Uncertainty analysis of reliability predictions for brittle fracture

Reliability analysis of ceramic components under stationary or transient loading is generally performed on the basis of a Finite Element stress analysis from which the failure probability according to the multi-axial Weakest Link theory is calculated with the help of a suitable post-processing routine. We use the STAU post-processing routine and the general purpose Finite Element code ABAQUS. Due to scatter in the material parameters, the resulting failure probability is also prone to statistical uncertainties. We present a method of assessing this scatter using so-called resampling simulation methods. The analysis leads to confidence intervals for the failure probability which is a novel and important result especially for the purpose of design sensitivity considerations and the assessment of pooling procedures. In a simple example using a four-point bend specimen, the effect of pooling (i.e. grouping of results from different experiments by suitable scaling procedures) on the numerical result and on the scatter of failure probability is demonstrated. Here, pooling is done using results of inert strength measurements at various temperatures and scaling to room temperature values. A technologically more relevant example deals with a ceramic component in a model clutch under thermo-mechanical frictional loading. As a first step, the local risk of rupture is calculated which leads to the identification of the most critical regions of the component. As a second step, resampling confidence intervals for the failure probability are determined. As resampling data base, we use inert strength values at different temperatures as well as material data for sub-critical crack propagation.