GATE ME 2018 Set 2 — Question 56
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Engineering Materials → Forming → Mechanical Properties & Stress-Strain
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Question
The true stress (in MPa) versus true strain relationship for a metal is given by . The cross-sectional area at the start of a test (when the stress and strain values are equal to zero) is . The cross-sectional area at the time of necking (in ) is ________ (correct to two decimal places)
Correct answer
65 to 70
Solution
Given the true stress-true strain relationship: .
At the point of necking, the true strain is equal to the strain hardening exponent .
So, .
True strain is defined as , where is the initial cross-sectional area and is the instantaneous cross-sectional area.
Given .Thus, the cross-sectional area at the time of necking is approximately .
At the point of necking, the true strain is equal to the strain hardening exponent .
So, .
True strain is defined as , where is the initial cross-sectional area and is the instantaneous cross-sectional area.
Given .Thus, the cross-sectional area at the time of necking is approximately .
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