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

Article type: Research Article

Authors: Fong, Jeffrey T.^a; | Heckert, N. Alan^b | Freiman, Stephen W.^c

Affiliations: [a] Applied & Computational Mathematics Division, National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA | [b] Statistical Engineering Division, National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA | [c] Freiman Consulting, Potomac, MD, USA

Correspondence: [*] Corresponding author: Jeffrey T. Fong, Applied & Computational Mathematics Division, National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA. E-mails: [email protected], [email protected]

Abstract: 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.

Keywords: Brittle material, BK-7 glass, component-scale, constant stressing rate test, coverage, crack growth, DATAPLOT, dynamic fatigue, environment-assisted, error propagation, failure probability, failure probability upper bound, glass, graphite, laboratory-scale, level of confidence, lifetime, lower tolerance limit, minimum time-to-failure, multi-scale, nonlinear regression analysis, prediction intervals, reliability, tolerance intervals, uncertainty

DOI: 10.3233/SFC-230020

Journal: Strength, Fracture and Complexity, vol. 17, no. 1, pp. 27-50, 2024