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GATE 2019 ME (ME1) – Question 44

Casting, Forming and Joining Processes · Plastic deformation and yield criteria, hot and cold working · 2 marks · Multiple choice

The plane-strain forging block shown has zero z strain and uniaxial-compression yield strength 300 MPa, obeying Tresca’s criterion. The entire block is yielding. At a point with $\sigma_x=-40$ MPa (compression) and $\tau_{xy}=0$, find $\sigma_y$.

Diagram for GATE 2019 ME (ME1) question 44
  1. 340 MPa compressive
  2. 340 MPa tensile
  3. 260 MPa compressive
  4. 260 MPa tensile

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Show answer and explanation

Correct answer: (A) 340 MPa compressive

Explanation

The x and y stresses are principal stresses, with the constrained-direction stress between them. Tresca yielding requires $\sigma_x-\sigma_y=300$ MPa. Thus $\sigma_y=-40-300=-340$ MPa. **340 MPa compressive, A**.