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Cast iron when tested in tension and compression has an ultimate strength of $({}_{\text{u}\text{l}\text{t}}{)}_T=280$MPa and $({}_{\text{u}\text{l}\text{t}}{)}_C=420$MPa, respectively. Also, when subjected to pure torsion it can sustain an ultimate shear stress of ${}_{\text{u}\text{l}\text{t}}=168$MPa. Plot Mohr's circles for each case and establish the failure envelope by connecting the circles.

If a part made of this material is subjected to the state of plane stress shown below, determine if it fails according to Mohr's failure criterion.

Does it fail?

$($circle one$)$

Yes or No