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Created new from the old YL repo for single phase
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This is for solid solution stage i.e. does not consider elastic or plastic inclusions as in precipitation strengthened alloys.
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@manasijy
manasijy authored Jan 10, 2024
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56 changes: 56 additions & 0 deletions BHfile.txt
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28 changes: 28 additions & 0 deletions BHfile_half.txt
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28 changes: 28 additions & 0 deletions DC_matrix_function.m
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%% This function creates the direction cosine matrix for one set of euler angles
% This is a common utility function used in many of the programs in other repositories

function [DC] = DC_matrix_function(phi1,phi,phi2)

c1 = cosd(phi1);
c2 = cosd(phi2);
c0 = cosd(phi);
s1 = sind(phi1);
s2 = sind(phi2);
s0 = sind(phi);

% Now calculating direction cosine matrix for conversion into the
% crystal reference frame
a11= c1*c2-s1*s2*c0;
a12= s1*c2+c1*s2*c0;
a13= s2*s0;
a21= -c1*s2-s1*c2*c0;
a22= -s1*s2+c1*c2*c0;
a23= c2*s0;
a31= s1*s0;
a32= -c1*s0;
a33= c0;

DC = [a11,a12,a13;a21,a22,a23;a31,a32,a33];

end

70 changes: 70 additions & 0 deletions ITC2euler.m
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%% This program calculates the euler angles for the given hkl, uvw crystal orientation
clear
close

fprintf('This program calculates the euler angles \n for the given {hkl}<uvw> \n')
fprintf('PLEASE ENTER h k l u v w of the crystal\n')
O= input(''); % crystal_orientation array
XO = sscanf(O,'%d');


h=XO(1);
k=XO(2);
l=XO(3);
u=XO(4);
v=XO(5);
w=XO(6);
t1=k*w-l*v;
t2=l*u-h*w;
t3=h*v-k*u;

b=sqrt(u^2+v^2+w^2); % modulus of uvw vector
n=sqrt(h^2+k^2+l^2); % modulus of hkl vector
t=sqrt(t1^2+t2^2+t3^2); % modulus of transverse vector

%% alternative calculation
phi = acosd(1/n);

if (h^2 + k^2)<0.01
phi1=0;
phi2=phi1;
else
phi1= asind((w/b)*(n/sqrt(h^2 + k^2)));
phi2 = acosd(k/sqrt(h^2 + k^2));

end



%% Other method of calculating euler angles


% %% Calculation of direction cosines form hkl uvw and t1 t2 and t3
%
% a11= u/b;
% a12= t1/t;
% a13= h/n;
% a21= v/b;
% a22= t2/t;
% a23= k/n;
% a31= w/b;
% a32= t3/t;
% a33= l/n;
%
%
% % A = [a11,a12,a13;a21,a22,a23;a31,a32,a33];
%
% if a33>0.99 || a33<-0.99
% phi = 0;
% phi1 = (atand(a12/a11)); % As per formula given in Rollet L3, RHS is divided by 2 and phi2=phi1
% phi2=0; % but if phi is 0, phi1 and phi2 are same rotations so they add.
% else
% phi=acosd(a33);
% phi1=atan2d((a31/sin(phi)),(-a32/sin(phi)));
% phi2=atan2d((a13/sin(phi)),(a23/sin(phi)));
% end

%% output

fprintf('phi1 = "%f" \n phi= "%f" \n phi2= "%f" \n',phi1, phi, phi2)

76 changes: 76 additions & 0 deletions Poly_crystal_YL_3D.m
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% clear;
% close;

%% Creating Bishop Hill stress state matrix from the text file named: BHfile.txt

B = fopen('BHfile.txt');
BH = textscan(B, ' %f %f %f %f %f %f');
fclose(B);

%% Reading the orientation file

prompt = 'The euler angle file name with .txt extension \n';
g_vectorfile = input(prompt);
g = fopen(g_vectorfile);
g_matrix = textscan(g, '%f %f %f');
l_g = length(g_matrix{1,1});

%% Reading the strain file

S = fopen('strains.txt');
strain = textscan(S, ' %f %f %f ');
l_s = length(strain{1,1});
fclose(S);
M = zeros(1,l_s);
ro = zeros(1,l_s);

for u=1:1:l_s
for v = 1:1:11
gamma12 = -1 + 0.2*(v-1);
e_ext=[strain{1,1}(u),gamma12,0;gamma12,strain{1,2}(u),0;0,0,strain{1,3}(u)];
Wmax= zeros(l_g,1);
for c=1:1:l_g
A = DC_matrix_function(g_matrix{1,1}(c),g_matrix{1,2}(c),g_matrix{1,3}(c));
[e]= transform_e_function(e_ext,A);
W= zeros(1,56);
BH_state = zeros(56,6);

for m=1:1:56
W(m)= -(BH{1,2}(m)*e(1,1))+ BH{1,1}(m)*e(2,2)+ BH{1,4}(m)*(e(2,3)+e(3,2))+BH{1,5}(m)*(e(1,3)+e(3,1))+BH{1,6}(m)*(e(1,2)+e(2,1));
BH_state(m,:) = [BH{1,1}(m),BH{1,2}(m),BH{1,3}(m),BH{1,4}(m),BH{1,5}(m),BH{1,6}(m)]; % [A,B,C,F,G,H]
end

Wmax(c)= max(abs(W));
end
M(u,v) = mean(Wmax)/e_ext(1,1);
ro(u,v) = -strain{1,2}(u)/strain{1,1}(u);
g(u,v) = gamma12/strain{1,1}(u);
end
end

%% Matix to store YL data points
azimuth = 0:5:360;
elevation = -90:5:90;
[az, el] = meshgrid(azimuth, elevation);
radius = 2*ones(size(az));

for u=1:1:l_s
for v=1:1:11
%aX+bY+cZ = M, a =1; b = -rho,c = 2gamma
b= -ro(u,v);
c= 2*g(u,v);
m = M(u,v);
r = abs(m./(cosd(az).*cosd(el)+ b.*cosd(el).*sind(az)+ c.*sind(el)));
radius = bsxfun(@min,r,radius);
end
end

%% Plotting the YL
[X,Y,Z] = sph2cart(az*(pi/180),el*(pi/180),radius);
surf(X,Y,Z)
xlim([-1.5 1.5]);
ylim([-1.5 1.5]);
zlim([-1.5 1.5]);
xlabel('SigmaXX');
ylabel('SigmaYY');
zlabel('TauXY');
113 changes: 113 additions & 0 deletions Poly_crystal_YL_3D_Quadrant_visulalization.m
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%% This program plots the 3D quadrant section of the yield volume.
% It is good for visulatization. Basically it shows how the yield locaus
% is the inner envelope of the all planes passing the stress space

clear;
close;

%% Creating Bishop Hill stress state matrix from the text file named: BHfile.txt

B = fopen('BHfile.txt');
BH = textscan(B, ' %f %f %f %f %f %f');
fclose(B);

% %% ppt details
% f = 0.008;
% sigma_bar = 10000e6;
% tau = 88e6;

%% Reading the orientation file

prompt = 'The euler angle file name with .txt extension \n';
g_vectorfile = input(prompt);
g = fopen(g_vectorfile);
g_matrix = textscan(g, '%f %f %f');
l_g = length(g_matrix{1,1});

%% Reading the strain file

S = fopen('strains.txt');
strain = textscan(S, ' %f %f %f ');
l_s = length(strain{1,1});
fclose(S);
M = zeros(1,l_s);
ro = zeros(1,l_s);


for u=1:1:l_s
% for rho = -1:0.1:1
for v = 1:1:11
gamma12 = -1 + 0.2*(v-1);
e_ext=[strain{1,1}(u),gamma12,0;gamma12,strain{1,2}(u),0;0,0,strain{1,3}(u)];
% e_ext=[strain{1,1}(u),0,0;0,strain{1,2}(u),0;0,0,strain{1,3}(u)];
Wmax= zeros(l_g,1);
for c=1:1:l_g


A = DC_matrix_function(g_matrix{1,1}(c),g_matrix{1,2}(c),g_matrix{1,3}(c));
[e]= transform_e_function(e_ext,A);
W= zeros(1,56);
BH_state = zeros(56,6);

for m=1:1:56

W(m)= -(BH{1,2}(m)*e(1,1))+ BH{1,1}(m)*e(2,2)+ BH{1,4}(m)*(e(2,3)+e(3,2))+BH{1,5}(m)*(e(1,3)+e(3,1))+BH{1,6}(m)*(e(1,2)+e(2,1));
BH_state(m,:) = [BH{1,1}(m),BH{1,2}(m),BH{1,3}(m),BH{1,4}(m),BH{1,5}(m),BH{1,6}(m)]; % [A,B,C,F,G,H]
end

Wmax(c)= max(abs(W));

end
M(u,v) = mean(Wmax)/e_ext(1,1);
ro(u,v) = -strain{1,2}(u)/strain{1,1}(u);
g(u,v) = gamma12/strain{1,1}(u);
end
end



%% Plotting the YL
figure
for u=1:1:l_s
for v=1:1:11
%aX+bY+cZ = M, a =1; b = -rho,c = 2gamma

b= -ro(u,v);
c= 2*g(u,v);
% Y = -4:0.2:4;
% Z = -4:0.2:4;
[Y,Z] = meshgrid(0:.2:2);
X = M(u,v) - b*Y - c*Z;
surf(Y,Z,X,'LineWidth',1,'EdgeColor',[1 0 0]);
% surf(Y,Z,X);
hold on
end
end

% % % For negative M values
% for u=1:1:l_s
% for v=1:1:11
% %aX+bY+cZ = M, a =1; b = -rho,c = 2gamma
%
% b= -ro(u,v);
% c= 2*g(u,v);
% % Y = -4:0.2:4;
% % Z = -4:0.2:4;
% [Y,Z] = meshgrid(0:.2:2);
% X = -M(u,v) - b*Y - c*Z;
% % surf(Y,Z,X);
% surf(Y,Z,X,'LineWidth',1,'EdgeColor',[1 0 0]);
% hold on
% end
% end

xlim([-1.5 1.5]);
ylim([-1.5 1.5]);
zlim([-2 2]);
xlabel('SigmaXX');
ylabel('SigmaYY');
zlabel('TauXY');
% shading faceted;%interp %flat
hold off


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