Probabilistic Low Cycle Fatigue Life Prediction Using an Energy-Based Damage Parameter and Accounting for Model Uncertainty

Probabilistic methods have been widely used to account for uncertainty of various sources in predicting fatigue life for components or materials. The Bayesian approach can potentially give more complete estimates by combining test data with technological knowledge available from theoretical analyses and/or previous experimental results, and provides for uncertainty quantification and the ability to update predictions based on new data, which can save time and money. The aim of the present article is to develop a probabilistic methodology for low cycle fatigue life prediction using an energy-based damage parameter with Bayes’ theorem and to demonstrate the use of an efficient probabilistic method, moreover, to quantify model uncertainty resulting from creation of different deterministic model parameters. For most high-temperature structures, more than one model was created to represent the complicated behaviors of materials at high temperature. The uncertainty involved in selecting the best model from among all the possible models should not be ignored. Accordingly, a black-box approach is used to quantify the model uncertainty for three damage parameters (the generalized damage parameter, Smith–Watson–Topper and plastic strain energy density) using measured differences between experimental data and model predictions under a Bayesian inference framework. The verification cases were based on experimental data in the literature for the Ni-base superalloy GH4133 tested at various temperatures. Based on the experimentally determined distributions of material properties and model parameters, the predicted distributions of fatigue life agree with the experimental results. The results show that the uncertainty bounds using the generalized damage parameter for life prediction are tighter than that of Smith–Watson–Topper and plastic strain energy density methods based on the same available knowledge.