MICRESS Forum

Hello forum, your support during the CMSX-4 simulations was tremendously helpful.
Now I am working on simulating the laser welding process of 247LC alloy and this solidification process predominantly occurs in a cellular mode. As you know, in this alloy, in addition to the γ/γ′ phases, the formation of carbides also plays a critical role. I have a few questions regarding this.

1. In the A017_M247_Additive_constGV example, it is shown that the primary dendrites are γ while γ′ precipitates form in the interdendritic regions. However, in reality, both the dendrite cores and interdendritic regions consist of a γ/γ′ eutectic-like structure. Considering this, I understand that the representation in the simulation is a simplification, mainly due to limitations in spatial resolution and in order to avoid unnecessary computational expense. Would this simplification be justified by the fact that, in reality, the dendrite cores are predominantly γ with minor γ′, whereas the interdendritic regions tend to show the opposite balance (higher γ′ fraction)? I would appreciate any additional thoughts you might have.

For the reasons mentioned above, the BSE images of the experimentally observed solidification microstructure (cellular solidification) do not clearly reveal a distinct γ–γ′ transition in the intercellular regions. Therefore, in our calculations, we intend to reduce γ′ formation in these regions.
When applying the nucleation parameters defined in A017 to our case, most of the intercellular regions become filled with γ′. To address this, we arbitrarily increased the min. undercooling value of that seed from 5 K to 50 K. The reason for not completely deactivating the seed is that we did not want to eliminate γ′ entirely. seed 4 was kept unchanged.

2 We are performing multiple simulations in order to fit the computational results to experimental data. First, we will fit PDAS (primary dendrite arm spacing), and we also plan to fit the spatial distribution of MC carbides.

2.1 We are taking into account variations at the liquid/γ interface such as interfacial energy, interface mobility, stiffness anisotropy, and mobility anisotropy. For interface mobility, I understand that setting a sufficiently large mobility value (e.g., ≥10) together with using mob_corr is generally sufficient. If we want to treat interface mobility as a fitting parameter, would it be valid to vary the input mobility only within a range smaller than the mobility values that are automatically calculated by mob_corr? Alternatively, would it be better to apply a scaling factor after mob_corr? In addition to interface mobility, I would appreciate a checklist of other parameters and effects that should be considered during fitting.

2.2 In the A017 example results, the MC phase appears only at a level that is hardly visible in the DP output. However, in our welding experiments, we observe much larger and more numerous MC particles, so we are considering ways to increase the MC fraction in the simulation.
As an initial attempt, we reduced the min. undercooling value for MC nucleation from 25 K to 2 K, which resulted in a noticeable increase of MC particles compared to the example, to the extent that they can now be clearly seen in the DP output. Nevertheless, their size still remains small.
I understand that lowering the min. undercooling mainly enhances the nucleation probability. To further increase the particle size, should we modify the phase interactions involving the MC interfaces? If so, what kinds of approaches would be worth trying?

3 Regarding the following seed-type input:
# Reference phase (integer) [min. and max. fraction (real)]?
0 0.8 1.0
I do not fully understand how the minimum and maximum values are applied. From the documentation, I interpreted this as meaning that the seed becomes active only when phase 0 is present between 80% and 100%. However, in practice the calculation does not seem to behave in that way. Could you explain how this actually works?

4 It seems that when nucleation is selected outside of the bulk option, the nucleation density parameter cannot be applied. If that is the case, are there any thermodynamic input parameters, other than min. undercooling, that can be used to control nucleation in non-bulk cases?
If not, what is the basis for determining the appropriate value of min. undercooling? Are there experimental data or literature values available that can be used as a reference?
Additionally, which parameters could be adjusted in order to better reflect the thermodynamic phenomena associated with nucleation? As for the shield option, my understanding is that it is more of an artificial control intended to efficiently reproduce the phenomenon rather than a direct physical parameter.

5 Finally, I do not want too many grains to form during the calculation, as this slows down the simulation. I understand that the categorize function is supposed to address this, but it still seems that more grain numbers are assigned than I expected. Is there a way to optimize this further?

Thanks for taking the time to read. Have a great day!

Hello Ku shihyeon,

It took me some time to respond because you ask quite a lot of different questions which cannot not answered straightforward. I will try to answer them one by one:

1. You are absolutely right that inside each primary phase region there should be nucleation of the respective other phase when the temperature is decreased further after complete solidification. The fundamental problem about incorporating this solid-state precipitation within simulations is the length scale, given that secondary precipitates often are at least two orders of magnitude finer than the primary precipitates. Therefore, the question is whether it is necessary to include this precipitates in the simulation scenario, and, if this is the case, how this can be done. Generally, precipitation processes need to be included into the scenario if it is part of the simulation goals, or if precipitation has important effect on other important processes during simulation time. Otherwise, it could be handled in some type of post-processing.
Precipitation e.g. has a direct effect on latent heat release, solid state diffusion, on melting, and on precipitation of further phases from the solid state. This is the reason why we have included γ'-precipitation from fcc for simulation of welding and diffusion brazing processes (see [1-3]). Here we had to make the approximation to allow the precipitates getting bigger than in realitywhich was necessary due to the low grid resolution. But the main goal here was to achieve correct thermodnamic behaviour, which is especially important for the melting processes and for diffusion.
To the contrary, in our Example A017_M247_Additive_constGV.dri, we assumed that precipitation of γ' in fcc or fcc in γ' is not so important for the formation of the solidification microstructure under conditions of L-PBF. Furthermore, I would not expect relevant precipitation to happen already in the direct solidification step, but rather later during subsequent heating cycles.

2.
2.1. Fitting of interface mobility normally should not be necessary, if we can assume diffusion controlled growth kinetics and if we use "mob_corr" in the way you described. When fitting is still necessary, I like the method using a factor on the mobility correction rather than the mobility itself, because the diffusion-controlled interface mobility (obtained via "mob_corr") is strongly temperature-dependent. Thus one would have to fit the complete curve. The optional real value which can be given after the "mob_corr" keyword is a factor on the growth restriction behaviour of the element. Thus, using identical values higher than 1 for all elements would proportionally reduce the interface mobility.
On th other hand, using such a factor may be not so easy to motivate in publications...
Regarding other possible fit parameters, I would suggest to use the prefactor for the anti-trapping current ("atc") which can be specified withing the numerical parameters for the concentration solver.

2.2 Regarding MC-precipitation in Ni-based superalloys, my first consiteration is whether they appear blocky or more script-like. In the first case, which e.g. is typical for alloy 718 castings, I typically assume nucleation from the bulk liquid rather than from the interface. Under these conditions, the carbides have sufficient time to grow and tend to be more round. On the other hand, script-like MC-carbides grow in eutectic manner, which typically means that they nucleate at interfaces. Of course, there may me mixed behaviour also. It is recommended to use the seed_density model then in order to avoid regular grid-like structures.
Generally, reducing critical undercooling often helps, also concentrating nucleation towards the outer side of the interface as you did in 3. It is especially important to use the shield data, the nucleation distance and the checking frequency in order to fit the number of particles which appear realistic. Setting too many seeds always leads to very small particles. Furthermore, 2D-simulations generally tend to produce smaller precipitates compared to 3D-simulations. A specific problem with eutectic precipitates also is that they easily get overgrown rapidly by the primary phase. This problem can be reduced by increasing the grid resolution and by properly adjusting the interfacial energies.

3. This "trick" works exactly as you found out, and can help to give the precipitates a small lead. Why do you think it does not behave properly?

4. Indeed, the seed density model is not available for interface nucleation. It is a model for heterogeneous nucleation from the melt, and it is the only "physical" model available in MICRESS. Nucleation based on the "seed undercooling" model is rather empiric and must be calibrated to obtain realistic behavior. Unfortunately, to our knowledge there are no quantitative models for interface nucleation which could be implemented, and also rarely data available from literature for critical undercoolings.
As said above, with interface nucleation, the shield parameters, the nucleation distance, and the checking interval should be used to get a reasonable number of seeds. The "restrictive" option can help to avoid clustering e.g. at triple junctions or getting nucleation of top of already existing precipitates. If a high number precipitates is explicitly required (e.g. like in our case of γ'-precipitation from the solid), the option "add_to_grain" with suboption "new_set" can be used to set many nuclei which belong to the same grain number and thus are less detrimetal with respect to calculation performance.

5. The "categorize" option only applies to precipitate grains which have identical orientation, which are already "big", and which do not yet touch each other. It "joins" the grainy by assigning identical grain numbers. Due to these restrictions, the effect to reduce the effective number of grains may not be sufficient. Alternatively, the use of "add_to_grain" (as mentioned above )puts them to the same grain number right from the beginning. Possible drawbacks are that they may easily coalesce, and that the "small grain models" cannot work in this case. For that reason it is recommended that the initial grain radius is somewhat increased (but still smaller than the grid spacing), so that the initial fraction is above the 2x the minimal fraction (which is the case if the radius is 0) and thus stable growth is fostered.

Best wishes
Bernd

[1] B. Böttger, M. Apel, T. Jokisch, A. Senger, Phase-field study on microstructure formation in Mar-M247 during electron beam welding and correlation to hot cracking susceptibility, IOP Conf. Ser.: Mater. Sci. Eng. 861 012072 (2020)https://iopscience.iop.org/article/10.1 ... 012072/pdf
[2] B. Böttger, B. Daniels, L. Dankl, T. Göhler, T. Jokisch, Systematic Phase-Field Study on Microstructure Formation During Brazing of Mar-M247 with a Si-Based AMS4782 Filler, Metallurgical and Materials Transactions A (2019) Pages 1-16, https://doi.org/10.1007/s11661-019-05113-3
[3] B.Böttger, M.Apel, B.Laux, S.Piegert, Detached Melt Nucleation during Diffusion Brazing of a Technical Ni-based Superalloy: A Phase-Field Study, 2015 IOP Conf. Ser.: Mater. Sci. Eng. 84 012031, DOI:http://dx.doi.org/10.1088/1757-899X/84/1/012031

Thank you for your response.
As far as I know, last Friday was a public holiday in Germany, so I did not consider the delay in your reply to be an issue.


1.
In both the A017 example and the case I attached, it can be seen that solidification terminates with the formation of γ′ during the final stage of solidification.
Furthermore, when I intentionally increased seed undercooling for γ′ to suppress its formation, I observed a significant delay in the completion of solidification of the liquid phase (which I believe is independent of the residual liquid removal by add_to_grain seed).

Since my main objective is to predict the solidification temperature range accurately, my current focus is on controlling the secondary phase precipitation such as γ′ and MC carbides during the solidification process.


2.1
Regarding ATC in concentration solver , are you referring to the numerical parameter section?
I was unable to find any specific ATC-related options.
Also, following your previous advice (that using ATC may introduce numerical artifacts), I am currently not using ATC in the interface interaction settings.
If so, is it still possible to define or modify ATC-related parameters in this situation?


2.2
Then, to control the precipitate size of MC carbides, would it be reasonable to set the MC seed type as bulk and adjust the liquid/MC interfacial energy as the main fitting parameter?
When fitting the nucleation density for bulk seeds, our current experimental limitation is that we can only measure the number density and area fraction of nearly spherical particles on 2D SEM micrographs.
Would it be acceptable to convert this 2D number density into a corresponding 3D seed density and use it as input for the simulation?

Additionally, if nucleation of these seeds occurs at the final stage of solidification where only small interdendritic liquid pools remain, will the user-defined seed density (which is specified for the entire computational domain) still be applied properly?

This concern arises from the fact that the input seed density reflects the density over the entire simulation domain, whereas in reality, there may be discrepancies due to the difference between this and the actual liquid droplets that exist interdendritics at the time of nucleation.

3.
Upon a quick check, I noticed that nucleation of liquid seeds seems to occur even when the liquid fraction drops below 80%. This might be my misunderstanding; however, based on your explanation, I am uncertain about the intention behind this input condition.
In my opinion, such nucleation should indeed be allowed even at liquid fractions below 80%.

4–5.
I would appreciate further clarification on the functions and proper usage of the “add to grain” and “new set” options.
Although I have already checked the documentation on the website, I still do not fully understand their practical meaning and application.
If there are any existing discussion threads or references that explain these in more detail, could you please share them?

Thank you always for your help.
Best regards,
Ku

Hello Ku shihyeon,

1. This is exactly what I intended with the A017 example by not including precipitation from the solid phase. For solidification and for reaching a fully solid microstructure, only precipitation of MC and γ' from the melt is needed.

2.1. It is correct that ATC is not needed. However, you explicitly asked for parameters which can be useful to fit the simulation results to experimental findings. In MICRESS we have the possibility to use ATC with a prefactor for systematically modulating its effect (and also the risk of artifacts). The option to set the prefactor for ATC is quite new, but it it already is available in MICRESS 7.300 (just the input syntax description has been erroneously forgotten in the Options list). The command should be put inside the "terse" block in Numerical Parameters / Concentration solver before the "end_of_options" keyword and has the syntax:

# atc_prefactor <phase1> <phase2> <value>

2.2 Adjusting the interfacial energy and the seed density should be a good strategy. Of course, the seed density distribution is a physical parameter which however is practically impossible to measure. Thus you need to adjust it by fitting. If you want to do systematic fitting, it makes sense to use the "log_normal" function (which has only few parameters) instead of specifying explicit distribution curves.

Practically, according to the selected seed-density radius distribution, explicit positions with respective critical radii are selected at initialisation time, which can be activated later-on by nucleation. Those positions which later are covered by the primary dendrite will not be taken into account, so that only those remain which are occasionally located in the regions of final liquid. Thus, the seed density is still correct, but the absolute number of potential seed positions (as given in the .log-file output) is much smaller.

3. If no input is given for the optional fraction range, nucleation is allowed everywhere in the interface. However, if the user explicitly specifies the allowed fraction range of the reference phase, this should be obeyed. For checking whether this is the case or not, you should use the nucleation option "out_nucleation", which creates an extra output exactly at the time of nucleation. Otherwise you cannot know how the fraction was at nucleation time. Please let us know in case the condition is really violated, because then it would be an error which has to be corrected.

The reason why we implemented this option is that interface precipitates, if they grow from the liquid phase and are placed at low liquid fractions, are often quickly overgrown by the primary phase, so that no formation of a coupled eutectic growth is possible.

4. -5. The "add_to_grain" functionality has first been described here. Its use appears quite complex to many users because it has not only a direct function, but also side-functions which are maybe even more interesting and which can be used for totally different problems.

In your case, you want to use the original function, namely to add a new instance of an already existing grain at a further position. Imagine the case that you want to include precipitation of γ' inside a solid phase, but at a length scale where the precipitates will be hardly resolved. With normal nucleation (bulk, seed_density) this would lead to a high number of individual particles (i.e. with individual orientation) which have their own phase-field parameters. Consequently, as all pair-wise interactions are pricipially possible, this leads to a severe performance problem which increases quadratically with the particle number. After exceeding 10000-20000 individual particles, latest, memory requirements get enormous and performance will be killed. Here, "add_to grain" can help by creating nuclei which belong to the same grain number (and have the same phase-field parameter), leading to only a small number of real grains, and thus to a better performance.

In this context and for the given seed-type, "add_to_grain" with suboption "new_set" creates only one grain which exist at multiple locations. This is nice, because it circumvents the performance problem specified above (and also - in principle - allows to treat unlimited numbers of particles) . But it has some important implications or drawbacks:
1.) If instances of the same grain get in touch, they do not form a grain boundary and tend to coalesce rapidly. This may be wanted in case of the liquid phase, but not necessarily for solid precipitates. To avoid coalescence, a certain number of seed-types using "add_to_grain may be used, so that the probability of direct contact of instances of the same grain is reduced (btw. this also allows to somehow calibrate the coalescence behaviour e.g. of γ'-precipitates in the solid state!)
2.) Because only 1 grain essentially exists per seed-type, statistical outputs of MICRESS (TabK, TabGD) cannot give you any information about the number of precipitates which exist.
3.) All precipitates have the same properties (e.g. orientation). If different orientations or types of precipitates are needed, multiple seed-types must be used.
4.) "Small grain" models for precipitates with radius <Δx cannot work, because those would need individual size parameters. Small grains nevertheless can grow (if fd_correction is used), but sometimes they need some help by setting them with already small initial fraction (by chosing a grain radius of 0 < r < Δx).

Best wishes
Bernd