Bimodal Weibull statistical analysis of CVD-ZnSe and CVD-ZnS flexural strength data

Abstract

The results of flexural strength The results of flexural strength testing performed on brittle materials are usually interpreted in the light of a "Weibull plot," i.e., by fitting the estimated cumulative failure probability (CFP) to a linearized semiempirical Weibull distribution. This procedure ignores the impact of the testing method on the measures stressed at failure-specifically the stressed area and the stress profile-thus resulting in an inadequate characterization of the material under consideration. In a previous publication [Opt. Eng. 41, 3151 (2002)] the author reformulated Weibull's statistical theory of fracture in a manner that emphasizes how the stressed area and the stress profile control the CFP, a 1-sq.cm uniformly stressed area. Fitting the CFP of IR-transmitting materials was performed by means of nonlinear regressions but produced evidence of systematic deviations. In this paper we demonstrate that, upon extending the previously elaborated model to distributions involving two distinct types of defects (bimodal distributions), fitting the estimated CFP of CVD-ZnS or CVD-ZnSe leads to a much improved description of the fracture process. In particular, the availability of two sets of statistical parameters (characteristic strength and shape parameter) can be taken advantage of for evaluating the failure-probability density, thus providing means of assessing the nature, the critical size, and the size distribution of the surface/subsurface flaws.