3D modelling of deformation and recrystallization in polycrystals, combining a level set framework with adaptive meshing techniques

International audienceNew 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