Evaluation of Weibull parameters for static strengths of ceramics by Monte Carlo simulation

Monte Carlo simulation method was used to evaluate the theoretical distributions of the estimates of Weibull modulus and scale parameter for various sample sizes. It was found that the theoretical distributions of the estimates of Weibull modulus and scale parameter are well app oximated by log-normal distributions, and the scatter and bias of each distribution decrease with the increase of sample size. The comparison of the distribution of Weibull modulus estimated by experiments with the theoretical distribution indicates that the scatter of the experimentally obtained Weibull modulus results from the statistical nature of the estimates depending on the sample size and the difference of test conditions is not a major factor for the scatter. And it was also revealed that the distribution of scale parameter obtained by experiments does not agree with the theoretical one obtained by Monte Carlo simulation. This means that the scale parameter or the intrinsic strength of sintered silicon nitride and sintered silicon carbide depends on the fabrication and testing techniques.