# Chatper 19 : Composite Materials¶

### Example 19.1 pageno : 507¶

In [3]:
# Variables
t_s = 3.;			#in mm
t_c = 24.;			#in mm
b = 100.;			#in mm

# Calculations
d = (t_s+t_c)/2;			#in mm
is_ = ((b*t_s**3)/12)+(b*t_s*d**2);			#in mm**4
ic = b*t_c**3/12                			#in mm**4
Es = 7000.;    			                #moduli of polyester skin in N/mm**2
m_f = 20.;  			                    #moduli of foam core in N/mm**2
d_fr = (2*Es*is_)+(m_f*ic);			        #in N/mm**2

Ts = 6
D_s = (Es*b*Ts**2)/12
c = d_fr/D_s

# Results
print "Flexural rigidity (in N/sqm)  =  %.2e"%d_fr
print "Ds = %.1e N mm**2"%D_s
print "Flexural rigidity of sandwich beam is %d times more"%c

# Note : answer in book is wrong for D_s please check manually.

Flexural rigidity (in N/sqm)  =  7.71e+08
Ds = 2.1e+06 N mm**2
Flexural rigidity of sandwich beam is 367 times more


### Example 19.2 page no : 520¶

In [2]:
# Variables
ec = 210.;			#in GPa
ea = 71.;			#in GPa
eb = 440.;			#in GPa

# Calculations
va = (ec-eb)/(ea-eb);
vb = 1-va;
c = vb/va;

# Results
print "Volume ratio  =  %.2f"%c

# note : answer in book is wrong . please calculate manually.

Volume ratio  =  0.60


### Example 19.3 pageno : 521¶

In [14]:
# Variables
ef = 430.;			#in GPa
e = 3.6;			#in GPa
m = ef/e;
vf = 0.15;			#by volume

# Calculations
vm = 1-vf;
x = vm/vf;
pf = m;
pc = m+x;
y = pf/pc;
vf1 = 0.65
vm1 = 1-vf1;
z = vm1/vf1;
pc1 = m+z;
zz = pf/pc1;

# Results
print "fraction of load carried by fibres (15 %% by volume)  =  %.2f"%y
print "fraction of load carried by fibres (65 %% by volume)  =  %.4f"%zz

fraction of load carried by fibres (15 % by volume)  =  0.95
fraction of load carried by fibres (65 % by volume)  =  0.9955


### Example 19.4 page no : 522¶

In [17]:
# Variables
vf = 0.65;
vm = 1-vf;
kts = 2.8;  			#in Gpa
ets = 0.0025;			#in GPa

# Calculations and Results
ac = (kts*vf)+(ets*vm);			#in GPa
print "Longitudinal Strength (in GPa)  =  %.2f"%ac

ktm = 130.;			#in GPa
etm = 3.5;			#in GPa
ec = (ktm*vf)+(etm*vm);
print "Longitudianl Modulous (in GPa)  =  %.2f"%ec

e_c = 1/((vf/ktm)+(vm/etm));
print "Transverse Modulous (in GPa)  =  %.2f"%e_c

kp = 0.34;			#in GPa
ep = 0.36;			#in GPa
vlt = (vf*kp)+(vm*vm);
print "Poissons Ratio  =  ",vlt

glt = 1./((vf/2.2)+(vm/1.2));			#in GPa
print "Shear Modulous (in GPa)  =  %.2f"%glt

# note: answer in book is wrong for part a. please calculate manually.

Longitudinal Strength (in GPa)  =  1.82
Longitudianl Modulous (in GPa)  =  85.72
Transverse Modulous (in GPa)  =  9.52
Poissons Ratio  =   0.3435
Shear Modulous (in GPa)  =  1.70