%% Function name
%       alpha_micro

%% Revised:
%       13 January 2014

%% Author
%       Trey Moore & Autar Kaw
%       Section: All
%       Semester: Fall 2013

%% Purpose
%       Given elastic moduli, Poisson's ratios, and coefficients of 
%       thermal expansion for a fiber and matrix, as well as fiber volume
%       fraction, find the outputs coefficient of thermal expansion in the 
%       local directions for the specified unidirectional lamina.

%% Usage 
%       function [alpha12] = alpha_micro(Ef,Em,nuf,numm,alphaf,alpham,Vf)
% Input variables
%       Ef=fiber modulus
%       Em=matrix modulus
%       nuf=fiber Poisson's ratio
%       numm=matrix Poisson's ratio
%       alphaf=thermal expansion of fiber
%       alpham=thermal expansion of matrix
%       Vf=fiber volume fraction
% Output variables 
%       alpha12=vector of thermal expansion of unidirectional lamina
%       [alpha12]=[alpha1 alpha2 alpha12]
% Keywords
%       coefficient of thermal expansion

%% License Agreement
%       http://www.eng.usf.edu/~kaw/OCW/composites/license/limiteduse.pdf

%% Testing Code
clc
clear all
%% Inputs
% Material: Glass/Epoxy
Ef=85E9;
Em=3.4E9;
nuf=0.2;
numm=0.3;
alphaf=5E-6;
alpham=63E-6;
fprintf('\nFiber Elastic Modulus: %g ',Ef)
fprintf('\nMatrix Elastic Modulus: %g ',Em)
fprintf('\nFiber Poisson`s Ratio: %g',nuf)
fprintf('\nMatrix Poisson`s Ratio: %g',numm)
fprintf('\nFiber Coefficient of Thermal Expansion: %g',alphaf)
fprintf('\nMatrix Coefficient of Thermal Expansion: %g',alpham)
%% Test 1 
% Testing for a particular Vf
% Input desired Vf
Vf=0.6;
% Call function: alpha_micro
[alpha12] = alpha_micro(Ef,Em,nuf,numm,alphaf,alpham,Vf);
% Results for a particular Vf
fprintf('\n\nFiber Volume Fraction: %G\n\n',Vf)
disp('      Lamina Coefficient of Thermal Expansion')
disp('___________________________________________________')
fprintf('\n alpha1  | %G\n alpha2  | %G\n alpha12 | %G\n\n\n\n',...
    alpha12(1),alpha12(2),alpha12(3))
%% Test 2
% Table of Thermal Expansion Coefficients of a Unidirectional Lamina
% as a Function of Fiber Volume Fraction
for i=1:1:11
    Vf(i)=i/10-0.1;
    [alpha12] = alpha_micro(Ef,Em,nuf,numm,alphaf,alpham,Vf(i));
    alpha1(i)=alpha12(1);
    alpha2(i)=alpha12(2);
    alpha_12(i)=alpha12(3);
end
% Table of results
disp('          Lamina Coefficient of Thermal Expansion')
disp('______________________________________________________________')
disp('    Vf     |     alpha1      |      alpha2    |     alpha12   ')
for i=1:1:11
fprintf('   %3.2f    |  %E  |   %E  |        %g\n',Vf(i),alpha1(i),...
    alpha2(i),alpha_12(i))
end
%% Test 3
% Graph of Thermal Expansion Coefficients of a Unidirectional Lamina
% as a Function of Fiber Volume Fraction
for i=1:1:101
    Vf(i)=i/100-0.01;
    [alpha12] = alpha_micro(Ef,Em,nuf,numm,alphaf,alpham,Vf(i));
    alpha1(i)=alpha12(1);
    alpha2(i)=alpha12(2);
    alpha_12(i)=alpha12(3);
end
hold on
plot(Vf,alpha1,'LineWidth',2)
plot(Vf,alpha2,'r','LineWidth',2)
plot(Vf,alpha_12,'m','LineWidth',2)
grid
legend('alpha1','alpha2','alpha12')
title('Coefficient of Thermal Expansion vs. Fiber Volume Fraction')
xlabel('Fiber Volume Fraction')
ylabel('Coefficient of Thermal Expansion')
hold off