Unusual carbon profile after the first step (no phase transformation)

solid-solid phase transformations, influence of stresses and strains
pmecozzi
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Unusual carbon profile after the first step (no phase transformation)

Post by pmecozzi » Fri Nov 20, 2020 10:24 am

Dear Bernd,

I am now simulating the kinetics of BCC and cementite formation on cooling starting from a FCC microstructure of a Fe-C-Mn-Cr-Ni steel. I attached the initial microstructure. The initial carbon concentration is constant (0.8 wt% C) while the substitutional elements profiles along z-direction are described by a sinusoidal function in z.
I am wondering why just after the first step of the simulation the carbon profile is affected by the profile of the other elements as shown in the attached Fig1_Carbon_Profile and Fig2_Mn_Profile; Ni and Cr profile is also sinusoidal in z as Mn.
I attach the driving file and please let me if you need other input/output files.

Best Regards

Pina
Attachments
Bainite_seg11_in.txt
(38.18 KiB) Downloaded 64 times
Initial_FCC_microstructure.png
Initial_FCC_microstructure.png (12.13 KiB) Viewed 1223 times
Fig2_Mn_profile.png
Fig2_Mn_profile.png (33.13 KiB) Viewed 1223 times
Fig1_C_profile.png
Fig1_C_profile.png (98.21 KiB) Viewed 1223 times

Bernd
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Re: Unusual carbon profile after the first step (no phase transformation)

Post by Bernd » Fri Nov 20, 2020 8:09 pm

Hi Pina,

I would interpret the black regions in the c-profile as very small oscillations around the initial composition (you can check by reducing the z-range, so that you can see them individually), modulated by the profile of the other elements.
I believe that it is due to the discretization of the composition profiles of the other elements: Given the fact that you included cross diffusion of carbon (i.e. also diffusion of C due to the gradients of the other elements), and assuming that just one single diffusion time step has passed, each discretization step would create a flux which is highest where the steps are highest, i.e. the slopes of the other composition profiles are highest. If between the steps there is a plateau which is longer than diffusion can reach in this time, you can create such an oscillation on each discretization step, which would perfectly explain what you see.

Anyway, the oscillations are extremely small and should vanish after the substitutional profiles are smoothened by diffusion of these elements. For interpretation of what happens after longer time, please don't forget that the C-profile will adapt to the substitutional profiles not only due to cross diffusion, but also due to the representation in wt% (while diffusion is driven by gradients in at%)!

Bernd

pmecozzi
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Re: Unusual carbon profile after the first step (no phase transformation)

Post by pmecozzi » Sat Nov 21, 2020 3:11 pm

Dear Bernd,

Many thanks for your clarification.
I have already changed the input condition for the diffusivity of carbon in FCC from cross-diffusion to diagonal but there were again jumps in the carbon distribution because, I understand now, the diffusivity is derived from the at % of the elements. The calculations were indeed affected by the profiles of the alloy elements!
I am now running the simulation using at % instead of wt% and the problem disappears.

Best regards

Pina

pmecozzi
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weird feature in the microstructure after cementite growthDera

Post by pmecozzi » Wed Dec 02, 2020 3:28 pm

Dear Bernd,

I am simulating the kinetics of cementite formation at low temperature (593 K) starting from an austenite and ferrite microstructure as shown in the figure together with the initial carbon concentration in at%. I linearise the pseudo-phase diagram Fe-C under para-equilibrium condition to get the thermodynamic data (no substitutional alloy elements are considered this time).
I attached the microstructure and carbon map after 140 s.
What is the reason for the “blue dots” in the austenite near the growing cementite as it is more evident in the zoomed picture (also attached)?
The driving file is attached as well.

Best Regards

Pina
Attachments
Phas&conc1_ini_mcr.png
Phas&conc1_ini_mcr.png (162.57 KiB) Viewed 1168 times
Phas&conc1_140s_mcr.png
Phas&conc1_140s_mcr.png (117.17 KiB) Viewed 1168 times
Phas&conc1_140s_zoom_mcr.png
Phas&conc1_140s_zoom_mcr.png (65.38 KiB) Viewed 1168 times
cementite_formation_LPD_at%_rid_in.txt
(46.91 KiB) Downloaded 68 times

Bernd
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Re: Unusual carbon profile after the first step (no phase transformation)

Post by Bernd » Fri Dec 04, 2020 12:32 am

Dear Pina,

It is difficult to say exactly, but obviously these are a lot of very small particles. Given the fact that you defined nucleation only on interfaces, I could imagine that you had nucleation on a moving interface, leaving behind those particles, which were detached from their "mother" phase, and thus cannot grow further. You can easily find out the phase identity by looking at .frac2 or .frac3, I would guess it is phase 3.
Together with the information of the location of the interfaces over time, you should be able to check out whether my suspicion is correct.

Bernd

pmecozzi
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Re: Unusual carbon profile after the first step (no phase transformation)

Post by pmecozzi » Sat Dec 05, 2020 10:30 am

Dear Bernd,

Many thanks for your replay.
I do not understand why the blue spots could be cementite particles. They are in the bulk of FCC phase and no interface crossed this region at an early stage of the simulation; actually, it seems that some carbides are precipitate along some FCC/FCC grain boundary as shown in the attached files frac1 (FCC) and the frac3 (cementite).

Best Regards

Pina
Attachments
Frac1&frac3_140s_mcr.png
Frac1&frac3_140s_mcr.png (129.07 KiB) Viewed 1143 times

Bernd
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Re: Unusual carbon profile after the first step (no phase transformation)

Post by Bernd » Sun Dec 06, 2020 5:51 pm

Hi Pina,

As confirmed by the .frac3 output which you provided, it is definitively cementite which forms the "blue spots". However, I agree that cementite obviously is not formed by nucleation: The spots appear only in the .phas output due to fluctuations in the cementite phase fraction, given that in the .phas output interfaces (with blue color or -1 value) are characterized by phase fractions between 30 and 70%, and only few cells exceed 30% of cementite.

This means, the 1/3 phase interaction probably is unstable and starts spreading into the grains. This could be due to a too large interface mobility (a value of 1.E-6 cm**4/(Js) essentially could be higher than what is required to account for diffusion limited growth). Therefore, I would suggest you to try using "atc mob_corr", like you already do for the 1/2-interface, also for 1/3 and 2/3. This could reduce the interface mobility to a value which corresponds to the physical value of 1.E-6 and which may more stable numerically.

If this does not help or is not sufficient, it could indicate that spatial resolution is not sufficient for the simulation scenario (interface energies, diffusion coefficients, etc). Alternatively, you could rethink the choice of your interface energies (which span a range over a factor of 10 from 2.E-6 to 2.E-5). Increasing the very low value for the 1/3 interface would be equivalent to increasing spatial resolution (and further reduce the risk of having numerical issues with the triple point terms due to the wide range of interface energies!).

Bernd

pmecozzi
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Re: Unusual carbon profile after the first step (no phase transformation)

Post by pmecozzi » Mon Dec 07, 2020 6:58 pm

Hi Bernd,

Many thanks for the advice.
At first, I tried with “atc mob_corr” in the redistribution_control option; in this case, the cementite nuclei neither grow nor shrink (cementite fraction remain constant).
Then I reduced the 1/3 interface mobility but the instability problem remains.
Afterwards, I increased the 1/3 interface energy but the nuclei do not grow.
I think the best option will be to increase the resolution and reduce the domain by considering only a small portion of the original domain.

Best Regards

Pina

Bernd
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Joined: Mon Jun 23, 2008 9:29 pm

Re: Unusual carbon profile after the first step (no phase transformation)

Post by Bernd » Mon Dec 07, 2020 7:12 pm

Hi Pina,

so, you made the 1/3-interface energy so small because otherwise you do not get nucleation of cementite? Then, you should rather use "analytical_curvature", so that you can define a critical radius which is bigger than deltaX...

Bernd

pmecozzi
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Re: Unusual carbon profile after the first step (no phase transformation)

Post by pmecozzi » Tue Dec 08, 2020 11:19 am

Hi Bernd,

I did and then I solve the problem of not growing cementite nuclei! Thanks.

Unfortunately, the increase of the 1/3 interface energy from 2e-6 J/cm^2 to 2e-5 J/cm^2 still did not solve the 1/3 interface instability problem.

Pina

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