# Chapter 11: Fracture Mechanics¶

### Example 11.1, Fracture Toughness, Page No. 354¶

In [1]:
from math import sqrt
from math import pi
from math import cos

#variable declaration
a=5;
a=a*10**-3;             #conversion to m
t=1.27;          #in cm
t=t*10**-2;        #conversion to m
def sec(x):
return 1/cos(x);

#calculation
K_Ic=24;
sigma=K_Ic/(sqrt(pi*a)*sqrt(sec(pi*a/(2*t))));

#result
print('Since Fracture Toughness of the material is = %g MPa\n and the applied stress is 172 MPa thus the flaw will propagate as a brittle fracture')%(sigma);

Since Fracture Toughness of the material is = 172.852 MPa
and the applied stress is 172 MPa thus the flaw will propagate as a brittle fracture


### Example 11.2, Fracture Toughness, Page No. 354¶

In [2]:
from math import pi

#variable declaration
K_Ic=57;
sigma0=900;
sigma=360;
Q=2.35;

#calculation
a_c=K_Ic**2*Q/(1.21*pi*sigma**2);
a_c=a_c*1000;                         #conversion to mm

#result
print('\nCritical Crack depth = %g mm\nwhich is greater than the thickness of the vessel wall, 12mm')%(a_c);

Critical Crack depth = 15.4981 mm
which is greater than the thickness of the vessel wall, 12mm


### Example 11.3, Plasticity, Page No. 361¶

In [3]:
from math import sqrt
from math import pi

#variable declaration
a=10;
a=a*10**-3;                 #conversion to m
sigma=400;
sigma0=1500;

#calculation
rp=sigma**2*a/(2*pi*sigma0**2);
rp=rp*1000;                      #conversion to mm
K=sigma*sqrt(pi*a);
K_eff=sigma*sqrt(pi*a)*sqrt(a+pi*rp);

#result
print('\nPlastic zone size = %g mm\nStress Intensity Factor = %g MPa m^(1/2)\n\n\nNote: Calculation Errors in book')%(rp,K_eff);

Plastic zone size = 0.113177 mm
Stress Intensity Factor = 42.8659 MPa m^(1/2)

Note: Calculation Errors in book