Concept explainers
A 20-cm-long rod with a diameter of 0.250 cm is loaded with a 5000 N weight. If the diameter decreases to 0.210 cm, determine (a) the engineering stress and strain at this load and (b) the true stress and strain at this load.
a)
Engineering stress and strain has to be determined.
Answer to Problem 51AAP
The magnitude of engineering stress is 1019 MPa.
The magnitude of engineering strain is 0.417.
Explanation of Solution
Write the expression for initial area of the bar:
Here, initial diameter of the bar is
Write the expression for initial area of the bar:
Here, final diameter of the bar is
The volume of the bar before and after deformation is same.
Write the expression for the engineering stress as given as follows.
Here, applied force is
Write the expression for the engineering strain as given as follows.
Substitute equation (III) in equation (V).
Conclusion:
Substitute
Substitute
Substitute
Thus, the magnitude of engineering stress is 1019 MPa.
Substitute
Thus, the magnitude of engineering strain is 0.417.
b)
true stress and strain has to be determined.
Answer to Problem 51AAP
The magnitude of true stress is 1443 MPa.
The magnitude of true strain is 0.349.
Explanation of Solution
Write the expression for the true stress as given as follows:
Write the expression for the true strain as given as follows:
Conclusion:
Substitute
Thus, the magnitude of true stress is 1443 MPa.
Substitute
Thus, the magnitude of true strain is 0.349.
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