13th International Conference on Fracture (ICF13) June 16–21, 2013, Beijing, China When considering both phenomena occurring simultaneously, it needs to be considered that the probability of a propagation event in CF or SCC is mutually influenced by both damaging phenomena. A possible approach to obtain probability bounds for a system subjected to both CF and SCC and the relative probability of each mode of propagation is the use of failure tree diagrams and common cause failure, as described by the authors elsewhere [1]. Note that all of the Kitagawa like diagrams shown correspond to a specific R-ratio level; multiple diagrams can be constructed for a single material at different R-ratios. 3. Reliability Methods The modeling of the intrinsic variability of the controlling variables in a system is the foundation for the determination of a measure of reliability of a structure. The development of a statistical framework for a developed model is advantageous since it introduces mathematical and statistical concepts into the model and attempts to derive the statistical variability of the desired output directly computing the uncertainties associated with the parameters used in the model [13, 14]. First order and second order reliability methods are two analytical approaches that are used in this work to handle the variability of the stochastic inputs in the developed framework. The goal is the estimation of the probability of onset of HCF subcritical defect growth, in fatigue or CF and SCC, depending on the framework. The name of First Order Reliability Method (FORM) comes from the fact that the performance function g(X) is approximated by the first order Taylor expansion (linearization), around the Most Probable Point (MPP). Two steps are involved in these approximation methods to make the probability integration easy to compute and to obtain the probability of exceeding a specified threshold. The first step is to simplify the joint probability distribution, i.e. the function to be integrated, so that its contours become more regular and symmetric. The second step involves the approximation of the integration boundary on the limit state function g(x) at limit state g(x) = 0. After these two steps, an analytical solution to the probability integration can be obtained. For ease of analytical development, all the variables are transformed into their standard forms. The transformation of the joint probability distribution is performed by mapping the Figure 5: schematic of FORM and SORM calculation methods.
RkJQdWJsaXNoZXIy MjM0NDE=