Hello,
I'm calculating arc welds for CMSX-4. I'm trying to understand the microweld metallurgy that affects segregation by varying various parameters. I have other questions.
1. I converted both the phase and composition fields from ppii(num.22) to gggg(num.26), which resulted in artifact errors. Is it wrong to calculate based on the slope?
2. Excluding process conditions like cooling rate, I found that the parameter that affects segregation under the same welding conditions is the interfacial energy term. I'd also like to know if segregation is affected by other factors, such as mobility or diffusion.
3. I also read Bernd's paper, which uses the Newton-Raphson equation to calculate interfacial equilibrium. This approach appears to limit shale solute entrapment.
4. He also claims that using a thin interfacial compensation model can prevent entrapment, but I'm not sure what he means.
5. Does the differential partition coefficient obtained from TabLin represent the compositional change between the two phases in space through time differentiation?
6. The concentration slover seems to limit the redistribution of components in the diagonal direction. Is there a suitable way to correct this? I'd like to see the effect of the parameters.
7. Also, does MICRESS version 7.3 automatically apply the multiple ternary approximation?
8. I changed the diffusion parameter from diagonal_dilute to multi, but there was no significant difference in the mushy region. Why?
9. How is the solute partition coefficient calculated within MICRESS? Among the values listed in the Tablin file, which one should be selected — m/ph1 or dcdT?”
Boundary condition of Arc welding solidification
-
Kim Hee Eun
- Posts: 4
- Joined: Mon Sep 15, 2025 7:05 am
- anti_bot: 333
Boundary condition of Arc welding solidification
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Re: Boundary condition of Arc welding solidification
Dear Kim Hee Eun,
Welcome to the MICRESS Forum.
Let me try to answer your questions one by one:
1.) Using gradient ("g") boundary conditions is very tricky and often leads to unexpected results. When using "g" for the composition fields, a source term for concentration is implemented based on the actual gradient which is present at the boundary. If any phase interfaces are in contact with that boundary, on top, there is a completely undefined behaviour to be expected due to the intrinsic gradient within the interface.
Using (g) for the phase-field parameter, instead, can sometimes be helpful for avoiding effects of the domain boundaries on grain interfaces. However, even here, the applicability of the gradient ("g") boundary condition is limited.
2.) Interface mobility and diffusion can also affect segregation, as long as the system is not reaching a state close to equilibrium. Whether this is the case or not, of course, depends on the process conditions like cooling rate. Interfacial energy, to the contrary, also affects segregation (equilibrium compositions at the interface) when we are close to equilibrium (Gibbs-Thomson-Effect).
Which is the paper you refer to?
3.) Calculating (quasi-)equilibrium via the Newton-Raphson method is the way how the interface condition is solved in MICRESS if we use TQ.coupling to a thermodynamic database. The "local (quasi-) equilibrium assumption" implies minimal entrapment of elements in case of a moving interface, because solute is rejected from the interface and can move away by diffusion.
4.) "Thin interface correction" means the intention to avoid numerical artefacts which are due to the finite interface thickness. Solute trapping effects can be real, but using a numerical interface thickness well above the atomic length scales can lead to unphysical artefacts. "Thin interface correction" means to apply equations that ensure a behavior corresponding to an infinitely thin interface, even if the interface is much thicker in the numerical implementation. In MICRESS, thin interface correction (TIC) consists of two components, namely the mobility correction ("mob_corr") and the anti-trapping correction ("atc"). "mob-corr" should be always used if diffusion-limited growth kinetics can be assumed, while "atc" can be helpful to minimize local entrapment.
5.) No, partition coefficients always refer to the same position at which 2 phases are co-existing. Whether a spatial concentration gradient is formed always depends on the time development of the system.
6.) I am not sure whether I understand what you mean. Do you refer to artefacts of the numerical grid? Those typically vanish if the grid resolution is chosen fine enough.
7.) The multi-ternary approximation must be applied manually by the user. In multicomponent systems, it is possible only to use ternary subsystems
using the "interaction" keyword (followed by the numbers of the 2 elements which are assumed to form a sub-ternary together with the matrix component).
8.) This probably shows that "diagonal_dilute" is a quite good approximation for the full diffusion matrix (multi) in this case. "diagonal_dilute" can be understood as a projection of the diffusion matrix onto the diagonal. Especially in high-alloyed systems with a spinodal, "diagonal_dilute" is numerically more stable than "multi" and avoids negative diffusion coeffcients on the diagonal. This is achieved by respective replacement of the flux component by the matrix element (dilute limit).
9.) This depends on the applied redistribution model. Per default, MICRESS applies "multi-binary" extrapolation, and the partition coefficient is defined using the phase-diagram slopes:
K = m(ph2)/m(ph2)
In high-alloyed systems like CMSX-4, "diagonal" extrapolation is more favorable and should be invoked using the "diagonal" keyword in section "Numerical Parameters" (like in your example). Then, the partition coefficients are calculated as
K = dc(ph1)/dc(ph2)
and additionally written out to the .TabLin-output file. dc/dT is the temperature dependency of the equilibrium composition which is not linked to the phase diagram slopes.
Best regards
Bernd
Welcome to the MICRESS Forum.
Let me try to answer your questions one by one:
1.) Using gradient ("g") boundary conditions is very tricky and often leads to unexpected results. When using "g" for the composition fields, a source term for concentration is implemented based on the actual gradient which is present at the boundary. If any phase interfaces are in contact with that boundary, on top, there is a completely undefined behaviour to be expected due to the intrinsic gradient within the interface.
Using (g) for the phase-field parameter, instead, can sometimes be helpful for avoiding effects of the domain boundaries on grain interfaces. However, even here, the applicability of the gradient ("g") boundary condition is limited.
2.) Interface mobility and diffusion can also affect segregation, as long as the system is not reaching a state close to equilibrium. Whether this is the case or not, of course, depends on the process conditions like cooling rate. Interfacial energy, to the contrary, also affects segregation (equilibrium compositions at the interface) when we are close to equilibrium (Gibbs-Thomson-Effect).
Which is the paper you refer to?
3.) Calculating (quasi-)equilibrium via the Newton-Raphson method is the way how the interface condition is solved in MICRESS if we use TQ.coupling to a thermodynamic database. The "local (quasi-) equilibrium assumption" implies minimal entrapment of elements in case of a moving interface, because solute is rejected from the interface and can move away by diffusion.
4.) "Thin interface correction" means the intention to avoid numerical artefacts which are due to the finite interface thickness. Solute trapping effects can be real, but using a numerical interface thickness well above the atomic length scales can lead to unphysical artefacts. "Thin interface correction" means to apply equations that ensure a behavior corresponding to an infinitely thin interface, even if the interface is much thicker in the numerical implementation. In MICRESS, thin interface correction (TIC) consists of two components, namely the mobility correction ("mob_corr") and the anti-trapping correction ("atc"). "mob-corr" should be always used if diffusion-limited growth kinetics can be assumed, while "atc" can be helpful to minimize local entrapment.
5.) No, partition coefficients always refer to the same position at which 2 phases are co-existing. Whether a spatial concentration gradient is formed always depends on the time development of the system.
6.) I am not sure whether I understand what you mean. Do you refer to artefacts of the numerical grid? Those typically vanish if the grid resolution is chosen fine enough.
7.) The multi-ternary approximation must be applied manually by the user. In multicomponent systems, it is possible only to use ternary subsystems
using the "interaction" keyword (followed by the numbers of the 2 elements which are assumed to form a sub-ternary together with the matrix component).
8.) This probably shows that "diagonal_dilute" is a quite good approximation for the full diffusion matrix (multi) in this case. "diagonal_dilute" can be understood as a projection of the diffusion matrix onto the diagonal. Especially in high-alloyed systems with a spinodal, "diagonal_dilute" is numerically more stable than "multi" and avoids negative diffusion coeffcients on the diagonal. This is achieved by respective replacement of the flux component by the matrix element (dilute limit).
9.) This depends on the applied redistribution model. Per default, MICRESS applies "multi-binary" extrapolation, and the partition coefficient is defined using the phase-diagram slopes:
K = m(ph2)/m(ph2)
In high-alloyed systems like CMSX-4, "diagonal" extrapolation is more favorable and should be invoked using the "diagonal" keyword in section "Numerical Parameters" (like in your example). Then, the partition coefficients are calculated as
K = dc(ph1)/dc(ph2)
and additionally written out to the .TabLin-output file. dc/dT is the temperature dependency of the equilibrium composition which is not linked to the phase diagram slopes.
Best regards
Bernd
-
Kim Hee Eun
- Posts: 4
- Joined: Mon Sep 15, 2025 7:05 am
- anti_bot: 333
Re: Boundary condition of Arc welding solidification
Thank you for your answer, it was very helpful.
I have an additional question regarding the setup of the multi-ternary approximation.
Does the numerical parameter concentration solver work in conjunction with the diffusion settings?
For example, if I want to simulate the interdiffusion of elements between the liquid and solid phases in CMSX-4:
1. If I set diagonal_dilute in the diffusion section, but define interactions in the concentration solver, will the interactions defined in the concentration solver still produce meaningful results?
2. Or, do I need to change the diffusion setting from diagonal_dilute to multi in order for the interactions defined in the concentration solver to be meaningful?
And i have some another questions about rapid solidification simulation of the laser welding.
1. Under rapid solidification conditions such as laser melting (high temperature gradient, high cooling rate), I anticipated segregation reduction and narrowing of the solidification temperature range. However, solidification temperature range appeared to be enlarged by about a factor of 2.5 compared to Thermo-Calc Scheil calculations or MICRESS calculations under slow solidification conditions.
If solute trapping does not occur, my understanding of the fundamental principle of solidification is that with increasing cooling rate, non-equilibrium solidification is emphasized and segregation increased. Is the entire MICRESS model based on this assumption, or does it depend on the specific redistribution model applied?
2. Referring to previous forum posts, I confirmed that MICRESS does not account for solute trapping as a function of solidification velocity. In that case, is there any way to simulate segregation reduction through rapid solidification? The only approach that I think is dendrite refinement, but this is ultimately still dependent on the cooling rate.
Of course, I recognize that the solidification velocities in our current simulations are not sufficient to induce solute trapping (on the order of a few cm/s). However, I would like to observe the velocity-dependent partition coefficient approaching unity as the velocity approaches the critical value (> 1 m/s).
2-2. I would like to ask about interface mobility in relation to solidification velocity.
Is there a criterion for determining the value to be assigned as the kinetic coefficient for phase interaction?
Furthermore, does this value govern whether the growth is diffusion-controlled or interface-controlled?
Finally, is this parameter related to solute trapping?
3. In this context, the solidification temperature range was obtained simply by reading the temperature at which the tabF output indicated completion of solidification (the tabF output seems to represent the lowest temperature within the domain). I am uncertain whether this approach is appropriate.
If necessary, we could enlarge the simulation domain such that the entire dendrite, from the tip that first grows to the root where dendrites impinge and fully eliminate the interdendritic liquid, is captured within a single domain,at once. Then, the temperature range could be extracted from the tip to the root. Do you think this would be a more appropriate approach?
4. Apart from the previous question, under rapid solidification conditions I observed that the solidification temperature range expands abruptly in the final stage of solidification, specifically from a solid fraction of about 99–99.9% to 100% (complete solidification). Should this phenomenon itself be regarded as a problem?
I have an additional question regarding the setup of the multi-ternary approximation.
Does the numerical parameter concentration solver work in conjunction with the diffusion settings?
For example, if I want to simulate the interdiffusion of elements between the liquid and solid phases in CMSX-4:
1. If I set diagonal_dilute in the diffusion section, but define interactions in the concentration solver, will the interactions defined in the concentration solver still produce meaningful results?
2. Or, do I need to change the diffusion setting from diagonal_dilute to multi in order for the interactions defined in the concentration solver to be meaningful?
And i have some another questions about rapid solidification simulation of the laser welding.
1. Under rapid solidification conditions such as laser melting (high temperature gradient, high cooling rate), I anticipated segregation reduction and narrowing of the solidification temperature range. However, solidification temperature range appeared to be enlarged by about a factor of 2.5 compared to Thermo-Calc Scheil calculations or MICRESS calculations under slow solidification conditions.
If solute trapping does not occur, my understanding of the fundamental principle of solidification is that with increasing cooling rate, non-equilibrium solidification is emphasized and segregation increased. Is the entire MICRESS model based on this assumption, or does it depend on the specific redistribution model applied?
2. Referring to previous forum posts, I confirmed that MICRESS does not account for solute trapping as a function of solidification velocity. In that case, is there any way to simulate segregation reduction through rapid solidification? The only approach that I think is dendrite refinement, but this is ultimately still dependent on the cooling rate.
Of course, I recognize that the solidification velocities in our current simulations are not sufficient to induce solute trapping (on the order of a few cm/s). However, I would like to observe the velocity-dependent partition coefficient approaching unity as the velocity approaches the critical value (> 1 m/s).
2-2. I would like to ask about interface mobility in relation to solidification velocity.
Is there a criterion for determining the value to be assigned as the kinetic coefficient for phase interaction?
Furthermore, does this value govern whether the growth is diffusion-controlled or interface-controlled?
Finally, is this parameter related to solute trapping?
3. In this context, the solidification temperature range was obtained simply by reading the temperature at which the tabF output indicated completion of solidification (the tabF output seems to represent the lowest temperature within the domain). I am uncertain whether this approach is appropriate.
If necessary, we could enlarge the simulation domain such that the entire dendrite, from the tip that first grows to the root where dendrites impinge and fully eliminate the interdendritic liquid, is captured within a single domain,at once. Then, the temperature range could be extracted from the tip to the root. Do you think this would be a more appropriate approach?
4. Apart from the previous question, under rapid solidification conditions I observed that the solidification temperature range expands abruptly in the final stage of solidification, specifically from a solid fraction of about 99–99.9% to 100% (complete solidification). Should this phenomenon itself be regarded as a problem?
Re: Boundary condition of Arc welding solidification
Dear Kim Hee Eun,
Diffusion and redistribution of elements are treated independently in MICRESS. That means, if you have chosen to approximate diffusion by effective diagonal terms using "diagonal_dilute", you still can use e.g. ternary redistribution to improve extrapolation of quasi-equilibrium. Or the other way round, you can use off-diagonal diffusion in order to incorporate "uphill" diffusion effects without needing ternary extrapolation.
However, of course, the basic reason why strong element interactions may occur in redistribution and diffusion comes from the thermodynamic factors, and thus are identical. Nevertheless, the effects are different and treated differently in MICRESS.
Please note that the potentially better extrapolation of quasi-equilibrium by including ternary interactions into the redistribution scheme can always be achieved also by more frequent updating of thermodynamic linearisation data. This perhaps is the reason why ternary extrapolation hasn't been used much so far, especially when taking into account that selecting the most relevant sub-ternary systems is not easy in multi-component systems like superalloys.
Your further questions address several fundamental topics which would easily fill seperate threads. I try to give you short answers:
1.) MICRESS is based on the local (quasi-)equilibrium approach, and thus in standard mode cannot predict (non-equilibrium) solute trapping into the interface in a strictly physical sense. There may occur numerical solute trapping which is due to the diffuse interface approach, but this effect is to be avoided and cannot be used as a substitute for physical solute trapping. There have been efforts to alternatively implement a"dissipative" approach for non-equilibrium effects, which however unfortunately has never been finished until now. However, full trapping (massive transformations or trapping of substitutional elements only) can be achieved by the present MICRESS version using specific redistribution models (para).
For solidification, physical solute trapping get important and dominant only at very high front velocities which typically are even not reached in SLM processes. For all other cases, segregation (and thus the increase of the solidification interval with respect to the equilibrium case) depends on the interplay of the process conditions and morphology formation. If we neglect pure phase transformation kinetics in a first place, the Scheil condition is the one which produces maximum segregation (and a maximum solidification interval) by assuming local equilibrium and infinite diffusion inside the liquid phase. As soon as concentration gradients occur inside the liquid phase during solidification, segregation is reduced, and the solidification interval gets smaller. In the extreme case of a planar interface with a strong pile-up of solute before the front, the solidification iterval corresponds to the equilibrium case, and all solute is "trapped" into the solid. Please note that this is a different form of trapping which occurs with local equilibrium, in contrary to non-equilibrium solute trapping.
If kinetic effects of phase transformation are included, of course, the real solidification interval can be higher than for the Scheil model, e.g. if there is nucleation undercooling, or precipitation does not occur.
2.) Es explained above, MICRESS does not include non-equilibrium partitioning, and therefore cannot be used to directly obtain velocity dependent partition coefficients. The only way to achieve non-equilibrium in a controlled way would be to use corrected thermodynamics. Numerical solute trapping is uncontrolled and could only qualitatively be pushed into the same direction.
2-2.) In order to achieve diffusion-controlled growth kinetics despite of numerical solute trapping, we use mobility correction ("mob_corr"). If the physical mobility (the input value) is high, "mob_corr" automatically calculates the numerical interface mobility for diffusion controlled growth (which can be seen in the .mueS ouput). The input value should be at least 1-2 orders of magnitude above the numerical interface mobility to ensure correct kinetics.
If the interface mobility is arteficially increased (by using a prefactor f<1 for "mob_corr", or by removing the "mob_corr" option completely), then the front moves too fast and "overruns" part of the solute pile-up, which results in "numerical" solute trapping. When the mobility is reduced (e.g. by using a "physical" interface mobility as input which is not big compared to the numerical mobility obtained from "mob_corr", the outcome is an interface controlled phase transformation.
3.) The .TabF-output is not suited for obtaining fs_T-curves if a temperature gradient is present, because the fraction value is integrated over the whole domain, while the temperature value is taken at the bottom of the domain. The best way to correctly obtain the relation between phase fractions and temperature in such cases is to write profiles in z-direction for the .frac*-outputs and the .temp-output using DP_MICRESS ("Virtual EDX/Show average of X/Y overZ"). Then you can plot the fraction of the phases against temperature (e.g. in Excel) after aggregating data for several output time steps. For this method it is not necessary that the whole mushy zone fits into the MICRESS domain, if you allow the dendrites to hit the top boundary (and remove the uppermost part with artefacts from analysis).
4.) It is not easy to ensure that the solidification interval obtained from a simulation is correct, because any mistake or numerical problem will probably slow down the solidification process and lead to a falsely increased solidification range. If you e.g. forget to include a phase which is thermodynamically stable at some place, if you do not check nucleation often enough within each liquid pocket, etc., solidification will be retarded. This is especially true towards the end of solidification, where only small rests of liquid are entrapped somewhere, without contact to all phases required for final solidification, perhaps with numerical issues like negative concentration values. Thus, in practice, for multicomponent/multiphase solidification, rest liquid fractions below ~0.1 % cannot be considered as physical anymore. Especially if a solid state simulation is intended based on the obtained solidification microstructure, the rest liquids must then be "killed" arteficially. This e.g. is done in A006_CMSX4_dri with seed type 3 (using "add_to_grain) or in A018_Al4Cu_Additive_Rosenthal_dri with seed type 6 (using "split_from_grain").
Bernd
Diffusion and redistribution of elements are treated independently in MICRESS. That means, if you have chosen to approximate diffusion by effective diagonal terms using "diagonal_dilute", you still can use e.g. ternary redistribution to improve extrapolation of quasi-equilibrium. Or the other way round, you can use off-diagonal diffusion in order to incorporate "uphill" diffusion effects without needing ternary extrapolation.
However, of course, the basic reason why strong element interactions may occur in redistribution and diffusion comes from the thermodynamic factors, and thus are identical. Nevertheless, the effects are different and treated differently in MICRESS.
Please note that the potentially better extrapolation of quasi-equilibrium by including ternary interactions into the redistribution scheme can always be achieved also by more frequent updating of thermodynamic linearisation data. This perhaps is the reason why ternary extrapolation hasn't been used much so far, especially when taking into account that selecting the most relevant sub-ternary systems is not easy in multi-component systems like superalloys.
Your further questions address several fundamental topics which would easily fill seperate threads. I try to give you short answers:
1.) MICRESS is based on the local (quasi-)equilibrium approach, and thus in standard mode cannot predict (non-equilibrium) solute trapping into the interface in a strictly physical sense. There may occur numerical solute trapping which is due to the diffuse interface approach, but this effect is to be avoided and cannot be used as a substitute for physical solute trapping. There have been efforts to alternatively implement a"dissipative" approach for non-equilibrium effects, which however unfortunately has never been finished until now. However, full trapping (massive transformations or trapping of substitutional elements only) can be achieved by the present MICRESS version using specific redistribution models (para).
For solidification, physical solute trapping get important and dominant only at very high front velocities which typically are even not reached in SLM processes. For all other cases, segregation (and thus the increase of the solidification interval with respect to the equilibrium case) depends on the interplay of the process conditions and morphology formation. If we neglect pure phase transformation kinetics in a first place, the Scheil condition is the one which produces maximum segregation (and a maximum solidification interval) by assuming local equilibrium and infinite diffusion inside the liquid phase. As soon as concentration gradients occur inside the liquid phase during solidification, segregation is reduced, and the solidification interval gets smaller. In the extreme case of a planar interface with a strong pile-up of solute before the front, the solidification iterval corresponds to the equilibrium case, and all solute is "trapped" into the solid. Please note that this is a different form of trapping which occurs with local equilibrium, in contrary to non-equilibrium solute trapping.
If kinetic effects of phase transformation are included, of course, the real solidification interval can be higher than for the Scheil model, e.g. if there is nucleation undercooling, or precipitation does not occur.
2.) Es explained above, MICRESS does not include non-equilibrium partitioning, and therefore cannot be used to directly obtain velocity dependent partition coefficients. The only way to achieve non-equilibrium in a controlled way would be to use corrected thermodynamics. Numerical solute trapping is uncontrolled and could only qualitatively be pushed into the same direction.
2-2.) In order to achieve diffusion-controlled growth kinetics despite of numerical solute trapping, we use mobility correction ("mob_corr"). If the physical mobility (the input value) is high, "mob_corr" automatically calculates the numerical interface mobility for diffusion controlled growth (which can be seen in the .mueS ouput). The input value should be at least 1-2 orders of magnitude above the numerical interface mobility to ensure correct kinetics.
If the interface mobility is arteficially increased (by using a prefactor f<1 for "mob_corr", or by removing the "mob_corr" option completely), then the front moves too fast and "overruns" part of the solute pile-up, which results in "numerical" solute trapping. When the mobility is reduced (e.g. by using a "physical" interface mobility as input which is not big compared to the numerical mobility obtained from "mob_corr", the outcome is an interface controlled phase transformation.
3.) The .TabF-output is not suited for obtaining fs_T-curves if a temperature gradient is present, because the fraction value is integrated over the whole domain, while the temperature value is taken at the bottom of the domain. The best way to correctly obtain the relation between phase fractions and temperature in such cases is to write profiles in z-direction for the .frac*-outputs and the .temp-output using DP_MICRESS ("Virtual EDX/Show average of X/Y overZ"). Then you can plot the fraction of the phases against temperature (e.g. in Excel) after aggregating data for several output time steps. For this method it is not necessary that the whole mushy zone fits into the MICRESS domain, if you allow the dendrites to hit the top boundary (and remove the uppermost part with artefacts from analysis).
4.) It is not easy to ensure that the solidification interval obtained from a simulation is correct, because any mistake or numerical problem will probably slow down the solidification process and lead to a falsely increased solidification range. If you e.g. forget to include a phase which is thermodynamically stable at some place, if you do not check nucleation often enough within each liquid pocket, etc., solidification will be retarded. This is especially true towards the end of solidification, where only small rests of liquid are entrapped somewhere, without contact to all phases required for final solidification, perhaps with numerical issues like negative concentration values. Thus, in practice, for multicomponent/multiphase solidification, rest liquid fractions below ~0.1 % cannot be considered as physical anymore. Especially if a solid state simulation is intended based on the obtained solidification microstructure, the rest liquids must then be "killed" arteficially. This e.g. is done in A006_CMSX4_dri with seed type 3 (using "add_to_grain) or in A018_Al4Cu_Additive_Rosenthal_dri with seed type 6 (using "split_from_grain").
Bernd