Monte Carlo Simulations of Strength Distributions of Brittle Materials – Type of Distribution, Specimen and Sample Size

Abstract

Abstract Strength data of brittle materials have a large scatter. Therefore, probabilistic methods have been developed for designing with brittle materials. In general, a Weibull-type strength distribution function is determined by strength testing of a sample of about 30 specimens. This function is then used to predict a tolerable load level for a high component’s reliability. Curved structures in Weibull plots are often attributed to special features of the strength distribution function, e. g. to a threshold strength for failure or to bi- and multimodal flaw distributions. For such strength distributions the usual extrapolation is impossible. By means of Monte Carlo simulations it is shown that on the basis of small samples (containing around 30 experiments) real structures in strength distributions can hardly be distinguished from artefacts arising from the statistical nature of the data. On the basis of a small sample it is also not possible to decide whether a distribution is of a Weibull-type or any other distribution. Requirements for the determination of strength distribution functions and possible problems are discussed. Safe data extrapolations are possible if the flaw size distribution, which causes the strength distribution, is known. This knowledge can be acquired by testing a sample containing several subsamples with specimens of different size.