The objective of this note is to demonstrate the necessity of using an appropriate automatic adaptive meshing technique so as to handle complex microstructural evolutions. Examples of such microstructural evolutions include the deformation and recrystallization of polycrystalline aggregates or the growth of dendrites occurring during the solidification of metallic alloys. In such applications, it is required to track and/or capture accurately the interface between two or several domains having different mechanical behaviour. Also, the interface is a region where strong physical and/or kinematic incompatibilities, stemming from the heterogeneity of the mechanical response, occur. Gradients of the various mechanical fields develop across the interface and are expected to be significant in the direction perpendicular to the boundary. For these reasons, anisotropic mesh refinement along the interface, with a smaller mesh size in the perpendicular direction to it, is needed. This strategy represents a good compromise between accuracy and computation time as the mesh refinement is performed only where it is necessary. The level set framework used in our approach to represent and follow the boundaries is fully compatible with this meshing technique and allows for the remeshing to be handled quite easily throughout the evolution of the microstruture as often as needed.

New tools are progressively emerging for the construction of Representative Volume Elements (RVEs) of complex microstructures. In this work, a level set framework is used to locate interfaces in polycrystalline aggregates. Adaptive refinement of finite element meshes lead to virtual microstructures which describe very accurately the boundaries between grains or phases. Crystal Plasticity Finite Element (CPFEM) simulations show that the lowest accuracy regions are almost systematically located close to grain boundaries, while the reverse conclusion is not true. Mesh sizes are consequently refined close to these boundaries. It is further demonstrated that reducing the mesh size only in the direction perpendicular to the interface (anisotropic meshing) is enough to significantly reduce the local errors; this allows to limit the computation time. When dealing with large deformations, automatic remeshing is implemented and microstructural variables are readily transported using a zero-order scheme. Interfaces are well conserved by linear interpolation of the level set function (distance function) values. This allows to investigate the mechanical behaviour of constructed RVEs under large deformations, as well as to monitor detailed, local microstructure evolutions. In both cases, a Homogeneous Equivalent Medium (HEM) may be used around the RVE in order to limit edge effects. A sensitivity analysis on the properties of this HEM is performed, looking at the effects on the global mechanical behaviour, and on local microstructural features. A practical case is studied, concerning plane strain compression of an aluminium alloy for which initial and final EBSD maps are compared with the numerical predictions. Finally, a first step is taken in the direction of multiscale modelling of recrystallization, by considering grain boundary motion after or during plastic deformation of the polycrystalline aggregate. Grain boundary motion is implemented within the level set framework, using a kinetic equation describing the velocity of boundaries as a function of thermodynamic driving forces. Periodic update of the mesh is needed for geometrical stability. The approach is numerically validated in 2D and in 3D by comparison with the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. The influence of (a) non random nucleation based on mechanical and/or crystallographic criteria, and (b) the stored energy field, are analyzed. It is shown to lead, in some cases, to deviations with respect to the JMAK theory.

The construction of Representative Volume Elements (RVEs) of polycrystalline microstructures is illustrated in the solid and semi-solid states. Using a level set framework, adaptive refinement of finite element meshes lead to virtual microstructures which describe very accurately the boundaries between grains or phases. In the solid state, Crystal Plasticity Finite Element (CPFEM) simulations show that the lowest accuracy regions are almost systematically located close to grain boundaries, while the reverse conclusion is not true. Mesh sizes are consequently refined close to the boundaries. The mechanical behaviour of constructed RVEs is investigated, under plastic deformation, and local microstructure evolutions are detailed. An Homogeneous Equivalent Medium (HEM) is used around the RVE in order to limit edge effects, and a sensitivity analysis on the properties of this HEM is performed. Comparisons with experimental data are given. Finally, primary recrystallization is modelled following plastic deformation of the polycrystalline aggregates. Grain boundary motion and nucleation of new grains are implemented within the level set framework. Boundary motion is described by a kinetic equation which is a function of thermodynamic driving forces. Comparisons with the Johnson-Mehl-Avrami-Kolmogorov theory are reported.

Procedures for synthesizing and meshing digital polycrystalline microstntctures are demonstrated. The meshing operation relies on a metric field, yielding a nonuniform mesh size and a nonuniform mesh aspect ratio. Isotropic meshing is done in the grains interior, while anisotropic meshing is used close to the grain boundaries. Digital mechanical testing can then take place using crystal plasticity finite element simulations, which provides an estimate of the spatial distribution of strain energy within the polycrystalline aggregate. The latter quantity is used as an input for modelling subsequent static recrystallization, grain boundary motion being described with a level set framework. The kinetic law for interface motion uses the stored strain energy as an input to define local interface velocities. The possibility to include nucleation events within the level set framework is discussed, as well as the evolving topology of the grain boundary network.

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.

Procedures for synthesizing digital polycrystalline microstructures are illustrated, from either 2D statistical data or 3D deterministic data. Finite element meshes representing the digital microstructures are generated using anisotropic and adaptive mesh refinement close to the grain boundaries. Digital mechanical testing based on crystal plasticity theory provides an estimate of the spatial distribution of strain energy within the polycrystalline aggregate. The latter quantity is used as an input for modelling subsequent static recrystallization, grain boundary motion being described within a level set framework. The kinetic law for interface motion accounts for both the stored strain energy and the grain boundary energy. The possibility to include nucleation events within the level set framework is illustrated, as well as the evolving topology of the grain boundary network. The recrystallization model is tested in different configurations and compared to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory.

This 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 generation of associated anisotropic meshes and to the finite element modelling of the polycrystalline microstructure deformation under large strains. 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.