# Chapter 16: Forging¶

### Example 16.1, Forging in Plain Strain, Page No. 574¶

In [2]:
from math import sqrt
from math import exp
from math import log

#variable declaration
sigma=1000;
mu=0.25;
a=2;
b=6;
h=0.25;
x=0;
mu=0.25;

#calculation
p_max=2*sigma*exp(2*mu*(a-x)/h)/sqrt(3);
print('\nAt the centerline of the slab = %g psi\n')%(p_max);
print('\nPressure Distributon from the centerline:');
print('\n---------------------------------\n');
print('x\tp (ksi)\t\tt_i (ksi)\n');
print('---------------------------------\n');
while x<=2:
p=2*sigma*exp(2*mu*(a-x)/h)/(1000*sqrt(3));             #in ksi
t_i=mu*p;
print('%g\t%g\t\t%g\n')%(x,p,t_i);
x+=0.25;
print('---------------------------------\n');
k=sigma/sqrt(3);
x=0;
p_max1=2*sigma*((a-x)/h+1)/sqrt(3);
x1=a-h/(2*mu)*log(1/(2*mu));
p=2*sigma*(a/(2*h)+1)/sqrt(3);
P=2*p*a*b;
P=P*0.000453;                      #conversion to metric tons

#result
print('\nFor sticking friction:\np_max = %g ksi')%(p_max1/1000);
print('\n\nThe Forging load = %g tons')%(P);

At the centerline of the slab = 63044.5 psi

Pressure Distributon from the centerline:

---------------------------------

x	p (ksi)		t_i (ksi)

---------------------------------

0	63.0445		15.7611

0.25	38.2384		9.55961

0.5	23.1928		5.7982

0.75	14.0671		3.51678

1	8.53215		2.13304

1.25	5.17501		1.29375

1.5	3.1388		0.7847

1.75	1.90378		0.475945

2	1.1547		0.288675

---------------------------------

For sticking friction:
p_max = 10.3923 ksi

The Forging load = 62.7695 tons