Hierarchical probabilistic modeling of short-crack growth behavior in AISI 4340 steel

Probabilistic analyses of non-uniform crack growth data sets require a flexible statistical framework to determine the influence of each crack on the resulting inference. Hierarchical generalized linear models provide a rigorous method to analyze such data sets properly. Bayesian techniques are well-suited to analyze these models, especially when the inference, or portions thereof, are ill-posed. A hierarchical generalized linear crack growth model is developed using a semi-conjugate formulation that enables Gibbs sampling simulation. The model is applied to create a probabilistic crack growth model from short-crack data generated from AISI 4340 steel single-edge-notch tension (SENT) specimens. Simulation of the model is performed using a Gibbs sampling procedure, and key results are discussed. Stress ratio effects on experimental scatter and crack growth rates are quantified and discussed.