Optical EngineeringFlexural strength of infrared-transmitting window materials: bimodal Weibull statistical analysis
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The results of flexural strength testing performed on brittle materials are usually interpreted in 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 measured stresses at fracture-specifically, the stressed area and the stress profile-thus resulting in inadequate characterization of the material under investigation. In a previous publication, the author reformulated Weibull's statistical theory of fracture in a manner that emphasizes how the stressed area and the stress profile control the failure probability distribution, which led to the concept of a characteristic strength, that is, the effective strength of a 1-cm2 uniformly stressed area. Fitting the CFP of IR-transmitting materials (AlON, fusion-cast CaF2, oxyfluoride glass, fused SiO2, CVD-ZnSe, and CVD-ZnS) was performed by means of nonlinear regressions but produced evidence of slight, systematic deviations. The purpose of this contribution is to demonstrate that upon extending the previously elaborated model to distributions involving two distinct types of defects-bimodal distributions-the fit agrees with estimated CFPs. Furthermore, the availability of two sets of statistical parameters (characteristic strength and shape parameter) can be taken advantage of to evaluate the failure-probability density, thus providing means of assessing the nature, the critical size, and the size distribution of surface/subsurface flaws.