Failure surfaces in principal stress space

Criteria for failure in multiaxial states of stress have associated with them geometrical representations as surfaces in principal stress space. Any combination of stresses is safe if the corresponding point in principal stress space falls within the failure surface. The material will fail if the point lies on or outside of the surface. The geometry of some simple surfaces and means for determining them on isotropic bodies are discussed, and the scanty information on failure surfaces for polymeric materials is reviewed.