Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

dendritic solidification, eutectics, peritectics,....
Atur
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Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Atur » Fri Jul 29, 2022 6:27 pm

Dear Bernd,

I would like to construct a simulation to observe the solidification sequence in a low alloyed steel under SLM conditions. From Scheil simulations, delta-ferrite starts to form in the beginning of solidification (hypoperitectic composition) at around 1797 K and towards the end, austenite starts to form around 1765 K and solification proceeds as austenite till the end . I would like to monitor if the initial delta-ferrite will transform to austenite or somehow will surpressed during initial solidification under SLM conditions (and then maybe later in HAZ to see C redistribution if a re-construction is possible from a restart file). In parallel, I also would like to screen corresponding Mn and C segregation.

Although I set the interface nucleation of austenite on delta-ferrite boundaries and corresponding nucleation temperatures (1675 K) I dont see any austenite formation and growth along the simulation, independent from nucleation temperature and min. undercooling value (force automatic start value appears in .log file). My nucleation and phase interaction paramters are shared below (simple interface nucleation on delta-ferrite boundaries). I started my simulation with a flat bcc grain and set the bottom temperature to 1K below the liquidus temperature. I would appreciate your help to identify what is missing in my approach :)!

Thank you and kind regards,
Ahmet

# Enable further nucleation?
# Options: nucleation nucleation_symm no_nucleation [verbose|no_verbose]
nucleation
# Additional output for nucleation?
# Options: out_nucleation no_out_nucleation
no_out_nucleation
#
# Number of types of seeds?
1
#
# Input for seed type 1:
# ----------------------
# Type of 'position' of the seeds?
# Options: bulk region interface triple quadruple front [restrictive]
interface
# Phase of new grains (integer) [unresolved|add_to_grain|split_from_grain]?
1
# Reference phase (integer) [min. and max. fraction (real)]?
0
# Substrate phase [2nd phase in interface]?
# (set to 0 to disable the effect of substrate curvature)
2
# Maximum number of new nuclei of seed type 1?
# (set negative for unlimited number)
-1
# Grain radius [micrometers]?
0.000
# Choice of growth mode:
# Options: stabilisation analytical_curvature
stabilisation
# min. undercooling [K] (>0)?
20
# Determination of nuclei orientations?
# Options: random randomZ fix range parent_relation
random
# Shield effect:
# Shield time [s] [shield phase or group number] ?
5.E-5
# Shield distance [micrometers] [ nucleation distance [micrometers] ]?
0.9
# Shall categorization be applied to this seed type?
# Options: categorize {Number} no_categorize
no_categorize
# Nucleation range
# min. nucleation temperature for seed type 1 [K]
0
# max. nucleation temperature for seed type 1 [K]
1765
# Time between checks for nucleation? [s]
# Options: constant from_file
constant
# Time interval [s]
1.00000E-05
# Shall random noise be applied?
# Options: nucleation_noise no_nucleation_noise
no_nucleation_noise

The interaction between fcc and bcc also enabled in phase interactions:
# 1 (FCC_A1) / 2 (BCC_A2)
# -------------------------
# Simulation of interaction between 1 (FCC_A1) and 2 (BCC_A2) ?
# Options: phase_interaction no_phase_interaction identical phases nb
# [ standard | particle_pinning[_temperature] | solute_drag ]
# | [ redistribution_control ] or [ no_junction_force | junction_force ]
1 2 phase_interaction redistribution_control
# 'DeltaG' options: default
# avg ...[] max ...[J/cm^3] smooth ...[Deg] noise ...[J/cm^3] offset ...[J/cm^3]
avg 0.5 smooth +45.0 max 1000
# I.e.: avg +0.50 smooth +45.0 max +1.00000E+03
# Type of interfacial energy definition between 1 (FCC_A1) and 2 (BCC_A2) ?
# Options: constant temp_dependent
constant
# Interfacial energy between 1 (FCC_A1) and 2 (BCC_A2) ? [J/cm**2]
# [max. value for num. interface stabilisation [J/cm**2]]
5.0E-05 5.0E-04
# Type of mobility definition between FCC_A1 and BCC_A2?
# Options: constant temp_dependent dg_dependent [fixed_minimum]
constant
# Kinetic coefficient mu between FCC_A1 and BCC_A2 [cm**4/(Js)] ?
1.E-6
# Shall misorientation be considered?
# Options: misorientation no_misorientation
# [low_angle_limit <degrees (default=15)>] [special_orient <nb>]
no_misorientation
# Is interaction isotropic?
# Options: isotropic
# anisotropic [junction_force] [harmonic_expansion]
isotropic
# Which phase diagram is to be used?
# Options: database {local|global|interface|fragment}[<maximal distance>]
# | linear | linearTQ
database global 2
# Relinearisation interval for interface FCC_A1 / BCC_A2
# Options: automatic manual from_file none
manual 1.00000E-05
# Please specify the redistribution behaviour of each component:
# Format: forward [backward]
# Options: nple para paratq normal [mob_corr] atc [mob_corr] [verbose]
# Component C:
atc mob_corr
# Component MN:
atc mob_corr

Bernd
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Bernd » Mon Aug 01, 2022 6:11 pm

Dear Atur,

From the technical side I found 2 problems: One is that the interface mobility which you apply is too small for giving diffusion-limited growth. Given the low-alloyed steel with only little segregation, you need to put at least a value of 100 or 1000 cm**4/(Js) to be on the safe side. You should always check the .mueS output whether the effective mobility, which is obtained by the "mob_corr" option, is significantly smaller than the assumed (physical) interface mobility which you specified.

The second point is that grid resolution seems to be not fully sufficient, leading to some artificial solute trapping. Unfortunately, it is not that easy to define the needed resolution, while the exact choice has a very strong impact on calculation time! The best method is to try finer resolution (i.e. 0.005 µm in your case) with a small simulation domain and check out whether results are getting much different.

Nevertheless, although the simulation results get more correct and reliable with these two measures, there was no nucleation of austenite phase, even when I extended the nucleation temperature range to higher values in order to catch up the semisolid region. However, I generally doubt that you should expect getting austenite from the liquid with this alloy, even for normal solidification conditions, because Scheil is not realistic in this case. If you include fast C-diffusion in the Scheil calculation (what is more realistic!), no austenite is predicted anymore!

Bernd

Bernd

Atur
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Atur » Tue Aug 02, 2022 4:42 pm

Dear Bernd,

Thank you for your reply! I will integrate your suggestions and try to run couple more simulations.

Regarding the Scheil simulations, I always enable fast C-diffusion in classical Scheil settings but for me, the austenite always forms after 0.90 mole fraction fo solid. Therefore I am confused how austenite is not predicted. For this calculations I am using ThermoCalc 2020b and TCFE10 database. Did you use the Scheil calculations in ThermoCalc 2021 release with solute trapping modules?

I actually think I have some strong experimental evidence that Austenite nucleated at the interface of delta-ferrite solification cells/grains. What I know from literature is (e.g. for HMnS; https://doi.org/10.1016/j.addma.2020.101389), when delta-ferrite solidifes first and fcc is nucleated on delta-ferrite interface, the crystallogaphic texture weakens. When the solidification is mainly controlled by one phase, then what is observed is strong texture due to the epitaxial growth over several melt-pool boundaries. In addition, change from delta-ferrite to austenite during solidification from liquid also refines the grain size substantially. In my case, the as-SLMed state has weak crystallographic texture and microstrcutre looks like martensite (in-line with almost random orientation and SEM images) with some retained austenite on triple junctions (e.g. nucleation in HAZ probably), and it is clearly visible that the growth was not epitaxial. So probably the similar case is happened, where delta-ferrite solidified first and probably due to the C diffusion, the liquid composition is shifting towards regions where austenite is able to nucleate in the interfaces. I would expect if the solidification was mainly dominated by delta-ferrite, the grain morphology would be more different (e.g. maybe large elongated grains along the BD). Of course, I consider there is no massive transformation of delta-ferrite to austenite (which is also reported in some literature depending on composition and undercooling). I hope I clearly explained it and looking forward to your comments!

I think I might give it another try with lower colling rates and temperature gradients, thinking that maybe the settings I selected was supressing austenite solidification.

Regards,
Ahmet

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

Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Bernd » Tue Aug 02, 2022 10:04 pm

Dear Ahmet,

Could it be that your composition is in weight percent rather than in atom percent?

Bernd

Atur
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Atur » Tue Aug 02, 2022 10:29 pm

Dear Bernd,

Sometimes the answer is actually really simple.. :oops: Sorry for my lack fo attention! I somehow assumed the equilibrium input was already in wt%, therefore havent converted! Now actually I run a quick simulation with coarser grid solidifcation starts with delta-ferrite and proceeds with austenite!

Thanks for the input anyways! I will run the simulations and contact to you with more relevant questions if needed :)

regards,
Ahmet

Atur
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Atur » Thu Aug 04, 2022 8:10 pm

Dear Bernd,

I run some simulations with the 1D temperature profile obtained by FE simulations and selected 4 connection points to describe corresponding graident and cooling rate change over the domain. The simulation stops when the temperature reaches to 1000°C. The austenite nucleation is defined in delta-ferrite-liquid interface, in triple junctions and also at delta-ferrite/delta-ferrite interfaces. The results are actually in good agreement (lets say observed trends) with the prior austenite grain analysis from the ebsd data. So what is observed is, solidifcation starts as delta-ferrite and shifts to austenite after some delta ferrite solidification, meanwhile, austenite also starts to nucleate at delta-ferrite grain boundaries and forms clusters of small grains in the bototm of the melt pool.

Nevertheless, I have some doubts before I switch to expensive computations and would appreciate your comments to reduce artifical effects;
- what kind of redistribution behavior I should select for austenite/delta ferrite interaction? In the example file A017_M247_Additive_constantGV the redistribution behavior of carbon is selected as atc mob_corr for solid-solid interactions. I wonder if using paratq option would be preferable in a low alloy steel and make any drastic change in the end?

-I also realized the interface mobility has a critical value to start nucleation at solid-solid phase boundaries and triple junctions. If I set it below 1 cm4/js, nucleation is not observed, however austenite nucleation starts to occur in delta ferrite boundaries when interface mobility in austenite-delta interface is set to i.e. 100 cm4/js as you suggested. Considering my previous bullet point, is it an atc mob_corr effect?

-Also, for the seed types of austenite in delta-delta interfaces and triple junctions, the minimum undercooling value for stable growth is changin from 80K to 420K(!) when the grid spacing is reduced from 50 to 10 nm. The nucleation is observed for min undercooling of 5K and fcc-delta interface velocity of 100 cm4/js for 50 nm grid, however I dont see it anymore when the grid is finer. The undercooling for stabilisation is extremely high and I would appreciate some tips for stabilizing the austenite nuclei. I tried analytical curvature approach, the minimum undercooling for stable growth for seeds appears to highly dependt on the defined critical radius. Are there any rule of thumbs to define critical radius in this case?

-Lastly, I have the impression that seeing this sharp and cornered solidifcation grains are kind of wrong. I checked the .driv output and at the tip, the value is around -25 to -45 during solidification. As far as I remember, it should be rather close to 0 to capture correct behavior. This might be related to sharp temperature drop (e.g. 100K)/gradient change in defined distances due to the 1D temperature profile. When switched to constant GV approach, the values in .driv output rather concentrates between -10 to 0. Since I would like to continue using 1D temperature profile, I would appreciate an input regarding how to proceed to obtain correct morphologies. I am also confused why in this case you suggested that the kinetic coefficient in solid/liquid, solid/solid should be set to 100 or 1000 cm4/js when earlier I actually read 1 to 10 cm4/js was sufficient for solid/liquid ( for solid-solid it was even lower) for simulation of SLM process . I would be very happy to hear your comment on that as well :)

Regards,
Ahmet
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Bernd
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Bernd » Tue Aug 09, 2022 11:17 pm

Dear Ahmet,

Sorry for the late answer, but you ask a lot of detailed questions, and I am on holidays currently...

First of all I am glad that your simulation has advanced. I will try to give you short comments to your questions:
  • In the example A017_M247_Additive_constantGV no emphasis has been put to the solid-solid reactions, and at the given time-scale practically no such transformation can be expected. In your case, however, the delta-austenite transformation can really happen in nple or para-equilibrium mode. I cannot tell you which one is more realistic. You should apply nple or para/paratq-mode for all but the fast-moving elements (C).
  • I did not fully get the point of your second question about nucleation at solid-solid-interfaces: Did you mean delta-ferrite interfaces? Which phase should nucleate there? Anyway, if you assume diffusion-limited growth at least for carbon, there should be no change with the specified interface mobility, as long as it is high enough...
  • Using "analytical_curvature" is the right way to cope with numerical issues at high grid resolution. Of course there is a strong influence of the chosen value for the critical radius, which has to be chosen bigger than the grid spacing to obtain realistic nucleation undercooling: If e.g with "stabilization" you got a "minimum undercooling value for stable growth" of 420K, it should be 42 K with "analytical_curvature" and a critical radius of 10 times the grid spacing.
  • Finally, I also have the impression from the "cornered solidification grains" that grid resolution is insufficient in your case. With finer resolution dendrites should look more realistic, and driving forces should be smaller. The reason why you need more than normally high interface mobility is because of the alloy with very low compositions and low segregation.
Bernd

Atur
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Atur » Mon Aug 15, 2022 12:06 pm

Dear Bernd,

Thank you for your reply and I wish you nice vacations!

1- I switched Mn and Si to paratq for delta-austenite interaction. However I kept atc mob_corr option for all elements for liquid/delta and liquid/austenite interaction assuming that some Mn should still enrich in liquid during solidification.

2- Yes, I meant austenite nucleation on delta-delta interfaces and triple junctions. Actually I am not sure what to assume for C (e.g. diffusion limited growth), but using atc_mob corr with high interface mobility seem to work fine and form austenite from delta as expected, so I will keep it this way.

3- Thanks!

4- I had some improvements with respect to the driving forces after updating the temperature profile, but then I encountered a different problems such as the error "Incorrect segmentation in spfMobilityCorrection" (Ralph will mention it to you I guess). This error stops the simulation at random time steps (e.g. different in every iteration). So far we tried changin the T profile (e.g. smaller step sizes), enablin/disbaling tic_z_segment and tic_tq_segments options, changing diffusion input. In addition, I also started to observe negative C concentrations (in single or few grids) which seem to appear in some steps and then dissapear in the next. I wonder how to cope with it as well.

Besides the updates, I have two more doubts;

-My simualtion domain is 60 µm and I start with an inital austenite grain which occupies half (30µm) of the domain. The idea is that 30 µm austenite grain represents previously deposited layer where as the remaining 30 µm is the experimental powder layer thickness in liquid form. When the simulation starts, the previously deposited layer melts partially, leading to the approximate melt pool depth observed from the experiments. The solidification proceeds from partially melted asutenite interface. However, the initial C and Mn concentration in the austenite is initiated by Micress is very low compared to the equilibrium Liquid concentration. This forms a large concentration gradient (I think its high considering the steel is low alloyed) in the melt (see attached), leading to wrong/twisted solidification behavior. I tried setting nominal C, Mn and Si compositions for all phases by "input" option to circumvent this issue and homogenize the liquid composition. Nevertheless, I am not sure if it is the right way of assumption. Can you comment on this?

-Lastly, I have one question about undercooling. Sometimes I see quite high undercooling (not sure if it makes sense) in delta interfaces/triple junctions when the bottom temperature drops. Such as:
seed 1
at an interface, zp = 3818
Phase: 1 (FCC_A1)
Seed type: 4
Local temperature = 1628.1 K
Undercooling = 95.022 K
Grain number = 11

But does that mean all of these seeds will be stable and growing? Or this is just a feedback that seed has set and "might" grow.

Thank you and regards,
Ahmet
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Bernd
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Bernd » Tue Aug 16, 2022 6:53 pm

Dear Ahmet,

It is correct to use "input" option for definition of the initial microstructure, where the initial solid grain corresponds to the base metal and the liquid to the new layer. Both regions should have nominal composition, and defining "equilibrium" compositions instead does not make sense.

For the undercooling value which is shown for the nucleation events, it is important to know that they are just a function of temperature and the local composition of the reference phase. This means that even with high undercooling the seed may not be able to grow significantly if there is very little reference phase present, or if the local composition was caused only by some sort of numerical fluctuation.

I will have a look at the "Incorrect segmentation" problem when I am back at office.

Bernd

Atur
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Re: Simulation of delta-ferrite/austenite solidifcation sequence under SLM conditions

Post by Atur » Tue Aug 16, 2022 8:07 pm

Dear Bernd,

Thank you for your reply and sorry for keeping you busy. I just wanted to update you about the segmentation problem, which might reduce the effort you invest for this problem in following.

I tried running simulations by keeping everything same, but only changing the redistribution behavior of Mn and Si for delta-austenite interaction. The problem appears to be with the "paratq" option. I tried to switch to atc_mobb corr or to para with bottom_temperature option and segmentation problem dissapeared for both individual options, simulation is now completed. So somehow the settings I use apparently disturbs something in TQ-coupling. Therefore I can stick to para option, however does using bottom_temperature is numerically more stable or should I try local_veloctiy?

Regards,
Ahmet

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