A two-scale weakest link model based on a micromechanical approach

For brittle materials in engineering, it is well known that the defect structure governs the macroscopic strength. However, there is a class of materials [34] where the failure events occur on the micro-structure level with characteristic length smaller than the characteristic length of the defect. In this case, a mean field approach in which the stress fluctuations are estimated by a second-order moment approach in combination with a quantification of failure probabilities may give useful insight to the level of failure. Weibull's type failure probabilities are introduced in this work without reference to a defect microstructure.