Hello,
I'm currently doing MICRESS simulations for martensitic tool steel during selective laser melting process. I'm frequently facing the following errors during the simulation,
trying harder! Error = 1
trying hard phases 0 1 level: 4 zp= 40164 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 4 zp= 40166 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 4 zp= 40169 error= 1
trying hard phases 0 1 level: 4 zp= 40170 error= 3
trying harder! Error = 3
trying hard phases 0 1 level: 4 zp= 40171 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 6 zp= 40172 error= 3
trying harder! Error = 1
trying hard phases 0 1 level: 5 zp= 40173 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 4 zp= 40174 error= 3
trying harder! Error = 3
trying hard phases 0 1 level: 4 zp= 40175 error= 3
trying harder! Error = 1
trying hard phases 0 1 level: 4 zp= 40176 error= 3
trying harder! Error = 1
trying hard phases 0 1 level: 5 zp= 40177 error= 1
trying hard phases 0 1 level: 4 zp= 40178 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 4 zp= 40179 error= 1
trying harder! Error = 3
trying hard phases 0 1 level: 4 zp= 40368 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 4 zp= 40371 error= 3
trying harder! Error = 3
trying hard phases 0 1 level: 4 zp= 40373 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 5 zp= 40374 error= 1
trying harder! Error = 1
trying hard phases 0 1 level: 5 zp= 40375 error= 3
trying hard phases 0 1 level: 4 zp= 40379 error= 104
trying harder! Error = 1
--> Relinearisation in interface of grains 0/ 1 t=0.8155584E-03
due to a T deviation of 1143008. K
trying hard phases 1 0 level: 5 zp= 1603 error= 1
trying hard phases 1 0 level: 3 zp= 6049 error= 3
There is no such error until 50% of solidification. After around 50% of solidification, terminal showing this error between every time steps. Because of this, simulation became very slow. It took 5-6 days to finish 80% solidification because of the errors. Now after 80% of solidification, there is no progress in the simulation. I can only see continuous errors as shown above. I only have two phases Liquid and Austenite (FCC_A1), 6 components. It is strange that the simulation is taking too much time. But the cooling rate is high, -1.0E6K/s. Please have a look at .GES5 file for the components, phases details.
Simulation parameters:
size: 200 x 200, spacing: 0.025
Phase interaction between 0/1:
Surface energy between phases Liquid and 1, 5.0E-5 J/cm**2
Kinetic coeff µ between phases Liquid and 1, 1.0E-2 cm**4/Js
No phase interaction between 1/1
Allowed diffusion of components 1,2,3,4,5,6 in 0
Prefactor 1.0E-05
Activation energy 0.0
No diffusion of components 1,2,3,4,5,6 in 1(Carbon)
I tried to optimize the above parameters to resolve the issue. But I couldn't stop these errors. Kindly have a look at my simulation and give your opinions. Please also write me if you need any further details.
Thank you very much!
Best regards
Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
- Attachments
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- Error_1011.JPG (174 KiB) Viewed 7422 times
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- TC_DATA_TCFe9.GES5
- (96.2 KiB) Downloaded 284 times
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Dear vamsi,
The error you show are not very characteristic. I would look first for the following:
1.) Thermodynamic problems like apparent demixing due to the pseudo-binary approximation, or solidus/liquidus slopes which are close to 0. To find this problem, you need to check the .TabLin output. Remedies would be to use the "interaction" keyword to switch to diagonal extrapolation mode in case of demixing, or to define those components manually as stoichiometric.
2.) Check whether poor numerical conditions lead to spreading of the interface which indirectly leads to the error messages. You should check any output which allows you to see the thickness of the interface (.intf, .mueS, .driv, .frac1, ...). The remedy would be to decrease the interface mobility, use averaging of the driving force, increase the interface stiffness, add a stabilisation to the interface stiffness, increase spatial resolution.
3.) Interface undercooling is too high which leads to thermodynamic problems (as a consequence of a too large deviation from equilibrium). Check the .driv output to see whether this is the case. The solution would be to increase the interface mobility.
4.) Negative compositions could occur in one of the two phases. To find out, you need to check the .c*pha0 and .c*pha1 outputs whether there are regions (not just single points) which are negative. To solve the problem, more frequent relinearisation or using user limits ("limits" keyword in section of stoichiometric phases) can be the solution.
Of course, it can be something else - but I would check out these four things first...
Bernd
The error you show are not very characteristic. I would look first for the following:
1.) Thermodynamic problems like apparent demixing due to the pseudo-binary approximation, or solidus/liquidus slopes which are close to 0. To find this problem, you need to check the .TabLin output. Remedies would be to use the "interaction" keyword to switch to diagonal extrapolation mode in case of demixing, or to define those components manually as stoichiometric.
2.) Check whether poor numerical conditions lead to spreading of the interface which indirectly leads to the error messages. You should check any output which allows you to see the thickness of the interface (.intf, .mueS, .driv, .frac1, ...). The remedy would be to decrease the interface mobility, use averaging of the driving force, increase the interface stiffness, add a stabilisation to the interface stiffness, increase spatial resolution.
3.) Interface undercooling is too high which leads to thermodynamic problems (as a consequence of a too large deviation from equilibrium). Check the .driv output to see whether this is the case. The solution would be to increase the interface mobility.
4.) Negative compositions could occur in one of the two phases. To find out, you need to check the .c*pha0 and .c*pha1 outputs whether there are regions (not just single points) which are negative. To solve the problem, more frequent relinearisation or using user limits ("limits" keyword in section of stoichiometric phases) can be the solution.
Of course, it can be something else - but I would check out these four things first...
Bernd
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Hello Bernd,
Thank you very much for your inputs. I have gone through your feedback and my feedback below goes in the same order.
1) In the .TabLin output, what do you mean by solidus/liquidus slopes which are close to 0 ?. The lowest slope I can find is -0.01. Is this number is close to 0 or is it ok ?. I think "interaction" keyword that you mentioned is from Phase input data . I just used "interaction" before, but there it says to mention "interaction, component 1, component 2". How these both keywords differ? In case, I have to choose the second one for the current error, how do I choose the components(e.g. interaction 1 2)? I couldn't decide which components I should insert after 'interaction' from the slope data.
2) poor numerical conditions lead to spreading of the interface: As of now, I feel this is not the reason for the error.
3) Interface undercooling is too high which leads to thermodynamic problems : I checked the .driv file. I can the interface goes beyond -100 and +100. But the max allowed value is 100 in the phase interaction data. So as you've advised, I increased the interface mobility to 2E-2 from 1E-2 and running a simulation separately.
4) Negative compositions : In .TabC file, I can see the negative compositions in the only in the Minumum column for 6 components in phases 0 and 1. Out of 6, 4 in 0, 2 in 1, 5 in 1 showed frequent negative compositions, rarely showed in 3 in 1, started showing negative compositions just before the simulation stopped. To check this, I put up two simulations with using Limits for the above combinations. One simulation using Limits for 3 frequent ones (0 1, 1 2, 1 5) of 6 and the other with all 6 combinations(0 4, 1 2, 1 5, 1 1, 0.5, 1 3). I also used "interaction" just before using "Limits" for these two simulations. I'm running one more simulation with increased relinearization steps as you've advised.
I'll write again once I finish the above-mentioned simulations. Meanwhile, please write me if something wrong in my understanding of your feedback. I'm attaching the driving file (without compositions), could you please check it and give further ideas regarding the error.
Thank you very much for your inputs. I have gone through your feedback and my feedback below goes in the same order.
1) In the .TabLin output, what do you mean by solidus/liquidus slopes which are close to 0 ?. The lowest slope I can find is -0.01. Is this number is close to 0 or is it ok ?. I think "interaction" keyword that you mentioned is from Phase input data . I just used "interaction" before, but there it says to mention "interaction, component 1, component 2". How these both keywords differ? In case, I have to choose the second one for the current error, how do I choose the components(e.g. interaction 1 2)? I couldn't decide which components I should insert after 'interaction' from the slope data.
2) poor numerical conditions lead to spreading of the interface: As of now, I feel this is not the reason for the error.
3) Interface undercooling is too high which leads to thermodynamic problems : I checked the .driv file. I can the interface goes beyond -100 and +100. But the max allowed value is 100 in the phase interaction data. So as you've advised, I increased the interface mobility to 2E-2 from 1E-2 and running a simulation separately.
4) Negative compositions : In .TabC file, I can see the negative compositions in the only in the Minumum column for 6 components in phases 0 and 1. Out of 6, 4 in 0, 2 in 1, 5 in 1 showed frequent negative compositions, rarely showed in 3 in 1, started showing negative compositions just before the simulation stopped. To check this, I put up two simulations with using Limits for the above combinations. One simulation using Limits for 3 frequent ones (0 1, 1 2, 1 5) of 6 and the other with all 6 combinations(0 4, 1 2, 1 5, 1 1, 0.5, 1 3). I also used "interaction" just before using "Limits" for these two simulations. I'm running one more simulation with increased relinearization steps as you've advised.
I'll write again once I finish the above-mentioned simulations. Meanwhile, please write me if something wrong in my understanding of your feedback. I'm attaching the driving file (without compositions), could you please check it and give further ideas regarding the error.
- Attachments
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- micress.dri
- (17.69 KiB) Downloaded 315 times
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Dear vamsi,
let me answer one by one:
1.) A value of -0.01 is is definitively small, because it means that changing this composition by 1% in this phase would only cause an undercooling of 0.01 K! That means, if it is true, that the system can change it easily without counter-force, which makes the system very unstable. The expected fluctuations of this element should be visible in the corresponding .concX or .cXpha1 output.
I would advise you to use "interaction" without further specifying the two components. Without further arguments it switches fully to diagonal extrapolation mode. With two element numbers given, it would introduce ternary extrapolation terms for the sub-ternary consisting of the matrix component plus the two specified components. This is not helpful here.
2.) ok
3.) If the .driv output fluctuates between -100 and 100, the mobility could be too high. However, if the .driv output sticks to -100 you should increase the interface mobility. A factor of 2 could be not sufficient.
4.) You should not check .TabC for negative compositions, because you always see only the minimum, even if it is just one irrelevant grid cell. Please check the .c*pha* output which you should write for both phases:
out_conc_phase 0 | 1
Then, check for persistent negative regions (not just single grid points). This could give a hint for the origin of the errors.
Furthermore, you specified double updating of the thermodynamic data: first by a constant interval of 1E-7 s, and second by a temperature deviation of 10 K (which is effectively calculated including the local concentration deviations). The latter is not necessary and not helpful - please put "none" instead of "automatic".
You also should set a much smaller tab_log interval so that you can take advantage of the tablog outputs (.TabL, .TabT, .TabP, .TabTQ).
Bernd
let me answer one by one:
1.) A value of -0.01 is is definitively small, because it means that changing this composition by 1% in this phase would only cause an undercooling of 0.01 K! That means, if it is true, that the system can change it easily without counter-force, which makes the system very unstable. The expected fluctuations of this element should be visible in the corresponding .concX or .cXpha1 output.
I would advise you to use "interaction" without further specifying the two components. Without further arguments it switches fully to diagonal extrapolation mode. With two element numbers given, it would introduce ternary extrapolation terms for the sub-ternary consisting of the matrix component plus the two specified components. This is not helpful here.
2.) ok
3.) If the .driv output fluctuates between -100 and 100, the mobility could be too high. However, if the .driv output sticks to -100 you should increase the interface mobility. A factor of 2 could be not sufficient.
4.) You should not check .TabC for negative compositions, because you always see only the minimum, even if it is just one irrelevant grid cell. Please check the .c*pha* output which you should write for both phases:
out_conc_phase 0 | 1
Then, check for persistent negative regions (not just single grid points). This could give a hint for the origin of the errors.
Furthermore, you specified double updating of the thermodynamic data: first by a constant interval of 1E-7 s, and second by a temperature deviation of 10 K (which is effectively calculated including the local concentration deviations). The latter is not necessary and not helpful - please put "none" instead of "automatic".
You also should set a much smaller tab_log interval so that you can take advantage of the tablog outputs (.TabL, .TabT, .TabP, .TabTQ).
Bernd
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Dear Bernd,
Thank you again!
In continuation of your previous response (In 4th answer), you've said the checking persistent negative regions will give a hint of the origin of the error. How do I avoid those negative regions? Do you mean by using <Limts>?
As you've advised, I put up the all new simulations with adding output "out_conc_phase 0 | 1", using "interaction" without specifying two components in the Phase input data and put "none" for Relinearisation mode for interface 0 / 1.
Simulation 1) I increased mobility to 2E-02 from 1E-02. It showed noticeable impact, the simulation was running fastly as expected and finished. The final fraction of Liquid and Phase 1 after completion is mentioned below. After the completion, terminal showed continuous errors like before. With the liquid fraction below, can I consider this simulation as finished?
# Simulation Temperature Fraction Fraction
# time [s] [K] Liquid Phase 1
5.190000E-04 1233.50000 0.00149554 0.99850446
However, I can see negative compositions in the .c*phase* output files. Continuous negative compositions have been observed for .c4phas0 , .c2phas1, .c3phas1, .c5phas1 files and few other .c*phas* files showed negative compositions at the end just before the simulation stopped. So I didn't consider that. I updated the code with 'Limits' keyword as below and started a new simulation. Kindly find the attachemnt of driving file for this simulation.
Limits 0 4 0 100
Limits 1 2 0 100
Limits 1 3 0 100
Limits 1 5 0 100
The new simulation is finished as well and showed continuous negative compositions for .c4phas0 , .c2phas1, .c5phas1 files and few other .c*phas* files showed negative compositions at the end just before the simulation stopped. Do you think the upper and lower values that I mentioned in the code are good enough?
The other three simulations(mentioned below) like I mentioned in the previous message with mobility 1E-2 are showing the same errors and running slowly with 60% of phase 1 solidification. These three have negative compositions for the same .c4phas0 , .c2phas1, .c5phas1 files.
Simulation 2) mobility 1E-2 + using Limits keyword as in simulation 1
Simulation 3) mobility 1E-2 but not <Limits> . I ran this just to check the differences in the results because of Limits keyword. By comparing the .c*phas* files, I couldn't really understand the effect of <Limts> keyword. will decreasing the upper value in the code help?
Simulation 4) mobility 1E-2 + increased relinearizatin steps. I think the relinearization mode which is changed to 5e-8 to 1e-7 is not helping much.
As you advised, I'll increase the mobility more than 2E-2 and will compare the results. Kindly provide your feedback.
Thank you
Thank you again!
In continuation of your previous response (In 4th answer), you've said the checking persistent negative regions will give a hint of the origin of the error. How do I avoid those negative regions? Do you mean by using <Limts>?
As you've advised, I put up the all new simulations with adding output "out_conc_phase 0 | 1", using "interaction" without specifying two components in the Phase input data and put "none" for Relinearisation mode for interface 0 / 1.
Simulation 1) I increased mobility to 2E-02 from 1E-02. It showed noticeable impact, the simulation was running fastly as expected and finished. The final fraction of Liquid and Phase 1 after completion is mentioned below. After the completion, terminal showed continuous errors like before. With the liquid fraction below, can I consider this simulation as finished?
# Simulation Temperature Fraction Fraction
# time [s] [K] Liquid Phase 1
5.190000E-04 1233.50000 0.00149554 0.99850446
However, I can see negative compositions in the .c*phase* output files. Continuous negative compositions have been observed for .c4phas0 , .c2phas1, .c3phas1, .c5phas1 files and few other .c*phas* files showed negative compositions at the end just before the simulation stopped. So I didn't consider that. I updated the code with 'Limits' keyword as below and started a new simulation. Kindly find the attachemnt of driving file for this simulation.
Limits 0 4 0 100
Limits 1 2 0 100
Limits 1 3 0 100
Limits 1 5 0 100
The new simulation is finished as well and showed continuous negative compositions for .c4phas0 , .c2phas1, .c5phas1 files and few other .c*phas* files showed negative compositions at the end just before the simulation stopped. Do you think the upper and lower values that I mentioned in the code are good enough?
The other three simulations(mentioned below) like I mentioned in the previous message with mobility 1E-2 are showing the same errors and running slowly with 60% of phase 1 solidification. These three have negative compositions for the same .c4phas0 , .c2phas1, .c5phas1 files.
Simulation 2) mobility 1E-2 + using Limits keyword as in simulation 1
Simulation 3) mobility 1E-2 but not <Limits> . I ran this just to check the differences in the results because of Limits keyword. By comparing the .c*phas* files, I couldn't really understand the effect of <Limts> keyword. will decreasing the upper value in the code help?
Simulation 4) mobility 1E-2 + increased relinearizatin steps. I think the relinearization mode which is changed to 5e-8 to 1e-7 is not helping much.
As you advised, I'll increase the mobility more than 2E-2 and will compare the results. Kindly provide your feedback.
Thank you
- Attachments
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- micress.dri
- (17.78 KiB) Downloaded 278 times
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Dear Vamsi,
I fear that using "limits" is not the right way to handle the problem at this stage. Anyway, the form you use them should not do anything - you would have to increase the lower limit to something above 1.E-12.
However, you did not answer my question about the .driv output. I think, in a first step, the interface mobility has to be put to a reasonable value, it could be completely off. Due to the extreme conditions you apply, the mobility is difficult to estimate. If you could use MICRESS version 6.3, I would advise you to use automatic mobility (mob_corr)...
Bernd
I fear that using "limits" is not the right way to handle the problem at this stage. Anyway, the form you use them should not do anything - you would have to increase the lower limit to something above 1.E-12.
However, you did not answer my question about the .driv output. I think, in a first step, the interface mobility has to be put to a reasonable value, it could be completely off. Due to the extreme conditions you apply, the mobility is difficult to estimate. If you could use MICRESS version 6.3, I would advise you to use automatic mobility (mob_corr)...
Bernd
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Hi Bernd,
I think I misunderstood about the output in .cphas files. There are no persistent negative regions in my output but there is a negative composition(Minimum). Just like in the screenshot attached below (cPhase_output.jpg). I think this is not a big problem for the simulation. Is it?
Currently, I have access to MICRESS 06.2 version. So I can't try the auto mobility option right now. But I'll try to get the latest version soon. The simulation with mobility 2.1E-2 and without using LIMITS is finished. Please check the attached screenshot of TabF file(TabF_output.jpg). I'm attaching 4 screenshots of.dri output file of this simulation(dri_output.jpg). Screenshots taken for time steps just before the simulation is finished. Can you give your on interface undercooling from this?
If I used the mobility higher than 2.1E-2, phase 1 is dissolving completely just after I run the simulation. I'll update if there is any change in the result if I use 1E-12 as the lower limit for Limits keyword.
Thank you
I think I misunderstood about the output in .cphas files. There are no persistent negative regions in my output but there is a negative composition(Minimum). Just like in the screenshot attached below (cPhase_output.jpg). I think this is not a big problem for the simulation. Is it?
Currently, I have access to MICRESS 06.2 version. So I can't try the auto mobility option right now. But I'll try to get the latest version soon. The simulation with mobility 2.1E-2 and without using LIMITS is finished. Please check the attached screenshot of TabF file(TabF_output.jpg). I'm attaching 4 screenshots of.dri output file of this simulation(dri_output.jpg). Screenshots taken for time steps just before the simulation is finished. Can you give your on interface undercooling from this?
If I used the mobility higher than 2.1E-2, phase 1 is dissolving completely just after I run the simulation. I'll update if there is any change in the result if I use 1E-12 as the lower limit for Limits keyword.
Thank you
- Attachments
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- dri_output4.JPG (53.58 KiB) Viewed 7383 times
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- dri_output3.JPG (55.47 KiB) Viewed 7383 times
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- dri_output2.JPG (59.54 KiB) Viewed 7383 times
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- dri_output1.JPG (65.82 KiB) Viewed 7383 times
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- TabF_output.JPG (173.33 KiB) Viewed 7383 times
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- cPhase_output.JPG (64.78 KiB) Viewed 7383 times
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Dear Vamsi,
From the attachments it is obvious that the interface mobility should be much higher, because the driving force is getting higher and higher due to the cooling rate. Interface mobility must be high enough that growth is fast enough to follow the cooling, and the driving force should stay all the time (small compared to the effect of curvature which you (then) can also see in the .driv output).
If your initial grain vanishes with higher mobility, the initial temperature is probably above the liquidus temperature. Please check in the .log file that in the initial linearisation output dG is negative, otherwise you are above liquidus!
Bernd
From the attachments it is obvious that the interface mobility should be much higher, because the driving force is getting higher and higher due to the cooling rate. Interface mobility must be high enough that growth is fast enough to follow the cooling, and the driving force should stay all the time (small compared to the effect of curvature which you (then) can also see in the .driv output).
If your initial grain vanishes with higher mobility, the initial temperature is probably above the liquidus temperature. Please check in the .log file that in the initial linearisation output dG is negative, otherwise you are above liquidus!
Bernd
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Hi Bernd,Bernd wrote: ↑Fri Nov 10, 2017 10:55 pmDear vamsi,
The error you show are not very characteristic. I would look first for the following:
1.) Thermodynamic problems like apparent demixing due to the pseudo-binary approximation, or solidus/liquidus slopes which are close to 0. To find this problem, you need to check the .TabLin output. Remedies would be to use the "interaction" keyword to switch to diagonal extrapolation mode in case of demixing, or to define those components manually as stoichiometric.
2.) Check whether poor numerical conditions lead to spreading of the interface which indirectly leads to the error messages. You should check any output which allows you to see the thickness of the interface (.intf, .mueS, .driv, .frac1, ...). The remedy would be to decrease the interface mobility, use averaging of the driving force, increase the interface stiffness, add a stabilisation to the interface stiffness, increase spatial resolution.
3.) Interface undercooling is too high which leads to thermodynamic problems (as a consequence of a too large deviation from equilibrium). Check the .driv output to see whether this is the case. The solution would be to increase the interface mobility.
4.) Negative compositions could occur in one of the two phases. To find out, you need to check the .c*pha0 and .c*pha1 outputs whether there are regions (not just single points) which are negative. To solve the problem, more frequent relinearisation or using user limits ("limits" keyword in section of stoichiometric phases) can be the solution.
Of course, it can be something else - but I would check out these four things first...
Bernd
regarding point number 2, spreading of the interface- Do you consider following as interface spreading (indicated by arrow). at that location nucleation of phase 2 happen but then it vanishes.
- Interface spreading.PNG (90.23 KiB) Viewed 6639 times
However part of the interface seems to left behind during the phase 1 growth. I have used averaging, smoothing and interface stabilization for 0/2 interaction. But did not use a stabilization value for 1/2 interaction. can this also be related to low mobility of 1/2. I used mob_corr for both 0/1 [1 cm**4/(Js)]and 1/2 [1E-04 cm**4/(Js)]
BR
Chamara
Re: Error: Solidification in Martensitic tool steel during Selective Laser Melting (SLM) process
Hi Chamara,
In this case I cannot see "spreading" of the interface, because I do not see any interface which is thicker that normal. For me it looks as if the nucleus does not grow fast enough and just gets overgrown. This could be the reason why interface remains inside phase 1.
Thus, everything which facilitates growth of 0/2 could help in this case. What about the 0/2 interface mobility? It could also be a too low undercooling or too high curvature undercooling (interfacial energy of 0/2).
Bernd
In this case I cannot see "spreading" of the interface, because I do not see any interface which is thicker that normal. For me it looks as if the nucleus does not grow fast enough and just gets overgrown. This could be the reason why interface remains inside phase 1.
Thus, everything which facilitates growth of 0/2 could help in this case. What about the 0/2 interface mobility? It could also be a too low undercooling or too high curvature undercooling (interfacial energy of 0/2).
Bernd