# Chapter 8: The Tension Test¶

### Example 8.1, Standard properties of the material, Page No. 281¶

In [1]:
from math import pi

#variable declaration
D=0.505;
Lo=2;
Lf=2.53;
Py=15000;
Pmax=18500;
Pf=16200;
D_f=0.315;

#calculation
A0=pi*D**2/4;
Af=pi*D_f**2/4;
s_u=Pmax/A0;
s0=Py/A0;
s_f=Pf/A0;
e_f=(Lf-Lo)/Lo;
q=(A0-Af)/A0;

#result
print('\nUltimate Tensile Strength = %g psi\n0.2 percent offset yield strength = %g psi\nBreaking Stress = %g psi\nElongation = %g percent\nReduction of Area = %g percent\n\n\nNote: Slight Computational Errors in book')%(s_u,s0,s_f,e_f*100,q*100);

Ultimate Tensile Strength = 92363.2 psi
0.2 percent offset yield strength = 74889.1 psi
Breaking Stress = 80880.2 psi
Elongation = 26.5 percent
Reduction of Area = 61.092 percent

Note: Slight Computational Errors in book


### Example 8.2, True Strain, Page No. 288¶

In [2]:
from math import log

#case 1
#variable declaration
Af=100.0;
Lf1=60.0;
A0=150.0;
L01=40.0;
Lf=83.0;
L0=40.0;
Df=8.0;
D0=12.8;

#calculation
L1=float (Lf1/L01);
A1=float (A0/Af);
ef11=log(L1);
ef21=log(A1);
L2=(Lf/L0);
D2=D0/Df;5
ef12=log(L2);
ef22=2*log(D2);

#result
print('\nTrue Strain to fracture using changes in length = %g\nTrue Strain to fracture using changes in area = %g')%(ef11,ef21);
print('\n\n\nFor More ductile metals\nTrue Strain to fracture using changes in length = %g\nTrue Strain to fracture using changes in diameter = %g')%(ef12,ef22);

True Strain to fracture using changes in length = 0.405465
True Strain to fracture using changes in area = 0.405465

For More ductile metals
True Strain to fracture using changes in length = 0.729961
True Strain to fracture using changes in diameter = 0.940007


### Example 8.3, Ultimate Tensile Strength, Page No. 290¶

In [3]:
from math import exp

#variable declaration
def sigma(e):
return 200000*e**0.33;
E_u=0.33;

#calculation
sigma_u=sigma(E_u);
s_u=sigma_u/exp(E_u);

#result
print('Ultimate Tensile Strength = %g psi')%(s_u);

Ultimate Tensile Strength = 99729.2 psi


### Example 8.4, Effect of Strain Rate, Page No. 298¶

In [4]:
#variable declaration
C_70=10.2;
C_825=2.1;
m_70=0.066;
m_825=0.211;
e1=1;
e2=100;

#calculation 1
print('\nAt 70deg F\n');
sigma_a=C_70*e1**m_70;
sigma_b=C_70*e2**m_70;

#result 1
print('sigma_a = %g ksi\nsigma_b = %g ksi\nsigma_b/sigma_a = %g\n')%(sigma_a,sigma_b,sigma_b/sigma_a);

#calculation 2
print('\n\nAt 825deg F\n');
sigma_a=C_825*e1**m_825;
sigma_b=C_825*e2**m_825;

#result 2
print('sigma_a = %g ksi\nsigma_b = %g ksi\nsigma_b/sigma_a = %g\n')%(sigma_a,sigma_b,sigma_b/sigma_a);

At 70deg F

sigma_a = 10.2 ksi
sigma_b = 13.8229 ksi
sigma_b/sigma_a = 1.35519

At 825deg F

sigma_a = 2.1 ksi
sigma_b = 5.54906 ksi
sigma_b/sigma_a = 2.64241