Characterization of Residual Stress Fields from Cold Expansion Using Spatial Statistics and Incorporation into Multi-Point Fracture Mechanics Analyses

Residual stress fields from cold expansion have been widely used to extend the fatigue life of aircraft structures. However, the spatial statistical character of these residual stress fields has not been established and has not been incorporated in current analysis methods. The objective of this study was to establish a spatial statistical method to quantify the residual stress field around a cold expanded hole and validate the method using experimental fatigue test data. A framework called the Spatial Analysis of Residual Stress (SpARS) was developed utilizing spatial correlation, response surface modeling techniques, and statistical resampling methods to characterize the residual stress field. Our results showed that tolerance bounds on residual stress can be quantified using this method and demonstrated that the use of the residual stress tolerance bounds provides a range of estimations of fatigue crack growth life. Comparison with fatigue test data demonstrated that the less compressive 95% upper bound from the mean of the residual stress field provides reasonable estimations of the fatigue life. These results are consistent with the results of the recent round robin fatigue analyses associated with the experimental data. The use of SpARS to incorporate a statistically representative residual stress field in fatigue crack growth analyses will be useful to provide guidance to aircraft structural management and allow for extending inspection intervals for fatigue and fracture critical structure.