Hi Bernd,
I am a newcomer to phase-field approach, and do the 1D simulation of Gama-Alpha transformation in Fe-C-Mn alloys recently. By adopting the assumption of para-equilibrium, I can do the calculations easily with my own codes. However, a problem coufused me that is the interfacial energy (Sigma) would even generate significant effect to the transformation kinetics, as shown in the attached file (In addition, the transformation fraction predicted by both of this two conditions are much lowever then the equilibrium fraction). I guess the problem may come from the discontinuity at the edge of interface in the MPF model, while the simple central difference scheme is also adopted at the edge of interface in my codes. Could you give me some advices for this problem? Thank you!
Gama-Alpha transformation under para-equilibrium
Gama-Alpha transformation under para-equilibrium
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- f-t.jpg (662.67 KiB) Viewed 4087 times
Re: Gama-Alpha transformation under para-equilibrium
Dear Kuang WW,
Welcome to the MICRESS forum!
You may have heard that phase-field model do not give quantitatively correct results if the length of the diffusion fields (pile-up of C) is not much bigger than the interface thickness. If this is the case (and it is in almost every practical application), then the diffuse interface is "overrunning" the relatively short pile-up or the diffusing element, leading to a too fast interface kinetics ("artificial solute trapping"). To avoid that, the interface mobility must be corrected to a smaller value (compared to the physical value) to compensate for that. Furthermore, an additional diffusion flux ("antitrapping current") may be added in order to facilitate this type of correction.
Further, in the MICRESS phase-field model, the interface energy sigma is linked not only to curvature undercooling but at the same time serves for stabilisation of the diffuse interface. While in your 1D-simulation curvature is absent, interface stabilisation still plays an important role, especially under conditions of "artificial solute trapping": If the gradient of the driving force over the interface gets too big, the interface is deformed and may even be destroyed completely. This effect typically increases further the interface velocity while the interface width is broadened.
In your 1D-case it is relatively simple to overcome the trapping problem by choosing a sufficiently fine grid spacing. However, still the interface mobility needs to be chosen correctly if diffusion limited growth shall be obtained. If grid resolution is fine enough, it is sufficient to make it big enough until further increase does not change results anymore. However. a too high value will always lead to numerical instability (with destroyed interface) and high calculation times.
An alternative is to use the "mob_corr" functionality (see here) which automatically determines locally the correct interface mobility for diffusion limited growth.
In all cases, it is important to monitor the phase transformation process and check whether conditions are reasonable:
- .driv output: chemical driving force (would include curvature in 2D/3D). This values should be stable (oscillation is a sign for instability) and small (compared to curvature in 2D/3D or compared to total driving force / undercooling
- . .frac1/.frac2: Shows you the phase field parameters of phase 1 and 2 and allows to check the correct interface profile
- . conc1 / .c1pha1 / .c1pha2: Allow you to see the total composition / composition in phase 1 / compostion in phase 2 and thus to see how the pile-up looks like
- .mueS: Interface mobility
Bernd
Welcome to the MICRESS forum!
You may have heard that phase-field model do not give quantitatively correct results if the length of the diffusion fields (pile-up of C) is not much bigger than the interface thickness. If this is the case (and it is in almost every practical application), then the diffuse interface is "overrunning" the relatively short pile-up or the diffusing element, leading to a too fast interface kinetics ("artificial solute trapping"). To avoid that, the interface mobility must be corrected to a smaller value (compared to the physical value) to compensate for that. Furthermore, an additional diffusion flux ("antitrapping current") may be added in order to facilitate this type of correction.
Further, in the MICRESS phase-field model, the interface energy sigma is linked not only to curvature undercooling but at the same time serves for stabilisation of the diffuse interface. While in your 1D-simulation curvature is absent, interface stabilisation still plays an important role, especially under conditions of "artificial solute trapping": If the gradient of the driving force over the interface gets too big, the interface is deformed and may even be destroyed completely. This effect typically increases further the interface velocity while the interface width is broadened.
In your 1D-case it is relatively simple to overcome the trapping problem by choosing a sufficiently fine grid spacing. However, still the interface mobility needs to be chosen correctly if diffusion limited growth shall be obtained. If grid resolution is fine enough, it is sufficient to make it big enough until further increase does not change results anymore. However. a too high value will always lead to numerical instability (with destroyed interface) and high calculation times.
An alternative is to use the "mob_corr" functionality (see here) which automatically determines locally the correct interface mobility for diffusion limited growth.
In all cases, it is important to monitor the phase transformation process and check whether conditions are reasonable:
- .driv output: chemical driving force (would include curvature in 2D/3D). This values should be stable (oscillation is a sign for instability) and small (compared to curvature in 2D/3D or compared to total driving force / undercooling
- . .frac1/.frac2: Shows you the phase field parameters of phase 1 and 2 and allows to check the correct interface profile
- . conc1 / .c1pha1 / .c1pha2: Allow you to see the total composition / composition in phase 1 / compostion in phase 2 and thus to see how the pile-up looks like
- .mueS: Interface mobility
Bernd
Re: Gama-Alpha transformation under para-equilibrium
Hi. Thanks for this interesting topic.
@Bernd: I tried to see what happens if we use a 'normal' diffusion behaviour instead of 'nple' for a gamma-alpha simulation. Please see the attached images for the phase field, driving force and interface output. Am I not seeing the 'artificial solute trapping' and destruction of the interface here?
How can we describe what's happening in the interface output where you still see the prior austenite interface?
Deepu
@Bernd: I tried to see what happens if we use a 'normal' diffusion behaviour instead of 'nple' for a gamma-alpha simulation. Please see the attached images for the phase field, driving force and interface output. Am I not seeing the 'artificial solute trapping' and destruction of the interface here?
- Driving force and phase field output respectively
- driv_phase.png (299.45 KiB) Viewed 3931 times
- Interface output
- inf_output.png (25.7 KiB) Viewed 3931 times
Re: Gama-Alpha transformation under para-equilibrium
Hi Deepu,
Sorry for the late answer! I am currently in the US on holidays, and my internet connection is very bad...
It is like you said - if you don't use nple or para/paraTQ model, there is strong uncontrolled trapping, especially if the content of substitutional elements is high. In fact, the problem is not the "trapping" itself, because this will always happen if substitutionals are slow and the driving force is high enough. The important point here is that you get a concentration gradient in the phase composition which leads to a driving force gradient: While the front side of the interface moves forward due to high driving force, the back side does not move or even goes backward due to opposite sign of driving force. This leads to a spreading of the interface, which can hardly be prevented by averaging or interface stabilisation. This is also explains why you still see the old gamma interfaces as triple junctions in the .intf output: The rests of the gamma grains are still there, because transformation could not be completed in any of the grid cells.
When using nple or para, the model produces a constant driving force all over the interface (the value of which depends on whether a pile up of substitutionals is assumed or not).
Just for testing you could try to use maximal averaging of the driving force ("agv 1.0") and interface stabilisation (second optional parameter in the same line with the interface energy, values normally should not exceed about 10 times the value of the interface energy) to prevent spreading of the interface. However, kinetics still will be badly defined and lie somewhere between the nple and para models.
Bernd
Sorry for the late answer! I am currently in the US on holidays, and my internet connection is very bad...
It is like you said - if you don't use nple or para/paraTQ model, there is strong uncontrolled trapping, especially if the content of substitutional elements is high. In fact, the problem is not the "trapping" itself, because this will always happen if substitutionals are slow and the driving force is high enough. The important point here is that you get a concentration gradient in the phase composition which leads to a driving force gradient: While the front side of the interface moves forward due to high driving force, the back side does not move or even goes backward due to opposite sign of driving force. This leads to a spreading of the interface, which can hardly be prevented by averaging or interface stabilisation. This is also explains why you still see the old gamma interfaces as triple junctions in the .intf output: The rests of the gamma grains are still there, because transformation could not be completed in any of the grid cells.
When using nple or para, the model produces a constant driving force all over the interface (the value of which depends on whether a pile up of substitutionals is assumed or not).
Just for testing you could try to use maximal averaging of the driving force ("agv 1.0") and interface stabilisation (second optional parameter in the same line with the interface energy, values normally should not exceed about 10 times the value of the interface energy) to prevent spreading of the interface. However, kinetics still will be badly defined and lie somewhere between the nple and para models.
Bernd
Re: Gama-Alpha transformation under para-equilibrium
Hi Bernd,
No problem at all. Thanks for the explanation and suggestion. I will work on it.
Deepu
No problem at all. Thanks for the explanation and suggestion. I will work on it.
Deepu