Concept explainers
(a)
The change in radius of specimen.
(a)
Answer to Problem 6.2P
The change in radius of specimen is not significant and the final radius of specimen is
Explanation of Solution
Given:
Poisson’s ratio is
Radius of specimen is
Elongation in steel rod is
Write the expression for tensile stress in rod.
Here,
Substitute
Here,
Write the expression for axial strain in steel rod.
Here,
Write the expression for axial strain in
Here,
Write the expression for final radius of specimen.
Here,
Substitute
Substitute
Substitute
Substitute
Thus, the change in radius of specimen is not significant and the final radius of specimen is
(b)
The difference between true stress and engineering stress.
(b)
Answer to Problem 6.2P
There is no difference between true stress and engineering stress for this specimen.
Explanation of Solution
As the change in radius of specimen is not significant, the actual and original radius of specimen can be considered as same. The true stress is evaluated on the basis of actual cross-sectional area of specimen and engineering stress is calculated on original cross-sectional area of specimen. As the value of area is constant for same final radius there will be no difference in Engineering stress and true stress.
The calculate engineering stress or true stress of specimen is
Thus, there is no difference between true stress and engineering stress for this specimen.
(c)
The value of true strain and compare it with engineering strain.
(c)
Answer to Problem 6.2P
The true strain for the specimen is
Explanation of Solution
Write the expression for true strain of specimen.
Here,
Substitute
The engineering strain and true strain will remain same for the specimen.
Thus, the true strain for the specimen is
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Chapter 6 Solutions
Materials Science And Engineering Properties
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- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning