The Effects of Incorporating System Level Variability Into the Reliability Analysis for Ceramic Components

Abstract

Probabilistic failure analyses evaluate the effects of strength variability in brittle materials on the design of ceramic components. However, strength is not the only stochastic parameter in ceramic components and making such an assumption can result in failed designs. Other variable parameters such as geometry, fabrication, materials, and service load histories should also be considered when evaluating the total probability of failure for the component. Slight variations in these variables can alter the stress distribution within the ceramic, and change the probabilities of failure for the system. This effort demonstrates an approach for incorporating the statistical scatter in material properties and system conditions, as well as the Weibull properties of the ceramic in the probability of failure calculations. The evaluated system is an internally pressurized ceramic tube with a steel sheath that imparts a pre-stress through a shrink-fit operation. Two analyses have been performed where the initial analysis is deterministic in nature, in that there is no variability in the inputs to the Weibull analysis. The first analysis calculates the optimal geometry and pre-stress levels for the lowest probability of failure. The second analysis was performed using ANSYS PDS (Probabilistic Design System) and CARES/Life software to evaluate the total probability of failure for a more realistic system with variability in the different material properties, Weibull parameters, pre-stress levels, pressure loading, and geometric inputs. The results of the PDS analysis illustrate that the probability of failure is not a single value, as defined by the first analysis, but a range spanning several orders of magnitude.