# Chapter 17 Composites :Teamwork and Synergy in Materials¶

## Example 17_1 pgno:655¶

In [1]:
from math import pi
# Initialisation of Variables
per1=2.;#Percent weight of ThO2
per2=98.;#Percentage weight of Nickle
rho1=9.69;#Density of ThO2 in g/cm**3
rho2=8.9;#Density of Nickel in g/cm**3
r=0.5*10**-5;#Radius of ThO2 particle in cm
#calculations
f=(2/rho1)/((per1/rho1)+(per2/rho2));#Volume fraction of ThO2 per cm**3 of composite
v=(4/3)*(pi)*r**3;#Volume of ech ThO2 sphere in cm**3
c=f/v;#Concentration of ThO2 particles in particles/cm**3
print "Concentration of ThO2 in particles/cm**3:",c

#the difference in answer is due to round off error

Concentration of ThO2 in particles/cm**3: 4.68538254249e+13


## Example 17_2 pgno:656¶

In [2]:
# Initialisation of Variables
per1=75.;#Percent Weight of WC
per2=15.;#Percent Weight of TiC
per3=5.;#Percent Weight of TaC
per4=5.;#Percent Weight of Co
rho1=15.77;#Density of WC in g/cm**3
rho2=4.94;#Density of TiC in g/cm**3
rho3=14.5;#Density of TaC in g/cm**3
rho4=8.90;#Density of Co in g/cm**3
#Calculations
f1=(per1/rho1)/((per1/rho1)+(per2/rho2)+(per3/rho3)+(per4/rho4));#Volume fraction of WC
f2=(per2/rho2)/((per1/rho1)+(per2/rho2)+(per3/rho3)+(per4/rho4));#Volume fraction of Tic
f3=(per3/rho3)/((per1/rho1)+(per2/rho2)+(per3/rho3)+(per4/rho4));#Volume fraction of Tac
f4=(per4/rho4)/((per1/rho1)+(per2/rho2)+(per3/rho3)+(per4/rho4));#Volume fraction of Co
rho=(f1*rho1)+(f2*rho2)+(f3*rho3)+(f4*rho4);#Density of composite in g/cm**3
print "Density of composite in g/cm**3:",round(rho,1)

Density of composite in g/cm**3: 11.5


## Example 17_3 pgno:658¶

In [12]:
# Initialisation of Variables
rho1=19.3;#Density of pure Tungsten in g/cm^3
rho2=10.49;#Density of pure Silver in g/cm^3
f1=0.75;#Volume fraction of Tungsten
f2=0.25;#Volume fraction of Silver and pores
#Calculations
per=((f2*rho2)/((f2*rho2)+(f1*rho1)))*100;#Percentage weight of silver
print "Percentage Weight of Silver:",round(per)

15.0 Percentage Weight of Silver:


## Example 17_4 pgno:659¶

In [3]:
# Initialisation of Variables
rho1=0.95;#Density of polyethylene in g/cm^3
rho2=2.4;#Density of clay in g/cm^3
f1=0.65;#Volume fraction of Polyethylene
f2=0.35;#Volume fraction of Clay
f3=1.67;#Volume fraction of polyethylene after sacrifice
f4=1.06;#Volume fraction of Clay after sacrifice
pa1=650;# No. of parts of polyethylene in 1000cm^3 composite  in cm^3
pa2=350;# No. of parts of clay in 1000cm^3 composite  in cm^3
#Calculations
pa3=(pa1*rho1)/454;#No. of parts of Polyethylene in 1000cm^3 composite  in lb
pa4=(pa2*rho2)/454;#No. of parts of clay in 1000cm^3 composite  in lb
co1=pa3* 0.05;#Cost of material Polyethylenein Dollars
co2=pa4* 0.05;#Cost of materials clay in Dollars
c0=co1+co2;#Cost of materials in Dollars
rho3=(f1*rho1)+(f2*rho2);#Composite density in g/cm^3
co3=f3* 0.05;#Cost of material polyethylene after savings in Dollars
co4=f4* 0.05;#Cost of material clay after savings in Dollars
c1=co3+co4;#Cost of materials after savings in Dollars
rho4=(0.8*rho1)+(0.2*rho2);#Density of composite after saving in g/cm^3
print "Composite density in g/cm^3:",round(rho3,2)
print "Composite densityafter saving in g/cm^3:",rho4

Composite density in g/cm^3: 1.46
Composite densityafter saving in g/cm^3: 1.24


## Example 17_7 pgno:664¶

In [4]:
f1=0.4;#Volume fraction of Fiber
f2=0.6;#Volume fraction of Aluminium
rho1=2.36;#Density of Fibers in g/cm**3
rho2=2.70;#Density of Aluminium in g/cm**3
psi1=55*10**6;#Modulus of elasticity of Fiber in psi
psi2=10*10**6;#Modulus of elasticity of Aluminium in psi
ts1=400000;#Tensile strength of fiber in psi
ts2=5000;#Tensile strength of Aluminium in psi
#Calculations
rho=(f1*rho1)+(f2*rho2);#Density of mixture in g/cm**3
Ec1=(f1*psi1)+(f2*psi2);#Modulus of elasticity of mixture in psi
TSc=(f1*ts1)+(f2*ts2);#Tensile Strength of mixture in psi
Ec2=1/((f1/psi1)+(f2/psi2));#Modulus of elasticity  perpendicular to fibers in psi
print "Density of mixture in g/cm**3:",rho
print "Modulus of elasticity of mixture in psi:",Ec1
print "Tensile Strength of mixture in psi:",TSc
print "Modulus of elasticity  perpendicular to fibers in psi:",Ec2

Density of mixture in g/cm**3: 2.564
Modulus of elasticity of mixture in psi: 28000000.0
Tensile Strength of mixture in psi: 163000.0
Modulus of elasticity  perpendicular to fibers in psi: 14864864.8649


## Example 17_8 pgno:665¶

In [5]:
# Initialisation of Variables
psi1=10.5*10**6;#Modulus of elasticity of Glass in psi
psi2=0.4*10**6;#Modulus of elasticity of Nylon in psi
a1=0.3;#area of glass in cm**3
a2=0.7;#area of Nylon in cm**3
#Calculations
psi=psi1/psi2;#Fraction of elasticity
fo=a1/(a1+(a2*(1/psi)));#Fraction of applied force carried by Glass fiber
print"Fraction of applied force carried by Glass fiber :",round(fo,2)
print"Almost all of the load is carried by the glass fibers."

Fraction of applied force carried by Glass fiber : 0.92
Almost all of the load is carried by the glass fibers.


## Example 17_9 pgno:670¶

In [6]:
# Initialisation of Variables
psi=10*10**6;#Modulus of elasticity of 7075-T6 in psi
psi1=55*10**6;#Modulus of elasticity of Boron fiber in psi
psi2=11*10**6;#Modulus of elasticity of Typical AL-LI in psi
f1=0.6;#Volume fraction of Boron Fiber
f2=0.4;#Volume fraction of typical AL-LI
rho1=0.085;#Density of  Boron Fibers in lb/in*3
rho2=0.09;#Density of typical AL-LI in lb/in**3
#Calculations
sm1=psi/(((2.7*(2.54)**3))/454);#Specific Modulus of current alloy in in.
rho=(f1*rho1)+(f2*rho2);#Density of composite in lb/in**3
Ec=(f1*psi1)+(f2*psi2);#Modulus of elasticity of mixture in psi
sm2=Ec/rho;#Specific Modulus of composite in in.
print "Specific Modulus of current alloy in in.:",sm1
print "Density of composite in lb/in**3:",rho
print "Modulus of elasticity of mixture in psi:",Ec
print "Specific Modulus of composite in 10**8 in.:",round(sm2/10**8,1)

Specific Modulus of current alloy in in.: 102610295.626
Density of composite in lb/in**3: 0.087
Modulus of elasticity of mixture in psi: 37400000.0
Specific Modulus of composite in 10**8 in.: 4.3


## Example 17_10 pgno:683¶

In [7]:
from math import pi
# Initialisation of Variables
psi=500000.;#Modulus Elasticity of Epoxyin psi
f=500.;#Force applied on Epoxy in pounds
q=0.10;#Stretchable distence in in.
rho=0.0451;#Density of Epoxy in lb/in**3
d=1.24;#Diameter of Epoxy in in
e=12000;#Yeild Strngth of Epoxy in psi
E2=77*10**6;#Modulus of high Carbon Fiber in psi
Fc=0.817;#Volume fraction of Epoxy remaining
Fc2=0.183;#Min volume Faction of Epoxy
rho2=0.0686;#Density of high Carbon Fiber in lb/in**3
emax=q/120;#MAX. Strain of Epoxy
E=psi*emax;#Max Modulus of elasticity in psi
A=f/E;#Area of Structure in in**2
W=rho*pi*((d/2)**2)*120;#Weight of Structure in ib
c=W*0.80;#Cost of Structure in Dollars
Ec=e/emax;#Minimum Elasticity of composite in psi
A2=f/e;#Area of Epoxy in in**2
At=A2/Fc;#Total Volume of Epoxy
V=At*120;#Volume of Structure in in**3
W2=((rho2*Fc2)+(rho*Fc))*V;#Weight of Structure in lb
Wf=(Fc2*1.9)/((Fc2*1.9)+(Fc*1.25));#Weight Fraction of Carbon
Wc=Wf*W2;#Weight of Carbon
We=0.746*W2;#Weight of Epoxy
c2=(Wc*30)+(We*0.80);#Cost of Each Struct.
print "Cost of Each Struct.:",round(c2,2)
#the diffrence in answer is due to erronous calculations

Cost of Each Struct.: 2.48