A Comparison of Different Theories of Failure:
We know that mild steel yields at a stress value of 260 MPa. The normal strain at this limit is 0.0013 and maximum shear stress at yield is 130 MPa.
Total strain energy density at yield u = σ2y/2E = 2602 /2E
Distortion energy density at yield ud = 1/12G (σ2y +(-σy)2)
Ud = σ2y /6G = 2602/6G