Project ForgeStrength of Materials
Stress & Strain
GATE 2018
Hard
The true stress (in MPa) versus true strain relationship for a metal is given by σ=1020ε^0.4. The cross-sectional area at the start of a test (when the stress and strain values are equal to zero) is 100 mm². The cross-sectional area at the time of necking (in mm²) is __________ (correct to two decimal places).
67 mm²(± 2.5 accepted)
Explanation
By Considère's criterion, necking begins where dσ/dε=σ, which for a power-law σ=Kεⁿ occurs at ε=n. Here n=0.4, so necking strain ε=0.4. By volume constancy, true strain ε=ln(A0/A) → 0.4=ln(100/A) → A=100/e^0.4 ≈ 100/1.4918 ≈ 67.03 mm².
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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