Uncertainty analysis of fatigue failure using a fuzzy approach
Über dieses Buch
Structural systems subjected to repeated or fluctuating loads are vulnerable to fatigue failure. This is because each cycle of loading causes damage to the system. Damage accumulates, causing cracks which reduce constituent member cross-sections, leading to an increased possibility of fracture. This can occur even when stresses remain below the yield limit. Fatigue failure is a multi-phase process that starts with a crack initiation phase and continues into a crack propagation phase. In the conventional crack-initiation approach using Miner's rule, it is assumed that each cycle contributes a small increment of damage until failure occurs. This method relies on Stress–Life (S–N) curves derived from experiments. However, this approach is deterministic and does not reflect measurement imprecision or inherent uncertainties. These uncertainties derive from, material properties, geometry, fabrication quality, and cyclic loading. Uncertainty significantly affects the fatigue life of the system. Probabilistic and interval approaches have previously been used to enumerate these uncertainties. However, the former requires a well-defined distribution, whereas the latter requires exact bounds. This work develops a new crack-initiation prediction method that uses a fuzzy approach for quantifying uncertainties in stress ranges as well as fatigue parameters. First, the fatigue coefficient and stress ranges are defined as fuzzy variables. These fuzzy variables are evaluated at multiple discrete levels of presumption, (α-cuts). Then, for each cut, the interval values of those variables are used to calculate the interval of damage and interval of fatigue life. Following that, the fuzzy values for interval damage and fatigue life are constructed. A numerical example is presented to demonstrate the applicability of the proposed method and it is compared with results obtained by Monte Carlo simulations. It is shown that obtaining fuzzy bounds on a system's fatigue life using this method does not require iterative methods.
