A1 Brittle Fracture and Weibull Statistics

Topic

Glass is the canonical system in which Weibull statistics were historically characterized; in glass, it is submicroscopic surface defects—rather than internal ones—that generate the statistical scatter in strength. These defects are superficial rather than internal because the glass surface, due to handling and environmental exposure, accumulates scratches and microscopic flaws that are more severe than any defects present within the material's interior. Since these submicroscopic surface defects govern glass failure, the model adopts the exact statistical framework used by another model in this set—which describes brittle fracture and Weibull statistics for ceramics—applying it to surface defects instead of internal ones.

This reused framework explains glass strength just as it does ceramic strength: each surface defect determines a specific failure stress based on its size, following the Griffith criterion (also adopted from the metal fracture model); and because these surface defect sizes vary randomly from one piece of glass to another, the failure stress of the glass as a whole—its strength—behaves according to a Weibull distribution, just like that of a ceramic. Because glass shares this statistical framework with ceramics, it also shares the same Weibull modulus, which characterizes the degree of scatter in that strength.

However, the scale effect in this model is not measured in the same way as it is for ceramics with internal defects: since failure is governed by surface defects rather than defects distributed throughout the volume, it is the exposed surface area of ​​the glass piece—not its effective volume—that determines its expected strength. A larger exposed surface area on a piece of glass increases the likelihood that the surface contains one of the more severe surface defects from the random distribution, thereby resulting in lower expected strength; conversely, a smaller exposed surface area leads to higher expected strength.

For this reason, the model—while retaining the glass surface defects present at its inception—fully incorporates both the Weibull framework and the scale effect established by another model in this set, as well as the Griffith Criterion (which that same model adapted from metal fracture theory), while simply adjusting the relevant scale-effect dimension from volume to surface area. The fact that glass was the historical case where this entire statistical framework originated makes it, in a sense, the model from which the rest of the set is derived, rather than the other way around.

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