An estimation of ceramic fracture at singularities by a statistical approach

A statistical analysis based on weakest link theory is employed to describe the brittle fracture induced at singularities in ceramic materials. Relationships are stated between the Weibull probability and the notch geometry. For low Weibull's modulus, survival probabilities only depend on the generalised stress intensity factor, whereas for high Weibull's modulus, probabilities also depend on the notch tip radius. The effect of the tip radius on the failure probabilities is equivalent to the exclusion of a small volume surrounding the notch tip. From these results, a numerical methodology based on the finite element analysis is proposed to state if singularity is harmful for a ceramic structure. Elsewhere, for a notch with high stress singularity order and symmetrically loaded, the Batdorf's theory gives the same results than the Weibull one. In the case of a low stress singularity order, the prediction of failure can strongly depend on the multi-axial criterion.