This document is a fourth year composite materials report submitted to Dr. Mohammad Tawfik. It includes a MATLAB code that calculates various properties of composite materials based on inputs like fiber modulus, matrix modulus, fiber volume fraction, thermal coefficients, and Poisson's ratios. The code is then tested on a sample problem from homework 4 to compute properties like modulus in fiber direction E1, transverse modulus E2, in-plane shear modulus G12, and Poisson's ratio ν12 for a composite with given fiber and matrix properties and 40% fiber volume fraction.

1. Fourth Year Composite
materials
Report: Project (1) Advance
Report No: 5 Date: 15/4/2013
Submitted to: Dr. Mohammad Tawfik
Name
 Mohammad Tawfik Eraky
‫عراقي‬ ‫أحمد‬ ‫توفيق‬ ‫محمد‬
2013/2014

2. The project is MATLAB code that calculate all the properties of composite
materials so the input GF, , 𝑬 𝒎 , 𝑬 𝒇 ,𝝂 𝒎 ,𝝂 𝒇 , 𝜶 𝒇, 𝜶 𝒎
𝑬 𝟏, 𝑬 𝟐 , 𝑮 𝟏𝟐 , 𝝂 𝟏𝟐, G23, 𝜶 𝟏 , 𝜶 𝟐
MATLAB code
clc;clear all;close all;
%given the following properities
e_f=55; % modlus of elasticty of Fibers [input in GPa]
e_m= 3.4 ; % Modlus of elasticty of matrix [input in GPa]
v_m= 0.22; % Representative volume of the matrix [input]
v_f=0.78; % Reprenstative volume of the fibers [input]
alpha_m= 60/1000000; % Thermal coefficient of the matrix [input/c]
alpha_f=5.4/1000000 ; % Thermal coeffient of the fibers [input/c]
new_m=0.38;
new_f=0.22;
g_m=e_m/(2*(1+new_m)); % modlus of regidity of the matrix
[input in Gpa]
g_f= e_f/(2*(1+new_f)); % modlus of regidity of the
fibers[input in Gpa]
%outputs
e_1=v_m*e_m+v_f*e_f; %
Modlus of elastisity in fiber direction
e_2=(e_m*e_f)/(v_f*e_m+v_m*e_f); %
modlus of elasticty in direction transverse to the fibers
alpha_1=(v_f*e_f*alpha_f+v_m*e_m*alpha_m)/(v_f*e_f+v_m*e_m); %
thermal coeffiecient in direction 1
alpha_2=alpha_f*v_f+alpha_m*v_m ; %
thermal coeffient in direction 2
new_12=new_f*v_f+new_m*v_m ;
new_21=(e_2*new_12)/e_1; %
inplane shear modlus
g12=(g_m*g_f)/(v_m*g_f+v_f*g_m);
eta_23=(3-4*v_m+(g_m/g_f))/(4*(1-v_m));
g_23=g_m*((v_f+eta_23*(1-v_f))/(eta_23*(1-v_f)+(v_f*g_m/g_f)));
%display outputs
display(e_1);
display(e_2);
display(alpha_1);
display(alpha_2);
display(g12);
display(new_12);
display(new_21);
display(g_23);

3. The code is tested on many problems in homework 4
Pb 4.5
Compute, 𝑬 𝟏, 𝑬 𝟐 , 𝑮 𝟏𝟐 and , 𝝂 𝟏𝟐 given that EF=230Gpa, Em =EF/50,
GF=EF/2.5, GM=EM/2.6, 𝝂 𝒇 = 𝟎. 𝟐𝟓 , 𝝂 𝒎 = 𝟎. 𝟑, and Vf = 40%.the fibers
have circular cross section .Assume there is no voids
Solution
Using MATLAB code project (1)
We get the following results
𝑬 𝟏 = 𝟗𝟒. 𝟕𝟔 𝐆𝐩𝐚
𝑬 𝟐 = 𝟕. 𝟓𝟔𝟓𝟖 𝐆𝐩𝐚
𝑮 𝟏𝟐 = 𝟐. 𝟗𝟏𝟏𝟒 𝑮𝒑𝒂
𝝂 𝟏𝟐 = 𝟎. 𝟐𝟖