If the maximum principal stress applied to an object exceeds the material's yield strength (|σ_max| ≥ σ_y), failure will occur

When the material is brittle or is likely to fail through fatigue – for ductile materials, other failure criterion are more applicable

It is dependent on plastic behaviour, where bonds between molecules are rearranged, and occurs due to shear forces (typically fails at an angle of 45°)

If the maximum shear stress applied to an object exceeds the material's shear strength (τ_max > τ_y), failure will occur

Uniaxial Loading – τ_y = σ_y / 2 Where τ_y is the shear yield stress and σ_y is the tensile yield strength, Dual-Axis Loading – τ_max = (σ¹ – σ²)/2 Where τ_max is the maximum shear stress and σ¹ & σ¹ are the maximum and minimum principal stresses

σ_max – σ_min ≥ σ_y

The stress state of a material where the principal stresses are the same along all three axes (σ¹ = σ² = σ³) – such a stress state will never result in failure under the Tresca criteria

A material will fail if the maximum shear energy applied exceeds the material's yield value (W_d,max > W_d,y)

W_d,max = (1 / 12G) • [(σ¹ – σ²)² + (σ² – σ³)² + (σ³ – σ¹)²] Where G is the shear modulus and σ represents the principal stresses along each axis, W_d,y = (1 / 6G) • (σ_y)² Where σ_y is the yield stress, W_d,y = (1 / 2G) • (τ_y)² Where τ_y is the shear yield stress

√(½ • ((σ¹ – σ²)² + (σ² – σ³)² + (σ³ – σ¹)²)) ≥ σ_y Where σ represents the principal and yield stresses