The maximum shear stress criterion, also known as Tresca yield criterion, is based on the Maximum Shear stress theory.
This theory predicts failure of a material to occur when the absolute maximum shear stress (τmax ) reaches the stress that causes the material to yield in a simple tension test. The Maximum shear stress criterion is used for ductile materials.
τmax >= σ limit / 2
τmax is the greatest of abs (σ12, σ23, σ13) where:
σ12 = (σ1 - σ2) / 2; σ23 = (σ2 - σ3 ) / 2; σ13 = (σ1 - σ3) / 2
σ1, σ2, σ3 are the principal stresses in descending order.
The Factor of safety (FOS) is given by:
FOS = σ limit / (2 * τmax )
Comparing the von Mises and Tresca Stress Criteria
The maximum shear stress criterion is more conservative than the von Mises stress criterion since the hexagon representing the shear stress criterion is enclosed within the ellipse representing the von Mises stress criterion.
For a condition of pure shear, von Mises stress criterion predicts failure at (0.577*yield strength), whereas the shear stress criterion predicts failure at 0.5 yield strength.
Actual torsion tests used to develop pure shear have shown that the von Mises stress criterion gives more accurate results than the maximum shear stress theory.