Christensen failure criterion

The fracture criterion (2) (applicable only over the partial range 0 ≤ T/C ≤ 1/2 ) cuts slices off the paraboloid, leaving three flattened elliptical surfaces on it.

The fracture cutoff is vanishingly small at T/C=1/2 but it grows progressively larger as T/C diminishes.

The organizing principle underlying the theory is that all isotropic materials admit a distinct classification system based upon their T/C ratio.

At the brittle limit, T/C = 0, it reduces to a form that cannot sustain any tensile components of stress.

Related criteria distinguishing ductile from brittle failure behaviors have been derived and interpreted.

Applications have been given by Ha[4] to the failure of the isotropic, polymeric matrix phase in fiber composite materials.

A criteron illustrated
For plane stresses, and T/C=0.3(brittle materials). Blue line is polynomial invariants failure criterion ( 1 ). Red lines are coordinated fracture criterion( 2 ).