Weld solidification

[superabc]

Hi Bernd,

It is me again. I am still confused about the anisotropy.

I have already read "input of static anisotropy changed!" post. Some contents are as follows:
For cubic ansitropy in 2D, sigma is defined by:
sigma(phi) = sigma0 (1 + delta cos (4 phi))
where delta is the static anisotropy coefficient From this, the effective stiffness can be derived to be:
sigma*(phi) = sigma0 (1 - 15 delta cos (4 phi))
= sigma0 (1 - delta* cos (4 phi))
This effective anisotropy coefficient delta*= 15 delta is read in the present MICRESS version.

And you also said that the the difference in the order of magnitude of static anisotropy coefficients comes from the facetor of 16 between anisotrypy in sigma and in sigma*.

Here, one is delta*= 15 delta, and another is the facetor of 16. I do not know when i use previous paper's anisotropies to try to simulate, I should use their delta multiplied by 15 or 16. And you just mentioned the changing of static anisotropy. In the case of 2D, cubic metal, whether kinetic anisotropy should also multiplied by 15 or 16.

Moreover, except for citing other references' parameters, are there some other effective methods to obtain suitable parameters like interface energy and kinetic and anisotropy and so on ? Or by changing parameters, check results and run again after modifying parameters again and Again, untill the relative correct parameters are discovered and the result is in a good agreement with experiment. I guess it need longer time.

Superabc

[Bernd]

You are right, it is 15 and not 16! The 16 comes from the second derivative of , but one cancels out with itself...

Unfortunately, there is no more effective way of obtaining those parameters - the physical ones have to be taken either from literature or have to be estimated or calibrated against experimental observations! The same holds for numerical parameters like the interface mobility (in case of diffusion-limited growth), although those can furthermore be obtained by calibration against high-resolution simulations where the results depend less on them...

Bernd

[superabc]

Hello Bernd,

Under the same physical parameters and only changing cooling rates and corresponding primary dendrite arms, when i run the simulation to 1.0 sec, it appeared warning and closed the window by itself at the cooling rate of 12.5 K/cm. However, for another two simulation it was no problem and could run to longer time like 5 sec. I did not understand. Could you explain? And here is the warning. I put the driving file.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Warning in spfAddPhInkr, t= 1.008331
Wrong fractions at nTupelp= 15258
sum = 0.000000
x,y,z = 805 1 3
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Superabc

[Bernd]

Hi superabc,

This error occurs when in one time step a high phase-field increment occurs at a triple junction which is bigger than 1. Then, the list operations may fail and this error message is displayed. The reason for such high increments can be not suitable numerical parameters like too high mobility, an extremely high driving force at this point, or other numerical incidences.

In a first step, you should check whether due to rescaling of the cooling rate you have left the numerically stable regime, and you would need to recalibrate the setup (grid resolution, interface mobility, etc.).

Sometimes, this problem occurs only at a certain time in a specific region, e.g directly after nucleation. If the general numerical setup is correct or cannot be changed, another solution for temporary extreme kinetic situations is available: For each phase interaction a maximum value can be chosen for the driving force dG in the driving force options (phase interaction data). This provides a smooth cutoff of the driving force (and thus of the increment), which should be well above all realistic dG values (please check in the .driv output).
I personally use this option by default. I typically chose "max 50" (J/cm3) for primary phases like fcc and bcc and "max 1000" for intermetallic phases.
This option must be used carefully because it would affect growth kinetics and anisotropy if chosen too small!

Bernd

[superabc]

Hi Bernd,

Thank you very much for your suggestions.

When I check driv. mcr file, the color scale range is between less than -1000 or -2000 to 0 and i could not find the driving force contour line. Normally, the value should be from -50 to 0, isn't it? Inaddition, today i did not change any parameters and tried again to run for investigating the initial driv. mcr file at the beginning. I found that at the beginning the value was just between -2 to 0. It means the running is OK just after nucleation. Thus, I guess maybe the problem will occur when the secondary phase appears.

And right now I set "max 50.0" between phase 0 and phase 1, phase 0 and phase 2, and phase 1 and phase 2. I hope later it shows desired resluts.

Superabc

[superabc]

Hi Bernd:

Recently, I want to know how to use noise [J/cm**3] in the DeltaG options in the part of "phase interaction data".

In the case of high cooling rate, the interface is unstable and small secondary arms should appear. However, in the case of previous simulation results, I could not obtain secondary dendrite arm in very narrow primary dendrite arm spacing 10 um (from experimental measurement) in spite of chaning lots of parameters, such as anisotropy, kinetic coefficient and interface thickness. I did not change the value of interface energy. I know interface energy affects mainly the dendrite morphology and if I decreased interface energy to an order of magnitude, I could obtain secodnary dendrite arm spacing. However, professor disagreed with the changing of interface energy (from reference paper) due to no theory about influence of cooling rate no interface energy.

So, I want to set noise to obtain proper secondary dendrite arm. Could you explain how I set the value of noise.

And could you give me some other suggestions in order to obtain secondary dendrite arm.

Superabc

[Bernd]

Hi superabc,

For including noise you just add the keyword "noise" with a corresponding value of the noise amplitude to the input line for dG options, e.g.

# 'DeltaG' options: default
# avg ... [] max ... [J/cm**3] smooth ... [degrees] noise ... [J/cm**3]
avg 0.55 max 100 noise 10.


You should see the effect in the .driv output and hopefully in the formation of side branches...

If you do not get side branches although you should, it could be due to incorrect physical parameters (interface energy, diffusion coefficients) or numerical parameters (interface mobility). But I think we discussed that already.

Bernd

[superabc]

Hi Bernd:

Thank you for your reply.

In the case of solidus temperature, before I have already had a test for checking whether "Tab F" could decide solidus temperature, however I think maybe it cannot decide the solidus temperature.
For example: two tests have the same prarmeters except "AnzZ". For "AnzZ", test 2 is test 1 two times.
And from "Tab F" the fraction of phase 1 in test 1 is just that test 2 two times at the same temperature during running simulation.
So, I think by using "Tab F" maybe it cannot decide the solidus temperature. The ''Fraction phase 1 in Tab F" means the ratio of the area of formed phase 1 to domain area.
Are there some other method to decide solidus temperature ?

All the best,
Superabc

[Bernd]

Dear superabc,

the problem of how to determine the solidus temperature is more complicated in your caseby due to the temperature gradient. For this reason, you are right, the global phase fraction of liquid taken from the .TabF output does not provide you this information.
In principle, one method could be to search for the lowest position of rest liquids and determine the temperature of these sites from the .temp output (or from the bottom temperature and the temperature gradient. This requires a stationary growth of the dendrite and leads only to statistical information, because for each output time step the analysis would lead to different results.

I remember that I had a similar problem for continuous casting of low-alloyed steels where I wanted to determine the coalescence temperature (B. Böttger, M. Apel, B. Santillana, and D.G. Eskin, Metallurgical and Materials Transactions A 44 5 (2013) 3765. Therefore it was necessary to determine the fraction solid-temperature curve in the presence of a temperature gradient. The solution was to build a script which allowed evaluating the fraction solid for each isothermal line, i.e. for each single row of grid cells perpendicular to the z direction. Accumulating these data for many output time steps and subsequent smoothing of the very noisy results lead to a smooth fraction solid-temperature curve which allowed me to estimate the coalescence temperature (for fraction solid 0.99).
In the same way, it should be possible to determine the solidus temperature. I don't know whether I still have this script, but it should also be possible to convert the data to ASCII format and to do the analysis in Excel.

Best wishes

Bernd

[superabc]

Hi Bernd:

I want to use teperature profile for simulation. In the case of boundary conditions for driving file, I want to chose “profiles_from_file” in the type of temperature trend. However, I do not know how to make the ASCII data files and set connecting point time. Could you please show me how to make this?

All the best
superabc