
(a)
Interpretation:
The amount of cold work for each of the given steps should be determined.
Concept Introduction:
The relationship between cold work and area is:

Answer to Problem 8.26P
Value of cold working for the diameter ranging from
Value of cold working for the diameter ranging between is
Explanation of Solution
Given information:
Steel bar having initial diameter of 25-mm is cold extruded to 22 mm, and then from 22 mm to a final diameter of 20 mm.
Initial diameter
Final diameter
The value of area is:
On substituting the value of area in the above formula of percentage cold working:
Now on substituting the value of initial diameter and final diameter:
If the diameter is changing from
The above equation gives dependency of diameter value on cold work
Initial Diameter
Final Diameter
The values of area based on diameter is:
On substituting the values in terms of diameter:
(b)
Interpretation:
The comparison between the amounts of cold work for each step to the amount of cold work for direct conversion from 25 mm to 20 mm should be done.

Explanation of Solution
Given information:
Diameter is changing from
Steel bar having initial diameter of 25-mm is cold extruded to 22 mm, and then from 22 mm to a final diameter of 20 mm.
Cold work is the measure of degree of deformation and its calculation is done based on the original and final value area and according to the below statement cold work is directly proportional to the change in area:
The above formula to be used for the calculation of percent cold working as given in the question the value of initial diameter that is
Initial Diameter
Final Diameter
On inserting the values of initial and final diameter we have
Taking
On solving and taking square:
The value of cold work is
As calculated in the above part
Value of cold working for the diameter ranging from
Value of cold working for the diameter ranging between is
Sum ofthe cold work of diameter ranging from
Sum of the cold work of diameter ranging from
The amount of cold work is more for diameter ranging from
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Chapter 8 Solutions
Essentials of Materials Science and Engineering, SI Edition
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