Grain morphology and crystallographic texture

The grain maps obtained through EBSD analysis on both the horizontal and vertical plane of the built sample are shown in figure 3.12. The low-angle boundaries, defined as the boundaries with a maximum mis-orientation angle ranging between 10° and 4°, are shown in the maps of figure 3.12 as lighter blue lines. On the other hand, the high-angle boundaries, with a mis-orientation angle of at least 10°, are marked in dark blue. The grains are here defined as the regions that are completely delimited by high-angle boundaries. Some of the largest grains are composed by sub-grain domains which are delimited also by low-angle boundaries.

These domains are depicted in figure 3.12 using different color shades. It’s possible to observe that some grains contain up to 11 or even more sub-granular domains.

On the horizontal plane, the grains have substantially equiaxed morphology. In the analyzed area, the mean grain size, expressed as equivalent diameter, is equals

to 11 m (only the grains that don’t touch the edges of the area are considered in this statistic). However, the dispersion on grain sizes is very high (standard deviation: 9 m) and large grains of 30-50 m are also present.

In agreement to what observed from the optical micrographs of figure 3.11, the grain map obtained along the vertical plane shows that grains have mostly an elongated shape with their longer axis oriented parallel to the building direction of the part. The calculated average values of the major axis of the grains is 28.5 m, however a high heterogeneity on the grain size can also be note along the vertical plane (standard deviation: 29.5 m) with the presence of grains up to 180 m along the major axis. The ratio between the major and the minor axes of the grains detected on the vertical plane has an average value, weighted on the grain sizes, equal to 5.4.

Laser related boundaries are not evidenced by the grain maps because, as already pointed out, the crystallographic orientation of the grains is independent from the laser scan lines and the deposited layers due to the occurring of epitaxial growth. For this reason, the longer grains can cross up to ten deposited layers leading to a good metallurgical bonding between them.

Figure 3.12. Grain maps obtained through EBSD analysis of the as built material on the horizontal plane (A) and vertical plane (B). The grains, defined here as the regions completely delimited by high-angle boundaries, are shown in the maps on the left. In the maps on the right, different color shades are used for indicating the sub-grain domains, the high-angle boundaries (mis-orientation of at least 10°) are marked in dark blue and the low-angle boundaries (maximum mis-orientation

angle between 10° and 4°) are marked in lighter blue. First published in [186].

The mean crystallographic orientation of each grain in the maps of figure 3.12 is shown through the {100}, {110} and {111} pole figures obtained on the horizontal plane (figure 3.13) and the vertical plane (figure 3.14), respectively. In these figures, the big squares represent the mean orientation of the detected grains with respect to the sample coordinates system. On the contrary, the small circles indicate the mean crystallographic orientation of the respective sub-granular domains.

For comparison, simulated pole figures representing the same number of grains detected on the horizontal plane, but with random orientation, are also reported in figure 3.13. The target of such comparison is to show the aspect of the pole figures if no crystallographic texture would be present.

Figure 3.13. Experimental pole figures relative to the EBSD analysis on the horizontal plane, each colored square represent the mean orientation of the respective grain of figure 3.12-A respect to the sample coordinate system. The small circles represent the mean orientation of the sub-granular

domains. Simulated pole figures for a material without preferential orientation with the same number of grains are also reported. First published in [186].

This analysis clearly demonstrates that the SLM built material has a strong preferential orientation of the {100} lattice planes along the building direction with respect to a material with a random crystallographic orientation.

Figure 3.14. Experimental pole figures relative to the EBSD analysis on the vertical plane, each colored square represent the mean orientation of the respective grain of figure 3.12-B respect to the sample coordinate system. The small circles represent the mean orientation of the sub-granular

domains. First published in [186].

The crystallographic texture can also be assessed from the Inverse Pole Figure (IPF) charts. In the following discussion, the axis of the sample coordinates system that is parallel to the building direction of the sample will be referred as R1 axis.

Instead, the other two axes will be referred as R2 and R3. It is worthwhile to note that the building direction is represented by Z axis in figures related to samples analyzed on the horizontal plane and by Y axis in figures related to samples analyzed on the vertical plane,

In the IPF chart relative to the R1 axis of figure 3.15, the density of the points collected on the horizontal plane increase near the [001] vertex of the standard triangle. Instead, the density of the points decreases near the [111] vertex of the IPF charts relative of both the R2 and R3 axes. A similar distribution of the points was obtained on the vertical plane.

Figure 3.15. Inverse Pole Figure (IPF) charts relative to the three axes on both the horizontal and vertical planes. First published in [186].

These distributions of the points can be understood by observing the path followed by the representative point of the orientation of a cubic cell on the IPF charts during the rotation of this cell around its [001] axis. When the rotation axis has a small inclination with respect to the R1 axis of the sample coordinate system, the followed path is similar to the ones shown in figure 3.16 as examples. Actually, each of these paths describes a 90 degrees rotation of the cell around its [001] axis, that corresponds to a continuous variation of the  Euler angle, during which both the  and  angles are kept to a fixed value. The paths of figure 3.16 are referred to the horizontal plane, in which the  angle represents the inclination of the [001] axis respect the building direction (i.e. the R1 axis). Similar paths are also followed in the vertical plane.

The example paths of figure 3.16 show that, whenever the angle  is low and the other Euler angles don’t assume preferential values, the points of the IPF charts are disposed along an arch near the [100] vertex of the standard triangle relative to the R1 axis and, in the meanwhile, they cover the region of the triangle opposite to the [111] vertex on the IPF charts relative to both the R2 and R3 axes. This is, precisely, the situation experimentally found and reported in figure 3.15, which therefore denotes both a preferential orientation of the <100> type axes along the building direction and a uniform random orientation with respect to the other dimensions.

Figure 3.16. Paths of the representative point on the IPF charts during the rotation of a crystal around the [001] direction oriented at a low angle to the building direction (R1 axis). This example

is referred to the horizontal plane, the paths relative to the vertical plane are analogous.

An intuitive representation of the <100> crystallographic texture of the as built material is given by the IPF maps (figure 3.17) of the horizontal plane and the vertical plane. These maps allow to visualize the crystallographic orientation of each grain detected with the EBSD analysis. A map with balanced color tones denotes an isotropic orientation respect to the reference axis of the map, instead crystallographic a texture is visible as a more uniform colored map. From the IPF

maps relative to the R1 axis on both the horizontal and vertical planes, it is possible to observe that most of the detected grains has a <100> crystallographic axis nearly oriented along the building direction. Conversely, the other IPF maps don’t reveal a similar texture, as it was expected because the material is substantially isotropic along the other spatial directions as already pointed out in previous discussion.

Figure 3.17. IPF maps on both the Horizontal plane (H. p.) and the vertical plane (V. p.) relative to the three axes. The IPF-Z maps have been previously published in [186].