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%% Copyright 2014 MERCIER David
function [beta, theta_eq, nu] = beta_hay(theta_eq, nu, varargin)
%% Function used to plot beta parameter in function of the equivalent
% semi-angle for a conical indentet and in funciton of the Poisson's
% coefficient of the material indented.
% See Hay J.C. (1999) - DOI: 10.1557/JMR.1999.0306
% theta_eq: Half-angle of the indenter in degrees
% nu: Poisson's coefficient of the sample
if nargin == 0
% First plot in function of theta_eq
nu = 0.3;
theta_eq = 0:0.1:90;
[beta, theta_eq, nu] = beta_hay(theta_eq, nu);
figure;
plot(theta_eq, beta, 'b-', 'LineWidth', 2, 'MarkerSize', 10);
xlabel('\theta_{eq} (°)', 'Color', [0,0,0], 'FontSize', 14);
ylabel('\beta', 'Color', [0,0,0], 'FontSize', 14);
set(gca, 'xlim', [0,90]);
set(gca, 'ylim', [0,2]);
set(gca, 'FontSize', 14);
grid on;
save_figure(pwd, gca, '_betaHay');
% Second plot in function of nu
nu = 0:0.02:0.5;
theta_eq = 70.32; % Equivalent cone angle (in degrees) of the Berkovich indenter
[beta, theta_eq, nu] = beta_hay(theta_eq, nu);
figure;
plot(nu, beta, 'b-', 'LineWidth', 2, 'MarkerSize', 10);
xlabel('\nu', 'Color', [0,0,0], 'FontSize', 14);
ylabel('\beta', 'Color', [0,0,0], 'FontSize', 14);
set(gca, 'FontSize', 14);
grid on;
save_figure(pwd, gca, '_betaHay');
end
if theta_eq > 60
beta = pi .* (((pi/4) + ...
(0.15483073.*cotd(theta_eq) .* ...
((1-2.*nu)./(4*(1-nu))))) ./ ...
((pi/2)-(0.83119312.*cotd(theta_eq) .* ...
((1-2.*nu)./(4.*(1-nu))))).^2);
else
beta = 1 + ((1-2*nu) ./ ...
(4.*(1-nu) .* tand(theta_eq)));
end
end
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