Incorrect fiber orientations?

[nbauermcl]

Hello, I recently started using the processing tools of the DAMASK suite for generation of simple crystallographic textures. More precisely, I used the method from_fiber_component of the Rotation class to generate a simple alpha fiber texture (<110> || RD=x) consisting of 200 orientations with sigma=3.0°, exactly like it is done in the examples:

alpha = Rotation.from_fiber_component(crystal=np.array([45., 0.]), sample=np.array([90., 0.]), sigma=3., shape=200, degrees=True)

I then plotted the inverse pole figures for the generated texture, taking into account cubic symmetry. For this, I used the Python package orix and first "converted" the DAMASK rotation to an equivalent orix rotation via axis-angle.

However, from the calculated IPFs (see attached file), it seems that the fiber orientations are incorrect. For an alpha fiber texture as defined above, to my knowledge, the poles in the IPF-X (X = RD) should concentrate solely around [110] crystal direction in the standard crystallographic triangle, and not follow the curved line as in the plotted IPF-X.

I am trying to find out where my mistake lies. Can someone help me? Much appreciated!

Kind regards

[MarDiehl]

This looks suspicious, I'll look into this. Just two remarks: There is not "the" α-fiber: The definitions are different from bcc to fcc. Also, conversion to orix could cause issues. They use the convention from the same paper, but with P=1 if I remember correctly. DAMASK uses P=-1.

[nbauermcl]

Hello Martin, thanks for your quick response! To my knowledge, the definition I used (<110> || RD) is how the alpha fiber is defined for bcc. I also found a solution that worked for me, for which I had to change only a few lines of your source code:

f = np.column_stack((np.broadcast_to(d_lab,(N,3)),rng.random(N)*np.pi))

I changed this to:

f = np.column_stack((np.broadcast_to(d_cr, (N, 3)), rng.random(N) * np.pi))

So the invariant axis of rotation to create random other fiber orientations is now the crystal lattice vector (e.g. [110]) instead of the sample vector (e.g. RD = X). The only other thing I changed is the order of rotations:

R_align.broadcast_to(N) * Rotation.from_axis_angle(p,normalize=True) * Rotation.from_axis_angle(f)).reshape(() if shape is None else shape)

I changed this to:

R_align.broadcast_to(N) * Rotation.from_axis_angle(f) * Rotation.from_axis_angle(p, normalize=True)).reshape(() if shape is None else shape)

So, the way I create the fiber orientations is that I first rotate the fiber axis from sample to crystal frame, then produce random orientations of the crystal around the fiber axis (the fiber axis is preserved), and then (from what I gather) small Gaussian-distributed perturbation rotations p are added.

With this (and keeping everything else - so also the conversion to orix - the same) I generated the following pole figures for 200 random orientations of the <110> || RD (alpha) fiber. To me, this looks good and as I would expect it.

[MarDiehl]

Thanks for checking. The definition is indeed for bcc.

I believe the issue is because of different conventions. DAMASK and orix follow https://doi.org/10.1088/0965-0393/23/8/083501, but DAMASK uses P=-1 and orix P=+1.

from orix.quaternion import Orientation
import damask

eu = damask.Rotation.from_random().as_Euler_angles()

print(damask.Rotation.from_Euler_angles(phi=eu))
print(Orientation.from_euler(eu))

So I believe that need to multiply the imaginary part of the quaternion with -1 before importing it to orix. DAMASK can do this with an argument when importing (https://damask-multiphysics.org/_modules/damask/_rotation.html#Rotation.from_quaternion), but not on export.

Attached are two Jupyter notebooks for pole figures and inverse pole figures. Results look good to me. Note that I had to change the extension from ipynb to txt for "security" reasons

inverse_pole_figure.txt
pole_figure.txt

If you can confirm my reasoning, I would like to document the data exchange with orix on the DAMASK website.

P.S. could you share the orix code?