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 $\left(S_y\right)$ 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 ${\sigma }_1=40MPa$ (compressive) and ${\tau }_{xy}=0,$ the stress component ${\sigma }_y$ is

• A. 340 MPa (compressive)
• B. 260 MPa (compressive)
• C. 340 MPa (tensile)
• D. 260 MPa (tensile)

Answer 1

The correct option is A 340 MPa (compressive)

According to Tresca's theory

${\sigma }_x+P=2K$

$where,K=\frac{{\sigma }_0}{2}=flowshearstress$

= $\frac{300}{2}=150MPa$

and ${\sigma }_x=-40MPa$

Now, ${\sigma }_x+P=2K$

$=-40+P=2\times 150$

or P = 340 MPa

P is pressure. If P = 340 MPa, stress $\left({\sigma }_y\right)$ will be - 340 MPa. i.e. 340 MPa (compressive)