Uncertainty Quantification in Fatigue Damage Prognosis

Shankar Sankararaman, You Ling, Chris Shantz, and Sankaran Mahadevan
Submission Type: 
Full Paper
phmc_09_51.pdf323.85 KBSeptember 17, 2009 - 6:05am

This paper presents a methodology to quantify the uncertainty in fatigue damage prognosis, applied to structures with complicated geometry and subjected to variable amplitude multi-axial loading. The crack growth analysis uses the concept of equivalent initial flaw size to replace small crack growth calculations and make use of a long crack growth model. A Gaussian process surrogate model, trained by a few finite element runs, is used to calculate the stress intensity factor used in crack growth calculation, as a function of crack size and loading. 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. The effect of various sources of uncertainty โ€“ physical variability, data uncertainty and modeling errors โ€“ on crack growth prediction is investigated. Physical variability includes variability in loading conditions, geometry, material properties, etc., represented as random variables. The uncertainty in experimental data is included. Different types of modeling errors are considered. The discretization error in finite element analysis is calculated using the Richardson extrapolation method. The error added by the surrogate model is included based on curve fitting statistics. The uncertainty in crack growth law is addressed by adding an error term to the crack growth equation and by treating the model parameters as random variables. The different kinds of uncertainty are incorporated into the prognosis methodology to predict the probability distribution of crack size as a function of number of load cycles. Further, the marginal contribution of each source of uncertainty is also analyzed. The proposed method is illustrated using an application problem, surface cracking in a cylindrical structure.

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Submission Keywords: 
crack detection
damage detection
damage modeling
damage propagation model
fatigue crack growth
materials damage prognostics
structural health management
structural health monitoring
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