Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
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Chapter 2, Problem 9P

A part made from annealed AISI 1018 steel undergoes a 20 percent cold-work operation.

  1. a) Obtain the yield strength and ultimate strength before and after the cold-work operation. Determine the percent increase in each strength.
  2. b) Determine the ratios of ultimate strength to yield strength before and after the cold-work operation. What does the result indicate about the change of ductility of the part?

(a)

Expert Solution
Check Mark
To determine

The yield strength if annealed AISI 1018 steel undergoes a 20 percent cold-work operation.

The ultimate strength if annealed AISI 1018 steel undergoes a 20 percent cold-work operation.

The percentage increase in yield strength.

The percentage increase in ultimate strength.

Answer to Problem 9P

The yield strength if annealed AISI 1018 steel undergoes a 20 percent cold-work operation is 62.529kpsi.

The ultimate strength if annealed AISI 1018 steel undergoes a 20 percent cold-work operation 61.875kpsi.

The percentage increase in yield strength is 95.40%.

The percentage increase in ultimate strength is 25%.

Explanation of Solution

Write the expression for work load factor and area.

A0Ai=11W (I)

Here, the original area is A0, the area after load is Ai and work load factor is W.

Write the expression for true strain.

εi=lnA0Ai (II)

Here, the true strain is εi.

Calculate the new yield strength after cold work.

Sy=σ0εmi (III)

Here, the new yield strength is Sy, the strength coefficient is σ0 and strain strengthening exponent is m.

Calculate the new ultimate strength after cold work.

Su=Su1W (IV)

Here, the new ultimate strength after clod work is Su and the ultimate strength before cold work is Su.

Calculate the percentage increase in yield strength.

dy=((SySy)(Sy))×100%                                               (V)

Here, the percentage increase in yield strength is dy, the yield strength before cold-work is Sy.

Calculate the percentage increase in ultimate strength.

du=((SuSu)(Su))×100% (VI)

Here, the percentage increase in ultimate strength is du.

Conclusion:

Refer to Table A-22 “Results of Tensile Test of Some Metals” for annealed AISI 1018 steel.

Obtain the yield strength as 32kpsi, the ultimate strength before cold work as 49.5kpsi, the strength coefficient as 90kpsi and strain strengthening exponent as 0.25.

The steel undergoes 20 percent cold work operation therefore the value of work load factor W is 0.20.

Substitute 0.20 for W in Equation (I).

A0Ai=110.20=1.25

Substitute 1.25 for A0Ai in Equation (II).

εi=ln1.25=0.223

Substitute 0.223 for εi, 0.25 for m and 90kpsi for σ0 in Equation (III).

Sy=(90kpsi)(0.233)0.25=(90kpsi)(0.694766)62.529kpsi

Thus, the yield strength is 62.529kpsi.

Substitute 32kpsi for Sy and 62.529kpsi for Sy in Equation (V).

dy=((62.529kpsi32kpsi)(32kpsi))×100%=(30.529kpsi32kpsi)×100%=95.40%

Thus, the percentage increase in yield strength is 95.40%.

Substitute 49.5kpsi for Su and 0.20 for W in Equation (IV).

Su=(49.5kpsi)(10.20)=(49.5kpsi)(0.80)=61.875kpsi

Thus, the ultimate strength is 61.875kpsi.

Substitute 49.5kpsi for Su and 61.875kpsi for Su in Equation (VI).

du=((61.875kpsi)(49.5kpsi)(49.5kpsi))×100%=(12.375kpsi49.5kpsi)×100%=25%

Thus, the percentage increase in ultimate strength is 25%.

(b)

Expert Solution
Check Mark
To determine

The ratio of ultimate and yield strength before cold-work operation.

The ratio of ultimate and yield strength after cold-work operation and explain the ductility of part with the help of result.

Answer to Problem 9P

The ratio of ultimate and yield strength before cold-work operation is 1.55.

The ratio of ultimate and yield strength after cold-work operation is 1 and after cold working operation steel lost most of its ductility.

Explanation of Solution

Calculate the ratio of ultimate strength to yield strength before cold work.

r1=SuSy                                                          (VII)

Here, the ratio of ultimate strength to yield strength is r1, the ultimate strength before cold work is Su and yield strength before cold work is Sy.

Calculate the ratio of ultimate strength to yield strength after cold work.

r2=SuSy (VIII)

Here, the ratio of ultimate strength to yield strength after cold work is r2, the ultimate strength after cold work is Su and the yield strength after cold work is Sy.

Conclusion:

Substitute 49.5kpsi for Su and 32kpsi for Sy in Equation (VII).

r1=(49.5kpsi)(32kpsi)=1.54681.55

Thus, the ratio of ultimate strength to yield strength before cold work is 1.55.

Substitute 61.9kpsi for Su and 61.8kpsi for Sy in Equation (VIII).

r2=(61.9kpsi)(61.8kpsi)=1.00161

Thus, the ratio of ultimate strength to yield strength after cold work is 1.

From the calculated value of r1 and r2, it is obtained that r1>r2. So, it can be concluded that the steel loses its difficulty after the cold working.

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