Getting nucleation right for CET investigation

[joschamu]

Dear Mircress Team,
I am trying to simulate the solidification of an Aluminum (AlMgSi) alloy in the Wire Arc Additive Manufacturing process (WAAM). Specifically, I would like to investigate the Columnar to Equiaxed transition that is observed in the real process. The real process shows that at high cooling rates/higher scan speeds, we tend to have equiaxed grains, at lower cooling rates/lower scan speeds columnar growth. That means that the CET is happening faster/earlier with higher cooling rates and slower/later with lower cooling rates. This is basically what I would like to understand further and investigate.
For now, I have set up the simulation domain with a base microstructure of random oriented grains at the bottom of the domain, interface nucleation to allow for dendrite growth and bulk nucleation with undercooling to allow for new grains in front of established dendrites. The thermal profile attached is from one of our thermal models and represents the higher cooling rate/faster scan speed.
My question now would be how I can set up the bulk nucleation correctly so that the effect of the temperature zones and different gradients is represented in the nucleation and shows the influence of the thermal history on the CET. I hope you can help with tuning the parameters of the simulation so it can represent the actual process.
I have included the thermal profile (the higher cooling rate) of the process (data and graph) and the driving file as well as an experimental image and an image of the running simulation and the GES file.

Kind regards

Joscha

[Bernd]

Dear joschamu,

Welcome to the MICRESS Forum. Putting aside for a moment that CET is a difficult beast, and that your overall approach is still very simple and approximating, I can confirm that your setup for bulk nucleation basically is already correct. You apply a seed-density approach for heterogeneous nucleation which reflects the potential seeds and their required local undercooling, so that they can start growing once the local composition and temperature is favorable. At least, in a first step, which such an approach it should be possible to qualitatively get the transition between columnar and equiaxed growth, once the physical parameters are in the correct range, and the numerical setup runs sufficiently well.

However, for getting results for the CET which can quantitatively be compared to experimental findings, the hurdles are very high:

- 2D-calculations cannot correctly simulate CET because any equiaxed dendrite which forms ahead of the columnar front immediately blocks columnar growth. In reality (3D), the columnar front can pass by in the 3rd dimension (i.e. in front or behind the equaxed grain), so that CET will occur much later.
- Another problem of 2D-simulations is that the dendrite tip undercooling is much higher than in reality. Thus, the conditions for nucleation of equiaxed grains are very different from the 3D-case.
- Even when simulating in 3D, it must be ensured that the dendrite front grows with the correct undercooling. This is not trivial. It requires a sufficiently high grid resolution and further calibration (see B. Böttger et. al., Computational Materials Science, Vol. 236, 112854, 2024
https://doi.org/10.1016/j.commatsci.2024.112854).
- Furthermore it is necessary to input the correct seed-density distribution of the material, which is close to impossible to obtain experimentally. Also, it is not clear if the seed parameters are really independent from the process conditions, because the seeds could also be formed during the melting process by fragmentation.

Thus, your first goal should be to stepwise improve the numerical conditions and to come closer to the correct physical conditions in terms of dendrite tip temperatures and local solutal and thermal undercooling. Having a look at your first simulation results which you attached, it can be noted that all dendrites grow in the direction of the temperature gradient/along the numerical grid despite having different crystallographic orientations. This is a clear sign that grid resolution is insufficient and must be reduced. The dendrites should always follow their orientation, even for small angles down to ~10°.
In order to keep simulation times viable despite of a sufficiently high grid resolution, I think it will at some point be necessary to use a moving frame setup, so that the simulation domain can be restricted to only contain the upper part of the mushy zone and the small region of the liquid where nucleation may happen. Unfortunately it is not possible to use the distance criterion for the moving frame, because then it the domain would jump each time a seed is formed. This problem makes a moving-frame setup more complex.

What I did not understand is why you use a seed type for interface nucleation (seed type 1) which creates new fcc grains at the fcc-liquid interface. I cannot imagine that this makes any sense...

A further detail: You cannot use a global relinearisation scheme without a distance restriction for the 0/1-interface (and also for 0/2 and 1/2 once you will include them). The reason is the high temperature range inside the domain: Using a single set of linearisation parameters everywhere is as bad as having a linearized phase diagram only. You can refer to example A_018 where the problem is similar. You can use the .refR output to see the regions which use averaged relinearisation data.

Bernd

[joschamu]

Dear Bernd,
Thank you very much for your extensive feedback. It really helped a lot. We now have a somewhat working single phase FCC model with a CET transition that agrees somewhat with our experimental results.
We want to extend the model now to include grain refinement of TiB2 particles. And getting that right seems to be an issue too. What I did until now is:
I used the (adjusted) simulation from before and added the following
- Second Phase (TiB2) and all the necessary updated (composition, GES, diffusion etc.)
- Precipitation of the second phase via nucleation or initial microstructure
- Add interface nucleation for FCC in the interface of Liquid/TiB

The issue I run into now is, that is seems that micress can’t get the linearisation right as soon as the simulation gets to the nucleation temperature for FCC in the interface LIQ/TiB. I am wondering why that is. I tried different values for the interface interaction from other internal simulations and examples from you, as well as changing the relinearisation parameters (even local doesn’t help).
I know that error no 18 is somewhat related to "SolidusSlopes" (viewtopic.php?f=23&t=734&p=3388) but cant make the connection to what I have to modify in the dri.

I have attached the driving file and the error below.

Thank you very much and kind regards

Joscha

Code: Select all

Intermediate output for t = 3.00000E-05 s
CPU-time: 1 s
Current phase-field solver time step = 1.05E-04 s
Average conc. of comp. B = 0.0107989, Variation = -0.0000000 wt%
Average conc. of comp. FE = 0.4188412, Variation = +0.0000000 wt%
Average conc. of comp. MG = 0.7484226, Variation = +0.0000000 wt%
Average conc. of comp. MN = 0.4294407, Variation = +0.0000000 wt%
Average conc. of comp. SI = 0.8577889, Variation = -0.0000000 wt%
Average conc. of comp. TI = 0.0563898, Variation = -0.0000000 wt%
Temperature at the bottom = 895.98492 K
Temperature gradient = 38.17684 K/cm
Updating of diffusion data from database...
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
 trying hard phases  1  2  level: 4 zp=     1156 error=       18
 trying harder! Error =                    18
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
trying even harder! Error       18

--> Force automatic start values
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc

--> Force automatic start values
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
  Thermo-Calc error 1611  MICRESS error   18  Thermo-Calc
 #  Error number     18  in Interface    13/   576
 #  time:   1.400000000000000E-004 s
 # Serious error in linearisation!

[Bernd]

Hi Joscha,

I do not understand why you use a particle pinning model for the phase interaction between TiB2 and fcc, i.e. phases 1/2. This for me does not make any sense in this context, and leads to uncontrolled and too high interface mobility. Why don't you just use phase interaction parameters like for 0/1 or 0/2 with diffusion-limited mobility?

Bernd

[joschamu]

Dear Bernd,
thank you for your answer. I did use the particle pinning just for testing purposes and forgot to remove it. Sorry for not cleaning the file sufficiently. I have attached you the present version of the driving file with the log and scr as well as some pictures of the simulations.

I looked into the error messages a bit further and got to the point that the “force automatic start values” means, that Micress calls Thermocalc to recalculate the start values for the equilibrium. I would guess that this is the case because Thermocalc can’t calculate equilibrium values from the process parameters at that point in time. It looks like this is only necessary for the Liquid to TiB2-Phase/Phase 2/ALB2_C23-Interface. Also, the error happens only when the melt becomes undercooled/tries to nucleate on the AlB2_C23 as far as I can see since the error messages start to appear below a specific temperature and not above. So, FCC seems to be also somewhat involved.
The following error “Thermo-Calc error 1611 MICRESS error 16” looks like it results from the forced automatic start values reset of the equilibrium values to initial conditions.
Further down the line, this turns into the “trying hard phases”-error.
What I have tried so far:
• I thought initially it might be an issue originating from thermocalc by not having diffusion coefficient for the elements in AlB2_C23-Phase. I set the diffusion for testing purposes for these elements (B, Fe, Mg, Mn, Si in ALB2_C32) to infinite, but this solved nothing.
• I tried to change the used phase diagram for the liq/ALB2_C32 interactions from global to local / interface / interface_fragment but also nothing changed.
Can you give any insight into why this is happening? The simulation does work now, and we have the FCC growing on the TiB2-phase, but we get the error described above quite frequently and it would be obviously better to have that reduced for higher confidence in the results.

[Bernd]

Dear joschamu,

Sorry for the late answer, I have been on holidays. Unfortunately, it is quite difficult to figure out details about your problems without executing the driving file myself. Please provide all necessary input files (.ges5-file, file for temperature profiles).

What I can see is that you nucleate ALB2_C32 with a very high undercooling, which easily can be the reason for error 16 to occur for interface 0/2. It would be much safer and more realistic to start at high temperature (close to the liquidus temperature of ALB2_C32) with precipitation of this phase, and then nucleate fcc on cooling down.

Obviously, you heat up at the beginning - I don't understand why you do that, if most of the domain is liquid already. I cannot see your temperature profiles to make sense of it.

If you really want to start with already existing fcc-precipitates, it is essential to set the temperature for initialisation to the initial temperature (911.17578 K). Otherwise, fcc and liquid are not in equilibrium at the beginning, probably leading to numerical issues.

Best wishes
Bernd

[joschamu]

Dear Bernd,
thank you for your answer. I have attached the requested files for you to be able to run the simulation yourself.

About the heating: I have specifically cropped the thermal profile to not include any heating but forgot to change the profile in the .dri. After changing to only cooling, the errors start right away.

I have also moved the inital temperature to the solidus of AlB2_C32 and transitioning from there to the thermal profile. I simply set the intial temperatures for the whole domain to the solidus and transitioned into the real temperature profile from there. But this seems to change nothing.

TabNuc also says that the undercooling for AlB2_C32 nuclei is very large (usually above 500 K) even after adjusting the profile.

Basically, the linearisation fails completely. I also tried to change the phase diagram used for the phase interaction (was at global 2.5) to interface 1 but that didnt help.

EDIT: I also remove the inital microstructure to have a better equilibrium state at the start of the sim and allow for "natural" nucleation of FCC.

Thank you in advance for your help.

Kind regards

Joscha

[Bernd]

Dear Joscha,

In principle, it is a good idea to include some initialisation time at the beginning of your temperature cycle, so that TiB2 (AlB2_C32 ) can grow at higher temperature. However, the way you do it does not have any effect. The reason is that you already switch to the process temperature curve at t=1.E-5. This is exactly the time when you check nucleation of TiB2 for the first time - so there is no difference to before! But if you increase the time for this initial period it can work.

What I found out is that the error 16 of interface 0/2 obviously appears always if the interface is too far from equilibrium (driving force ~-1000 J/cm3 in .driv output). This happens if you nucleate them at too low temperatures, or if you cool down too rapidly while they are growing. I guess that in such cases the quasi-equilibrium compositions move into some miscibility gap region in the phase diagram, which could provoke the problem. It is a general problem of Calphad databases, that moving too far into metastable regions can lead to such behaviour (oscillations due to overfitting). In principle, these errors are not critical as long as they appear only few times. However, this can be achieved only by avoiding too strong undercooling of TiB2 in liquid.


The way you should handle the problem with the AlB2_C32 phase depends a bit on how this phase forms in the real process. There are basically two scenarios:

1.) TiB2 already exists in the pre-material (e.g. wire) and does not melt completely during processing. If this is the case, the particles typically would be quite large (>1µm). In this case, one could think of 2 solutions:
a) If the precipitates are large enough with respect to the grid spacing, you could set them as initial grains with a certain radius distribution which is characteristic for the pre-material (and not for the arc wire process=. This means that the nucleation condition for fcc on this particles would not depend on the arc wire process neither. If you set AlB2_C32 particles as initial microstructure (e.g. by random initial grain setting), you would have to correct the initial liquid composition accordingly (reduce B and Ti).
b) You could create the AlB2_C32 particles in an extra simulation (with artificial process conditions or with conditions which resemble the production process of the pre-material) and include it into the wire-arc simulation by reading the initial microstructure from the restart-file.

2.) If TiB2 is completely dissolved during the wire arc process, it would be best if you had the thermal parameters (temperature profiles) already from this early stage. Then you could simulate the formation of these precipitates with correct conditions, and could (in principle) correctly predict their effect on the CET. By introducing curvature into the nucleation undercooling it is possible to correctly predict the critical nucleation undercooling as function of the real TiB2 particle sizes - just as in the seed density model with analytical seed radius distribution.

As a first approach (or you do not have the high-temperature history needed for scenario 2), you can resemble the growth conditions for TiB2 in the way which you already proposed, namely by adding an extra initialisation into the thermal history file time with continuous transition to the known process condition profiles. I would propose to add 1 second of time (instead of 1.E-5 s) and shift the other times of the profiles correspondingly. It would still be nicer if you had some earlier profiles to start with after initialisation, where the temperture is still higher than the fcc-liquidus everywhere. Otherwise, fcc would nucleate already during the introduced initialisation time.

In the long term I would advice you to simulate melting and re-solidification by starting with an initial microstructure from a prior simulation run. This requires that you have the temperature profiles for the whole cycle and you nucleate liquid to initiate the melting process (just like in A018_Al4Cu_Additive_Rosenthal.dri). Then, TiB2 would automatically survive or not (or something inbetween), and fcc would start growing epitaxially. Nucleation of fcc on TiB2 would happen only when CET comes into play.

Bernd