Méthodologie de mesures de contraintes avec la méthode multireflection pâturage d'incidence(MGIXD) a été étudié et développé. La géométrie du faisceau parallèle a été appliquée pour mensurationsde stress. Le faisceau incident dans diffractomètres classiques a été collimaté par le miroir Göbel et lesessais de configuration en parallèle ont été effectuées pour Al poudre. Les résultats confirmé que le erreurstatistique et l'erreur d'alignement peuvent être réduits lorsque le miroir Göbel est utilisé. Facteursphysiques ont été prises en compte dans la CSX (analyse aux rayons X du stress): Lorentz - polarisationet facteur d'absorption (LPA) et aussi correction de la réfraction (RC). Les résultats montrent quel'influence de LPA est mineur dans CSX, mais la RC peut influencer de manière significative l'analyse.Dans la thèse de la question de RC a été examiné et comparé avec les approches présentées dans lalittérature. Dans la thèse de deux développements théoriques de la méthode MGIXD ont été présentés: laprocédure de détermination de paramètre c/a et l'influence des défauts d'empilement sur les résultats. Il aété montré que les deux développements améliore de manière significative la qualité de l'analyse desdonnées expérimentales. Dans le présent travail le problème de la X -ray facteurs de stress (XSF) utiliséspour l'interprétation des résultats CSX a été étudiée. Différents modèles théoriques de grains élastoplastiqueinteraction ont été envisagées et appliquées dans la CSX. Vérification de la XSF durant l'essaide traction pour l'échantillon élastique anisotrope (en acier inoxydable austénitique) et pour l'échantillonisotrope (Ti - note2). Anisotropie de XSF a également été observée dans: rectifié alliage Ni, acierinoxydable austénitique poli et revêtement CrN. Les résultats montre que Reuss et modèle de la surfacelibre sont en meilleur accord avec les résultats expérimentaux. Enfin, la méthode MGIXD a été vérifiée enutilisant le rayonnement synchrotron et 3 longueurs d'onde différentes. La méthodologie a été développéepour traiter les données non seulement pour les différents angles d'incidence, mais aussi en utilisantdifférentes longueurs d'onde simultanément. Contraintes en fonction de «vraie profondeur» a été calculéeen utilisant la transformée de Laplace inverse. Analyse Wiliamson-Hall a été appliquée pour les données.Méthode MGIXD a été appliqué pour les mesures de diffraction de dispersion d'énergie dans lequel lefaisceau blanc a été utilisé: 0,3 à 0,18 Å. L' analyse des contraintes a été effectuée en utilisant troisméthodes différentes : la méthode de sin2ψ norme, la méthode de terrain universelle et en utilisantmultireflection analyse . Dans la gamme de profondeur de pénétration à 0-15 um de la convergence desrésultats obtenus à partir de différentes méthodes a été acquise . En outre, les données de synchrotronparfaitement en accord avec les résultats obtenus en laboratoire sur diffractomètre (rayonnement Cu Ka) àproximité de la surface . Pour profondeur supérieure à 14 um points expérimentaux présentent desvariations importantes et ne sont pas d'accord avec les résultats de la méthode standard.Mots clés : contraintes résiduelles, diffraction des rayons X, méthode de l’incidence rasante, miroir Göbel / Methodology of stress measurements with multireflection grazing incidence method (MGIXD)was investigated and developed. The parallel beam geometry was applied. The incident beam in classicaldiffractometers was collimated by Göbel mirror and the tests of parallel configuration were performed for Alpowder. Results confirmed that both statistical error and the misalignment error can be reduced when theGöbel mirror is used. Physical factors were taken into account in XSA (X-ray stress analysis): Lorentzpolarizationand absorption factor (LPA) and also refraction correction (RC). Results showed that theinfluence of LPA correction is minor in XSA but the RC can significantly influence analysis. In the thesisthe issue of RC was considered and compared with approaches presented in the literature. In the thesistwo theoretical developments of the MGIXD method were presented: the procedure of c/a parameterdetermination and the influence of stacking faults on the results was taken into account. It was shown thatboth developments significantly improves the quality of experimental data analysis. In the present work theproblem of X-ray stress factors (XSF) used for the interpretation of XSA results was studied. Differenttheoretical grain elasto-plastic interaction models were considered and applied in XSA. Verification of theXSF was during tensile test for austenitic stainless steel and for the isotropic sample. Anisotropy of XSFwas also observed in: ground Ni alloy, polished austenitic stainless steel and CrN coating. The resultsshows that Reuss and free surface grain interaction models are in the best agreement with theexperimental results. Finally the MGIXD method was verified using synchrotron radiation and 3 differentwavelengths. The methodology was developed to treat data not only for different incident angles but alsousing simultaneously different wavelengths. Stresses vs. z – ‘real depth’ was calculated using the inverseLaplace transform applied to polynomial function. Wiliamson-Hall analysis was applied for collected data.Next multireflection method was applied for the energy dispersion diffraction measurements in which whitebeam containing radiation having different wavelengths was used (λ (Ǻ): 0.3–0.18/ E (keV): 40-68). Thestress analysis was performed using three different methods: standard sin2ψ method, Universal plotmethod and by using multireflection analysis. In the range of penetration depth to 0-15 μm theconvergence of the results obtained from different methods was gained. Moreover the synchrotron dataperfectly agree with the results obtained on laboratory diffractometer (Cu Kα radiation) close to the surface.For depth larger than 14 μm the experimental points exhibit significant spread and do not agree with theresults of standard method

Une analyse numérique basée sur la méthode des éléments finis permettant de quantifier les coefficients d'atténuation et de diffusion ultrasonores dans un polycristal en domaine temporel et fréquentiel est présentée. En particulier, une méthode originale basée sur le théorème de réciprocité pour l'évaluation numérique du coefficient de diffusion est proposée. Des formules analytiques bidimensionnelles (2D) pour les coefficients d'atténuation ultrasonore et de rétrodiffusion sont développées en utilisant l'approximation de Born pour valider les évaluations numériques. L'approche numérique proposée est appliquée au titanium, un polycristal monophasé et non texturé. Premièrement, des simulations sont effectuées dans des microstructures idéalisées composées de grains en taille unimodale. Une comparaison cohérente entre les évaluations numériques et les prédictions analytiques 2D est obtenue. Par ailleurs, les effets de l'atténuation induite par la diffusion multiple sur la mesure de rétrodiffusion, qui sont négligés par les modèles théoriques, sont quantifiés. Deuxièmement, l'approche numérique proposée est appliquée aux polycristaux composés de grains en taille bimodale. Les résultats numériques indiquent que les coefficients d'atténuation et de rétrodiffusion en domaine fréquentiel se situent au milieu des coefficients pour les microstructures unimodales et sont principalement déterminés par les fractions volumiques des grains constitutifs. Cependant, ils ne sont que légèrement affectés par la répartition des gros grains. Une étude de la fonction d'autocorrélation spatiale dans des telles microstructures bimodales est proposée afin d’obtenir une interprétation analytique des phénomènes expérimentés numériquement. / A numerical approach based on the finite element method to quantify ultrasonic attenuation and grain-noise scattering coefficients in both time and frequency domains for polycrystalline materials is presented. More particularly, an original method based on the reciprocity theorem for the numerical evaluation of the grain-noise scattering coefficient is proposed. Twodimensional (2D) analytical formulas of ultrasonic attenuation and backscattering coefficients are developed by using the Born approximation to validate numerical evaluations. Then the proposed numerical approach is applied to the single-phase and untextured polycrystalline titanium. Firstly, 2D FE simulations are performed in idealized microstructures composed of equiaxed grains with different unimodal grain sizes. Coherent comparison between numerical estimates and 2D analytical predictions is obtained. Effects of attenuation due to multiple scattering on the backscattering measurement, which are neglected in the theoretical model, are quantified. Secondly, polycrystals with bimodal grain sizes are considered. Numerical results indicate that attenuation and backscattering coefficients in bimodal microstructures are inbetween the ones of unimodal microstructures and are mainly determined by volume fractions of the constituent grains. However they are only slightly affected by the grain location distributions. The spatial autocorrelation function in bimodal microstructures is further quantified to gain an analytical interpretation of the above phenomena.

Methodology of stress measurements with multireflection grazing incidence method (MGIXD)was investigated and developed. The parallel beam geometry was applied. The incident beam in classicaldiffractometers was collimated by Göbel mirror and the tests of parallel configuration were performed for Alpowder. Results confirmed that both statistical error and the misalignment error can be reduced when theGöbel mirror is used. Physical factors were taken into account in XSA (X-ray stress analysis): Lorentzpolarizationand absorption factor (LPA) and also refraction correction (RC). Results showed that theinfluence of LPA correction is minor in XSA but the RC can significantly influence analysis. In the thesisthe issue of RC was considered and compared with approaches presented in the literature. In the thesistwo theoretical developments of the MGIXD method were presented: the procedure of c/a parameterdetermination and the influence of stacking faults on the results was taken into account. It was shown thatboth developments significantly improves the quality of experimental data analysis. In the present work theproblem of X-ray stress factors (XSF) used for the interpretation of XSA results was studied. Differenttheoretical grain elasto-plastic interaction models were considered and applied in XSA. Verification of theXSF was during tensile test for austenitic stainless steel and for the isotropic sample. Anisotropy of XSFwas also observed in: ground Ni alloy, polished austenitic stainless steel and CrN coating. The resultsshows that Reuss and free surface grain interaction models are in the best agreement with theexperimental results. Finally the MGIXD method was verified using synchrotron radiation and 3 differentwavelengths. The methodology was developed to treat data not only for different incident angles but alsousing simultaneously different wavelengths. Stresses vs. z - 'real depth' was calculated using the inverseLaplace transform applied to polynomial function. Wiliamson-Hall analysis was applied for collected data.Next multireflection method was applied for the energy dispersion diffraction measurements in which whitebeam containing radiation having different wavelengths was used (λ (Ǻ): 0.3-0.18/ E (keV): 40-68). Thestress analysis was performed using three different methods: standard sin2ψ method, Universal plotmethod and by using multireflection analysis. In the range of penetration depth to 0-15 μm theconvergence of the results obtained from different methods was gained. Moreover the synchrotron dataperfectly agree with the results obtained on laboratory diffractometer (Cu Kα radiation) close to the surface.For depth larger than 14 μm the experimental points exhibit significant spread and do not agree with theresults of standard method

abstract: Fracture phenomena have been extensively studied in the last several decades. Continuum mechanics-based approaches, such as finite element methods and extended finite element methods, are widely used for fracture simulation. One well-known issue of these approaches is the stress singularity resulted from the spatial discontinuity at the crack tip/front. The requirement of guiding criteria for various cracking behaviors, such as initiation, propagation, and branching, also poses some challenges. Comparing to the continuum based formulation, the discrete approaches, such as lattice spring method, discrete element method, and peridynamics, have certain advantages when modeling various fracture problems due to their intrinsic characteristics in modeling discontinuities. A novel, alternative, and systematic framework based on a nonlocal lattice particle model is proposed in this study. The uniqueness of the proposed model is the inclusion of both pair-wise local and multi-body nonlocal potentials in the formulation. First, the basic ideas of the proposed framework for 2D isotropic solid are presented. Derivations for triangular and square lattice structure are discussed in detail. Both mechanical deformation and fracture process are simulated and model verification and validation are performed with existing analytical solutions and experimental observations. Following this, the extension to general 3D isotropic solids based on the proposed local and nonlocal potentials is given. Three cubic lattice structures are discussed in detail. Failure predictions using the 3D simulation are compared with experimental testing results and very good agreement is observed. Next, a lattice rotation scheme is proposed to account for the material orientation in modeling anisotropic solids. The consistency and difference compared to the classical material tangent stiffness transformation method are discussed in detail. The implicit and explicit solution methods for the proposed lattice particle model are also discussed. Finally, some conclusions and discussions based on the current study are drawn at the end. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2015

The variance of the Taylor factor due to variations in the microstructure and window size is explored using both a random sampling method and a previously developed statistical relationship. The results from the random sampling method correlated well with the statistical variance relationship when the magnitude of the variance was greater than that of the numerical errors observed in the statistical calculation. An empirical relation was developed to model the results and the constants for this relationship were determined for pseudo-three dimensional Fe-3%Si. Implementation of the statistical variance relationship in true 3D microstructures is not limited by material opacity, since it depends only upon the 2-point pair correlation functions. The connection between the variance of the R-value and variance of the Taylor factor is considered. Although only a weak connection was found, it was observed that relatively small variations in the Taylor factor yield large variances in the R-value.

The presence of residual stresses in engineering components may significantly affect damage evolution and progression towards failure. Correct evaluation of residual stress is of crucial importance for assessing mechanical components, predicting response and ensuring reliability. For example, when failure occurs due to cyclic loading, the underlying damage begins at the nano-, and then micro-scale. It is clear that improving engineering reliability at the micro-scale requires the ability to evaluate residual stress and mechanical properties at the appropriate scale. The key objective of the thesis is to advance the understanding and practice of residual stress evaluation at the micro-scale, and to examine the implications and applications that follow. Significant effort was devoted to the evaluation of two aspects of the relatively novel FIB-DIC micro-ring-core experimental technique: assessing the effects of Ga-ion damage and the quantification of uncertainty in stress evaluation due to unknown crystal orientation. FIB-DIC micro-ring-core milling was then used alongside with synchrotron XRD to study residual stress effects on fatigue crack growth propagation rate following the occurrence of overload or underload. The effects of the two principal mechanisms of crack retardation following an overload, residual stress and crack closure, were separated by testing samples at different loading ratios. Whilst, the acceleration after an underload was studied using validated non-linear FEM analyses. Conceptual focus was placed on the macro-micro-nano residual stress decomposition into Type I, II & III according to scale and, detailed examination was conducted experimentally and numerically. In the context of shot-peening surface treatment, residual stresses were modelled using a novel eigenstrain-based modelling procedure for arbitrarily shaped components. Furthermore, a fine scale characterisation was performed of the recast layer produced by EDM, with particular attention paid to the residual stress. The investigations presented in this thesis open new perspectives for the assessment of material reliability. Improved failure prediction models will be elaborated based on the insights obtained in the present study.

Phase field models have played an important role in shaping our understanding of a variety of micro structural phenomena in materials. Their attractive features include (a) their ability to capture instabilities in microstructures, and (b) their ability to handle topological transitions { such as splitting or coalescence { gracefully. Therefore, we have chosen to use a phase field model in our study of instabilities in cylindrical pores in nanoporous membranes which eventually lead to their failure. Our study is motivated by recent studies on thermal stability of nanoporous membranes of alumina, titania and zirconia. The key feature in our model is its ability to incorporate surface discussion as the mechanism for mass transport. We first benchmark the model through a critical comparison of our results on early stages of surface evolution during Rayleigh instability and grain boundary grooving with those from linear theories of these phenomena. We have then used longer simulations (which go beyond early stages, and therefore, can incorporate non-lineare effects) to study instabilities in a hollow cylinder in three different systems: single crystal or amorphous solid (which fails through Rayleigh instability), a model sys-tem with parallel grain boundaries (which fails through grain boundary grooving), and a polycrystal (whose failure depends on a combination of grain growth and grooving). In all the cases, the surface energy is assumed to be isotropic, and the operative mechanism for mass transport is assumed to be surface discussion.

Le calcul de la réponse macroscopique des agrégats polycristallins à partir des propriétés de leurs constituants est un problème important en mécanique des matériaux. Lors de la déformation plastique, les grains du matériau sont réorientés. Une texture cristallographique, responsable de l'anisotropie, peut alors se développer. Donc, la modélisation de l'évolution de la texture est importante afin de prévoir les effets d'anisotropie lors des procédés industriels.La formulation de la plasticité des polycristaux métalliques a fait l'objet de nombreuses études et différentes approches d’homogénéisation ont été proposées. En 2008, Ahzi et M'Guil ont développé un modèle viscoplastique, baptisé le modèle-phi. Ce modèle prend en compte les effets d'interaction entre les grains sans passer par la théorie de l'inclusion d’Eshelby. Dans ce travail, le modèle-phi a été appliqué à différentes structures cristallographiques et sous différentes conditions de chargement. Le mécanisme de maclage a été pris en compte. Pour le laminage des métaux CFC, la transition de texture du type cuivre au type laiton a été étudiée. L’essai de cisaillement des métaux CFC a été également étudié. Nous montrons que le modèle est capable de prédire une transition de texture de cisaillement caractérisant une gamme de métaux CFC ayant une EDE élevée/moyenne à une EDE faible. Dans une étude dédiée aux métaux CC, nous avons comparé nos résultats à ceux prédits par un modèle auto-cohérent. Nous présentons également une comparaison avec des textures expérimentales de laminage à froid issues de la littérature. Le modèle a également été étendu aux métaux HC. Nous avons simulé le comportement de déformation d’un alliage de magnésium pour différentes niveaux d'interaction inter-granulaire. Nous montrons que le modèle prédit des résultats en bon accord avec les résultats expérimentaux. / The computation of the macroscopic response of polycrystalline aggregates from the properties of their single-crystal is a main problem in materials mechanics. During the mechanical deformation processing, all the grains in the polycrystalline material sample are reoriented. A crystallographic texture may thus be developed which is responsible for the material anisotropy. Therefore, the modeling of the texture evolution is important to predict the anisotropy effects present in industrial processes. The formulation of polycrystals plasticity has been the subject of many studies and different approaches have been proposed. Ahzi and M’Guil developed a viscoplastic phi-model. This model takes into account the grains interaction effects without involving the Eshelby inclusion problems.In this thesis, the phi-model was applied to different crystallographic structures and under different loading conditions. The mechanical twinning has been taken into account in the model. The FCC rolling texture transition from copper-type to brass-type texture is studied. The shear tests in FCC metals are also studied. The predicted results are compared with experimental shear textures for a range of metals having a high SFE to low SFE. For BCC metal, we compare our predicted results with those predicted by the VPSC model. We study the slip activities, texture evolutions and the evolution of yield loci. We also present a comparison with experimental textures from literatures for several BCC metals under cold rolling tests. The model has also been extended to HCP metals. We predict the deformation behavior of the magnesium alloy for different interaction strengths. We also compare our predicted results with experimental data from literatures. We show that the results predicted by the phi-model are in good agreement with the experimental ones.

In order to understand and predict the fracture behaviour of polycrystalline materials from a fundamental perspective, it is important to first investigate plastic deformation at a crack tip in a ductile single crystal. In this context, it may be noted that when the crack opening displacement is much less than the grain size, the crack tip fields are entirely contained in a single grain. Further, some key structural components are being fabricated in single crystal form. For example, blades in high pressure turbines of jet engines are made of single crystals of Nickel-based superalloys. In view of the above considerations, a combined experimental and computational study of the crack tip stress and strain fields in FCC single crystal is carried out in the present work. The effect of constraint level, which is characterized by the T-stress under mode I, plane strain small scale yielding conditions, on the near-tip response is first analyzed for a crystal orientation in which the crack plane coincides with (010) and ¯the crack front lies along[101]direction. A family of finite element solutions are generated by employing a boundary layer approach within continuum crystal plasticity framework. The results show that the near-tip deformation field, especially the development of kink and slip shear bands, is sensitive to the constraint level. On imposition of negative T-stress, a significant drop in the hydrostatic stress level is noticed in the region ahead of the tip. This suggests loss of crack tip constraint with negative T-stress, which is akin to isotropic plastic solids. The reason for the loss of crack tip constraint is traced to the occurrence of an elastic sector near the notch tip. The results also show that a two-parameter (such as K-T or J-Q) characterization of near-tip fields is necessary to accommodate different constraint levels in FCC single crystals. The results of the boundary layer formulation are used to guide the construction of asymptotic solutions near the crack tip corresponding to various constraint levels in elastic-perfectly plastic FCC single crystal. Two families of alternate asymptotic solutions are constructed by introducing an elastic near-tip sector. These families of stress fields are parameterized by the normalized opening stress ahead of the tip, τA22/τo, where τo is the critical resolved shear stress, and a quantity (p) which characterizes the coordinates of the point where elastic unloading commences in stress plane. The results show that the stress distribution corresponding to each member of these families, as well as the trajectories in stress plane as the crack tip is traversed, agree well with finite element results for a certain value of T-stress. In order to validate the above numerical and analytical solutions, the nature of crack tip deformation in aluminium single crystals is examined experimentally in a high constraint three point bend (TPB) specimen and in a low constraint single edge notch tensile (SENT) geometry. These experiments provide evidence, based on in-situ Electron Back Scattered Diffraction (EBSD) of the existence of kink shear bands (involving lattice rotation) exactly as predicted by Rice [J.R. Rice, Mech. Mater. 6 (1987) 317] and the present finite element analysis. The experimental investigation of a low constraint SENT geometry is also supplemented by 3D finite element computations based on continuum crystal plasticity. These computational results enable assessment of 3D effects near the tip. Finally, the effects of different lattice orientations (especially ones for which the slip systems are not symmetric with respect to the notch line) on the near-tip fields are studied pertaining to various constraint levels. The results obtained for different orientations show that the near-tip deformation field is sensitive to the constraint level. The stress distribution and the size and shape of plastic zone near the notch tip are also strongly influenced by the level of T-stress. It is clearly established that ductile single crystal fracture geometries, would progressively lose stress triaxiality with increase in negative T-stress irrespective of lattice orientation. Also, the near-tip field is shown to be part of a family which can be characterized by two parameters (such as K – T or J - Q).

The computation of the macroscopic response of polycrystalline aggregates from the properties of their single-crystal is a main problem in materials mechanics. During the mechanical deformation processing, all the grains in the polycrystalline material sample are reoriented. A crystallographic texture may thus be developed which is responsible for the material anisotropy. Therefore, the modeling of the texture evolution is important to predict the anisotropy effects present in industrial processes. The formulation of polycrystals plasticity has been the subject of many studies and different approaches have been proposed. Ahzi and M'Guil developed a viscoplastic phi-model. This model takes into account the grains interaction effects without involving the Eshelby inclusion problems.In this thesis, the phi-model was applied to different crystallographic structures and under different loading conditions. The mechanical twinning has been taken into account in the model. The FCC rolling texture transition from copper-type to brass-type texture is studied. The shear tests in FCC metals are also studied. The predicted results are compared with experimental shear textures for a range of metals having a high SFE to low SFE. For BCC metal, we compare our predicted results with those predicted by the VPSC model. We study the slip activities, texture evolutions and the evolution of yield loci. We also present a comparison with experimental textures from literatures for several BCC metals under cold rolling tests. The model has also been extended to HCP metals. We predict the deformation behavior of the magnesium alloy for different interaction strengths. We also compare our predicted results with experimental data from literatures. We show that the results predicted by the phi-model are in good agreement with the experimental ones.