GATE 2023 ME – Question 57
Ignoring the small elastic region, the true stress ($\sigma$) – true strain ($\varepsilon$) variation of a material beyond yielding follows the equation $\sigma = 400\varepsilon^{0.3}$ MPa. The engineering ultimate tensile strength value of this material is ________ MPa. (Rounded off to one decimal place)
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Correct answer: 205.47 to 207.53
Explanation
The ultimate tensile strength is reached when necking starts. For a power law $\sigma = K\varepsilon^n$ this happens at a true strain $\varepsilon = n = 0.3$. The true stress there is $400 \times 0.3^{0.3} = 278.75$ MPa. The engineering stress is the true stress divided by $e^{\varepsilon}$ (since $\sigma_{true} = \sigma_{eng}(1 + e) = \sigma_{eng}e^{\varepsilon}$): $\sigma_{eng} = \frac{278.75}{e^{0.3}} = \frac{278.75}{1.3499} = 206.5$ MPa.