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The present work deals with the investigation of the micromechanical behaviour of a duplex steel, which consists of two phases (austenite and ferrite) exhibiting significantly different mechanical properties. The stresses in both phases were experimentally determined in the elastic and plastic ranges of deformation using synchrotron radiation diffraction experiments. The used methodology enabled to determine the values of initial stresses and to study the evolutions of the principal phase stresses and the second order stresses during the elastic, as well as the plastic range of deformation. With the help of a self-consistent model, the critical resolved shear stresses and the work hardening parameters for slip systems, active in each phase, were also estimated. Comparison of the measured phase stresses and lattice strains evolutions with the model results showed a good agreement between prediction and experiment when the initial stress state in the sample and shape of grains approximated by ellipsoidal inclusions were taken into account. The overall outcome of the work is the determination of stress partitioning between the two phases of a polycrystalline material for all deformation stages, determined directly from diffraction experiment. The results enabled analyses of von Mises, hydrostatic stresses as well as second order stresses evolutions in both phases during tensile deformation. Finally, the experimental data were successfully compared with predictions of the self-consistent deformation model.

The main purpose of this work is to develop neutron diffraction methodology in order to determine stresses localised in polycrystalline grains during elastoplastic deformation, directly from experiment. As a result, for the first time, the von Mises stress for chosen grain orientations and Critical Resolved Shear Stresses (CRSS) for active slip systems were unambiguously measured without the help of crystallographic models, which introduce different theoretical assumptions. The stresses measured for groups of grains and the determined CRSS values are important characteristics of a material, which allow to study plastic deformation in textured material at different scales: slip system and grain, which play a key role in mechanical properties and formability of the material. The new method was successfully tested and applied to textured AZ31 alloy subjected to tensile deformation and the components of stress tensor were for the first time determined from measured lattice strains corresponding to chosen orientations of crystallite lattice. The obtained results positively verified hypotheses that, during plastic deformation, a large difference in the hardness as well as in the localised stresses occurs for grains having different lattice orientations. It was found directly from experiment that, the activation of basal glide, having small CRSS, does not lead to significant plastic deformation, and the activation of other non-basal systems (with higher CRSS) induces the development of plasticity at the macroscopic scale. The early plastic deformation occurring due to slip on basal system is small but it can destructively affect fatigue life, limiting applicability of the material for structural components. Finally, the comparison of experimental results with a modified version of Elastic-Plastic Self-Consistent (EPSC) model showed its capability to simulate the mechanical behaviour of such materials.

The multireflection grazing-incidence X-ray diffraction method is used to test surface stresses at depths of several micrometres in the case of metal samples. This work presents new ways of analysing experimental data obtained by this method for Ni samples exhibiting significant elastic anisotropy of crystals. Three different methods of determining biaxial stresses and lattice parameter were compared. In the first approach, the calculations were performed using the linear least-squares method, and then two simplified procedures based on simple linear regression (weighted and non-weighted) were applied. It was found that all the tested methods give similar results, i.e. almost equal values of the determined stresses and lattice parameters and the uncertainties of their determination. The advantage of analyses based on simple linear regression is their simplicity and straightforward interpretation, enabling easy verification of the influence of the crystallographic texture and the presence of shear stresses, as well as graphical determination of the stress-free lattice parameter.

Multireflection grazing-incidence X-ray diffraction was used to investigate the structure and residual stress gradients in the near-surface region of mechanically treated titanium samples. The development of this method by using a white synchrotron beam during an energy dispersive diffraction experiment is proposed., The main focus of the presented work was the investigation of structure and residual stress gradients in the near-surface region of materials studied by X-ray diffraction. The multireflection method was used to measure depth-dependent stress variation in near-surface layers of a Ti sample (grade 2) subjected to different mechanical treatments. First, the multireflection grazing incidence diffraction method was applied on a classical diffractometer with Cu Kα radiation. The applicability of the method was then extended by using a white synchrotron beam during an energy dispersive (ED) diffraction experiment. An advantage of this method was the possibility of using not only more than one reflection but also different wavelengths of radiation. This approach was successfully applied to analysis of data obtained in the ED experiment. There was good agreement between the measurements performed using synchrotron radiation and those with Cu Kα radiation on the classical diffractometer. A great advantage of high-energy synchrotron radiation was the possibility to measure stresses as well as the a 0 parameter and c 0/a 0 ratio for much larger depths in comparison with laboratory X-rays.

International audience; The mechanical behaviour of each phase in two-phase titanium Ti-18 was studied at room temperature under a low strain rate tensile test until fracture. Due to its selectivity, the X-ray diffraction method was applied for in-situ tensile test to analyse the behaviour of each phase in the direction perpendicular to the loading force. In addition, the biaxial stress states of the initial sample, as well as those of the sample during the tensile test, were determined using multi-reflection grazing incidence X-ray diffraction (MGIXD). The experimental data were compared with the prediction of an elasto-plastic self-consistent model in order to study slips on crystallographic planes and mechanical effects occurring during plastic deformation.

International audience; In the present work, the mechanical behavior of phases in duplex steel during tensile test was studied. Special interest was taken in the analysis of damage process just before failure. In this aim two diffraction methods: in-situ time of flight neutron diffraction and X-ray synchrotron diffraction were applied. Using diffraction data, the slip mechanism on crystallographic planes during plastic deformation was investigated. In the case of aged UR45N steel, it was found that significant softening caused by damage process was initiated in the ferritic phase. The lattice strains measured in situ by two above mentioned diffraction methods were compared with prediction of the self-consistent model.

Multireflection grazing-incidence X-ray diffraction (MGIXD) was used to determine the stress- and strain-free lattice parameter in the surface layer of mechanically treated (polished and ground) tungsten and austenitic steel. It was shown that reliable diffraction stress analysis is possible only when an appropriate grain interaction model is applied to an anisotropic sample. Therefore, verification of the X-ray stress factors (XSFs) was accomplished by measuring relative lattice strains during anin situtensile test. The results obtained using the MGIXD and standard methods (χ and ω geometries) show that the Reuss and free-surface grain interaction models agree with the experimental data. Moreover, a new interpretation of the MGIXD results was proposed and applied for the first time to measure the probability of stacking faults as a function of penetration depth for a polished and ground austenitic sample. The XSF models verified in the tensile test were used in the analysis of residual stress components.

International audience; Owing to its selectivity, diffraction is a powerful tool for analysing the mechanical behaviour of polycrystalline materials at the mesoscale, i.e. phase and grain scale. In situ synchrotron diffraction (transmission mode) during tensile tests and modified self-consistent elastoplastic model were used to study elastic and plastic phenomena occurring in polycrystalline specimens during deformation. The evolution of stress for grains which belong to different phases of duplex stainless steel and pearlitic steel was analyzed.

International audience; The time-of-flight neutron diffraction technique and the elastoplastic self-consistent model were used to study the behaviour of single and multi-phase materials. Critical resolved shear stresses and hardening parameters in austenitic and austenitic–ferritic steels were found by analysing the evolution of the lattice strains measured during tensile tests. Special attention was paid to the changes of the grain stresses occurring due to transition from elastic to plastic deformation. Using a new method of data analysis, the variation of the stress localisation tensor as a function of macrostress was measured. The experimental results were successfully compared with model predictions for both phases of the duplex steel and also for the austenitic sample.

Owing to its selectivity, diffraction is a powerful tool for analysing the mechanical behaviour of polycrystalline materials at the mesoscale (phase and/or grain scale).In situneutron diffraction during tensile tests and elastoplastic self-consistent modelling were used to study slip phenomena occurring on crystallographic planes at small and large deformation. The critical resolved shear stresses in both phases of duplex stainless steel were found for samples subjected to different thermal treatments. The evolution of grain loading was also determined by showing the large differences between stress concentration for grains in ferritic and austenitic phases. It was found that, for small loads applied to the sample, linear elastic deformation occurs in both phases. When the load increases, austenite starts to deform plastically, while ferrite remains in the elastic range. Finally, both phases undergo plastic deformation until sample fracture. By using an original calibration of diffraction data, the range of the study was extended to large sample deformation. As a result, mechanical effects that can be attributed to damage processes initiated in ferrite were observed.

International audience; Time of flight neutron diffraction method was applied to measure elastic lattice strains in austenitic steel during "in situ" tensile test. Comparing experimental data with self-consistent model, the critical resolved shear stress and hardening parameters were determined for polycrystalline grains. The result allowed us to determine the main component of the stress localization tensor, relating the rate of grain stress with the applied macrostress rate. The evolution of concentration tensor in function of the applied macrostress was analyzed. Finally, the load transfer between grains during yielding of the sample was studied.

International audience; Different experimental approaches have been performed in order to extract damage at several scales. In this paper two experimental methods are treated. Neutron diffraction coupled with tensile test has been performed to study damage at mesoscopic scale. At macroscopic scale, classical tensile test has been used to extract damage effects, from material hardening evolution. Optical measurements and particular data treatment have been used in order to correct data for the necking phenomenon at large deformation, for each experimental method. Damage process in duplex steels has then been analysed at both macroscopic and mesoscopic scales using scale transition models. Eventually, investigations at those scales have been compared to understand correlation between mesoscopic and macroscopic behaviour of our material.

In this work the parameters characterizing the individual elastoplastic mechanical behaviour of each phase in austeno-ferritic duplex stainless steels are determined by using X-ray diffraction during a uniaxial tensile test. The interpretation of the experimental data is based on the diffraction elastic constants calculated by the self-consistent model taking the anisotropy of the studied materials into account. The elastoplastic model is used to predict the evolution of the internal stresses during loading, and to identify the critical resolved shear stresses and strain hardening parameters of the material. The effect of the chemical composition on the individual elastoplastic behaviour of the studied phases is established by comparing results from three different samples. Finally, the X-ray diffraction results are compared with those previously obtained by using neutron radiation.

The mechanical properties of both phases in duplex stainless steel have been studied in situ using neutron diffraction during mechanical loading. Important differences in the evolution of lattice strains are observed between tests carried out in tension and compression. An elastoplastic self-consistent model is used to predict the evolution of internal stresses during loading and to identify critical resolved shear stresses and strain hardening parameters of the material. The differences between tensile and compressive behaviours of the phases are explained when the initial stresses are taken into account in model calculations. The yield stresses in each phase of the studied steel have been experimentally determined and successfully compared with the results of the elastoplastic self-consistent model.

A new method for calculation of the diffraction elastic constants, based on the selfconsistent model, is proposed and tested. This method is especially useful in the interpretation of the results of X-ray measurements since the ellipsoidal inclusion near the sample surface is considered. In X-ray diffraction the information volume of the sample is defined by absorption, causing unequal contribution of different crystallites to the intensity of the measured peak. Consequently, the surface grains participate more effectively in diffraction than the grains which are deeper in the sample.

An X-ray diffraction method based on measurement of lattice strains has been applied to determine residual stresses in plastically deformed duplex stainless steel. In this method the interplanar spacings are measured for various orientations of the scattering vector. The non-standard interpretation of the experimental data is based on the least square fitting procedure, in which the theoretical results of the self-consistent model are used. The method was successfully applied to the study of residual stresses in two-phase steel subjected to tensile deformation. Significant anisotropy of the incompatibility stresses was observed in textured samples. The values of the anisotropic microstresses exceeded those of the macrostresses and increased with the magnitude of applied deformation. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A new method for determining the parameters characterising elastoplastic deformation of two-phase material is proposed. The method is based on the results of neutron diffraction and mechanical experiments, which are analysed using the self-consistent rate-independent model of elastoplastic deformation. The neutron diffraction method has been applied to determine the lattice strains and diffraction peak broadening in two-phase austeno-ferritic steel during uniaxial tensile test. The elastoplastic model was used to predict evolution of internal stresses and critical resolved shear stresses. Calculations based on this model were successfully compared with experimental results and the parameters characterising elastoplastic deformation were determined for both phases of duplex steel.

The X-ray diffraction measurements based on the grazing incident geometry were applied to determine lattice strains in polycrystalline materials. This method enables a non-destructive measurement at chosen depth below the sample surface. The volume, for which the stress is measured, is well defined and it does not vary during experiment. The multireflection method was used for analysis of the experimental results since the interplanar spacings were measured for various orientation of the scattering vector as well as for various crystallographic planes {hkl}. Applying two different wavelengths of X- ray radiation and various incident angles non-destructive measurements of the residual stresses in function of penetration depth were performed. The variation of stresses in plastically deformed surface layers of steel samples was successfully determined and the values of the stresses were confirmed by standard diffraction measurement.

The thesis is dedicated to the study of elasto-plastic behavior of multiphase polycrystalline materials and ductile damage at different scales. The microscopic heterogeneities have important influence on the macroscopic mechanical behavior of materials. Ductile damage is still difficult to measure at small scales. The following issues are the main topic involved in this thesis: 1. The evolution of mechanical behavior in phases and groups of grains, under external load until fracture.2. The influence of intrinsic heterogeneity on the macroscopic behavior of two-phase materials.3. The influence of necking and ductile damage, on the behavior of grains with different orientation families.4. The indirect measurement of ductile damage at small scales by diffraction. To answer these questions, duplex steels and two-phase titanium are tested. The diffraction method is used to perform in situ measurements during tensile test until fracture. Predictions are carried out by an elasto-plastic self-consistent model, in which ductile damage have been integrated. Experimental data on different scales are compared with these predictions. In addition, nano-indentation tests are carried out to study the evolution of phases’ mechanical properties along the neck until fracture edge. Microscopic images were also taken in order to observe the fracture surfaces of studied materials, Cette thèse est dédiée à l’étude du comportement élasto-plastique des matériaux polycristallins multiphasés ainsi que de l’endommagement ductile à différentes échelles. Les hétérogénéités microscopiques ont une influence importante sur la réponse mécanique macroscopique des matériaux. Et l’endommagement ductile est encore difficile à mesurer aux échelles fines. Cette thèse traite des problématiques suivantes : 1. L’évolution du comportement des phases et des grains sous chargements jusqu’à la rupture.2. L’influence de l’hétérogénéité intrinsèque au niveau micro, sur le comportement macroscopique des matériaux biphasés.3. L’influence de la striction et de l’endommagement sur le comportement de familles d’orientation de grains.4. La mesure indirecte de l’endommagement échelle fine par diffraction. Afin d’enquêter sur ces questions, l’acier duplex et le titane biphasé sont testés. La diffraction est utilisée pour effectuer des mesures in situ non-destructive au cours d’essais de traction et jusqu’à la rupture. Des simulations sont réalisées grâce à un modèle auto-cohérent élasto-plastique, dans lequel est introduite la modélisation de l’endommagement ductile. Les données expérimentales aux différentes échelles y sont comparées. En outre, des tests de nano-indentation et observation micrographiques sont effectués pour observer l’évolution spatiale des propriétés mécaniques des phases le long de la striction et jusqu’à la surface de rupture

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, 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