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GATE 2017 ME (ME1) – Question 31

Casting, Forming and Joining Processes · Casting: patterns, moulds, cores, solidification, riser and gating design, defects · 1 mark · Numerical answer

A material has just begun yielding in metal forming, with principal stresses $\sigma_1=180$ MPa, $\sigma_2=-100$ MPa, $\sigma_3=0$. By von Mises theory, find its uniaxial yield stress in MPa.

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Correct answer: 245 to 246

Explanation

At yield, uniaxial yield stress equals von Mises equivalent stress: $\sigma_y=\sqrt{[(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2]/2}$. Substitute the principal stresses to obtain $\sqrt{[280^2+100^2+180^2]/2}=\sqrt{60400}=245.764$ MPa.

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