Modélisation du comportement effectif de milieux hétérogènes, viscoélastiques, non linéaires et vieillissants ; application à la simulation du comportement des combustibles MOX

Abstract : The prediction of the macroscopic mechanical behavior of heterogeneous materials based on the properties of their constituents is possible for different type of behaviors (elastic, viscoelastic, etc.) thanks to homogenization techniques. Nevertheless, the extension of the existing homogenization theories to nonlinear viscoelastic (or elasto-viscoplastic) behaviors remains an open question. In this work, we want to address this question in order to evaluate the macroscopic mechanical behavior of Mixed Oxides fuels (MOX) used in French nuclear reactors (PWRs). MOX fuels are three-phase composites consisting of high and low Plutonium concentration clusters surrounded by a continuous matrix with an intermediate Plutonium concentration. Under irradiation, the mechanical behavior of these fuels is similar to a nonlinear viscoelastic behavior with dierential dilations in the phases. Firstly, a purely analytical approach, based on the composite sphere model, is proposed in order to evaluate the local elds as well as the effective properties of two-phase microstructures under isotropic loading when the volume fraction of inclusions is low ( ≤ 30%). This loading is representative of the differential swellings appearing with irradiation in MOX fuels. This analytical model is in excellent agreement with full-field computations and shows that the distribution of the equivalent stress is the driving force of the relaxation phenomena in the microstructure. However, the scope of this model remains limited to specific (isotropic) loadings. To derive a macroscopic model regardless of the loading, the proposed methodology consists in linearizing the (nonlinear) relation between the viscous strain rate and the stress. To obtain a tractable problem, the linearized properties are chosen uniform per phase and are computed for reference stresses per phase in order to obtain a tractable linear viscoelastic problem for which classical homogenization theories are available (internal variables approach equivalent to the results obtained with the correspondence principle). Various methods associated to different choices of the linearization procedure (Secant, Affine) as well as the reference stresses per phases can be obtained. For the particular loading considered above (differential swelling), estimates as predicted by these dierent methods are systematically compared with the reference solutions (sphere composite model). These comparisons show that all methods based on the first moment of the stress field provides unrealistic estimates. The use of the second moment of the stress in the matrix phase leads to qualitatively correct estimates. Nevertheless, only a new method (called improved Affine) based on an ane linearization and the use of the fluctuations of the stress field yields a good quantitative agreement in the considered situation. Comparisons with full field computations conducted for more general loadings confirm the advantages of the proposed alternative. Finally, this improved affine model is extended to three-phase composites (MOX fuels) and implemented in ALCYONE which is a reference application dedicated to the simulation of thermo-mechanical and physico-chemical behavior of PWR fuel rods. The results of the numerical simulation (finite elements in 3D), obtained with the implemented law, are then evaluated and validated by comparison with experimental results obtained on irradiated fuels.
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Mohamed El Bachir Seck. Modélisation du comportement effectif de milieux hétérogènes, viscoélastiques, non linéaires et vieillissants ; application à la simulation du comportement des combustibles MOX. Mécanique des matériaux [physics.class-ph]. Aix Marseille Université; CEA Cadarache, 2018. Français. ⟨tel-02264771⟩

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