Solidification during welding

[Ku shihyeon]

Hello,
I am currently modeling the welding solidification of the CMSX-4 nickel-based superalloy.

I prepared a driving file with reference to the following examples:
0. A006_CMSX4 (base code)

A017_M247_additive_constGV

T10_02_GrainGrowthMisorientation_2D

Based on Example 0,

From Example 1, I referred to the general aspects related to directional solidification, as well as some constants, numerical values, and numerical parameter items.

From Example 2, I referred to the phase interaction entries between identical phases in order to account for changes in interfacial energy with misorientation and the shift in dendrite coalescence timing.

In addition, I entered our experimental process conditions, namely the temperature gradient and cooling rate.

At present, the calculation proceeds smoothly from the initial to the intermediate stages.
However, during the final stage of solidification (when the dendrite tip reaches the top of the domain), errors occur. According to the DP output, the overall composition field fluctuates abnormally, and in some cases partial remelting of the solid phase is also observed.
What could be the cause of this problem?-->

MICRESS_ask.png

TIME STEP is 3.6~3.64 s

When this phenomenon occurs, the following error appears and the calculation slows down significantly

trying hard phases 1 0 level: 4 zp= 53205 error= 10004
trying harder! Error = 10004
trying even harder! Error 10004


And as for the following error, I do not know why it occurs or how it affects the calculation results.

Warning: Diffusion in 1D-Extension halted!





Additionally, we would like to investigate the effect of CET under our process conditions.
For this purpose, modification of the nucleation entries is required, but we are not sure how to define nucleation of the primary phase, i.e., the gamma FCC phase.

Could you also review not only the modifications we intend to make but also any general issues with the code itself?

[Bernd]

Hi Ku,

Welcome to the MICRESS Forum.

Whenever you get error with some error numbers which you don't know, you can look up here what the error could mean. In your case, "error= 10004" means that a user limit for the phase composition is encountered in phase 0 for element 4. Then, the corresponding quasi-equilibrium is not accepted, and MICRESS tries to find equilibria which do not violate the user limits.

Looking at the input in your driving file, I noted that you exessively use "limits" in section "Numerical Parameters" for the concentration solver. You explicitly forbid for all elements in LIQUID and FCC_L12 to reach a content of more than 30 at% - I don't understand what is the reasoning behind! It is very probable in a high-alloyed system that at any point in the segregated liquid one of the elements may reach more than 30 at%. "limits" typically is used to prevent some phases from switching to a composition range where it constitutes a different phase ("composition set"), like it is the case e.g. for carbon in FCC_A1: At low composition, it is a typical austenite phase, at high composition it is a MC carbide. I would expect your problems to vanish as soon as you remove all the user-defined limits.

The warning

"Warning: Diffusion in 1D-Extension halted!"

is not an error but only a reminder. It refers to the 1d-extension of the concentration field which is used in your case. If this is done without "moving frame", the dendrites eventually will touch the top boundary, where the 1d-concentration field is attached. Due to the way how the 1d-field is connected to the 2D/3D-simulation domain, this would inevitably lead to numerical issues. Therefore, MICRESS kills the 1d-extension as soon as the dendrite front comes close to the top boundary (closer than the 1d_distance). At this point, the above warning is written to remind the user.

Finally, for implementation of CET I would propose to use the seed density model of nucleation. As a template, you could use seed type 1 of the application example A002_AlCu_1dTemp.dri. By adjusting the seed density distribution, you can fit the formation of stray grains in front of the dendrites to experimental findings. Instead of using discrete classes for the radius-density distribution, you also can take a log-normal model like in the trainings example "T51_10_NucleationSeedDensityLogN1.dri".

Best wishes
Bernd

[Ku shihyeon]

Thank you for your reply.
In the initial calculation without any limit applied, the same issue (abnormal remelting) occurred even more severely and over a broader region. When the error was first detected, abnormal solute concentration values appeared immediately before and after it (concentration values of 6000% or even negative values were observed). So I added the limit. However, this seems to have introduced a new error (10004).

I was not able to check the error code at the moment when the initial abnormal remelting was confirmed.
For now, I will follow your advice and remove the excessive limit.

In addition to error 10004, errors 1, 2, and 3 also seem to occur frequently. However, these errors do not appear to be listed in the post you provided. Could you let me know what might be causing them?

At this point, I suspect the problem arises because the lower bound of the time step is not sufficiently small. In the tabT output, the time at which the time step reach to its min. value with the occurrence of the error.

Could this also have been the cause of the error in the initial calculation?


----I made a revision----

Even though I set a sufficient lower limit for the time step, the same problem still occurs.
I checked tabT, but the error occurred even while using steps larger than the lower limit.

ERROR.png

The problem I am currently experiencing has worsened.


Based on your advice, I am currently running the calculation again with all restrictions removed.
However, once the solid fraction in the domain exceeds 70%, the "tring hard phase #/# error = 2, 3" appears again.


Best regards,
Ku.

[Bernd]

Dear Ku,

There is no obvious error in your setup which would directly explain the behaviour which you describe. If the original error (before trying the limits) was linked to the nucleation of the γ'-phase, however, it is very possible that it has to do with the relinearisation options for the 0/2 ane 1/2-interfaces. There, you use "global" without any distance criterion, which means that linearisations are based upon different phase regions which have very different temperature (because of the strong T-gradient in z-direction). You should definitively use such a criterion, what you are already doing fotr the 0/1-interface.

By the way, choosing 3 µm as a distance criterion is excessively low, leading to high computation times for updating TQ-equilibria. On the other side, you should reduce the updating interval, which is probably too big.

If your problem was not linked to the fromation of the γ'-phase, I could imagine some other factors which may play a role:

- the too big updating interval could lead to numerical issues at the regions which connect to different TQ-updating regions (see .refR-output). If this connection points, which bring somewhat different thermodynamic data together, are not shifted often enough to other places (which happens each time you update TQ-data), this could perhaps lead to local artifacts.

- the "atc" model for antitrapping sometimes has led to artefacts in high-alloyed systems, if the interface thickness is small and the grid resolution coarse. You should try to replace it by "normal" to see whether this could be the problem. At the same time should remove the extra factor of 0.7 (to the mobility correction) which was a specific calibration in the original application file.

- all in all, the grid resolution you have applied so far is too low. It is clear that increasing grid resolution make simulations much slower, but it is worth it.

Hopefully, one of the above tips (or a combination of them) will remove your problem.

I would not share your suspicion that the time-stepping could be an issue here. In most cases, where there is a numerical problem, the time-stepping goes down drastically - not as cause but rather as consequence of the problem.By the way, errors 1-3 are different types of convergence errors in the Newton-Raphson scheme. But knowing the exact way how convergence is failing is probably not that helpful for the user.

Bernd

[Ku shihyeon]

Thank you.

At present, regardless of the solution you suggested, when the cooling rate in the process condition input is increased, leading to a faster solidification rate and shorter calcuration time, abnormal remelting did not appear.
However, I still believe this is not a fundamental solution. I will, of course, try applying the method you proposed.

Additionally, I have a few questions.

1. The diffusion calculation interval was set as follows:
# Interval for updating diffusion coefficients data? [s]
10
As I mentioned in the first post, when writing the current dri, it was based on the A006CMSX4 example, and it seems we have been still using that value.
Is this value suitable for the process we want to simulate (high gradient and cooling rate at the level of 20 K/s)? Or could this part affect our error?

2. Relinearisation interval
When you said "you should reduce the updating interval," were you referring to the global relinearisation interval in the Database section?

If so, I have also modified that part. Currently, I am using 0.05 s, but the error still occurs.

Separately, in the A006 example, the default values are as follows:

#Which global relinearisation interval shall be used?
manual
0.1000000000000

Then, in the # Phase Interactions section:

#Relinearisation interval for interface LIQUID / FCC_L12
none
As shown, it is deactivated for each phase.

Are these two term unrelated, and should I understand that the Relinearisation in the # Phase Interactions section is not performed, and only the Relinearisation in the rest section is performed at 0.1 s intervals?

Currently, I have entered 0.05 s for both the global relinearisation and the # Phase Interactions Relinearisation.

3. ATC model
If we reduce the grid size, is it reasonable to activate ATC?
I am using an interface thickness of 2.85 cells as recommended.

4. In the process of generating a GES file

there is no input specifying a sublattice phase such as FCC_L12#2, but in the MICpad terminal it appears to be loaded correctly.
Does this mean that sublattices are automatically imported?

Additionally, in the case of the M247 example, only FCC_L12 is loaded, and it seems that the user separately assigns compositions to each sublattice.
Am I correct in understanding that even without performing this step, the default values are automatically loaded?


I am worried that I may be asking questions that are too basic or that could easily be resolved through literature review, documentation, or a simple search. Thank you, as always, for your kind answers.

Ku.

[Bernd]

Dear Ku,

Let me first go through your questions one by one:

1.) I overlooked the high updating interval of 10s for diffusion coefficients, you are right. Typically, I suggest updating diffusion data after having cooled by about 10-20K, so your interval should be rather 1.0 or below. In most cases, you will not note any strong effects of too large updating intervals for diffusion data, because an Arrhenius description is used for extrapolating temperature dependence (which is the strongest). But of course, you should update more often to get more exact results.
Generally, when switching process conditions, all time constants like updating intervals (diffusion data, linearisations, enthalpies, molar volumes), check interval for nucleation, output intervals, etc. should be adapted correspondingly. In some places of the input file we already allow to use "automatic" updating intervals (thermodynamic updating per phase interaction, nucleation interval), where a temperature difference is specified rather than a time interval. This helps to prevent such mistakes.

2.) Updating the linearisation data (quasi-equilibrium and derivatives) the temperature interval should be even smaller than for diffusion, because extrapolation is less exact. I typically recommend to update after 1-2 K of cooling.
But when using "global" updating scopes with a distance criterion, there is an additional effect: At the places where two different updating domains come together, there is a small "step" in the thermodynamic description which produces noise, and which eventually can lead to artifacts when it stays too long in the same place. Each time thermodynamic data are updated, the regions which belong to the same dataset are shifted, so that more frequent updating prevents such effects. You may also notice that the noise which comes from this source has a strong effect on the break-up of your initally flat interface, and also for the formation of side-branches. In this context, I suggest using a rather big size of the relinearisation regions in combination with a very small updating interval.
Whether you apply updating to all interfaces equally (by using the general updating scheme in section "Database") all for each phase interaction individually (in section "Phase Interactions") is up to you. But please note that if you do both, the effect will be additive. I.e., each phase interaction will be updated as well by the general updating interval as by the phase interaction specific one.

3.) Since the release of Version 7.3 of MICRESS we noticed that the ATC correction under certain circumstances leads to artifacts, which occur only with some high-alloyed systems and at certain places where the interface is aligned with the numerical grid. We think we solved that problem for the next version of MICRESS. For the time being, I recommend not to use ATC in this case. I also do not expect ATC to be important for your application.

4.) For phases with more than one sublattice, Thermo-Calc uses different sets of start values for the site fractions of each element to ensure that iteration converges into the correct phase equilibria. In case of phases like FCC_L12 (or also FCC_A1) there often are several composition regions where the same phase description can be stable simultaneously. Then, automatically, extra "composition sets" are added (e.g. FCC_L12#2) for these regions. For each composition set, a set of major constituents is stored to determine a suitable start composition for equilibrium iteration.
If you are unsure what is the meaning of the composition sets in the .GES5-file, you should examine the MICRESS output on screen or in the log-file:

Start Composition and Limits for quasi-equilibrium
--------------------------------------------------
NI in LIQUID: 10.0474 at% (>0 - 100.000at% )
CR in LIQUID: 9.76303 at% (>0 - 100.000at% )
CO in LIQUID: 9.66825 at% (>0 - 100.000at% )
MO in LIQUID: 9.95261 at% (>0 - 100.000at% )
W in LIQUID: 10.4265 at% (>0 - 100.000at% )
TA in LIQUID: 10.2370 at% (>0 - 100.000at% )
AL in LIQUID: 9.57346 at% (>0 - 100.000at% )
TI in LIQUID: 10.3318 at% (>0 - 100.000at% )
RE in LIQUID: 10.1422 at% (>0 - 100.000at% )
HF in LIQUID: 9.85782 at% (>0 - 100.000at% )
NI in FCC_L12: 57.5643 at% (>0 - 100.000at% )
CR in FCC_L12: 0.431984 at% (>0 - 100.000at% )
CO in FCC_L12: 37.8338 at% (>0 - 100.000at% )
MO in FCC_L12: 0.531633 at% (>0 - 100.000at% )
W in FCC_L12: 0.780756 at% (>0 - 100.000at% )
TA in FCC_L12: 0.681107 at% (>0 - 100.000at% )
AL in FCC_L12: 0.332335 at% (>0 - 100.000at% )
TI in FCC_L12: 0.730932 at% (>0 - 100.000at% )
RE in FCC_L12: 0.631283 at% (>0 - 100.000at% )
HF in FCC_L12: 0.481809 at% (>0 - 100.000at% )
NI in FCC_L12#2: 44.4203 at% (>0 - 100.000at% )
CR in FCC_L12#2: 0.426371 at% (>0 - 100.000at% )
CO in FCC_L12#2: 27.2736 at% (>0 - 100.000at% )
MO in FCC_L12#2: 0.525373 at% (>0 - 100.000at% )
W in FCC_L12#2: 0.772878 at% (>0 - 100.000at% )
TA in FCC_L12#2: 0.673876 at% (>0 - 100.000at% )
AL in FCC_L12#2: 9.74993 at% (>0 - 100.000at% )
TI in FCC_L12#2: 15.0574 at% (>0 - 100.000at% )
RE in FCC_L12#2: 0.624375 at% (>0 - 100.000at% )
HF in FCC_L12#2: 0.475872 at% (>0 - 100.000at% )

Here, the start composition (as summed up over the different site fractions) as well as the solubility range of each element in each phase is shown. You can see that in FCC_L12 Ni and Co are the major elements (fcc-phase), while in FCC_L12#2 Al and TI are also elevated because they are the major constituents on the second sublattice. The major constituents in each sublattice can be controlled when creating the .GES5-file. Otherwise, they are defined by defaults which are included in the corresponding thermodynamic database.


Meanwhile, I performed a simulation with your input file and the following modifications:

- I replaced "ATC" with "normal" and removed all prefactors "0.7" (for all phase interactions)

- I reduced the general updating of thermodynamic data to 0.01 s

- I increased the distance criterion for global updating from 3 to 30 µm and used that for all phase interactions

- I removed all the "limits" definitions in section "Numerical Parameters"

The results did not show the artefacts you experienced:



Bernd

A006_CMSX4_conc1.png

Best wishes
Bernd

[Ku shihyeon]

Thank you for your response.

Following your advice, I set appropriate update intervals and linearization distance criteria, and was able to carry out the calculation successfully. Although there was some numerical variation that increased the computational load, in practice I found that the errors were reduced and the calculation was completed more quickly.

As always, thank you for your clear explanation.