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A. Cruzado et al.
Fig. 10 Representative volume elements (RVEs) of a polycrystalline microstructure. (a) Voronoi
tessellation-based RVE. (b) Voxelized RVE generated using [18]
generated from the tessellation of a set of points, which divided the initial volume in
a number of polyhedra. In particular, because the grain size distributions considered
in this study are log-normal distributions and grains are equiaxial, simple Voronoi
tessellations are used. A Monte Carlo algorithm was developed to generate the
position of the set of points used for the tessellation, so the resulting polyhedra
in which the RVE is divided fulfill the experimental grain size distribution (e.g.,
the distribution in Fig. 9). The tessellations during the Monte Carlo process were
carried out using an extended cloud of points obtained using periodic copies of the
original cloud in the three directions of space in order to preserve the periodicity
of the microstructure in the RVE. Although RVEs present cubic periodicity, the
final shape of the RVE was not a cube because grains intersecting the cube faces
were not cut and copied into the opposite face but were maintained in their original
positions. This strategy avoided meshing problems related with the development
of very small grains near the cube surfaces. The periodic RVE was finally meshed
with the open source program Gmsh [22]. Ten-node quadratic tetrahedral elements
(C3D10M with full integration in [1]) were used for the discretization. It must be
noted that this strategy leads to planar grain boundaries because the actual geometry
defined by the tessellation is preserved in the discretization. The second type of
RVEs (Fig. 10b), voxelized RVEs, corresponds to the rasterization of a periodic
synthetic microstructure generated in a regular grid by compacting in the RVE
volume a set of ellipsoids which sizes fulfill the experimental grain size distribution.
These types of synthetic microstructures are generated using the software [18] and
do not necessarily correspond to any tessellation of points. After the rasterization,
each voxel of the synthetic microstructure was transformed to a linear hexahedral
element (C3D8 in Abaqus).
A. Cruzado et al.
Fig. 10 Representative volume elements (RVEs) of a polycrystalline microstructure. (a) Voronoi
tessellation-based RVE. (b) Voxelized RVE generated using [18]
generated from the tessellation of a set of points, which divided the initial volume in
a number of polyhedra. In particular, because the grain size distributions considered
in this study are log-normal distributions and grains are equiaxial, simple Voronoi
tessellations are used. A Monte Carlo algorithm was developed to generate the
position of the set of points used for the tessellation, so the resulting polyhedra
in which the RVE is divided fulfill the experimental grain size distribution (e.g.,
the distribution in Fig. 9). The tessellations during the Monte Carlo process were
carried out using an extended cloud of points obtained using periodic copies of the
original cloud in the three directions of space in order to preserve the periodicity
of the microstructure in the RVE. Although RVEs present cubic periodicity, the
final shape of the RVE was not a cube because grains intersecting the cube faces
were not cut and copied into the opposite face but were maintained in their original
positions. This strategy avoided meshing problems related with the development
of very small grains near the cube surfaces. The periodic RVE was finally meshed
with the open source program Gmsh [22]. Ten-node quadratic tetrahedral elements
(C3D10M with full integration in [1]) were used for the discretization. It must be
noted that this strategy leads to planar grain boundaries because the actual geometry
defined by the tessellation is preserved in the discretization. The second type of
RVEs (Fig. 10b), voxelized RVEs, corresponds to the rasterization of a periodic
synthetic microstructure generated in a regular grid by compacting in the RVE
volume a set of ellipsoids which sizes fulfill the experimental grain size distribution.
These types of synthetic microstructures are generated using the software [18] and
do not necessarily correspond to any tessellation of points. After the rasterization,
each voxel of the synthetic microstructure was transformed to a linear hexahedral
element (C3D8 in Abaqus).