Application of probabilistic fracture mechanics for life prediction of metallic materials

Abstract

A statistically based analytical method was developed to improve the reliability of fatigue failure predictions for metallic components of various geometric configurations subjected to constant amplitude fatigue loads. The method required the determination of the distribution of equivalent initial flaw sizes. The equivalent initial flaw size associated with an actual crack is influenced by the geometric configuration of the body, the applied loading conditions and the crack growth model employed. In this study four factors were identified including two types of crack configurations and their influence on the equivalent initial flaw size distribution was investigated. Also the influence of the four factors on the equivalent initial flaw size distribution was examined. These are the stress concentration factor, tg K, the uncracked ligament length, n w, the maximum stress, max S and mean stress, mean S, of the applied constant amplitude fatigue loading. Two types of initial crack configurations were assumed; corner and surface flaw. Five specimen types were investigated; smooth unnotched, open-hole, Kt = 3, 4 t K = and 5 t K = specimens all of which have different stress concentration factors. Two statistical models were fitted and investigated. One model assumed that the initial crack started as a corner crack, transitioned into a through crack, and then propagated till final fracture. The other model assumed that the initial crack started as a surface crack, transitioned into a through crack, and then propagated till final fracture. For each crack configuration, a statistical model was fitted between the mean and the standard deviation of the distributions of the equivalent initial flaw sizes and the stress concentration factor, the uncracked ligament length, the maximum stress, and the mean stress of the fatigue loading. Multiple regression techniques were used to fit these models. Using the statistical models together with Monte Carlo simulation, a distribution of estimated fatigue lives were generated using the FASTRAN-II crack growth code for the Kt = 3 and 4 t K = specimen types, at various stress levels. Hypothesis testing was used to compare the estimated fatigue lives of the specimen with the measured fatigue lives obtained from testing at a level of significance of 0.05. An acceptance criterion was established to determine if the predicted fatigue lives compared well with experimentally obtained fatigue lives. As a conclusion, the methodology provided adequate approximation of fatigue life for some of the fatigue loading cases of the 4 t K = specimens and for one of the fatigue loading cases of the 3 t K = specimens. The initial crack configuration type did not have any significant effect on the proposed methodology.