Blocks in martensite

[jorgenasorhaug]

I'm a little confused about how the blocks are determined. To me it looks like the block boundaries are overlapping perfectly with the child grains? Why aren't blocks defined according to pairs of variants? (See 10.1016/j.actamat.2014.01.058.)

[frankNiessen]

Hi @jorgenasorhaug,

thanks for your request. I would like to elaborate on this, but can you be a bit more specific one which blocks, which example or dataset?

Best wishes
Frank

[jorgenasorhaug]

Hi @frankNiessen, thank you for the response

If I'm running example 7 as it is written, the function plotMap_blockWiths gives me a map of what I assume is showing the identified blocks and corresponding boundaries. However, if I compare this map with the map of the child grains that I start with, the boundaries in the two maps overlap perfectly. If I then change the child grain boundary threshold before reconstructing the parent grains, by e.g. setting the threshold from 3 deg to 2 deg, the same observation can be made. (If I reduce it to 1 deg, the blocks look unreasonable and almost nothing like the maps from using a higher child grain boundary threshold.) This means that the block boundaries and therefore also the block widths are defined by how the user is defining the child grain boundaries prior to the reconstruction.

I find this a little bit strange. I often read that blocks can be viewed as effective grains in lath martensite. But if the blocks are defined according to how the user defines the child grain boundaries in the reconstruction, this can become contradicting. So my question is practically: why aren't the block widths more independent on the child grains like the packets are?

Forgive me if I'm missing some common knowledge here.

Cheers,
Jørgen

[frankNiessen]

Hi @jorgenasorhaug,

at first, sorry for the delay in replying, it has been a busy week.
At second, I am not sure I can give you a fully satisfying answer to your question, you point at a difficult issue.

At first, I would like to refer to the paper that is quoted in the function that creates the block boundary maps

S. Morito, A.H. Pham, T. Hayashi, T. Ohba, Block boundary analyses to
identify martensite and bainite, Mater. Today Proc., Volume 2,
Supplement 3, 2015, Pages S913-S916.
(https://doi.org/10.1016/j.matpr.2015.07.430)

Here it says in the introduction:

To apply crystallographic analyses, it is necessary to redefine the morphological terms from crystallographic viewpoint as follows. A packet is a lath group with the same close–packed plane parallel relationship with austenite, i.e. CP group [3]. A block is a lath group with the same lattice correspondence, i.e. Bain group [3] or crystallographic packet [2], in a packet. A sub–block is a group of laths with a single Kurdjumov–Sachs (KS) variant. In these morphologies, there are many types of boundaries. To identify the morphologies, the block and sub–block boundaries are used, because the frequency of the block boundaries has specific features [1–4].

As you can see, packets have a large misorientation with each other, as they form from different habit planes of the austenitic phase, so it is clear that these are well-defined. Blocks are laths that have the same Bain Group and crystallographic packet, also this is rather well defined. Then we have sub-blocks, which are groups of laths of the same variant.

When referring to the martensite example dataset, the resolution of the map does not allow resolving laths, so we are looking at sub-block or block resolution. This is why virtually all the boundaries in the block map are colored.

From here on it gets tricky. The lowest misorientation angle between blocks is V1-V4, which experimentally is about 7 deg (see Table 1 in the above referenced paper). Individual laths can also have about 2 deg misorientation with each other, see

Sandvik, B. P. J., & Wayman, C. M. (n.d.). Characteristics of Lath Martensite: Part I. Crystallographic and Substructural Features.

The MTEX grain reconstruction algorithm is also not amazing at reconstructing grains with large intragranular misorientation at low intergranular misorientation. This means that changing the reconstruction angle can have an effect on how the block boundaries are identified.

Your comment however shows to me that I need to update some parts of ORTools to be more well-defined. This topic clearly needs more work. Since I changed into the private sector I do not have as much time for the maintenance of this repository unfortunately, but I will see what I can do later this year.

I would also like to hear whether @nyyssont maybe has some thoughts on this?

[jorgenasorhaug]

No worries :) I appreciate your replies irrespective of how long it takes.

Correct me if I'm wrong, but does this mean that if I run an initial PG reconstruction to get the variant map, I can then re-run the PG reconstruction by using the variant grains (cf. computeVariantGrains) instead to get a map of the sub-block structure (plotMap_blockWidths)? Can I then also get the blocks by computing the Bain grains within each packet, re-run the reconstruction and then use the function plotMap_blockWidths?

[nyyssont]

Hello! As Frank says, in MTEX we are just about able to segment martensite at the sub-block level, when we leverage the information from the reconstructed parent grain map in the segmentation.

To obtain the width of the blocks:

1. the sub-blocks would need to be merged together to fulfill the description of "block", which would be sub-blocks that share a V1-V4 type boundary with each other.
2. Some sort of averaged out habit plane suitable to describe the co-habit plane of the block would need to be described. If the habit plane is 575 for variant 1, it would be 755 (if I remember right) for variant 4. Perhaps a descriptive habit plane would be some sort of area-weighed mean of the habits.
3. The trace of the habit plane would need to be calculated and the boundaries somehow projected against it. Here (as in ORTools), the projection is taken for a trace passing through the center of the block: Block width in martensite (assumed dimension of grain perpendicular to selected plane) mtex-toolbox/mtex#522
4. Using the angle of the habit plane normal, the length of the projections parallel to the habit plane is calculated.
5. The projections are averaged and multiplied by two (since they were done on the trace passing through the centerpoint of the block).
6. These values are then averaged for all blocks.

In ORTools, I don't think the sub-blocks are merged together (not sure). The block widths are also calculated using 111 for the habit plane, instead of some determined habit plane.