# Chapter09:Fracture of Metals¶

## Ex9.1:pg-200¶

In [2]:
#Example 9.1 : difference
import math
#given data :
E=200*10**9; # in N/m**2
C=(4*10**-6)/2;# in m
gama=1.48; # in J/m**2
sigma=math.sqrt((2*E*gama)/(math.pi*C));
print round(sigma*10**-6),"= fracture strength,sigma(MN/m**2) "

307.0 = fracture strength,sigma(MN/m**2)


## Ex9.2:pg-200¶

In [2]:
#Example 9.2 : the fracture strength and compare

import math
#given data :
E=70*10**9; # in N/m**2
C=(4.2*10**-6)/2;# in m
gama=1.1; # in J/m**2
sigma=math.sqrt((2*E*gama)/(math.pi*C));
print "{:.3e}".format(sigma),"= fracture strength,sigma(N/m**2)  "

1.528e+08 = fracture strength,sigma(N/m**2)


## Ex9.3:pg-200¶

In [5]:
#Example 9.3 : maximum length of surface
import math

#given data :
sigma=36;#in MN/m**2
gama=0.27;# in J/m**2
E=70*10**9;#in N/m**2
C=((2*E*gama)/(sigma**2*math.pi))*10**-6;
C2=2*C;
print round(C2,3),"= maximum length of surface flow,C2(micro-m)   "

18.568 = maximum length of surface flow,C2(micro-m)


## Ex9.4a:pg-203¶

In [8]:
# Example 9.4.a: Temperature

import math
E=350;# in GN/m**2
Y=2;# in J/m**2
C=2;# in micro meter
sg=math.sqrt((2*E*10**9*Y)/(math.pi*C*10**-6));# IN mn/M**2
e=10**-2;# per second
T=173600/(round(sg*10**-6)-20.6-61.3*(math.log10(e)));# in kelvin
print round(T,1),"= temperature in kelvin for ductile to brittle transition at a strain rate of 10**-2 per second"

302.4 = temperature in kelvin for ductile to brittle transition at a strain rate of 10**-2 per second


## Ex9.4b:pg-203¶

In [10]:
# Example 9.4.b: Temperature
import math

E=350;# in GN/m**2
Y=2;# in J/m**2
C=2;# in micro meter
sg=math.sqrt((2*E*10**9*Y)/(math.pi*C*10**-6));# IN mn/M**2
e=10**-5;# per second
T=173600/(round(sg*10**-6)-20.6-61.3*(math.log10(e)));# in kelvin
print round(T),"= temperature in kelvin for ductile to brittle transition at a strain rate of 10**-5 per second"

229.0 = temperature in kelvin for ductile to brittle transition at a strain rate of 10**-5 per second