The validity of Weibull estimators - Experimental verification

A sufficiently large number of bending tests of a recrystallized silicon carbide ceramic was performed, which gave a fundamental set of strength values. From this fundamental set, arbitrary subsets of size M were chosen by a Monte-Carlo procedure and the parameters of the two-parametric Weibull distribution were calculated by the maximum likelihood method. The dependence of the statistical distribution of the two parameters, obtained by this procedure, on the size of the subset M was investigated. It was found that the variation coefficient of the scale parameter could be well described by the equations given in the literature, whereas the variation coefficient of the Weibull modulus was much higher. It has been shown that the reason for this behaviour is that the distribution of flaws and therefore the strength of the material does not perfectly obey the Weibull statistics, for which the theoretical equations were derived. Thus, in real ceramics the numerical value for the Weibull modulus obtained from a certain number of experiments is even more indeterminate than described by the theoretical solution.