Standardized Weibull statistics of ceramic strength

Abstract

In order to estimate Weibull parameters in the Weibull statistical fracture theory as truly material properties independent of specimen geometry and loading mode, first the Weibull statistical fracture theory is transformed into the ordinary Weibull distribution function under certain approximation. Then the standardized format of ordinary Weibull distribution is introduced to enable Weibull modulus as the single parameter for estimation via the maximum likelihood method. The method of using standardized Weibull distribution for strength data synchronization and Weibull modulus estimation is validated by analyzing extensive strength data sets measured from uniaxial flexure, biaxial flexure and their combination, and from smooth and notched specimens. The technical path to estimate the scale parameter and threshold strength as material properties in the Weibull statistical fracture theory and effect of sample size on the estimation accuracy are also discussed.