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
📷 Figure: Stress-strain curve showing loading to 200 MPa at 0.03 strain and unloading to 0 MPa at 0.01 strain
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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