On the estimation of the Weibull modulus

Abstract

It is well documented that nominally identical specimens of brittle materials, e.g. ceramics, show a large variation of tensile fracture stresses and in order to use brittle materials as engineering materials the strength has to be characterized. The most widely used expression for characterization is the cumulative distribution function proposed by Weibull [ 1 ]. The Weibull function is also known to statisticians as Fisher-Tipper Type Ill distribution of smallest values or as the third asymptotic distribution of smallest extreme value [2]. The Weibull statistics is based on the the "weakest link-hypothesis" which means that the most serious flaw in the specimen will control the strength. The most serious flaw is not necessarily the largest one because its severity also depends on where it is situated. In other words, the flaw which is subjected to the highest stress intensity factor will be strength controlling. The flaws initiating fracture can conveniently be classified as intrinsic or extrinsic [3]. The intrinsic flaws are introduced during fabrication and are predominantly inclusions and voids. The extrinsic flaws are stress-induced cracks, such as surface cracks introduced during machining and microcracks resulting from large residual stresses, e.g. due to thermal contraction