Grain axis distribution in StatsGenerator

[Vicky Liu]

Hi,

I'm currently working on the 3dRVE generation on cold-rolling steel. I'm glad to see that Dream3D achieves the grain shape morphology distribution in the StatsGenerator. This quite helps my study. But I still confused about these Euler 1/2/3 definitions.

I've already got the idea of A/B/C axes definition according to their length (A>=B>=C). I would like to know the mathematical definition of the grain axis Euler angles. Did you apply the same definition here as the crystal orientation Euler angles? To explain my question in detail, let's assume the grain has a rectangular shape with three axes A-B-C. Then the material coordinate system is x-y-z (as shown in the pole figure), for cold-rolled material, which is normally x/RD-y/TD-z/ND. If the grain is elongated along x/RD, then we can define Euler1=0, Euler2=0, and Euler3=0 (marked as 0_0_0 for simplification), I can show the following pole figure (figure1_input0_0_0). If the grain is elongated along y/TD, I can use Euler1=90 (90_0_0), then I can see on the pole figures (figure2_input90_0_0), the points of A-axis locate on y pole point, and the B/C-axes change responsively. For simple rotation of grain on the RD-TD plane, it's easy to achieve, then my question is how about rotation on the RD-ND plane or even ND-TD plane? E.g. how could I define an elongated grain along 45° direction on RD-ND plane? Or for a more complex realistic case, from my EBSD measurement, I realize the orientation of the grain longest axis could be arbitrary in the 3D space. How could I define the rotated grain shape in 3d? Is it the same Euler angle definition method? I.e. we only assume here the crystal coordinate system [100]-[010]-[001] becomes the grain shape coordinate system A-B-C, and then rotate the material coordinate system x/RD-y/TD-z/ND into A-B-C? Does it use the same rotation method, like the Bunge method? Or am I totally wrong? Did you only use the projection system, i.e. the Eluer1/2/3 here is not the Euler angles but the project angles between A-x/RD, B-y/TD, and C-z/ND?

I also searched for other similar questions in this group, but I'm afraid I could not find a clear description of this topic.  It would be appreciated if you could give me a more detailed explanation, it's better if you could offer more examples. Thank you in advance!

Best regards, 

Liu

[Michael Jackson]

Dear Liu,

   I will try to answer your questions as best possible.

 

It looks from the code that we apply the same definition for the Euler angles for the Axis ODF as the Crystal Orientation Euler Angles. For orientation operations we use Orthorhombic Laue class within EbsdLib. I’m not the primary author of the Synthetic generation codes. If you are looking for a strong Axis ODF along a particular axis the easiest way to achieve this would be to use the “Orientation Utility” filter and enter the rotation as something that you are familiar with such as an “Axis Angle”. I have included a sketch of the Axis ODF pole figure, A Axis only, with an example of moving a weighted cluster from one point to another semi-arbitrary point. I used the “Orientation Utility” to enter an Axis Angle of <1,1,0>(90) which is rotating 90 Degrees about the <1,1,0> direction (Axis). Once this is entered the equivalent Euler angle is also computed. You can take this result directly enter it into the Axis ODF Eulers with a weight of like 100000 and a sigma of 1 and you should see the cluster move to the appropriate position in the pole figure.

 

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Mike Jackson

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