Q. 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 sx = 40 MPa (compressive) and txy = 0, the stress component s y is
Ans: 340 MPa (compressive)
Sol:
According to Tresca’s theory
σx+P=2K
where,K=σ0/2=flow shear stress
= 300/2=150MPa
and σx=−40MPa
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)