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

Titanium gas turbine disks are subject to a rare but not insignificant probability of fracture due to metallurgical defects, particularly hard $α$⁠. 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 $α$⁠) 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 zone-based 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.