How MICRESS calculates average grain radius in grain growth problems?
As you know there are different experimental methods to find average grain radius of metallographic pictures. Which method of measuring average grain size is consistent with the method used in MICRESS?
If we do a 2-D grain growth simulation in MICRESS, how we can compare it with the 3-D experimental results? Is there a correction factor?
Average grain size
Re: Average grain size
Dear mtoloui,
I think, average radii are calculated from the average phase fractions, i.e. overall fraction devided by number of grains, assuming circular or spherical shape. I will ask whether someone knows it better ...
Bernd
I think, average radii are calculated from the average phase fractions, i.e. overall fraction devided by number of grains, assuming circular or spherical shape. I will ask whether someone knows it better ...
Bernd
Re: Average grain size
There are not only different experimental methods to find average grain radius, but also many different mathematical models to determine avergae grain size from a simulation. MICRESS uses a relative simple one:
3D)
First, the average grain volume is calculated as ratio of total volume and number of grains and afterwards, the radius of an equivalent 3D-sphere with this mean grain volume is determined:
V_grain_mean = V / nb_grains = 4/3 * Pi * R^3
=> R_3D = ( 3 * V / (4 * Pi * nb_grains ))^-3
2D)
First the average grain area is calculated as the ratio of total area and number of grains and afterwards, the radius of an equivalent 2D-sphere with this mean grain area is determined:
A_grain_mean = A / nb_grains = Pi * R^2
=> R_2D = ( A / (Pi * nb_grains ))^-2
From this two equations you can determine the 2D/3D correction factor either for the output radii or the input grain densities as e.g. has been done by Militzer in:
http://www.alemi.ca/pdf/militzer07.pdf
Janin
3D)
First, the average grain volume is calculated as ratio of total volume and number of grains and afterwards, the radius of an equivalent 3D-sphere with this mean grain volume is determined:
V_grain_mean = V / nb_grains = 4/3 * Pi * R^3
=> R_3D = ( 3 * V / (4 * Pi * nb_grains ))^-3
2D)
First the average grain area is calculated as the ratio of total area and number of grains and afterwards, the radius of an equivalent 2D-sphere with this mean grain area is determined:
A_grain_mean = A / nb_grains = Pi * R^2
=> R_2D = ( A / (Pi * nb_grains ))^-2
From this two equations you can determine the 2D/3D correction factor either for the output radii or the input grain densities as e.g. has been done by Militzer in:
http://www.alemi.ca/pdf/militzer07.pdf
Janin
Re: Average grain size
In addition you can generate a .TabGD output file by setting tab_grain_data.
This file contains a vast amount of information, e.g. the grain volume derived by integrating over the phase field variable, the surface area of each grain, the number of neighboring grains, ...
You can use this data e.g. to create grain size histograms.
This file contains a vast amount of information, e.g. the grain volume derived by integrating over the phase field variable, the surface area of each grain, the number of neighboring grains, ...
You can use this data e.g. to create grain size histograms.