**3.3.2 Surface reconstruction**

6 Polycrystalline Materials

Fig. 6. Reconstructed geometry of a 400 *μ*m diameter stainless steel wire. Left: holes in the original experimental data. Right: wire after the hole treatment, surface grooves present.

The experimental data used in this work is of a 400 *μ*m diameter stainless steel wire characterized in 3D by DCT (King et al., 2008a). The data has been kindly provided by the University of Manchester, Materials Performance Centre, School of Materials and comprises of 362 grains and some 1600 grain boundaries. The data provides information on the crystallographic orientation in points of a 346 by 346 by 282 grid. The experimental data can be represented as an array of 282 slices, separated in the depth (Z) direction by 1.4 *μ*m. For each slice, crystallographic orientation has been measured on a 346 by 346 grid with 1.4 *μ*m distance between the points on a grid (in the X and Y direction). Voxels having the same

DCT characterization of a polycrystalline aggregate results in voxel-based data. Voxel-based data is also obtained in other experimental techniques like computed tomography (CT) or magnetic resonance imaging (MRI). To obtain the shapes of individual grains their surfaces

The original DCT data contains 'holes' in the reconstructed grains, see the left-hand-side of Fig. 6. These are typical artifacts due to the limited number of projections available for each grain and the presence of erroneous contrast (Johnson et al., 2008; Ludwig et al., 2008). Since the holes are not expected in the experimental data, a simple and efficient treatment algorithm

• The layers with depth of one voxel are successively added to the grains in the holes vicinity. Each layer is defined along the border between grains and holes by inspecting the one voxel deep neighborhood of the voxels within holes. Only the hole voxels with exactly one

• Only the hole voxels with multiple neighbors remain after the first step. These are assigned

to the grains dominating their immediate (one voxel deep) neighborhood.

**3.2 Experimental data**

**3.3.1 Treatment of holes**

crystallographic orientation constitute a grain.

**3.3 From the measured data to the surfaces**

can be used to fill the holes by grain growth:

neighboring grain are added to this grain within each layer.

need to be reconstructed from the voxel-based data.

Geometries of individual grains need to be reconstructed from the voxel-based data. This is usually achieved through reconstructing the surfaces of individual grains. Surface reconstruction from voxels is available in a number of commercial visualization tools. The origins of these tools can mainly be traced to the field of medical visualization. The tools were later further developed for the application to material science. In this work surfaces are reconstructed as sets of triangles with Amira package (Visage Imaging GmbH, 2010). A label is assigned to each measured point, defining to which grain this point belongs. The labels are equal to the index of the crystallographic orientation. Label 1 refers to grain 1 with crystallographic orientation index 1 and so forth.

Amira's built-in SurfaceGen tool with unconstrained smoothing option is used. This tool partitions the bounding volume into 362 grains depending on the number of different labels in the 8 vertices of a given voxel. Near the triple points between the grains and near the grain boundaries vortices of a given voxel will be distributed among several grains. In these cases the voxel is subdivided into up to 6<sup>3</sup> sub-vortexes to give a topologically correct representation of the implicitly defined separating surfaces (Westerhoff, 2003). If two adjacent sub-vortexes are of different grains, their common face is added to the list of boundaries between the two grains. A comprehensive explanation of the procedure is given in (Stalling et al., 1998; Westerhoff, 2003) and was later implemented in Amira. Described approach automatically increases the resolution near the triple points between the grains and near the grain boundaries where vortices of a given voxel are distributed among several labels/grains. This is especially important since stress increases at these points can be expected due to different crystallographic orientations of the adjacent grains. Further details on the implemented approach can be found in (Simonovski & Cizelj, 2011a).

The density of the triangles forming the reconstructed surfaces is limited by the resolution of the experimental data. At full resolution the number of triangles is 4 758 871, resulting in FE model with 51 211 552 finite elements. The number of triangles therefore needs to be decreased. This is done using Amira's built-in surface simplification tool (Zachow et al., 2007). The simplification decreases the details as well as resolution at the triple lines between the grains, see Fig. 7 where the number of triangles has been decreased to 30 000 (case 30K), 150 000 (case 150K) and 300 000 (case 300K).
