Some notes on the correlation between fracture and defect statistics: Are Weibull statistics valid for very small specimens?

Strength data of brittle materials show a significant scatter. Therefore probabilistic methods have to be used for designing with these materials. So far this has been done on the basis of the Weibull statistics. The Weibull statistics (implicitly) implies a particular type of defect distribution, which can be observed in many (but not in all) ceramic materials. The correlation between the strength and the flaw size distribution is discussed in some simple examples. Then the situation for very small specimens is discussed. This case will be of high relevance for the testing of miniaturised electroceramic components and materials of the microsystem technique. It is shown that the Weibull theory gets inconsistent and should overestimate the strength of the specimens (components), due to the fact that the effective volume becomes smaller than the fracture origin.