A plane-strain compression (forging) of a block is shown

A plane-strain compression (forging) of a block is shown in the figure. The strain in the zdirection is zero. The yield strength (S_y) in uniaxial tension/compression of the material of the block is 300 MPa and its follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where σ_x = 40 MPa (compressive) and τ_xy = 0, the stress component σ_y is

1. 260 MPa (compressive)
2. 260 MPa (tensile)
3. 340 MPa (tensile)
4. 340 MPa (compressive)

σ_x, σ_y & σ_z are principal stresses.

Under plane strain condition, ε_z = 0

⇒	σ_z	-	μσ_y	-	μσ_x	= 0
	E		E		E

⇒ σ_z = (σ_x + σ_y) = μ (σ_x + σ_y)
but σ_x = -40
⇒ σ_z = μ(-40 + σ_y)
From Tresca theory,

= 300
But μ is not given
Hence if we neglect σ_z then
max [|40 + σ_y|, |σ_y|, |+40|] = 300
⇒ |40 + σ_y| = 300
40 + σ_y = 300
⇒ σ_y = 260 MPa