Course:MTRL578

Microstructural Simulation of Materials

Phase Field Model

Recrystallization

Initial Structure

Grains Impingement

End of Recrystallization

The executable and source code for Windows is here and for Linux is here. Compile it with g++.

The input file for program should be in the same directory as executable. It contains all settings required to run the code.

-------------- Inpput file for Recrystallization Simulations ------------

Saving directory:
C:\directory\that\I\want\the\results\to\be\saved\

size in x direction (grid points):
200

System size in y direction (grid points):
200

Delta x:
1

Threshold value for choosing active nodes:
0.00000000001

Delta t:
0.1

Total number of time steps to finish calculation:
30000

Sequence of time steps which the results is written on hard disk:
500

Model parameter "L":
1

Model parameter "m":
1

Model parameter "kappa":
1

Total number of nuclei in the domain:
40

Stored energy of matrix grain:
0.1

Nucleus radius (in grid points):
12

Visualisation

Use Fullres_tn.txt for creating a grayscale snapshot of the structure. Grain boundaries are dark and grains are white. Use Inds_tn.txt to create a colour map representing index of each grain. This code makes a structure where matrix is red:


%% Recrytallization structure
clear
 figure
 start=0;
 step=500; 
ending=10000
 ni=0;
 for tn=[start:step:ending]  
   ni=ni+1;
 delt=0.15; 
savedir='/home/cenna/Results/2000/';
 phi=importdata([savedir '/Fullres_' num2str(tn) '.txt']);
 inds=importdata([savedir '/Inds_' num2str(tn) '.txt']);
 im(:,:,1)=phi;
 im(:,:,2)=phi.*[inds~=1];
 im(:,:,3)=phi.*[inds~=1];
 imshow(im);
 caxis([0 1]);
 shading flat
 axis off
 box off
 title(['Time= ' num2str(tn)]) set(gca,'DataAspectratio',[1 1 1]) 
pause(01);
 print([savedir '/' num2str(ni) '.png'],'-dpng','-r200',gcf) 
end

Interface and Particles Interaction

See result of simulation in Zener_pinning Zener Pining article at Wikipedia.

Code for energy calculation is here. Program for interaction of an interface with ensemble of particles is here.

Model Parameters

Model parameters $m,\;\kappa$ and $L$ are related to physical characteristics of the interface. Interface energy is: mobility=3/2*L*sqrt(2*kappa/m);intenergy=1/3*sqrt(2*m*kappa);

\sigma _{gb}={\frac {1}{3}}{\sqrt {2m\kappa }}

and interface mobility is:

M_{gb}={\frac {3}{2}}L{\sqrt {\frac {2\kappa }{m}}}

One can check accuracy of calculations by testing the interface mobility and energy with corresponding values obtained from simulation.