Analyzing average compositions in dendritic and interdendritic regions

aspects of evaluating simulation results and their graphic presentation using either DisplayMICRESS or other software tools. Features and possibilities of DisplayMICRESS
Atur
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Atur » Thu Dec 16, 2021 8:07 pm

Dear Bernd,

Thank you for your reply. I am sorry if I repeat the similar questions in different ways, but it is quite challenging for me to grasp the most of it..

I think I understood this time but partly. Therefore I will go through it a little. In the picture attached, I measured the distance when the cell number changes. The distance was equal to ~2.5 µm (except the start of the simulation, planar interface). What I did not understand completely is, does the thermodynamics averaged for every 2.5 µm, in this case with slightly different linearization, even though I set dG avg as 0.5? Also couldnt find the reference number in TabL which I can correlate with refR.

As far as I understand you suggest me to use noise in dG options coupled with global [distance] option. So if I couple both of them, I assume I should be getting ranges (every 2.5 µm) where slightly different linearization parameters will be used and the averaging and the noise will be adjusted in each interval. Is it correct? I gave it a short try. In attached pictures I used the options:
# 'DeltaG' options: default
# avg ...[] max ...[J/cm^3] smooth ...[Deg] noise ...[J/cm^3] offset ...[J/cm^3]
avg 0.50 smooth +45.0 max 500 noise 20.
# Which phase diagram is to be used?
# Options: database {local|global|interface|fragment}[<maximal distance>]
# | linear | linearTQ
database global 2.5

This time it shows that dendrites are advancing to the similar heights, planar interface brokes earlier, which are initially okay I think. Also, are there any disadvantages using noise ...[J/cm^3] in additive process simulations? Are there any options I should avoid? Driving forces seem to be in the desired range, but they look like a bit crusty instead fo being continous (e.g. on the tip). I wonder why is that.

I also checked the example A017_M247_Additive_constGV. Here you also added smooth parameter of 45 degrees, which is defined in documentation to be a directional noise on averaging to reduce the grid anisotropy. Does using averaging, smooth and noise ...[J/cm^3] together would cause any disturbances or interference with each other? Can you suggest any value to insert as noise and smooth?

Lastly, are there any rule of thumb from your experiences to set the global distance? For example, the gradients in LMD and LPBF is highly different that each other. Should I shorten this interval incase of LPBF?

thank you and regards,
Ahmet
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Bernd
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Bernd » Mon Jan 03, 2022 5:33 pm

Dear Ahmet,

Sorry that I somehow missed your reply before leaving for Christmas holidays. Wish you a Happy New Year, anyway.

Perhaps my last answer was not clear enough: For simulation of additive processes (or other dendritic simulations with large temperature differences inside the domain) I recommend using only relinearisation noise by using "global" and a suitable distance option and no noise in the dG options. The distance used with "global" should always be chosen bigger than the interface thickness and smaller than the dimensions of the simulation domain. Furthermore, the distance should be small enough so that in gradient direction the corresponding temperature difference (which is averaged inside a region which same linearisation parameters) is not too large (~<10K). On the other hand, the smaller the distance is, the bigger the number of different linearisation parameters, and the bigger the calculation time for thermodynamic data (to be checked in .TabP output). In the .numR output you can distinguish the individual regions (more than 250 in your case), which parameter sets of which are given in the .TabLin (not .TabL!) output.

At the same time, the distance influences the length-scale of the noise. However, as the linearisation areas are constantly moving with each update, there is no problem even if the distance is large (as long as it is smaller than half of the domain width). In your case you still can increase the values for speeding up your simulation.

The "directional" noise which is introduced by the "smooth" option is not helpful for breaking up a planar interface, because it is essentially not doing anything at this stage. Is is rather meant to avoid grid effects, and not necessary at all (it is even still not clear under which conditions it is helpful at all...).

dG-averaging is done across the interface in direction of the interface gradient and helpful for stabilizing the interface against driving force gradients. Significant interference with the thermodynamic noise coming from the distance option of "global" would exist only if the distance is chosen similar or smaller than the interface thickness.

Bernd

Atur
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Atur » Mon Jan 10, 2022 11:55 am

Dear Bernd,

Happy new year!

Thank you for the clarification!

Regards,
Ahmet

Atur
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Atur » Thu Jan 27, 2022 2:48 pm

Dear Bernd,

I tried to run some new simulations after sometime. I have a question regarding the TabF output. Here the approach is both processes (conditions) forms dendrites from planar front instability. Therefore I think now their features will be more comparable than what I tried before. Process number 1 has lower cooling rate and lower solidification velocity (Product of CR/G, isotherm velocity) compared to number 2.
Some of the data (segregation profiles, dendrite spacings) gives quite reasonable trends, however I want expand my analysis availabilities.

Yet when I check the TabF. output, the area fraction of second phase is higher for process number 2. My question is, does the fraction of second phase calculated according to the relative area of second phase divided to the total area of the simulation domain? Because I think in reality this shouldnt be the case when we compare a process with another process which has higher interface velocity and higher cooling rate (diffusion will be comparatively limited). Do you have any suggestions how can I compare their relative secondary phase contents? Besides the cooling conditions and grid spacings, I only varied the nucleation parameters where minimum undercooling in first process is 4K and in the second 16K. Do you think increasing(calibrating) the minimum undercooling value for process 2 would help to reduce area fraction as an alternative?

Also, second phase starts to form at higher temperatures in process number 1, in contrary to Scheil solute trapping model. I think, in reality, since the solidifcation interval of process number 2 will be way shorter than process number 1 this also should not be the case and second phase should from at higher temperatures for process 2 (and in the end the fraction should also be lower). From the TabF output, I see the end temperature in process number 2 is way lower, but naturally completed faster. Is all these data/trends related to the fact that I am using constant cooling conditions and different domain sizes? I think of to equalizing the domain sizes but it will be very unpractical and time expensive for process number 2. Do you have any suggestions how can I compare both domains for respective data?

Lastly, my interdendritic areas are always continuous. Even though it is npt a big deal for my approach, it looks quite artifical. Does that has something to do with interface energies or it is like this because I set the diffusion only in Z direction?

Regards,
Ahmet
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Bernd
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Bernd » Thu Jan 27, 2022 9:34 pm

Dear Ahmet,

First of all, the .TabF output really gives you the average fraction of all phases in the whole simulation domain. You can check that if you display the .frac2 output (I assume your precipitate is phase 2) with DP_MICRESS and use 'Data analysis/Properties' to evaluate the average value (=fraction of phase 2) over the domain. With this functionality of DP_MICRESS you can also evaluate the average fraction in partial regions of the domain if you zoom into the specific region before analyzing. There is also an option 'Show average X/Y over Z' under 'Virtual EDX' which would give you an average fraction profile over Z (which you further could align with the corresponding temperature information in .temp). If sticking to the .TabF output, please bear in mind that this output for the whole domain is not comparable for different domain sizes and thermal conditions as long as solidification (and precipitation) has not completely finished.

When quantitatively analyzing MICRESS results like you are doing it is important to get a feeling how strong numerical effects are. One of the major problems of phase-field methods is the artificial "solute trapping" which is a consequence of the numerical interface thickness. While, in principle, choosing a high grid resolution solves this problem, in practice high resolution leads to enormously high simulation times. Thus, it is one of the most important quality criteria how good a phase-field model behaves at lower grid resolutions. To achieve that, we use a combination of approaches in MICRESS:

1.) By using a multi-obstacle potential function, fd-correction and other numerical features like dG-averaging or interface stabilisation, MICRESS works with a very small number of interface cells across the interface (down to 2.5), which reduces artificial trapping and increases effective resolution.

2.) Mobility correction ("mob_corr") automatically adjusts the effective kinetic coefficient such that the user-defined physical value is realized independent from grid resolution.

3.) The antitrapping current ("atc") compensates for artificial solute trapping, which is important to get the correct

Nevertheless, all these approaches are first-order corrections, so that numerical errors come into play if resolution gets too coarse (essentially I am currently working hard to further improve these models in order to achieve an even better scaling...). My experiences (as of Version 7.1) with SLM show that when increasing Δx, the tip temperature of the dendrites starts dropping, the amount of secondary phase precipitation is reduced, and, finally, the direction of the dendrites start following the grid direction, leading to wrong kinetics and altered selection behavior.

For this reason, if working quantitatively, it is important to check out which effect has changing grid resolution. Especially if you compare to different cooling conditions (and thus use different grid resolution), it could be that one of the simulations has a relatively fine mesh while the other is too coarse (for the given conditions). This would create a numerical bias to the comparison. The only way to rule this out is to increase grid resolution for both cases step-wise (e.g. by factors of 2) and see how much results are changing. Because finer grid resolution means much higher simulation times, you should take the smallest possible representative domain size for this trial. Afterwards you can use the coarsest resolution for each case which still gave you comparable results with the highest resolved reference simulation.

Another question is whether you really should expect a lower amount of precipitate phase for higher cooling rates. I am unsure about that, but it is clear that you cannot compare respective MICRESS results with Thermo-Calc Scheil solute trapping, because the model approaches are (at least as far as I understand) completely contrary.

Finally I don't think that adjusting nucleation undercooling is very prospective. It would be physically unsound and look like tweaking the results into the expected direction. Under normal conditions anyway it should not have a very big impact.

Best wishes

Bernd

Atur
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Atur » Fri Jan 28, 2022 12:02 am

Dear Bernd,

Thank you so much for your reply :) . Indeed when I tried to analyze the region by data analysis properties/the results are slightly turned into the direction I expected. I think the reason was the area difference in planar phase 1 over the domains. Until it breaks down it occupies larger fraction in process number 1.

-I am currently applying the combination of the approaches suggested (e.g. multi-obstacle, atc, mob_corr). Actually for process one I am already using Δx= 0.075 µm and for process 2 Δx=0.0075 µm with the interface thickness of 3 and 2.85 cells, respectively. For the first process, I can maybe try your suggestion of increasing the grid spacing and see if anything changes, but I think they are already quite fine to avoid some of the artefacts.

-I dont understand what do you mean by "dendrites start following the grid direction". Do you think that is the explanation of my continuous interdendritic areas over the domain?

-What I was trying to say was actually different than only considering the cooling rate. I think the cooling rate itself is not enough to describe second phase formation. I was rather focusing on solidification velocity (Cooling rate/temperature gradient ratio). In current set up, process 1 has 0,4 cm/s where as process 2 has 5 cm/s solidifcation velocity (of liquidus isotherm). That is whay I was expecting rather significant difference between their second phase fractions. By the way, is there anyway to check diffusion length scales?

-This is why I suggested to calibrate the nucleation undercooling. Since I could not find so much information on how to really calibrate min. undercooling parameter for seed stabilization model, I was using the approach to select an undercooling value larger than "undercooling for stable nuclei growth" value, which is directly effected by grid spacing. I think I should anyway differ the undercooling values for both processes since the initial nucleation sizes will be different due to the Δx value. However how high or how small/close I should take seem to be a bit unclear. If I select same undercooling value, I think then I may not even form any second phase in process number 2, since the value will not overcome numerical barrier. This is the only parameter I change for nucleation (besides shield spacings and nucleation check time check). Your comments are more than welcome, I will send you my respective drive files.

Regards,
Ahmet

Bernd
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Bernd » Fri Jan 28, 2022 4:10 pm

Dear Ahmet,

Thank you for sending me your input files by PM. With them, I think, I found what could be the reason for missing comparability between your two simulations. If you change time and length scales between simulations it is important to also change all numerical parameters which have a length or time unit. There are several of them in the nucleation input data, namely the checking interval, the shield time and the shield distance. E.g. checking for nucleation of precipitates with the same rate (every 1.E-5 s) in both cases cannot be the same if your cooling rates differ by a factor of 500!
There are more such parameters like the updating intervals for thermodynamics, diffusion coefficients and enthalpy, and also the length of the scope for relinearisation which you define after the "global" keyword.
I can easily imagine that these parameters, especially those for nucleation, make a difference for the fraction of preciptates which you get...

With "following the grid direction" I meant an effect which you can observe only if your dendrites are growing with an orientation different from 0° (or 90° in case of cubic). If you e.g. would change the orientation ("Rotation") of your initial grain from 0° to 10° you could see this effect, if your grid resolution is significantly too low.

Bernd

Atur
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Atur » Fri Jan 28, 2022 4:28 pm

Dear Bernd,

Thank you so much for your reply. Some of them are actually different by 10 times but I never think that it would have such a drastic effect.

I would appreciate if you can suggest me a relationship for example if I would like to keep the parameters in process number 2 constant,
and calibrate the process number 1 accordingly:

-How often should I check the nucleation for slower cooling rate, and how should I calibrate the shield distance and shield time? Are there any ranges or relationships you can suggest me? I also thought how often I check actually does not matter since they either form and grow or not.

-diffusion and thermodynamic data is updated in every 1.00000E-05 or -06 seconds and domain is divided into 10 segments for diffusion and the rest of the input is obtained from the database. Which range should I consider for distance and interval for process number 1? Should I reduce it towards 1.0E-03 or to even -02? I would like to keep the length scope after global keyword for both processes since otherwise it occupies huge domain size for both processes to destabilize the planar front..

Regards,
Ahmet

Bernd
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Bernd » Fri Jan 28, 2022 6:22 pm

Hi Ahmet,

I would propose the following scaling:

All time parameters should be converted according to the cooling rate, i.e with a factor of 500. Checking for nucleation every 1.E-5s for process 2 would translate to checking all 5.E-3 s for process 1. The same holds for updating intervals of diffusion coefficients or thermodynamics.

All length scale parameters should be converted according to the characteristic microstructure length scales, i.e. with primary spacing. The most important one here is the shield distance of nucleation, because it also defines the nucleation distance (if you do not explicitly specify it as second parameter) and thus the number of seeds you get.

I don't understand the problem with scaling the "global" distance - maybe check again with adjusted updating interval for thermodynamic linearisation parameters.

Bernd

Atur
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Re: Analyzing average compositions in dendritic and interdendritic regions

Post by Atur » Tue Feb 08, 2022 3:47 pm

Dear Bernd,

I tried to use segregation analysis one more time to understand the Al micro-segregation after different processing conditions. Your comment on my input would be very valuable;

- I again encountered that the segregation analysis suggests that the peak Al concentration will be highest after SLM in interdendritic regions and will gradually decrease in LMD followed by a further decrease towards casting. The difference is roughly 4 to 5 at% between each process. As expected, the finer interdendritic spacing will be present in SLM with few nanometers and it increases significantly going towards casted microstrcutre together with the amount of secondary phase. Also, in SLM, the denrite core has slightly more Al is compared to other two.

Now my question is, would that be possible to have higher peak Al concentration in interdendritic regions in SLM compared to casting or LMD? My argument is: the diffusion distances is shorter during SLM (smaller dendrite spacing), therefore there might be no time to re-arrange this concentration spike/gradient and it basically gets trapped between interdendrites upon rapid solidification. However, during casting or LMD, the diffusion distances are longer, are there is more time to re-adjust these concentration gradients.

Nevertheless, I feel these observations contradicts with the literature, where we know the segregation is reduced "overall" in rapid solidification (smaller spacing), hence elements with higher diffusivity should experience lower rate of segregation under faster solidification conditions since they spend less time in their precipitation window. However, if we think locally and consider concetration peaks in interdendritic areas, the simulations might still make sense from my perspective. Do you have any observations or comments about these concentration spikes in simulations?

One should also consider that the simulations I performed is considers the initial time they get solidified, with cyclic reheating during AM, these concentration gradients can eventually get reduced to a level that it might not make any difference experimentally. So my argument actually is about the very first moment after complete solidification in the given area (or domain).

Regards,
Ahmet

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