Dear Bernd,
First of all, apologies for the late reply. I come back to this project from time to time, so there can be quite a gap between my responses. Regarding homogeneous nucleation, I agree that the required undercooling should be high. However, I think such undercooling can theoretically be reached at the bottom of the melt pool. Based on the experimental data I have analysed across a broad range of materials, I believe that homogeneous nucleation of Al₃X from the liquid should be considered a plausible mechanism. Of course, I cannot exclude the possibility of nucleation on impurities, as has been reported for some alloy systems, or on surviving Al₃X particles. However, I do not think either mechanism is likely to be dominant. My reasoning is that the experimentally observed thickness of the fine-grained region varies considerably between different processing conditions. If surviving Al3X particles were the dominant mechanism, I would expect the thickness of this region to be governed primarily by the temperature range between the liquidus and solidus of Al3X. However, our process simulations suggest that the variation in this thickness is not particularly large, in contrast to the significant differences observed experimentally.
For this reason, I think it would be worth assuming homogeneous nucleation of Al3X or, more generally, the formation of nanoscale nucleation sites and systematically investigating the effect of undercooling on their stabilisation and subsequent grain refinement. My idea is to investigate five or six scenarios with progressively changing undercooling requirements for Al3X formation. For each scenario, I would then evaluate the thickness. However, I have already tried this approach, using the seed_undercooling option in combination with analytical_curvature and stabilisation, but I have not managed to obtain the trends I was looking for. The main difficulty is that seeds seem to form almost everywhere unless I reduce their maximum number when using analytical_curvature so I see fully equiaxed grains everywhere. For stabilisation option, Columnar grains start to form after some moment (e.g., columnar front overcomes seeds before fcc nucleates) but grain refinement is observed again at the top of the domain since seeds again forms everywhere.
In particular, I am not entirely sure how MICRESS determines whether a seed is activated at a given location and whether it subsequently becomes stabilised based on the local driving force and undercooling. With my current settings, the artificially stabilised seeds also cause grain refinement near the top of the simulation domain, which is physically inconsistent with the behaviour I am trying to reproduce. Given this, I would really appreciate your advice on how you would approach this problem. If your objective were to systematically investigate the influence of the minimum undercooling required for Al3X formation on grain refinement, would you follow a similar strategy, or would you recommend a different approach? In particular, are there specific settings or adjustments to the nucleation and stabilisation models that you would suggest to ensure that seeds are only activated and stabilised under the appropriate local conditions? I have mailed you the input files.
Thanks again for your time and help.
Best regards,
Ahmet
LPBF simulation of Al-alloy
Re: LPBF simulation of Al-alloy
Dear Ahmet,
It is absolutely legitimate and makes sense to check scenarios with different critical undercooling for the Al3X phase, and to check whether you can reproduce your experimental results. Herewith, in principal, it makes no difference if you do that by using a "bulk" nucleation type with or without analytical curvature, or whether you use a seed density approach and correspondingly adapt the seed radius distribution.
Between "analytical curvature" and "stabilisation" there should be no principal difference, apart from numerical deviations of the growth kinetics during the "small grain" stage. This is logic, because there is no resolution inside one single cell, so that the diffusion problem cannot be solved correctly. However, I did not find relevant differences with your input file (for the first layer, as I don't have the .rest-file for the second one). Nevertheless, the "stabilisation" model may have problems with high resolution simulations, if the undercooling is not high enough compared to the curvature undercooling which corresponds to one grid cell. Generally, the differences should get smaller with higher grid resolution, because the time interval, when the "small grain" models are applied, is strongly reduced.
I noticed a strange behaviour of the initial melting in the first layer, which is due to a wrong setting of the initial grain. It should be defined larger in x-direction to avoid a small liquid channel at the beginning.
For seed type 1 (homogeneous nucleation of Al3X) I would not use a nucleation distance which is smaller than the shield distance, because this can lead to lines of grains. It is reasonable to just use the shield distance alone (without defining a nucleation distance) and set it to a value which is typical for the experimental grain sizes in the equiaxed zone.
For seed type 2 (nucleation of fcc on Al3X), I would use a small value for the critical undercooling (perhaps even 0 K), because when we assume perfect wetting, the critical undercooling consists only of the curvature contribution from the substrate, which is added anyway. This means whether nucleation occurs then depends mainly on the size which the Al3X-particles can reach.
Generally, nucleation should be checked often enough to be sure not to have empty zones where nucleation was never checked. I would also be cautious with the temperature ranges for nucleation in order not miss nuclei unintendently. There is no need for an upper limit in seed type 2 and a lower limit in seed type 1 (because the matrix or substrate phases are missing otherwise), the other limits are only needed for saving calculation time (when checking nucleation in not relevant temperature ranges), and should be extended somewhat to be on the safe side.
Generally, grid resolution is very critical for a correct prediction of the nucleation scenarios. To avoid wrong interface kinetics due to artificial solute trapping at low grid resolution (i.e. unphysical large interface thickness), the interface mobility is corrected automatically ("mob_corr"). This leads to a kinetic undercooling of the dendrite front (see .driv ouput) which can significally alter the nucleation conditions of Al3X close to the dendrites. This problem can be reduced by using a sufficiently high grid resolution and/or by calibration of the "mob_corr" function by a prefactor on each element. Anyway, Δx=0.03 µm is definitively too coarse in your case. Further, I am not sure about your restart scheme which uses a zoom factor of 4 - is it meant for increasing resolution to 0.0075 µm in the second layer?
Best wishes
Bernd
It is absolutely legitimate and makes sense to check scenarios with different critical undercooling for the Al3X phase, and to check whether you can reproduce your experimental results. Herewith, in principal, it makes no difference if you do that by using a "bulk" nucleation type with or without analytical curvature, or whether you use a seed density approach and correspondingly adapt the seed radius distribution.
Between "analytical curvature" and "stabilisation" there should be no principal difference, apart from numerical deviations of the growth kinetics during the "small grain" stage. This is logic, because there is no resolution inside one single cell, so that the diffusion problem cannot be solved correctly. However, I did not find relevant differences with your input file (for the first layer, as I don't have the .rest-file for the second one). Nevertheless, the "stabilisation" model may have problems with high resolution simulations, if the undercooling is not high enough compared to the curvature undercooling which corresponds to one grid cell. Generally, the differences should get smaller with higher grid resolution, because the time interval, when the "small grain" models are applied, is strongly reduced.
I noticed a strange behaviour of the initial melting in the first layer, which is due to a wrong setting of the initial grain. It should be defined larger in x-direction to avoid a small liquid channel at the beginning.
For seed type 1 (homogeneous nucleation of Al3X) I would not use a nucleation distance which is smaller than the shield distance, because this can lead to lines of grains. It is reasonable to just use the shield distance alone (without defining a nucleation distance) and set it to a value which is typical for the experimental grain sizes in the equiaxed zone.
For seed type 2 (nucleation of fcc on Al3X), I would use a small value for the critical undercooling (perhaps even 0 K), because when we assume perfect wetting, the critical undercooling consists only of the curvature contribution from the substrate, which is added anyway. This means whether nucleation occurs then depends mainly on the size which the Al3X-particles can reach.
Generally, nucleation should be checked often enough to be sure not to have empty zones where nucleation was never checked. I would also be cautious with the temperature ranges for nucleation in order not miss nuclei unintendently. There is no need for an upper limit in seed type 2 and a lower limit in seed type 1 (because the matrix or substrate phases are missing otherwise), the other limits are only needed for saving calculation time (when checking nucleation in not relevant temperature ranges), and should be extended somewhat to be on the safe side.
Generally, grid resolution is very critical for a correct prediction of the nucleation scenarios. To avoid wrong interface kinetics due to artificial solute trapping at low grid resolution (i.e. unphysical large interface thickness), the interface mobility is corrected automatically ("mob_corr"). This leads to a kinetic undercooling of the dendrite front (see .driv ouput) which can significally alter the nucleation conditions of Al3X close to the dendrites. This problem can be reduced by using a sufficiently high grid resolution and/or by calibration of the "mob_corr" function by a prefactor on each element. Anyway, Δx=0.03 µm is definitively too coarse in your case. Further, I am not sure about your restart scheme which uses a zoom factor of 4 - is it meant for increasing resolution to 0.0075 µm in the second layer?
Best wishes
Bernd