Project ForgeA plane-strain compression (forging) of a block has zero strain in the z-direction. The yield strength (Sy) in uniaxial tension/compression of the block's material is 300 MPa, following the Tresca criterion. At a point where σx=40 MPa (compressive) and τxy=0, once the entire block has started yielding, the stress component σy is
- 340 MPa (compressive)
- B340 MPa (tensile)
- C260 MPa (compressive)
- D260 MPa (tensile)
Explanation
The plane-strain condition (εz=0) under the flow rule forces σz to equal the average of the other two principal stresses: σz=(σx+σy)/2, making σz the intermediate principal stress. Tresca then applies directly between σx and σy: |σy−σx|=Sy=300. Since the moving platen compresses more strongly along y, σy is the more compressive value: σy = σx − 300 = −40−300 = −340 MPa (340 MPa compressive).
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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