Hi all,
Coarsening of gamma' precipitates is a process which is well-known and has a high importance for the mechanical behaviour of Ni-based superalloys. As simulation of this process using the MICRESS software may be of common interest, I want to open a discussion on how to achieve that. To start, I will share some of my experiences and thoughts in this field.
When trying to quantitatively analyse the coarsening kinetics in such alloys, numerical performance is a key issue, especially in 3D. Performance is mainly determined by the domain size, the grid resolution, the coarsening time and the required numerical time steps (of phase-field and especially of diffusion). This automatically leads to a limitation to relatively high volume fractions of gamma', because only then a sufficiently high number of precipitates fits into a smallest possible domain with a grid resolution which is high enough to properly resolve interface curvature. The high number of elements which have to be taken into account for typical technical superalloys increases further the required simulation time.
In principle, in my opinion, coarsening of precipitates with a high volume fraction should always be simulated in 3D to obtain quantitatively reasonable results. The channels between precipitates are not big compared to the particle size, so a quantitative correlation of 2D and 3D coarsening is not easily possible. It is important to realize that this channel width, which is very important for the mechanical properties in Ni-based superalloys, is completely different in 2D and 3D. Nevertheless it is always recommendable to start with 2D for setting up the simulation, and switch to 3D once the numerics and performance are optimized.
Apart from the 2D/3D-question and its implication for the observed ripening kinetics, the initial microstructure is a key design question: If a defined initial microstructure is to be used (either synthetic or from experiment), the question always is whether it is sufficiently representative, whether the radius distribution is realistic, and whether the phase fractions are consistent with thermodynamics. A trick for fine-tuning the initial phase fraction has been given here. But keep in mind that average curvature will shift the equilibrium fraction of the precipitate phase to a somewhat smaller value.
An alternative approach which I recommend is to nucleate the precipitates from a supersaturated pure single-phase fcc. This allows to create a very high number of particles at the beginning, even if the grid resolution is not high enough to resolve them perfectly at the very beginning. After an initial growth up to the equilibrium phase fraction, coarsening will start automatically, and at the time when a sufficient size is reached for quantitative curvature evaluation, the spatial and size distribution will probably already be much closer to stationary compared to synthetic initial structures.
I want to invite you to share your experiences, questions and thoughts in this tread. I also will add further comments later on.
Bernd
Simulation of gamma prime coarsening in Ni-based superalloys
Coalescence and Stress
Coalescence
Coarsening at high volume fractions of the precipitate phase may easily lead to coalescence. With gamma' precipitates in Ni-alloys there is a restriction: Due to the existence of topologically equivalents, two particles can join without forming a grain boundary when they touch each other. However, if they are not equivalent, they avoid touching due to the very high interface energy between them. This is naturally achieved if all topologically equivalent precipitates belong to the same grain number, i.e. there are only 4 grains present (although each simultaneously at different locations). This can be achieved by using the nucleation option "add_to_grain new set" and randomly distributing an equal number of seeds of each of the 4 equivalents by an extra seed type. Furthermore, the interface energy between (not equivalent)gamma' should be a factor 2-3 higher compared to the gamma-gamma' interfaces.
Stress Coupling
Coherency stress has a strong effect on the ripening as well as on the morphology of the precipitates. Stress coupling should be switched on, and elastic data need to be specified for each of the two phases. This is not so easy if no measurements have been published for the specific alloys and/or for the given temperature. However, for coarsening only, the exactness is not so critical and estimated values or valued from similar materials can be used. In principal, even the same set of values could be used for both phases without causing too much errors. This is different for simulation of elastic rafting (stress-induced coarsening): Here, the difference between the elastic constants are decisive for the process kinetics!
In both cases, the misfit is very important. Therefore, molar volumes of both phases have to be provided. If the TCNI database is available, it can be directly read from there.
Coarsening at high volume fractions of the precipitate phase may easily lead to coalescence. With gamma' precipitates in Ni-alloys there is a restriction: Due to the existence of topologically equivalents, two particles can join without forming a grain boundary when they touch each other. However, if they are not equivalent, they avoid touching due to the very high interface energy between them. This is naturally achieved if all topologically equivalent precipitates belong to the same grain number, i.e. there are only 4 grains present (although each simultaneously at different locations). This can be achieved by using the nucleation option "add_to_grain new set" and randomly distributing an equal number of seeds of each of the 4 equivalents by an extra seed type. Furthermore, the interface energy between (not equivalent)gamma' should be a factor 2-3 higher compared to the gamma-gamma' interfaces.
Stress Coupling
Coherency stress has a strong effect on the ripening as well as on the morphology of the precipitates. Stress coupling should be switched on, and elastic data need to be specified for each of the two phases. This is not so easy if no measurements have been published for the specific alloys and/or for the given temperature. However, for coarsening only, the exactness is not so critical and estimated values or valued from similar materials can be used. In principal, even the same set of values could be used for both phases without causing too much errors. This is different for simulation of elastic rafting (stress-induced coarsening): Here, the difference between the elastic constants are decisive for the process kinetics!
In both cases, the misfit is very important. Therefore, molar volumes of both phases have to be provided. If the TCNI database is available, it can be directly read from there.
Re: Simulation of gamma prime coarsening in Ni-based superalloys
Evaluation
Due to the strategy explained above to represent each group of topologically equivalent precipitates by the same grain number, grain statistic outputs like in .TabK or .TabGD are not very helpful anymore as there are only four grains present. Qualitatively, the shape and position of the different kinds of precipitates can be distinguished looking at the .korn output which shows the grain number and thus the topological equivalents. However, quantitative evaluations of the size distribution of all precipitates or the precipitates within each group must be made via post-processing.
With this aim, a new functionality has recently been developed for DP_MICRESS which will allow for analysis on interconnected regions inside an output field. Applied to the .frac output for the gamma' phase, the number and sized of all particles can be determined, independent from their grain numbers. This functionality is planned to be part of the next release of DP_MICRESS.
Other types of analyses can be done using the HOMAT module which is based on mathematical homogenization. The evaluation of the anisotropy of thermal or mechanical properties e.g. can be used for quantification of the progress of rafting, replacing the manual "measurement" of aspect ratios.
Due to the strategy explained above to represent each group of topologically equivalent precipitates by the same grain number, grain statistic outputs like in .TabK or .TabGD are not very helpful anymore as there are only four grains present. Qualitatively, the shape and position of the different kinds of precipitates can be distinguished looking at the .korn output which shows the grain number and thus the topological equivalents. However, quantitative evaluations of the size distribution of all precipitates or the precipitates within each group must be made via post-processing.
With this aim, a new functionality has recently been developed for DP_MICRESS which will allow for analysis on interconnected regions inside an output field. Applied to the .frac output for the gamma' phase, the number and sized of all particles can be determined, independent from their grain numbers. This functionality is planned to be part of the next release of DP_MICRESS.
Other types of analyses can be done using the HOMAT module which is based on mathematical homogenization. The evaluation of the anisotropy of thermal or mechanical properties e.g. can be used for quantification of the progress of rafting, replacing the manual "measurement" of aspect ratios.