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A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero. The yield strength (S_y) in uniaxial tension/compression of the material of the block is 300 MPa and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where σₓ = 40 MPa (compressive) and τ_xy = 0, the stress component σ_y is

1. 340 MPa (compressive)
2. 340 MPa (tensile)
3. 260 MPa (compressive)
4. 260 MPa (tensile)

Correct answer: 340 MPa (compressive)

Solution

According to the Tresca criterion, yielding occurs when the maximum shear stress reaches a critical value. Given that the yield strength is 300 MPa and the stress state indicates a compressive stress of 40 MPa in the x-direction, the corresponding stress in the y-direction must be 340 MPa (compressive) to satisfy the yield condition, ensuring that the difference between the principal stresses does not exceed the yield strength.

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