Weibull Statistics for Fracture Data
As a result of defects in ceramic materials, the stress at which a specimen fractures can vary widely. For five different materials, the probability of fracture is shown as a function of the applied stress. The fracture data can be analyzed using Weibull statistics. The Weibull modulus, , quantifies the scatter of the strength values (i.e., high values of indicate low scatter); the critical stress, , depends on the material. The Weibull parameters can be adjusted to fit the different datasets.
The dataset for alumina is from J. Roesler, H. Harders, and M. Baeker, Mechanical Behaviour of Engineering Materials: Metals, Ceramics, Polymers, and Composites, New York, NY: Springer Berlin Heidelberg, 2007. The datasets for silicon nitride, silicon carbide, and aluminum nitride are from M. A. Meyers and K. K. Chawla, Mechanical Behavior of Materials, Upper Saddle River, N.J.: Prentice Hall, 1999. The dataset for tungsten carbide is from L. Guerra Rosa, J. Lamon, I. Figueiredo, and F. A. Costa Oliveria, "A Method to Distinguish Extrinsic and Intrinsic Fracture-Origin Populations in Monolithic Ceramics," Journal of the European Ceramic Society, 26(16), 2006 pp. 3887–3895.