Convergent Zone-Refinement Method for Risk Assessment of Gas Turbine Disks Subject to Low-Frequency Metallurgical Defects

Abstract

Titanium gas turbine disks are subject to a rare but not insignificant probability of fracture due to metallurgical defects, particularly hard ␣. A probabilistic methodology has been developed and implemented in concordance with the Federal Aviation Administration (FAA) Advisory Circular 33.14-1 to compute the probability of fracture of gas turbine titanium disks subject to low-frequency metallurgical (hard ␣) defects. This methodology is further developed here to ensure that a robust, converged, accurate calculation of the probability is computed that is independent of discretization issues. A zonebased material discretization methodology is implemented, then refined locally through further discretization using risk contribution factors as a metric. The technical approach is akin to "h" refinement in finite element analysis; that is, a local metric is used to indicate regions requiring further refinement, and subsequent refinement yields a more accurate solution. Supporting technology improvements are also discussed, including localized finite element refinement and onion skinning for zone subdivision resolution, and a restart database and parallel processing for computational efficiency. A numerical example is presented for demonstration.

Automated fatigue crack growth analysis of components

“…The total probability of component fracture is then the sum of all the zone probabilities. By always placing the hypothetical anomaly in each zone at the life limiting location within that zone, a conservative result is assured, and the calculated reliability converges from above to the exact solution as the zones are refined (as the number of zones increases) [9]. A zone in a preliminary discretization that makes a negligible contribution to total risk does not need to be further refined.…”

Efficient Integration of Sampling-Based Spatial Conditional Failure Joint Probability Densities

“…If there are no physical interactions among anomalies in a zone, then the zone risk can be estimated by assuming that all anomalies are at the life limiting location of the zone. This provides a conservative (upper bound) risk estimate that converges to the true solution as the number of zones becomes large 12 . For materials with large numbers of anomalies, the component probability of fracture becomes 13 :…”

Methodology for Probabilistic Life Prediction of Multiple-Anomaly Materials

“…This provides a conservative (upper bound) risk estimate that converges to the true solution as the number of zones becomes large. 16 Some anomaly types, for example, titanium hard alpha, have negligible formation lives and form growing cracks almost immediately. 11 However, in other materials, the crack formation life may be nonnegligible and must be considered in the risk computation.…”

“…When the expressions in Eqs. (15) and (16) are substituted into Eq. (11), the probability of fracture for a zone becomes which can also be expressed as 9…”