Three-parameter (3P) weibull distribution for characterization of strength of ceramics showing R-Curve behavior

Strength distribution of advanced ceramics is commonly characterized by two-Parameter (2P) Weibull distribution. However, deviation of strength distribution from 2P-Weibull distribution may occur in ceramics due to various mechanisms. R-curve behavior is one of these mechanisms where increase of fracture resistance with the extension of crack occurs. In such cases, 2P-Weibull distribution may not be the best fitting distribution function based on the goodness-of-fitness tests. This article examines the effectiveness of three-parameter (3P) Weibull distribution function for fitting the strength variation due to R-curve effect by using experimental and virtual strength data. The effect of Weibull parameters, degree of increase in crack resistance and number of samples on effectiveness of fitting via 3P-Weibull distribution is investigated. It is reported that 3P-Weibull distribution function fits the strength distribution better than 2P-Weibull distribution function for materials showing R-curve behavior when the crack resistance curve is steep and Weibull modulus is high. Furthermore, it is shown that at least 100 samples should be used for a reliable estimate when the material exhibits R-curve behavior.

Automated summary

This article investigates the effectiveness of three-parameter Weibull distribution function for fitting strength variation due to R-curve effect. It is found that the 3P-Weibull distribution function fits the strength distribution better than the 2P-Weibull distribution function for materials exhibiting R-curve behavior, especially when the crack resistance curve is steep and the Weibull modulus is high. Additionally, it is recommended to use at least 100 samples for reliable estimation when the material shows R-curve behavior.