Von Mises and Tresca Yield Criteria
Compare a multiaxial stress state with uniaxial yield strength
Difficulty
Advanced
Read time
6 min
Review status
Needs review
Concept sketch
Von Mises and Tresca Yield Criteria
Illustrative model, not experimental data
Overview
Von Mises and Tresca turn a multiaxial stress state into a yield check for suitable ductile materials. Their envelopes show where idealized elastic behavior gives way to the onset of yielding; they do not predict fatigue life or brittle fracture by themselves.
How to read it
- Use principal stresses, including σ₃ = 0 for plane stress.
- Compare the point with the envelope for the same Sᵧ.
- Read the boundary as first yield, not rupture.
When to use it
- Interpreting a static plane-stress result for a ductile metal.
- Comparing von Mises and maximum-shear predictions.
Yielding is different from fracture and fatigue
For many isotropic ductile metals under a static load, yield depends mainly on the distortional part of stress. A yield criterion estimates the onset of plastic flow. Cyclic life requires fatigue data, and brittle or pressure-sensitive materials need a different failure model.
Von Mises in principal stress coordinates
For plane stress the third principal stress is zero. The equivalent stress σᵥ can be compared with the uniaxial yield strength Sᵧ. All stresses must use the same units.
Why the Tresca boundary is different
Tresca compares the largest principal-stress difference with yield strength. Include the zero third principal stress in a plane-stress calculation. Its hexagonal boundary lies inside or on the von Mises ellipse for the same yield strength.
Interpret the margin carefully
A point below the chosen boundary is below predicted first yield for this model. It is not a complete design approval. Stress concentrations, load uncertainty, temperature, fatigue, buckling, and an appropriate design factor still matter.
Worked example
At a plane-stress point, the principal stresses are 120 MPa and −40 MPa. The uniaxial yield strength is 240 MPa. Compare the two criteria.
1.Calculate the von Mises equivalent stress.
2.Include the zero principal stress for Tresca, then compare margins.
3.Compute the model-specific yield factors.
Both criteria place this point below first yield; Tresca gives the smaller margin.