The paper describes a robust finite element model of interface motion in media with multiple domains and junctions, as is the case in polycrystalline materials. The adopted level set framework describes each domain (grain) with a single level set function, while avoiding the creation of overlap or vacuum between these domains. The finite element mesh provides information on stored energies, calculated from a previous deformation step. Nucleation and growth of new grains are modelled by inserting additional level set functions around chosen nodes of the mesh. The kinetics and topological evolutions induced by primary recrystallization are discussed from simple test cases to more complex configurations and compared with the Johnson–Mehl–Avrami–Kolmogorov theory.
In finite element simulations dedicated to the modelling of microstructure evolution, the mesh has to be fine enough to: (i) accurately describe the geometry of the constituents; (ii) capture local strain gradients stemming from the heterogeneity in material properties. In this paper, 3D polycrystalline aggregates are discretized into unstructured meshes and a level set framework is used to represent the grain boundaries. The crystal plasticity finite element method is used to simulate the plastic deformation of these aggregates. A mesh sensitivity analysis based on the deformation energy distribution shows that the predictions are, on average, more sensitive near grain boundaries. An anisotropic mesh refinement strategy based on the level set description is introduced and it is shown that it offers a good compromise between accuracy requirements on the one hand and computation time on the other hand. As the aggregates deform, mesh distortion inevitably occurs and ultimately causes the breakdown of the simulations. An automatic remeshing tool is used to periodically reconstruct the mesh and appropriate transfer of state variables is performed. It is shown that the diffusion related to data transfer is not significant. Finally, remeshing is performed repeatedly in a highly resolved 500 grains polycrystal subjected to about 90% thickness reduction in rolling. The predicted texture is compared with the experimental data and with the predictions of a standard Taylor model.
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