Dear Bernd
I am a new hand to use Micress and my major is welding. Comparing with casting, the cooling rate is very high when welding, especially high welding speed.
e.g. cooling rate is the value less than about -20K/s when casting, while in case of welding, cooling rate is much higher, more than -100K/s or maybe more than -400K/s and the temperature gradient is more than 1000 K/cm under the condition of high welding speed. Right now, I have tried to run Micress. However, the dendrite morphology during growth is different from my experimental solidifying microstructure. It must be not suitable parameters I set. So, I want to consult which parameters should be treated more carefully at the high cooling rate. And can you introduce some solidification examples like this condition.
I am looking forward to your reply.
Thank you.
Best wishes
Weld solidification
Re: Weld solidification
Hi superabc,
Sorry for not answering before, but I am on a trip to the US right now and was not able to contact the forum before!
Essentially, simulation of solidification at high cooling rates makes no specific difference compared to "normal" cooling rates, as long as cooling is not such fast that the local quasi-equilibrium condition doesn't hold anymore. In your case, there should be no such problem. Fast cooling even has some advantages with respect to performance!
Without knowing more details it is difficult to say why in your case there is a strong difference between simulation results and experiments. The best would be if you could show the differences by uploading the corresponding pictures and paste or upload the input file (if not confidential). It is easily possible that some numerical parameters like interface mobility, grid resolution or anisotropy parameter are not chosen correspondingly.
Best wishes
Bernd
Sorry for not answering before, but I am on a trip to the US right now and was not able to contact the forum before!
Essentially, simulation of solidification at high cooling rates makes no specific difference compared to "normal" cooling rates, as long as cooling is not such fast that the local quasi-equilibrium condition doesn't hold anymore. In your case, there should be no such problem. Fast cooling even has some advantages with respect to performance!
Without knowing more details it is difficult to say why in your case there is a strong difference between simulation results and experiments. The best would be if you could show the differences by uploading the corresponding pictures and paste or upload the input file (if not confidential). It is easily possible that some numerical parameters like interface mobility, grid resolution or anisotropy parameter are not chosen correspondingly.
Best wishes
Bernd
Re: Weld solidification
Dear Bernd,
Thank you very much for your reply.
I want to simulate the solidification process during welding. I have upload the dri and GES files. The cooling rate, temperature gradient and liquidus temperature come from experimental data. In case of my experiment, the liquidus temperature is 1670K while normally I think it should be around 1681K compare to our lab previous measurement. Next time I will try to measure temperature history again in order to make sure it is right. I do not know how much the error of liquidus temperature affects simulation data. In addition, this time I did not consider the "latent heat" model. I want to know in case of high cooling rate whether it is necessary to employ "latent heat" model and this time the cooling rate is lowest in my experiment, in the future I will also simulate solidification process using much higher cooling rate.
Moreover, my present simulation data shows that it is like cellular growth and the tip is like triangle. But, my experiment data shows it is cellular dendrite. So, I am confused.
I am looking forward to your reply.
All the best
Thank you very much for your reply.
I want to simulate the solidification process during welding. I have upload the dri and GES files. The cooling rate, temperature gradient and liquidus temperature come from experimental data. In case of my experiment, the liquidus temperature is 1670K while normally I think it should be around 1681K compare to our lab previous measurement. Next time I will try to measure temperature history again in order to make sure it is right. I do not know how much the error of liquidus temperature affects simulation data. In addition, this time I did not consider the "latent heat" model. I want to know in case of high cooling rate whether it is necessary to employ "latent heat" model and this time the cooling rate is lowest in my experiment, in the future I will also simulate solidification process using much higher cooling rate.
Moreover, my present simulation data shows that it is like cellular growth and the tip is like triangle. But, my experiment data shows it is cellular dendrite. So, I am confused.
I am looking forward to your reply.
All the best
- Attachments
-
- FeCrNi dri and GES.rar
- (12.85 KiB) Downloaded 411 times
Re: Weld solidification
Hi superabc,
Indeed, in your case the initial undercooling is critical! If you check the driving force in the initial linearisation output in the .log file, you find a driving force dG of about -18J/cm3 which correspond to an undercooling of
T = G/S of about 25K. Such a high undercooling value would lead to a transient very fine microstructure which requires different numerical parameter compared to "stationary" growth.
So, the crucial point is to find suitable numerical parameter for the process conditions, i.e. primarily the interface mobility and grid resolution for the given undercooling/cooling rate. In your case, the choice of a high initial undercooling on one side and a low interface mobility on the other side has lead to a practically linear solidification front forming the "triangle" as you said. The reason is that the high kinetic undercooling (due to a low interface mobility) completely overrides the curvature contribution which would trigger the morphological (dendritic) instability. At the same time, diffusion is so slow (or grid resolution) that the component pile-up before the front and corresponding differences in constitutional undercooling are not formed - essentially, the diffusion length should always be bigger than the interface thickness!
As you see, there are several things to consider, and typically several steps are needed to approach suitable numerical conditions. As a first step, you should increase the initial temperature at the bottom by say 20K in order to start closer to steady state conditions. You will see that morphology is already much different. But you will also see that the kinetic undercooling (as seen in the .driv output) will increase steadily, denoting a too low interface mobility. Essentially, what you see as chemical driving force is the sum of the kinetic and the curvature undercooling. A qualitatively correct interface mobility is reached when the curvature contribution is visible (alternating sign of .driv output along the concave and convex parts of the dendrite arms, see also here).
But probably, while stepwise increasing the interface mobility, at some point, the interface will become numerically unstable, leading to a broadening of the interface or even completely semisolid structures. If this is the case, either the interface mobility is already too high, or a higher grid resolution is needed. I guess that in your case, a higher resolution,i.e a smaller grid size will be necessary. But be careful, as too high resolution kills performance...
But before starting this adventure, you should consider to make some further corrections:
- On the screen output, you get some warning about multibinary "demixing" for element Ni. The best way to get around that is to use our new ternary extrapolation scheme which is simple and fine for a ternary system. You can achieve that by adding the line
interaction 1 2
to the phase diagram input data just before the "no_stoichio" keyword.
- It may be better to use the fd_correction scheme (extra keyword after "double_obstacle" in the flags section) and reduce the interface thickness to 3 or even 2.5 cells. This reduces the tendency of interface broadening
- for the same reason, you should use stronger averaging of the driving force (a value closer to 1, like e.g. 0.9, after the keyword "avg" in the dG options (phase interaction data)), and perhaps reduce the static anisotropy parameter from 0.5 to perhaps 0.2
- you should start your trials with a much smaller simulation domain, otherwise the procedure will take you forever!
- you should decrease the output interval for tablog outputs (.TabL, .TabP, .TabT, etc.) to get more information on how the simulation is proceeding (at the end of "Selection of Outputs")
Please tell me how it works for you!
Good luck!
Bernd
Indeed, in your case the initial undercooling is critical! If you check the driving force in the initial linearisation output in the .log file, you find a driving force dG of about -18J/cm3 which correspond to an undercooling of
So, the crucial point is to find suitable numerical parameter for the process conditions, i.e. primarily the interface mobility and grid resolution for the given undercooling/cooling rate. In your case, the choice of a high initial undercooling on one side and a low interface mobility on the other side has lead to a practically linear solidification front forming the "triangle" as you said. The reason is that the high kinetic undercooling (due to a low interface mobility) completely overrides the curvature contribution which would trigger the morphological (dendritic) instability. At the same time, diffusion is so slow (or grid resolution) that the component pile-up before the front and corresponding differences in constitutional undercooling are not formed - essentially, the diffusion length should always be bigger than the interface thickness!
As you see, there are several things to consider, and typically several steps are needed to approach suitable numerical conditions. As a first step, you should increase the initial temperature at the bottom by say 20K in order to start closer to steady state conditions. You will see that morphology is already much different. But you will also see that the kinetic undercooling (as seen in the .driv output) will increase steadily, denoting a too low interface mobility. Essentially, what you see as chemical driving force is the sum of the kinetic and the curvature undercooling. A qualitatively correct interface mobility is reached when the curvature contribution is visible (alternating sign of .driv output along the concave and convex parts of the dendrite arms, see also here).
But probably, while stepwise increasing the interface mobility, at some point, the interface will become numerically unstable, leading to a broadening of the interface or even completely semisolid structures. If this is the case, either the interface mobility is already too high, or a higher grid resolution is needed. I guess that in your case, a higher resolution,i.e a smaller grid size will be necessary. But be careful, as too high resolution kills performance...
But before starting this adventure, you should consider to make some further corrections:
- On the screen output, you get some warning about multibinary "demixing" for element Ni. The best way to get around that is to use our new ternary extrapolation scheme which is simple and fine for a ternary system. You can achieve that by adding the line
interaction 1 2
to the phase diagram input data just before the "no_stoichio" keyword.
- It may be better to use the fd_correction scheme (extra keyword after "double_obstacle" in the flags section) and reduce the interface thickness to 3 or even 2.5 cells. This reduces the tendency of interface broadening
- for the same reason, you should use stronger averaging of the driving force (a value closer to 1, like e.g. 0.9, after the keyword "avg" in the dG options (phase interaction data)), and perhaps reduce the static anisotropy parameter from 0.5 to perhaps 0.2
- you should start your trials with a much smaller simulation domain, otherwise the procedure will take you forever!
- you should decrease the output interval for tablog outputs (.TabL, .TabP, .TabT, etc.) to get more information on how the simulation is proceeding (at the end of "Selection of Outputs")
Please tell me how it works for you!
Good luck!
Bernd
Re: Weld solidification
Dear Bernd,
Thank you very much for your explanation and advice.
I have already run simulation according to your suggestions. Yes, the morphology of dendrite is much different from the previous one.
However, there are still some points I am confused.
1) The initial temperature at the bottom was increased to 1690K from actual liquidus temperature 1970K in order to start closer to steady state conditions. However, by checking "_TabF" file when the temperature decreased to 1670K, the fraction of phase 1was about 23%. I do not know why temperature just reaches to liquidus temperature, the fraction of phase 1 is so high.
2) The surface energy, kinetic coefficient, anisotropy of interfacial stiffness and anistropy of interfacial mobility are important factors with respect to morphology of dendrite. However, I do not understand how to set surface energy or anistropy in case of high cooling rate. Could you give me some detail information?
3) In case of high laser welding speed, according to the freezing solidifying structure, there is an angle between the dendrite growth direction and temperature gradient. Thus, I think that in actual simulation the "rotation angle" of initial grain is just set to the same value compared with the angle between dendrite growth direction and temperature gradient.
Here I upload the concentration 1 field and modified drive file.
I am looking forward to your reply.
All the best,
Thank you very much for your explanation and advice.
I have already run simulation according to your suggestions. Yes, the morphology of dendrite is much different from the previous one.
However, there are still some points I am confused.
1) The initial temperature at the bottom was increased to 1690K from actual liquidus temperature 1970K in order to start closer to steady state conditions. However, by checking "_TabF" file when the temperature decreased to 1670K, the fraction of phase 1was about 23%. I do not know why temperature just reaches to liquidus temperature, the fraction of phase 1 is so high.
2) The surface energy, kinetic coefficient, anisotropy of interfacial stiffness and anistropy of interfacial mobility are important factors with respect to morphology of dendrite. However, I do not understand how to set surface energy or anistropy in case of high cooling rate. Could you give me some detail information?
3) In case of high laser welding speed, according to the freezing solidifying structure, there is an angle between the dendrite growth direction and temperature gradient. Thus, I think that in actual simulation the "rotation angle" of initial grain is just set to the same value compared with the angle between dendrite growth direction and temperature gradient.
Here I upload the concentration 1 field and modified drive file.
I am looking forward to your reply.
All the best,
- Attachments
-
- drive file and picture.rar
- (65.17 KiB) Downloaded 304 times
Re: Weld solidification
Hi superabc,
looks much better!
1.) From where do you know that 1670K is the "actual" liquidus temperature? According to the database, it is slightly above 1690K, and that is what we are using! Maybe, the database is wrong...
2.) The way how you chose all these values in principle does not depend on whether you have fast or slow cooling! The most important parameter which depends on the cooling conditions is the interface mobility. The way how to determine it is always the same (see link in my previous post). The resulting value of course depends on the cooling conditions, but also on the resolution etc.
Anisotropy values are, strictly speaking, physical values, but mostly unknown and often used to compensate numerical effects like grid anisotropy...
3.) That is correct! In a later stage, you could think of setting different initial grains with different orientations, then you could observe selection of different orientations.
If you observe that the dendrites are not following its given orientation, numerical parameters are possibly wrong or resolution is too low.
Bernd
looks much better!
1.) From where do you know that 1670K is the "actual" liquidus temperature? According to the database, it is slightly above 1690K, and that is what we are using! Maybe, the database is wrong...
2.) The way how you chose all these values in principle does not depend on whether you have fast or slow cooling! The most important parameter which depends on the cooling conditions is the interface mobility. The way how to determine it is always the same (see link in my previous post). The resulting value of course depends on the cooling conditions, but also on the resolution etc.
Anisotropy values are, strictly speaking, physical values, but mostly unknown and often used to compensate numerical effects like grid anisotropy...
3.) That is correct! In a later stage, you could think of setting different initial grains with different orientations, then you could observe selection of different orientations.
If you observe that the dendrites are not following its given orientation, numerical parameters are possibly wrong or resolution is too low.
Bernd
Re: Weld solidification
Dear Bernd,
Thanks for your explanation.
In case of "actual" liquidus temperature, I measured the temperature history using fiber optical thermometer during welding solidification experiment. Then, according to differential curve, the experimental liquidus temperature shows 1670K. Yes, the equilibrium temperature is around 1690K from the calculation of thermo-clac. However, it is non-equilibrium during solidification, specially at the high cooling rate and my data is 1670K. In addition, in the future, the cooling rate of my experiment may be around 4000K/s, I want to know whether Micress can afford.
I want to simulate two dendrites growth process during solidification compared with experiement. From the experiment, the primary dendrite arm spacing is about 9 μm. I want to ask how to set the distance between two initial nucleation grains when setting the drive file.
All the best
Thanks for your explanation.
In case of "actual" liquidus temperature, I measured the temperature history using fiber optical thermometer during welding solidification experiment. Then, according to differential curve, the experimental liquidus temperature shows 1670K. Yes, the equilibrium temperature is around 1690K from the calculation of thermo-clac. However, it is non-equilibrium during solidification, specially at the high cooling rate and my data is 1670K. In addition, in the future, the cooling rate of my experiment may be around 4000K/s, I want to know whether Micress can afford.
I want to simulate two dendrites growth process during solidification compared with experiement. From the experiment, the primary dendrite arm spacing is about 9 μm. I want to ask how to set the distance between two initial nucleation grains when setting the drive file.
All the best
Re: Weld solidification
OK, you are right! In the ideal case one would set the initial seed close to the stationary tip temperature which may be well below the liquidus (equilibrium) temperature! But taking the experimental "liquidus" temperature may be dangerous because a) the database or the experiment may be incorrect, and b) tip undercooling in 2D and 3D are strongly different!
My proposal was to start the simulation close to equilibrium temperature (at least as first trial) as it is the safest variant because it is more easy to calibrate coming from the "stable" side...
If you want to do a simulation with exactly 2 dendrites, then you should set them with the experimental distance. You can also simulate a "selected" distance like you did, but it is not so straightforward to compare this distance to the experimental, as there is the 2D/3D problem, and there is the problem of a stability range of a factor of 2 in 2D, and thus, that the primary distance is history dependent!
The question whether you can simulate 4000K/s without special considerations is not so easy to answer - important is whether under these circumstances the local equilibrium is still reasonable, or whether there is already substantial solute trapping. If there really is strong solute trapping, it could either be taken into account by modification of thermodynamics, or by (at least qualitatively) making use of the numerical trapping "artefacts" of the phase-field model. Complete trapping of one element could be simulated using the MICRESS para-equilibrium models.
Best wishes
Bernd
My proposal was to start the simulation close to equilibrium temperature (at least as first trial) as it is the safest variant because it is more easy to calibrate coming from the "stable" side...
If you want to do a simulation with exactly 2 dendrites, then you should set them with the experimental distance. You can also simulate a "selected" distance like you did, but it is not so straightforward to compare this distance to the experimental, as there is the 2D/3D problem, and there is the problem of a stability range of a factor of 2 in 2D, and thus, that the primary distance is history dependent!
The question whether you can simulate 4000K/s without special considerations is not so easy to answer - important is whether under these circumstances the local equilibrium is still reasonable, or whether there is already substantial solute trapping. If there really is strong solute trapping, it could either be taken into account by modification of thermodynamics, or by (at least qualitatively) making use of the numerical trapping "artefacts" of the phase-field model. Complete trapping of one element could be simulated using the MICRESS para-equilibrium models.
Best wishes
Bernd
Re: Weld solidification
Dear Bernd,
Thank you for your advice.
I have already tried to simulate two dendrites growth process. Before running, the distance between two initial nucleation grains is 10 μm. In my experiment, the primary dendrite arm spacing is about 9 μm and the secondary dendrite arm can be identified clearly, about 3 μm. I just want to know how it works during two dendrites growth. However, the result looks like cell growth parallelly along the temperature gradient from bottom to top of domain and no secondary dendrite arm appears between two dendrites. I also tried to reset the parameters, like surface energy and mobility (adjusting range is not too much), while morphology did not change much. Thus, I want to know how to deal with, or maybe some parameters (like temperature gradient or cooling rate from experiment) is not very precise.
All the best
Thank you for your advice.
I have already tried to simulate two dendrites growth process. Before running, the distance between two initial nucleation grains is 10 μm. In my experiment, the primary dendrite arm spacing is about 9 μm and the secondary dendrite arm can be identified clearly, about 3 μm. I just want to know how it works during two dendrites growth. However, the result looks like cell growth parallelly along the temperature gradient from bottom to top of domain and no secondary dendrite arm appears between two dendrites. I also tried to reset the parameters, like surface energy and mobility (adjusting range is not too much), while morphology did not change much. Thus, I want to know how to deal with, or maybe some parameters (like temperature gradient or cooling rate from experiment) is not very precise.
All the best
Re: Weld solidification
Hi superabc,
When a dendrite is not showing side branches, this can be either due to the physical parameters (too low primary distance, too high interface energy), or due to numerical parameters (interface mobility). You can distinguishing the two cases by looking at the .driv output: In case of a too low mobility, the values of the driving force shown in this output (kinetic plus curvature undercooling) is too high, and the sign is not alternating with the sign of curvature (i.e. curvature undercooling is not bigger than kinetic undercooling). In the latter case, the formation of side branches may be suppressed.
If increasing the interface mobility leads to broadening of the interfaces, grid resolution or dG averaging must be increased.
Bernd
When a dendrite is not showing side branches, this can be either due to the physical parameters (too low primary distance, too high interface energy), or due to numerical parameters (interface mobility). You can distinguishing the two cases by looking at the .driv output: In case of a too low mobility, the values of the driving force shown in this output (kinetic plus curvature undercooling) is too high, and the sign is not alternating with the sign of curvature (i.e. curvature undercooling is not bigger than kinetic undercooling). In the latter case, the formation of side branches may be suppressed.
If increasing the interface mobility leads to broadening of the interfaces, grid resolution or dG averaging must be increased.
Bernd