Question
A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero. The yield strength (Sy ) 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 τxy = 0, the stress component σy is
Options :
340 MPa (compressive)
340 MPa (tensile)
260 MPa (compressive)
260 MPa (tensile)
Answer :
340 MPa (compressive)
Solution :
According to Tresca’s theory
σx + P = 2K
where K = σ0/2 = flow shear stress
= 300 / 2 = 150 MPa
and σx = – 40 MPa
Now, σx + P = 2K
– 40 + P = 2 × 150
or P = 340 MPa
P is pressure. If P = 340 MPa, stress (σy ) will be – 340 MPa. i.e. 340 MPa (compressive)
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