Computational studies on selective aromatic C-F bond activation at rhodium and ruthenium

Density functional theory (DFT) calculations have been carried out to study the selective C–F bond activation of fluoroaromatics at rhodium and ruthenium complexes. The C–F activation reaction of C6F5H with [Rh(SiR3)(PMe3)3] (R3 = Me2Ph, Ph3) to give [Rh(4-C6F4H)(PMe3)3] and FSiR3, has been studied computationally. Using a model system, [Rh(SiMe3)(PMe3)3], calculations show that the lowest energy process occurs via initial phosphine dissociation and subsequent C–F oxidative addition to give trans-[Rh(4-C6F4H)(F)(SiMe3)(PMe3)2], with computed free energies of activation (∆G‡) of +13.2 kcal/mol and +12.4 kcal/mol, respectively. Reductive elimination and phosphine association to give the final products [Rh(4-C6F4H)(PMe3)3] and FSiMe3 are found to be facile. In addition, calculations show that C–F activation at trans- [Rh(SiMe3)(PMe3)2] is more accessible kinetically and thermodynamically than C–H activation (∆∆G‡ = 2.9 kcal/mol, ∆∆G = 51.3 kcal/mol). DFT calculations have been used to model the reaction of C5NF5 at the 2-position with [Rh(X)(PEt3)3] (X = Si(OEt)3, Bpin, where Bpin = pinacolate = –OCMe2CMe2O–). C–F activation at the computational models [Rh(X)(PMe3)3] (X = Si(OMe)3 and Bpin) shows that the lowest pathways proceed via novel silyl- and boryl-assisted C–F activation in which short RhN contacts are computed in the transition states. These occur via modest barriers (∆G‡ = +26.1 kcal/mol and +20.1 kcal/mol, respectively, relative to the two separated reactants) and also account for the experimental selectivity. The hydrodefluorination (HDF) reaction of C6F5H at [Ru(H)2(CO)(NHC)(PR3)2] (NHC = SIMes, SIPr, IMes, IPr; R = Ph) to give 1,2,3,4-C6F4H2, has been investigated. Calculations on small (NHC = IMe, R = H) and full systems (NHC = IMes, R = Ph) have allowed a novel class of reaction mechanism to be defined involving a nucleophilic attack of one hydride ligand at C6F5H. The most accessible pathway has a computed transition state energy of +20.1 kcal/mol in THF (PCM, approach). In addition, calculations reveal that the use of a more sterically encumbered full model system is essential to explain the unusual ortho-regioselectivity observed experimentally

Computational study of the hydrodefluorination of fluoroarenes at [Ru(NHC)(PR₃)<sub style="vertical-align: sub;">2</sub>(CO)(H)<sub style="vertical-align: sub;">2</sub>]: predicted scope and regioselectivities

Density functional theory calculations have been employed to investigate the scope and selectivity of the hydrodefluorination (HDF) of fluoroarenes, C6F6-nHn (n = 0-5), at catalysts of the type [Ru(NHC)(PR3)(2)(CO)(H)(2)]. Based on our previous study (Angew. Chem., Int. Ed., 2011, 50, 2783) two mechanisms featuring the nucleophilic attack of a hydride ligand at a fluoroarene substrate were considered: (i) a concerted process with Ru-H/C-F exchange occurring in one step; and (ii) a stepwise pathway in which the rate-determining transition state involves formation of HF and a Ru-sigma-fluoroaryl complex. The nature of the metal coordination environment and, in particular, the NHC ligand was found to play an important role in both promoting the HDF reaction and determining the regioselectivity of this process. Thus for the reaction of C6F5H, the full experimental system (NHC = IMes, R = Ph) promotes HDF through (i) more facile initial PR3/fluoroarene substitution and (ii) the ability of the NHC N-aryl substituents to stabilise the key C-F bond breaking transition state through F center dot center dot center dot HC interactions. This latter effect is maximised along the lower energy stepwise pathway when an ortho-H substituent is present and this accounts for the ortho-selectivity seen in the reaction of C6F5H to give 1,2,3,4-C6F4H2. Computed C-F bond dissociation energies (BDEs) for C6F6-nHn substrates show a general increase with larger n and are most sensitive to the number of ortho-F substituents present. However, HDF is always computed to remain significantly exothermic when a silane such as Me3SiH is included as terminal reductant. Computed barriers to HDF also generally increase with greater n, and for the concerted pathway a good correlation between C-F BDE and barrier height is seen. The two mechanisms were found to have complementary regioselectivities. For the concerted pathway the reaction is directed to sites with two ortho-F substituents, as these have the weakest C-F bonds. In contrast, reaction along the stepwise pathway is directed to sites with only one ortho-F substituent, due to difficulties in accommodating ortho-F substituents in the C-F bond cleavage transition state. Calculations predict that 1,2,3,5-C6F4H2 and 1,2,3,4-C6F4H2 are viable candidates for HDF at [Ru(IMes)(PPh3)(2)(CO)(H)(2)] and that this would proceed selectively to give 1,2,4-C6F3H3 and 1,2,3-C6F3H3, respectively.</p

Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method

[EN] Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of finite element numerical simulations that involve complex domains. By locally improving the approximation quality, for example, by using the extended finite element method (XFEM), we can solve expensive problems which could result intractable otherwise. Here, we present an error estimation technique for enriched finite element approximations that is based on an equilibrated recovery technique, which considers the stress intensity factor as the quantity of interest. The locally equilibrated superconvergent patch recovery is used to obtain enhanced stress fields for the primal and dual problems defined to evaluate the error estimate.This work was supported by the EPSRC grant EP/G042705/1 "Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method". Stephane Bordas also thanks partial funding for his time provided by the European Research Council Starting Independent Research Grant (ERC Stg Grant Agreement No. 279578) "RealTCut Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery". This work has been carried out within the framework of the research project DPI2010-20542 of the Ministerio de Ciencia e Innovacion (Spain). The financial support of the FPU program (AP2008-01086), the funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged.González Estrada, OA.; Ródenas, J.; Bordas, S.; Nadal, E.; Kerfriden, P.; Fuenmayor Fernández, FJ. (2015). Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method. Computers and Structures. 152:1-10. https://doi.org/10.1016/j.compstruc.2015.01.015S11015

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

[EN] An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a ¿smooth + singular¿ decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.Stephane Bordas would like to thank the partial financial support of the Royal Academy of Engineering and of the Leverhulme Trust for his Senior Research Fellowship Towards the next generation surgical simulators as well as the financial support for Octavio A. Gonzalez-Estrada and Stephane Bordas from the UK Engineering Physical Science Research Council (EPSRC) under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method. Stephane Bordas also thanks partial financial support of the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) and the FP7 Initial Training Network Funding under grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology, INSIST". This work has been carried out within the framework of the research project DPI2010-20542 of the Ministerio de Ciencia e Innovacion (Spain). The financial support from Universitat Politecnica de Valencia, PROMETEO/2012/023 and Generalitat Valenciana are also acknowledged.González Estrada, OA.; Natarajan, S.; J.J. Ródenas; Nguyen-Xuan, H.; Bordas, S. (2013). Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Computational Mechanics. 52(1):37-52. https://doi.org/10.1007/s00466-012-0795-6S3752521Liu GR, Dai KY, Nguyen TT (2006) A smoothed finite element method for mechanics problems. Comput Mech 39(6): 859–877. doi: 10.1007/s00466-006-0075-4Liu GR, Nguyen TT, Dai KY, Lam KY (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71(8): 902–930Nguyen-Xuan H, Bordas SPA, Nguyen-Dang H (2008) Smooth finite element methods: convergence, accuracy and properties. Int J Numer Methods Eng 74(2): 175–208. doi: 10.1002/nmeBordas SPA, Natarajan S (2010) On the approximation in the smoothed finite element method (SFEM). Int J Numer Methods Eng 81(5): 660–670. doi: 10.1002/nmeZhang HH, Liu SJ, Li LX (2008) On the smoothed finite element method. Int J Numer Methods Eng 76(8): 1285–1295. doi: 10.1002/nme.2460Nguyen-Thoi T, Liu G, Lam K, Zhang G. (2009) A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics using 4-node tetrahedral elements. Int J Numer Methods Eng 78: 324–353Liu G, Nguyen-Thoi T, Lam K (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J Sound Vib 320: 1100–1130Liu G, Nguyen-Thoi T, Nguyen-Xuan H, Lam K (2009) A node based smoothed finite element method (NS-FEM) for upper bound solution to solid mechanics problems. Comput Struct 87: 14–26Liu G. Smoothed Finite Element Methods. CRC Press, 2010Liu G, Nguyen-Xuan H, Nguyen-Thoi T (2010) A theoretical study on the smoothed FEM (SFEM) models: Properties, accuracy and convergence rates. Int J Numer Methods Biomed Eng 84: 1222–1256Nguyen T, Liu G, Dai K, Lam K (2007) smoothed finite element method. Tsinghua Sci Technol 12: 497–508Hung NX, Bordas S, Hung N (2009) Addressing volumetric locking and instabilities by selective integration in smoothed finite element. Commun Numer Methods Eng 25: 19–34Nguyen-Xuan H, Rabczuk T, Bordas S, Debongnie JF (2008) A smoothed finite element method for plate analysis. Comput Methods Appl Mech Eng 197: 1184–1203Nguyen NT, Rabczuk T, Nguyen-Xuan H, Bordas S (2008) A smoothed finite element method for shell analysis. Comput Methods Appl Mech Eng 198: 165–177Bordas SPA, Rabczuk T, Hung NX, Nguyen VP, Natarajan S, Bog T, óuan DM, Hiep NV (2010) Strain smoothing in FEM and XFEM. Comput Struct 88(23–24): 1419–1443. doi: 10.1016/j.compstruc.2008.07.006Bordas SP, Natarajan S, Kerfriden P, Augarde CE, Mahapatra DR, Rabczuk T, Pont SD (2011) On the performance of strain smoothing for óuadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). Int J Numer Methods Biomed Eng 86: 637–666Liu G, Nguyen-Thoi T, Nguyen-Xuan H, Dai K, Lam K (2009) On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM). Int J Numer Methods Eng 77: 1863–1869. doi: 10.1002/nme.2587Strouboulis T, Zhang L, Wang D, Babuška I. (2006) A posteriori error estimation for generalized finite element methods. Comput Methods Appl Mech Eng 195(9–12): 852–879Bordas SPA, Duflot M (2007) Derivative recovery and a posteriori error estimate for extended finite elements. Comput Methods Appl Mech Eng 196(35–36): 3381–3399Xiao óZ, Karihaloo BL (2004) Statically admissible stress recovery using the moving least sóuares technique. In: Topping BHV, Soares CAM (eds) Progress in computational structures technology. Saxe-Coburg Publications, Stirling, pp 111–138Ródenas JJ, González-Estrada OA, Tarancón JE, Fuenmayor FJ (2008) A recovery-type error estimator for the extended finite element method based on singular + smooth stress field splitting. Int J Numer Methods Eng 76(4): 545–571. doi: 10.1002/nme.2313Panetier J, Ladevèze P, Chamoin L (2010) Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM. Int J Numer Methods Eng 81(6): 671–700Barros FB, Proenca SPB, de Barcellos CS (2004) On error estimator and p-adaptivity in the generalized finite element method. Int J Numer Methods Eng 60(14):2373–2398. doi: 10.1002/nme.1048Nguyen-Thoi T, Liu G, Nguyen-Xuan H, Nguyen-Tran C (2011) Adaptive analysis using the node-based smoothed finite element method (NS-FEM). Int J Numer Methods Biomed Eng 27(2): 198–218. doi: 10.1002/cnmGonzález-Estrada OA, Ródenas JJ, Bordas SPA, Duflot M, Kerfriden P, Giner E (2012) On the role of enrichment and statical admissibility of recovered fields in a-posteriori error estimation for enriched finite element methods. Eng Comput 29(8)Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2): 337–357Ródenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2010) Accurate recovery-based upper error bounds for the extended finite element framework. Comput Methods Appl Mech Eng 199(37–40): 2607–2621Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plate in extension. J Appl Mech 19: 526–534Szabó BA, Babuška I (1991) Finite element analysis. Wiley, New YorkBarber JR. (2010) Elasticity. Series: solid mechanics and its application, 3rd edn. Springer, DordrechtChen JS, Wu CT, Yoon S, You Y (2001) A stabilized conforming nodal integration for Galerki mesh-free methods. Int J Numer Methods Eng 50: 435–466Yoo J, Moran B, Chen J (2004) Stabilized conforming nodal integration in the natural element method. Int J Numer Methods Eng 60: 861–890Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33(7): 1331–1364Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33(7): 1365–1382Wiberg NE, Abdulwahab F (1993) Patch recovery based on superconvergent derivatives and eóuilibrium. Int J Numer Methods Eng 36(16): 2703–2724. doi: 10.1002/nme.1620361603Blacker T, Belytschko T (1994) Superconvergent patch recovery with eóuilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37(3): 517–536Stein E, Ramm E, Rannacher R (2003) Error-controlled adaptive finite elements in solid mechanics. Wiley, ChichesterDuflot M, Bordas SPA (2008) A posteriori error estimation for extended finite elements by an extended global recovery. Int J Numer Methods Eng 76: 1123–1138. doi: 10.1002/nmeBordas SPA, Duflot M, Le P (2008) A simple error estimator for extended finite elements. Commun Numer Methods Eng 24(11): 961–971Ródenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint eóuations: the SPR-C technique. Int J Numer Methods Eng 70(6): 705–727. doi: 10.1002/nme.1903Díez P, Ródenas JJ, Zienkiewicz OC (2007) Eóuilibrated patch recovery error estimates: simple and accurate upper bounds of the error. Int J Numer Methods Eng 69(10): 2075–2098. doi: 10.1002/nmeYau J, Wang S, Corten H (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47(2): 335–341Ródenas JJ, González-Estrada OA, Fuenmayor FJ, Chinesta F (2010) Upper bounds of the error in X-FEM based on a moving least sóuares (MLS) recovery technique. In: Khalili N, Valliappan S, Li ó, Russell A (eds) 9th World congress on computational mechanics (WCCM9). 4th Asian Pacific Congress on computational methods (APCOM2010). Centre for Infrastructure Engineering and SafetyRódenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2007) Upper bounds of the error in the extended finite element method by using an eóuilibrated-stress patch recovery technique. In: International conference on adaptive modeling and simulation (ADMOS 2007). International Center for Numerical Methods in Engineering (CIMNE), pp 210–213Menk A, Bordas S (2010) Numerically determined enrichment function for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals. Int J Numer Methods Eng 83: 805–828Menk A, Bordas S (2011) Crack growth calculations in solder joints based on microstructural phenomena with X-FEM. Comput Mater Sci 3: 1145–1156Ródenas JJ (2001) Error de discretización en el cálculo de sensibilidades mediante el método de los elementos finitos. PhD Thesis, Universidad Politécnica de ValenciaAinsworth M, Oden JT (2000) A posteriori error estimation in finite element analysis. Wiley, Chicheste

Étude des mécanismes de migration du césium dans le dioxyde d'uranium stoechiométrique et sur-stoechiométrique : influence du molybdène

In the nuclear fuel UO2, which is widely used in Pressurized Water Reactor (PWR), Cs is a volatile element and is one of the most abundant fission product (FP). Furthermore, 137Cs is known to be highly radiotoxic. During a hypothetical accident, release of Cs would be particularly problematic for the environment. Hence, study of this element is of major concern for nuclear safety. To assess this issue, the French nuclear safety institute (IRSN) develops codes to predict FP release from nuclear fuel in normal and accidental conditions. This code requires fundamental data on FP behavior such as diffusion coefficient of these elements in UO2 as a function of temperature and atmosphere conditions (leading to UO2+x formation in oxidative conditions). The aim of this PhD, supported by the IRSN, is to study Cs migration in stoichiometric and hyper-stoichiometric uranium dioxide with and without the presence of Mo, in normal and accidental conditions of a PWR. This latter element is also an abundant FP, which is important to consider because it acts as an oxygen buffer in the fuel and may interact chemically with Cs. Such interactions may affect Cs behavior, hence its release from the fuel. Therefore, Cs-Mo interactions are considered in our study. The experimental procedure consists in simulating the Cs and/or Mo presence in UO2 and UO2+x pellets by ion implantation of stable isotopes 133Cs and/or 95Mo. Then, high temperature annealing (950 °C - 1600 °C) under controlled atmosphere or electronic excitations induced by irradiation coupled with temperature are performed to induce Cs and Mo migration. Secondary Ion Mass Spectrometry (SIMS) is used to follow the concentration profile evolution of these elements, allowing extracting effective diffusion coefficients of Cs in UO2 and UO2+x as a function of irradiation or thermal treatment. Microstructure characterizations were made by Raman spectroscopy and transmission electron microscopy (TEM). We show that Cs is mobile in UO2 under reducing atmosphere, even though some of the Cs is trapped in Cs-bubbles located near the surface. We evidence that Mo presence prevents Cs to be mobile. The same tendency is observed in UO2+x under oxidizing atmosphere. Nevertheless, Cs immobilization mechanisms in presence of Mo vary upon redox conditions used during annealing. In reducing conditions, TEM experiments showed formation of Cs bubbles associated with Mo metallic precipitates in co-implanted samples. In oxidative conditions, absence of Cs mobility could be explained by Mo oxidation leading to possible Cs-Mo chemical interactions. For the first time, semi-empirical potentials were used to perform molecular dynamic (MD) calculations on Cs and Mo diffusion in UO2 and UO2+x. These simulations also allowed characterizing oxygen diffusion mechanisms in these matrixes in presence of Cs and MoDans le combustible nucléaire UO2, utilisé dans les réacteurs à eau pressurisée (REP), le Cs, élément volatil compte parmi les produits de fission (PF) les plus abondamment produits. De plus, l’isotope 137Cs est connu pour être particulièrement radiotoxique. En cas d’accident, le relâchement de cet isotope est donc problématique et son étude est cruciale pour la sûreté nucléaire. En France, l’IRSN (Institut de Radioprotection et de sureté nucléaire) développe des codes de prédictions du relâchement des PF depuis le combustible, tels que MFPR (Module for Fission Product Release). Ces codes nécessitent d’être alimentés par des données fondamentales sur le comportement des PF. Ainsi, la connaissance des coefficients de diffusion de ces éléments dans la matrice combustible en fonction de la température et de l’atmosphère (pouvant oxyder le combustible en UO2+x) est primordiale. Dans ce contexte, l’objectif de cette thèse, menée en collaboration avec l’IRSN, est d’étudier la migration du Cs dans le dioxyde d’uranium stœchiométrique et sur-stœchiométrique, en conditions représentatives d’un fonctionnement normal et accidentel d’un REP, avec et sans la présence de Mo. Ce dernier est un PF abondamment produit qui agit comme tampon d’oxydation du combustible et est capable d’avoir des interactions chimiques avec le césium. De telles interactions pourraient affecter le comportement du Cs, et donc son relâchement depuis le combustible. Il a donc été nécessaire d’envisager les éventuelles interactions entre le Cs et le Mo dans le cadre de notre étude. La démarche expérimentale a consisté à simuler la présence de Cs et/ou Mo dans des pastilles d’UO2 ou d’UO2+x. par implantations ioniques des isotopes stables 133Cs et/ou 95Mo. Des recuits à haute température (950-1600°C) sous atmosphère contrôlée ou des irradiations en régime électronique couplées en température ont ensuite été réalisés, permettant d’induire la migration du Cs et du Mo. La spectrométrie de masse à ionisation secondaire (SIMS) a été utilisée pour suivre l’évolution des profils de concentration des éléments implantés, permettant d’extraire les coefficients de diffusion apparents du Cs dans UO2 et UO2+x en fonction des différents traitements. Une étude complémentaire de la microstructure a été réalisée par spectroscopie Raman et microscopie électronique en transmission (MET). Le Cs est très mobile dans UO2 sous atmosphère réductrice même si une partie et piégée sous forme de bulles à faible profondeur. Nous avons mis en évidence que la présence de Mo diminuait fortement cette mobilité. La même tendance est observée dans UO2+x sous atmosphère oxydante. Néanmoins les mécanismes d’immobilisation du Cs par le Mo diffèrent selon les conditions redox de recuit. En atmosphère réductrice, les expériences MET ont montré la formation de paires bulles de Cs-précipités métalliques de Mo dans les échantillons co-implantés. En atmosphère oxydante, l’absence de mobilité du Cs pourrait être liée à l’oxydation du Mo rendant possible des interactions chimiques Cs-Mo. Pour la première fois, des potentiels semi-empiriques ont été utilisés pour réaliser des calculs de dynamique moléculaire sur la diffusion du Cs et du Mo dans UO2 et UO2+x. Ces calculs nous ont aussi permis de caractériser les mécanismes de diffusion de l’oxygène dans ces matériaux en présence de ces deux P

Study of Cesium migration mechanisms in stoichiometric and hyper-stoichiometric uranium dioxide : influence of Molybdenum

Dans le combustible nucléaire UO2, utilisé dans les réacteurs à eau pressurisée (REP), le Cs, élément volatil compte parmi les produits de fission (PF) les plus abondamment produits. De plus, l’isotope 137Cs est connu pour être particulièrement radiotoxique. En cas d’accident, le relâchement de cet isotope est donc problématique et son étude est cruciale pour la sûreté nucléaire. En France, l’IRSN (Institut de Radioprotection et de sureté nucléaire) développe des codes de prédictions du relâchement des PF depuis le combustible, tels que MFPR (Module for Fission Product Release). Ces codes nécessitent d’être alimentés par des données fondamentales sur le comportement des PF. Ainsi, la connaissance des coefficients de diffusion de ces éléments dans la matrice combustible en fonction de la température et de l’atmosphère (pouvant oxyder le combustible en UO2+x) est primordiale. Dans ce contexte, l’objectif de cette thèse, menée en collaboration avec l’IRSN, est d’étudier la migration du Cs dans le dioxyde d’uranium stœchiométrique et sur-stœchiométrique, en conditions représentatives d’un fonctionnement normal et accidentel d’un REP, avec et sans la présence de Mo. Ce dernier est un PF abondamment produit qui agit comme tampon d’oxydation du combustible et est capable d’avoir des interactions chimiques avec le césium. De telles interactions pourraient affecter le comportement du Cs, et donc son relâchement depuis le combustible. Il a donc été nécessaire d’envisager les éventuelles interactions entre le Cs et le Mo dans le cadre de notre étude. La démarche expérimentale a consisté à simuler la présence de Cs et/ou Mo dans des pastilles d’UO2 ou d’UO2+x. par implantations ioniques des isotopes stables 133Cs et/ou 95Mo. Des recuits à haute température (950-1600°C) sous atmosphère contrôlée ou des irradiations en régime électronique couplées en température ont ensuite été réalisés, permettant d’induire la migration du Cs et du Mo. La spectrométrie de masse à ionisation secondaire (SIMS) a été utilisée pour suivre l’évolution des profils de concentration des éléments implantés, permettant d’extraire les coefficients de diffusion apparents du Cs dans UO2 et UO2+x en fonction des différents traitements. Une étude complémentaire de la microstructure a été réalisée par spectroscopie Raman et microscopie électronique en transmission (MET). Le Cs est très mobile dans UO2 sous atmosphère réductrice même si une partie et piégée sous forme de bulles à faible profondeur. Nous avons mis en évidence que la présence de Mo diminuait fortement cette mobilité. La même tendance est observée dans UO2+x sous atmosphère oxydante. Néanmoins les mécanismes d’immobilisation du Cs par le Mo diffèrent selon les conditions redox de recuit. En atmosphère réductrice, les expériences MET ont montré la formation de paires bulles de Cs-précipités métalliques de Mo dans les échantillons co-implantés. En atmosphère oxydante, l’absence de mobilité du Cs pourrait être liée à l’oxydation du Mo rendant possible des interactions chimiques Cs-Mo. Pour la première fois, des potentiels semi-empiriques ont été utilisés pour réaliser des calculs de dynamique moléculaire sur la diffusion du Cs et du Mo dans UO2 et UO2+x. Ces calculs nous ont aussi permis de caractériser les mécanismes de diffusion de l’oxygène dans ces matériaux en présence de ces deux PFIn the nuclear fuel UO2, which is widely used in Pressurized Water Reactor (PWR), Cs is a volatile element and is one of the most abundant fission product (FP). Furthermore, 137Cs is known to be highly radiotoxic. During a hypothetical accident, release of Cs would be particularly problematic for the environment. Hence, study of this element is of major concern for nuclear safety. To assess this issue, the French nuclear safety institute (IRSN) develops codes to predict FP release from nuclear fuel in normal and accidental conditions. This code requires fundamental data on FP behavior such as diffusion coefficient of these elements in UO2 as a function of temperature and atmosphere conditions (leading to UO2+x formation in oxidative conditions). The aim of this PhD, supported by the IRSN, is to study Cs migration in stoichiometric and hyper-stoichiometric uranium dioxide with and without the presence of Mo, in normal and accidental conditions of a PWR. This latter element is also an abundant FP, which is important to consider because it acts as an oxygen buffer in the fuel and may interact chemically with Cs. Such interactions may affect Cs behavior, hence its release from the fuel. Therefore, Cs-Mo interactions are considered in our study. The experimental procedure consists in simulating the Cs and/or Mo presence in UO2 and UO2+x pellets by ion implantation of stable isotopes 133Cs and/or 95Mo. Then, high temperature annealing (950 °C - 1600 °C) under controlled atmosphere or electronic excitations induced by irradiation coupled with temperature are performed to induce Cs and Mo migration. Secondary Ion Mass Spectrometry (SIMS) is used to follow the concentration profile evolution of these elements, allowing extracting effective diffusion coefficients of Cs in UO2 and UO2+x as a function of irradiation or thermal treatment. Microstructure characterizations were made by Raman spectroscopy and transmission electron microscopy (TEM). We show that Cs is mobile in UO2 under reducing atmosphere, even though some of the Cs is trapped in Cs-bubbles located near the surface. We evidence that Mo presence prevents Cs to be mobile. The same tendency is observed in UO2+x under oxidizing atmosphere. Nevertheless, Cs immobilization mechanisms in presence of Mo vary upon redox conditions used during annealing. In reducing conditions, TEM experiments showed formation of Cs bubbles associated with Mo metallic precipitates in co-implanted samples. In oxidative conditions, absence of Cs mobility could be explained by Mo oxidation leading to possible Cs-Mo chemical interactions. For the first time, semi-empirical potentials were used to perform molecular dynamic (MD) calculations on Cs and Mo diffusion in UO2 and UO2+x. These simulations also allowed characterizing oxygen diffusion mechanisms in these matrixes in presence of Cs and M

Vérification des facteurs d'intensité de contrainte calculés par XFEM

In the field of fracture mechanics, the analysis of a structure containing cracks involves the calculation of some quantities of interest like the stress intensity factors (SIF) or the energy release rate. It is necessary to assess the quality of these quantities when they are computed by a numerical scheme. These past decades, efficient tools were developed to calculate accurate bounds for linear outputs of interest computed by the finite element method (FEM). The most widespread technique involves the resolution of the well known adjoint problem. It derives from the global error estimators in energy norm. The technique developped at the LMT Cachan allows one to easily get sharp and strict bounds. The local error estimator for the stress intensity factors has already been succesfully tested for the standard FEM. Herein, we focus on the verification of the computed SIF with the extended finite element method introduced. We take into account the enrichment both by the asymptotic and by the discontinuous functions. The use of asymptotic fields and the exploitation of intrinsic properties of the error estimator allows us to get strict bounds in respect with the XFEM framework.La prévision de la tenue des structures fissurées nécessite le calcul du taux de restitution d'énergie ou des facteurs d'intensité de contrainte (FIC) en pointe de fissure. Ces quantités sont généralement évaluées après une analyse éléments finis. Plus récemment l'apparition de la XFEM a permis d'améliorer la description des champs en pointe fissure et de s'affranchir des remaillages successifs après chaque pas de propagation. Néanmoins, la solution ainsi calculée demeure une solution approchée de la solution du problème de référence. Il est donc important de pouvoir évaluer la pertinence de ces calculs. Ces travaux de thèse proposent une technique à même de fournir un encadrement conservatif des FIC évalués par une méthode éléments finis classique et par la XFEM. L'utilisation des techniques d'évaluation d'erreur sur les quantités d'intérêt et de l'erreur en relation de comportement permet dans un premier temps de fournir des bornes de bonne qualité pour les FIC. On propose ensuite une méthode permettant d'évaluer l'erreur globale commise lors d'une analyse XFEM. Elle fait intervenir l'erreur en relation de comportement et des techniques de construction de champs de contrainte adéquates. On est alors en mesure de proposer un encadrement assez fin des FIC pour un coût numérique très raisonnable. L'estimation d'erreur peut finalement être envisagée comme un moyen de déterminer les quantités d'intérêt avec précision