Primary Dendrite Arms spacing (PDAS) prediction

[CharMIC]

Hi,

I want to set up a simulation to predict PDAS of Superalloy. Thermal gradient and initial bottom temperature will be kept constant. Only cooling rates will be changed to see the effect on cooling rates on PDAS.

My question is how to set up initial grain. Since the purpose of the modelling is to predict PDAS, I don't want to set initial grains at a distance with experimental PDAS.

My idea is to set up a rectangular grain at the bottom of the domain. The width equal to the width of the domain and height zero. Or is there any other way.

Any thoughts on this matter?

Chamara

[Bernd]

Dear Chamara,

My experience is that starting from a completely flat front like you propose by setting a rectangular initial grain would take long until dendrites form and select. Just setting a normal small or round grain in the lower left corner instead leads to a rapidly growing side branch along the bottom which itself rapidly branches to form tertiary arms which develop to new primary dendrite arms.

However, I think it is important to think about what you really want to get out. Keep in mind that starting from a too small PDAS which coarsens by selection, or starting from a too high PDAS which refines by branching, will lead to different results, as also can be observed in experiments. Starting from a single small grain like I proposed above would reflect the first case because you would start with a too fine PDAS.

You could also think about doing it systematically, i.e. starting from a domain with two dendrites (starting from the lower left and lower right corner) and growing both simultaneously. You could now on one hand step-wise decrease the domain width until one of both vanishes, or on the other hand increase it until a third one forms by branching. This would give you a criterion for the maximum and minimum stable PDAS.

However, selection of the PDAS in 2D in 3D also is different. In 3D you would need to assume some basic geometrical arrangement of the dendrites for your systematic simulations, and you probably also would need two different setups for getting the maximum and minimum stable PDAS...

Bernd

[CharMIC]

Hej Bernd,

Many thanks for your valuable thoughts.

If you set the grains at the left and/or right corner of the domain, I have to neglect the dendrite that grows along the boundary (left and/or) when calculating the PDAS?

I was also thinking setting up higher number of small round grains at the bottom of the domain. Then the grains will starts to grow and depend upon the cooling rates, they will compete with each other and will give the resultant dendrite structure which can be used to calculate PDAS.

BR
Chamara

[Bernd]

Hi Chamara,

when you use the systematic method with two dendrites at the left and right side of the domain (using symmetric boundary conditions!), the domain width is identical to the PDAS either when one of the two just stops growing, or half of the domain width when just a third one starts developing.

If you start with many seeds at the beginning, you will get the lower limit of the stable PDAS range as a result, and you need to have a sufficiently large simulation domain for good statistics on PDAS (i.e. you need a sufficiently high number of surviving dendrites).

Bernd

[CharMIC]

Hej Bernd,

I have set up a simulation to simulate the growth of PDAS, as you mentioned. I am not able to get any stable simulation. Simulation finishes quickly and gives completely wrong results. The two grains that I have put is not growing at all.

In the beginning (t=0) of the simulation I get error massages as follows
=========================================================
.....
One-dimensional approximation from z = 65
Temperature at the bottom = 1641.7 K
Temperature gradient = 500.000 K/cm
Simulation area shifted by 0 layers
Velocity of the comoving frame = 0.000 cm/s
trying hard phases 0 1 level: 4 zp= 105 error= 104
trying harder! Error = 104
try even harder! Error = 104
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
# Error number 105 in Interface 0/ 1
# time: 7.288473408805417E-003s
# Serious error in linearisation!
trying hard phases 0 1 level: 4 zp= 206 error= 104
trying harder! Error = 104
try even harder! Error = 104
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
# Error number 105 in Interface 0/ 1
# time: 7.288473408805417E-003s
# Serious error in linearisation!
trying hard phases 0 1 level: 4 zp= 203 error= 104
trying harder! Error = 104
try even harder! Error = 104
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
Forcing automatic start values
Automatic start values will be set

--> Force automatic start values
# Error number 105 in Interface 0/ 2
# time: 7.288473408805417E-003s
# Serious error in linearisation!
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t=1.0526919E-02

Phase 0 disappeared at 1.7003809E-02 s


Phase 1 disappeared at 1.7003809E-02 s
...
========================================================

I have send the files through PM to you.

What could be the reason for this. Waiting for your valuable thoughts and suggestions.

Best Regards
Chamara

[Bernd]

Dear Chamara,

When I try to run your input files on my Windows Notebook, I get exactly the same problem as you. However, I get also the following error messages on calculation of diffusion coefficients during initialisation:

Updating of diffusion data from database...
Old start values kept

*** ERROR 1601 IN QSELEQ
*** NO SUCH EQUILIBRIA

*** ERROR 1601 IN QSELEQ
*** NO SUCH EQUILIBRIA
Thermo-Calc error 1607 MICRESS error 22 phases 1/ 1

This sounds as if there is something wrong with the .GES5 file...

Can you please check the combination of databases? I will have a closer look as soon as possible...

Bernd

[CharMIC]

Hej Bernd,

I didn't understand what you meant by "please check the combination of databases?"

BR
Chamara

[CharMIC]

Hej Bernd,

I also get the error

*** ERROR 1601 IN QSELEQ
*** NO SUCH EQUILIBRIA

*** ERROR 1601 IN QSELEQ
*** NO SUCH EQUILIBRIA

BR
Chamara

[Bernd]

Hej Chamara,

The problem seems to come from the TQ-interface. If I use a newer version than tq9 (version 6.3) in our test environment, the problem vanishes!
Unfortunately, this is not an option for you, as you cannot change easily to a newer TQ version before the next release (MICRESS6.4 is scheduled for November and will come with a TQ-version equivalent to TC2017a).

So, the workaround in the meantime is not to read the diffusion data of phase LIQUID from database. You can use the diffusion coefficients from what I got with the newer version of TQ:

Diffusion coefficients in LIQUID (global):
Time: 0.0000 s
Temperature: 1649.47500000000 K
Composition CR: XXXXXXX wt%
Composition FE: XXXXXXX wt%
Composition NB: XXXXXXX wt%
Components Diff. Coeff. Frequency Term Activation energy
Flux Gradient [cm**2/s] [cm**2/s] [J/mol]
CR CR +3.949E-05 +2.012E-04 +2.233E+04
FE FE +3.360E-05 +1.573E-04 +2.117E+04
NB NB +3.865E-05 +1.521E-04 +1.879E+04

I hope this also works for you

Bernd

[CharMIC]

Hej Bernd,

I have change the code as follows. Hope this is correct.
=============================================
....
# How shall diffusion of component 1 in phase 0 be solved?
1 0 diagonal d
# Diff.-coefficient:
# Prefactor? (real) [cm**2/s]
2.012E-04
# Activation energy? (real) [J/mol]
2.233E+04
#
# How shall diffusion of component 2 in phase 0 be solved?
2 0 diagonal d
# Diff.-coefficient:
# Prefactor? (real) [cm**2/s]
1.573E-04
# Activation energy? (real) [J/mol]
2.117E+04
#
# How shall diffusion of component 3 in phase 0 be solved?
3 0 diagonal d
# Diff.-coefficient:
# Prefactor? (real) [cm**2/s]
1.521E-04
# Activation energy? (real) [J/mol]
1.879E+04
#
......
===================================================


But now the simulation starts. But ran into another problem.
====================================================
Intermediate output for t = 1.0000 s
CPU-time: 21 s
Current phase-field solver time step = 1.00E-02 s
Average conc. of comp. 1 = xxxxxxxx wt%
Average conc. of comp. 2 = xxxxxxxx wt%
Average conc. of comp. 3 = xxxxxxxx wt%
Temperature at the bottom = 640.00 K
Temperature gradient = 500.000 K/cm
Simulation area shifted by 0 layers
Velocity of the comoving frame = 0.000 cm/s
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t= 1.010000
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t= 1.020000
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t= 1.030000
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t= 1.040000
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t= 1.050000
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t= 1.060000
Error number 105 in Interface 0/ 1
time: 1.06000000000000 s
Serious error in linearisation!
Error number 105 in Interface 0/ 2
time: 1.06000000000000 s
Serious error in linearisation!
complete relinearisation!
Relinearisation interface: LIQUID/FCC_L12 t= 1.062039
Error number 105 in Interface 0/ 1
time: 1.06203912986078 s
Serious error in linearisation!
Error number 105 in Interface 0/ 1
time: 1.06203912986078 s
Serious error in linearisation!
Error number 105 in Interface 0/ 1
time: 1.06203912986078 s
Serious error in linearisation!
Error number 105 in Interface 0/ 1
time: 1.06203912986078 s
Serious error in linearisation!
==========================================================

Up to 1 sec there was no error. But at 1 sec. the error occurred. Is this related to TQ interface?