In [1]:

```
#initiation of variable
from math import acos, asin, sqrt, cos, sin
u1 = 0.0 # Bravais index
v1 = 1.0 # Bravais index
w1 = 0.0 # Bravais index
u2 = 1.0 # Bravais index
v2 = 1.0 # Bravais index
w2 = 0.0 # Bravais index
u3 = -1.0 # Bravais index
v3 = 1.0 # Bravais index
w3 = 1.0 # Bravais index
tau_r1 = 30.0 # Critical resolved shear stress
sigma = 52.0 # Tensile strength in MPa
#Part A:
#calculation
phi = acos((u1*u2+v1*v2+w1*w2)/sqrt((u1**2+v1**2+w1**2)*(u2**2+v2**2+w2**2)))
Lambda = acos((u3*u1+v3*v1+w3*w1)/sqrt((u1**2+v1**2+w1**2)*(u3**2+v3**2+w3**2)))
tau_r = sigma*cos(phi)*cos(Lambda)
#results
print" Resolved shear stress is %.1f MPa" %tau_r
print "Answer in book is 21.3 MPa which is due to approximation"
#Part B
sigma1 = tau_r1/(cos(phi)*cos(Lambda))
#result
print" Applied tensile force to initiate yielding is %.1f MPa" %sigma1
print "Answer in book is 73.4 MPa which is due to approximation"
```

In [2]:

```
#initiation of variable
d1 = 15.2 # Initial diameter in mm
d2 = 12.2 # Final diameter in mm
#calculation
per_CW = (d1**2 - d2**2)*100/d1**2
# Some values are deduced from figures
#result
print" The tensile strength is read directly from the curve for copper(figure 10.9b) as 340 MPa From figure 10.19c, the Ductility at %0.1f CW is about 7%% EL." %per_CW
```

In [3]:

```
#initiation of variable
from math import acos, asin, sqrt, cos, sin
d1 = 6.4 # Initial diameter in mm for first drawing
sigma = 345.0 # tensile strength in MPa
el = 20.0 # ductility in percent
d2 = 5.1 # Final diameter in mm
per_cw = 21.5 # deformation
#calculation
per_CW = (d1**2 - d2**2)*100/d1**2
d0 = sqrt((d2**2*100)/(100.0-el))
#result
print" Theoretical %% Cold Work is %.1f" %per_CW
print" Original Diameter for second drawing is %.1f mm" %d0
print "Answer in book is 5.8 mm which is due to approximation at intermediate steps"
```