Summary of Failure Criteria

The following table summarizes the failure criteria used to assess the safety of designs.

Criterion Factor of Safety Material Type
Maximum von Mises stress σlimit / σvonMises Ductile
Maximum shear stress σ limit / (2 * τmax ) Ductile
Mohr-Coulomb stress

  • If ( σ1> 0 and σ3 > 0 ) then ( σ1 ≥ σTensileLimit )

  • If ( σ1< 0 and σ3 < 0 ) then ( σ3 ≥ -σCompressiveLimit )

  • If ( σ1≥ 0 and σ3 ≤ 0 ) then ( σ1 / σTensileLimit + σ3 / -σCompressiveLimit ≥1 )
 Brittle materials with different tensile and compressive strengths
Maximum normal stress σ limit / σ1 Brittle
Maximum stress criterion (composites)

FOS = 1 / F.I.

 Brittle
1 and 2 stand for material directions. X and S are normal and shear strengths of the composite.
Tsai-Hill Failure criterion (composites)

FOS = 1 / SQRT (F.I.)

 Brittle
Tsai-Wu Failure criterion (composites)

Brittle