A robust probabilistic fatigue crack growth model based on walker's crack growth rate equation for metallic materials

Abstract

The fatigue crack growth data inherits statistical variation despite carefully controlled test procedures. The available probabilistic models rely extensively on fatigue crack growth test data of the coupon material under replicate loading conditions. In view of the often unavailability of such a database, this work proposes a new probabilistic model based on Walker's crack growth rate equation and considers the variability in both the stress intensity factor range, ΔK and stress ratio, R. The optimum estimates of the model parameters are established using the maximum likelihood estimation (MLE) method. The model is examined using selected sets of measured fatigue crack growth curves of 7075-T6 and 2024-351 aluminum alloys. It demonstrates acceptable predictions for fatigue crack growth data on replicate and variable R-ratio loadings with failure probabilities in the range of 0.10 ≤pF≤ 0.90. The error on the observed fatigue crack growth rate data is normally distributed. The criterion of the minimum number of replicate tests for a valid probabilistic assessment of the fatigue crack growth data is established. Based on the mean squared error (MSE) parameter, the model provides a better representation of the mean fatigue crack growth rate behavior of the material for fatigue loading with variable R-ratios.