Deriving the primary cumulative distribution function of fracture stress for brittle materials from 3- and 4-point bending tests

In this article, the primary three-parameter Weibull cumulative distribution function (cdf) of the critical stress provoking failure in a brittle material for a uni-axially and uniformly tensioned area ΔA is derived from 3- and 4-point bending test data. The model proposed finds application in the characterization of ceramics and glasses, and is intended as an initial step to be extended to different practical cases in future applications, as for instance, element design and local models in fracture mechanics, with previous consideration of the randomly distributed crack orientations. A comparison of the results provided by the model proposed with those found using another one referred to in the literature, demonstrates good agreement between both, whereas the former simplifies the convergence procedure and can be applied for the assessment of data obtained from different test geometries and types. Thus, the suitability of the new approach is confirmed.