No abstract

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.

Evolution of the thermodynamic entropy generation during fatigue crack initiation life of notched specimens is studied. A set of experimental results of AA7075‐T651 is examined to determine applicability of the thermodynamic entropy generation as an index of fatigue crack initiation. Entropy accumulation is calculated from hysteresis energy and temperature rise. An increasing trend of entropy accumulation with the number of cycle to failure is observed on macroscale measurements. Results also determine that the entropy generations from the samples under the same operating conditions are similar as the crack grows. Scanning electron microscope analysis is performed on the fractured surfaces to observe the fatigue striations, and persistent slip bands are observed employing an optical microscope. A discussion is presented regarding the length scales on which crack initiation occurs and entropy calculation is made.

Over the past twenty years, computer-based simulation codes have emerged as the leading tools to assess risks of severe events such as fire. The results of such simulation codes are usually used to estimate the magnitude, frequency and consequence of hazards. A typical simulation program/model utilizes many different sub-models, each characterizing a physical or chemical process contributing to exposure of the hazard or occurrence of certain adverse failure events. The final prediction made by such simulation codes can be temporal, spatial or just a single estimate for the measure of interest. The predictions made by the simulation codes are subject to different contributing uncertainties, including the uncertainty about the inputs to the code, uncertainty of sub-models used in the codes and uncertainty in the parameters of the probabilistic models (if applicable) used in the codes to characterize (e.g., validate) code outputs. A primary way to measure the model uncertainties is to perform independent experiments and assess conformance of the models to observations from such experiments. It is very important to note that the experimental results themselves may also involve uncertainties, for example due to measurement errors and lack of precision in instrumentation. In this research experimental data collected as part of the Fire Model Verification and Validation [1] are used to characterize the share of model uncertainty in the total code output uncertainty, when experimental data are compared to the code predictions. In this particular case, one should assume the uncertainty of experiments (e.g., due to sensor or material variability) is available from independent sources. The outcome of this study is the probabilistic estimation of uncertainty associated with the model and the corresponding uncertainty in the predictions made by the simulation code. A Bayesian framework was developed in this research to assess fire model prediction uncertainties in light of uncertain experimental observations. In this research the complexity of the Bayesian inference equations was overcome by adopting a Markov Chain Monte Carlo (MCMC) simulation technique. This paper will discuss the Bayesian framework, examples of using this framework in assessing fire model uncertainties, and a discussion of how the results can be used in risk-informed analyses.

Fire simulation codes are powerful tools for use in risk-informed and performancebased approaches for risk assessment. Given increasing use of fire simulation code results, accounting for the uncertainty inherent in fire simulation codes is becoming more important than ever. This research presents a "white-box" methodology with the goal of accounting for uncertainties resulting from simulation code. Uncertainties associated with the input variables used in the codes as well as the uncertainties associated with the sub-models and correlations used inside the simulation code are accounted for. A Bayesian estimation approach is used to integrate all evidence available and arrive at an estimate of the uncertainties associated with a parameter of interest being estimated by the simulation code.Two example applications of this methodology are presented.