GATE ME 2021 Set 1 — Question 16
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Engineering Materials → Stress, Strain & Elastic Constants → Mechanical Properties & Stress-Strain
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Question
The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to 200 MPa stress, respectively, are
Correct answer
(B) 0.02 and 0.01
Solution
To find the elastic and plastic strains corresponding to a stress of , we analyze the loading and unloading behavior shown in the stress-strain curve:
$\varepsilon$_{\text{total}} = 0.03
$\varepsilon$_p = 0.01
$\varepsilon$_{\text{total}} = $\varepsilon$_e + $\varepsilon$_p Substituting the known values:
0.03 = $\varepsilon$_e + 0.01 $\varepsilon$_e = 0.03 - 0.01 = 0.02Thus, the elastic and plastic strains corresponding to stress are 0.02 and 0.01, respectively.Correct Option: B
1.Total Strain ():
During loading, the material is stressed up to . At this peak stress, the total strain reached is:$\varepsilon$_{\text{total}} = 0.03
2.Plastic Strain ():
When the material is fully unloaded from to , the elastic strain is recovered, leaving only the permanent (plastic) deformation. From the figure, the residual strain after complete unloading is:$\varepsilon$_p = 0.01
3.Elastic Strain ():
The total strain is the sum of the elastic and plastic strains:$\varepsilon$_{\text{total}} = $\varepsilon$_e + $\varepsilon$_p Substituting the known values:
0.03 = $\varepsilon$_e + 0.01 $\varepsilon$_e = 0.03 - 0.01 = 0.02Thus, the elastic and plastic strains corresponding to stress are 0.02 and 0.01, respectively.Correct Option: B
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