Cast iron when tested in tension and compression has an ultimate strength of (left(sigma_{mathrm{ult}} ight)_{t}=280 mathrm{MPa}) and

Cast iron when tested in tension and compression has an ultimate strength of \(\left(\sigma_{\mathrm{ult}}\right)_{t}=280 \mathrm{MPa}\) and \(\left(\sigma_{\mathrm{ult}}\right)_{c}=420 \mathrm{MPa}\), respectively. Also, when subjected to pure torsion it can sustain an ultimate shear stress of \(\tau_{\text {ult }}=168 \mathrm{MPa}\). Plot Mohr's circles for each case and establish the failure envelope. If a part made of this material is subjected to the state of plane stress shown, determine if it fails according to Mohr's failure criterion.

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120 MPa 100 MPa -220 MPa