An error-analysis-based multi-scale reliability model for predicting the minimum time-to-failure of brittle components with environment-assisted crack growth

We developed an error-propagation-analysis-based multi-scale reliability model in three steps to estimate the minimum time-to-failure of a full-size brittle component with environment-assisted crack growth. First, we use a time-to-failure formula according to Fuller et al. (1994), which was based on laboratory experiments on brittle materials for measuring time-to-failure of specimens that undergo moisture-enhanced crack growth under constant stressing. The formula predicted the mean time-to-failure of a specimen-size component in a power-law relationship with the applied stress involving two strength test parameters, S and Sv, and two constant stressing test parameters from regression analysis, 𝜆 and N′. Second, we use the classical laws of error propagation to derive a formula for the standard deviation of the time-to-failure of a specimen-size component and apply it to computing the standard deviation of the time-to-failure of a specimen-size component for a specific applied stress. Third, we apply the statistical theory of tolerance intervals and develop a conservative method of estimating the failure probability of the full-size components by introducing the concept of a failure probability upper bound (FPUB). This allows us to derive a relationship for the minimum time-to-failure, min-tf, of a full-size brittle component at a specific applied stress as a function f of the FPUB. By equating (1 – FPUB) as the Reliability Lower Bound, RELLB, we arrive at a relation, min-tf = f (RELLB), which expresses the min. time-to-failure as a function of the reliability lower bound, or conservatively as a function of reliability.