This document provides examples of calculating the elastic properties of composite materials made of fibers and matrices at different volume fractions. In Example 1, it shows how to calculate the elastic modulus, Poisson's ratio, and shear modulus of a composite. Example 2 calculates these properties for composites made of different fiber and matrix combinations. Example 3 uses MATLAB to select a fiber, matrix, and fiber volume fraction to achieve a desired elastic modulus and strength ratio. It determines D-glass fiber and Bismaleimide matrix with a 24% fiber volume fraction achieves this.

1. )4HW (
Example (1):
Givens:
= 230 GPa
= = = 4.6 GPa
= = = 92 GPa
= = = 1.769 GPa
= 0.25
= 0.3
= 0.6
= 0.4
,,,:Calculate
= . + . = (0.4*230) + (0.6*4.6) = 94.76 GPa
= = = 7.565 GPa
= . + . = (0.3*0.6) + (0.25*0.4) = 0.28
= = = 2.911 GPa

2. Example (2):
Calculate: , , , for a unidirectional lamina for the
following material combinations: = 0.45 and = 0.55
1. E-glass and polyester (isophthalic)
From table 2.1:
E-glass has the following properties:
= 72.345 GPa
= 0.22
= 3.45 GPa
From table 2.4:
Polyester has the following properties:
= 3.4 GPa
= 0.38
= 75.9 GPa
= . + . = (0.55*72.345) + (0.45*3.4) = 41.32
= = = 7.145 GPa
= . + . = (0.38*0.55) + (0.22*0.45) = 0.308
= = = 6.047 GPa

3. 2. S-glass and epoxy9310:
From table 2.1:
S-glass has the following properties:
= 85 GPa
= 0.22
= 4.8 GPa
From table 2.4:
Epoxy9310 has the following properties:
= 3.12 GPa
= 0.38
= 75.8 GPa
= . + . = (0.55*85) + (0.45*3.12) = 48.154
= = = 6.635 GPa
= . + . = (0.38*0.55) + (0.22*0.45) = 0.308
= = = 8.297 GPa
3. Carbon T300 and vinyl esler:
From table 2.1:
Carbon T300 has the following properties:
= 230 GPa
= 0.2
= 3.53 GPa
From table 2.4:
Vinyl esler has the following properties:
= 3.4 GPa
= 0.38
= 82.7 GPa

4. = . + . = (0.55*230) + (0.45*3.4) = 128.03
= = = 7.421 GPa
= . + . = (0.38*0.55) + (0.2*0.45) = 0.299
= = = 6.202 GPa
Example (3):
Select a matrix, fiber and fiber volume fraction to obtain
material with and
for different fibers and matrices we find that toBy using matlab
get these conditions we use:
D-glass as fiber and Bismaleiraide as a matrix
Matlab code:
clear;clc;close all;
Vm = 0.24;
Vf = 1-Vm;
Ef = 55;
Em = 3.583;
E1 = (Vf*Ef)+(Vm*Em)
E2 = (Em*Ef)/((Vf*Em)+(Vm*Ef))
F = E1/E2
Output:
E1 = 42.6599
E2 = 12.3761
F = 3.4470 =