Visualizing Mild Steel

stress_strain_curve.m

% Stress-Strain Curve Simulation
% *Important: The X-axis (strain) scale has been exaggerated
% for educational purposes to enhance graph visibility

%% Visual Data Generation
% [Settings: MPa]
sig_upper_yield = 280; % Upper Yield Point
sig_lower_yield = 240; % Lower Yield Point
sig_uts = 450;         % Ultimate Tensile Strength (UTS)
sig_frac = 350;        % Fracture Strength

% [Strain Settings per Section (X-axis)]
% Intervals widened to enhance visual slope
eps_1_elastic = linspace(0, 0.05, 30);       % 1. Elastic Region
eps_2_drop    = linspace(0.05, 0.06, 10);    % 2. Yield Drop
eps_3_plateau = linspace(0.06, 0.10, 20);    % 3. Yield Plateau
eps_4_harden  = linspace(0.10, 0.25, 60);    % 4. Strain Hardening
eps_5_necking = linspace(0.25, 0.30, 20);    % 5. Necking

% [Stress Calculations per Section (Y-axis)]

% 1. Elastic Region
sig_1_elastic = linspace(0, sig_upper_yield, length(eps_1_elastic));

% 2. Yield Drop Region
sig_2_drop = linspace(sig_upper_yield, sig_lower_yield, length(eps_2_drop));

% 3. Yield Plateau Region
sig_3_plateau = linspace(sig_lower_yield, sig_lower_yield, length(eps_3_plateau));

% 4. Strain Hardening Region
a_val = (sig_lower_yield - sig_uts) / (0.10 - 0.25)^2;
sig_4_harden = a_val * (eps_4_harden - 0.25).^2 + sig_uts;

% 5. Necking Region 
sig_5_necking = linspace(sig_uts, sig_frac, length(eps_5_necking));

% Build Strain and Stress Data
strain = [eps_1_elastic, eps_2_drop, eps_3_plateau, eps_4_harden, eps_5_necking];
stress = [sig_1_elastic, sig_2_drop, sig_3_plateau, sig_4_harden, sig_5_necking];

%% Graph Style Settings
figure('Name', 'Stress-Strain Simulation', 'Color', [0,0,0], 'Position', [100, 100, 900, 600]);
hold on; grid on; box on;

% Set Axis Limits and Labels
xlim([0, 0.32]);
ylim([0, 550]);

% X-axis and Y-axis Labels and Title Settings
xlabel('Strain', 'FontSize', 12, 'FontWeight', 'bold');
ylabel('Stress [MPa]', 'FontSize', 12, 'FontWeight', 'bold');
title('Stress-Strain Curve Simulation', 'FontSize', 15, 'Color', [1, 1, 1]);

% Graph Line, Marker, Annotation Text Settings
hLine = plot(strain(1), stress(1), 'b-', 'LineWidth', 3);
hMarker = plot(strain(1), stress(1), 'ro', 'MarkerFaceColor', 'r', 'MarkerSize', 10);
hText = text(0.02, 500, 'Start', 'FontSize', 12, 'BackgroundColor', [1,1,1], 'EdgeColor', 'k', 'Color', [0, 0, 0]);

% X,Y Axis Color Settings
ax = gca;
ax.XColor = [1,1,1];
ax.YColor = [1,1,1];

%% Draw Graph
for i = 1:length(strain)
    % Graph Line, Marker Data Update
    set(hLine, 'XData', strain(1:i), 'YData', stress(1:i));
    set(hMarker, 'XData', strain(i), 'YData', stress(i));
    
    curr_eps = strain(i); % Current Strain
    
    % 1. Elastic Region
    if curr_eps <= 0.05
        msg = '1. Elastic Region';
        if i == length(eps_1_elastic)
            text(strain(i), stress(i)+20, 'Upper Yield Point', 'Color', [1,1,1], 'FontWeight', 'bold');
            pause(0.7);
        end
        pause(0.05);
    % 2. Yield Drop Region
    elseif curr_eps <= 0.06
        msg = '2. Yield Drop Region';
        if i == length(eps_1_elastic) + length(eps_2_drop)
             text(strain(i), stress(i)+20, 'Lower Yield Point', 'Color', [1,1,1], 'FontWeight', 'bold');
             pause(0.7);
        end
        pause(0.2);
    % 3. Yield Plateau Region
    elseif curr_eps <= 0.10
        msg = '3. Yield Plateau Region';
        if i == length(eps_1_elastic) + length(eps_2_drop)
             text(strain(i), stress(i)+20, 'Lower Yield Point', 'Color', [1,1,1], 'FontWeight', 'bold');
             pause(0.7);
        end
        pause(0.05);
    % 4. Strain Hardening Region
    elseif curr_eps <= 0.25
        msg = '4. Strain Hardening Region';
        if abs(curr_eps - 0.25) < 0.002
             text(strain(i), stress(i)+20, 'UTS', 'Color', [1,1,1], 'FontWeight', 'bold', 'HorizontalAlignment', 'center');
             pause(0.7);
        end
        pause(0.03);
    % 5. Necking Region
    else
        msg = '5. Necking Region';
        pause(0.1);
    end
    set(hText, 'String', msg);
    drawnow;
end

% Draw Marker and Text
plot(strain(end), stress(end), 'kx', 'MarkerSize', 25, 'LineWidth', 4, 'Color', [1,1,1]);
text(strain(end), stress(end)+30, 'Fracture!', 'Color', [1,1,1], 'FontSize', 14, 'FontWeight', 'bold', 'HorizontalAlignment', 'center');