Effect of pore size, morphology and spatial distribution on the thermal conductivity of UO2 ceramics

Dans un réacteur nucléaire, le comportement des combustibles est piloté par des phénomènes thermiques. C'est pourquoi il est important de modéliser précisément leur comportement thermique.L’objectif de ces travaux est d’évaluer l’impact de la microstructure sur les propriétés thermiques d’un combustible UO2 à 50°C.Des céramiques UO2 ont été fabriquées. Deux familles de porosité ont été identifiées à l’aide de différentes techniques d’imagerie (microscopie optique, MEB-FIB et tomographie X) : la porosité occluse de forme quasi-sphérique et localisée dans les granulats d’UO2 et un réseau de porosité "d'assemblage" localisée à l’interface des granulats. Des paramètres descripteurs ont été déterminés par mesures par immersion et par analyse d’images. Des études par homogénéisation analytique et numérique (calculs par transformée de Fourier rapide) ont été réalisées afin d’évaluer l’impact de ces caractéristiques sur la conductivité thermique. Les calculs numériques ont été réalisés sur des images 2D et 3D obtenues par imagerie et générées avec un modèle morphologique original reproduisant les spécificités des structures poreuses observées. Ces études ont mis en évidence l’impact de la répartition spatiale et de l’interconnexion de la porosité d’assemblage sur la conductivité thermique des céramiques UO2. Finalement, le modèle proposé a été comparé à des mesures expérimentales de diffusivité thermique obtenues par méthode Flash. Cette comparaison a permis de montrer que le modèle reproduit les tendances associées à la dégradation de la conductivité thermique mesurée sur les céramiques étudiées.Inside a nuclear reactor core, the behavior of fuels is largely controlled by thermal phenomena. That is why it is very important to model the thermal behavior of fuels very precisely.The objective of this study is to develop a model that indicates the influence of porosity on thermal conductivity at 50° that is representative of the thermal behavior of the UO2 fuels. UO2 fuels were manufactured and their microstructures were studied using optical microscopy, SEM-FIB and X-ray tomography. Two types of porosity were identified: 1) sealed and near-spherical pores which are located in UO2 aggregates, and 2) an interconnected "assembly" porosity located at the interfaces of aggregates. Several descriptive parameters were estimated by immersion measurements and image analysis. Studies based on analytical and numerical homogenization were conducted. Numerical calculations using the Fast Fourier Transform method were performed on images of slice planes obtained with imaging technologies or 3D simulated microstructures generated with an original morphological model reproducing some characteristics of the observed porosity networks. The significant impact of the spatial distribution and the interconnection of the assembly porosity on the thermal conductivity of manufactured UO2 fuels were highlighted. Finally, the proposed model was compared with experimental thermal diffusivity measurements obtained by the Flash method.Discrepancies between the model and the experimental measurements have been largely reduced with the proposed model compared with the standard models, which means that the developed model is more representative of the UO2 thermal behavior

Influence de la taille, de la morphologie et de la distribution spatiale despores sur la conductivité thermique de céramiques UO2

Inside a nuclear reactor core, the behavior of nuclear fuels is largely controlled by thermal phenomena. That is why it is very important to model the thermal behavior of fuels very precisely. A precise estimation of the fuel thermal conductivity is a key part of controlling the thermal phenomena occurring in irradiated fuels. This thermal property depends on several parameters such as the shape and spatial distribution of the pores in fuel microstructures.Standard UO2 nuclear fuels have been used in pressurized water reactors (PWR). They exhibit a standard network of pores with near-spherical shape. The effect of this porosity on the thermal conductivity of standard UO2 fuels has been studied extensively and accordingly modelled. By changing the manufacturing conditions of UO2 fuels, the fuels can exhibit very different pore networks compared to standard UO2 fuels in terms of shape, spatial distribution and volume fraction. However, the standard models only show the influence of the porosity volume fraction on the thermal conductivity of standard UO2 fuels and do not represent the thermal behavior of the manufactured UO2 fuels.The objective of this study is to develop a model that indicates the influence of porosity on thermal conductivity and that is representative of the thermal behavior of the manufactured UO2 nuclear fuels. This study is performed on non-irradiated UO2 fuels which simulate microstructures of non-irradiated and irradiated UO2 fuels.Two complementary approaches were used to develop and validate this model: 1) experimental characterizations of UO2 microstructures and 2) studies based on analytical and numerical homogenization.UO2 fuels were manufactured and their microstructures were studied using optical microscopy, SEM-FIB and X-ray tomography. Two types of porosity were identied: 1) sealed and near-spherical pores which are located in UO2 aggregates, and 2) an interconnected network of pores located at the interfaces of aggregates (named here "assembly porosity"). Several descriptive parameters (porosity volume fraction, shape, size, spatial distribution, angular distribution and interconnection) were estimated by immersion measurements and image analysis. Studies based on analytical and numerical homogenization were conducted. Numerical calculations using the Fast Fourier Transform method were performed on images of slice planes obtained withimaging technologies or 3D simulated microstructures generated with an original morphological model reproducing some characteristics of the observed porosity networks. The impact of the descriptive parameters on thermal conductivity was investigated. The significant impact of the spatial distribution and the interconnection of the assembly porosity on the thermal conductivity of manufactured UO2 fuels were highlighted. Finally, the proposed model was compared with experimental thermal diffusivity measurements obtained by the Flash method.Discrepancies between the model and the experimental measurements have been largely reduced with the proposed model compared with the standard models, which means that the developed model is more representative of the UO2 thermal behavior.En modifiant les conditions de fabrication, il est possible d'obtenir des microstructures de dioxyde d'uranium (UO2) possédant des réseaux de porosité différents (en termes de fraction volumique de pores, de taille, de morphologie et de distribution spatiale) par rapport à celui des céramiques utilisées comme combustibles standard dans le parc électronucléaire français.L'objectif est d'évaluer l'impact de la microstructure sur les propriétés thermiques d'un combustible UO2. Pour cela, un modèle donnant l'influence du réseau poreux sur la conductivité thermique d'une céramique UO2 est développé à partir d'une étude à 50°C sur des céramiques vierges représentatives de microstructures après fabrication et simulant l'évolution avec l'irradiation du réseau poreux observé sur des combustibles UO2 non standard.Le développement et la validation de ce modèle sont basés sur deux approches complémentaires : des caractérisations expérimentales de la microstructure des céramiques et des études par homogénéisation double-échelle (analytique et numérique).Des lots différents de céramiques UO2 ont été fabriqués de façon à obtenir des céramiques présentant des réseaux poreux variés en termes de fractions volumiques de porosité totale, ouverte et fermée. Deux familles de porosité ont été identifiées à l'aide de différentes techniques d'imagerie (microscopie optique, MEB-FIB et tomographie X) : la porosité occluse de forme quasi-sphérique et localisée dans les granulats d'UO2 et un réseau interconnecté de porosité localisée à l'interface des granulats (ce réseau est appelé dans cette étude porosité d'assemblage).Des paramètres descripteurs (taux, morphologie, taille pour les deux familles de pores et distribution angulaire pour la porosité d'assemblage) ont été déterminés par mesures par imbibition et par analyse d'images. La tomographie X et le MEB-FIB ont permis d'observer le caractère interconnecté 3D des pores d'assemblage. Des études par homogénéisation analytique et numérique (calculs par transformée de Fourier rapide) ont été réalisées afin d'évaluer l'impact de ces caractéristiques sur la conductivité thermique. Les calculs numériques ont été réalisés sur des images issues de plans de coupes obtenues par imagerie et ainsi que sur des images 2D et3D générées avec un modèle morphologique original reproduisant les spécificités des structures poreuses observées. Ces études ont mis en évidence l'impact important de la morphologie de type fissures, de la répartition spatiale et de l'interconnexion de la porosité d'assemblage sur la conductivité thermique des céramiques UO2. Des caractérisations sur céramiques proches du 100% dense ont par ailleurs permis d'évaluer la conductivité thermique de ces céramiquesdans ce cas limite. Finalement, le modèle proposé dépend du taux de porosité occluse et de la porosité d'assemblage, laquelle est assimilée à un réseau interconnecté de fissures distribuées autour des granulats UO2 et associée à une densité de fissures donnée. La comparaison de ce modèle aux mesures expérimentales de diffusivité thermique (méthode Flash) confirme le rôlemajeur joué par la porosité d'assemblage qui permet effectivement de différencier les propriétés thermiques des différents lots. Par ailleurs, le modèle reproduit les tendances associées à la dégradation de la conductivité thermique mesurée sur les céramiques étudiées

Int J Pharm

Predicting tablet defects, such as capping, that might occur during manufacturing, is a challenge in the pharmaceutical industry. In the literature, different parameters were presented to predict capping but no general consensus seems to have been reached yet. In this article, we chose to study a wide range of products (18 formulations, 8 of which presenting capping) to predict capping on biconvex tablets using the properties characterized on defect-free flat-faced tablets (tensile strength, solid fraction, elastic recovery, etc.), made using the same process parameters. Single parameters and predictive indices presented in the literature were evaluated on this set of formulations and were found not suitable to predict capping. A predictive model was then developed using a decision tree analysis and was found to depend only on three in-die tablet properties: the plastic energy per volume, the in-die elastic recovery and the residual die-wall pressure. This model was tested on another set of 13 formulations chosen to challenge it. The capping behavior of 29 out of the 31 formulations studied in total was well estimated using the developed model with only two products which were predicted to cap and did not. This shows the potential of the used approach in terms of risk analysis and assessment for capping occurrence

Int J Pharm

Capping is a common defect that can occur during the manufacturing of pharmaceutical tablets. Several studies showed that decreasing the unloading speed of the manufacturing cycle plays a role in the occurrence of such defects. Following this idea, we study in this work the influence of the unloading step on capping using a compaction simulator. Measuring the die wall pressure made it possible to detect precisely that tablets capped just after the unloading (some milliseconds only). To evaluate the impact of the unloading speed on capping, we developed a two-step unloading phase controlled by three manufacturing parameters. It was possible to mitigate capping by decreasing the speed at which the contact between the punches and the tablet was lost. Capping seemed due to dynamical effects related to the release of the axial pressure. The modification of the unloading step to mitigate capping led to significant changes in tablet density but no clear trends were found for the residual die-wall pressure and tablet strength. This work made it possible to improve the understanding of capping. Moreover, the two-step unloading cycle gave a new idea for possible modifications that could be done on rotary presses in order to mitigate capping

Characterization of the viscoelasticity of pharmaceutical tablets using impulse excitation technique

Pharmaceutical tablets can be produced on different kinds of presses that may have very different compaction kinematics. Strain rate sensitivity (SRS) is thus an important property for the powders used to produce pharmaceutical tablets. Viscoelasticity is one of the aspects of the SRS and can be sometimes difficult to characterize. In this work, impulse excitation technique was used as an easy-to-implement method for characterizing viscoelasticity using the fact that this property induces damping which can be detected on resonance spectra as peak enlargements. A damping ratio, related to the first flexural vibration mode, was determined on impulse excitation frequency spectra using the half-power bandwidth method on tablets made with different products. This method made it possible to obtain reproducible results for the damping ratio. As viscoelasticity is not the only phenomena that can promote damping, tests were made in order to assess the influence of other parameters: viscoplasticity, porosity and tablet dimensions. Results indicated that the influence of these phenomena could be considered as negligible. Finally, the damping ratios determined were in good accordance with the known viscoelastic behavior of the studied products. This made it possible to confirm that impact resonance is an easy and quick way to characterize the viscoelastic nature of pharmaceutical tablets

Use of impulse excitation technique for the characterization of the elastic anisotropy of pharmaceutical tablets

Capping and lamination are common defects occurring during the manufacturing of pharmaceutical tablets. Several studies showed that tablet anisotropy can play a role in the occurrence of such defects. In this work, we propose a new and easy methodology to characterize the anisotropy of flat-faced cylindrical tablets, which are considered as transversally isotropic due to the process, through the study of their elastic properties using impulse excitation technique and finite-element method (FEM) simulations. The study was performed for tablets with a thickness-to-diameter-ratio between and FEM simulations showed that it was possible to determine three out of the five elastic constants of the tablet using the first three natural vibration modes. An anisotropic index was then built as the ratio of the two apparent shear moduli. Moreover, in order to simplify the estimation of tablet anisotropy and to avoid the systematic use of FEM simulations, an analytical model was also developed. It only requires the measurement of the tablet dimensions and of the first three natural frequencies. Using this technique, experimental measurements on tablets made of classical pharmaceutical excipients were done and found coherent with the existing literature. This indicates thus that this methodology is a quick, easy and reliable characterization method in order to access tablet anisotropy

Caractérisation du réseau de porosité d'une céramique de dioxyde d'uranium en vue de la modélisation de sa conductivité thermique

National audienceLes céramiques de dioxyde d’uranium (UO2) obtenues par frittage sont utilisées comme combustibles dans les réacteurs à Eau Pressurisée (REP) du parc électronucléaire français. Ces céramiques possèdent une microstructureconstituée d’une matrice solide d’UO2 et d’un réseau de porosités. La porosité totale est l’ensemble des pores présents dans un combustible. Deux familles de porosités peuvent être distinguées : les pores isolés dans la phase solide (la porosité fermée) et ceux interconnectés et accessibles à des fluides extérieurs (la porosité ouverte)

Effective properties of an isotropic solid weakened by micro-cracks located at inter-granular boundaries

International audienceThis study presents a new methodology for estimating the effective properties of solids containing cracks along the inter-granular boundaries, using analytical developments and numerical simulations. The latter are based on the generation of virtual microstructures of such type obtained by superimposing a Voronoï tessellation modeling the granular network with a random dispersion of overlapping spheres in 3-D, or disks in 2-D, which serve to locate the cracks at the inter-granular boundaries. The different features of this microstructure model are studied herein, especially the morphological effects induced by varying the size ratio between grains and spheres/disks. By means of full-field simulations, the effective thermal conductivities of the generated microstructures are estimated and compared with those of uniformly weakened solids (presenting uniform crack dispersion). For the latter microstructures, the Ponte-Castañeda & Willis (1995) upper bound turns out to be close to the full-field results. In addition, the full-field computations show that the spatial distribution of inter-granular cracks induces a dramatic degradation of the effective thermal conductivity. Modifying only the cutoff crack density in the mathematical expression of the Ponte Castañeda and Willis bound provides a relevant analytical estimate of the effective conductivity of solids weakened by inter-granular cracks. This cutoff crack density only depends on the microstructural parameters. This new estimate is shown to improve the one derived by Sevostianov & Kachanov (2019) and based on the differential scheme at least for the microstructures considered herein. Finally, new estimates of the moduli of elasticity for isotropic cracked solids weakened at inter-granular boundaries are also provided. The effective bulk modulus thus estimated for 3-D solids is shown to remain below the upper bound which can also be generated by injecting the effective conductivity predicted by full-field computations into the classical cross-property relations

Realistic morphological models of weakly to strongly branched pore networks for the computation of effective properties

International audienceWe provide a detailed expository report of a new methodology aiming at building a numerical model of the complex pore distribution of porous UO$_2$ ceramics, tunable to real materials, in view of computing their effective thermal behavior. First, based on 2D optical microscopy images, we characterize the material of interest, dedicating a special attention to the porous network because of its major influence on the thermal behavior. Following Meynard et al. (2022), we then propose a simple morphological model combining a Voronoi tessellation and a boolean model, involving a limited number of parameters, from which 3D virtual microstructures (and so 2D cross-sections) can be generated. These parameters are tuned in order to select within our class of models the microstructures that are the most representative of the real ones ; in practice, this optimization process minimizes a cost function based on morphological descriptors computed from the 2D cross-sections. Last, we perform 2D full-field thermal simulations on cross-sections through Representative Volume Elements of both the numerical and the experimental microstructures. We validate our approach by qualitative and quantitative comparisons relative to both global properties and local field statistics