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-0,0 +1,640 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/images/Twin_reorientation_check_23_0.png b/images/Twin_reorientation_check_23_0.png new file mode 100644 index 0000000..8bd49b6 Binary files /dev/null and b/images/Twin_reorientation_check_23_0.png differ diff --git a/images/Twin_reorientation_check_24_0.png b/images/Twin_reorientation_check_24_0.png new file mode 100644 index 0000000..b929031 Binary files /dev/null and b/images/Twin_reorientation_check_24_0.png differ diff --git a/images/Twin_reorientation_check_25_0.png b/images/Twin_reorientation_check_25_0.png new file mode 100644 index 0000000..6017fbb Binary files /dev/null and b/images/Twin_reorientation_check_25_0.png differ diff --git a/images/Twinning represented in 1D.tex b/images/Twinning represented in 1D.tex new file mode 100644 index 0000000..6b5d6ad --- /dev/null +++ b/images/Twinning represented in 1D.tex @@ -0,0 +1,67 @@ +\begin{circuitikz} +\tikzstyle{every node}=[font=\LARGE] +\draw [short] (11.5,23) -- (2.5,23) ; +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (2.75,25.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (5.5,25.25) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (4.5,22.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (3.75,24.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (5,24.5) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (5.25,23) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (4.25,25.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (6.75,25.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (6.25,24.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (8,25.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (4.5,23.75) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (10,24.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (7.5,24.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (9.25,25.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (5.75,23.75) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (7,23.75) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (8.25,23.75) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (8.75,24.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (9.5,23.75) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (10.75,23.75) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (6.5,23) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (7.75,23) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (9,23) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (10.25,23) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (11.5,23) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (3.75,21.5) circle (0.25cm); +\draw [short] (11.5,20.75) -- (2.75,20.75); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (2.75,20.75) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (5.75,22.25) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (7,22.25) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (8.25,22.25) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (9.5,22.25) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (10.75,22.25) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (5,21.5) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (6.25,21.5) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (7.5,21.5) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (8.75,21.5) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (10,21.5) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (4.25,20.75) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (5.5,20.75) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (6.75,20.75) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (8,20.75) circle (0.25cm); +\draw [ fill={rgb,255:red,29; green,250; blue,0} ] (9.25,20.75) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (3.5,20) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (5,20) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (6.25,20) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (7.5,20) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (8.75,20) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (10,20) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (4.25,19.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (5.75,19.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (7,19.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (8.25,19.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (9.5,19.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (10.75,19.25) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (5.25,18.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (6.5,18.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (7.75,18.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (9,18.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (10.25,18.5) circle (0.25cm); +\draw [ fill={rgb,255:red,0; green,17; blue,250} ] (11.5,18.5) circle (0.25cm); +\node [font=\large] at (13.5,23) {Twin Boundary}; +\node [font=\large] at (13.5,20.75) {Twin Boundary}; +\end{circuitikz} diff --git a/images/Twinning_in_kinematics.tex b/images/Twinning_in_kinematics.tex new file mode 100644 index 0000000..b1256ec --- /dev/null +++ b/images/Twinning_in_kinematics.tex @@ -0,0 +1,145 @@ +\begin{circuitikz} +\tikzstyle{every node}=[font=\LARGE] +\draw (22.5,30.5) rectangle (30,21.75); +\draw [short] (23.75,30.5) -- (23.75,21.75); +\draw [short] (25,30.5) -- (25,21.75); +\draw [short] (26.25,30.5) -- (26.25,21.75); +\draw [short] (27.5,30.5) -- (27.5,21.75); +\draw [short] (28.75,30.5) -- (28.75,21.75); +\draw [short] (22.5,29.25) -- (30,29.25); +\draw [short] (22.5,28) -- (30,28); +\draw [short] (22.5,26.75) -- (30,26.75); +\draw [short] (22.5,25.5) -- (30,25.5); +\draw [short] (22.5,24.25) -- (30,24.25); +\draw [short] (22.5,23) -- (30,23); + +% Sheared config + +\draw [short] (21.25,8) -- (22.5,16.75); +\draw [short] (21.25,8) -- (28.75,8); +\draw [short] (28.75,8) -- (30,16.75); +\draw [short] (22.5,16.75) -- (30,16.75); + +\draw [short] (22.33,15.5) -- (29.83,15.5); +\draw [short] (22.15,14.25) -- (29.65,14.25); +\draw [short] (21.97,13) -- (29.47,13); +\draw [short] (21.79,11.75) -- (29.29,11.75); +\draw [short] (21.61,10.5) -- (29.11,10.5); +\draw [short] (21.43,9.25) -- (28.93,9.25); + +\draw [short] (22.5,16.75) -- (22.5,8); +\draw [short] (23.75,16.75) -- (23.75,8); +\draw [short] (25,16.75) -- (25,8); +\draw [short] (26.25,16.75) -- (26.25,8); +\draw [short] (27.5,16.75) -- (27.5,8); +\draw [short] (28.75,16.75) -- (28.75,8); + +%Twinned config + +\draw [short] (40,16.75) -- (47.5,16.75); +\draw [short] (36.25,8) -- (43.75,8); +\draw [short] (39.4,15.5) -- (46.9,15.5); +\draw [short] (38.75,14.25) -- (46.25,14.25); +\draw [short] (36.9,9.25) -- (44.4,9.25); +\draw [short] (37.5,10.5) -- (45,10.5); + +\draw [short] (46.25,16.75) -- (46.25,14.25); +\draw [short] (45,16.75) -- (45,14.25); +\draw [short] (43.75,16.75) -- (43.75,14.25); +\draw [short] (42.5,16.75) -- (42.5,14.25); +\draw [short] (41.25,16.75) -- (41.25,14.25); +\draw [short] (40,16.75) -- (40,14.25); +%\draw [short] (38.75,16.75) -- (38.75,14.25); +\draw [short] (43.75,10.5) -- (43.75,8); +\draw [short] (42.5,10.5) -- (42.5,8); +\draw [short] (41.25,10.5) -- (41.25,8); +\draw [short] (40,10.5) -- (40,8); +\draw [short] (38.75,10.5) -- (38.75,8); +\draw [short] (37.5,10.5) -- (37.5,8); +%\draw [short] (36.25,10.5) -- (36.25,8); + + +\draw [short] (43.75,10.5) -- (45,14.25); +\draw [short] (42.5,10.5) -- (43.75,14.25); +\draw [short] (41.25,10.5) -- (42.5,14.25); +\draw [short] (40,10.5) -- (41.25,14.25); +\draw [short] (38.75,10.5) -- (40,14.25); +\draw [short] (37.5,10.5) -- (38.75,14.25); % left edge y = 3 x - 102 +%\draw [short] (36.25,10.5) -- (37.5,14.25); +\draw [short] (45,10.5) -- (46.25,14.25); % right edge y = 3 x - 124.5 + +\draw [short] (38.625,13.875) -- (45.375,11.625); %x = 45.375 and y = 11.625, x = 38.625 and y = 13.875 +\draw [short] (41.25,14.25) -- (45.75,12.75); % x = 45.75 and y = 12.75 +\draw [short] (45,14.25) -- (46.125,13.875); % x = 46.125 and y = 13.875 +\draw [short] (38.25,12.75) -- (45,10.5); % x = 38.25 and y = 12.75 +\draw [short] (37.875,11.625) -- (41.25,10.5); %x = 37.875 and y = 11.625 + +\draw [short] (43.75,8) -- (45,10.5); +\draw [short] (46.25,14.25) -- (47.5,16.75); +\draw [short] (36.25,8) -- (37.5,10.5); +\draw [short] (38.75,14.25) -- (40,16.75); + + +%Final config + +\draw [short] (38.022,28.218) -- (39.000,30.500); % left vertical +\draw [short] (36.708,21.985) -- (45.458,23.208); % bottom horizontal +\draw [short] (39.000,30.500) -- (47.750,31.750); % top +\draw [short] (46.772,29.468) -- (47.750,31.750); % right +\draw [short] (45.947,24.350) -- (37.191,23.099); % +\draw [short] (46.437,25.491) -- (37.687,24.241); % bottom 2 +\draw [short] (38.511,29.359) -- (47.261,30.609); % +\draw [short] (38.022,28.218) -- (46.772,29.468); %top 2 + +\draw [short] (37.687,24.241) -- (36.708,21.985);% +\draw [short] (39.145,24.449) -- (38.167,22.167);% bott +\draw [short] (40.603,24.658) -- (39.625,22.375);% +\draw [short] (42.062,24.866) -- (41.083,22.583); % +\draw [short] (43.520,25.074) -- (42.542,22.792); % +\draw [short] (44.978,25.283) -- (44.0,23); +\draw [short] (46.437,25.491) -- (45.458,23.208); + +\draw [short] (39.480,28.426) -- (40.458,30.708); +\draw [short] (40.939,28.634) -- (41.917,30.917); +\draw [short] (42.397,28.843) -- (43.375,31.125); % tops +\draw [short] (43.855,29.051) -- (44.833,31.333); +\draw [short] (45.313,29.259) -- (46.292,31.542); + +\draw [short] (37.687,24.241) -- (38.022,28.218); %Twin +\draw [short] (39.145,24.449) -- (39.480,28.426); %2 +\draw [short] (40.603,24.658) -- (40.939,28.634); %3 +\draw [short] (42.062,24.866) -- (42.397,28.843); +\draw [short] (43.520,25.074) -- (43.855,29.051); +\draw [short] (44.978,25.283) -- (45.313,29.259); +\draw [short] (46.437,25.491) -- (46.772,29.468); + +\draw [short] (45.313,29.259) -- (46.687,28.466); +\draw [short] (43.855,29.051) -- (46.604,27.474); +\draw [short] (42.397,28.843) -- (46.520,26.483); +\draw [short] (40.939,28.634) -- (46.437,25.491); +\draw [short] (39.480,28.426) -- (44.978,25.283); +\draw [short] (38.022,28.218) -- (43.520,25.074); +\draw [short] (37.939,27.226) -- (42.062,24.866); +\draw [short] (37.855,26.235) -- (40.603,24.658); +\draw [short] (37.772,25.243) -- (39.145,24.449); + + +%Explanation + +\draw [->, >=Stealth] (25.75,20.75) -- (25.75,18); +\draw [->, >=Stealth] (32,12.25) -- (34.5,12.25); +\draw [->, >=Stealth] (43.5,18.25) -- (43.5,21.25); +\draw [line width=1.2pt, ->, >=Stealth] (33.25,26.5) .. controls (34.25,27) and (35,27.25) .. (36.25,26.5) ; +\node [font=\Huge] at (26.5,19.5) {$F_p$}; +\node [font=\Huge] at (33,13) {$(\Delta F_p)F_p$}; +\node [font=\Huge] at (46,19.5) {$F_e(\Delta F_p)F_p$}; +\node [font=\Huge] at (34.75,27.5) {$F = F_e(\Delta F_p)F_p$}; +\node [font=\Huge] at (25.5,31.5) {\textbf{Reference Configuration}}; +\node [font=\Huge] at (40,31.5) {\textbf{Current Configuration}}; +\node [font=\Huge] at (41.5,7) {\textbf{Intermediate Configuration,}}; +\node [font=\Huge] at (41.5,6) {\textbf{Slip + Twin}}; +\node [font=\Huge] at (26.5,7) {\textbf{Intermediate Configuration,}}; +\node [font=\Huge] at (26.5,6) {\textbf{Slip}}; + + +\end{circuitikz} \ No newline at end of file diff --git a/images/Typical_Crystal_Plasticity_model.pdf b/images/Typical_Crystal_Plasticity_model.pdf new file mode 100644 index 0000000..abbef7d Binary files /dev/null and b/images/Typical_Crystal_Plasticity_model.pdf differ diff --git a/images/monte_carlo_area.png b/images/monte_carlo_area.png new file mode 100644 index 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