Eutectic solidification during additive processes

dendritic solidification, eutectics, peritectics,....
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Atur
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Eutectic solidification during additive processes

Post by Atur » Fri Dec 17, 2021 3:40 pm

Dear Bernd,

I would like to simulate the evolution of eutectic coupled growth under large range of thermal gradients and cooling rates (casting, SLM, etc..) while keeping the composition constant. The eutectic morphology is expected to be lamellar.

I would like to have comparable simulation set up for all conditions. I have couple of starting questions;

1- When setting the initial grain, should I start with one of the phases which has slightly larger undercooling?
2- If I want to see lamellar features, does it necessary to use smaller domain (e.g. 10µmx10µm) and finer grid spacing?
3- Would it be possible to simulate the eutectic growth without using the moving_frame option? I tried couple of simulations, havent managed to get lamellar growth using no_moving_frame option with relatively larger domain.
4- How should I set # min. undercooling [K] (>0) for interface nucleation? I dont want to use analytical_curvature and according to the grid spacing, the undercooling for stable nuclei growth will differ, maybe siginificantly. In this case (interface nucleation), would it be okay to set the min. undercooling to the value approximately similar to undercooling for stable nuclei growth?
5- Should the kinetic coefficient liquid and both solid phases (0/1 and 0/2) equal?

Thank you in advance and regards,
Ahmet

Bernd
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Re: Eutectic solidification during additive processes

Post by Bernd » Mon Dec 20, 2021 5:33 pm

Dear Ahmet,

I will try to answer one by one:

1.) This is difficult to say, because the undercooling depends on your initial situation which may be different from stationary eutectic growth. I would rather say it makes sense to start with the phase with higher expected fraction. You need to bear in mind that nucleation of the second phase is probably artificial because in 3D you simply would have branching instead of nucleation...

2.) If you want to simulate the eutectic microstructure, you need a resolution which is fine enough for the lamellae. Otherwise, you may want to use the "unresolved" model.

3.) The question whether you need "moving_frame" or not depends on how close you can put your initial conditions to the stationary conditions, and - of course - whether you are at all interested in stationary conditions. For invariant eutectic systems (e.g. binary) stationary state is reached rapidly, while for monovariant eutectics it may take very long time.

4.) The "Minimum undercooling for stable growth" is a technical criterion which depends on resolution. This means for the finest resolution simulation you will need the highest undercooling in order to overcome the curvature corresponding to one grid cell (if you do not want to use "analytical_curvature"). However, as I said above, nucleation is artificial, but needed to replace branching of the lamellae which happens in reality, and which would come automatically in a 3D simulation. According to the higher curvature effects of a finer microstructure, I would say it would be more comparable if you would scale nucleation undercooling with the average curvature of the lamellae. Or you try to simulate a thin 3D structure which is just thick enough to allow for branching...

5.) This does not matter if you use "mob_corr" (and you definitively should do that!). This option ensures diffusion-limited growth kinetics, as long as the input value for the interface mobility (=physical value) is big enough.


Bernd

Atur
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Re: Eutectic solidification during additive processes

Post by Atur » Mon Dec 20, 2021 7:19 pm

Dear Bernd,

Thank you for your answers. I have two follow up questions:

1- You suggested that I should scale nucelation undercooling with the average curvature of the lamellae. Does this mean I should modify the nucleation undercooling with respect to the grid spacing by using the sum of kinetic undercooling and curvature undercooling (ΔG=ΔS*ΔT)? In this case, which range (min-max?) should I select from the .driv output for ΔG? (I assume ΔS can be find from .log file)

2- I am using atc mob_corr for all of my simulations in order to aviod numerical trapping effects on interface as described. However I have some confusion at two points. Firstly, I wonder if should use mob_corr and atc options for microstructure evolution during slower processes, e.g. casting? My second question is, in my LPBF and LMD simulations the cooling rate is almost 1000 times different than each other (and velocity of the liquidus isotherm ~10 times different). However the interface mobility for S/L interfaces are adjusted to the same physical value of 10 cm**4/(Js) (calibrated by .driv output). I wonder whether this makes a critical difference in solidification microstructure while using mob_corr? I was thinking I should use lower coefficient for slower processes, e.g. LMD compared with LPBF, since I think precipitation of the second phase (content, morphology) should be effected by it.

Thanks,
Ahmet

Bernd
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Re: Eutectic solidification during additive processes

Post by Bernd » Tue Dec 21, 2021 11:34 am

Dear Ahmet,

1.) As already said, this is a difficult topic, and my answer is tentative. I think it could be reasonable to do what you propose. You should use the dG value which you typically find at the top (center) of the lamella of the phase to be nucleated. The argument would be that this is the typical undercooling of the lamella which would also be active during branching.

2.) The "mob_corr" and "atc" option should always be used if you can assume diffusion limited growth, and the length scales connected to this type of growth can be resolved. The value which you specify as interface mobility in this case is interpreted as "physical" mobility which in principle does not depend on the process conditions. Using "mob_corr" a suitable numerical interface mobility is calculated automatically which corrects for numerical artifacts due to the finite interface thickness. In practice, you chose a sufficiently high value for the "physical" mobility (= intput value) and check whether the chosen numerical value (in .mueS output) is at least one order of magnitude smaller. Then, the input value was sufficiently big and does not have any influence on kinetics. I guess this will be the case if you use a value of 10 cm**4/(Js) for all cases.

Bernd

Atur
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Re: Eutectic solidification during additive processes

Post by Atur » Mon Feb 07, 2022 5:40 pm

Dear Bernd,

I finally had chance to screen inital parameters for eutectic composition. I attached an image below. My aim was to screen whether the eutectics (nucleation at interfaces in this case) are forming in given process conditions.
Bernd wrote:
Mon Dec 20, 2021 5:33 pm
3.) The question whether you need "moving_frame" or not depends on how close you can put your initial conditions to the stationary conditions, and - of course - whether you are at all interested in stationary conditions. For invariant eutectic systems (e.g. binary) stationary state is reached rapidly, while for monovariant eutectics it may take very long time.
During my first trials, I set the equilibrium and bottom temperature to eutectic temperature and checked when the front temperature will reach a steady value. I observed that temperature was 1610K from tabF. output and was not changing over the time. At this setup, only phase 1 grow as dendrites however there was no secondary phase nucleation at the phase 1 interfaces.

Then I set the bottom temperature to where I observed steady front temperatute (keeping initial equilibrium T constant), and I somehow get features attached. Again the front temperature stayed constant at 1610K. I think this also means that I introduced some undercooling by setting the bottom temperature to couple of tens K lower temperature, which might have induced nucleation of second phase. Do you think can this set up utilized to different conditions? Would it be comparable? Can you give me some hints how can I probe the steady-state of the growth? I wanted to start everything from eutectic temperature, however no matter how much I wait, I havent see any nucleation of second phase in different set-ups.

I also see weird and amorphous solidification front forming with an angle to the temperature gradient (initial microstructure set directly to Z (gradient) direction 0°). I wonder if this is an artifact.

Regards,
Ahmet
Attachments
Picture1.png
Picture1.png (350.83 KiB) Viewed 4556 times

Bernd
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Re: Eutectic solidification during additive processes

Post by Bernd » Tue Feb 08, 2022 12:39 pm

Dear Ahmet,

I think one of the main problems of your simulation setup is that it is 2D: In 2 dimensions, lamellae cannot branch, so that you need to apply nucleation constantly in order to achieve steady state (or something which resembles that). This however is not how things works in reality, so that essentially by choosing artificial nucleation conditions you somehow "design" your results...

In the case you show it seems that you haven't sufficient nucleation, leading to remaining liquid ponds and to a very high undercooling (including the preferential growth along the 45°-direction which probably is due to numerical instabilities).

I would see 2 major ways how to avoid the problem:

1.) If you really want to simulate an irregular eutectic growth in steady state, you need to switch to a 3D simulation. It would be sufficient to have a relatively small number of cells in y-direction, just enough to allow for branching in this direction.

2.) If you assume a regular initial microstructure with already existing lamellae, and you choose the initial lamellar distance small enough, you will not need any branching, because the expected steady-state microstructure can be reached only by reduction of the number of lamellae. The initial state should be chosen close to this expected stationary state. Otherwise it may be difficult to enter into steady state without completely loosing the initial structure.

Bernd

Atur
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Re: Eutectic solidification during additive processes

Post by Atur » Tue Feb 08, 2022 3:23 pm

Dear Bernd,

Thank you for your reply :)

I am afraid it might be very time and resource expensive for me to go for 3D. But as far as I understand, you are suggesting me to introduce some cells in y-direction just to initiate branching so that the microstructure evolution will be somehow refined. So some compromise between time expenses and results quality. Does this also mean I can still screen my process mainly in XZ direction but with a better microstructural accuracy?

In this case, for a simulation domain of 500x1x500 with grid spacing of 0.1 µm how many cells in Y direction I should introduce? Do you have any suggestions about the boundary conditions? normaly I was using ppii and ppif. Lastly, would you suggest that I start from the eutectic temperature?

Do you think starting from an initial lamellae would be representative for different cases? I think it might not really representative for each condition. I would expect in SLM conditions, eutectic coupled growth might be even hindered completely, maybe it is better to start from a initial flat grain as my previous approach and follow the solidification front by moving frame option. Here the aim is predicting certain trends and mechanisms window rather than being very accurate with microstructure.

Regards,
Ahmet

Bernd
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Re: Eutectic solidification during additive processes

Post by Bernd » Tue Feb 08, 2022 6:28 pm

Dear Ahmet,

The thickness of the domain in y-direction, which is required for allowing branching, depends on the boundary conditions. If you would use symmetric boundary conditions here (i.e. ppssif), then the thickness should be enough to cover a half lamella of each phase. Based on your simulation results you have shown this could be around 1-2 µm (i.e. only 10-20 cells). With symmetric boundary conditions the eutectic growth would still be forced into the xz-plane, so that the simulation remains (quasi-)two-dimensional and can be analyzed accordingly.

If you would take periodic conditions (i.e. ppppif), then eutectic lamellae also could grow oblique to the xz-plane, so that you essentially would have a small section of a 3d-eutectic structure. However, you would need to have at least the double thickness (i.e. 20-40 cells), because one whole lamella of each phase must fit. Of course, depending on the microstructure you eventually will get, the estimation of the required thickness may be somewhat different.

Generally, it is recommendable to start at the eutectic temperature with already both phases existing. However this also depends on your simulation goals, and what you believe is the mechanism you want to model. I would try to avoid including nucleation, if this is not really the mechanism which decides whether you get eutectic or single-phase growth in reality, because nucleation always brings a whole set of parameters into play which you do not know a priori. Depending on the composition, the primary phase may also overgrow the secondary phase, even if you started with 2 phases.

The moving-frame option will probably be very helpful, if you have strong temperature gradient, and the solidification interval (i.e. the thickness of the mushy zone in this case) is rather small.

In the following paper you can find a perhaps similar case of 3D-eutectic growth under SLM-conditions which was simulated using MICRESS and which could be helpful:

G. Boussinot, M. Döring, S. Hemes, O. Stryzhyboroda, M. Apel, M. Schmidt,
Laser powder bed fusion of eutectic Al-Ni alloys: Experimental and phase-field studies,
Materials & Design, Volume 198, 2021, 109299.
https://www.sciencedirect.com/science/a ... 7520308352

Bernd

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