1 1 2] (1 1 1) NT causes nucleation of ordinary ± 1 2 [1 1 0] dislocation loops gliding in (1 1 1) plane. It thus forms an ellipsoid surrounding the NT to form a pile-up area.

• The pile-up expends by adding dislocation loops at its extremity.

• Then, the pile-up extends until it encounters an obstacle, such as a TB.

• At the interception between B2 and the TB, a stress concentration appears thus causing a local deformation of this interface.

In summary, nanoindentation tests combined with A-ECCI observations before and after deformation have been able to shed new light on deformation mechanisms of Ti-Al alloys:

• At room temperature, twinning appears to be the main mechanism to accomodate plastic strain.

• A TB is an obstacle to the propagation of the deformation leading to stress concentration at the intersection with TB. For higher loads, it can lead to micro-cracking [START_REF] Simkin | A factor to predict microcrack nucleation at γ-γ grain boundaries in TiAl[END_REF][START_REF] Zambaldi | Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation[END_REF][START_REF] Bieler | Fracture initiation/propagation parameters for duplex TiAl grain boundaries based on twinning, slip, crystal orientation, and boundary misorientation[END_REF].

IV.IV.3 Study of fundamental deformation mechanisms near a low-angle grain boundary in a medium entropy alloy

IV.3 Study of fundamental deformation mechanisms near a low-angle grain boundary in a medium entropy alloy IV.3.1 Presentation of high and medium entropy alloys

Medium Entropy Alloys (MEA) and High Entropy Alloys (HEA) consist of two to four and at least five elements, respectively, with almost equiatomic concentrations [START_REF] Gao | High-Entropy Alloys[END_REF][START_REF] Yeh | High-Entropy Alloys -A New Era of Exploitation[END_REF]. Among these new classes of materials, CrMnFeCoNi and one of its ternary equiatomic derivatives, CrCoNi, are currently attracting increasing interest in literature [START_REF] Wu | Temperature dependence of the mechanical properties of equiatomic solid solution alloys with facecentered cubic crystal structures[END_REF][START_REF] Ming | Strength and ductility of CrFeCoNiMo alloy with hierarchical microstructures[END_REF]

Chapter IV. Evolution of crystalline defects close to a real interface

One of the explanations for the exceptional damage tolerance of CrCoNi is its low stacking fault energy (∼ 22 mJ m -2 [START_REF] Laplanche | Reasons for the superior mechanical properties of medium-entropy CrCoNi compared to high-entropy CrMnFeCoNi[END_REF]) and its high shear modulus [START_REF] Laplanche | Processing of a single-crystalline CrCoNi medium-entropy alloy and evolution of its thermal expansion and elastic stiffness coefficients with temperature[END_REF], of defects [START_REF] Pöhl | Pop-in behavior and elastic-to-plastic transition of polycrystalline pure iron during sharp nanoindentation[END_REF]. It is interesting to notice that the three imprints the nearest to the LAGB (n°: 5, 4 and 3) either do not show any pop-in ( 4 and 5), or have pop-in load lower than the mean value ( 3). Consequently, a detailed comparison of the evolution of the microstructures before and after deformation for these indents is required in order to establish a relation with their local mechanical behavior. It is interesting to note that imprints 5 and 4 on and near the LAGB in the subgrain A, respectively, do not show pop-in and deviate at low loads from the Hertz law (equation IV.1), even if they show changes in their microstructure after nanoindentation. For imprint 4, the absence of pop-in can be related to the subsurface structure of LAGB dislocations. Indeed, if the LAGB is inclined towards the nanoindentation axis below the sample surface and deeper than the extinction depth of the ECCI (≈100 nm), the stress field under the indenter may have interacted with the inclined LAGB dislocations. Therefore, plasticity is accommodated by glide and multiplication of these pre-existing LAGB dislocations.

thus

IV.IV.3 Study of fundamental deformation mechanisms near a low-angle grain boundary in a medium entropy alloy

It has been proposed in HEA-MEA literature that the dendritic microstructure of single crystals and especially their LAGB density, resulting from different processing routes and parameters, may be at the origin of the significant dispersion observed for the CRSS of HEA and MEA of the Cr-Mn-Fe-Co-Ni system [START_REF] Kawamura | Plastic deformation of single crystals of the equiatomic CrMnFeCoNi high-entropy alloy in tension and compression from 10 K to 1273 K[END_REF]. In the present study, our observations at the dislocation scale clearly confirm these hypotheses and show that even a LAGB with a very small disorientation angle of ≈0.24°profoundly modifies the local micromechanical response and deformation mechanisms.

Chapter V

Mesoscale and statistical comparison between polycrystalline plasticity models and experiments

In metals, elementary mechanisms, such as dislocation glide, operate at the atomic scale or even at the electronic scale; typically, ångström and picosecond. These mechanisms can strongly influence the macroscopic response at the laboratory scale, i.e. centimeter and second. For example, ab-initio simulations of dislocation cores in BCC metals have shown non-Schmid effects, which could explain an asymmetry between traction and compression at the macroscopic scale [START_REF] Ismail-Beigi | Ab Initio Study of Screw Dislocations in Mo and Ta: A New Picture of Plasticity in bcc Transition Metals[END_REF][START_REF] Rodney | Ab initio modeling of dislocation core properties in metals and semiconductors[END_REF][START_REF] Li | Dislocation-core symmetry and slip planes in tungsten alloys: Ab initio calculations and microcantilever bending experiments[END_REF].

To understand and ultimately control the mechanical behavior of metallic materials with respect to their microstructures, one has to face this incredibly complex multiscale problem that can extend over more than 10 orders of magnitude over time and in space. This is why, advanced theoretical and experimental tools are

V.1.1 Specimen geometry

Bulk specimen were cut from a 1.78 mm thick rolled sheet of β-Ti21S alloy provided by Titanium Metals Corporation (Toronto, ON, Canada). The exact chemical composition of the material is Ti-15.97Mo-2.79Nb-2.99Al-0.26Fe-0.2Si. Quench at 843 °C for 14 min was applied before air cooling. Tensile samples were cut parallel to the rolling direction using water jet cutting (80 mesh, 3500 bar) to avoid heating and changes in the microstructure.

Developed in 1989, Ti21S is a purely β-metastable titanium alloy with a BCC structure [154,[START_REF] Weiss | Mechanical properties and microstructural study of homogeneous and heterogeneous laser welds in α, β, and α + β titanium alloys[END_REF]. Its main characteristics are high temperature resistance, creep resistance, good cold formability, corrosion/oxidation and good thermal stability for applications up to 593 °C. It is also a popular candidate material for both aerospace and biomedical applications.

In-situ tensile tests were performed at room temperature with a DEBEN machine (Suffolk, UK) equipped with a 1 kN force cell. Measurements were carried out under an imposed force and with a strain rate of 3.3 × 10 -4 s -1 . Samples were mechanically polished with a 1 µm diamond paste, followed by chemical mechanical polishing with a colloidal silica suspension in order to produce a very flat surface and to minimize

V.V.1 Development of in-situ deformation testing coupled with ECCI

hardening due to conventional polishing. Finally, a 2 h ion polishing in a PECS II machine (GATAN, Pleasanton, CA, USA) was performed with a 3 keV beam, to improve the surface quality, so that a higher signal/noise ratio can be achieved for the BSE signal. Characterizations were made after 15 min of relaxation.

Observed areas were chosen to be in the middle of the gauge length. It is also For each of the 7 selected zones, channeling contrast was optimized, in order to obtain good channeling conditions simultaneously on both sides of GBs. Given these working conditions, the diffraction vector is -→ g =(1 1 0).

We report, here, observations for zone E, chosen because it contains several de-

Chapter V. Mesoscale and statistical comparison between polycrystalline plasticity models and experiments

formation features, since the objective of this part is mainly to explore the potential of the in-situ experiment. Therefore, we have successfully combined in-situ macroscopic tensile testing of a bulk polycrystalline sample with microstructure observations. For the first time, we can track the evolution of crystalline defects under stress. This pioneers the potential of in-situ experiments coupled with ECCI, which becomes now very popular in the materials science community [START_REF] An | Direct observations of collinear dislocation interaction in a Fe-17[END_REF][START_REF] Nakafuji | In-Situ Electron Channeling Contrast Imaging under Tensile Loading: Residual Stress, Dislocation Motion, and Slip Line Formation[END_REF][START_REF] Wei | Deformation faulting in a metastable CoCrNiW complex concentrated alloy: A case of negative intrinsic stacking fault energy[END_REF].

In conclusion, such experiment makes possible to cover large areas of interest, offering statistically relevant multiscale information to deepen deformation mechanisms. The observed slip/dislocation configurations explore an interesting route for exploring and determining involved mechanisms.

V.2 Statistical comparison between models and experiments

Majority of models reveal that each configuration has its own behavior, especially with regard to dislocation interactions, from which a large number of simulations are required for characterizing all possible mechanisms. Analysis of individual configurations by molecular dynamics (e.g. [START_REF] Gao | Molecular dynamics study of the interaction between nanoscale interstitial dislocation loops and grain boundaries in BCC iron[END_REF][START_REF] Kim | Molecular dynamics simulation of dislocation behavior during nanoindentation on a bicrystal with a Σ=5 (210) grain boundary[END_REF][START_REF] Guénolé | Exploring the transfer of plasticity across Laves phase interfaces in a dual phase magnesium alloy[END_REF][START_REF] Zepeda-Ruiz | Atomistic insights into metal hardening[END_REF]) does not generally take or cannot take into account the influence of surrounding microstructure on local mechanisms.

For example, activation of a particular slip system in a grain or interaction of a dislocation with a GB is dependent on elastic fields induced by neighboring grains, GBs, triple points and other possible defects, such as solutes or precipitates.

Few studies attempted to provide an overview of constitutive laws and theories

V.V.2 Statistical comparison between models and experiments

for modeling polycrystal plasticity [START_REF] Roters | Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications[END_REF][START_REF] Kochmann | Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals[END_REF], none of them provided quantitative comparisons and statistics between these different modeling methods, which could shed new light on the inherent mechanisms. In this part, a combined experimental/theoretical approach is proposed to fill this gap.

By using information provided by in-situ ECCI, it is possible to examine the effect of anisotropic elastic and plastic properties on the local slip and dislocation activity distribution within grains at different stages of deformation and gather statistical information for identifying or tuning relevant micromechanical and microstructural variables that influence the material behavior.

V.2.1 Few words on the atypical plasticity of BCC metals

β-Ti21S has a BCC structure, so that it is expected that Burgers vector of dislocations is among the four dense 1 1 1 . As BCC metals, such dislocations are supposed to glide in the most dense planes i.e. {1 1 0}. But packing density of {1 1 0} is similar to the packing of {1 1 2} and {1 2 3}. It has been reported from trace analyses on BCC metals that slip occurs mainly on {1 1 0}, {1 1 2} and in some particular cases on {1 2 3} planes [START_REF] Taylor | Experiments on the deformation of niobium single crystals[END_REF]. In total, β-Ti21S has 48 slip systems available to accommodate plastic deformation. Note that at the atomic scale, slip traces consist of several atomic step combinations [START_REF] Douat | Atomic-scale insight into non-crystallographic slip traces in body-centred cubic crystals[END_REF].

Chapter V. Mesoscale and statistical comparison between polycrystalline plasticity models and experiments

Due to the multiplicity of slip planes of BCC, it is challenging to clearly identify glide planes at low temperature. Indeed, screw segments can easily cross-slip on several planes containing the same 1 1 1 as zone axis. Therefore, slip lines are curved and this phenomenon is called "pencil glide" [START_REF] Taylor | The distortion of iron crystals[END_REF][START_REF] Seeger | Anomalous Slip -A Feature of High-Purity Body-Centred Cubic Metals[END_REF][START_REF] Pichl | Slip Geometry and Plastic Anisotropy of Body-Centered Cubic Metals[END_REF]. By examining such curved lines at high magnification (Figure V.5), it appears that they form a stair-like shape, which results in a curved appearance when the images are taken at a lower magnification [START_REF] Ben Haj Slama | In situ macroscopic tensile testing in sem and electron channeling contrast imaging: Pencil glide evidenced in a bulk beta-ti21s polycrystal[END_REF]. Therefore, BCC metals disobey the Schmid-Boas law, so that several modifications were proposed [START_REF] Gilormini | Theoretical analyses of <111> pencil glide in b.c.c. crystals[END_REF][START_REF] Dezerald | Plastic anisotropy and dislocation trajectory in BCC metals[END_REF][START_REF] Le | Efficient simulation of single and polycrystal plasticity based on the pencil glide mechanism[END_REF].

V.2.2 Feature engineering from in-situ ECC micrographs

Prior to any comparison, extracting relevant information from experiment data sets is necessary. Indeed, this step (i.e. feature engineering) is crucial. It consists in transforming experimental data into useful information that can be used afterwards. In this frame work, a novel method was developped for automated slip trace detection and analysis based on the Hough transform algorithm and apply it to ECC micrographs. This is further augmented with an automation procedure for the determination of slip-trace crystallography in conjunction with orientation data acquired via EBSD. Automation is required for faster indexation of the slip traces and for more reliable statistical studies. In concrete terms, each slip line -where coordinates of both extremities are (x 1 , y 1 ) and (x 2 , y 2 ) -is discretized into K points, whose the coordinates of the k th points is given by [START_REF] Ben Haj Slama | Electron channeling contrast imaging characterization and crystal plasticity modelling of dislocation activity in Ti21S BCC material[END_REF][START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF]:

x k = [2 k -(2 k -1)]x 1 + (2 k -1)x 2 2 k ; y k = [2 k -(2 k -1)]y 1 + (2 k -1)y 2 2 k (V.1)
In order to match the EBSD data with ECCI micrographs, a correlation vector, -→ Π can be defined as [START_REF] Ben Haj Slama | Electron channeling contrast imaging characterization and crystal plasticity modelling of dislocation activity in Ti21S BCC material[END_REF][START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF]:

- → Π = 3 i=1 r i f i = 3 i=1 cos(∆κ i ) f i (V.2)
where:

V.V.2 Statistical comparison between models and experiments

• f i is a base vector for each family of glide planes i.e. f 1 = (1, 0, 0) stands for {1 1 0}, f 2 = (0, 1, 0) stands for {1 1 2} and f 3 = (0, 0, 1) stands for {1 2 3};

• r i is the i th component of - → Π written in the base ( f 1 , f 2 , f 3 );
• ∆κ i is the difference between angle measured by EBSD and angle measured on ECCI micrographs for the glide plane family i, both with respect to a common direction as reference (e.g. the loading direction)

Because of some ambiguities to the uncertainties on the angle estimation, it is more convinient to define another correlation vector as [START_REF] Ben Haj Slama | Electron channeling contrast imaging characterization and crystal plasticity modelling of dislocation activity in Ti21S BCC material[END_REF][START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF]:

- → Π = | - → Π -max[r i ]J 3,1 | (V.3)
where J 3,1 is a matrix of one with one column and three rows.

Therefore, the total number of counts, υ, corresponding to each family of slip planes for K points on P detected lines is [START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF]:

- → υ ( - → Π ) = P ×K k=1 - → υ k ( - → Π ); - → υ k = 1 K or 1 2K (V.4)
Finally, the probability, P i of observing a slip line corresponding to a given slip plane family, i [START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF]:

P i = υ i ( - → Π ) i υ i ( - → Π ) (V.5)
This automation procedure is applied to different regions of interest on a β-Ti21S sample loaded in-situ in tension. Multiple regions of interest are analyzed.

The acquired slip distribution statistics reveals that the majority of the slip traces belong mainly to the {1 1 2} and {1 2 3} slip families as shown in Figure V.6.

V.2.3 Comparison with micromechanical modeling

The deformation response of the observed regions of interest is also simulated using a several models/codes, with expected agreement of increasing predictions: Sachs [START_REF] Reuss | Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle[END_REF], VPSC [START_REF] Molinari | A self consistent approach of the large deformation polycrystal viscoplasticity[END_REF][START_REF] Lebensohn | A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys[END_REF], EVPS [START_REF] Mareau | An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method[END_REF][START_REF] Lhadi | Micromechanical modeling of the effect of elastic and plastic anisotropies on the mechanical Bibliography behavior of β-Ti alloys[END_REF] CPFFT [START_REF] Lebensohn | An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials[END_REF][START_REF] Roters | DAMASK -The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale[END_REF]. The slip system ac- Adapted from [START_REF] Ben Haj Slama | Electron channeling contrast imaging characterization and crystal plasticity modelling of dislocation activity in Ti21S BCC material[END_REF][START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF].

Chapter V. Mesoscale and statistical comparison between polycrystalline plasticity models and experiments

tivity distribution from each codes is compared with the slip distribution statistics observed experimentally. The plasticity parameters for β-Ti21S are taken from the literature [START_REF] Hounkpati | In situ neutron measurements and modelling of the intergranular strains in the near-β titanium alloy Ti-β21S[END_REF]. Quantitative results are given in Table V.1.

From this statistical comparison, it is clear that for small plastic strains (<0.25 %) under uniaxial tensile loading, the Schmid law is satisfied statistically. Under these circumstances, changes in CRSS are minimal and accommodation of incompatible deformation between grains has not yet become important.

Moreover, by minimizing the sum of least squared differences of P i obtained either by experiments (exp) or by simulations (simul) for several initial CRSS ratios, i.e. [START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF]:

χ = i (P (exp) i -P (simul) i ) 2 (V.6)

V.V.2 Statistical comparison between models and experiments

Models Error percentage

Sachs (constraint of uniform stress) 14%

VPSC (mean field) 14%

EVPSC (mean field) 10%

CPFFT (full field) 12%

Table V.1 -Statistics of predicted slip events in agreement with experimental determination. From [START_REF] Ben Haj Slama | Electron channeling contrast imaging characterization and crystal plasticity modelling of dislocation activity in Ti21S BCC material[END_REF].

the initial CRSS values can be also adjusted to match the slip-distribution statistics experimentally (Figure V.7) [START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF]. As the statistical distributions are being obtained from multiple points on a detected slip line, this makes the data obtained statistically relevant. It aims to be first steps towards data mining processes and model parameter optimization using a variety of different techniques [START_REF] Kusche | Large-area, high-resolution characterisation and classification of damage mechanisms in dual-phase steel using deep learning[END_REF][START_REF] Medghalchi | Damage Analysis in Dual-Phase Steel Using Deep Learning: Transfer from Uniaxial to Biaxial Straining Conditions by Image Data Augmentation[END_REF][START_REF] Purushottam Raj | Estimating single-crystal elastic constants of polycrystalline β metastable titanium alloy: A Bayesian inference analysis based on high energy X-ray diffraction and micromechanical modeling[END_REF][START_REF] Sedighiani | An efficient and robust approach to determine material parameters of crystal plasticity constitutive laws from macro-scale stress-strain curves[END_REF].

V.2.4 Dimensionality reduction to classify different GB slip transfer regimes

Complex interactions between dislocations and GBs have a significant influence on the macroscopic properties. Therefore, it is important to understand operating

Chapter V. Mesoscale and statistical comparison between polycrystalline plasticity models and experiments

mechanisms via statistical approach for identifying important parameters originating GB-dislocation interactions. In long term, such an approach aims to build statistical criteria that can be implemented in crystal plasticity modeling and also guide microstructure tailoring. Concerning slip transfer, features span several internal length scales and hence it is difficult to develop rigorous quantification procedures that enable the visualization of correlations that exist between the different underlying parameters. In this context, a Principal Component Analysis (PCA) approach was developed [START_REF] Venkatraman | Dimensionality reduction using principal component analysis to classify different grain boundary slip transfer regimes in BCC-Titanium Ti21S: A feature engineering-based approach[END_REF]. PCA is a method of multivariate statistics, which consists in transforming correlated variables into new decorrelated variables, thus allowing to reduce the number of variables and to make the information less redundant. Mathematically, the problem consists in finding the eigen values and the eigen vectors of a matrix constituted with the slip-transfer metrics such as slip transmission factor (f GαGβ ), three angular variables and three geometric parameters associated with slip transfer.

V.V.2 Statistical comparison between models and experiments

Gα and Gβ, respectively)

f GαGβ =        n Gα n Gβ , if n Gα < n Gβ n Gβ n Gα , , if n Gβ < n Gα (V.7)
is used as a classifier, with the aim of distinguishing several slip transfer regimes.

The mean value of f GαGβ (here equal to 0.7) is related to the ease of slip transfer between the interacting grains. More precisely, a value greater than 0.7 indicates that the two interacting slip systems share the applied stress equally by the activation of close to equal number of slip systems and are classified as easy slip transfer events.

For values less than 0.7, one of the interacting slip systems is accommodating a larger part of the applied stress, as a result of which higher number slip traces are activated for this particular slip system. They are classified as hard slip transfer events.

From as crucial aspect of the democracy [190]. But it is true to say that this kind of pedagogy is under-developed in France and not well recognized by our institutions.

To perpetuate the results of my research in virtuous dynamics around the transfer of knowledge and know-how between research and society, my popularization actions are, among others, focused on two aspects, as detailed in the followings.

VI.1 Popularization for participating to scientific progress and their benefits

This action is mentioned in the article 27 of the Universal Declaration of Human Rights: "Everyone has the right freely to participate in the cultural life of the community, to enjoy the arts and to share in scientific advancement and its benefits"

VI.VI.2 Popularization for arousing interest for scientific careers

Subjects are for example:

• mechanics and microstructures of chocolate.

• how to help Santa Claus to glide in the chimney?

• what is the cold?

• etc

An experience very enriching!

VI.2 Popularization for arousing interest for scientific careers

We must admit that few students wish to become scientists and even less materials scientists. This field is unknown because it does not appear to them sufficiently important and significant. It seems "out of date" and obsolete. Therefore, intense work must be done in first years of university studies. That is why, I give some lectures in front of students. For example, from 2021, my lecture entitled Save the world with materials science! is included in the 1st year of BUT (Bachelor Universitaire et Technologique)-GMP. Here, I give basics of research in materials science in the framework of the current energetic transitions. The targeted audience is the students with a light scientific background.

Of course, I am aware that all these actions will not be enough. But they merit to initiate dynamics that I hope being transferred to my colleagues.

Conclusions and projects

Unearthing the missing links between, on one hand, the history of a material (its microstructure), and on the other hand, its mechanical properties and therefore its performances, is the fundamental question of materials science. Understanding how microscopic mechanisms operating against GBs evolve, while loading macroscopi- All these aspects will have to be further explored by new frontier between ex-

Conclusion and perspectives

periments and modeling, as motto for the next cutting-edge experiments advancing materials science especially in the customization of the microstructures according to desired performances. In this framework, some of my on-going projects or submitted are briefly described in the following.

Projects

Not available online.

Résumés en français

Résumé de mes travaux doctoraux (2010 -2013)

Teaching experience

In my opinion, teaching is very formative both on the human level and on knowledge. The contact with students, the management of a group, the presentation efforts are all experiences that allow me to usefully supplement my research work.

-2022

IUT de Metz -GMP, France • 2021: Weekly podcasts at France Bleu Lorraine-Nord (Metz, France)

• 2021: Lecture during the Science Day (Metz, France)

• 2021: One-to-one with a researcher: research in materials science for energy transitions (Metz, France)

• 2021: Interview on France Bleu Lorraine-Nord (regional radio) about materials science in energy transition: link to the podcast (in French)

• 2021: Lecture at Collège-Lycée Vauban (Luxembourg-City, Luxembourg)

• 2020: Chercheur.e dans ma ville and video on the research in materials science (with Dr. N. Gey): link to the video (in French)

• 2019: Lecture during the Science day (Metz, France)

• 2018: Lecture at Lycée Fabert (Metz, France)

• 2018: Lecture during the Science day (Metz, France)

• 2018: Lecture at Lycée de la Communication (Metz, France)

• 2017: Lecture during the Science day (Metz, France)

• 2016: Lecture at Université de Lorraine -IUT de Metz, MP (Metz, France)

Peer-reviewed publications

Updated list on my webpage: www.antoine-guitton.fr.

27.

Brittleness of metallic ceramics: surface severe plastic deformation on Ti 2 AlC and its TiAl 3 intermetallic composite. A. Heinzelmerier, M. Novelli, A. • ERC remote referee (2020)

• Selected within the Université de Lorraine (only 8 persons) to follow the working group of excellence "CODEV: develop the leadership of researchers" (2019-2020)

• ANR referee (2019)

• Special issue editor in Materials journal "New progress on electron microscopies for characterizing microstructures" (2019)

• Co-responsible of the bachelor in metallurgy (work/study program) with Prof. N. Allain (from 2017)

• Member of the board of the GUMP (French-speaking association of users of Philips-FEI-ThermoFisher electron microscopes) and member of the organization committee of symposia (from 2015)

  with who I am pleased to work and chat with.

IntroductionIχ

  Microstructure: a major and complex role in polycrystalline plasticity I.1 From one interface to polycrystals with grain boundaries . . . . . . . I.1.1 Plasticity of monocrystal . . . . . . . . . . . . . . . . . . . . . I.1.1.1 Slip systems and Schmid-Boas law in a monocrystal I.1.1.2 Dislocations . . . . . . . . . . . . . . . . . . . . . . . I.1.2 Plasticity of polycrystal . . . . . . . . . . . . . . . . . . . . . I.1.2.1 Grain boundaries . . . . . . . . . . . . . . . . . . . . I.1.2.2 Interactions between dislocations and GB . . . . . . I.1.2.3 Micromechanical modeling . . . . . . . . . . . . . . . I.2 Effect of microstructure anisotropy on deformation mechanisms: case of MAX phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I.2.1 Presentation of MAX phases . . . . . . . . . . . . . . . . . . . I.2.2 Overview of deformation mechanisms of MAX phases . . . . . I.3 Towards the influence of strain-path changes on metal plasticity . . . I.3.1 Strain-path changes . . . . . . . . . . . . . . . . . . . . . . . . I.3.2 Development of a novel biaxial machine . . . . . . . . . . . . . iii Table of contents II Contribution of electron microscopy II.1 Overview of electron microscopes . . . . . . . . . . . . . . . . . . . . II.1.1 Transmission Electron Microscope . . . . . . . . . . . . . . . . II.1.2 Scanning Electron Microscope . . . . . . . . . . . . . . . . . . II.1.2.1 SEM imaging . . . . . . . . . . . . . . . . . . . . . . II.1.2.2 Electron backscatter diffraction . . . . . . . . . . . . II.2 From electron channeling contrast imaging to accurate electron channeling contrast imaging . . . . . . . . . . . . . . . . . . . . . . . . . . III Physics of ECCI and optimization of experimental conditions III.1 Perfect crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.2 Imperfect crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III.2.1 Planar defects . . . . . . . . . . . . . . . . . . . . . . . . . . . III.2.1.1 Theoretical approach . . . . . . . . . . . . . . . . . . III.2.1.2 Confrontation with experiment in the case of a twin boundary . . . . . . . . . . . . . . . . . . . . . . . . III.2.2 Dislocations and their configurations . . . . . . . . . . . . . . III.2.2.1 Screw dislocation . . . . . . . . . . . . . . . . . . . . III.2.2.2 Edge dislocation . . . . . . . . . . . . . . . . . . . . III.2.2.3 Extinction conditions . . . . . . . . . . . . . . . . . . IV Evolution of crystalline defects close to a real interface IV.1 Procedure of a localized deformation test by instrumented nanoindentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV.1.1 Instrumented nanoindentation testing . . . . . . . . . . . . . . IV.1.2 Procedure for studying deformation mechanisms in the vicinity of a real GB . . . . . . . . . . . . . . . . . . . . . . . . . . IV.2 Deformation mechanisms near a twin boundary in a TiAl alloy . . . . IV.2.1 Presentation of TiAl alloys . . . . . . . . . . . . . . . . . . . . IV.2.2 Deformation mechanisms of TiAl based alloys . . . . . . . . . IV.2.3 Evolution of microstructures near a twin boundary . . . . . . Angle between the loading axis and the slip direction ϕ Angle between the loading axis and the normal to the slip plane (α) or (β) The slip systems of interest

sT

  Deviation parameter of the incident beam respect with the Bragg condition θ Angle between the incident beam and the diffracting plane (h k l) θ B Angle between the incident beam and the diffracting plane (h k l) ω DP Tilt parameter due a planar defect z DP Depth of a planar defect η sup Contribution of the upper crystal with an equivalent thickness of z DP η inf Contribution of the translated lower crystal with an infinite thickness η inf Contribution of the lower crystal with an infinite thickness η inf Contribution of the lower crystal with an equivalent thickness of z DP xii Nomenclature Term of the BSE signal dependent on ω and z DP

Figure 1 -

 1 Figure 1 -Scale bridging between the microscopic and the macroscopic scales. A major challenge for materials scientists.

I. 1 I. 1 . 1 I. 1 . 1 . 1 Figure I. 1 -

 1111111 Figure I.1 -Schematic of the Schmid-Boas law.

Figure I. 2 -

 2 Figure I.2 -Schematic of a tilt GB (left) and twist GB (right).

I. 3 Figure I. 3 -

 33 Figure I.3 -Variations of GB energy with misorientation (in mJ•m -2 ) a) calculated at 0 K for tilt GB symetric around 1 1 0 in Al, from[9] and b) for a twist GB in Ti 3 AlC 2 , with magnified views of the stress field σ zz , from [16].

Figure I. 4 Figure I. 4 -

 44 Figure I.4 -Schematics of several mechanisms of interaction between dislocations and a GB for grains A and B (adapted from [21]). n GB is the normal to GB plane; N (α,β) A,B and B (α,β) A,B are respectively the normal to the slip plane and the slip direction.

Figure I. 5 -

 5 Figure I.5 -Overview of polycrystalline plasticity.

Figure I. 6 -

 6 Figure I.6 -The main stable MAX phases. Adapted from [44].

Figure I. 7 -

 7 Figure I.7 -The three primitive cells (211, 312 and 413).

Figure I. 8 -

 8 Figure I.8 -Grain shape in MAX phases: (a) Scanning electron microscope micrograph of Ti 2 AlN [47]; (b) schematic of the platelet shape.

I. 9 Figure I. 9 -

 99 Figure I.9 -Stress-strain curves of Ti 2 AlN [51]. (a) monotonous loading; (b) cycled loading.

Figure I. 10 -

 10 Figure I.10 -Scheme of Incipient Kink Band. Adapted from [53].

Figure I. 11 -

 11 Figure I.11 -Post-mortem observations of the surface of Ti 2 AlN deformed at room temperature and a schematic of the microstructure [51].

I.I. 2 Figure I. 12 -

 212 Figure I.12 -Dislocation network observed in Ti 2 AlN deformed under confining pressure at room temperature [62].

Frank

  partial c -dislocations associated with a diffusion mechanism of Cu into Ti 2 AlC were recently reported in Ti 2 AlC[START_REF] Yu | Frank partial dislocation in Ti2AlC-MAX phase induced by matrix-Cu diffusion[END_REF]. Such crystalline defects were not expected to be found in such material, because of energetic reasons due to the high c/a ratio.

Figure I. 13 -

 13 Figure I.13 -Cross-slip observed in Ti 2 AlN deformed under confining pressure at 900 °C.

  This part briefly summerizes the research done during my 20 months of postdoctoral fellow (2014 -2015) at Paul Scherrer Institut (PSI) in Switzerland. My research was the first part of the ERC Advanced Grant of Prof. Helena Van Swygenhoven (MULTIAX).

  of optical instruments limit its suitability for micromechanical tests. Consequently, in-situ SEM observations are becoming indispensable for studying the evolution of surface microstructures during the experiments, giving complementary insights on mechanical behavior of the samples.With the on-going miniaturization of engineering components there is an increasing need for novel deformation devices that can handle samples below the micrometer scale. For simple uniaxial deformation a variety of such devices has been developed in recent years. For instance, many test rigs for in-situ SEM and TEM observations are currently available on the commercial market. While in-situ miniaturized uniaxial deformation setups are nowadays relatively common, miniaturized multi-axial deformation devices are less frequent yet. For instance, there exist only few biaxial tensile set-ups combined either with SEM observations[START_REF] Tasan | Multi-Axial Deformation Setup for Microscopic Testing of Sheet Metal to Fracture[END_REF] or coupled with x-ray reflection diffraction[START_REF] Geandier | Development of a synchrotron biaxial tensile device for in situ characterization of thin films mechanical response[END_REF][START_REF] Collins | A synchrotron X-ray diffraction study of in situ biaxial deformation[END_REF]. But there are none that combine nanometer scale deformation with in-situ microscopy observations or with synchrotron x-ray diffraction on small bulk materials. My postdoctoral work consisted in the development of a new miniaturized insitu biaxial deformation machine, which is not only compatible with synchrotron lines (transmission and reflection modes) but also with SEM observations (see Figure I.14). The latter allows to in-situ access an area of interest by digital image correlation. To face this technological challenge, different techniques have been de-Chapter I. Microstructure: a major and complex role in polycrystalline plasticity veloped. In particular the thinning of cruciform samples by pulsed laser ablation with ultra-short pulses (from the femtosecond to the picosecond) [72]. This new strategy essentially has the advantage of machining samples while minimizing damage, which makes it an excellent alternative to the focused ion beam milling.

Figure I. 14 -

 14 Figure I.14 -Schematic design of the in-situ biaxial deformation rig. From [73].

Figure II. 1 -

 1 Figure II.1a. Closed channel (red); b. open channel (green) and c. conversion of an open channel to a closed channel.

Figure II. 2 -

 2 Figure II.2 -First ECP reported by Coates on Ge, when the bulk specimen was tilted 10°and -10°from the {1 1 1} direction. From [90].

Figure II. 3 -

 3 Figure II.3 -Gemini column cut scheme showing all the deflections that result in the beam rocking necessary for SACP collection. (a) Double deflection in the Aperture alignment Coils (ApC) results in beams parallel to the optic axis. (b) Deflection of the off-axis beam by the magnetic field of the Scanning coils (SC) and correction using the beam shift control to center the beam on sample pivot point. (c) Backscattered information collection and construction of the BSE map intensity according to the position on the ApC scanning grid. Distances between elements are not representative. From [95].

  Figure II.4 -Characterization of dislocations in a grain of the 2% Si IF-steel. (a) Four HR-SACPs superimposed on a simulated EBSD pattern. (b) Stereographic projection showing the {1 1 1} poles. The fading dotted lines represent the directions of the inclined 1 1 1 screw dislocations and show how the channeling contrast from screw dislocations with these three 1 1 1 line directions will decrease as the dislocations extend below the sample surface. (c-f) ECC micrographs of dislocations collected using the four channeling conditions shown in (a): (c) g = (0 1 1); (d) g = (1 2 1); (e) g = (1 0 1); (f) g = (1 1 0). Two dislocation line directions corresponding to u = b = [1 1 1] (dislocations a) and [1 1 1] (dislocations b) are seen. The dislocations are labeled in red where they disappear. From [96].

-

  s: deviation parameter of the incident beam respect with the Bragg condition; -θ: angle between the incident beam and the diffracting plane (h k l); -θ B : angle between the incident beam and the diffracting plane (h k l) in Bragg condition.

Figure III. 1 -

 1 Figure III.1 -Variations of the BSE intensity with the angle between the incident beam and the diffracting plane (h k l). The Bragg condition corresponds to θ = θ B and θ = θ c is the channeling condition.

Figure III. 2 .

 2 Figure III.2.

Figure III. 2 -

 2 Figure III.2 -Schematic of an inclined planar defect with an angle ζ from the surface of observation.

Figure III. 3 Figure III. 3 -

 33 Figure III.3 shows η sup (ω) profiles for several thicknesses, z DP , of a perfect crystal. It is obvious that these intensity profiles have several regimes and the origin lies in the competition competition between transmission and channeling of electrons.For small thickness (≈ 0.2ξ g ), no band is observed, thus favoring transmission. For thickness around 1.6ξ g , the curve has the same evolution as the one given by equation III.4, describing electron channeling. However, for intermediate thicknesses, the competition between transmission and channeling leads to a transitory regime, where oscillations are observed at the curve edges. Substituting equation III.7 into equation III.6, it is possible to write η tot as a function of x and -→ g • -→ R . Therefore, several cases can be distinguished (Figure III.4):

Figure III. 4 -

 4 Figure III.4 -BSE intensity profiles calculated as a function of x. From [105].

III. 2 . 1 . 2 Figure III. 5 -

 2125 Figure III.5 -ECC micrograph of a TB observed in a TiAl alloy. From [105].

Figure III. 5

 5 Figure III.5 shows an ECC micrograph of a TB in (1 1 1) observed in a TiAl alloy. The TB separates two γ grains (labeled zone 1 and zone 2 in Figure III.5). Observations planes of both grains are respectively (4 5 7) and (0 1 3). The common direction between both grains is [2 3 1]. Therefore, the TB is inclined by 11°with respect to the surface of the sample. As shown in the experimental profile of Figure III.5, the previous model reproduces qualitatively the main features observed: at the intersection between the TB and the observation surface, the contrast is bright. Then, intensity oscillations are observed, while moving away from the TB (toward increasing x in Figure III.4).

9 )

 9 By introducing equation III.9 in equation III.2, and by supposing that distorsions are linear at the vicinity of the depth z D (Figure III.6, the problem is simplified in the study of a new deviation parameter, s , such as [106]:

Figure III. 6 -

 6 Figure III.6 -Schematic of an edge dislocation parallel to the surface and localized at a depth z D . Distorted planes, perpendicular to the surface, are localized at a distance x for the dislocation core.

13 )Figure III. 7 -

 137 Figure III.7 -Profiles of I BSE for a screw dislocation parallel to the surface with s exp = 0; (a) +g and (b) -g. (a') et (b') experimental ECC micrographies. From [106].

Figure III. 8 -

 8 Figure III.8 -Profiles of I BSE for a screw dislocation parallel to the surface with s exp > 0; (a) +g and (b) -g. (a'), (b')) experimental ECC micrographies. From [106].

Figure III. 9 -

 9 Figure III.9 -First ECCI characterization of a dislocation dipole in an IF steel. From [104].

  profiles are shown in Figure III.10. Note that in the case of an edge dislocation, a residual contrast is observed when -→ g • -→ b × -→ u = 0. This behavior is similar to those observed in TEM.

Figure III. 10 -

 10 Figure III.10 -Extinction conditions. From [106].

(IV. 1 IV. 1 . 1 1 .Figure IV. 1 -

 11111 Figure IV.1 -Typical nanoindentation curve with a pop-in and schematic of important parameters. Adapted from [115].

TiAl alloy 1 . 1

 11 deformation mechanisms near a TB in a TiAl alloy; 2. deformation mechanisms near a LAGB in a medium entropy alloy. Presentation of TiAl alloys Titanium aluminide alloys have attracted considerable attentions due to their unique combination of properties such as high specific strength and stiffness, good creep properties and resistance against oxidation and corrosion [119, 120], which make them suitable candidate materials for high temperature structural use [121, 122]. Blades of the low-pressure-turbine in the last generation of aircraft engines (GEnx -General Electric Next-generation -and LEAP -Leading Edge Aviation Propulsion) are made by cast GE (General Electric) titanium aluminide alloy -47Al-2Cr-2Nb (at.%) -replacing Ni-superalloys two times heavier. This significantly contributes to the decrease of fuel consumption and CO 2 emission.

Figure IV. 2 -

 2 Figure IV.2 -Binary Ti-Al diagram. From [123].

of

  Ti and Al planes along [0 0 1]. But the stacking along the other directions [1 0 0] and [0 1 0] are formed of an alternation of mixed TiAl planes. Therefore, the three 1 1 0 directions are not equivalent: [1 1 0] is constituted of one type of atoms, while [1 0 1] and [0 1 1] are composed of an alternation of either Ti atoms or Al atoms. Some other phases can be present, such as the high temperature β phase with the BCC structure and its ordered B2 variant. A broad range of engineering alloys, with baseline compositions of Ti-(42-49)Al-(0.1-10)X (at.%) with X = Cr, Nb, V, Mn, Ta, Mo, Zr, W, Y, Si, C and B, has emerged in the past, two decades ago. The single phase γ-TiAl based alloys, like many intermetallic phases, suffer from both poor ductility and fracture toughness. Considerably improved ductility and toughness can be achieved in (γ+α 2 ) dual-phase alloys. The microstructures of dualphase alloys are complex but can be roughly classified into four groups (Figure IV.3) [124, 125]: • Near-γ (NG): constituted of γ equiaxed grains with a few α 2 grains at at grain boundaries and triple junctions (Figure IV.3.a); • DuPlex (DP): constituted of a mixture of monolithic γ grains and small lamellar colonies of (γ+α 2 ) (Figure IV.3.b); • Nearly Lamellar (NL): mainly constituted of big lamellar colonies and small γ grains (Figure IV.3.c); • Fully Lamellar (FL): organized in big lamellar (γ+α 2 ) colonies (Figure IV.3.d).

Figure IV. 3 -

 3 Figure IV.3 -Micrographs of the different microstructures of Ti-48Al-2Cr: (a) near-γ; (b) duplex; (c) nearly lamellar; and (d) fully lamellar. From [126].

  L10 structure. From Figure IV.4, one can see that along the 110]-directions there is only one sort of atoms (Ti or Al). These dislocations are called ordinary dislocations and their Burgers vectors are 1 0 0 , 1 2 110] types. By contrast Ti-atoms and Alatoms interchange in 011]-directions and the so called superdislocations are 1 2 112] (twinning dislocations) and 101]. These two types of superdislocations can undergo various dissociations into superpartial and partial dislocations and the associated planar faults.

1 2 110 ]Figure IV. 4 -

 11104 Figure IV.4 -Potential slip systems of the L10 structure, schematic drawing of a threelayer sequence of atom stacking on the (1 1 1) plane shown by small, medium and large circles. b 1 = [1 0 0], b 2 = 1 2 [1 1 0] are Burgers vectors of ordinary dislocations. B 1 = [0 1 1], B 2 = [1 0 1] and B 3 = 1 2 [1 1 2] are Burgers vectors of superdislocations.

Figure IV. 5

 5 is composed on two grains separated by a true TB of the system [1 1 2](1 1 1): A (left) and B (right) with surface orientation respectively as ∼(4 5 7) and ∼(0 1 3) (Figure IV.5.a). Before deformation, dislocations in grain A are highly inclined with the surface. They are either isolated or piled up into walls. Burgers vectors (determined from extinction conditions of equation II.1) are consistent with ± 1 2 [1 1 0]. One Nano-Twin (NT) of system [1 1 2](1 1 1

Figure IV. 5 -

 5 Figure IV.5 -Region of interest observed by A-ECCI before (a.) and after (b.) µNnanoindentation. Grain A (surface orientation: (4 5 7)) and grain B (surface orientation: (0 1 3)) are separated by a true TB of the system [1 1 2](1 1 1). (c.) 3D scheme explaining the formation of the pile-up areas B1 and B2. From [128].

1 6 11 2 ]

 2 {1 1 1} by ordinary 1 2 110] {1 1 1} dislocations Chapter IV. Evolution of crystalline defects close to a real interface has already been reported by TEM experiments in Ti-Al alloys [129, 130], no mechanism has been proposed. From these results, the following scenario can be proposed (Figure IV.5.b):

1 2

 1 Figure IV.6)[START_REF] Gludovatz | Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures[END_REF][START_REF] Strife | The effect of heat treatment on microstructure and cryogenic fracture properties in 5Ni and 9Ni steel[END_REF]. Therefore, CrCoNi is a promising alloy for low temperature applications[START_REF] Praveen | High-Entropy Alloys: Potential Candidates for High-Temperature Applications -An Overview[END_REF].

Figure IV. 6 -

 6 Figure IV.6 -Ashby map of the fracture toughness versus the yield strength. From [133].

IV. 3 . 2 6 with b = ± a 2 1 1 0Figure IV. 7 -

 32617 Figure IV.7.b. shows that the LAGB is composed of stacking of dislocations spaced in average of 60 nm. This order of magnitude can be found by invoking equation I.6 with b = ± a 2 1 1 0 as Burgers vector. A network of 56 indents was performed around the LAGB of interest. Among these imprints, 15 imprints closest to the LAGB (yellow curve in Figure IV.7.a) were selected. Distribution of their pop-in load is represented as a function of the distance from the LAGB in Figure IV.7.b). For imprints the most distant from the LAGB, the distribution is centered around 158 µN as mean value. The observed dispersion (standard deviation: 23 µN) can be attributed to differences in initial local density

Figure IV. 8 -

 8 Figure IV.8 -Network of nanoindentation imprints near the LAGB. The yellow curve encircles the imprints used for plotting the pop-in load with the distance from the LAGB, shown in b. Numbers show imprints analysed in the following. From [148].

Figure IV. 10 -

 10 Figure IV.10 -(a) Positions of the indents superimposed on the subgrain orientation map. (b) Load-displacement curves of nanoindentation tests performed at the LAGB ( 5), 0.42 µm from the LAGB in subgrain A ( 4), and 0.44 µm in subgrain B ( 3). The initial elastic loading follows the Hertz contact theory (light blue curve). (c) ECC micrograph of indent 5 performed at the LAGB and (d) corresponding schematic. From [148].

Figure IV. 11 -

 11 Figure IV.11 -(a,b) ECC micrographs before and after nanoindentation showing the evolution of the dislocation configurations in the subgrain A at 0.42 µm from the LAGB (indent 4. (c,d) schematics of (a,b). The red ellipsis in (b) and red line in (d) show a stacking fault. The blue arrows in (b) show directions along which the NID pile ups extend. The blue dashed lines in (c) and (d) show the trace of the LAGB before and after deformation. The green straight lines allow to compare the positions of the LAGB dislocations 1, 2, and 3 before and after nanoindentation while the green arrows show the direction of the slight motion of LAGB dislocations. From [148].

Figure IV. 12 -

 12 Figure IV.12 -Interactions between NIDs and the dislocations constituting the LAGB.(a-b) ECC micrographs before and after nanoindentation, respectively (indent 3). (c-d) Enlargement ECC micrograph of a portion of the LAGB before and after nanoindentation and (e-f) are their corresponding schematics. The red ellipses highlight stacking faults. Blue ellipses show dislocations that form a '>' like shape. From [148].

V. 1

 1 constantly being developed, aiming to relate relevant length scales and to understand involved mechanisms. This is the framework of postdoctoral works of Meriem Ben Haj Slama (2018-2020) and Kaustubh Venkatraman (2020-2022).Chapter V. Mesoscale and statistical comparison between polycrystalline plasticity models and experiments Development of in-situ deformation testing coupled with ECCIDeveloping new experimental techniques allowing to understand and to predict mechanical properties of materials becomes a necessity for the materials science community in order to follow the fast evolution of our society. In this framework, this chapter reports the development of macroscopic uniaxial tensile testing of a bulk polycrystalline specimen combined with in-situ observations at the dislocation scale of changes in deformation microstructures at several stress states. Observations at the dislocation scale are carried out by A-ECCI in order to follow the evolution of the defects and their interactions with GBs for several regions of interest during macroscopic loading.

Figure V. 1 -

 1 Figure V.1 -(a) Tensile sample geometry and sizes (mm); (b) Elastic deformation simulation on COMSOL. From [156].

Figure V. 1

 1 Figure V.1 shows the geometry and dimensions of a tensile sample, which have been designed to fit into the tensile machine. A simulation of the elastic regime was carried out with COMSOL [157] in order to confirm that the stress field is macroscopically uniaxial and homogeneous in the gauge length.

Figure V. 2 V. 1 . 2 1 .Figure V. 2 -

 21212 Figure V.2 shows the assembly of the tensile machine and the sample inside the SEM. The configuration allows an inclination of about 15°inside the chamber with the BSE detector inserted.

Figure V. 3 -

 3 Figure V.3 -Left: in-situ obtained stress-strain curve of the Ti21S showing the positions where observations were made: before loading (1), during elastic deformation (2: no defect formation was observed), at the beginning of the plastic domain (3), and for six intermediate states of the second tensile cycle before unloading (four to 10). The dashed vertical lines correspond to the relaxation after plastic deformation. Right: observed area of 600×450 µm 2 with the seven zones of interest in white dashed frames. From [156].

3 .

 3 A second cycle, which was holded at intermediate stress states to perform ECCI of each area of interest (positions 4 to 10 on the curve in Figure V.3).

V.V. 1

 1 Development of in-situ deformation testing coupled with ECCI chosen far from the edges in order to avoid any edge effect. Seven zones with several slip/dislocation trace configurations are identified, as shown in Figure V.4.

Figure V. 4 -

 4 Figure V.4 -(a) BSE micrographs in channeling condition (with g =(1 1 0)) in the grain of interest) presenting the evolution of the defect structure corresponding to each deformation step of the tensile curve. The letter refers to the zone (E) and the number refers to the load state from the curve. Black arrows indicate slip lines, orange arrows indicate dislocations and yellow crosses indicate an increase in dislocation length; (b) Example of SE vs BSE images from zone (E8). From [156].

Figure V. 4

 4 shows the evolution of the defect structure associated with different loading states for zone E; the letter refers to the zone (E) and the number refers to the state of charge of the curve. No defect is found before loading. When it is plastically deformed, several glide systems are activated and dislocations are visible. Note that dislocations are easily distinguished from surface slip traces, because they are not contrasted on micrographs acquired with the SE detector, while they are visible with the BSE detector.

Figure V. 5 -

 5 Figure V.5 -(a) SE micrographs showing curved slip lines resulting from pencil glide phenomenon and (b) a corresponding schematic representation. From [156].

Figure V. 6 -

 6 Figure V.6 -Images (i) -(iii) are EBSD maps of the deformed region of interest with the ECC micrographs of the slip traces superimposed on the EBSD maps. (iv), (v) and (vi) are the results from the automated slip line detection algorithm for these deformed regions and (vii), (viii) and (ix) are the slip family distributions obtained from these regions of interest.Adapted from[START_REF] Ben Haj Slama | Electron channeling contrast imaging characterization and crystal plasticity modelling of dislocation activity in Ti21S BCC material[END_REF][START_REF] Venkatraman | Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach[END_REF].

Figure V. 7 -

 7 Figure V.7 -(i) The accumulated plastic slip distribution for all slip families compared to the slip-lines visible in the deformed region of interest. (ii) Sum of squared difference, (χ SSD ) plot for different CRSS ratios. From [176].

Figure V. 8 -

 8 Figure V.8 -Clustering of the slip-transfer regimes in three-dimensional principal component space. Plane 1 represents the separation between the two slip transfer regimes and planes 2 and 3 represent the bounds for the easy and hard slip transfer regimes, respectively. From [189].

Figure V. 8 ,

 8 a clustering of those slip transfer regimes is obvious and they are separated by planes 1 , 2 and 3 . As a conclusion of the procedure, the sliptransfer events can be classified based on a linear function of the input variables weighted by the loadings corresponding to each of the slip-transfer metrics. This lower-dimensional representation of the slip-transfer data can be used for estimating the slip transmission factor, f GαGβ , for a range of active slip-systems involved in sliptransfer close to a given GB.Chapter VIOn the importance of popularizationBoth current crises (COVID pandemic and global warming) reveal the necessity of popularizing science. Not only for arousing interest for scientific careers, but also for assisting decision makers in their choices and for developing the analytic mind of populations. It is the reason why science popularization is the oldest program of UNESCO (United Nations Educational, Scientific and Cultural Organization),

[

  191]. As scientists, we aim to change the world, but it is our responsibility to explain how we change it. The place of science in our society makes scientific knowledge the essential baggage of any future citizen, both in terms of knowledge and methods or values. Therefore, I give popularization lectures entitled The mysteries of materials deformation in the fantasy to high-schools. By using some famous Chapter VI. On the importance of popularization fantasy films/books such as Game of Thrones from G.R.R. Martin and The Lord of the Rings from J.R.R. Tolkien, I give basics of plasticity, microscopies and metallurgy. The targeted audience is the general population (adults and teenagers) without any knowledge in materials sciences (see Figure VI.1). Since 2021, my talks received the support of the French Society of Physics (SFP).

Figure VI. 1 -

 1 Figure VI.1 -24/06/2021: invited talk in Vauban High-School (Luxembourg-City, Luxembourg). Photo taken by Adrien Heinzelmeier.

Figure VI. 2 -

 2 Figure VI.2 -03/12/2021: podcast recording at France Bleu Lorraine-Nord.

  cally a specimen and observe their series of consequences to the macroscopic scale is currently of high relevance. Indeed, mesoscale and statistical approaches are necessary to bring information allowing linking the multiscale aspects of the mechanical behavior of materials (Figure VI.3).

Figure VI. 3 -

 3 Figure VI.3 -The full potential of ECCI for multiscale confrontations between experiments and simulations.

  La plupart de nos connaissances sur le comportement mécanique des métaux provient essentiellement d'essais uniaxiaux conventionnels. Cependant la production industrielle de composants métalliques implique de nombreux changements de chemins de Résumé en français déformation, qui modifient drastiquement leur réponse mécanique. Dans ce cadre, les essais de déformation in-situ peuvent apporter de précieux renseignements sur les mécanismes de déformation qui pourraient apparaître ou pourraient être modifiés durant des changements de chemins de déformation. La miniaturisation continue des composants d'ingénierie entraîne inexorablement l'augmentation des besoins de nouveaux dispositifs de déformation à l'échelle microscopique. Mon travail postdoctoral a consisté au développement d'une nouvelle machine miniaturisée de déformation biaxiale in-situ qui est aussi bien compatible avec des lignes synchrotron (modes transmission et réflexion) mais également avec des observations MEB. Ces dernières nous permettent d'accéder de manière in-situ à la déformation dans notre zone d'intérêt par corrélation d'images numériques. Pour faire face à ce défi technologique, différentes techniques ont été développées. Notamment l'amincissement localisé des échantillons par ablation laser pulsé à pulses ultra-courts (de la femtoseconde à la picoseconde). Cette nouvelle stratégie présente essentiellement l'avantage d'usiner les échantillons en minimisant l'endommagement, ce qui en fait une excellente alternative au canon à ions focalisés ou FIB (Focused Ion Beam) [72]. Par ailleurs, mes simulations en éléments finis ont permis de modéliser le comportement mécanique des échantillons utilisés dans la machine de traction biaxiale, permettant ainsi d'optimiser leur forme et leur taille. Nos études in-situ ont été réalisées aux lignes synchrotron MS et MicroXAS du Swiss Light Source (SLS) : • à la ligne MS : des échantillons nanocristallins de nickel et d'aluminium ont été étudiés avec un faisceau X monochromatique ; • à la ligne MicroXAS : des échantillons d'aluminium monocristallins et bicristallins sont analysés par microdiffraction Laue. Les résultats expérimentaux sont alors discutés en parallèle avec ceux obtenus en simulations et permettent d'apporter des éclairages nouveaux sur l'influence des changements de chemins de déformation sur l'activation des systèmes de glissement de dislocations, les Joints de Grains (JdG) ainsi que sur la formation de contraintes résiduelles [73]. Résumé en français afin suivre l'évolution des microstructures de déformation. Avec les chercheurs postdoctoraux que j'ai encadrés (recherches postdoctorales de Meriem Ben Haj Slama 2018-2020 et de Kaustubh Venkatraman 2020-2022), nous avons développé une méthode de détection automatisée, basée sur un algorithme de transformée de Hough, des traces de glissement (dislocations et marches en surface) apparaissant lors de la déformation in-situ d'un alliage de Ti cubique centré (Ti21S) [175, 176]. La distribution des systèmes de glissement actifs obtenue à partir d'une loi micromécanique à champ complet a ensuite été comparée statistiquement à la distribution des systèmes de glissement observée expérimentalement par A-ECCI. Notre méthode nous a notamment permis d'ajuster les cissions projetées critiques en comparant les statistiques des distributions de glissement (sur environ 3000 points), obtenues d'une part par la loi micromécanique, et d'autre part expérimentalement. Ainsi ces comparaisons statistiques entre les modèles de plasticité cristalline et les expériences se veulent être une première étape vers l'ingénierie des fonctionnalités. Mon projet scientifique d'HDR Approches expérimentales, mésoscopiques et statistiques de la plasticité dans les polycristaux Déformation des matériaux : un défi multi-échelle et statistique Développer de nouveaux matériaux et comprendre comment ils se déforment est le principal défi des chercheurs pour suivre et prédire l'évolution rapide de notre société.Par exemple, dans un cadre de réduction des coûts énergétiques, l'augmentation des performances mécaniques des matériaux est conditionnée à l'amélioration constante des techniques expérimentales conduisant à de nouvelles connaissances sur leurs mécanismes fondamentaux de déformation. Bien que la recherche en plasticité des matériaux soit âgée de plus d'un siècle, il est juste de dire qu'elle recèle encore de nombreux secrets, notamment en raison des difficultés à extrapoler des modèles simplistes à des échantillons réels, loin des cas idéaux. Cottrell a résumé ce conflit en qualifiant la théorie de l'écrouissage plastique comme "the first problem to be attempted by dislocation theory and may be the last to be solved"[START_REF] Cottrell | Dislocations and Plastic Flow in Crystals[END_REF]. Transitions d'échelles en Sciences des Matériaux. En effet, la mécanique des matériaux doit encore faire face à de nombreux problèmes conceptuels. Nous devons ainsi relier deux échelles extrêmes : l'échelle de l'échantillon (c.-à-d. Macroscopique) et l'échelle des mécanismes fondamentaux (c.à-d. Microscopique).

  Kriaa 2015-2018, co-direction avec Nabila Maloufi)[START_REF] Kriaa | Fundamental and experimental aspects of diffraction for characterizing dislocations by electron channeling contrast imaging in scanning electron microscope[END_REF][START_REF] Kriaa | Modelling Electron Channeling Contrast Intensity of Stacking Fault and Twin Boundary Using Crystal Thickness Effect[END_REF][START_REF] Kriaa | Modeling dislocation contrasts obtained by accurate-electron channeling contrast imaging for characterizing deformation mechanisms in bulk materials[END_REF].Approche expérimentale et mésoscopique des mécanismes de déformation au voisinage d'une interface réelleFort de ces travaux, j'ai initié, comme perspective de la thèse de Hana Kriaa, la Recherche sur l'exploration de la potentialité de l'A-ECCI pour suivre l'évolution des défauts cristallins combinée avec des essais de déformation localisée par nanoindentation au voisinage d'une interface (recherche doctorale de Frederic Habiyaremye 2018-2012, co-direction avec Nabila Maloufi)[START_REF] Guitton | A Dislocation-Scale Characterization of the Evolution of Deformation Microstructures around Nanoindentation Imprints in a TiAl Alloy[END_REF][START_REF] Habiyaremye | Plasticity induced by nanoindentation in a CrCoNi medium-entropy alloy studied by accurate electron channeling contrast imaging revealing dislocation-low angle grain boundary interactions[END_REF]. L'essai de nanoindentation est un essai de déformation localisée sur un échantillon massif. Il consiste, comme dans le cas de la mesure de dureté, à faire pénétrer une pointe dans un matériau pour en déduire ses propriétés mécaniques. L'évolution de la force appliquée sur la pointe d'indentation et son enfoncement dans le matériau sont mesurés en continu, sur un cycle charge-décharge. Les charges appliquées restent faibles, allant de la centaine de micronewtons à la centaine de millinewtons. Cette combinaison expérimentale a ouvert la voie à l'étude des mécanismes proches d'un JdG unique sont discutés dans le cadre, d'une part, d'un alliage TiAl et d'autre part, d'un alliage à entropie moyenne. Les alliages d'aluminure de titane ont attiré une attention considérable en raison de leur combinaison unique de propriétés telles qu'une limite d'élasticité élevée, de bonnes propriétés de fluage et une résistance à l'oxydation et à la corrosion qui en font des matériaux candidats appropriés pour applications aux hautes températures [120]. Citons par exemple, les pales de la turbine basse pression de la dernière génération de moteurs d'avion (GEnx, General Electric Next-generation et LEAP, Résumé en français Leading Edge Aviation Propulsion) qui sont fabriquées en alliage d'aluminure de titane GE (General Electric) remplaçant ainsi les superalliages à base Ni, deux fois plus lourds. Nos essais de nanoindentation combinés aux observations A-ECCI avant et après la déformation ont pu suggérer qu'à température ambiante, le maclage semble être le mécanisme principal de déformation et qu'une paroi de macle est un obstacle à la propagation de la déformation entrainnant une concentration de contraintes au niveau de la paroi [128]. Concernant les alliages à entropie moyenne (MEA : Medium Entropy Alloy) et les alliages à haute entropie (HEA : High Entropy Alloy), ils se composent respectivement de deux à quatre et d'au moins cinq éléments, avec des concentrations presque équiatomiques. Parmi ces nouvelles classes de matériaux, le CrMnFeCoNi et l'un de ses dérivés ternaires équiatomiques, le CrCoNi, suscitent actuellement un intérêt croissant dans la littérature en raison de leurs excellentes tolérances aux dommages aux basses voire très basses températures [137]. En comparant les courbes de nanoindentation, les charges des pop-in initiaux et les configurations des dislocations pour les empreintes effectuées à l'intérieur des sous-grains, sur un JdG de faible désorientation et proche de ce dernier, on constate que le JdG de faible désorientation étudié affecte la réponse micromécanique locale et les mécanismes de déformation fondamentaux sous-jacents [148]. Comparaison statistique entre les expériences et les modèles mésoscopiques de plasticité polycristalline Dans les métaux, les mécanismes élémentaires comme le glissement de dislocations, opèrent à l'échelle atomique voire à l'échelle électronique ; typiquement, l'ångström et la picoseconde. Ces mécanismes peuvent fortement influer sur la réponse macroscopique à l'échelle du laboratoire, c.-à-d. le centimètre et la seconde. Par exemple, des simulations ab-initio des coeurs de dislocations dans des métaux cubiques centrés ont mis en évidence l'apparition d'effets non-Schmid, qui pourraient expliquer une asymétrie entre la traction et la compression à l'échelle macroscopique [173]. Pour comprendre et finalement contrôler le comportement mécanique des matéri-Résumé en français aux métalliques en ce qui concerne leurs microstructures traitées, il faut faire face à ce problème multi-échelles d'une complexité impressionnante qui peut s'étendre sur plus de 10 ordres de grandeur dans le temps et dans l'espace. C'est pourquoi des outils théoriques et expérimentaux avancés sont constamment développés, visant à relier les échelles de longueur pertinentes et à comprendre les mécanismes impliqués. Dans ce contexte, j'ai ouvert la voie vers le développement d'essais macroscopiques de traction uniaxiale d'un échantillon massif combiné à des observations in-situ à l'échelle de dislocation de l'évolution des microstructures de déformation pendant le chargement à plusieurs états de contrainte [156]. Les observations à l'échelle des dislocations ont été réalisées par A-ECCI afin de suivre l'évolution des défauts et leurs interactions avec les JdG pour plusieurs régions d'intérêt pendant le chargement macroscopique. Nous avons, entre autres, développé une méthode de détection automatisée des traces de glissement (dislocations et marches en surface) apparaissant lors de la déformation in-situ d'un alliage de Ti cubique centré (Ti21S). La distribution des systèmes de glissement actifs obtenue à partir d'une loi micromécanique à champ complet a ensuite été comparée statistiquement à la distribution des systèmes de glissement observée expérimentalement par A-ECCI [175]. Notre méthode nous a notamment permis d'ajuster les cissions projetées critiques initiales en comparant les statistiques des distributions de glissement (sur environ 3000 points), obtenues d'une part par la loi micromécanique, et d'autre part expérimentalement. Ainsi ces comparaisons statistiques entre les modèles de plasticité cristalline et les expériences se veulent être une première étape vers l'ingénierie des fonctionnalités [176]. Retombées de mon projet À travers cet aperçu synthétique, il est clair que la déformation des matériaux est un problème de voisinage multi-échelle et statistiquement complexe. Multi-échelle, car il faut être capable d'appréhender la plasticité à toutes les échelles où elle se déroule. Complexe car les microstructures environnantes influencent profondément la réponse des grains, et c'est la combinaison de tous les grains qui donne le comportement Ma stratégie pour comprendre la plasticité des matériaux. macroscopique. D'un côté, la réponse macroscopique d'un échantillon est connue ; de l'autre côté, les mécanismes opérant à l'intérieur d'un grain sont plus ou moins bien compris. Mais tout l'enjeu dans la compréhension de ce qui se passe entre ces deux échelles. De plus, nous n'avons aucune idée si les mécanismes rapportés sont anecdotiques ou non, en raison des faibles statistiques d'observations. Il est vrai que plusieurs lois ou modèles ont déjà été proposés. Dans plusieurs cas, ils ont prouvé leur efficacité pour prédire quels mécanismes seront activés. Mais dans de nombreux autres, ils ne fonctionnent tout simplement pas. Ainsi, je vise à améliorer les modèles constitutifs de plasticité en prenant en compte statistiquement la microstructure. En effet, comprendre comment évoluent les mécanismes de déformation lors du chargement macroscopique d'un échantillon et observer leur série de conséquences à l'échelle macroscopique est le chaînon manquant. Cette amélioration passera inéductablement par des algorithmes d'apprentissage profond. Expérimentalement, un large jeu de données sera nécessaire pour vérifier/corriger le modèle/les paramètres, afin de devenir très prédictif et ensuite être utilisé, à terme, pour la sélection de microstructures. En ce sens, l'ECCI et plus largement le MEB, aura une place prépondérante. Résumé en français À partir de nos résultats, il sera possible d'étudier et voire même de comprendre la plasticité à toutes les échelles où elle se déroule, ouvrant ainsi de nouvelles pistes de recherche. Alors seulement, nous serons en mesure sélectionner judicieusement voire de personnaliser les microstructures en fonction des performances souhaitées, de la même manière que les fameux graphes d'Ashby pour la sélection des matériaux.

  Topics: continuum mechanics, fluid mechanics, metrology, microscopies Audience: 1st, 2nd and 3rd years of Bachelor. Electron microscopies: a powerful tool for understanding the fundamental deformation mechanisms of materials Audience: Master and doctoral researchers.

  including ≈ 50 h of pedagogical responsabilies) Topics: continuum mechanics, fluid mechanics, metrology, microscopies Audience: 1st, 2nd and 3rd years of Bachelor.2019 -2020IUT de Metz -GMP, France 464 h (including ≈ 50 h of pedagogical responsabilies)Topics: continuum mechanics, fluid mechanics, metrology, microscopiesAudience: 1st, 2nd and 3rd years of Bachelor.2018 -2019IUT de Metz -GMP, France354 h (including ≈ 50 h of pedagogical responsabilies)Topics: continuum mechanics, fluid mechanics, metrology, microscopiesAudience: 1st, 2nd and 3rd years of Bachelor.2017 -2018IUT de Metz -GMP, France316 h (including ≈ 50 h of pedagogical responsabilies)Topics: continuum mechanics, fluid mechanics, metrology, microscopies, thermodynamics Audience: 1st, 2nd and 3rd years of Bachelor.2016 -2017 IUT de Metz -GMP, France299 h (including ≈ 30 h of pedagogical responsabilies)Topics: continuum mechanics, fluid mechanics, metrology, thermodynamicsAudience: 1st and 2nd years of Bachelor.2015 -2016 IUT de Metz -GMP, France359 h (including ≈ 20 h of pedagogical responsabilies) Topics: fluid mechanics, metrology, thermodynamics Audience: 1st and 2nd years of Bachelor. Complementary to my teaching, I attach great importance to the popularization of Curriculum vitae and teaching science. I am involved in several actions such as invited talks entitled The mysteries of materials deformation in the fantasy in high schools. My lectures received the support of the French Society of Physics (SFP) and they are now included in the 1st year of BUT (Bachelor Universitaire et Technologique)-GMP as an initiation to science.

.2 Effect of microstructure anisotropy on deformation mechanisms: case of MAX phases I.2 Effect of microstructure anisotropy on defor- mation mechanisms: case of MAX phases I.2.1 Presentation of MAX phases

	I.IIn the 90s, the research work of Barsoum et al. from Drexel University (Philadelphia,
	USA) led them to focus on Ti 3 SiC 2 [42]. They showed that this compound is stiff,
	lightweight, machinable, made from relatively inexpensive raw materials, resistant
	to oxidation and thermal shock, and capable of remaining strong up to temperatures
	above 1300 °C in air. They synthesized about fifty compounds with the same range
	of promising properties. Because of their composition, Barsoum et al. called these
	remarkable materials M n+1 AX n phases, where [43, 44] (Figure I.6):
	• M is a transition metal from the groups 3 (Sc), 4 (Ti, Zr, Hf), 5 (V, Nb, Ta)
	or 6 (Cr, Mo);
	• A is an element from the groups 12 (Cd), 13 (Al, Ga, In, Tl), 14 (Si, Ge, Sn,
	Pb), 15 (P, As) or 16 (S);
	• X is carbone C and/or nitrogen N.
	n is an integer from 1 to 3, therefore the structures M 2 AX, M 3 AX 2 and M 4 AX 3 are
	respectively called 211, 312 and 413.
	Figure I.6 gives a non-exhaustive list of thermodynamically stable MAX phases.
	All of them are not yet synthesized to date. However, a large number of solid
	solutions on M, A and X sites were obtained. They enable to modify or even to
	One example is the case of MAX phases. Studying their fundamental deformation tune properties.
	mechanisms was the heart of my doctoral work at Pprime Institute (2010 -2013). MAX phases have a laminated structure with an hexagonal lattice (space group:
	P63/mmc). The primitive cell can be described as a stacking of n M 6 X octahe-
	dron layers with one layer of A element (Figure I.7). Furthermore, measurements
	of lattice parameters with numerous methods reveal that MAX phases exhibit an
	elevated crystalline anisotropy. The c/a ratio is generally higher than 3 [45]. MAX
	phases synthesized by powder metallurgy are polycrystalline bulk samples with ran-
	dom grain orientations. It is commonly observed that during synthesis grains grow

Chapter I. Microstructure: a major and complex role in polycrystalline plasticity

  favoring high work hardening rates. Low stacking fault energy promotes partial dislocation glide and it prevents cross slip, but also it promotes mechanical NT. This last deformation mechanism introduces coherent interfaces acting as barriers to the glide of dislocations and it results in a dynamic Hall-Petch effect without reducing the ductility[START_REF] Gludovatz | Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures[END_REF][START_REF] Laplanche | Reasons for the superior mechanical properties of medium-entropy CrCoNi compared to high-entropy CrMnFeCoNi[END_REF][START_REF] Zhang | Nanoscale origins of the damage tolerance of the high-entropy alloy CrMnFeCoNi[END_REF][START_REF] Zhang | Dislocation mechanisms and 3D twin architectures generate exceptional strength-ductility-toughness combination in Cr-CoNi medium-entropy alloy[END_REF]. From a more general point of view, reinforcement due to GBs and growth twins (Hall-Petch reinforcement) in CrCoNi has been shown to be particularly effective with a Hall-Petch slope ranging from 240 to

	600 MPa/m

1 2

[START_REF] Hansen | Hall-Petch relation and boundary strengthening[END_REF][START_REF] Yoshida | Friction stress and Hall-Petch relationship in CoCrNi equi-atomic medium entropy alloy processed by severe plastic deformation and subsequent annealing[END_REF][START_REF] Schneider | Analysis of strengthening due to grain boundaries and annealing twin boundaries in the CrCoNi mediumentropy alloy[END_REF][START_REF] Sangid | Energy of slip transmission and nucleation at grain boundaries[END_REF]

. However, although modeling studies have recently been reported in literature

[START_REF] Sangid | Energy of slip transmission and nucleation at grain boundaries[END_REF][START_REF] Chowdhury | Strength prediction in NiCo alloys -The role of composition and nanotwins[END_REF]

, there is still a lack of understanding regarding the relative contributions of different types of boundaries to the yield strength i.e.

interactions of dislocations with different types of interfaces such as LAGBs, coherent

TBs and general HAGBs.

  Avant toute exploitation industrielle des phases MAX, une meilleure compréhension de leurs mécanismes de déformation est essentielle. Il est couramment admis que la déformation plastique des phases MAX est due au glissement de dislocations dans les plans de base s'organisant en empilements et murs. Ces derniers peuvent former des zones de désorientation locale appelées kink bands. Cependant, les mécanismes élémentaires et le rôle exact des défauts microstructuraux sont encore mal connus. C'est dans ce cadre que s'est inscrit mon travail de thèse : étudier par diverses techniques expérimentales et à différentes échelles les mécanismes de déformation des phases MAX polycristallines en général, et de la phase Ti 2 AlN en particulier. À l'échelle macroscopique, deux types d'expériences ont été menés.Des essais de compression in-situ à température et pression ambiantes couplés à la diffraction neutronique ont permis de mieux comprendre le comportement des différentes familles de grains dans le Ti 2 AlN polycristallin[START_REF] Guitton | Effect of microstructure anisotropy on the deformation of MAX polycrystals studied by in-situ compression combined with neutron diffraction[END_REF]. Des essais de com-

	pression sous pression de confinement ont également été réalisés de la température
	ambiante jusqu'à 900 °C [60, 62, 67]. À l'échelle mésoscopique, les microstructures
	Mécanismes de déformation des phases MAX des surfaces déformées ont été observées par Microscopie Électronique à Balayage
	L'un des principaux défis de l'ingénierie est la nécessité d'élaborer de nouveaux (MEB) et Microscopie à Force Atomique (AFM). Ces observations complétées par
	matériaux qui permettent de répondre à l'évolution rapide de la société, des besoins des essais de nanoindentation ont montré que la forme des grains et leur orientation
	et des nouvelles technologies. Par exemple, dans un contexte de sobriété énergé-par rapport à la direction de sollicitation gouvernent la plasticité de ces matériaux.
	tique, l'amélioration des moteurs d'avions doit passer par l'augmentation de leur Finalement à l'échelle microscopique, des études détaillées par Microscopie Électron-
	température de fonctionnement. Les matériaux ainsi utilisés doivent donc être à ique en Transmission (MET) des échantillons déformés sous pression de confinement
	la fois toujours plus légers et plus résistants aux hautes températures. Durant les a révélé la présence de configurations de dislocations inédites dans les phases MAX.
	années 90, Barsoum et al. de l'université Drexel à Philadelphie ont été amenés à À la vue de ces résultats nouveaux, les propriétés mécaniques des phases MAX ont
	étudier le Ti 3 SiC 2 [42]. Ils ont montré que ce matériau est rigide, léger, facilement été rediscutées [62, 65, 67].
	usinable, fabriqué à partir de matériaux peu coûteux, résistant à l'oxydation, aux
	chocs thermiques et capable de rester solide à des températures au-delà de 1300	°C
	dans l'air. Ils ont ainsi élaboré une cinquantaine de composés possédant des pro-
	priétés similaires. Ils ont nommé ces matériaux les phases MAX, faisant référence à
	leur composition (M : métal de transition ; A : élément du groupe A et X : carbone
	et/ou azote).

  De plus, la statistique des observations est généralement extrêmement faible de sorte que d'une part l'incertitude est importante et d'autre part la représentativité des mécanismes est très discutable. La statistique de Cocheran

	Résumé en français
	résultats seront obtenus. En raison de ces problèmes conceptuels, des études signi-
	ficatives et statistiques sont alors nécessaires pour établir des modèles représentatifs
	basés sur le lien entre des paramètres importants à basse échelle et des propriétés à
	plus grande échelle.
	La plupart des matériaux utilisés sont généralement polycristallins [9]. Ces
	derniers se composent de millions de monocristaux appelés grains. Les grains ont
	des orientations différentes du réseau atomique et ils sont séparés des grains voisins
	par des interfaces appelées JdG. Il est bien établi que la déformation irréversible (ou
	plastique) d'un échantillon provient principalement de la nucléation et de la propa-
	explique parfaitement ce problème [192] : si un phénomène est observé à partir
	d'un échantillonnage d'expériences, alors il est impossible d'être sûr à 100 % que

le phénomène observé soit une représentation complète et exacte du comportement étudié. Par exemple, en considérant un niveau de confiance de 90 %, cela signifie qu'en répétant l'expérience un certain nombre de fois, 90 % du temps les mêmes gation de plus de centaines de milliards par cm 3 de défauts linéaires micrométriques (voire nanométriques) du réseau cristallin régulier appelé dislocations

[START_REF] Hirth | Theory of Dislocations[END_REF]

. Les dislocations se déplacent dans le grain et interagissent les unes avec les autres ou avec les JdG. Ces derniers peuvent agir de plusieurs manières : puits, pièges, obstacles et sources de dislocations. La combinaison d'études expérimentales et de simulations donne des informations précieuses sur les mécanismes fondamentaux de déformation.

Derniers défits de plasticité des matériaux.

  Guitton, W. Yu, T. Grosdidier TO BE SUBMITTED 26. Influence of the configurations of dislocations on the pop in load during nanoindentation in a CrCoNi medium entropy alloy. F. Habiyaremye, A. Guitton, X. Lei, T. Richeton, S. Berbenni, G. Laplanche, N. Maloufi TO BE SUBMITTED 12. A dislocation-scale characterization of the evolution of deformation microstructures around nanoindentation imprints in a TiAl alloy. A. Guitton, H. Kriaa, E. Bouzy, J. Guyon, N. Multi-scale approach for analyzing sub-boundaries induced during dislocational creep of uranium dioxide. M. Ben Saada, N. Gey, A. Guitton, B. Beausir, X. Iltis, N. On-axis TKD for orientation mapping of nano crystalline materials in SEM. E. Brodu, E. Bouzy, J.J. Fundenberger, J. Guyon, A. Guitton, Y. Zhang MATERIALS CHARACTERIZATION, 2017, 130, 92-96 DOI: 10.1016/j.matchar.2017.05.036 〈hal-02392258〉 7. A miniaturized biaxial deformation rig for in-situ mechanical testing. S. Van Petegem, A. Guitton, M. Dupraz, A. Bollhalder, K. Sofinowski, M.V. Dislocation modelling in Ti 2 AlN MAX phase based on the Pierls-Nabarro model. K. Gourriet, P. Carrez, P. Cordier, A. Guitton, A. Joulain, L. Thilly, C.

	Curriculum vitae and teaching
	Maloufi
	MATERIALS, 2018, 11 (2), 305
	DOI: 10.3390/ma11020305
	〈hal-02392252〉
	11. Fundamental and experimental aspects of diffraction for characterizing dislo-
	cations by electron channeling contrast imaging.
	H. Kriaa, A. Guitton, N. Maloufi
	SCIENTIFIC REPORTS, 2017 (9742)
	DOI: 10.1038/s41598-017-09756-3
	〈hal-02392256〉
	10. Maloufi
	SF2M PROCEEDINGS, 2017
	〈hal-03039964〉
	9. Electron channeling contrast imaging: influence of diffraction conditions on
	the dislocation contrast.
	H. Kriaa, A. Guitton, N. Maloufi
	SF2M PROCEEDINGS, 2017
	〈hal-03039936〉
	8. Upadhyay, H. Van Swygenhoven
	EXPERIMENTAL MECHANICS, 2017, 57 (4), 569-580
	DOI: 10.1007/s11340-016-0244-0
	〈hal-02392260〉
	6. Tro-
	mas
	PHILOSOPHICAL MAGAZINE, 2015, 95 (23), 2539-2552
	DOI: 10.1080/14786435.2015.1066938
	〈hal-01515323〉

Curriculum vitae and teaching

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• Member of the communication council of LEM3 (from 2021)

• Outstanding reviewer at Acta Materialia, Inc. (2020)

Abstract:

Research presented here focuses on experimental and mesoscopic methodologies to statistically establish the links between operating mechanisms at the dislocation scale and those operating at the polycrystal scale. The underlying assumption of this work is the development of experimental procedures, which allow on the one hand to observe and on the other hand, to characterize crystalline defects on bulk polycrystalline specimen. Therefore, obtained outcomes can be compared relevantly with micromechanical models. First chapter focuses on emphasizing the importance of the role of microstructures in deformation mechanisms. The example of MAX phases, whose microstructure is very anisotropic, is given. An opening on the influence of strain-path changes on plasticity is also done. Then, second chapter summarizes the contribution of electron microscopy, and in particular Scanning Electron Microscopy (SEM) for the fine characterization of microstructures. Third chapter emphases the physics and the optimization of the SEM technique of Electron Channeling Contrast Imaging (ECCI) in order to follow the evolution of microstructures with deformation. Chapter 4, on the other hand, highlights the potential of ECCI for capturing the evolution of crystalline defects in the vicinity of a single interface locally deformed by nanoindentation. Illustration is given with a titanium aluminide alloy and a medium entropy alloy. Finally, some models of crystal plasticity are compared statistically and in-situ with experiences in the case of a β-metastable titanium alloy.

Keywords: plasticity; microstructures; microscopies; ECCI; MAX phases; TiAl; medium entropy alloy; β-metastable Ti alloy.