An iterative method to obtain the specimen-independent three-parameter Weibull distribution of strength from bending tests

Abstract

Brittle materials, such as glass and ceramics, usually present a large strength scatter. Among other probability distributions, the Weibull distribution is widely used to characterize their resistance. Often the two-parameter model is employed, omitting the consideration of a threshold stress, leading to a simplified estimation method. For the sake of generality the present work uses fracture data from bending tests to obtain a three-parameter Weibull distribution function valid for a uni-axially and uniformly tensioned material element. The variable stress state prevailing in the flexural specimen and the size effect are simultaneously accounted for by means of an iterative fitting procedure. The method is extended to account for bimodal flaw distributions, discriminating between edge and surface failure results based on experimental observation. Finally, the model is applied to simulated data sets, obtaining satisfactory results.