Monte Carlo simulation of Weibull distribution of ceramic strength values

Brittle engineering ceramics usually fail due to flaws that are distributed in the material. Their strength depends on the length of the major flaw, which may be different from specimen to specimen, being described by a probability function. If the material exibits a statistical distribution of independent flaws and the weak link hypothesis is fulfilled, i.e., the specimen fails if its weakest volume element fails, the strength of such materials follows a Weibull distribution. This distribution results from the distribution of positions, sizes, types, shapes and orientations of microflaws present in the material. We have used the Monte Carlo simulation to introduce the edge microcracks in homogeneous and multilayered composite ceramic materials and the Griffith concepts of the material brittle fracture to calculate the distribution of apparent material strengths. This approach proves the Weibull distribution of the strengths in the studied cases and the size effect on the characteristic sample strength.