Integration of fracture mechanics and non-destructive testing. A probabilistic approach

Abstract

A methodology is presented for integrating probabilistic fracture mechanics with quantitative NDT for the purpose of failure risk assessment in load-carrying elements under fatigue circumstances. The definition of the failure risk of structural components is made in the context of the general approach of structural reliability with a discussion of the sources of uncertainties and variability encountered in the assessment. The quality of NDT is accounted by the probability of detection (POD) as function of the flaw size. The main focus is placed on the presentation on the fatigue failure risk assessment in conjunction with the quality and timing of the envisaged non-destructive inspection. On the base of Monte Carlo computer simulation, a rationale have been developed encompassing the fatigue crack growth under short- and long-crack regime, thus addressing the entire fatigue life. For this purpose, the concepts of "initial fictitious crack" size and "equivalent initial flaw" size are discussed and implemented in the analysis. By computer simulation, it is exemplified, for a notched member of an aluminum alloy, the modeling of the scatter of the total fatigue life and the scatter of the crack size at a given life. Further, by fitting the simulated random data into continuous statistical distributions enabled to model the key distributions involved in the failure risk assessment. Finally, the probability of failure, at a specific timing during the fatigue life, is estimated by Monte Carlo simulation of the failure on the base of Failure Analysis Diagram (FAD) approach. The benefit of applying a non-destructive inspection technique, qualified by a specific POD dependence on the crack size, is demonstrated by evincing the decrease in the predicted failure probability. Bootstrap techniques are also exemplified for constructing confidence intervals on POD vs. crack size. The integration of quantitative NDT with probabilistic fracture mechanics, in order to evince the failure risk, enables a better timing and ranking of inspection procedures.