Project ForgeStrength of Materials
Stress & Strain
GATE 2016
Medium
A hypothetical engineering stress-strain curve has three straight segments PQ, QR, RS with coordinates P(0,0), Q(0.2%,100 MPa), R(0.6%,140 MPa), S(0.8%,130 MPa), where Q is the yield point, R the UTS point, and S the fracture point. The toughness of the material (in MJ/m³) is __________.
0.85 MJ/m³(± 0.005 accepted)
Explanation
Toughness = area under the curve (strain as a fraction). PQ (0 to 0.002): 0.5(100)(0.002)=0.1. QR (0.002 to 0.006): 0.5(100+140)(0.004)=0.48. RS (0.006 to 0.008): 0.5(140+130)(0.002)=0.27. Total = 0.1+0.48+0.27 = 0.85 MJ/m³.
Source: GATE ME 2016 Set-1 (2016)
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