PDAS in Welding: Coarsening at dendrite tip?

dendritic solidification, eutectics, peritectics,....
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cboe
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PDAS in Welding: Coarsening at dendrite tip?

Post by cboe » Fri Jul 19, 2019 3:23 pm

Hi all:

I set up a simulation for AlMgSi alloy. I want to measure the PDAS for different solidification conditions. I started off with a smaller simulation domain (108x1x408) with a grid resolution of 0.07. I still think that the simulation is not valid yet regarding the numerical parameters. I still think that the interface at the tip is not stable and coarsens. Below I describe my simulation set-up. Attached is the IN-File.
Kin0_7_S0_driv_mcr.png
Kin0_7_S0_driv_mcr.png (21.78 KiB) Viewed 1510 times
I use a rectangular grain as the starting grain. There is only 1 phase forming FCC_L12, because other phases do not have a major impact on the PDAS. I use "redistribution_control" for the interaction of phase "0 1" to ensure diffusion-control solidification as described in https://board.micress.de/viewtopic.php? ... trol#p2055. Furthermore, as discussed in the aforementioned link I use "interface stabilization" with interfacial energy x10.
I started with a mobility coefficient of 1.0 and lowered it step-by-step until I got a different solidification behavior (overtime increasing driving force, artifacts in dG-output). The images posted have a kinetic coefficient of 0.7. Which is in the same order of magnitude as Bernd once mentioned inhttps://board.micress.de/viewtopic.php? ... ameter#p49:
interface mobility (cm4/(Js):
- solid liquid interface for solid solution phase (e.g. fcc-liq): 0.1-0.01
I am not quiete sure, why the interface looks like this. I do not have enough experience to say if this is a coarsening effect or not. How would you go from here?

1) Increase the interface thickness from 3 cells to 4, in order to allow more curvature undercooling?
2) Increase averaging of the driving force from 0.9 to 0.95? This would stabilize the interface as well, right?
3) Something completely different.

Thanks for your help.
Attachments
Kin0.7_S0_in.txt
(17.71 KiB) Downloaded 95 times
AKin0_7_S0_driv_mcr.png
AKin0_7_S0_driv_mcr.png (49.16 KiB) Viewed 1510 times
---- Constantin

Bernd
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Re: PDAS in Welding: Coarsening at dendrite tip?

Post by Bernd » Sun Jul 21, 2019 9:32 am

Dear Constantin,

I think what you see as "coarsening" of the interface is the leading grid cell at the tip of the dendrites. This typically occurs when grid resolution is low and the dendrite tip is not well resolved. So, a logical approach therefore would be to increase grid resolution.

However, the difficulty of simulating dendritic growth is that the tip radius typically is very small compared to the PDAS, so that the grid resolution required to get the growth of the dendrite tip correct would lead to immense computation times. On the other hand you probably are not really interested in the dendrite tip itself but rather in the correct selection of the PDAS which requires at least the tip undercooling to be correct. A possible approach could be to determine the tip undercooling using an analytical solution like the KGT theory, and then calibrate the interface mobility such that the correct tip undercooling is obtained during stationary growth. Then you can expect the simulation to reproduce realistic selection behaviour of the PDAS despite of the low resolution.

Unfortunately, the KGT theory for dendrite tip undercooling works only for binary alloys. Therefore, you need to calculate pseudo-binary phase diagram data. You can do that in the way I did some time ago (see here).

Bernd

cboe
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Re: PDAS in Welding: Coarsening at dendrite tip?

Post by cboe » Tue Jul 23, 2019 6:01 pm

Dear Bernd:

thanks for you tip.

I wanted to make sure, that I understood the pseudo binarization correctly.

Let's assume that I have the alloy Al - 1.0 Si - 0.5 Mg with a distribution coefficient k_si = 0.11 and k_mg = 0.51. This will lead to a pseudo initial concentration of

c_s^* = 1.0 + 0.5 = 1.5

and a pseudo enriched liquid concentration of

c_l^* = 1.5 + sqrt { (1.0/0.11 - 1.0)^2 + (0.5/0.51 - 0.5)^2 } = 9.6

Correct?

I thought of another way to calibrate my simulation. The G and cooling rate (CR) value is calculated by a CFD simulation. These values lead in the stationary condition to a growth rate equal to G divided by CR. Hence, I will alter the mobility coefficient in such a way that I will get a mean tip velocity or growth rate of G divided by CR.

Kindly
Constantin
Attachments
pseudo-binarization.png
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---- Constantin

Bernd
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Re: PDAS in Welding: Coarsening at dendrite tip?

Post by Bernd » Tue Jul 23, 2019 8:42 pm

Hi Constantin,

Yes, I think your formulation is ok. The difference to mine is just that you further assume that the solidus and liquidus line intersect at c=0, while mine is more general and can e.g. be applied to linearisation parameters obtained by TQ.

However, your calibration idea will not work, because the velocity will always reach a stationary value of G/CR, whichever mobility value you apply! The difference will be the tip undercooling...

Bernd

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