Benchmark 2D single grain growth with square law

[billyzhangubc]

Hi all,
Asking on behalf of a colleague:

My colleague is doing some benchmark work on grain growth. Basically he started by modelling the shrinkage of a single round grain inside an infinitely big grain (using periodical boundary conditions). He adapted the model from a recrystallization simulation and set the chemical driving force (difference in recrystallization energy) infinitely small (when he set it to 0 the simulation cannot run) so the shrinkage is mostly driven by curvature. He tried to benchmark MICRESS result with the parabolic grain growth law by Burke and Turnbull:


where the constant is related to interfacial energy.

He found a few problems:
(1) At the very first time step, the grain is supposed to shrink but instead it grew, and then started to shrink.
(2) The overall shrinking kinetics (change in grain radius) is not the same as the analytical model. The MICRESS result gives faster shrinkage.

All his model parameters seem reasonable to me and we wonder what could go wrong, especially why there is an initial growth.

Thanks,
Billy/KY

[janin]

Hi Billy,

first I like to comment that the shrinkage of a single round grain is one of the fundamental benchmarks provided in the Micress/example/benchmark folder under the name 'B007_1Grain_Shrinking_dri'. If you do not yet have this folder, you can download it from the Micress webpage https://micress.rwth-aachen.de/download.html or from github https://github.com/access-technology/mi ... /Benchmark.
Here you can already see that the Micress results are in very good agreement with the analytical solution. (This solution is given in the example header, however with a typing error, there is a wrong factor of 2 in the derivation of the area, but the final validation is correct.)

The example 'B007_1Grain_Shrinking' gives the shrinkage of a single grain from liquid. In this example grain and matrix have different phases and therefore one can get the grain fractions and radii from the tabulated outputs *TabF and *TabK. Your example 'Shrinking_circle" works in exactly the same way, but you have to evalute the grain areas and radii from the *TabGD output.

I have run your example without any modifications using my Micress version, but could not reproduce your problem. I used the grain fractions from *TabGD for validation and found perfect agreement with the analytical solution, which however strongly differs from your plot.

shrinking_circle_radius.png

The analytical evolution of the radius with time was plotted by: p sqrt( 100.**2 -2*mu*sigma*x )
and the MIcress results by: rep 'Shrinking_Circle.TabGD' u 1:(sqrt($4/pi)) every 2::1 w p
with mobility mu = 5.E+12 and interfacial energy sigma = 5.E-10 (taken from the input file).

I still like to mention that the interfacial energy seems to be about three orders of magnitude too high for a metallic alloy. Do you have any reason to choose it that high? Moreover I would recommend not to use more than 4 or 5 interface cells. An interface thickness of 10 will significantly slow down your computations and is not necessary when you use 'fd_correction'. Moreover I recommend always to select 'multi_obstacle' instead of 'double_obstacle'. The option 'double_obstacle' refers to the outdated anti-symmetric multiphase field model. This model cannot handle multiphase interaction with different interfacial energies. In the limited case of two grains it may still be applied, but even here I would recommend to use the more general and advanced ''multi_obstacle' model.

Could you ask your collegue to evaluate the results in exactly the same way I did in order to check whether there really is a difference?

Regards,
Janin

[billyzhangubc]

Hello Janin,
Thanks for your answer and sorry for the late reply. My colleague tried your method just now and got the correct result.

Billy