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Fast simulation of grain growth based on OrientatedTessellation Updating Method and probabilistic homogenization

Abstract : Grain growth is a thermally activated phenomenon that generally occurs during annealing processes. During grain growth, some grains grow while others disappear. This coalescence is a function of the grain size and crystal orientation. Classical statistical descriptors of the polycrystalline structure such as morphological and crystallographic textures (e.g., grain size, shape and crystal orientation distributions) evolve during the process. Thus, for different fabrication or forming processes (e.g., additive manufacturing), temperature conditions could be optimized to obtain targeted microstructures, especially for large heterogeneous parts.However, mechanisms involved during grain growth arise at the scale of grain boundaries(GB). Thus, numerical simulations of the evolution of morphological and crystallographic textures may be difficult to perform for macroscopic parts, which hinders the development of optimization loops to adjust process parameters.Therefore, this PhD thesis aims at developing an upscaling strategy to establish a macroscopic model of grain growth that fully relies on finer scales and whose state variables contain statistical descriptors of the grain structure. The proposed upscaling strategy involves considering grain growth at various scales: (i) the atomic scale (e.g., crystal lattice and interatomic potential), (ii) the microscopic scale (e.g., grain boundaries), (iii) the mesoscopic scale (e.g., polycrystalline structure) and (iv) the macroscopic scale (statistical descriptors of the grain structure). As energetic concepts are valid at all scales, the upscaling strategy fundamentally relies on various energetic contributions arising at different scales. This energetic upscaling strategy is developed within the framework of standard generalized media that are caracterized by their free energy and dissipated power. The proposed upscaling strategy consists in determining these two potentials not axiomatically (with parametric functions and experimental calibration), but on a more physical basis by using a large database of results from computations carried out at the mesoscopic scale.On this basis, we can identify the macroscopic free energy and dissipated power as a function of the macroscopic state variables in order to obtain an evolution law that accounts for statistical descriptors of the grain structure. Therefore, the database requires to intensively use a mesoscopic model of grain growth. As a consequence, a sufficiently fast mesoscopic model should be established. Many different approaches have been proposed to model grain growth at the mesoscopic scale. However, the computational cost is usually incompatible with an intensive use as suggested within the proposed framework.In this work, a fast mesoscopic model called Orientated Tessellation Updating Method (OTUM) has been proposed. It fully relies on Voronoi-Laguerre tessellation to approximate polycrystals at the mesoscopic scale. For the sake of simplicity, the proposed upscaling methodology is established for plane hexagonal polycrystals. Very efficient algorithms have been developed with the possibility of controlling statistical distributions of grain size and shape and GB misorientation. OTUM relies on the idea that the evolution law of the mesoscopic structure can be formulated directly by modifying the parameters defining the OT.Exploring and analyzing the database raises an epistemic uncertainty, which corresponds to the loss of information in the process of reducing the amount of data. This epistemic uncertainty has been modeled with random variables, leading to a probabilistic macroscopic model, even though the mesoscopic model is completely deterministic. Such a model can be directly used for structures at large scales subjected to thermal treatments
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Submitted on : Tuesday, June 22, 2021 - 5:00:13 PM
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Sofia Sakout. Fast simulation of grain growth based on OrientatedTessellation Updating Method and probabilistic homogenization. Materials. Université Paris-Est, 2020. English. ⟨NNT : 2020PESC1029⟩. ⟨tel-03267868⟩

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