Probabilistic fatigue crack growth analysis using response surface methodology

All aircraft operated by the United States Navy were designed to operate for a predetermined number of flight hours defined as the flight life expectancy (FLE). An aircraft is due to retire from service once the FLE is reached. Due to the end of the cold war and budget priority, it is anticipated that fleets of United States Naval aircraft will be used beyond their designed FLE. A study was performed for the US Navy to address the aging aircraft issue by examining crack growth at the logeron of the aircraft. The objective of the study was to develop a probability model for the number of load cycles (N) needed for a crack to grow from its initiation size to critical size Fatigue crack growth due to constant stress intensity as well as random stress block was examined.

The Paris equation was used to compute the fatigue crack growths. Response surface methodology was used to approximate the number of load cycles with respect to the geometric and material properties and stress intensity level. The most workable relationship was a linear function with all the input parameters and number of load cycles in their natural logarithmic base. The statistical analyses of the study showed that the mean number of load cycles (N) approximated from the response surface functions predicted the mean pseudo population load cycles at a 95 percent confidence level. The study also showed that the probability density function of the number of load cycles from the response surface functions, Gaussian distribution, fit the histogram of the pseudo population well.