Statistical calibration of ultrasonic fatigue testing machine and probabilistic fatigue life estimation

A new statistical technique is proposed to quantify the experimental uncertainty observed during ultrasonic fatigue testing of metals and its propagation into the stress-lifetime predictive curve. Hierarchical Bayesian method is employed during the calibration and operation steps of ultrasonic fatigue testing for the first time in this paper. This is particularly important due to the significant dispersion observed in stress-life data within the high and very high cycle fatigue regimes. First, the measurement systems, including displacement laser readings and high-speed camera system outputs, are cross-calibrated. Second, a statistical learning approach is applied to establish the stress-deformation relationship, leveraging Digital Image Correlation (DIC) measurements of strain and laser displacement measurements at the ultrasonic machine specimen's tip. Third, an additional hierarchical layer is introduced to infer the uncertainty in stress-life curves by incorporating learned stress distributions and the distribution of fatigue failure cycles. The results identify key sources of uncertainty in UFT and demonstrate that a hierarchical Bayesian approach provides a systematic framework for quantifying these uncertainties.