Relationship of Strength and Defects of Ceramic Materials and Their Treatment by Weibull Theory.

Abstract

For ceramic materials, the statistical distribution of defects is closely connected to the fracture stresses. This relationship has been used to derive the distribution of flaw sizes and their positions from different fracture experiments. Reversely, fracture stresses were predicted from the measurement of flaw populations, which would offer a non-destructive tool to measure mechanical properties. There are two obstacles for precise predictions, on the one hand the small size of the defects and on the other hand their complicated geometry. In the literature, considerable effort was undertaken to find an answer to this question and to develop suited tools for determining the size distribution of defects. For the description of the mechanical behaviour, the most frequently used approach is the Weibull theory. The Weibull statistics naturally arises if the number of the defects shows an inverse power law with respect to their size. Because of the technical importance for the prediction of strength and life-time of ceramic components, the limits and the restrictions by the statistical description were of particular interest. From theoretical considerations by analytical models as well as from computer simulations, the reliability of the Weibull theory is predicted, i.e. the variation coefficient of the Weibull modulus and the scale parameter are calculated for a certain material and a certain number of experimental tests. This allows to calculate the number of specimens required to predict the strength at a certain given accuracy.