Ceramic fracture statistics/Weibull statistic

A further and very important consequence of the Weibull distribution is the size effect, i.e. the mean strength decreases with increasing specimen size. This is the most important consequence of fracture statistics for designing with ceramics. 

R. Danzer, P. Supancic, J. Pascual, and T. Lube, Fracture Statistics of Ceramics - Weibull Statistics and Deviations from Weibull Statistics, Engineering Fracture Mechanics, 74, 2919-2932, (2007). 

R. Danzer, Some Notes on the Correlation between Fracture and Defect Statistics Are Weibull Statistics Valid for Very Small Specimens , J. Eur. Ceram. Soc., 26, 3043-3049, (2006). 

Danzer, R., Supancic, P., Pascual Herrero, J., and Lube, T. (2007) Fracture statistics of ceramics - Weibull statistics and deviations from Weibull statistics. Eng. Fract. Mech., 74 (18), 2919-2932. 

The dependence of the fracture stress on the size and the geometry of the defect gives statistical nature to the fracture behavior. The statistical distribution of the spontaneous fracture strength of many ceramic materials is reasonably well described by the one-parameter Weibull distribution described below. 

CARES. Ceramic Analysis and Reliability Evaluation of Structures. (Formerly known as scare - Structural Ceramic Analysis and Reliability Examination). A Fortran 77 computer program using Weibull and Batdorf fracture statistics to predict the fast-fracture reliability of isotropic ceramics. Carlton Shape. A tea-cup the top half of which is cylindrical, the bottom half being approximately hemispherical but terminating in a broad, shallow foot. For specification see B.S. 3542. 

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