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Modélisation aux échelles méso- et macroscopique du comportement mécanique de zones singulières de pièces de structure en CMC

Abstract : Woven ceramic matrix composites (CMC) exhibit an intricate multi-scale architecture. To be used as components of aircraft engines, the weaving of such parts could also incorporate specific features compared to « classical » woven CMC as they need to comply with complex geometries. My work focused on a stiffener-like fully woven junction that is made of a complex 3D woven fabric, and whose characteristic size lies at the frontier between the mesoscopic and the macroscopic scales, i.e. where scale separation hypothesis is not applicable.I have first developed an experimental device to perform shear/bending tests on the woven junction. These tests not only allowed to gain significant knowledge about the mechanical behavior of such part, but also to highlight the interplay between the load, material architecture and damage mechanisms that is particularly significant in the case of the woven junction. Therefore, numerical prediction of the mechanical behavior of the woven junction necessitates a sound knowledge of its inner structure.With this aim, I have developed an original segmentation method to build realistic numerical models of textile composites, using X-ray micro-computed tomography and a prior geometric model. The procedure includes a global-local heuristic to iteratively improve the resemblance of the initial model. This approach allowed to build “digital twins” of the woven junction. A conformal tetrahedral image-based mesh could then be obtained as the resulting models are free of interpenetration.  Mesoscale FE simulations, including non-linear behavior laws of the yarns and matrix, allowed to predict the maximal load leading to the first damage events, and to reproduce accurately the damage localization and its interaction with the architecture.However, with such level of details incorporated in the model, the simulations necessitate significant computational resources. An approximate macro-scale description may be sufficient to evaluate the elastic properties, or even to simulate damage initiation. Therefore, we have proposed a meso-informed macroscopic modelling framework where the behaviour of the macro-elements is derived from the knowledge of the local direction and volume fraction of constituents, thanks to the digital twin. The effective behaviour of the macro-elements is obtained through an equivalent lamina. This method drastically reduces the size of the model while preserving an approximate description of the underlying local anisotropy and heterogeneities. With respect to the damage initiation, the meso-informed macroscopic model accurately reproduced the results obtained using the reference mesoscale model, as long as the filtering size remains comparable to the yarn size. This allowed to propose an optimal modelling framework with an adequate level of description of meso-details and acceptable computational requirements.Finally, I have used these models to thoroughly compare the numerical simulations with the experimental results: variabilities of experimental boundary conditions have been analyzed, as well as the influence of specific heterogeneities related to the fabrication process. We have also used this framework to explore different weaving patterns in order to obtain an optimal design of the woven junction.
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Jean Benezech. Modélisation aux échelles méso- et macroscopique du comportement mécanique de zones singulières de pièces de structure en CMC. Matière Condensée [cond-mat]. Université de Bordeaux, 2019. Français. ⟨NNT : 2019BORD0309⟩. ⟨tel-02507082⟩

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