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%% Copyright 2014 MERCIER David
function Ap = projectedArea_3sidePyramid(hc, pyrAngle, tiltAngle, rotationAngle, varargin)
%% Function used to calculate the projected contact area of a 3-sided
% pyramidal indentation into a tilted surface
% from Kashani and Madhavan (2010) - http://dx.doi.org/10.1016/j.actamat.2010.09.051
% Ap: Projected contact area in nm2
% hc: Indentation contact depth in nm
% pyrAngle: Face angle of the pyramid in degrees
% tiltAngle: Angle of the tilted sample from the horizontal plane in degrees
% rotationAngle: Rotation angle of the pyramidal indenter in degrees
if nargin == 3
rotationAngle = 0;
end
if nargin == 2
tiltAngle = 0;
rotationAngle = 0;
end
if nargin == 1
tiltAngle = 0;
rotationAngle = 0;
pyrAngle = 65.3; % Berkovich indenter
end
if nargin == 0
figure('Name', 'Projected contact area of a triangular pyramidal indentation into a tilted surface',...
'NumberTitle', 'off');
hc = 1;
pyrAngle = 65.3; % Berkovich indenter
rotationAngle = (0:5:120)';
maxTilt = 5;
% Setting of color/width of lines
c1 = 0;
c2 = 0;
c3 = 0;
lw = 1;
for tiltAngle = 1:1:maxTilt
Ap = projectedArea_TiltAngle(hc, pyrAngle, tiltAngle, rotationAngle);
Ap0 = projectedArea_TiltAngle(hc, pyrAngle);
plot(rotationAngle, Ap/Ap0, ...
'Color',[c1 c2 c3],...
'Linewidth', lw);
xlabel('Rotation angle (in °)', 'Color', [0,0,0], 'FontSize', 14);
ylabel('A_p/A_{p0}', 'Color', [0,0,0], 'FontSize', 14);
set(gca, 'FontSize', 14);
legendInfo{tiltAngle} = (strcat('Tilt angle=', num2str(tiltAngle), '°'));
c1 = c1 + 1/maxTilt;
c2 = c2 + 1/maxTilt;
c3 = c3 + 1/maxTilt;
lw = lw + 1;
hold on;
end
grid on;
legend(legendInfo);
%save_figure(pwd, gca, '_projectedArea_TiltAngle');
end
Ap = (3.*(3.^0.5) .* (hc.^2) .* (tand(pyrAngle).^2)) ./ ...
(1 - (3.*(tand(pyrAngle).^2) .* (tand(tiltAngle).^2)) - ...
(2.*(tand(pyrAngle).^3) .* (tand(tiltAngle).^3) .* cosd(3.*rotationAngle)));
end
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