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GATE 2024 AE – Question 46

Structures · Strength of materials: Transformation of stress and strain, Mohr's circle, combined loading and failure criteria · 2 marks · Multiple select

The figure shows plots of two yield loci for an isotropic material, where $\sigma_I$ and $\sigma_{II}$ are the principal stresses, and $\sigma_Y$ is the yield stress in uniaxial tension. Which of the following statements is/are correct?

In the $\sigma_I$-$\sigma_{II}$ plane, criterion P is a smooth ellipse tilted along the diagonal. Criterion Q is a six-sided figure (dashed) that is inscribed in the ellipse and touches it at six points, with straight edges at $\pm\sigma_Y$ and diagonal edges in the second and fourth quadrants.
  1. Criterion $P$ represents the von Mises criterion
  2. Criterion $Q$ represents the Tresca criterion
  3. Criterion $P$ represents the Tresca criterion
  4. Criterion $Q$ represents the von Mises criterion

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Correct answer: (A) Criterion $P$ represents the von Mises criterion; (B) Criterion $Q$ represents the Tresca criterion

Explanation

The von Mises criterion plots as a smooth ellipse in principal stress space (P). The Tresca criterion plots as a hexagon with straight edges inscribed in it (Q). They agree in uniaxial tension and differ most in pure shear.