Analyse des mécanismes de glissement des dislocations dans l’UO2 à l’aide de la modélisation multi-échelles comparée à l’expérience

This thesis is part of the study of fuel elements of pressurized water reactors and, more specifically, focus on the understanding and modelling of the viscoplastic behavior of uranium dioxide (UO2) at polycrystalline scale. During the incidental operation of the reactor, the fuelundergoes a strong increase of temperature and thermal gradient between the center and the periphery of the pellet leading to viscoplastic strains due to dislocation movement mechanisms. First, a crystal plasticity model was developed in order to describe the viscoplastic anisotropy of the material considering the temperature and the loading rate. Finite element (FE) simulations on single crystals enabled to highlight that the three slip modes generally observed in UO2 are crucial to describe the anisotropic behavior of the material. Secondly, coefficients of the interaction matrix have been identified specifically for UO2 in order to improve the polycrystal modelling. Indeed, by calculating geometrically necessary dislocations (GNDs), which are responsible of the great increase of the stored dislocation density in polycrystals, the interactions between dislocations enable to simulate de grain size sensitivity and hardening of the fuel pellet. Finally, the model adapted for polycrystals, have been validated by comparing FE simulations with pellet compression tests and by comparing the simulated intra-granular behavior with EBSD measurements. Thanks to the latter comparison, it is possible to indirectly compare the strain heterogeneities in the grains.Dans le cadre de l'étude des éléments combustibles des réacteurs à eau pressurisée, cette thèse s'inscrit dans la compréhension et la modélisation du comportement viscoplastique du dioxyde d'uranium (UO2) à l'échelle du polycristal. Lors de fonctionnement de type incidentel du réacteur, le combustible subit une forte élévation de la température avec un gradient thermique entre le centre et la périphérie de la pastille engendrant des déformations viscoplastiques contrôlées par des mécanismes liés aux mouvements des dislocations. Dans un premier temps,un modèle de plasticité cristalline a été développé de manière à décrire l’anisotropie viscoplastique du matériau en fonction de la température et de la vitesse de sollicitation. Des simulations par éléments finis (EF) sur monocristaux ont permis d’identifier que les trois modes de glissement généralement observés dans l'UO2 ont une importance capitale pour décrire le comportement anisotrope du matériau. Dans un second temps, les coefficients de la matrice d'interactions entre dislocations ont été déterminés spécifiquement pour l’UO2 afin d’améliorer la modélisation des polycristaux. En effet, en calculant par EF les dislocations géométriquement nécessaires (GNDs), qui sont responsables d’une forte augmentation de la densité de dislocations stockées dans les polycristaux, les interactions entre dislocations permettent de simuler l’effet de taille de grain et l’écrouissage des pastilles. Finalement, le modèle, adapté pour les polycristaux, a été validé par comparaison avec les essais expérimentaux sur pastille et par comparaison du comportement intragranulaire simulé avec des mesures EBSD. Grâce à cette dernière comparaison, il est possible de remonter indirectement aux hétérogénéités de déformation dans les grains

Analysis of dislocation gliding mechanisms in UO2 thanks to multi-scale modelling compared to the experience

Dans l'étude des éléments combustibles des réacteurs à eau pressurisée, cette thèse s'inscrit dans la compréhension et la modélisation du comportement viscoplastique du dioxyde d'uranium (UO₂) à l'échelle du polycristal. Lors de fonctionnement de type incidentel du réacteur, le combustible subit une forte élévation de la température avec un gradient thermique de la pastille engendrant des déformations viscoplastiques contrôlées par des mouvements de dislocations. D'abord, un modèle de plasticité cristalline a été développé de manière à décrire l’anisotropie viscoplastique du matériau en fonction de la température et de la vitesse de sollicitation. Des simulations par éléments finis (EF) sur monocristaux ont permis d’identifier que les trois modes de glissement généralement observés dans l'UO₂ sont importants pour décrire le comportement anisotrope du matériau. Dans un second temps, les coefficients de la matrice d'interactions entre dislocations ont été déterminés spécifiquement pour l’UO₂ afin d’améliorer la modélisation des polycristaux. En effet, en calculant par EF les dislocations géométriquement nécessaires, qui sont responsables d’une forte augmentation de la densité de dislocations stockées dans les polycristaux, les interactions entre dislocations permettent de simuler l’effet dé taille de grain et l’écrouissage des pastilles. Finalement, le modèle, adapté pour les polycristaux, a été validé par comparaison avec les essais expérimentaux sur pastille et par comparaison du comportement intra-granulaire simulé avec des mesures EBSD. Grâce à cette dernière comparaison, il est possible de remonter indirectement aux hétérogénéités de déformation dans les grainsThis thesis is part of the study of fuel elements of pressurized water reactors and, more specifically, focus on the understanding and modelling of the viscoplastic behavior of uranium dioxide (UO₂) at polycrystalline scale. During the incidental operation of the reactor, the fuel undergoes a strong increase of temperature and thermal gradient between the center and the periphery of the pellet leading to viscoplastic strains due to dislocation movement mechanisms. First, a crystal plasticity model was developed in order to describe the viscoplastic anisotropy of the material considering the temperature and the loading rate. Finite element (FE) simulations on single crystals enabled to highlight that the three slip modes generally observed in UO₂ are crucial to describe the anisotropic behavior of the material. Secondly, coefficients of the interaction matrix have been identified specifically for UO₂ in order to improve the polycrystal modelling. Indeed, by calculating geometrically necessary dislocations (GNDs), which are responsible of the great increase of the stored dislocation density in polycrystals, the interactions between dislocations enable to simulate de grain size sensitivity and hardening of the fuel pellet. Finally, the model adapted for polycrystals, have been validated by comparing FE simulations with pellet compression tests and by comparing the simulated intra-granular behavior with EBSD measurements. Thanks to the latter comparison, it is possible to indirectly compare the strain heterogeneities in the grain

Plastic anisotropy and composite slip: Application to uranium dioxide

International audienceThe mechanical behaviour of UO$_2$ single crystal is under debate due to the unexpected multi-slip observations in the experiments that involve dislocations in $\frac{1}{2}$ {100} slip systems but also in $\frac{1}{2}$ {110} and $\frac{1}{2}$ {111}. We propose a multi-scale model based on a composite slip in which, under the effect of cross-slip, part of the dislocation density in primary slip systems can be transferred in secondary systems with a lower propensity to glide but a more favourable orientation regarding the shear stress. This approach allows to describe the anisotropic mechanical response of UO$_2$ single crystal with an accuracy never reached up to now. After identifying the relevant slip systems depending on the orientation using a Schmid approach, dislocation dynamics simulations are used to assert if the cross-slip induces a composite slip and to quantify its effect on the flow stress which appears constrained by the activity of $\frac{1}{2}$ {111} systems. In agreement with this result, the composite slip is adapted to couple the activity of slip systems with common Burger vectors in a crystal plasticity framework for a closer comparison to the experiment. This multi-scale approach significantly improves our current knowledge on the links between dislocation microstructures and mechanical properties in UO$_2$ . Composite slip mechanism appears as a candidate to explain unexpected plastic behaviours as often observed in complex materials with multiple slip modes underling that slip activation may be more complex than in usual constitutive laws

Athermal dislocation strengthening in UO2

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POROUS POLYCRYSTAL FULL-FIELD SIMULATIONS ON NUCLEARMOX FUEL MATERIALS

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Viscoplastic behavior of a porous polycrystal with similar pore and grain sizes: application to nuclear MOX fuel materials

International audienceThis study deals with the viscoplastic behavior of a porous polycrystal with pores and grains of similar sizes.Such a microstructure can be encountered in irradiated nuclear Mixed OXide (MOX) fuel materials. MIcronizedMASter blend (MIMAS) MOX are multi-phase materials mainly composed of two or three phases dependingon their fabrication process. One of these phases corresponds to plutonium-rich agglomerates which stronglyevolve during irradiation. The large Pu-rich agglomerates become highly porous due to the accumulation offission gases and to the apparition of irradiation bubbles. In a past study, Wojtacki et al. (2020) showedthat pores distributed inside the Pu-rich clusters have a strong impact on the overall viscoplastic behaviorof MOX fuel, when considering a purely isotropic behavior for the Pu-rich clusters. In the present study,the impact of pores similar in size to the surrounding anisotropic grains on the overall viscoplastic behavioris studied in details through numerical full-field simulations. A crystal plasticity model recently developedby Portelette et al. (2018) is used to describe the anisotropic behavior of the polycrystalline matrix withdislocation glide mechanisms. Three-dimensional full-field simulations are performed by a method based onFast Fourier Transforms (FFT) to compare the behavior of porous materials with that of dense materials. Thesesimulations show that, in the case of spherical pores, their relative size with respect to that of the grains playsa minor role in the overall viscoplastic behavior. However, in the case of polyhedral pores, the relative sizeeffect is more pronounced. With fixed porosity, decreasing the relative size of the cavities with respect to thesize of grains leads to a softening of the material and a decrease of the viscoplastic flow stress

POROUS POLYCRYSTAL FULL-FIELD SIMULATIONS ON NUCLEARMOX FUEL MATERIALS

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POROUS POLYCRYSTAL FULL-FIELD SIMULATIONS ON NUCLEARMOX FUEL MATERIALS

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Crystal viscoplastic modeling of UO2 single crystal

International audienceThe viscoplastic behavior of uranium dioxide (UO2) single crystal is of great interest to perform predictive multiscale modeling of the nuclear fuel. Here, a viscoplastic model is built considering dislocation glide in ½{100} and ½{110} slip systems. The constitutive law parameters are determined adjusting the temperature dependency of the experimental critical resolved shear stress for both principal slip modes. Crystal plasticity finite element simulations of single crystal compression tests show a reasonable agreement with experimental viscoplastic anisotropy of UO2. However, for specific orientations where ½{111} slip is observed experimentally, significant differences remain between experimental and computed compression stresses. Therefore, the role of ½{111} slip is investigated based on a parametric study that provides new insights on UO2 plastic deformation. Several parameterizations of ½{111} slip are tested highlighting the complexity of UO2 viscoplastic behavior. Significant improvements are still required to explain all simulation-experiment gaps

Numerical simulation of the UO2 viscoplasticity at the polycrystal scale : microscopic validation

International audienceA model based on dislocation glide in a single crystal has been developed in order to simulate uranium dioxide (UO2) viscoplastic behavior during reactor operation of PWRs (pressurized water reactors). This model is then implemented through a 3D finite element formulation to simulate the polycrystal behavior in the volume element application (VER) of the PLEIADES nuclear fuel behavior software environment. With this full field computation, the strain incompatibility induced by the disorientation at grain boundaries is computed along with associated stress and strain heterogeneities. In order to assess the grain size effect, the geometrically necessary dislocation densities are also computed from the viscoplastic strain field. The main objective of this study is to propose a validation methodology at the microscopic scale, in order to check that the computed stress-strain heterogeneity is in good agreement with experimental results. The experimental data used for this validation are based on 2D SEM-EBSD characterizations of polished sections of UO2 pellets, with as-fabricated grains in the 10 µm size range, following to uniaxial compressive creep tests. EBSD provides quantitative micronscale information relating to the crystal lattice orientation, which is strongly correlated to the local viscoplastic strain induced during the mechanical test. Regarding simulation results, the crystal lattice orientation is derived from the elastic rotation computed through a finite strain formulation of the elastoviscoplastic transformation. First a qualitative comparison between experiment and simulation is proposed which enables us to analyze the spatial variation of orientations within the original grains. Simulation results show that polycrystal viscoplas-ticity induces a non-uniform crystal lattice orientation as is observed from EBSD measurements. However the experimental spatial variation is discontinuous, as sub-grain boundaries appear, whereas our model describes a continuous variation in grain orientation. Statistical comparisons are provided of the orientation changes within the grains. In order to avoid grain size sensitivity and 2D-3D corrections, a variogram function is defined. According to these first results, it appears that the spatial statistical distribution is consistent with experimental results. However, the magnitude of the orientation variation is greater in the simulation, which suggests that the strain incompatibility is overestimated. Applying this methodology provides a more robust means of both analyzing basic deformation mechanisms and identifying the appropriate intragranular model to describe viscoplastic strains in uranium dioxide polycrystal