Grain size versus cooling rate ?

dendritic solidification, eutectics, peritectics,....
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stephane44
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Grain size versus cooling rate ?

Post by stephane44 » Tue Nov 28, 2023 11:02 am

Hello,

Using Micress 7.0, I would like to perform solidification simulation to capture the effect of cooling rate on grain size, which is to be compared to actual microstructures from additive manufacturing experiments.

In a first approach, I am only considering a fully liquid domain and nucleation of a BCC_B2 phase without initial microstructure. I am first focusing on nucleation density, thus disregarding for now the effects of grain growth/competition, solid state transformations, nucleation of other phases, etc.

I have tested multiple nucleation conditions by changing one parameter at a time using the seed_undercooling model/homogeneous nucleation to avoid inputting a nuclei distribution, although it is less representative of typical solidification conditions.


Parameters like shield/nucleation distance have a great effect on grain density but they are arguably artifical (although useful!). I would like nucleation density to depend more on processing conditions, undercooling etc.

But despite going through the documentation and testing various parameters, I do not really understand how nucleation density varies with cooling rate or undercooling with the seed_undercooling model.
Is the model based on Classical Nucleation theory, where nucleation rate can be linked to temperature and undercooling ?

Also I have noticed that when increasing the cooling rate, the grain density is decreased instead of being increased as in most experiments.
I guess this is because the time between checks for nucleation remained the same in my tests. So there are less nucleation events overall and the grains grow faster.

Maybe it would be preferrable to adjust the nucleation checks interval on a temperature basis, like every N Kelvins, to make things more physical and comparable.

I am testing the seed density model (without latent heat release for now) but this means having the seed density as an input instead of an output.


How would you approach this problem of modeling grain size versus cooling rate from nucleation in a liquid ?

Perhaps grain growth and other effects can be the main factor in modelling final grain size when changing the cooling rate, and initial nucleation density could stay the same.

But physically, with greater cooling rate comes higher undercooling and thus more homogeneous nuclei can form, thus yielding higher nucleation density, and i would like the model to reflect that if possible.


Any insight would be appreciated.

Thank you !

janin
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Re: Grain size versus cooling rate ?

Post by janin » Tue Nov 28, 2023 12:24 pm

Hi Stéphane,
You may perhaps find some answers in my presentation
‘Phase-Field Studies of the Interplay between Nucleation and Growth in Light Metal Alloys’ from March 2019 which you can find in ResearchGate
https://www.researchgate.net/publicatio ... tal_Alloys

Nucleation in the liquid typically occurs by hetergeneous nuclation on grain refiners or impurities of different size. In Micress, such inculants are called 'seed particles' and the user can input a 'seed density' function which defines the density (frequency) of the seed particles as function of their radius ( see e.g. the Micress tranings example T51_10_NucleationSeedDensityLogN1). According to the user-defined function favored position for potential nucleation are distributed in the simulation domain. A nucleation event only occurs if the local undercooling is exceeded at a given position.
Using the same seed density function, high cooling rates will results in higher undercooling and such in more nuclei, as illustrated by the example in my presentation. However, as you stated, it is important that the result is not biased by other nucleation conditions such as check frequency or shield distance. These parameters can be adjusted for good performance, but are in this type of nucleation modeling not expected to have an impact on the final number of nuclei.
With best regards,
Janin

Bernd
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Re: Grain size versus cooling rate ?

Post by Bernd » Tue Nov 28, 2023 12:52 pm

Dear Stephane,

When it comes to simulate grain size in case of equiaxed solidification, like Janin I would always prefer the seed-density model (together with latent heat release or 1d-temperature solver). The reason is that what you observe - a decreasing grain size with increased cooling rate - is physically linked to the existence of seeding particles with a certain size-distribution or other preferred nucleation sites (even if no grain refiners have been added explicitly). I further disagree with your statement that by defining a seed-density distribution you would already input what you want to get as a result: The seed-density distribution which you provide as an input is a property of the melt (level impurities or grain refiners, potential nucleation sites) and is not identical to the density of the actual "seeds" (nucleated grains)!

Of course, you can argue, that a homogeneous nucleation model with a nucleation rate which increases with undercooling can also predict the phenomenon of getting finer grains with faster cooling. However, I think this is an "academic" model approach which is not realistic for solidification experiments, except if you have extremely pure melts or small systems (like in levitated droplets). This is perhaps also the main reason why we still do not have such nucleation rate based models implemented in MICRESS.

It is clear that the pragmatic "seed_undercooling" model, which we alternatively offer in MICRESS, as such is not able to provide the expected behavior without further tweaking, because it is not physically based. As you said correctly, with a fixed checking rate and nucleation distance, the number of nucleation events will even decrease when increasing cooling rate. However, in principle, you also could use the seed_undercooling model as a building block for any arbitrary rate-based model by using a number of seed types instead of one, and vary the critical undercooling and checking rate/nucleation distance among the seed_types such as to rebuild your expected nucleation rate. Nevertheless, I still would prefer the seed_density approach...

Another question which must be raised is whether in additive processes conditions are comparable to the situation of equiaxed nucleation. Due to the high cooling rates and the small melt volumes, nucleation of impurity particles is less probable, and I personally consider fragmentation to be the most relevant mechanism at least in case of L-PBF (and without explicit addition of seeding particles):

B. Böttger, M. Apel
Phase-field simulation of the formation of new grains by fragmentation during melting of an ABD900 superalloy
IOP Conference Series: Materials Science and Engineering. Vol. 1281. No. 1. IOP Publishing, 2023
https://doi.org/10.1088/1757-899X/1281/1/012008


Bernd

stephane44
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Re: Grain size versus cooling rate ?

Post by stephane44 » Wed Nov 29, 2023 3:25 pm

Thank you very much Janin and Bernd for your answers, it is very helpful.

Looking at the presentation provided, I better see how the cooling rate affects the grain density with the seed density model. Indeed, as noted by Bernd, nucleants and nuclei are not the same thing, so I'm going to use that model from now on.

Regarding the nucleation mechanism in AM conditions, I do indeed assume equiaxial conditions apply for now as a major simplification, ignoring other mechanisms such as fragmentation which could indeed be prevalent at least for LPBF, as is well reflected in your example A018 for additive manufacturing. However I actually aim at simulating the conditions for an arc-based AM process at a mesoscale (one layer and later on multiple layers).

So in order to get the variation in grain density as a function of cooling rate, I understand that the latent heat release must be accounted for somehow in order to get a variation in maximum undercooling and thus see the effect on nucleation density.

As the latent heat model is more appropriate with negligible gradients, I will use the 1D_temp model to couple to process conditions, as in your recently published papers. However the proper heat flow boundary conditions have to be figured out, the cooling rate being more commonly reported.

In the paper referenced below, you discuss in section 3.4 that temperature field and thus latent heat is generally more consistent with the microstructure when using the 1D_temp model with proper BCs rather than with a temperature profile from external process simulations.

Could temperature profiles from an external process simulation still be used as input to effectively capture the grain size versus cooling rate relationship provided the solidification path is sufficiently accurate, (perhaps using a thermocalc scheil calculation in a first approximation, or even a MICRESS simulation) ? Otherwise, I suppose the external process simulation could be used to set the heat flow boundary conditions.

B. Böttger, M. Apel
On the choice of thermal boundary conditions for microstructure modelling of additive processes
12th CIRP Conference on Photonic Technologies [LANE 2022]
https://doi.org/10.1016/j.procir.2022.08.024

Bernd
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Re: Grain size versus cooling rate ?

Post by Bernd » Wed Nov 29, 2023 5:28 pm

Dear Stephane,

I think that the 1D_temp approach indeed is the best one for your case, because it allows combining temperature gradients with the effects of latent heat which you need for the seed density nucleation approach. In case you don't have a fast moving heat source like in L-PBF, perhaps a polar coordinate approach would be even better than the 1d-cylinder approach which I presented in the LANE2022 paper.

If you would instead directly use temperature profiles from external process simulation, then there is no effect of latent heat which allows for a competition between potential seeds - at least as long a you do not iteratively feed your response on the micro-scale back to the process tool in the sense of the iterative Homoenthalpic Approach:

B. Böttger, J. Eiken, M.Apel, Phase-field simulation of microstructure formation in technical castings – A self-consistent homoenthalpic approach to the micro–macro problem, J. Comput. Phys. 228 2009, pp. 6784-6795.

Obviously, the combination of a process simulation tool with MICRESS using the iterative Homoenthalpic Approximation would be the best solution at all, if the process simulation is able to deliver temperature fields with a sufficiently high spatial resolution (which is not easy!). Alternatively, as you suggested, you could use a heat flux boundary condition for the 1d_temp field which is calculated by the process model and which could be much closer to the microstructure domain than in my 1d-cylinder model. Such an approach could not describe the thermal interaction of microstructure formation with the melt-pool as a whole, but still deliver direct local feedback of latent heat which is important for the seed density nucleation model. Furthermore, it could perhaps be better suited to describe melt pool shapes which are not close to cylindrical or spherical.

Bernd

stephane44
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Re: Grain size versus cooling rate ?

Post by stephane44 » Tue Dec 05, 2023 5:48 pm

Thank you for your help.

I have been testing the 1D temp model with seed density approach and it does capture the change in grain density, at least provided that the initial undercooling isn't too high, so that's great !

My heat source is not as fast moving as in LPBF, but so far I have only tested the cartesian coordinates for the 1D temp field for my 2D test simulations where there is only cooling from a fully liquid state. However it could possibly be beneficial to use cylindrical or polar, but more so when including a heating/remelting phase i suppose as done in your LANE2022 paper i suppose, which I will do later on.

How do you typically go about setting numerical nucleation parameters, in particular the nucleation check frequency ? Should it really not affect grain density too much ultimately if the model is set properly, as hinted by Janin ? Now I've set it to be "relatively small" (which I agree does not mean by itself!), despite the toll on computing ressources, and I am going for zero shielding to limit the number of parameters involved.

Best regards,

Stéphane

Bernd
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Re: Grain size versus cooling rate ?

Post by Bernd » Tue Dec 05, 2023 10:47 pm

Dear Stéphane,

That sounds reasonable. The basic idea of the seed density model does neither have shielding nor nucleation rates, so, in principle, having infinitely small checking intervals and a shield distance of 0 (or shield time of 0) is perfect. We have left the shield effect available just for cases where the user perhaps wants to avoid very close nuclei, but I normally never use that.

If you want to use longer checking intervals for performance reasons, that does not matter so much, as long as not too many of the seeds are activated in the same time step (what could hamper the correct competition among them). Further, you need to make sure that nucleation undercooling is not increased too much during waiting between the checks. The most simple procedure to find out is to do a reference simulation with short intervals, and check how much you can increase it without changing result significantly.

Bernd

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