Probabilistic Damage Tolerance for Small Airplanes Using a Linear-elastic Crack Growth Fracture Mechanics Surrogate Model
Most general aviation (GA) aircraft are designed for safe-life based upon a crack initiation type failure mechanism, e.g., Miner's rule. However, newer GA aircraft have a fatigue crack growth as a design option. In addition, it may be necessary to evaluate a field event such as
a cracked structure to ascertain the remaining life. Therefore, a risk based probabilistic damage tolerance analysis (PDTA) program is needed in several aerospace situations.
Many military aircraft fleets (e.g. US DoD (MIL-STD-820), UK MoD (ADRM), and Canadian Forces (TAM)) have adopted a risk management program/tool to ensure aircraft safety and airworthiness. Now more non-military agencies are adopting these practices to guarantee aircraft safety and maintain airworthiness.
A comprehensive probabilistic damage tolerance method requires a combination of a deterministic crack growth model, inspection methods, probabilistic methods, and random variable modeling to provide a single probability-of-failure, cumulative probability-of-failure, and hazard rate with and without inspection.
Today's crack growth simulations are strongly based on complex computer codes and numerical analyses, which can only provide discrete information about the underlying relationship. This complexity makes the crack growth analysis very expensive and consequently the single probability-of-failure, cumulative probability-of-failure, and hazard rate very expensive to compute.
In this work, a general methodology to conduct probabilistic crack growth based damage tolerance methodology for small airplanes was developed and incorporated in computer software. The methodology overcomes the limitations from previous damage tolerance programs such as the number of random variables, extreme value distribution (EVD) loading generation, inspections/repair programs, and reduction on the computational time.
Existing probabilistic damage tolerance methodologies have a limitation on the number of random variables (initial crack size, fracture toughness, and loading). In this work additional random variables were included in the model using Monte Carlo sampling (MCS), efficient numerical integration algorithms, and a surrogate model for crack growth modeling. Algorithms to determine the extreme value distribution from real aircraft loading, generated in this research as well, were developed and incorporated into the code. New efficient inspection and repair programs were studied, improved if necessary, and implemented into the code. The main contribution of this work includes the reduction of the computational time using an error based adaptive surrogate model; the surrogate model included a comprehensive number of random variables (e.g. initial crack size, fracture toughness, correlated Paris constants, yield and ultimate stress, etc.). The surrogate model was used as a substitution for the original crack growth model.
Four different case studies are presented to demonstrate the different methodologies developed in this work.