A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero

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)