Ceramics Reliability: Statistical Analysis of Multiaxial Failure Using the Weibull Approach and the Multiaxial Elemental Strength Model

Methodology for designing reliable ceramic components requires a precise evaluation and correlation of strengths in different stress states. The present paper compares the merits of the Weibull approach and the Multiaxial Elemental Strength model on an experimental case involving mixed mode failure in the presence of bimodal flaw populations (surface and volume flaws). The experimental data were obtained using flexure specimens of Si₃N₄ tested at various spans, with the purpose of enhancing shearing effects. The analysis of data was refined by developing an advanced post-processor program to finite element codes, for failure probability determination based upon the Barnett-Freudenthal approximation of the Weibull approach and the Multiaxial Elemental Strength Model. In a second step, the strengths of the specimens exhibiting failures from the two concurrent populations of flaws (intermediate span) were predicted using both approaches from data obtained with different span lengths (long and short spans). Comparison with experimental data showed that the Multiaxial Elemental Strength Model is an improvement over the Weibull approach. It also allowed the short span bending test to be assessed. Finally, important implications for structural design with ceramics are discussed.