Project ForgeStrength of Materials
Stress & Strain
GATE 2023
Hard
Ignoring the small elastic region, the true stress (σ) — true strain (ε) variation of a material beyond yielding follows the equation σ=400ε^0.3 MPa. The engineering ultimate tensile strength value of this material is ______ MPa. (Rounded off to one decimal place)
206.5 MPa(± 1 accepted)
Explanation
For a power-law hardening material σ=Kεⁿ, necking (plastic instability) begins at true strain εu=n=0.3. True stress there: σu=400×(0.3)^0.3≈278.7 MPa. Converting to engineering stress: eu=e^εu−1=e^0.3−1≈0.3499, and engineering UTS=σu/(1+eu)=278.7/1.3499≈206.5 MPa.
Source: GATE ME 2023 Official Paper (2023)
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