Solution

Solution

Use table 2.4 for matrices properties and table 2.1 for fibers properties.

a)

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b)

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c)

I have tried a lot of combinations and volume fraction using data from tables

mentioned above and I couldn't choose materials that satisfy the requirements.

To be asked about in the lecture.

MATLAB Code

clear;clc;close all; Ef=input('Ef(in GPa) = ') Em=input('Em(in Gpa) = ') nu_f=input('fiber poisson ratio = ') nu_m=input('matrix poisson ratio = ') Vf=input('fiber volume fraction = ') alfa_f=input('fiber thermal expansion coeff = ') alfa_m=input('matrithermal expansion coeff = ')

Vm=1-Vf; Gf=Ef/(2*(1+nu_f)) Gm=Em/(2*(1+nu_m))

E1=Vm*Em+Vf*Ef E2=Ef*Em/(Vf*Em+Vm*Ef) G12=Gf*Gm/(Vf*Gm+Vm*Gf) eta23=(3-4*nu_m+Gm/Gf)/(4*(1-nu_m)) G23=Gm*((Vf+eta23*(1-Vf))/(eta23*(1-Vf)+Vf*Gm/Gf)) nu_12=nu_f*Vf+nu_m*Vm alfa1=alfa_f*Vf*Ef/(Vf*Ef+Vm*Em)+alfa_m*Vm*Em/(Vf*Ef+Vm*Em) alfa_2=alfa_f*Vf+alfa_m*Vm

Results On problem 4.6 part (C) Ef(in GPa) = 230

Ef =

230

Em(in Gpa) = 3.4

Em =

3.4000

fiber poisson ratio = 0.2

nu_f =

0.2000

matrix poisson ratio = 0.38

nu_m =

0.3800

fiber volume fraction = 0.55

Vf =

0.5500

fiber thermal expansion coeff = 0

alfa_f =

0

matrithermal expansion coeff = 0

alfa_m =

0

Gf =

95.8333

Gm =

1.2319

E1 =

128.0300

E2 =

7.4215

G12 =

2.6952

eta23 =

0.6020

G23 =

3.6382

nu_12 =

0.2810

alfa1 =

0

alfa_2 =

0