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.
International audienceThis work is currently under development within the framework of an American-European project (Digimat Project). The paper details the development of some numerical tools dedicated to the digital representation of metallic materials structures, to the finite element modelling of the polycrystalline microstructure deformation under large strains and to the subsequent recrystallization. The level set method used for the description of the microstructure interfaces is shown to represent a common base to all these developments
The development of a digital material framework is presented, allowing to build virtual microstructures in agreement with experimental data. The construction of the virtual material consists in building a multi-level Voronoï tessellation. A polycrystalline microstructure made of grains and sub-grains can be obtained in a random or deterministic way. A corresponding finite element mesh can be generated automatically in 3D, and used for the simulation of mechanical testing under large strain. In the examples shown in this work, the initial mesh was non uniform and anisotropic, taking into account the presence of interfaces between grains and sub-grains. Automatic remeshing was performed due to the large strains, and maintained the non uniform and anisotropic character of the mesh. A level set approach was used to follow the grain boundaries during the deformation. The grain constitutive law was either a viscoplastic power law, or a crystallographic formulation based on crystal plasticity. Stored energies and precise grain boundary network geometries were obtained directly from the deformed digital sample. This information was used for subsequent modelling of grain growth with the level set approach, on the same mesh.
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