Brittle materials can fail with little plastic deformation, and their tensile and compressive strengths may differ greatly. Failure criteria for brittle materials therefore emphasize principal normal stresses rather than ductile yielding.

Maximum normal stress

The Rankine criterion predicts failure when a principal stress reaches the corresponding uniaxial tensile or compressive strength.

This is simple and often useful when normal-stress fracture dominates.

Coulomb–Mohr ideas

The Coulomb–Mohr family of criteria accounts for different tensile and compressive strengths by defining a failure envelope in principal-stress space.

A stress state closer to the tensile limit can therefore be treated differently from one dominated by compression even when their magnitudes are similar.

Material behaviour matters

A failure criterion is a model chosen to represent a particular class of material and loading. A criterion that works well for ductile yielding is not automatically appropriate for brittle fracture.

Selecting a criterion therefore requires both the stress state and knowledge of how the material fails under simple tests.