Question

The Von-Mises stress at a point in a body subjected to forces is proportional to the square root of the

• A. distortional strain energy per unit volume
• B. dilatational strain energy per unit volume
• C. plastic strain energy per unit volume
• D. total strain energy per unit volume

Answer 1

The correct option is A distortional strain energy per unit volume

Condition for failure as per M.D.E.T. Distortion energy per unit volume under tri-axial state of stress > Distortion energy per unit volume under uni-axial state of stress.
Hence,
$\left(\frac{1+\mu }{6E}\right)\left[\right({\sigma }_1-{\sigma }_2{)}^2+({\sigma }_2-{\sigma }_3{)}^2+({\sigma }_1-{\sigma }_3{)}^2]>\left(\frac{1+\mu }{3E}\right)(S_{yt}{)}^2$
${({\sigma }_1-{\sigma }_2)}^2+{({\sigma }_2-{\sigma }_3)}^2+{({\sigma }_1-{\sigma }_3)}^2>2(S_{yt}{)}^2$
$\sqrt{{\sigma }_2^1+{\sigma }_2^2+{\sigma }_3^2+{\sigma }_1{\sigma }_2-{\sigma }_2{\sigma }_3-{\sigma }_1{\sigma }_3}>\left(S_{yt}\right)$
(Von Mises effective stress)
$S_{yt}$ = Von Mises effective stress is defined as the uni-axial yield stress that would create same distortion energy created by the tri-axial state of stress.