Model Calibration for Fatigue Crack Growth Analysis under Uncertainty
This paper presents a Bayesian methodology for model calibration applied to fatigue crack growth analysis of structures with complicated geometry and subjected to multi-axial variable amplitude loading conditions. The crack growth analysis uses the concept of equivalent initial flaw size to replace small crack growth calculations and makes direct use of a long crack growth model. The equivalent initial flaw size is calculated from material and geometrical properties of the specimen. A surrogate model, trained by a few finite element runs, is used to calculate the stress intensity factor used in crack growth calculations. This eliminates repeated use of an expensive finite element model in each cycle and leads to rapid computation, thereby making the methodology efficient and inexpensive. Three different kinds of models – finite element models, surrogate models and crack growth models - are connected in this framework. Various sources of uncertainty – natural variability, data uncertainty and modeling errors - are considered in this procedure. The various component models, their model parameters and the modeling errors are integrated using a Bayesian approach. Using inspection data, the parameters of the crack growth model and the modeling error are updated using Bayes theorem. The proposed method is illustrated using an application problem, surface cracking in a cylindrical structure.
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