Flaws, Statistics of Fracture, and Measurement Techniques

It should be obvious from Equation 9-1 that the criterion for failure is that Flaws, Statistics of Fracture, and Measurement Techniques 

Flaws produced in glass fabrication are usually a result of incomplete melting of the batch constituents or of attachment of contaminant particles to the surface of the glass during forming. Rapid quenching at contact with a mold can produce chill marks that result in high stress concentrations. 

Practical ceramics contain numerous flaws of varying severity and usually of various types. If the ceramic part is uniformly stressed to the point of failure, the origin for that failure will be the worst flaw in the part, that is, the one with the highest stress intensity. In the more usual case of a varying stress field in the part, failure will still be produced by the flaw whose stress intensity first reaches the critical value however, that may not be the largest flaw in the part. 

In most instances, a group of ceramic or glass samples produced under nominally identical conditions will have worst flaws that vary in severity and location. As a consequence, strength values for those samples will vary, often over a rather wide range. The distribution of failure stresses is usually analyzed in terms of the extreme value statistics developed by Weibull. The most common functional form used in these statistical treatments is 

Because of the importance of K. in the mechanical performance of ceramics, a variety of techniques have been developed to measure this parameter. Reference 10 is an excellent source of information on these techniques and on their use in characterization of ceramics. 

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