Yield Surface
σ₁σ₂

Von Mises Stress

An equivalent stress calculated from the complete stress state. For ductile metals, yielding is predicted when the Von Mises stress reaches the material's yield strength.

Criterion Formula
σᵥ = √[ ((σ₁−σ₂)² + (σ₂−σ₃)² + (σ₃−σ₁)²) / 2 ]
Design Behavior
Smooth yield surface; generally accurate for ductile metals

Engineering Interpretation

Distortion-Energy Criterion

σᵥ = √[ ((σ₁−σ₂)² + (σ₂−σ₃)² + (σ₃−σ₁)²) / 2 ]. Compare the resulting equivalent stress with the material yield strength after applying the project\'s safety factor and design-code requirements.

Yield Surface
σ₁σ₂

Tresca Criterion

A yielding criterion based on the maximum shear stress in the material. Yielding is predicted when the maximum principal stress difference reaches the uniaxial yield strength.

Criterion Formula
σₜ = max(|σ₁−σ₂|, |σ₂−σ₃|, |σ₃−σ₁|)
Design Behavior
Hexagonal yield surface; usually more conservative than Von Mises

Engineering Interpretation

Maximum-Shear-Stress Criterion

σₜ = max(|σ₁−σ₂|, |σ₂−σ₃|, |σ₃−σ₁|). Compare the resulting equivalent stress with the material yield strength after applying the project\'s safety factor and design-code requirements.

Yield Surface
σ₁σ₂

Design Comparison

Von Mises and Tresca are both commonly used for ductile-material design. Von Mises gives a smooth, direction-independent equivalent stress, while Tresca directly limits maximum shear stress.

Criterion Formula
Tresca prediction ≤ Von Mises prediction in conservatism
Design Behavior
Choose according to material behavior, standard, and design margin

Engineering Interpretation

Failure-Criterion Selection

Tresca prediction ≤ Von Mises prediction in conservatism. Compare the resulting equivalent stress with the material yield strength after applying the project\'s safety factor and design-code requirements.