MICRESS Forum

Dear Bernd,

I’m currently working on simulating the microstructure evolution of an Al-alloy that exhibits bimodal grain structures (equiaxed + columnar grains) during the LPBF process. My main objective is to understand how different thermal conditions influence the fraction of fine versus coarse grains.

According to experimental observations and proposed mechanisms (e.g., please see the figure), the Al₃X (L1₂) phase tends to form in the liquid first and subsequently acts as a potent heterogeneous nucleation site for the primary Al phase. Near the bottom of the melt pool, the solidification velocity is relatively low, so solute trapping is less effective, allowing primary Al to heterogeneously nucleate and grow, thus forming a fine-grained region.
As solidification velocity increases toward the middle and top of the melt pool, solute trapping becomes more pronounced, which may prevent the precipitation of Al₃X or lead to its consumption by the rapidly advancing solid–liquid interface, resulting in columnar grain growth.

I’ve tried to reproduce this mechanism in MICRESS by activating Al₃X seeds based on their formation interval (estimated from Scheil calculations, see figure) and allowing the thermal profile to drive the kinetics. However, this approach led to an equiaxed → columnar → equiaxed transition after remelting of the previous layer, which doesn’t match experimental observations (e.g. only equiaxed → columnar) .

My question is:
- Is there a way in MICRESS to include solute trapping effects that could help capture this transition more accurately?
- Or, do you recommend any specific strategy to limit heterogeneous nucleation at higher solidification velocities, for instance by coupling velocity-dependent partitioning or solute redistribution models?

Some of the input data I’m using are confidential and belong to our partners, so I’ve sent those details privately. I hope that's understandable!

Thank you very much for your time and support
Wishing you a nice day!
Ahmet

Hi Atur,

I think the mechanism of fcc nucleating on the Al3X-precipitates can make sense, although I am not sure why you think that solute trapping plays an important role here.

It is clear that formation of the Al3X-particles takes time, so that its formation and growth should happen preferentially during the initial stage where the front is moving slowly. When the front gets faster, there is less time, but the temperature gradient gets smaller, so that nucleation can happen farther away from the front. So, the question whether at all and at which stage the 2-step mechanism for fcc nucleation can happen, is an interesting question which can perfectly be addressed with MICRESS.

Before discussing your simulation results, which seem to contradict experimental findings, it is important to check and refine your simulation setup to make sure that the results can be trusted. I found several issues which require attention:

1.) As physical base for your problem, the counterbalance of local undercooling and curvature is essential to decide whether nucleation is possible. For the first step, the nucleation of Al3X, this is ensured by using the seed-density model, which takes the radius of the hypothetical seed particles as basis for calculating the corresponding curvature undercooling. Here, the assumed seed density/radius distrubution function is typically unknown and requires some type of calibration or reasonable assumptions.
But the second step, namely the nucleation of fcc on Al3X, is again strongly dependent on the size of the respective Al3X-particle, which is not reflected by a simple "interface" nucleation type. What is important is to include the curvature of the substrate by using the "substrate_curvature" keyword in seed type 2 of your nucleation input. Otherwise, the intrinsic physical mechanism of nucleation on particles is not included!

2.) A second important physical quantity in this counterbalance is the undercooling of the growing dendrite front. Apart from the 2D/3D-problematic (dendrite tip undercooling is much too high in 2D; also, the CET is much easier in 2D because equiaxed grains can much easier block a columnar front), there exists a strong issue with grid resolution: Ensuring diffusion-limited growth of an interface using mobility correction ("mob_corr") necessarily leads to an artificial excess kinetic undercooling, which is the bigger the coarser the grid resolution is. Thus, this effect systematically favors nucleation if resolution is too low. On top, in case the Al3X-particles are still unresolved when fcc nucleates, other types of numerical effects may retard fcc growth, also leading to a biased counterbalance of local undercooling and curvature. I think you will need to refine your numerical grid at least by a factor of 2-3 to largely avoid such effects.

3.) Running your input file I found large regions of negative composition, which emerge during solidification and which are also already present in the initial microstructure which is read from the .rest-file. For finding them it is necessary to write out the phase compositions of all elements in all phases and examine them in DP_MICRESS (best way is setting value range to -0.001 - +0.001, see also here). It seems that in this case there exist several reasons why this negative compositions emerge which you should tackle in order to avoid a loss of performance and accuracy:

a) the Al3X-phase is a nasty one, because there is an independent sublattice for Sc and Zr. This means that of the 6 elements Al, Mg, Sc, Zr, Fe, and Mn there are only 4 for which a composition can be defined independently. Although c(Al) (the matrix component) is already defined as dependent composition, c(Sc) and c(Zr) add up to exactly 25 at%, so that one of the two is also not independent. If MICRESS is executed without any special assumption for this phase, then an "independent_sublattice" model will be automatically invoked, which arbitrarily uses Sc (the first in the list) as dependent and Zr as independent element of this common sublattice and tries to approximate the interdependent redistribution of these two elements in the best way. Alternatively, the user can define the two elements as "stoichiometric", which often provides higher stability, but also cannot avoid the emergence of negative compositions up to a certain level. I this case, it turns out that using the "independent_sublattice"-model, redefined for using Zr as dependent composition, is more favorable:

#Numerical Parameters
#Concentration Solver
independent_sublattice 2 3 2

b) Penalty terms can be very efficient in avoiding negative concentrations stemming from extrapolation problems. They should be defined for the problematic element and phase, further restricted to a specific phase interface by giving a second phase number. In this case, Zr and Fe show problems in the liquid and fcc phase. Thus you should define

#Numerical Parameters
#Concentration Solver
penalty 1 2 4
penalty 0 2 3
penalty 1 2 3

c) it is dangerous to use diagonal terms of diffusion only, if the system is not dilute. The reason is that cross-terms can be strong and the diagonal values can be even negative! This happens in your case fore fcc and the elements Zr and Mn in certain temperature ranges and can lead to catastrophic diffusion behaviour if the negative coefficients persists long enough. Therefore you should either use the full diffusion matrix (which may exhibit further complications) or choose effective diagonal terms which can be obtained by

# Diffusion
diagonal_dilute z

d) As if your system was not complicated enough: In your case you also get some problems with the antitrapping current for Fe in the 0/1-interface. This is probably due to the strong segregation of this element and is not correctly caught-up by our safety algorithm (negotiating safety vs. efficiency). Therefore, you should either use "normal mob_corr" instead of "atc mob_corr" for Fe in the 0/1-interaction, or set a prefactor x (0<x<1) on the atc for this interface, e.g.

#Numerical Parameters
#Concentration Solver
atc_prefactor 0 1 0.5


4.) The time intervals for updating of diffusion data and linearisation data from database have been chosen unsufficiently in the input file you sent by PM, which may lead to inaccuracies, numerical problems, and even negative compositions. While the updating interval for diffusion coefficients is unnecessarily small (1.E-5 s would be sufficient), the updating interval for thermodynamic data should be smaller. Given the non-linear cooling behavior of L-PBF, it makes much sense to use the "automatic" mode which ties the updating interval to a local temperature change. For linearisation data, typically, a value of 1-5 K is reasonable, while for diffusion data 10-20K is usualy sufficient (an "automatic" mode for diffusion data will come with the next version ). Please note that if updating of linearisation data is defined for each interface separately, defining an additional global updating interval (in section "database") would lead to additional updating and should therefore be avoided.

I expect that using the recommendations given above should significantly change the result of your simulations, giving new impulses for their discussion. Please note that the suggested parameter settings are preliminary and may vary with the simulation conditions. You should always check for negative compositions and make sure that the simulation results are independent of grid resolution (as far as possible with reasonable calculation effort).

Finally, I would like to remark that the behavior which you want to model by nucleation of fcc on Al3X, could perhaps also be explained (and simulated) considering a fragmentation mechanism (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[/i]).


Bernd

Dear Bernd,

First of all, thank you very much for your detailed reply and valuable suggestions. I must say that most of the errors disappeared after applying your recommendations, and the simulations now run significantly more stably. Some errors (e.g., Error number 105 in Interface 275/173, trying hard phases 1 2 level, etc.) still appear once the simulation is complete, but this may be due to compositional effects (such as a reduction in liquid fraction) near the top of the insulated domain. I assume this is not crucial for the overall simulation since it only occurs during the last 2–3 time steps. The remaining issue is that I occasionally encounter the error “Unable to open file Results/xxxxconc3.mcr – STOP in routine outResult” after approximately 50–60% of the simulation runtime, which stops the simulation. I am not entirely sure why this occurs, as it is not reproducible for every run. Could this be related to the penalty parameters suggested for Zr in the independent_sublattice option?

To initiate further discussion based on your comments:
“Here, the assumed seed density/radius distribution function is typically unknown and requires some type of calibration or reasonable assumptions.”

- I selected the seed radius distribution based on TEM data reported in the literature, while planning to calibrate the seed density using experimentally observed effective grain sizes. I would greatly appreciate any further recommendations, particularly those considering numerical constraints and practical considerations. Moreover, I wonder whether refining the time step and spatial resolution of the temperature data could better capture local temperature variations, hence the nuceation behavior.

In addition, I reviewed the study you mentioned, and it appears that fragmentation may also contribute to grain refinement. However, based on the experimental literature, I would not expect fragmentation to be the dominant mechanism in this case. Studies on similar alloy systems (see, for example, https://doi.org/10.1016/j.matchar.2018.03.033, and https://doi.org/10.1016/j.actamat.2018.04.053, experimentally identify L1₂ precipitates as the primary source of grain refinement near the bottom of the melt pools. In contrast, these precipitates are reported to be largely absent within the columnar grain regions. Currently, the simulation results indicate complete grain refinement, whereas experimentally, this refinement should be limited to roughly the first 15–20 µm above the fusion line. In the new .dri file I sent via PM, reducing the average seed density still results in equiaxed grains but with larger ones toward the top of the simulation domain. My question is should I explicitly define an interaction for the fcc/fcc interface and activate nucleation at this interface to promote columnar grains over equiaxed ones (maybe similar to the fragmentation nucleation parameters where I define heteroeneous nucleation of fcc on fcc?). I suspect that otherwise, heterogeneous nucleation on L1₂ precipitates will always dominate so precipitation on L1₂ needs to be somehow surpressed and that should be fairly decided by energetics. What do you think? I would appreciate your guidance on how to identify this.

note: I am aware that substrate grains are not really in good condition, I will correct that

Once again, thank you for your detailed feedback and for highlighting these critical validation steps. I have PMed the latest driving file for your review.

Kind regards,
Ahmet

Hi Atur,

I do not really believe the explanation with "solute trapping", even if it is not meant literally, but only in the sense that the diffusion length of Zr and Sc ahead of the dendrite front gets very small. In the first reference you linked it is stunning to see that there are large amounts of seed particles visible in the lower regions with equiaxed structure, while there is a sudden change to no such particles in the higher columnar regions. Also, I cannot easily imagine that Al3X can rapidly nucleate on impurity particles, which would have to be very small (and which you currently approximate by the seed-density model).

Maybe it is worth thinking about what could happen if the Al3X particles instead were already present in the solid base metal or even in the powder particles. I think at least the first assumption is quite probable. Then, on laser melting, these particles would dissolve everywhere, except close to the bottom of the melt pool, where temperatures remain lower. Wouldn't this explain both: first that re-growth of the only partially molten Al3X-particles can be fast, and, secondly, that no nucleation of fcc is possible in regions in the upper part of the melt pool, because there are no Al3X-particles left. This mechanism would also explain that multiple-melting processes (as found in https://doi.org/10.1016/j.matchar.2018.03.033) lead to bigger equiaxed regions, as Al3X particles have time to get consecutively larger and larger.

You could try out the effect of Al3X-particles already existing in the base material if you include them when simulating the initial microstructure. Then, in the remelting simulation, you could observe the melting of these particles in higher regions, and you perhaps should be able to simulate these sharply separated regions with equiaxed grains, where Al3X did not dissolve completely.

When simulating with higher resolution like in the attached new driving-file - if you do not have an equally high-resolution initial microstructure - you may try use the zoom functionality for reading initial microstructures from restart-files in the correct scale (and also avoid badly shaped initial grains ):

#
# Structure from restart file
# ---------------------------
# Shall grain(s) be replaced by initial structure(s) from a restart file(s) ?
# Options: restart_file | no_restart_file
restart_file
# How many restart files shall be read?
1
# For each restart file a grain number and (optionally)
# shift (in grid cells) and zoom factor for all 3 dimensions
# as well as a character for rotation options must be specified:
# grain number [shift X (int) shift Y (int) shift Z (int)
# zoom X (int) zoom Y (int) zoom Z (int) rot(string)] ?
# Rotation options: "xz+90" "xz-90" "xz180" "xy+90" ... "yz180"
1 0 0 -750 3 1 3
# Name of restart file?
TUB_UW_Scalmalloy_columnar_no_Al3X



Finally, the error “Unable to open file Results/xxxxconc3.mcr – STOP in routine outResult” has nothing to do with penalties. It means that access to the output files is not possible at that moment, when MICRESS tries to append output to this file. This may be either because the network connection failed, the disk space is exceeded, or the corresponding file has been moved elsewhere.

Bernd