MICRESS Forum

Hi, I am currently trying to simulate the annealing process of copper to reproduce the CSRX (Continuous Static Recrystallization) mechanism, and I have encountered the following two issues:

1. MICRESS fundamentally employs a discrete nucleation model. To approximate the "continuous and gradual" behavior of CSRX within this framework, should we significantly shorten the nucleation time interval and couple it with local gradient differences? This would allow nucleation events to be distributed across different times and spatial locations, rather than having the entire global domain cross the nucleation threshold simultaneously.

2. Since CSRX relies on the heterogeneity of strain gradients to provide local differences in driving force, is it necessary to change the Phase 1 setting to recrystall mean_disloc or local_disloc, and fully enable Dislocation Coupling in the phase interactions? Would this be required for the system to truly "see" and utilize the spatial gradients provided by the VTK input?

Dear vincent00811,

Unfortunately, I am not so much familiar with recrystallisation in Cu, and also not to the CSRX-model. However, what I understood from literature (https://www.sciencedirect.com/science/a ... via%3Dihub) is that with CSRX there is no overgrowth of unrecrystallized grains by new "recrystallized" grains at all, i.e. that during transformation there is no mixture of both types of regions, but that the process is rather continuous inside each grain. At the subgrain level this means that there is no abnormal subgrain growth, which as a new "grain" can overgrow other unrecrystallized grains like in "normal" ReX. Instead - that at least is what I understood - through an extended recovery process the low-angle subgrain boundaries change to high-angle subgrain boundaries by orientation change, due to dislocation movements. I.e. subgrains transform continuously to normal grains, thus enabeling grain growth. This cannot be reasonably modelled as a "nucleation" in MICRESS, but perhaps would have to be treated on the subgrain level.

Maybe I am wrong - as I said I am not really an expert - and maybe I also misunderstand the approach you want to take. Can you explain in more detail how you understand CSRX and what is different to "normal" static recrystallisation (DSRC)? I think this is important for me to propose a proper way how that process can be best simulated in MICRESS.

Bernd

Dear Bernd,

Thank you very much for your thoughtful reply — your description of CSRX matches my understanding well, and I think it is exactly the right framing for the problem I am facing.

To answer your question about how I understand CSRX and how it differs from "normal" (discontinuous) SRX:

In my case, the driving force is not cold work but thermally-induced shear strain from the CTE mismatch between Cu and the surrounding glass (TGV structure). During heat treatment, geometrically necessary dislocations (GNDs) accumulate preferentially near the Cu/glass interface. Instead of new HAGB-bounded nuclei forming in a deformation-free matrix and sweeping it out (as in classical DSRX), the experimental EBSD evidence (Wang et al., ACS Appl. Electron. Mater. 2025) (https://pubs.acs.org/doi/10.1021/acsael ... r1&ref=pdf)shows that:

- Dislocations accumulate around existing subgrain boundaries within the deformed grains.
- Low-angle grain boundaries (LAGBs) progressively absorb more dislocations and rotate into high-angle grain boundaries (HAGBs).
- No new grain sweeps across unrecrystallized material; the refinement happens in-situ inside each parent grain.
- The result is a spatial gradient: finer grains near the interface (high GND) and coarser grains at the pillar center (low GND).

So I fully agree with your point that this cannot be modelled as classical nucleation-and-growth in MICRESS. My current v9 setup uses interface-based nucleation with `parent_relation` (0–15° rotation) precisely as an approximation of the LAGB → HAGB rotation, driven by a spatially graded dislocation density field (higher at the X edges, lower at the center). I am aware this is a compromise: MICRESS treats each rotation as a discrete nucleation event, whereas physically it should be continuous at the subgrain level.

This is where I would very much value your advice. Specifically:

1. Would `split_from_grain` be a more physically appropriate mechanism for CSRX than interface-based nucleation? My reading is that it produces new orientations from within the parent grain rather than at its boundary, which seems closer to the subgrain-level picture you described — subgrains continuously transforming into full grains inside the parent.
2. In the same spirit, would you recommend `local_disloc` over `mean_disloc`? My concern with `mean_disloc` is that averaging dislocation density within each grain may wash out the spatial gradient I need to preserve (interface vs. center).
3. Is the 0–15° `parent_relation` rotation range reasonable as a proxy for the LAGB → HAGB transition, or would you suggest a different treatment?

Any guidance — even to tell me which direction is more defensible — would be extremely helpful.

Best regards,
vincent

Dear vincent,

Thanky you for telling me that I was not completely wrong with my understanding of CSRX

To sum it up in my words: Due to the embedding of your samples, you have a gradient in dislocation density. Due to the higher dislocation density at the metal-glass surface, the transformation of LAGBs to HAGBs at the subgrain level is faster, leading to a higher probability of subgrains to develop to a "normal" grain and become visible. For the simulation model this means that new grains should be produced with a probability which increases with increasing dislocation density. Subsequent grain ripening can perhaps be neglected, at least in a first step.

For a simulation model, this leads to the following challenges:

- An initial microstructure must be defined which contains of a grain or subgrain structure, and which represents a dislocation density gradient.
- New grains which form by a continuous transition from subgrains must be introduced. Their shape is not defined by a growth process but by the shape of the former subgrain.
- Formation of new grains should be triggered by dislocation density, but not by a threshold mechanism but somehow probabilistic to be more realistic.

The approach which you propose, as I understand, does only treat normal grains and no subgrains. New grains are approximated by nucleation and growth (which has the disadvantage that they will be sherical or semispherical in a first place). Defining a dislocation density per grain of the initial microstructure could be too coarse to describe the gradient of deslocation densities. Using a continuous dislocation density field using "local_disloc" could be helpful, however this model is (by now) designed only for use in single-phase materials (but I guess you use two phases in your approach only for sake of more simple evaluation). Probabilistic nucleation can be introduced by "nucleation_noise" and by definition of several seed types with different checking interval and critical dislocation density.

This type of modelling you propose in principle is possible with MICRESS. However, I personally would prefer a model which is closer to the physical background and directly works on the subgrain level. The distinction of grains and subgrains could be only by the value of misorientation. I would propose to rather use the Read-Shockley and Humphreys model instead of a 15° threshold. By using the "add_to_grain" function of nucleation it is further possible to perform a "pseudo-nucleation", which does not create a new grain but changes the properties of an already existing (sub-)grain, e.g. the orientation and the dislocation density. Maybe, this is similar to the idea you thought to address with "split_from_grain" (which, however, only works for disjunct parts of a grain which exists at several locations simulataneously). With the current MICRESS implementation, the "rotation" of a subgrain by this "add_to_grain" mechanism by small steps is easily possible via the "parent_relation" function. A step-wise reduction of the dislocation density in a similar way would be more complex by now, but, maybe, could be implemented on our side in future...

Bernd